id
stringlengths 24
24
| idx
int64 0
402
| paragraph
stringlengths 106
17.2k
|
|---|---|---|
61e6fb42eab6ef9aeae57783 | 19 | First we note that the rate of convergence is different for different frequencies even though a possible pattern has not been identified. This confirms the importance of monitoring the convergence in a frequency-dependent manner in order to avoid unnecessary iterations for those frequencies already below a given convergence threshold. Moreover the convergence of the simple fixed-point algorithm suggests that the rs-SCS problem is well-conditioned even for the dense cluster of atoms taken as test system. It is also of interest to probe the effects of the DIIS extrapolation coupled to the fixed-point iterative solution of the screening equations and this is shown in Figure . As expected, the DIIS extrapolation accelerates the convergence, in particular for the slow converging frequencies observed previously in Figure ??. The total number of iterations is reduced, for the full set of frequencies, by 55%, underlining the benefits of the DIIS inclusion. As mentioned in the theoretical section, an additional aspect considered to improve the performance of the algorithm is the re-use of purely geometric-dependent terms (referred to as G i j in Algorithm 1) in the on-the-fly building of T SR i j (iν n ): this allows for further decreasing the computational cost by up to 40% for a 10-points quadrature as shown in Figure . A final aspect concerning the efficient solution of the rs-SCS sets of equations is the choice of the proper cutoff radius from which the neighbor lists can be built. The short-range nature of T SR responsible for its sparsity can be seen in Figure where the isotropized rs-SCS polarizability of one of the argon atoms in a dimer is plotted as function of the inter-atomic distance. At inter-atomic distances above 3 Ångstroms the effects of the self-consistent screening becomes negligible suggesting that a cutoff radius of 4 Ångstroms is more than enough to include all the anisotropic effects arising from the neighboring atoms. We wish add to the discussion of the proposed iterative rs-SCS algorithm described in Algorithm 1 the comparison between its computational scaling and the one relative to the direct inversion approach in Eq.( ), Figure . The remarkable computational gain introduced by the iterative solution of the reduced rs-SCS Dyson-like equations shown in Figure is, however, only one of the advantages introduced: a further aspect to take into account is in fact the memory efficiency. The solution of Eq.( ) requires to store the upper-triangular part of Ā(iν) for all the set of frequencies employed, thus involving quadratic-scaling memory requirements with the system size. The variable reduction involved by Eq.( ), on the other hand, only requires 9N elements to be stored for each of the frequencies employed, making the needed memory allocation linear scaling with the system size as shown in Figure . The advantages introduced by the here proposed strategy thus concerns both the computational performance and memory allocation requirements. |
61e6fb42eab6ef9aeae57783 | 20 | kk and ∆ (l) (k-1)k are given in the Supporting Information. Being the algorithm stochastic in its nature, it is of interest to analyze the distribution of the energy estimations in terms of the number of random samples (R) as well as the dimension of the Krylov subspace identifying the number of Lanczos quadrature points. This is shown in Figure where three distributions relative to three different values of R are reported for a Krylov subspace of dimension 20. The SL distributions are centered close to zero and this denotes a negligible bias toward the target energy value obtaineded via a direct diagonalization. Moreover, the distributions narrow with the increment of R as one would expect, thus allowing for a systematic improvement of the estimation. We note that by decreasing the dimension of the employed Krylov subspace to 10, the distributions remain well centered around zero with a bias smaller than 1% on the total MBD energy even for low values of R. |
61e6fb42eab6ef9aeae57783 | 21 | A more complete analysis of the standard deviation dependence on the number of random samples R is shown in Figure for two different Krylov subspace dimensions, 10 and 20 respectively: this reveals a typical Monte Carlo 1/ √ R scaling where the dimension of the Krylov subspace (i.e. the number of Lanczos quadrature points) has very little effects unless unresonably small subspaces are employed. We note at this point that Lanczos quadrature is extremely efficient in approximating the terms reported in Eq.( ) as it requires half of the points, for given target accuracy, compared to other quadrature strategies such as the ones based on Chebyshev polynomials. This, together with a rigorous mathematical error analysis of the SL trace estimator, is discussed in the original work of Ubaru, Chen and Saad. Figure shows the evolution of the stochastic trace estimation with the number of random samples for a single point estimation where the trace approaches the target value with a standard deviation magnitude becoming smaller with the increase of the number of random samples, in line to what shown in Figure . A further aspect to probe is the standard deviation's dependency on the system size. This is shown in Figure for increasingly larger argon clusters. The trend shows how the error decreases with the increase of the system size thus denoting a desirable statistical self-averaging of errors, in line with the fact that, in the thermodynamic limit, fluctuations die out. We note in passing that a similar behavior was observed in stochastic approaches to compute electronic correlation energies. Further words on this aspect will be spent later on in this section. It is now of interest to analyze the scaling with system size of the proposed SL trace estimation algorithm and to compare it with the standard approach requiring the full eigendecomposition of V. The building of the Krylov subspace only requires matrix-vector products which are performed in a linear-scaling fashion in contrast to the standard full-diagonalization approach which is cubic scaling with the system size as shown in Figure . We stress that the plot was generated by keeping the number of random samples constant, however, in virtue of the self- averaging property of the algorithm the number of random samples could have been notably reduced (for a given target accuracy) along with the system size and this would have contributed to an even better scaling of the SL algorithm's CPU-time with system size. |
61e6fb42eab6ef9aeae57783 | 22 | The stochastic algorithm presented here is by nature embarassingly parallel by dividing the random samples among the available processes while the only communication required is a reduction occurring when each of the independent processes has computed the contribution to the trace associated with its subset of random vectors. Though not being the computational bottleneck, the resolution of the Dyson equations for a set of frequencies is also parallelized with the spatial decomposition strategy embraced within the Tinker-HP package. Similarly to the resolution of the polarisation equations characterizing the AMOEBA force field, each process computes the contribution of the matrix-vector product due to its local p component. At each iteration, in order to compute this matrix vector product, a communication of p at the previous iteration has to be made before the computation and a communication of the result of the product has to be made after. Besides, reductions have to be made to compute the residual (Eq.( )) and the DIIS matrix at each iteration. Because the parallelization scheme is not the same between the iterative solution of the screening equations and the stochastic Lanczos trace estimation, a global broadcast of the screened polarizabilities has to be done between these two steps. Overall, the moderate amount of communication explains the small deviation from the ideal scaling that is observed in Figure after 200 cores. |
61e6fb42eab6ef9aeae57783 | 23 | The linear-scaling of the presented algorithm, the low memory requirements, its natural parallel implementation, the beneficial self-averaging of errors together with the possibility of employing a limited set of ab initio derived parameters opens up the possibility of evaluating many-body dispersion energies of large biomolecular systems within a few minutes'time. This is exemplified below for the solvated [Ala] 40 test system counting approximately 100000 atoms shown in Figure . Firstly atom types are assigned to each atom in the system: for simplicity we followed the AMOEBA's atom type assignment. Secondly, ab initio atomic parameters such as isotropic static polarizabilities are extracted from subsystems (isolated water molecules as well as [Ala] 3 for this specific test case) and then averaged to obtain atom type-based parameters. This approach bypasses the DFT computation of the electron density for the whole system and its subsequent atom-in-molecule decomposition, which, even for a linear-scaling DFT approach, is prohibitive for a system of the size as the one here considered. This strategy allows for evaluating the energy of the 100000 atoms system in approximately 2 minutes' time on 400 cores from Intel Skylake 8168 (2.7 GHz) fine nodes. We emphasize that these remarkable performances have to be attributed not only to the linear-scaling and nearly embarassingly parallel implementation of the algorithm but also to the self-averaging of errors which, for this 100000 atoms system, allows us to get an estimated relative standard deviation of 0.5% corresponding to an error of 0.003kcal/mol per atom by only employing 300 random samples. In general, systems composed by few thousands atoms (or above) do not necessitate of large numbers of random samples in virtue of the algorithm's pleasant self-averaging of errors. On the other hand, different types of systems may exhibit different degrees of locality: this can be taken care of by choosing a suitable cut-off radius in building the elements of the MBD potential matrix thus tuning its sparsity. In general, delocalized and periodic systems are expected to exhibit longer-range interactions therefore a suitable and large enough cutoff radius must be carefully chosen. The ab initio nature of the input quantities employed by the MBD model as well as the contained number of natural amino acids would make it possible to generate rigorously a complete set of general parameters to be used in the modelling of proteins in solution where the plasmonic nature of the solvated system can require a many-body treatment of dispersion interactions. This will be the object of forthcoming studies coming along with a further reduction of MBD's time-to-solution thanks to Tinker-HP's accelerated multi-GPUs (Graphics Processing Units) implementation. 64 |
619f1870568d3371e745ed5e | 0 | Molecular electronics enables miniaturization of the molecular devices that has essential applications in nanosized electronics circuits, and offered opportunity to study fundamentals of charge transport mechanisms in molecular scale. In molecular junctions two transport mechanisms that broadly studied are, tunneling and hopping. Tunneling mechanism is the mechanism where electron coherently tunnel through energy offset of a molecule. It has been observed that the coherent tunneling depends on the interaction between the molecule and the contact electrode, as well as energy offset between the Fermi energy level of the electrode and the molecule orbital (sometimes also referred as tunneling barrier though not very accurate). Tunneling mechanism can be modelled based on various suppositions, while the most commonly used is single level model (SLM) in both experimental and theoretical studies. In this model, single electroactive state is sandwiched between two electrodes with energy level offset to the Fermi level of the electrodes and electronic coupling to the electronic states of the electrode (figure ). Experimentally single state junction has been achieved by attaching electroactive group like ferrocene or conjugate organic molecules as the single electronic active state with alkane molecule as insert molecular linker to adjust the coupling of the electronic state with electrode. Function and special transport behaviors have been observed like, rectification , Coulomb blockade and Kondo effect through utilization of experimental techniques such as scanning tunneling microscope (STM), mechanical controllable break junctions (MC-BJ) , conducting probe atomic force microscope (CP-AFM) and liquid junction techniques like eutectic indium gallium (EGaIn) or mercury drop junctions . Theoretical analysis based on SLM depends on the mathematical modeling of the experimental I-V plot where coupling strength (Γ) and energy offset (ε0) can be obtained and cross compared to spectroscopy measurement like ultraviolet photoelectron spectroscopy (UPS) or ab initio calculation The currentvoltage (I-V) relation in single level model is described by Landauer formula (Eq 1) with single level transmission function (1. |
619f1870568d3371e745ed5e | 1 | The integration in Eq 1 is apparently not easy to perform due to the complex mathematical form of Fermi function and density of state. There is no simple analytical relation for current and voltage to be used for experimental data analysis. Various approximated modeling methods have been invented and applied to fit the experimental I-V results to extract transport parameters like coupling strength (Γ) and energy offset (ε0) . The first one is to perform numerical integration of Eq 1. By decreasing the step size in the numerical integration, a high accuracy can be achieved. On other hand, when the Fermi broadening is small relative to the density of states, or if at low temperature, the Fermi function in Eq 1 can be approximated by a step function, and an analytical expression of I-V can be obtained as |
619f1870568d3371e745ed5e | 2 | Where ∆𝜀 energy offset and Γ = (Γ L + Γ R )/2 , 𝑒𝑉 is the applied bias measured in electron volts. And the finite resistance arises at the interface between electrode and molecule, expressed as quantum conductance2e 2 /ℎ. We can see, more and more approximations were applied from Eq 1 to Eq 3, so the applicability should in principle reduce from Eq 1 to Eq 3 accordingly. |
619f1870568d3371e745ed5e | 3 | The current voltage (I-V) analysis using Eq 1 as the first recognized SLM expression in tunneling junction analysis achieves to unveil various features of the molecular junctions. For example, Luka-Guth et al studied the role played by the solvent in electronic transport in molecular junction, the junction analysis help them to make a reasonable conclusion on differentiated solvent conductance with that of molecular junction . On the other hand, Zotti et al revealed the effect of anchoring group in molecular junction by examining the influence of moleculemetal contact interaction in molecule junction . Tunneling junction analysis based on simplified I-V relation have been currently growing in popularity due to their simplifications. For example, Emanuel and coworkers reported their study using Eq 2 in junction analysis to compare the effect of thiols and isocyanide as anchoring group in 1,4 benzene dithiols and 1,4 benzene diisocyanide molecular junction. The conclusion drawn is the same as Zotti et al , though the molecule differ by one benzene ring, but the extracted key parameters appear to be significantly different. Eq 3 has also attracted many studies, and it closely related to another popular method in characterizing the energy offset in the molecular junctions, i.e. transition voltage spectroscopy (TVS) . TVS enables determination of transition voltage (V 𝑡𝑟𝑎𝑛𝑠 ) in a Fowler-Nordheim plot (F-N). However, as revealed by Vilan et al later on, V 𝑡𝑟𝑎𝑛𝑠 is actually not a sign of the F-N transition, rather it is a mathematical sign of none linearity of I-V plot. Baldea derived an approximated relation between V 𝑡𝑟𝑎𝑛𝑠 and energy offset based on Eq 3, i.e.eV 𝑡𝑟𝑎𝑛𝑠 = 2∆𝜀/√3, which later on was found to be effective and acceptable method in analyzing molecular energy levels. Frisbie and coworkers have extensively used this method to examine molecular junction of different molecules on metal contacts (Ag, Au and Pt) and explore fascinating junction characteristics and features. However, when making comparison of extracted parameters with other methods like Eq 2, we observed substantial difference in energy offset (ε0) for oligophenylene dithiols (OPD1) analyzed using Eq 3 (Frisbie et al. results) and Eq 2 (Emanuel et al results ) which was 0.87 eV and 0.26 eV respectively on Au/Au electrode. The observed variation can be attributed to different factors, such as adopted method for I-V measurement, among which the most important one is the applicability of SLM modeling methods. In addition, SLMs have also been applied to thermoelectricity studies, such like extracting the Seebeck Coefficient, which can help to understand electronic structure of the molecular junction, i.e., Fermi level of the electrodes with respect to the HOMO or LUMO levels of the molecules, through determining the type of charge carriers (either p-or n-type) . |
619f1870568d3371e745ed5e | 4 | SLM is the method that has triumphed theoretical I-V studies as powerful and valuable analyzing methods in exploring tunneling transport in molecular junction. The theoretical modeling of I-V is promising to understand energy level in charge transport at the molecular junction, which also relies crucially on our proficiency of utilizing these modeling methods. However, the applicability and accuracy of using these models have not been well evaluated. Indeed, different single level mathematical methods also rendered significant variation in extracted transport parameters. We thus developed the interest of detailed examination of condition and limitation of their application in modeling I-V response of the junction. This work provides extensive study on SLM methods, including the numerical integration of Landauer formula (Eq 1), and other two analytical tunneling models, Eq 2 and Eq 3, believing that the main problem is on appropriate condition in using each tunneling models in examining molecular structure. Our work will clarify the conditions and limitations inherited in I-V analysis using these methods and provide a proper guide for the modeling methods. |
619f1870568d3371e745ed5e | 5 | This manuscript is organized as following. First, I-V plots were generated using three methods under different ε0 and Γ, where we can observe the deviation of each equation from the other. We then compared ε0 and Γ extracted by fitting experimental results obtained from literature papers using the three Equations to evaluate the error level under different conditions. We certainly propose numerical recommended method in I-V analysis considering it adopts least theoretical approximation and showed the widest applicability, while the two methods (Eq 2 and Eq 3) have to be used under limited conditions. At last, we summarized a phase map of applicability of the three methods as a guide for their proper usage in charge transport study in molecular devices. |
619f1870568d3371e745ed5e | 6 | The tunneling transport through SLM can be describe by Landauer-Büttiker formalism (Eq 1) which shows relation of current with transmission probability (Tr) that depends on energy offset and the coupling strength between electrodes and molecule. In the simulation, we consider the energy offsets of 1 eV, 0.5 eV and 0.1 eV, while coupling was set to be 100 meV, 10 meV, 5 meV and 1 meV. These values were chosen based on experimental results reported in literatures. The quantum conductance was2e 2 / ℎ = 77.4 μS , and voltage division factor (γ) was 0.5, i.e. symmetric situation. The bias range for the simulation is 1.5 V in both positive and negative polarities. |
619f1870568d3371e745ed5e | 7 | In method 1, the energy step for numerical integration was set to be 0.2 meV and lower and upper limit of the integration is -5 eV and 5 eV. It should be emphasized that the integration step size should be significantly smaller than the width of the transmission peak, which is defined by the coupling parameter in Eq 1.3. We found this step size and integration limit are generally enough even down to the 1 meV coupling situation, and further smaller step size and wider integration range produce none noticeable difference in I-V plot. At last, the thermal energy (KBT) in the Fermi function in Eq 1 was set to be 0.025 eV for room temperature (298K). |
619f1870568d3371e745ed5e | 8 | In simulation of I-V response using analytical equations Eq 2 and Eq 3 in comparison to numerical integration Eq 1, the same parameters were adopted i.e. coupling strength (Γ), energy offset (εo) and the bias voltage (V) window. Plotting I-V data provides an overview of the general appearance of the I-V curves and how the shape of the curves differ from each other at different transport parameters using the above three tunneling equations. |
619f1870568d3371e745ed5e | 9 | The fitting were performed first, by extracting data from experimental I-V curves of corresponding literatures using Engauge Digitizer software and the I-V plot was digitized into 501 points. Then, after mathematical description of all code segments or/ parameters, the acquired data was fitted via nonlinear fitting regression in MATLAB software using three tunneling equations one at a time, and the initial guess values of energy offsets and coupling were adjusted during fitting until the best fit was obtained. |
619f1870568d3371e745ed5e | 10 | To explore the scope of applying single level tunneling models, we first studied I-V characteristics under different coupling and energy offset conditions (figure ) using the three methods, as summarized in figure . We can see the I-V characteristics by the three modeling methods are significantly dependent on coupling and energy offset. First, when coupling is relatively strong, ~100meV, Eq 1 and Eq 2 agree with each other very well, while Eq 3 does not work for small energy offset as low as 0.1 eV. When barrier increases to 0.5 eV, Eq 3 gradually conform and works only under low bias i.e. far from resonance. As the energy offset increase to 1 eV, Eq 3 fully worked at this energy offset at all provided bias range (Figure ). Clearly, the working bias range of Eq 3 depends on the barrier height, the larger energy offset is, the larger bias range that Eq 3 can works. When coupling strength decrease to 10 meV and 5 meV (mild coupling strength, Figure D-F and G-I), Eq 2 starts to deviate from Eq 1. This is because the broadening of Fermi distribution under room temperature (~25 meV) become comparable to the coupling strength, so that the step function condition for Eq 2 will incur more and more error. Eq 3 failed to work again at low barrier and partially work at the mild barrier height (0.5 eV). At a very weak coupling strength (1 meV), again Eq 1 can reasonably describes the tunneling process while Eq 2 and Eq 3 continue to work effectively at high barrier. In this situation, the Fermi distribution cannot be reduced to a step function as the precondition for Eq 2. Therefore, neither the conditions of Eq 2 nor Eq 3 can be satisfied (as seen in figure J and K). On contrary, the validity of these two analytical expressions at high barrier is contingent to a very small integration step size (≤ 0.2 𝑚𝑒𝑉) of Eq 1 that should be smaller than the width of the transmission peak (figure ). |
619f1870568d3371e745ed5e | 11 | In order to elaborate our idea on the limit of applicability of the three SLM modeling methods and their difference, we re-examined their modeling performance on experimental results from published literature papers. Figure summarized the reported fitting parameters, coupling strength and energy offset, of the selected literature , which provided general overview of the range of the reported values. The data presented below are acquired from their originate papers whereby those in red are obtained by using Eq 1 and for those appear in blue only coupling was obtained by Eq 3 while energy offset was from transition voltage (TVS). From the graph the data accommodated below 10 meV under mild and low energy offsets are vulnerable to inaccuracy according to our discussion above, which indicated the application of Eq 3 is quite limited at low coupling and energy offset (energy barrier). We next try to redo the model fitting on the experimental results using the three methods (Eq 1 to 3) and compare the extracted parameters with the values from the original paper to check their performance and reliability. |
619f1870568d3371e745ed5e | 12 | Figure and b are the plots of extracted coupling strength and energy offset using the three methods as mentioned above (fitted I-V curves can be found in supporting information figure ), and Xie's results. These results are also summarized in Table . It can be seen that the C8DT molecular junctions (figure ) had high energy offset and the coupling strength of ascends from Ag, Au and Pt. The results of both tunneling equations and literature are well coincided supporting the explanation above on similarity in I-V behavior for both three models under high barrier height. On the other hand, contemplating figure , the molecular junction exhibited low coupling and energy offset (see fitting I-V curves in supporting information figure ). Generally, under this condition the I-V curves of Eq 1 behaves different from that of Eq 2 and Eq 3 and the fitting results is also expected to vary because at this condition the applicability of Eq 2 and Eq 3 is highly limited by the small barrier and coupling strength. Therefore, Eq 2 and Eq 3 are not accurate enough any longer to be used and indeed we can see clear difference between the results from Eq 1 relative to Eq 2 and Eq 3. The reported results from Smith and Xie et al in ref 15 deviated from both two sides because they adopted the hybrid method of TVS plus Eq 3 as described above, which under estimated the energy barrier compared to Eq 1 and overestimated the coupling compared to all the three methods. |
619f1870568d3371e745ed5e | 13 | We next turn to check the literature results of those fitted based on Eq 1. Figure is the study done by Luka-Guth et al who studied the role played by the solvent in the transport of the single molecular junction. This molecular junction exhibits high energy offset and low coupling strength, similar to C8DT molecular junction (figure ). The fitting results are quite the same for all the three methods, which is reasonable for the high energy offset situation. However, for the coupling, our fitting results are significantly higher than the literature results. This spotted difference could is possibly related to the influence of energy step size in the numerical integration. We believe Luka-Guth et al did not use small enough step size when performing numerical fitting in their model study (see supporting information figure S6 for the fitting using big integration step ~0.032 eV). This obtained results in this situation emphasize on caution that should be taken on choosing energy step size for numerical simulation of tunneling transport. We propose a very small step sized as shown in section 0.2. |
619f1870568d3371e745ed5e | 14 | On the other hand, the experimental work of Zotti et al, 4,4-biscyanotolane (BCT), 4,4-bisthiotolane(BTT) and 4,4 bisnitrotolane (BNT) molecular junctions showed mild and low energy offset, ~0.45 eV to ~0.27 eV depending on the anchoring group (figurer 4d and I-V shown in supporting information S7). The results observed in this study has shown clearly different between three models particularly on BNT molecular junction while no substantial difference for BTT and BCT molecular junctions. The larger difference displayed on BNT molecular junction in Eq 3 can be highly related to low value of energy offset as shown in table 1. In the condition of low energy offset and high applied bias, the resonance effect emerges, which Eq 3 cannot account for (figure ). This behavior can significantly result to alter the value of extracted fitting parameters when performing numerical simulation as it violate the condition at which Eq 3 can be applied. |
619f1870568d3371e745ed5e | 15 | Based on I-V curves generated in figure and the analysis of the experimental fitting results, we developed a map as shown by Figure . This map provides a summary of conditions for applying Eq 2 and Eq 3 with respect to Eq 1, and highlights the following information: 1) the first modeling method (Eq 1) has the largest scope of applicability i.e., can be applied in all conditions to examine tunneling transport; 2) The scope of applicability of the other two methods (Eq 2 and Eq 3) is jointly restricted by the potential barrier and coupling strength. We categorize our developed map in four sections. These categories are based on extent at which extracted fitting parameters varies and the difference in I-V response of the three methods. First, Eq 2 and Eq 3 did not work when coupling strength is very low (below 1 meV) at mild and low energy offset, we have seen from figure that at low coupling strength there is pronounced difference between analytical expressions and Eq 1 which hinder their performance as molecular junction single level analysis model. However, this feature under mild energy offset deliberately vanishes when coupling increases. The variation between these expressions is so small that can be ignored. Likewise, further increase in coupling make Eq 1 and Eq 2 coincide meanwhile Eq 3 well behave under low bias far from resonance. On the other hand, Eq 3 failed to be applied at low energy offset regardless of coupling strength and we also observed this from BNT molecule fitting results of Zotti et al. On the contrary, Eq 2 works appropriately under this condition when coupling is relatively strong. |
619f1870568d3371e745ed5e | 16 | As we can see the application of Eq 3 is quite limited by coupling strength and energy offset, we strongly suggest high attention to be taken in analyzing experimental results based on it particular at low barrier. In addition, considering that Eq 3 is closely related to several other mathematical models, like transition voltage Spectroscopy (TVS) and law of corresponding states (LCS) , it is very important to be aware of the condition and scope at which TVS and LCS can work effectively. |
619f1870568d3371e745ed5e | 17 | In experimental studies, the number of molecules, or the number of channels, involved in charge transport is generally very hard to estimate. In single molecular junction like STM-BJ or MCBJ, the single molecule conductance was identified by statistical conductance peak. While in selfassembled monolayer (SAM) based junction, the active molecules under top electrode in the junction measurement can only be approximately estimated, which varied from 10 2 to 10 5 depending on the nature and contact geometry of the top electrode. In model fitting, the number of active molecules in the junction (or the channels) in the transport, was generally treated as a linear multiplication coefficient in front of the I-V response function. This is, a & b Eq 1 and Eq 3 respectively used for fitting in original literature work apparently, a very rough approximation. The multimolecule effect in the junction were explored and it was found the conductance is not a simple linear function of the number of molecules and the interaction between molecules can make significant difference .Nevertheless, in model fitting, it is quite common to put the guesstimated number of the molecules in front of the model as multiplication coefficient, which are |
619f1870568d3371e745ed5e | 18 | Since the magnitude of the current, especially at low bias, see Eq 3, is mainly determined by coupling, number of molecules and coupling are thus convoluted. Therefore, in modeling, the accuracy of coupling largely influenced by the number of molecules used in the fitting. When explaining charge transport in molecular junction, coupling strength and number of molecules (N) in the junctions are like twin sisters that are hard to separate, especially when using Eq 3, where N and 𝛤 are all pre-factors of the expression. However, for Eq 1 and Eq 2, 𝛤 also influences the shape of the I-V in addition to the magnitude, to be more precisely the non-linearity of the I-V. Therefore, number of molecules N can be obtained, in principle, as an independent parameter, using Eq 1 and Eq 2 at large enough bias that reached the nonlinear part of the I-V. In this study, our I-V plots (figure ) did not consider the effect of number of molecules or channel i.e. number of molecules/channel assumed or considered to be unit. Therefore, the misinterpretation of fitting results in this study can originate from mis-estimation of the number of molecules. However, our map in Figure can still be used to examine whether proper parameters were obtained by using correct modeling methods since it was developed under idea single molecule condition. |
619f1870568d3371e745ed5e | 19 | Theoretical modeling is an important strategy to identify transport mechanism and extract key transport parameters i.e. coupling strength and energy offset for tunneling mechanism. Proper utilization of the modeling methods in current voltage (I-V) analysis is crucial for obtaining reliable results and conclusion. Our extensive study in this work revealed the limitation of the modeling methods depending on the transport conditions, and possible misinterpretation of the transport parameters if the method were misused. In view of the discussion made on mathematical model of tunneling transport based on single level system current voltage (I-V) analysis, we would like to suggest following ideas in the practice of using SLM. |
619f1870568d3371e745ed5e | 20 | a) The modeling methods for single level system have their own limitation in practice. It is important to use the map in figure above as the guidance for the applicability of Eq 2 and Eq 3. b) Numerical integration Landauer formula (Eq 1) should provide more reasonable results relative to Eq 2 and 3. We would like to recommend it as a more general method than Eq 2 and Eq 3 for the modeling study of molecular junction study. We have included the MATLAB code for the practical use of the method in the supporting information. It is important to notice as well the limitation of the numerical integration of Eq 1. The single level is whatsoever a simplified model and it may fail to work for systems with multi transmission channel and complex transmission spectrum. On the other hand, Eq 1 neither took into consideration the effect of variation in the density of state with respect to the energy 𝐸 , and it also neglected the effect of electrostatic field under bias, like the energy level polarization, which is the basis of current rectification, and stark effect, which can make coupling strength bias dependent . Therefore, care must be taken as well when applying method 1. 𝐸 dependent DOS and bias dependent coupling could be further incorporated into the modelling method as done by Liu and Neaton. |
619f1870568d3371e745ed5e | 21 | Moreover, temperature dependent tunneling transport can in principle be captured by Eq 1 since the Fermi function have included the temperature effect. Unfortunately, the experimental study of this effect is still very limited, and it is not easy to distinguish from hopping transport. We provided one example on the usage of Eq 1 to study temperature dependent tunneling in the supporting information. |
619f1870568d3371e745ed5e | 22 | At last, we would like to emphasize that modeling methods based on physical model always have to face the problem of balancing between practicability vs. accuracy. While pure mathematical analyzing method like parabolic approximation (Taylor expansion) or polynomial expansion that does not required pre condition of single level model may be very valuable in the transport study in properly applied. |
658c2dd59138d231619f55db | 0 | ABSTRACT: Complexation of a bismuthinidene (RBi) with two equivalents of a highly fluorinated aryl iodide at low temperature allows the crystallographic identification of an unstable species that can be regarded as an intermediate of an oxidative addition reaction. Both C-I bonds are orientated towards the filled 6p orbital of bismuth (Bi-I distances 3.44-3.52 Å), leading to an elongation of the C-I bonds by 0.05 and 0.07 Å. DFT calculations confirm that the bismuth center is indeed acting as an electron donor, establishing two strong and directional halogen bonds. As such, this study presents the first structural proof of bismuth, (and more generally of heavy organopnictogen compounds in oxidation state +1), acting as halogen bond acceptors. |
658c2dd59138d231619f55db | 1 | In the past years, heavier main group elements have become increasingly popular for the activation of small molecules. In this context, bismuth is of great interest due to its low toxicity and rich redox chemistry, the latter showing parallels with transition metal chemistry. Due to the inert pair effect, the 6s 2 orbital is low in energy, resulting in the low basicities of Bi(III) compounds and highly oxidative behaviour of the +V oxidation state. Recently, interest in the reduced oxidation state +I of bismuth has significantly increased. Pioneering work by Dostal has given access to bismuthinidenes, compounds in which the bismuth atom in the formal oxidation state +I is stabilized by a NCN pincer framework. The second lone pair associated with Bi(I) is localized in a p-orbital which lies perpendicular to the plane of the pincer ligand. Besides fundamental studies regarding the electronic structure of Bi(I) compounds the increased nucleophilicity of Bi(I) compounds allows them to act as donor ligands to metals. Furthermore, they have also been shown to mediate important organic transformations, e.g. transfer hydrogenations or hydrodefluorination reactions. Additionally, bismuthinidenes have been reported to undergo oxidative addition of alkyl iodides and aryl halides. Whereas halogen bonding between aryl iodides and nitrogen-based molecules has found widespread use in many areas of crystal engineering, compounds of the heavier pnictogens have rarely been used as halogen bond acceptors. Only very few examples have been reported in the past years, e.g. using tertiary phosphines. In a seminal work, Friščić and Cinčić reported the successful cocrystallization of the halogen bond donor 1,3,5-trifluoro-2,4,6-triiodobenzene with Ph3P, Ph3As and Ph3Sb. However, no adduct could be isolated in case of Ph3Bi. Recently, Bujak and Mitzel reported cocrystals of Me3As/Me3Sb with C6F5I. The fact that no solid-state structures with a bismuth compound acting as a halogen bond acceptor have been reported, and such structural motifs are typically not even considered in theoretical investigations, prompted us to pursue this synthetic challenge. Bismuth's primary challenge lies in the inert pair effect, which refers to the low energy of the 6s orbital, resulting in the diminished nucleophilicity of Bi(III) compounds. The Molecular Electrostatic Potential (MEP) surface plots of Et3Bi and Ph3Bi (Figure , top), reveal its unsuitability as a halogen bond acceptor. For Ph3Bi, the minima/electron-rich regions are concentrated on the aryl rings, with a MEP value of -16.3 kcal/mol, being compared to that of the bismuth 6s lone pair (LP), -2.3 kcal/mol. Despite the presence of electron-donating alkyl substituents in Et3Bi, its MEP value remains modest (< 10 kcal/mol). To counteract the inert pair effect, we shifted our focus to Bi(I) compounds instead of Bi(III). Nonetheless, the MEP of the basic PhBi model compound indicates an anisotropic MEP surface at Bi (Figure ). This surface displays two π-holes (positive areas) and two negative areas, attributed to the stereo-active lone pairs positioned coplanar with the aromatic ring. As expected, the MEP values at these LPs are significantly more negative (-23.2 kcal/mol) than those found in the Bi(III) compounds. Furthermore, the pronounced MEP maximum values (53.6 kcal/mol, representing π-holes) reveal Bi(I)'s dominant electrophilic nature over its nucleophilic one, rendering it unsuitable as a halogen bond acceptor. To circumvent this limitation, we considered using the NCN-stabilized bismuthinidene 1. We reasoned that the LPs on the imine N-atoms could engage with the π-holes at Bi, positioning the stereo-active lone pairs above and below the plane of the aromatic ring (as shown in Figure ). Within this configuration, Bi(I) demonstrates pronounced nucleophilicity, as evidenced by a MEP value of -25.0 kcal/mol. |
658c2dd59138d231619f55db | 2 | Green bismuthinidene 1 was reacted with 2,6-bis(trifluoromethyl)iodobenzene 2 at -70°C in dry and degassed n-hexane. Upon warming to -65°C the appearance of a red colour in the reaction mixture was apparent after several minutes. Cooling to -70°C led to the formation of red crystals, while warming to room temperature led to discoloration, oxidation to Bi(III) and crystallization of known RBiI2 4. The highly unstable red species 3 crystallizes in the monoclinic space group P21/n, and the solid-state structure obtained by X-ray crystallography reveals a trinuclear complex formed by interaction of two intact aryl iodide molecules with the bismuth center. The alignment of the bismuth and two iodine atoms is almost linear (I-Bi-I angle of 160.659(12)°), implying the presence of interactions with the filled p-orbital of bismuth perpendicular to the NCN plane (Figure ). |
658c2dd59138d231619f55db | 3 | The distances between bismuth and iodine are 3.4382(5) Å (I1A) and 3.5226(5) (I1B), i.e. significantly below the sum of the respective van der Waals radii (∑vdWBiI = 4.05 Å), and corresponding to RXB values of 0.849 and 0.870. Interestingly, the pnictogen-iodine distances are similar or even shorter than in adducts of Ph3As•C6I3F3 (3.4211(3) Å), Ph3Sb•C6I3F3 (3.5747(3) Å) or Me3Sb•C6F5I (3.4951(4) Å. With regards to the C-I bond lengths (C1A-I1A 2.171(3) Å and C1B-I1B 2.147(4) Å), a significant increase is observed when compared with free C6H3(CF3)2I (2.100(5) A), consistent with population of the σ*(C-I) orbital. In addition to the electron-withdrawing effect of the CF3 groups, we hoped that their placement in the ortho-positions would additionally provide the possibility for weak H … F contacts with the tert-butyl groups of the bismuthinidene to augment the halogen bonded assembly. However, the crystal structure shows that these moieties are, in the main, too far away from each other: only one such contact (F2B-H14A: 2.607(3) Å) is observed. Instead, intermolecular H … F contacts between the CF3 groups and the hydrogen atoms of the tert-butyl groups (F2A-H15B 2.587(2) Å) and the aryl ring of the bismuthinidene are observed (H3- We have examined the potential halogen bonds present in the bismuthinidene•2,6-bis(trifluoromethyl)iodobenzene adduct 3 using Density Functional Theory (DFT) calculations. Initially, we compared the geometry of the halogen-bonded (HaB) adduct in the solid state with its optimized counterparts (Figure , ESI). Specifically, two DFT geometry optimizations were undertaken: one for the isolated adduct in the gas phase and another employing Periodic Boundary Conditions (PBC) to account for packing effects. Notably, the gas phase geometry closely resembles both the experimental and PBC geometries, with the latter two being nearly identical regarding the relative orientation of the crystal conformers (Figure ). Importantly, the I•••Bi halogen bonds persist in the gas phase with analogous distances (3.456 and 3.459 Å). This observation underscores the structure-directing capability of the halogen bonds and refutes any notion that they could be manifested merely due to packing effects. The primary variance between the gas phase and the experimental/PBC configurations is evident in the I-Bi-I angle. In the gas phase, this angle is calculated to be 147.9°, compared to 161.6° for PBC and 160.6° for the X-ray study. This reduced angle in the gas phase arises as the isolated adduct attempts to maximize intramolecular interactions. Figure presents the non-covalent interaction plot (NCIplot) of the trinuclear assembly. The Reduced Density Gradient (RDG) isosurfaces provide a visual representation of interactions in real space. Dual disk-shaped RDG isosurfaces are observed between the Bi and I-atoms, corroborating the presence of halogen bonds. Additionally, the NCIplot highlights (in green) RDG iso-surfaces between the methyltrifluoromethyl groups and between the methyl-iodine atoms, signifying weak van der Waals (vdW) interactions (Figure ). When examining the formation energy of the trinuclear assembly against isolated monomers, values of -24.6 kcal/mol (experimental geometry) and -24.3 kcal/mol (DFT-optimized, isolated adduct) have been calculated. This finding further affirms the assertion that packing effects are not the primary force behind adduct formation. The Natural Bond Orbital (NBO) analysis has been used to probe the significance of orbital donor-acceptor interactions within the halogen bonds. This analysis reveals that the two bismuth LPs reside in the 6s and 6p atomic orbitals. The LP within the 6p orbital participates in electron donation from bismuth to the antibonding σ*(C-I) orbitals (Figure ). The LP(Bi)→σ*(C-I) charge transfer energies (21 and 16.5 kcal/mol), further underscore the idea of predominant system stabilization arising from the HaB formation. To evaluate the HaB energies independent of the influence of vdW interactions, we also modelled a mutated adduct, substituting tert-butyl groups with H-atoms. This effectively eliminates the CF3•••H3C and CH3•••I interactions. Figure depicts this model, integrating both the quantum theory of atoms-in-molecules (QTAIM) and NCIPlot analyses. These methods confirm the exclusive establishment of HaBs in the mutated adduct, each characterized by a Bond Critical Point (BCPs) and bond path linking the I and Bi-atoms. The electron density values at the BCPs are consistent with strong halogen bonds. The interaction energy diminishes to -19.4 kcal/mol, relative to a value of -24.6 kcal/mol for the "full" system. Such findings underscore the assertion that the formation energy is predominantly attributed to the I•••Bi interactions, aligning with the pronounced and negative MEP value observed at the Bi-atom, as visualized in The two-dimensional (2D) electron localization function (ELF) plot of the trimeric assembly is depicted in Figure , offering further insight into the role(s) of the σ-holes in the interactions. This figure provides a sectional view of the ELF 2D map, focusing on the plane demarcated by the Bi-atom and its two interacting iodine counterparts. Through this ELF visualization, it becomes evident that the σ-holes on the iodine atoms are oriented towards the LP of the bismuth atom. Indeed, the bond path connecting I to Bi passes through both the iodine σ-hole and bismuth LP. This specific electron localization in the I-Bi-I plane at the Bi-atom aligns well with the findings from the NBO analysis, particularly emphasizing the involvement of the LP located at the atomic 6p orbital. |
658c2dd59138d231619f55db | 4 | In summary, we provide the first crystallographic and computational evidence for Bi(I) as the heaviest halogen bond acceptor. The crystal structure of this highly reactive adduct 3 displays Bi … I distances significantly below the sum of van der Waals radii as well as elongated C-I bonds of the fluorinated aryl iodide moieties. Upon warming, it decomposes to the Bi(III) species RBiI2 4. Consequently, this crystal structure can be regarded as a snapshot of an intermediate formed during an oxidative addition reaction of an aryl iodide with a low valent main group element. |
658c2dd59138d231619f55db | 5 | This study not only sheds light on the unique potential of bismuth in halogen bonding but also paves the way for further explorations into the realm of heavy main group elements. The findings underscore the utility of comprehensive computational and experimental investigations to truly understand the potential of these unique elements in molecular chemistry. Furthermore, the results emphasize the importance of considering alternative oxidation states and molecular frameworks to unlock unexpected bonding and reactivity avenues, as evident from the successful employment of the Bi(I) state in halogen bonding. As the field continues to grow and diversify, we anticipate that the learnings from this study will serve as a foundational reference, inspiring chemists to explore the uncharted territories of main group element chemistry. |
66fa233a12ff75c3a1e6b304 | 0 | Secondary ion mass spectrometry (SIMS) is a spatially resolved analytical method for characterizing solid samples. First invented in the 1960s 1, 2 , SIMS instruments have been developed along multiple lines of emphasis, with the class of magnetic sector "dynamic SIMS" instruments emphasizing high-sensitivity elemental and isotopic analyses . In the 1990s, Georges Slodzian, the inventor of SIMS, conceptualized a coaxial design that enabled dynamic SIMS with higher lateral resolution by improving the primary ion beam focusing for scanning ion imaging . Further developed by Francois Hillion and others, that design became the basis for the NanoSIMS 50 series of instruments . The key capabilities of these instruments are high mass resolving power (>9000 M/M) with high transmission (up to 25%) at high-lateral resolution (as good as 50 nm) . Five (NanoSIMS 50) or seven (NanoSIMS 50L) detectors can also be positioned for simultaneous detection to increase the fraction of ions detected from the sampled volume. |
66fa233a12ff75c3a1e6b304 | 1 | The NanoSIMS 50 series capabilities translate to high mass specificity and sensitivity for the analysis of small features and have enabled discoveries in fields as diverse as cosmochemistry, geology, soil science, structural biology, biomedical research, microbial ecology, and material science . Inspired by these successes, the scientific and analytical communities have sought improvements to the NanoSIMS 50 series to further improve spatial resolution, analytical performance and throughput. 50 nanometer lateral resolution has been a featured aspect of the NanoSIMS instruments. NanoSIMS instruments use a normal-incidence primary ion beam with a 16 keV impact energy to sputter the sample to generate secondary ions for analysis . At this energy, the primary ion beam can be finely focused for scanning secondary ion imaging. However, to achieve 50 nm lateral resolution, the primary current must be reduced by ~10x over typical operating conditions for biological samples (Mayali et al. 2023) increasing the analysis time proportionally. Primary ion source intensity ("brightness") is a factor controlling in the relationship between primary ion beam spot size and current , and multiple efforts have been made to increase both the positive cesium ion source-used to enhance the yield of negative secondary ions , and the negative oxygen ion source-used to enhance the yield of positive secondary ions . Increased ion source brightness would improve the lateral resolution of NanoSIMS instruments, allowing smaller features-from viruses to presolar grains-to be resolved. |
66fa233a12ff75c3a1e6b304 | 2 | Increased source brightness could also be leveraged to increase the depth resolution of NanoSIMS analyses while maintaining high lateral resolution. Depth profiling-the practice of using the primary ion beam to erode through the sample while collecting compositional data-is a standard SIMS method that can achieve a few nanometer depth resolution . By comparison, the depth resolution of the NanoSIMS series of instruments is on the order of 10s of nanometers because the normal incident 16 keV primary ion beam penetrates into the sample to depths >20 nm . Depth resolution could be improved by lowering the primary ion beam impact energy, but at the cost of lower lateral resolution. Higher source brightness would regain some of the loss in lateral resolution, which would allow depth profiling of features that cannot be resolved with standard SIMS instruments, such as thin film transistors and attached bacteria. |
66fa233a12ff75c3a1e6b304 | 3 | While NanoSIMS data can be quantitated to the extent that standards and good analytical and statistical practices are used, the small scale of the analyses (typically less than 50 x 50 µm 2 ) can present challenges with translating the results to the population scale. This issue is often encountered in microbial ecology studies, where single cell incorporation of an isotopically labeled substrate can vary by over 10x among cells and some cell types can be relatively rare, such as non-cyanobacterial nitrogen fixing bacteria in the open ocean . As a result, there is demand for automation and high throughput to increase data set sizes to collect representative samples. Cosmochemistry and other fields have similar needs. As discussed above, a higher brightness primary ion source is one potential route for increasing throughput. Other factors include stage reproducibility and navigation. |
66fa233a12ff75c3a1e6b304 | 4 | Here we test a new NanoSIMS-HR instrument for lateral resolution, depth resolution, limits of detection, stage reproducibility, and isotopic ratio reproducibility. Lateral resolution measurements were conducted on an aluminum sample containing silicon crystals, and representative images were collected for (1) microalgae and (2) plant roots colonized with arbuscular mycorrhizal fungi. Depth resolution measurements were conducted on a delta layer sample at 16, 8, and 4 keV impact energy. Limit of detection measurements were made on a phosphorus implant. Isotopic ratio data were collected on a Si wafer and a quartz standard. |
66fa233a12ff75c3a1e6b304 | 5 | Instrument: The NanoSIMS-HR, like its predecessors the NanoSIMS 50 and 50L, is a scanning ion microprobe coupled to a double-focusing mass spectrometer with a Mattauch-Herzog design, which enables multicollection of secondary ions over a large relative mass range (~22x for the 50L) . The primary ions are accelerated toward the sample surface and steered and focused to the desired spot size by a suite of Einzel lenses and deflectors. To optimize focusing, the instrument is designed so that the primary and secondary ions travel in opposite directions through a single "coaxial" lens stack near the sample. As a result, the primary ion source and the sample surface must be at the same potential and opposite polarity. Normal operation is with the source and sample at |8000V|, resulting in a primary ion impact energy of 16 keV. The NanoSIMS-HR multicollection system has seven detectors, six of which are on movable trolleys to enable mass selection. Electron multiplier (EM) ion detectors in pulse counting mode are used to enable imaging; these can be swapped for Faraday cups (FC) for high-current, higherprecision isotope measurements. Relative to its predecessor instruments, the NanoSIMS-HR includes several key upgrades: |
66fa233a12ff75c3a1e6b304 | 6 | Upgraded item 1: The ionizer, extraction optics and reservoir of the thermal Cs + primary ion source were redesigned to optimize the angular intensity of the Cs + beam, improving brightness. For operations in positive polarity, the NanoSIMS-HR has the same radio frequency plasma O -source included with the NanoSIMS 50L; analyses using that source are not included herein. |
66fa233a12ff75c3a1e6b304 | 7 | Upgraded item 2: The HV boards and electronics were redesigned to allow the primary ion source and sample to be changed to enable low-impact energy analyses. The range of operation is from the standard 16 keV impact energy to 2 keV. Upgraded item 3: The analysis chamber sample stage has been upgraded to include a position encoder from Horiba Scientific. This sample stage enables sample navigation over a 50 x 50 mm 2 sample holder, as well as between SIMS analysis, optical imaging and primary ion beam measurement positions, requiring up to 100 mm in movement. To increase point reproducibility, the stage is equipped with an encoded plate used as a coordinate reference. An optical microscope equipped with a camera monitors the encoded plate to determine the absolute coordinates of the sample holder. |
66fa233a12ff75c3a1e6b304 | 8 | In addition, we note here that the NanoSIMS-HR includes navigation upgrades related to the fact that the sample cannot be observed with an optical system while in the SIMS position because the coaxial lens is too close. As a result, to navigate the sample with optical imaging, the sample holder is moved approximately 40 mm to position the sample in front of an optical objective. In the NanoSIMS-HR, the optical system has been improved to allow approximately ≤1-micron lateral resolution light imaging and mosaic image collection co-registered with the ion beam for SIMS-mode navigation. |
66fa233a12ff75c3a1e6b304 | 9 | To compare lateral resolution of the NanoSIMS-HR to a NanoSIMS 50L, measurements were made on an aluminum sample with high silicon content ("Al-Si sample") because the Si forms Al-free domains that provide sharp chemical contrast for these measurements. The sample was polished with diamond paste down to 0.1 micron (Buehler) and then colloidal silica (Buehler). Additional imaging was performed with biological samples, detailed below. |
66fa233a12ff75c3a1e6b304 | 10 | Lateral resolution was determined for a range of primary Cs + beam currents (~0.2 pA to 600 pA) and impact energies (16 keV to 2 keV). Primary ion current selection and focusing was performed as is typical for NanoSIMS instruments. Ion currents were controlled using Einzel lenses (L0 and L1) and a primary beam limiting aperture (D1) located in the coaxial optics column, astigmatism was corrected with an octopole, and the final focusing of the primary beam onto the sample surface was performed with E0P, a lens in the coaxial lens stack. The impact energy was adjusted by sweeping the potential of the source tube containing the Cs reservoir and adjusting the sample potential to the optimized value. High voltages on the lenses and deflectors in between for primary and secondary optics were scaled down with the energy decrease. Imaging was performed with electron multipliers in pulse counting mode and secondary electrons (SE). The mass spectrometer was operated without an entrance or aperture slit (~2000 mass resolving power (MRP)) for the highest lateral resolution (lowest primary beam current) analyses to achieve the most precise beam resolution measurements by optimizing ion transmission. The beam size was measured by imaging an Al-Si sample with Si -. Al 1 H -counts at mass 28 were negligible. Image collection parameters were set to provide a beam overlap from 75% for high lateral resolution image to 99% for large beam for NanoSIMS 50L and from 85% to 97n% for NanoSIMS-HR (2 x 2 to 20 x 20 µm 2 for NanoSIMS-HR and 5 x 5 to 12 x 12 µm 2 for the NanoSIMS 50L; all with 512 x 512 pixels; beam overlap defined as the [beam diameter -pixel width] beam diameter x 100% ). The dwell time varied from 0.2 to 3 milliseconds per pixel. As the intensity profile across two chemically contrasting phases (Al and Si in this case) is a convolution between the sharp edge and gaussian beam intensity distribution, a cumulative gaussian distribution model was used to describe the 28 Si -profile. Beam size was defined as the distance represented by the 16 to 84% quantile of the intensity distribution containing 68% of the beam intensity. Ion count transects across selected features were extracted in WinImage ion image data processing software (CAMECA) using a region of interest (ROI) of 2 to 4 pixels wide line by 1 pixel deep to average adjacent pixels perpendicular. Lateral resolution was calculated in WinCurve data processing software (CAMECA) using a cumulative Gaussian distribution model to extract 16% and 84% beam intensity locations on the profile abscissa as the beam size or lateral resolution . |
66fa233a12ff75c3a1e6b304 | 11 | The microalga Phaeodactylum tricornutum (CCMP2561, Bigelow National Center for Marine Algae and Microbiota) was imaged to illustrate the different analysis conditions. The microalga was grown on C and N labeled inorganic C and N for 48 hours, then fixed with 10% formalin overnight and filtered onto 2 µm pore size polycarbonate membranes and rinsed with double distilled water. Filters were dried overnight at 50°C prior to excising a portion to mount onto a conductive carbon tab (Ted Pella, California, U.S.A.) adhered to an aluminum stub. Mounted samples were sputter coated with ~5 nm of gold. |
66fa233a12ff75c3a1e6b304 | 12 | A thin section of a mycorrhizal root sample was imaged for correlation with transmission electron micrographs. The sample was prepared from the grass Panicum hallii infected with the arbuscular mycorrhizal fungus Rhizophagus irregularis (formerly Glomus intraradices), grown as described in Hestrin et al. (2022). P. hallii seeds were germinated on Petri plates, transferred into cones filled with doubleautoclaved sand, inoculated with ~500 R. irregularis spores, and grown for eight weeks before being transplanted into cones filled with a 50:50 (v:v) mixture of double-autoclaved sand and a fine sandy loam soil collected from a pasture in Caddo County, OK (35.072417/-98.303667). The sand:soil mixture began at 15% moisture and declined to 5% over the course of the 3-month greenhouse experiment. The plants were grown with a 16 hr photoperiod and average daytime and nighttime temperatures of 27 °C and 24 °C, respectively. At harvest, roots were washed, fixed in 50% ethanol, and stored at 4 °C. To prepare samples for imaging, 1-2 mm root segments were excised and transferred to a fresh fixative buffer (2% Tween, 3% glutaraldehyde, 3% paraformaldehyde in 0.05M sodium cacodylate buffer, pH 7.2 (EMS, Hatfield, PA, USA)) and microwaved (Pelco BioWave; Ted Pella, Redding, CA, USA) while under vacuum at room temperature (2×; 1 min 150 W (watts) -hold 1 min -1 min 150 W -hold 1 min -1 min 150 W; 27 mbar (20 mm Hg vacuum)). Samples were then held under vacuum for 1 hr and stored overnight at 4 °C. Sample were rinsed (3×; 10 min) in 0.05M sodium cacodylate buffer (pH 7.2) and then immersed in a solution of 1% osmium tetroxide with 1.6% potassium ferricyanide in 0.05M sodium cacodylate buffer and microwaved (2×; 1 min 150 W -hold 1 min; 27 mbar at room temperature). Samples were rinsed in a solution of 0.05M sodium cacodylate buffer, pH 7.2 (3×; 10 min at room temperature) and then subjected to an ascending acetone gradient (10 min; 35%, 50%, 70%, 80%, 90%, 100%) followed by pure acetone (3×; 10 min at room temperature). Samples were progressively infiltrated while rocking with Epon resin and acetone mixtures (EMS, Hatfield, PA, USA). For the final 3 exchanges of 100% Epon resin, samples were microwaved at room temperature (1×; 1 min 250 W -hold 1 min; 27 mbar) and then rocked for 2 hr at each step. Finally, samples were polymerized at 60 C for 48 hours. Thin sections were cut using a Leica UC6 (Leica, Wetzlar, Germany). A 90 nm thin section was collected onto a formvar-coated copper-rhodium backed slot grid. The grid was post-stained for TEM imaging with 2% uranyl acetate followed by Reynold's lead citrate, for 5 min each. The section was imaged with a Tecnai 12 120-keV TEM (FEI, Hillsboro, OR, USA). Image data were recorded using a Gatan Rio16 CMOS camera with GWS software (Gatan Inc., Pleasanton, CA, USA). TEM sections were then sputter coated with ~5 nm of gold. |
66fa233a12ff75c3a1e6b304 | 13 | Depth resolution measurements were made using a custom "delta layer" sample consisting of a silicon substrate with thin phosphorus-rich layers of up to 5% P atoms per Si atoms (2.5 x 10 21 P at./cm 3 ) laid down by vapor deposition between silicon layers. The P-rich layers were at 30, 90, 180 and 330 nm depth from the surface (ihp-microelectronics.com). Depth profiles were acquired by using a Cs + primary beam from 16 keV to 4 keV at 500 pA and by rastering a 20 x 20 µm 2 area. MRP was >9000 at 8 keV of secondary ions energy as reported by the NanoSIMS software (based on peak side slope width from 10% to 90% of peak height; equivalent to ~6000 MRP for peak width at 10% height) . 31 P -and 30 Si - images were acquired with a counting time per frame of 4 s for a total acquisition time of about an hour. Images were processed with WinImage by defining a ROI of 8 x 8 µm 2 in the image center to extract the counts rates of phosphorus with minimal ion contributions from the analysis periphery. Profiles were then processed with WinCurve to scale the depth and extract depth resolution. Because P is known to diffuse into the overlying Si during deposition but not into the deeper layer (verified by IMS-7f), depth resolution was based on the rate at which the 31 P -counts drop off after each layer. |
66fa233a12ff75c3a1e6b304 | 14 | P detection limits were measured using a P-implanted silicon wafer for a range of Cs + primary currents and raster sizes to determine the minimum detection limit and optimal raster for each primary current setting. The dose of P was 5.48 x10 at./cm 3 implanted at 200 keV. The peak of the implant was at a depth of 250 nm (± 1%), verified by IMS-WF relative to NIST SRM 2133. The NanoSIMS-HR was tuned for >9000 MRP (10%-90% definition) with entrance slit (ES) 4, aperture slit (AS) 3, and a fully open energy slit (EnS) to simultaneously collect 31 P -and 30 Si -. The Cs + current on the sample was varied from 10 pA to 8000 pA, and the raster size was varied from 2 x 2 µm 2 to 40 x 40 µm 2 to test the optimal pairing of primary current and raster size. Depth profiles were collected in imaging mode with 128 x 128 to 256 x 256 pixels for 130 to 400 cycles. The data were processed with WinImage to extract depth profiles from ROIs ranging from the full image down to 10% of the imaged area, with the ROI always in the center of the image. Depth profiles were processed with Wincurve. Ion counts were converted to concentration (in P at./cm 3 ) as a function of depth after deriving a relative sensitivity factor based on the known total dose. The apparent P concentration in the background tail of the P profile, where no P is sputtered and background dominates the signal, is defined as the detection limit. |
66fa233a12ff75c3a1e6b304 | 15 | The stage movement reproducibility was measured by moving the stage ~40 mm away from the center location and back and then performing an internal measurement of the shift in subsequent ion images. A standard deviation on shifts in both directions is deemed as an estimation of the reproducibility of the movement. To test this performance, Si -ion images were acquired by scanning a 12 x 12 µm 2 area defined with 512 x 512 pixels and a dwell time of 0.3 ms/pixel, and a lateral resolution of 120 nm. An image was acquired in ~80 s in SIMS position, then the sample stage was moved in front of the optical microscope and moved back again in SIMS position for a subsequent image acquisition. This sequence was repeated until a total of 8 images were acquired. WinImage was then used to calculate the shift between 2 consecutive images. An algorithm of image registration with a subpixel precision calculated the shifts in x and y directions. The first image was defined as the reference image, and image shifts in both directions were calculated from it. |
66fa233a12ff75c3a1e6b304 | 16 | Multicollection (simultaneous) isotope ratio measurements were made with three different configurations: (1) three Si isotopes ( 28 Si -, Si -and 30 Si -) from silicon wafers (conductor) with ~1 pA Cs + and 4 x 4 µm 2 rasters measured on three EMs, (2) three Si isotopes from the same Si wafers with 600 pA Cs + and 10 x10 µm² rasters measured on three FCs, (3) oxygen isotopes ( 16 O -and 18 O -) from a polished Pt-coated quartz substrate (insulator) with 15 nA Cs + and 10 x10 µm² rasters measured on two FCs. The normal-incidence electron flood gun was used for charge compensation. The NanoSIMS-HR was tuned for >7000 MRP (10%-90% definition). Data were collected in multicollection "isotope mode" with 64 x 64 pixels. The duration of one analysis, including pre-analysis sputtering, automatic secondary ion beam focusing and centering, automatic mass line centering, and data acquisition, was 10 min, 2 min 30 sec, and 3 min, respectively. Multiple reproducibility tests were conducted, including tests with small (microns), medium (millimeters), and large (10s of millimeters) movements (Table ; see also Results). Magnet stability was maintained with NMR control. |
66fa233a12ff75c3a1e6b304 | 17 | Lateral resolution as a function of the primary Cs + ion current with 16 keV impact energy was quantified for the NanoSIMS-HR and a NanoSIMS 50L with the same Al-Si sample (Fig. & S1; Table ). For the NanoSIMS-HR tests, the primary current on the sample was set to values from <0.2 pA Cs + (below Faraday Cup detection limit) to 600 pA Cs + . The best lateral resolution for the NanoSIMS-HR Cs + source was 25 nm, compared to 45 nm for the 50L. The specifications are set to 30 nm and 50 nm, respectively. The NanoSIMS-HR resolution at 600 pA was ~600 nm, compared to 100 pA for similar resolution with the 50L. At 100 nm lateral resolution, the data show a 2.5-fold improvement in current density for the NanoSIMS-HR over the NanoSIMS 50L. We tested the improved lateral resolution of NanoSIMS-HR on a biological sample by imaging P. tricornutum algal cells with the ultimate resolution of the two instruments at 16 keV (Fig. ). At ~30 nm lateral resolution, the ion images revealed small holes in the algal cell that would not be distinguishable with a standard NanoSIMS 50L, even at the ultimate resolution of 50 nm. These holes form during the sputtering of the P. tricornutum cell wall. We also tested the ability of the NanoSIMS-HR to deliver more current within a 100 nm spot. As expected, the secondary ion current increased 2.5x, proportional to the increase in current density. High-lateral-resolution NanoSIMS-HR analyses were also conducted on a 90-nm-thick section of a P. hallii root infected with R. irregularis, an arbuscular mycorrhizal fungus (Fig. &). Figure shows correlated TEM and NanoSIMS-HR 12 C 14 N -images of a subportion of an R. irregularis vesicle in the root tissue. The 12 C 14 N -image was collected with the 30 nm lateral resolution settings. The NanoSIMS-HR 12 C 14 N -image shows details that could be seen in the TEM image, as well as chemical contrast that could not. The TEM image shows sub-micron structures inside the vesicle that were visualized with the 12 C 14 N -ion in the NanoSIMS-HR, indicating that it was N-rich. The NanoSIMS-HR 12 C 14 N -image also shows that the vesicle wall is composed of multiple micron-scale layers of N-rich material. This material exhibited 100-nm-scale texture in the NanoSIMS-HR 12 C 14 N -image that is not visible in the TEM image, which we suspect was caused by extended ion bombardment. |
66fa233a12ff75c3a1e6b304 | 18 | The standard NanoSIMS impact energy of 16 keV is optimized to provide high lateral resolution and high transmission but is expected to result in worse depth resolution than lower impact energies as the primary ions penetrate deeper into the samples. We investigated this trade off with lateral and depth resolution measurements. |
66fa233a12ff75c3a1e6b304 | 19 | Lateral resolution was measured at 16, 8, 4, and 2 keV on the Al-Si sample. As expected, lateral resolution decreased with impact energy (Fig. &). The degradation of lateral resolution between 16 keV and 2 keV was on the order of a factor of 5 to 10 depending on beam current. Depth resolution was measured on the trailing edge of P delta layers deposited on a silicon wafer (Fig. and Table ; see Methods for sample and measurement descriptions). The results are expressed as the depth in which the 31 P -count rate declined by a decade (nm/decade). The depth resolutions for the two surface layers are not used because they are too close to the next deeper layer, resulting in 31 P -counts from the deeper layer interfering with the measurement. Based on the two deeper layers, the depth resolution is ~22 nm/decade at the 16 keV impact energy, ~15 nm/decade at 8 keV and ~12 nm/decade at 4 keV. |
66fa233a12ff75c3a1e6b304 | 20 | A Si wafer implanted with a known dose of P was used to determine the minimum P detection limit and corresponding minimum raster size and optimum ROI for a range of Cs + primary ion currents (Fig. , S4 & S5). The detection limit for P improved from 10 17 atoms per cubic centimeter (at./cm 3 ) for 10 pA Cs + with a 0.6 x 0.6 µm 2 ROI from a 2 x 2 µm 2 raster, to 10 14 at./cm 3 for 8 nA Cs + with a 12 x 12 µm 2 ROI from a 40 x 40 µm 2 raster. We found a consistent relationship between detection limit, minimum raster size and relative ROI size (Fig. ). The detection limit was lower for higher beam currents because of the larger dynamic range between the peak of the P implant and the tail, but the raster size had to be increased to obtain the minimum detection limit because the primary beam diameter increased with beam current . |
66fa233a12ff75c3a1e6b304 | 21 | We found that the minimum raster size was approximately 20 to 30 times the beam diameter, and the optimum ROI was approximately 10% of the raster area (Fig. ). Figure . P detection limit for 10 to 8000 pA (16 keV) vs. ROI width. These ROIs are ~10% of the total raster size. The Cs + current in pA is on the sample. IMS-7f data for comparison. |
66fa233a12ff75c3a1e6b304 | 22 | The X and Y reproducibility of the sample stage was tested by moving the sample back and forth between the SIMS analysis position and the optical microscope and collecting an ion image eight times (Table ). Shifts in the imaged feature are measured as pixel shifts and translated to nm based on the number of pixels per nm for the collected images. The observed reproducibility was ≤ 250 nm, which is well within the 500 nm specification. |
66fa233a12ff75c3a1e6b304 | 23 | No significant changes were made to the double focusing mass spectrometer part of the instrument, and therefore no change in isotopic ratio measurement performance was anticipated for the NanoSIMS-HR, and none was found (Table ; Fig. ). All measurements were within the precision specified for both instruments, and in this case, all but one had sub-permil precision (1). For the Si isotope measurements, high current analyses with Faraday cups achieved ~10x higher precision for the small (microns) and medium (millimeters) movement test, and ~2x higher precision for the large (10s of millimeters) movement test, relative to the lower current analyses with EMs. The O isotope measurements with Faraday cups and the electron flood gun (e-gun) also achieved sub-permil precision. |
66fa233a12ff75c3a1e6b304 | 24 | Our tests on the newly redesigned CAMECA NanoSIMS, called the NanoSIMS-HR, demonstrate that features of the new instrument substantially improve imaging, depth profiling, detection limits and automated performance while maintaining secondary ion mass spectrometer performances, such as mass resolution, transmission, and isotope analyses presented here. The redesigned higher intensity thermal Cs + ion source is central to the improved performance, but other upgrades such as high-voltage control, an encoded sample stage, a higher resolution optical system, an automated sample exchange system, and new electronics further contribute to improved performance. The ion optics, secondary ion mass spectrometer and multicollection detector system are unchanged. |
66fa233a12ff75c3a1e6b304 | 25 | The redesigned, higher intensity Cs + ion source is a significant benefit of the NanoSIMS-HR. While the NanoSIMS 50 and 50L instruments had to meet the 50 nm lateral resolution specification, researchers have pushed to improve on this benchmark. Some researchers have reported better than 50 nm lateral resolution for the standard thermal Cs + ion source on NanoSIMS 50 series , but such performance would not be guaranteed by CAMECA. Others have sought to redesign the Cs + ion source to improve its intensity with some reported success , but no product is available yet for testing. Therefore, a reliable and commercially backed instrument that produces a 30 nm lateral resolution Cs + beam and overall higher Cs + current density is a significant advance for consumer access. |
66fa233a12ff75c3a1e6b304 | 26 | The ion images of biological samples in this study show the benefit of the improved lateral resolution. The NanoSIMS-HR was able to resolve finer features, such as the holes in the P. tricornutum cell wall (Fig. ) and the structure of the contents of the AMF vesicle (Fig. ). The relationship between imaging lateral resolution and analytical lateral resolution is somewhat complicated because it includes feature composition, feature spacing, analyte and analyte background , but in any case, improved resolution has benefits for navigation and feature identification. It is worth noting that although the highest resolution measurements in this study were made at low MRP to optimize the number of detected ions during a scan to achieve more accurate measurements of the analysis spot size, the same resolution scans could be made with higher MRP. For trace element and isotope analyses, multiple scans are typically made of an analysis area to accumulate statistically meaningful counts of the minor species. |
66fa233a12ff75c3a1e6b304 | 27 | While "ultimate resolution" is the featured specification, the higher current density benefits all analyses by enabling faster analyses, improving low impact energy imaging depth profiling, and lowering detection limits. For example, bacterial analyses with 100 nm lateral resolution can be performed at least 2.5 times faster with the NanoSIMS-HR (5 pA vs. 2 pA for 50L; Fig. &). The majority of published papers do not use the ultimate resolution of the NanoSIMS 50 or 50L but rather a lower-resolution, higher-current primary ion beam setting that allows faster analyses, lower detection limits, and generally more straight forward operation. One notable point is that secondary electron imaging, which can be used with the Cs + ion source for navigation and feature identification, can be very poor at the very low primary current setting (~0.2 pA) necessary to achieve the ultimate resolution. |
66fa233a12ff75c3a1e6b304 | 28 | The ability to vary the NanoSIMS-HR source and sample high voltage from 8 keV down to 1 keV allows the user to trade off lateral resolution for depth resolution. Our results show that at 4 keV impact energy (2 keV on source, -2 keV on the sample), there is an approximately 2-fold improvement in depth resolution with an approximately 5-fold loss in lateral resolution. While the actual lateral resolution is better than it would have been with the previous thermal Cs + source, the source intensity is still affected by reducing the source high voltage because it extracts the electrons that heat the source, and the ability of the electronics to compensate has limits. We tested the P detection limit with 10 to 8000 pA Cs + primary beam current. The improvement in the detection limit with higher beam current reflects the increase in the dynamic range between the implanted P and the background . The relationship between beam current and detection limit in the P analyses in this study reflects an optimal relationship between the primary current resolution, the sputtered area and the target area for data extraction (Fig. ). We found that the optimum relationship between primary beam diameter and raster size was a factor of 20 to 30. Smaller rasters result in significant contribution of P -counts from the periphery of the analysis crater to the central ROI. We also found that the optimal ROI size is ~10% of the raster size; smaller ROIs result in a reduced dynamic range and limitation on the number of atoms in the analyzed area (Fig. ). We do not have comparable 50L data, but we would expect the ROI for any given detection limit to be larger because of the lower beam intensity. Based on previous work, the minimum size that a feature of interest could be is the size of the ROI plus two beam widths . Higher primary beam current density also lowers background for analyses such as H and O, where the background count rate is proportional to the rate at which these species in the analysis chamber vacuum interact with the sample surface . Higher spatial resolution also increases sensitivity to the composition of the target feature by sampling the feature and not the adjacent material. |
66fa233a12ff75c3a1e6b304 | 29 | The improved stage control can further speed up automated analyses by allowing the primary beam raster to be more tightly framed on a series of preselected targets, such as cells or particles. The analysis area has to be scaled based on the stage precision to ensure that selected targets are hit. The proportional increase in area directly translates to analysis time to collect sufficient ions from the target. The greatest improvement is for small targets (e.g., 1 m ), where the increase in analysis speed would be between 30 and 100 times, depending on whether one allows for 5-or 10-micron stage reproducibility with a NanoSIMS 50L (analysis time is proportional to the square of the target size + 2x stage reproducibility; Fig. ). For larger targets, the increase in analysis speed reduces geometrically down to 2 to 3 times for 30-micron diameter targets, which is still a significant time savings. |
67959d016dde43c9086a1f4b | 0 | The characterization of material properties serves as a pivotal link in deciphering the structureproperty relationship and holds the key to optimizing the device performance. For functional materials, specific property requirements vary across different application scenarios, making comprehensive property characterization of utmost importance. However, such processes demand multidisciplinary knowledge, professional operational expertise, costly instrumentation, and significant time investment, which have posed a substantial obstacle to the development of functional materials. |
67959d016dde43c9086a1f4b | 1 | Organic optoelectronic materials, a burgeoning frontier in functional materials, have found extensive applications in diverse academic and commercial arenas such as display, clean energy, and biosensing, owing to their unique tunability in optoelectronic and charge transport characteristics. These materials typically comprise conjugated molecules and are utilized in the form of solid films as the core constituents of optoelectronic devices. Experimentally characterizing the optoelectronic and charge transport properties of molecules in solution and/or solid film and elucidating their influence on the performance of various devices is crucial for driving the advancement of the organic optoelectronics industry. Nevertheless, as previously noted, the associated property characterization costs and the prerequisite for researchers' multidisciplinary knowledge and technical proficiency have become hurdles in the development of novel devices. Hence, an open question emerges: can we devise virtual characterization tools to acquire relatively accurate material properties at a reduced cost, thereby substantially diminishing the reliance on experimental characterization during device development? |
67959d016dde43c9086a1f4b | 2 | Attempts from various levels of theory have been made to address this question. On the one hand, at the molecular level, traditional quantum chemistry methods can delineate the electronic relaxation processes among different electronic states based on the geometric configuration of a single molecule, enabling relatively accurate predictions on the material's optoelectronic properties. The feasibility of such method actually lies in the fact that the intermolecular interaction between organic molecules is weak. 12 By leveraging the geometric configuration of bimolecules in films, the electronic coupling (transfer integral) between molecules can be described to assess the electron transport probability. However, the aforementioned simulation methods entail high computational demands as well as master specialized computational techniques of the researcher, such as the selection of functionals and basis sets and the preparation of force field topology files. On the other hand, data-driven methods have exhibited significant potential in predicting computational or experimentally characterized properties with high accuracy and efficiency. Yet, these methods usually rely on feature engineering predicated on expert domain knowledge, often suffering from poor transferability to dissimilar property tasks and being at a disadvantage when dealing with high-diversity databases. |
67959d016dde43c9086a1f4b | 3 | Recent deep learning approaches for optoelectronic property prediction primarily extract a series of predefined atom and bond features, such as the formal charge on the atom, from the 2D graph of the molecule and construct the molecular representation via the message passing mechanism. Currently, the state-of-the-art (SOTA) accuracy has been attained in multiple optoelectronic property prediction tasks. However, this 2D graph convolution method disregards 3D information and restricts its applicability to tasks involving 3D information, such as predicting the transfer integral(TI) of the film system based on the geometry of bimolecules. In the prediction of charge transport properties, Bhat et al. constructed a transfer integral database using a crystal structure library and predicted the transfer integral in a crystal environment based on the 3D graph convolution molecular representation. Owing to the dearth of experimental data and certain force field parameters in the molecular dynamic (MD) simulations of conjugated systems, no structural database of optoelectronic films has been reported thus far. For film systems, most existing studies predict the transfer integral of a single system based on the Coulomb matrix. In principle, deep learning can yield a molecular representation comparable to that obtained through domain expert feature engineering by pre-training on relevant large-scale (usually over 3M) 3D positions or low-precision labels within the field. This paradigm has been demonstrated to outperform previous methods in data-rich scenarios such as large language models, small molecule drug property prediction, and general force fields of inorganic materials. To achieve accurate and efficient virtual characterization of functional materials considering both optoelectronic and transport properties, we introduce OCNet to bridge the gap in achieving general and low data-requirement molecular representations of these properties. Firstly, we construct a large-scale conjugated molecular database containing 12M GFN2-xTB optimized structures and sTDA-xTB 40 level optoelectronic properties, together with a conjugated bimolecular database with 9M bimolecular conformations collected from 100K molecular dynamic(MD) simulations of organic films and transfer integrals with GFN1-xTB 41 accuracy. Based on these two large-scale databases, our OCNet realizes a general conjugated molecular representation and a bimolecular representation using the SE(3) Transformer architecture. Additionally, for specific downstream property prediction tasks, we support domain experts in fusing domain knowledge features with molecular representations to enhance the interpretability of OCNet and further improve its performance on scarce datasets. The accuracy of our OCNet on various computationally and experimentally labeled properties is remarkably enhanced compared to the previously reported models, attesting to the superiority of our general molecular representation. Moreover, we also establish a bimolecular transfer integral dataset containing 1.8M data points computed via density functional theory (DFT) based on 45K molecular films. The accuracy performance of our OCNet on this dataset can be exploited for subsequent quantitative prediction of film transport properties, marking a significant advancement in film transfer integral prediction from single-system modeling to general model prediction. Finally, to make the OCNet more accessible to the broader research community, we provide both the OCNet code, pre-training database and corresponding molecular and bimolecular representation online. We also provide a user-friendly web application to predict downstream properties in this work. With the free and user-friendly accessibility of OCNet, we anticipate that the general molecular representation of OCNet will serve as an effective tool for the virtual characterization of the optoelectronic and transport properties of organic optoelectronic materials, expediting the development of optoelectronic devices and demonstrating the potential for application in other functional material research scenarios related to organic conjugated molecules. |
67959d016dde43c9086a1f4b | 4 | Due to the lack of large-scale databases for pre-training conjugated molecular and bimolecular representations, we construct a conjugated molecular and bimolecular database that contains 10 million(M) level geometries and corresponding optoelectronic properties or transfer integrals at the tight-binding (TB) level. Our database includes 16 different elements (H, B, C, 5 N, O, F, Si, P, S, Cl, Br, I, Ir, Ge, Se, As) and three distinct types of conjugated molecules (metal-organic complexes, condensed hetero-polycyclic aromatic molecules, and fragmentassembly-based aromatic molecules), thereby covering a broad range of the chemical space of organic conjugated systems. We illustrate the construction process of the molecular and bimolecular database in Figure . |
67959d016dde43c9086a1f4b | 5 | Firstly, we collect the Ir complex open-source dataset 42 containing 0.84M structures and the COMPAS-2x open-source dataset 43 comprising 0.5 M cata-condensed hetero-polycyclic aromatic molecules. Then, we generate an additional 11M molecular structures using ring fusion and fragment assembly methods (detailed in the Methods section, Figures and). When generating million-level condensed poly(hetero)cyclic aromatic molecules using the ring fusion method, we allow carbon or heteroatoms to be shared by two or three rings (Figure ). This approach makes our database the first to include molecules with multiple resonance structures. Moreover, we also generate millions of fragment-assembly-based molecules by connecting carbon atoms across different conjugated fragments for the first time. |
67959d016dde43c9086a1f4b | 6 | To further demonstrate the diversity of our molecular database, we compare our molecular database with the open-source COMPAS-2x dataset in terms of heavy atom numbers (Figure ) and molecular weight (Figure ) distribution. It can be observed that our molecular database contains larger molecules: while most molecules in COMPAS-2x have fewer than 50 heavy atoms and a molecular weight of less than 600 Da, approximately 60% of the molecules in our database have more than 50 heavy atoms and a molecular weight greater than 600. We also compare the distribution of our molecular database with the COMPAS-2x database and the largest fragment-assembly-based database, FORMED with 0.1M structures, in the 2D space of our molecular representation using t-SNE analysis(Figure ). It can be observed that COMPAS2 and FORMED only occupy partial regions of our molecular database, which further indicates that our molecular data is widely distributed across the chemical space of conjugated systems. |
67959d016dde43c9086a1f4b | 7 | To achieve this, we first select molecules with relatively low electron or hole reorganization energies at the GFN2-xTB level from our molecular database. Then, we obtain the film structures through MD simulations using the force field we develop for organic conjugated molecules (detailed in the methodology section). We also demonstrate the distribution of heavy atoms and molecular weight in our bimolecular database (Figure ). It can be seen that the maximum heavy atom count reaches 350, and the maximum molecular weight reaches 9000 Da, indicating that our bimolecular database possesses significant molecular diversity. |
67959d016dde43c9086a1f4b | 8 | To ensure generality, we only use the system's elements and distance kernel matrix as the initial atomic and pair representations. These representations are then aggregated into a global molecular representation through 15 encoder layers using the attention mechanism (detailed in Figure and the Methods section). In this work, we choose a SE(3) Transformer architecture which contains 15 encoder layers to construct molecular representation learning (MRL) models, as it has demonstrated high performance on small organic and drug molecules. Then, we optimize all the weight parameters of the molecular representation learning (MRL) models through pre-training on our molecular and bimolecular databases(Figure ). By learning from large amounts of unlabeled structures and TB-level optoelectronic properties and transfer integral data, we can significantly reduce the data requirements of our molecular and bimolecular representation when fine-tuning downstream optoelectronic and transport-related tasks. |
67959d016dde43c9086a1f4b | 9 | For specific downstream tasks, OCNet provides two approaches for virtual characterization: directly modeling the downstream properties based on molecular representations or inte-grating prior knowledge to further enhance the molecular representation's capability and interpretability. Specifically, we use multilayer perceptrons to extract both molecular representations and domain-specific features, which are then fused into a single representation for downstream property prediction (Figure , and detailed in the methodology section). |
67959d016dde43c9086a1f4b | 10 | To comprehensively demonstrate the performance of OCNet in different downstream scenarios, we evaluate its accuracy on QM-calculated or experiment-measured optoelectronic properties and transfer integrals in crystal or film environments. For all property prediction tasks, we set the training-to-test ratio at 8:2 and used mean absolute error (MAE) and the coefficient of determination (R 2 ) to evaluate model accuracy. Moreover, to make the OCNet more accessible to the broader research community, we also integrated these downstream property prediction models into a user-friendly interactive web app() for material design in various scenarios(Figure ), such as photovoltaic and display. |
67959d016dde43c9086a1f4b | 11 | We utilize the open-source OCELOT chromophore dataset, which provides DFT and TDDFT-computed data, to evaluate the accuracy of OCNet in predicting QM-calculated optoelectronic properties. Specifically, we compare the performance of OCNet with reported SOTA models in terms of the HOMO-LUMO gap (H-L), lowest-lying singlet excitation energies (S0-S1), electron reorganization energies (ER), and hole reorganization energies (HR) (Figure ). We define the accuracy score of OCNet on the dataset as the ratio of the MAE of the SOTA model to the MAE of OCNet. It can be observed that OCNet achieves the highest accuracy across all four property prediction tasks, with accuracy scores improving by at least 15% for all tasks and by 60% for the HR prediction task. We also demonstrate the correlation between the OCNet predictions and the corresponding QM-calculated values for all four properties(Figure ). OCNet successfully achieves quantitative predictions for the S0-S1 and H-L tasks, with MAEs of 0.199 eV and 0.008 eV, and R 2 values of 0.803 and 0.987, respectively. OCNet achieves MAEs of 0.082 eV and 0.087 eV for the ER and HR prediction tasks, with R 2 values of 0.575 and 0.511, respectively. This level of accuracy is sufficient for screening molecules with low reorganization energies. We further compare the MAE and R 2 of the reported SOTA model, as well as OCNet with(w/) and without(w/o) pre-training, across all four properties (Table and Subsequently, we evaluate the accuracy of OCNet on the experimental optoelectronic dataset, Deep4Chem. Given the complexity of the solution environment, reported SOTA models typically employ strategies such as directed message passing, introducing additional edge and subgraph information or integrating domain prior knowledge to enhance molecular representation. We integrate domain-specific features utilized in SuboptGraph into our molecular representation to predict absorption wavelength (Abs.), emission wavelength (Emi.), photoluminescence quantum yield (PLQY), and full width at half maximum (FWHM). We compare the performance of OCNet with SOTA models in predicting these four properties (Figure ). The accuracy score of OCNet on the datasets is defined as the ratio of the MAE of the SOTA model to the MAE of OCNet. Although SOTA 2D graph convolutional models incorporate additional edge and subgraph information to enhance molecular representation, our 3D geometry-based OCNet achieves improvements of 18% and 13% in accuracy score for the prediction of absorption and emission wavelengths, respectively. Since our pre-training does not include tasks related to PLQY or FWHM, the performance improvement of OCNet for these properties is relatively modest, approximately 5%. We also demonstrate the correlation between the OCNet predicted values and experimental values(Figure ). OCNet accurately predicts absorption and emission wavelengths, achieving MAEs of 7.085 nm and 11.167 nm, respectively, with corresponding R 2 values of 0.982 and 0.949. The accuracy of OCNet in predicting PLQY and FWHM is also capable of screening molecules with high PLQY and narrow emission, with MAEs of 0.101 and 9.123 nm, and R 2 values of 0.722 and 0.719. We further compare the MAEs and R 2 values of the reported models (Uni-Mol and reported SOTA model SuboptGraph), along with OCNet w/ and w/o pre-training, for absorption and emission wavelength predictions (Figure , Tables and). Due to significant structural differences between drug molecules and conjugated molecules, Uni-Mol, which is pre-trained on drug molecule conformations, exhibits relatively poor accuracy in absorption and emission wavelength prediction tasks. Specifically, the MAE for emission energy prediction reaches 16 nm, whereas the MAE for the other models remains below 13 nm. Furthermore, both OCNet w/ and w/o domain features achieve lower MAEs compared to the reported SOTA model, demonstrating the effectiveness of our molecular representations pre-trained on conjugated systems. In addition, OCNet w/ domain features exhibits slightly higher accuracy in terms of both MAE and R 2 metrics. This indicates that integration with domain knowledge can enhance the representational capacity of OCNet, further relieving the data scarcity in materials science. |
67959d016dde43c9086a1f4b | 12 | To demonstrate the performance of OCNet in transport-related tasks, we utilize OCNet's bimolecular representations to predict intermolecular electronic couplings (transfer integrals) in both crystalline and film environments. We first evaluate the performance of OCNet on the OCELOT dimer dataset, 13,46 a diverse dataset containing 438,000 DFT-derived transfer integrals from about 25,000 molecular crystal structures. Inspired by the work of Valeev et al., we select domain features including the distance between molecular centroids, the angle between molecular plane normal vectors, and the angle between the centroid-to-centroid vector and the molecular plane normal vectors. Subsequently, we demonstrate the correlation between the predictions of the domain feature-integrated OCNet and the corresponding QM calculation results. Leveraging pre-training on bimolecular conformations and TB level transfer integrals, we achieved accurate predictions of H-H and L-L transfer integrals. in the OCELOT dimer dataset, with MAEs of 0.058 eV and 0.061 eV, respectively, and R 2 values of 0.909 for both cases. We also compare the accuracy of OCNet with reported SOTA model in predicting H-H and L-L transfer integrals (Figure , Tables and). |
67959d016dde43c9086a1f4b | 13 | We set the accuracy score in Figure as the ratio of the MAE of the SOTA model to the MAE of OCNet. Compared to the prediction accuracy of the SOTA model for H-H and L-L transfer integrals. (MAEs: 0.081 eV and R 2 :0.83), our OCNet demonstrates significantly improved performance, achieving a 50% increase in accuracy score. In addition, the performance of OCNet w/o pre-training is inferior to the reported SOTA model (Figure ). For instance, in the prediction of H-H transfer integrals, the MAE for OCNet w/o pre-training is approximately 0.12 eV. These results further highlight the superiority of our bimolecular molecular representations, pre-trained on large-scale datasets, in accurately describing electron or hole transfer tasks. |
67959d016dde43c9086a1f4b | 14 | Considering that the functional layers of functional material devices primarily exist in film states, we construct the first DFT-accuracy database (detailed in the methods section) comprising 1.8 OCNet transfer integrals across 5,500 distinct molecular types. We construct the domain features by integrating structural features: the distance between centroids, the angle between plane normal vectors, and the angle between plane normal vectors and the centroid connection vector, and TB-level electronic properties. These electronic properties include overlap integrals, transfer integrals, effective integrals for the HOMO or LUMO orbital, and total effective transfer integrals for all occupied or unoccupied molecular orbitals. Subsequently, we utilize the domain feature-integrated OCNet to predict the transfer inte-grals database in film environments. As no other models have yet reported similar results, the accuracy score of OCNet is set to 1 (Figure ). We further evaluate the correlation between OCNet predictions and corresponding QM values for H-H and L-L transfer integrals(Figure ). OCNet demonstrates high accuracy, achieving R 2 values of 0.844 and 0.872 and MAEs of 0.2 eV and 0.204 eV for H-H and L-L transfer integrals, respectively. This marks the first successful realization of a general model for transfer integral prediction in film environments. The accuracy of this general model is comparable to that of reported SOTA models for predicting transfer integrals in crystalline environments, making it suitable for subsequent calculations of molecular mobility in film environments. |
67959d016dde43c9086a1f4b | 15 | To ensure the acquisition of high-quality molecular and bimolecular representations with low data requirements, we pre-train the SE(3) transformer models using a self-constructed, large-scale database containing optoelectronic and electronic coupling properties. For specific downstream tasks, OCNet integrates domain-specific features with general molecular representations, enhancing its expressive power and interpretability. On QM optoelectronic datasets, experimental optoelectronic datasets, and transport-related transfer integral datasets, OCNet significantly outperforms reported state-of-the-art models in prediction accuracy. Additionally, we construct the first large-scale bimolecular transfer integral database, comprising 1.8 million DFT-accuracy data points derived from 55,000 films. This advancement demonstrates OCNet's capability to achieve quantitative predictions on the dataset, laying a foundation for developing generalizable models for transfer integrals in thin-film systems. Consequently, OCNet provides a unified framework for the virtual characterization of both optoelectronic and transport properties in functional materials, facilitating the establishment of structure-property-function relationships in optoelectronic devices. Furthermore, OCNet's molecular and bimolecular representations have great potential to be transferred to other areas related to conjugated molecular materials, such as photocatalysis and dyes. |
67959d016dde43c9086a1f4b | 16 | The large-scale molecular database includes 12M conjugated molecules with structures optimized at the GFN2-xTB level and opto-electronic properties (HOMO-LUMO GAP, absorption energy, absorption transition dipole moment) calculated at the sTDA-GFN2-xTB level. Part of the structures is mined from two open-source databases: an iridium complex database 42 with 0.84 M structures and COMPAS-2x database 43 with 0.5 M cata-condensed hetero-polycyclic aromatic molecules. We generate the remaining structures through aromatic or anti-aromatic ring fusion and fragment assembly. |
67959d016dde43c9086a1f4b | 17 | Firstly, we generate condensed hetero-polycyclic aromatic molecules using 12 kinds of five or six-membered aromatic or anti-aromatic hetero-rings (Figure ) as building blocks. To cover the chemical space of condensed hetero-polycyclic aromatic molecules for organic op-13 toelectronic applications, our building blocks feature various compositions (including monoand di-substituted variants with B, N, O, S, and C=O), which are commonly reported in previous studies. Furthermore, when fusing the rings in original condensed hetero-polycyclic aromatic molecules and building blocks (Figure ), we allow carbon or hetero atoms to be shared by two or three rings. This approach ensures that part of the generated molecules exhibit multiple resonance features, which are widely used for the preparation of devices with narrow band emission, high luminescence quantum efficiency and have not been considered in previous open-source datasets. To avoid unnecessary resource consumption, we set the maximum ring number to 15, ultimately generating 2 M condensed hetero-polycyclic aromatic molecules. |
67959d016dde43c9086a1f4b | 18 | Besides condensed hetero-polycyclic aromatic molecules and metal-organic complexes, we also create fragment assembly-based aromatic molecules by connecting carbon atoms on the rings that belong to different conjugated molecules(Figure ). To achieve this, we mine various conjugated molecules from previous publications using the molecular recognition app, and construct a fragment library by severing the carbon-carbon single bonds between different rings of those molecules. We also mark the bond-breaking atoms of all fragments and connect hydrogen atoms to them for valence saturation. Finally, we construct 9 M fragment assembly-based aromatic molecules by randomly combining molecular fragments through the automated connection of marked carbon atoms. |
67959d016dde43c9086a1f4b | 19 | We construct the large-scale dimer database consisting of 9.5 million dimer conformations sampled from 100,000 molecular films obtained through MD simulations. These 100,000 molecules are randomly sampled from 1cM molecules with relatively low electron or hole reorganization energies in our molecular database, considering that molecules used for transport applications typically exhibit low reorganization energies. Based on these 100,000 molecules, we use Packmol 56 to construct initial boxes with a length of 10 nm, each containing 100 monomers. We then run 4 ns MD simulations under 1 bar and 300 K, using the v-rescale thermostat and the c-rescale barostat. During the MD simulations, we choose OSCFF, a force field we develop for organic conjugated molecules that is compatible with the GAFF force field, to describe the intermolecular interactions within the film. Our OSCFF completes the missing force field parameters for conjugated molecules and shows accuracy in torsional potential scans comparable to the reference QM method. For detailed specifics, please refer to ref. After 4 ns of MD simulation, the densities of all the film systems have converged. We randomly select 90 dimer conformations with a centroid distance less than 1 nm from the final frame of each system's MD simulation and calculate the HOMO-HOMO and LUMO-LUMO transfer integrals at the GFN1-xTB 41 level. |
67959d016dde43c9086a1f4b | 20 | The geometries of the OCELOT chromophore and the Deep4Chem dataset are converted from SMILES using rdkit 60 and are further optimized using GFN2-xTB. We also select 1.8 M conformations from our bimolecular database. To reduce the computational demands, we limit the maximum number of atoms to 200. Additionally, to increase the proportion of conformations with larger transfer integrals in the dataset, we first randomly sample 0.8 M conformations from the bimolecular database, and then randomly select 1 M conformations from those with HOMO-HOMO or LUMO-LUMO transfer integrals greater than 0.27 eV, calculated at the GFN1-xTB level. The final set with 1.8 million bimolecular conformations contains 5.5k unique molecular types, exhibiting high chemical diversity. We calculate all HOMO-HOMO and LUMO-LUMO transfer integrals for the bimolecular conformations at the PW91/6-31G(d) level 61 using MOMAP and Gaussian16, as the combination of PW91 and 6-31G(d) has demonstrated high accuracy in calculating transfer integrals and carrier mobility. |
67959d016dde43c9086a1f4b | 21 | To construct an accurate and general molecular and bimolecular representation for organic functional materials, we employ atomic numbers and pairwise distances as the initial repre-sentation to encode both atomic and 3D spatial information of the molecular or bimolecular system. Then, we employ the self-attention mechanism in Transformer architecture to couple and update the initial atomic and pair representations, thereby obtaining representations that accurately capture the complex interactions within the molecules or bimolecules. Similar to using the CLS token as a sequence representation aggregator for 1D sequence tasks in the BERT model, we choose the geometric centers of the molecules or bimolecules as the CLS atoms to aggregate atomic features, thereby reflecting the overall structural characteristics of the molecules or bimolecules. We denote the initial atomic representation as: |
67959d016dde43c9086a1f4b | 22 | all atoms within the molecule or bimolecule are encoded using embedding layer according to their elements, while the first element in eq (1) represents the embedding layer of CLS atom. n max refers to the maximum number of atoms in a molecule or bimolecule within the database. We employ PAD token to ensure a fixed input size when the number of atoms is less than n max . The initial pair representation is denoted as the molecular or bimolecular distance kernel matrix P 0 , where |
67959d016dde43c9086a1f4b | 23 | Based on the initial atomic and pair representations x 0 and P 0 , we update the atomic and pair representations with 15 encoder layers (Figure ). For the l-th layer, we first construct the weight matrix W l Q , W l K ∈ R d model ×d k and W V ∈ R d model ×dv , to obtain the query matrix |
67959d016dde43c9086a1f4b | 24 | We construct both the molecular and bimolecular representations with 15 layers and an embedding dimension of 512, using a Gaussian kernel size of 128. We pre-train the molecular and bimolecular representations on 8 Tesla A100 GPUs, which take approximately 20 days to complete. We use the Adam optimizer with a learning rate of 0. Freq. |
65d79de59138d23161bec6e6 | 0 | Data science is emerging as a means to probe structureactivity relationships, design and analyze chemical space, and optimize chemical reactions, ultimately impacting a range of applications in the chemical enterprise. However, the computational infrastructure required to do so can be prohibitive to laboratories with experimental data but limited experience with and/or access to high performance computing (HPC) resources. To combat this issue, density functional theory (DFT)-level molecular descriptor libraries for commonly used substrates, 2, 3 ligands, and drug-like molecules have been constructed and disseminated to reduce redundancy of expensive calculations in the field. Descriptor libraries can be built agnostic to a particular reaction, and thus can be used in a range of applications; libraries of this type have been demonstrated to guide the selection of diverse reaction substrates, predict the outcome (e.g., selectivity, rate, or yield ) of chemical reactions, and elucidate key mechanistic features. In particular, we have found success applying atom-or bond-level descriptors focused on conserved moieties in each reaction component of a dataset, which are hypothesized to lend specific insight into the reactive site in order to maximize interpretability and mechanistic understanding. |
65d79de59138d23161bec6e6 | 1 | While published descriptor libraries may attempt to incorporate common substrates or ligands, it is not practical (or possible) to precompute DFT-level descriptors for every compound a user may wish to featurize. For successful dataset design or predictive modeling, the defined descriptor set needs to be calculated for each new compound of interest. Replicating a full descriptor calculation workflow to add even a single compound to the library can require tedious coordination of numerous software packages, license agreements, computing clusters, etc. Automated workflows to perform these tasks can mitigate several of these challenges but do not circumvent the computational cost. Thus, it would enable downstream applications if an existing library could be exploited to predict relevant descriptors for new compounds within seconds Across the chemical sciences, machine learning (ML) models have demonstrated the ability to serve as surrogates for electronic structure calculations and other simulation techniques connecting molecular structures to computed properties. Previously, prediction of DFT-level descriptors has been accomplished for single properties on a broad range of mole-cules. Additionally, ML property prediction has been used to expand a DFT-level descriptor library of monophosphines 200-fold by combinatorializing substructures present in the existing library. Herein, we describe a case study investigating the prediction of a set of conformationally-informed descriptors collected for a single conserved reactive moiety-either a carboxylic acid or a primary/secondary alkyl amine (Figure ). Our selection of carboxylic acids and amines was motivated by the ubiquity of amide couplings in medicinal chemistry, as well as our recent efforts to correlate the reaction rates of amide couplings with DFT-level molecular descriptors of carboxylic acid derivatives and primary alkyl amines. We envisioned a method wherein a user would be able to simply supply a SMILES string (or draw a chemical structure) to obtain high-fidelity predictions of DFT-level descriptors for use in downstream applications without the need for HPC resources (Figure ). To obtain accurate predictions, we needed to address the challenge of predicting diverse descriptors (i.e., steric, electronic, and stereoelectronic properties at the molecule-, atom-, and bond-level) that account for the dynamic range of properties stemming from the conformational flexibility of compounds in these classes (Figure ). We applied graph neural networks (GNNs) trained on expansive libraries to predict these diverse DFT-level descriptors. We demonstrated these predicted descriptors are appropriate for data-driven modeling of medicinally-relevant carboxylic acid and alkyl amines. Moreover, Hammett parameters for aryl carboxylic acids are a cornerstone of physical organic chemistry; therefore, we envision an extensive library of carboxylic acid descriptors should have widespread applications as surrogate descriptors. The rapid prediction of descriptors also greatly expands the direct applicability of the carboxylic acid and alkyl amine descriptor libraries, reducing the barrier of entry to dataset design and predictive modeling. |
65d79de59138d23161bec6e6 | 2 | In order to obtain representative libraries of carboxylic acids and amines, the Reaxys database 34 was queried to identify commercially available carboxylic acids, primary alkyl amines, and secondary alkyl amines that would be applicable to amide coupling reactions (Figure ). To ensure broad representation of molecules relevant to medicinal chemistry for downstream library applications, external validation sets of acids and amines were also compiled from Enamine's building block sets 36 and from acid and amine fragments of existing amide-containing drugs mined from the Broad Institutes Drug Repurposing Hub. The full lists of compounds are available on Figshare. Previous studies have revealed the utility of molecular descriptors that encompass the dynamic range of conformers that a molecule can adopt within a given energetic window. To this end, we conducted automated conformational searching and clustering with Schrodinger's Maestro 39 to access representative conformational ensembles for each compound, which were then further optimized using the Gaussian 16 software at the M06-2X/def2-TZVP-SDD(I, Sn, Se)// B3LYP-D3(BJ)/6-31G(d,p)-LANL2DZ(I, Sn, Se) level of theory. Natural bond orbitals (NBO) and spectroscopic parameters were further evaluated at the DFT level of theory on these optimized geometries. To process these calculations, a Get Properties jupyter notebook was developed to enable the collection of descriptors at the molecule-level, in addition to atom-and bond-level properties for a conserved moiety of interest. Specifically, for each of these three libraries, we collected global properties (e.g., frontier molecular orbital energies of the HOMO and LUMO, polarizability, dipole moment, solvent accessible surface area, and solvent accessible volume) of the molecule, and tabulated the atom-level properties (e.g., NBO natural population analysis partial charge, NMR chemical shift, and buried volume) of conserved atoms (Figure ). In the case of the amine libraries, additional atom-level properties relevant to the nitrogen of the amine (i.e., pyramidalization, lone pair energy, and lone pair occupancy) were also collected. Bond-level Sterimol values were calculated for both the acid and the primary amine moieties to give insight into the steric environment of their substituents. Additionally, for the acid library, the IR harmonic stretching frequency of the carbonyl was compiled. |
65d79de59138d23161bec6e6 | 3 | For a given conformational ensemble, the minimum property value, the maximum property value, the property value from the lowest energy conformer, and Boltzmann-weighted average were calculated. These condensed descriptors encompass both the extreme conformers a molecule can adopt (within an allowable energetic window of 5 kcal/mol) as well as accessible, aggregate conformations. It can be important to represent conformational flexibility, as the active conformer in a given transformation cannot be determined a priori; thus, it is difficult to hypothesize which condensed descriptor will be deemed important/insightful. Descriptors of this type have been used to classify ligation states and have since gained traction in uncovering reactivity trends. Of note, the Get Properties notebook, available on GitHub (), is automated and adaptable to facilitate descriptor collection for any conserved moiety with a SMARTS string input. 50 Similar automated workflows (utilizing various software packages) from the Doyle and the Paton 17 groups have also been developed to generate conformers and collect DFT-derived descriptors, often extracting all possible descriptors rather than focusing on a single moiety. |
65d79de59138d23161bec6e6 | 4 | These efforts resulted in three libraries: 1) 8528 carboxylic acids from 71,324 unique conformers condensed into 275 molecular descriptors, 2) 4272 primary alkyl amines from 41,452 conformers described by 170 molecular descriptors, and 3) 3849 secondary alkyl amines encompassing 39,207 unique conformers to provide 145 molecular descriptors. All conformer properties and ensemble descriptors are provided on Figshare. To evaluate models for these DFT-level descriptors, each library was randomly divided into a training, a validation, and a test set, with the Enamine-and Drug Repurposing Hub-derived 36, 37 external validation set held back for final model evaluation (acids: 7301/480/476/149, 51 primary amines: 3209/500/500/63, secondary amines 2798/500/500/51, combined amines 6007/1000/1000/114). The dimensionality reduction technique uniform manifold approximation and projection (UMAP) was used to provide a 2D chemical space representation of each of these libraries (Figure ). The external validation sets of medicinally relevant acids and amines were mapped onto their respective chemical spaces, showing that such molecules are similar to those in our libraries. |
65d79de59138d23161bec6e6 | 5 | These libraries would be poised for application in numerous unique reaction development campaigns, including training set design, as well as statistical modeling and subsequent virtual screening with mechanistically interpretable descriptors. However, given the expansive nature of substrate variations, it is probable that a user will be interested in a compound not included in the library. While DFT calculations of additional acids and amines could be performed, this would not be feasible to do on-the-fly for large virtual screening campaigns, thus motivating our interest in predicting DFTlevel descriptors. |
65d79de59138d23161bec6e6 | 6 | GNNs are well-suited to supervised learning problems involving graph-structured data and align well with the task at hand of predicting features from a molecular structure. Previous studies on molecular descriptor prediction have found success employing 2D/3D graph inputs (i.e., without conformational ensemble information embedded) for properties such as chemical shift and bond dissociation energy. As such, we first aimed to evaluate a message-passing GNN employing 2D-input representations for our application to predict condensed descriptors encompassing the dynamic range of accessible conformers and their electronic, steric, and stereoelectronic properties. |
65d79de59138d23161bec6e6 | 7 | The Boltzmann-weighted average (Boltz), minimum (min), maximum (max), and lowest energy conformer (low E) descriptors are normally distributed for most properties (SI section 2.2) and consistent with atom types of C, O, H, N, F, S, Cl, Br, I, P, B, and Si in the acid dataset and C, O, H, N, F, S, Cl, Br, I, P, B, Si, Sn, and Se for the amine dataset (SI section 2.3). The atoms of interest correspond to the conserved atoms in the (R)3C 4 -C 1 O 2 O 3 H 5 acid functional group, (R)C 2 -N 1 H 3 H 4 in the primary amines, and (R)2N 1 H 4 in the secondary amines (Figure ). |
65d79de59138d23161bec6e6 | 8 | Each molecule was encoded as a 2D molecular graph where the nodes/edges correspond to atoms/bonds, respectively. Using the open-source cheminformatics package RDKit, 54 information on the type of atom, valence electrons, chirality, formal charge, aromaticity, ring information, degree, and total number of hydrogens bonded to each atom was one-hot encoded into each node of the graph. Similar information for the bond including bond-type, conjugation, ring information, and stereochemistry was one-hot encoded to the edges of the molecular graph (all features are listed in the SI section 4.2). These molecular graph inputs were used for training a neural network where the node and edge representations were updated at each layer based on neighboring nodes and edges, allowing for information flow within the molecular graph. This information flow (i.e., message-passing) was performed using a graph isomorphism network with edge features (GINE) convolutions, and the final representations were utilized to make predictions of atom-, bond-, and molecule-level descriptors. (more information on the architecture can be found in SI section 4.1). |
65d79de59138d23161bec6e6 | 9 | We trained one GNN for each molecule-, atom-, and bondlevel descriptor individually, and evaluated model accuracy using the withheld test sets for both the acids and amines. For the primary and secondary amines, models for the conserved descriptors for both functional groups (e.g., HOMO, N 1 NMR, N 1 NBO, etc.) were trained using the combined dataset, while models for descriptors that were only collected for primary amines (i.e., Sterimol values, C 4 NMR, C 4 NBO) or secondary amines (i.e., H NMR and H 4 NBO) were trained solely on their respective libraries. For each molecule-level descriptor, the models achieved high accuracy (R 2 > 0.95) across the condensed descriptor set for both acids and amines, with the exception of the dipole moment. For the atom-level descriptors of acids, the models obtained higher accuracy (R 2 > 0.94) for NBO partial charges on C 1 and C 4 compared to those on O 2 , O , and H 5 (0.61 < R 2 < 0.91). Upon analyzing the outliers for NBO partial charges, we noted that hydrogen-bonding had a significant impact on the charges of O 2 , O , and H 5 . To investigate prediction failures, the lowest energy conformers were considered, as they have the greatest influence on the Boltzmann-averaged descriptor. For example, the acid molecule with the maximum deviation showed that our model underpredicts the charge on H and may not account for the increase in positive charge on the H 5 atom attributed to H-bonding (1, Figure ). Similar trends were observed for NMR chemical shifts, where we noted enhanced performance for C 1 and C 4 compared to H 5 (R 2 > 0.96 vs. R 2 < 0.73), which can again be ascribed to the presence of an intramolecular H-bond (2). Models for amine atom-level descriptors such as NBO partial charges on N 1 and C 2 achieved high accuracy (R 2 > 0.94) but exhibited poorer performance for H 4 (R 2 < 0.74). Similar to the carboxylic acids, H-bonding impacts the charge on the H 4 atom of amine 3. Additionally, model performance was compromised for the lone pair energy of the N 1 atom. Upon analyzing the most extreme outlier (4), destabilizing interactions due to eclipsing lone pair and methyl substituents increase the lone pair energy. With respect to NMR chemical shifts, while adequate performance is obtained for N 1 and C 2 (R 2 > 0.85), H 4 shifts had significantly lower R 2 values (< 0.69). The most extreme outlier was due to an anomeric effect caused by the back donation of LPN1 to s * (C-S) (interaction energy of 18.88 kcal.mol -1 obtained from second-order perturbation analysis of the Fock matrix in the NBO basis), which deshields the proton (H 4 ) (5). The same compound was also an outlier in the prediction of N 1 lone pair occupancy, wherein the reduction in occupancy is found due to back-donation. These examples highlight the limitations of using simple 2D representations that may fail to capture critical stereoelectronic effects. |
65d79de59138d23161bec6e6 | 10 | However, for the acid and amine bond-level descriptors Sterimol L, B1, and B5 values, the models obtain varied accuracies. This can be partially explained by the pronounced directional and conformational dependence of these descriptors. Because the GNNs employ 2D molecular representations, they may be less adept at capturing conformational-and directionality-based information to which Sterimol descriptors are acutely sensitive. Hence, significant differences in Sterimol L, B1, and B5 values were observed, even within Boltzmannaveraged, minimum, maximum, and lowest energy conformer properties for a single descriptor. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.