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65d39af766c13817290035c1 | 12 | The dynamic nature of the communication between Chemspyd and the instrument is emphasized in a third experiment, in which we perform a two-step amide coupling with continuous reaction monitoring. Here, a Python script dynamically orchestrates the execution of the individual reaction steps, the timed preparation and derivatization of aliquots, and their injection to our HPLC system. At the same time, the script interacts with the HPLC instrument to ensure synchronization of both instrument operations. The kinetic traces of both reagents, the proposed intermediate, and the reaction product are shown in Fig. , and are in good agreement with the traces obtained by Liu et al. in their dedicated reaction monitoring platform. |
65d39af766c13817290035c1 | 13 | To further facilitate the adoption of Chemspyd and its rapid implementation into new laboratory routines, we provide a natural language interface for generating Chemspyd code. Such interfaces have recently proven to be powerful enabling technologies for automated or self-driving laboratories. Similar to our recent work, we provide a web interface that uses a large language model to convert the natural language inputs into structured Chemspyd output. In our implementation, all Chemspyd functions, along with their natural language documentation and all parameters, are organized in an associative array. Incoming natural language instructions are segmented into structured commands, which are then matched to the classes and functions in the associative array based on cosine distance. Subsequently, OpenAI's GPT-4 is employed to translate the instructions into the corresponding code. Command-by-command, each section of the generated Chemspyd code is sent back to the user for feedback and validation. This match-translate cycle is repeated iteratively until satisfactory Chemspyd code is reached (Figure ). Eventually, the outcome is a responsive interface that effectively bridges the gap between user intent and the correct Chemspyd code, showcasing the power of NLP in user-system interactions, and providing a useful tool for nonexpert programmers to generate experiments with Chemspyd. |
65d39af766c13817290035c1 | 14 | We have introduced Chemspyd as a simple, lightweight and easy-to-use Python API for Chemspeed platforms. In contrast to existing software interfaces, Chemspyd allows for fine-grained, dynamic instrument control, thereby facilitating the usage of Chemspeed instruments in custom workflows and SDLs. With the rapid spread of Chemspeed platforms across academic and industrial laboratories across the world, we envision widespread adoption of this package, particularly in those scenarios where dynamic control and flexible integration with third-party software or hardware is required. Importantly, Chemspyd is an open-source project. Therefore, we encourage feedback and contributions from the community, and hope to inspire development of further functionality based on the needs of users outside our laboratory. |
65d39af766c13817290035c1 | 15 | Beyond extending the package's functionality, the next critical steps will be to integrate Chemspyd with open-source standards for laboratory instrumentation, such as the XDL standard for encoding synthesis procedures, the SiLA2 standard for inter-device communication, and operating frameworks for orchestrating self-driving laboratories. We are convinced that such open, community-driven standards will be key for reusable, open-source software development. Eventually, we believe that Chemspyd can serve as an inspiration and blueprint for instrument manufacturers to provide the open APIs necessary for operating experimental modules in self-driving labs. |
661cd447418a5379b0df725d | 0 | Institut für Energie und Klimaforschung (IEK-9), Forschungszentrum Jülich GmbH, Jülich, We present for the first time a multiscale machine learning approach to jointly simulate atomic structure and dynamics with the corresponding solid state Nuclear Magnetic Resonance (ssNMR) observables. We study the use-case of spin-alignment echo (SAE) NMR for exploring Li-ion diffusion within the solid state electrolyte material Li3PS4 (LPS) by calculating quadrupolar frequencies of 7 Li. SAE NMR probes long-range dynamics down to microsecond-timescale hopping processes. Therefore only a few machine learning force field schemes are able to capture the time-and length scales required for accurate comparison with experimental results. By using a new class of machine learning interatomic potentials, known as ultra-fast potentials (UFPs), we are able to efficiently access timescales beyond the microsecond regime. In tandem, we have developed a machine learning model for predicting the full 7 Li electric field gradient (EFG) tensors in LPS. By combining the long timescale trajectories from the UFP with our model for 7 Li EFG tensors, we are able to extract the autocorrelation function (ACF) for 7 Li quadrupolar frequencies during Li diffusion. We extract the decay constants from the ACF for both crystalline -LPS and amorphous LPS, and find that the predicted Li hopping rates are on the same order of magnitude as those predicted from the Li dynamics. This demonstrates the potential for machine learning to finally make predictions on experimentally relevant timescales and temperatures, and opens a new avenue of NMR crystallography: using machine learning dynamical NMR simulations for accessing polycrystalline and glass ceramic materials. |
661cd447418a5379b0df725d | 1 | Probing dynamical effects is particularly important for energy materials, in which mobile ions drive the device functionality. The mobility of species and structural features such as disorder and defects are closely interwoven, and often are the critical factors for determining device performance. In order to establish a correlation between structure and dynamics, various experimental ssNMR methods can be employed . One such method is SAE NMR, which is commonly used to study Li dynamics in operando within solid-state Li-ion battery materials . SAE probes the quadrupolar interaction of the EFG tensor at the 7 Li nucleus (spin I = 3/2) with its local surrounding environment in order to observe the motion of Li-ions hopping between various sites in a material. |
661cd447418a5379b0df725d | 2 | Combining static experimental ssNMR spectra with first principles density functional theory (DFT) is already an established method for elucidating structure in crystalline and amorphous battery materials . Yet, up to now, this field has placed a strong focus on calculating chemical shielding (CSA) tensors, and a less prominent focus on calculating EFG tensors, mainly as quadrupolar interactions are only observed for nuclei with I > 1/2. While the calculation of static EFG tensors using DFT is a straightforward approach, a technique such as SAE requires computational methods that are capable of following dynamic processes over both long length and timescales. Studying these dynamics is of course impossible with DFT calculated ssNMR tensors (both CSA and EFG tensors), due to the computational constraints associated with the fact that DFT typically scales as O(N 3 ). Even recent applications of machine learning to NMR have been limited to static use-cases , incapable of capturing dynamical or time-dependent effects. A classical approach using the Sternheimer approximation has proven successful for tracking ion motion in liquid electrolytes, where the fast ion motion reduces the requirements for computing NMR observables to picosecond timescales . However, for slower ion motion (relative to the liquid state), this approach is not feasible, and therefore cannot be applied to study solid-state Li-ion motion, which requires simulations on the order of microseconds. |
661cd447418a5379b0df725d | 3 | Fortunately, the recent introduction of machine learning inter-atomic potentials (MLIPs) has enabled simulations of such long-timescale processes within reasonable computational time and at sufficient fidelity for complex materials . The first generation of MLIPs achieved speedups of three orders of magnitude over DFT, making nanosecond simulations possible in many cases . Even more recently, a set of Ultra-Fast machine learning Potentials (UFPs) was introduced which provides a speedup of nearly five orders of magnitude over DFT, while maintaining the same accuracy as some of the most accurate MLIPs such as the Gaussian Approximation Potential (GAP) . With the UFP, it is now possible to routinely simulate up to the microsecond timescale almost at DFT accuracy . |
661cd447418a5379b0df725d | 4 | By using the UFP combined with a machine learning model for EFG tensors, we can now extend the capabilities of NMR crystallography to make dynamical simulations on microsecond timescales a reality. Using this UFP+ML-EFG model, we will demonstrate how to calculate the relevant ACF of quadrupolar precession frequencies for SAE experiments in the fast ion conductor Li 3 PS 4 (LPS). LPS is the ideal system to study dynamic Li processes as it has both a crystalline ( -LPS) and amorphous (am-LPS) phase which are Li-ion conducting with predicted Li hopping mechanisms in the 10 5 to 10 7 s 1 range . We finally propose to use this method in combination with experimental SAE in order to further study the intermediate glass-ceramic LPS materials, which are known to have large amounts of disorder , as we show that SAE would be highly sensitive to understanding Li-ion motion in these materials on the micro-structural level. |
661cd447418a5379b0df725d | 5 | SAE NMR is a probe of the change in the quadrupolar precession frequency (! Q ) over time for a specific nucleus with a spin I > 1/2, such as 7 Li, which has a nuclear spin of I = 3/2. For the nucleus of a single Li atom, ! Q is extracted from the EFG tensor V, which describes the interaction between the quadrupole of the nucleus and its surrounding electric field. The EFG tensor is the second positional derivative of the electric field V around the nucleus, |
661cd447418a5379b0df725d | 6 | In Equation , C Q is the quadrupolar coupling constant of a single atom of 7 Li, which defines the magnitude of the tensor V, ⌘ is the asymmetry parameter which describes the shape of the tensor V, and ✓ and describe the orientation of the tensor V with respect to an external reference system . Using DFT, it is possible to calculate an individual C Q and ! Q for every single Li atom in the simulation. An SAE NMR experiment measures an ensemble average of the single particle correlation functions for each Li atom within different electronic environments, which have distinct ! Q . |
661cd447418a5379b0df725d | 7 | To generate an echo experimentally, which is proportional to the ! Q (t), a Jeener Broekaert pulse-sequence is used , and the resulting hACF ! Q i, measures the phase of ! Q (t = 0) with ! Q (t = t m ) where t m is the mixing time used in the pulse sequence. In the case of |
661cd447418a5379b0df725d | 8 | (3) The total hACF ! Q i is calculated as an ensemble average over all the Li sites within the sample for a given pulse time t p , decay time t d , and mixing time t m . In the case of a simulated hACF ! Q i, the pulse and decay time follow {t p , t d } ! 0, allowing us to simplify Equation 3 to , |
661cd447418a5379b0df725d | 9 | The hACF ! Q i measures the probability of finding a Liion at time t = t m in a position with an equivalent ! Q as it had at time t = 0. Thus, in materials in which the Li atoms visit sites with different ! Q , the hACF ! Q i in Equation 4 typically behaves as a decaying exponential function and one can extract the decay time ⌧ SAE directly using a stretched exponential form of the Lipari Szabo relation , |
661cd447418a5379b0df725d | 10 | The exponential Lipari Szabo decay assumes normal translational diffusion and a random orientation of the local environment with respect to the magnetic field. This assumption holds for glasses or polymer solutions which have a random distribution of environments either due to the amorphous nature of the material or due to the tumbling motion of the polymer in a liquid . In an ideal liquid with fast diffusion, the stretching factor is 1.0, and the exponential decays to 0. However, in complex solids, some memory of previous sites may be retained during the decay and averaging might not be complete, and therefore the exponential decays to a constant value and < 1 occurs e.g. for cases of subdiffusion as in a diffusion-trap model . From the SAE decay time, ⌧ SAE , the effective Li hopping rate is then given by ⌧ 1 SAE . |
661cd447418a5379b0df725d | 11 | DFT simulations access the limit of {t p , t d } ! 0, as in Equations 4 and 5, and neglect any experimental dead time, hence allowing us to naturally simulate a nonensemble averaged ACF ! Q for site specific trajectories within a molecular dynamics (MD) simulation. We can therefore target processes which are faster than the lower limit of what is possible in experimental SAE, as the experiment is limited by the lower bound on the order of 10 µs, defined by t d and t p as well as the inverse of the quadrupolar interaction . It is therefore possible to extract an atomistic ACF ! Q from an MD simulation as long as one can calculate the EFG tensors for all Li atoms across every snapshot of the simulation. A single snapshot of the MD simulation with ! Q and C Q calculated for each individual atomic site from DFT is the equivalent of the 0 K temperature limit, in which all motion in the system is frozen and all ions remain in their initial site. Under realistic room temperature experimental conditions for SAE, the quadrupolar observables are averaged ( CQ and !Q ), not only over the fast timescale hopping events which are masked in experiment but also over thermal effects and different Li sites. for LPS to the final training of the UFP (B) and ML-EFG model (C). The UFP has an RMSE in the energies of 3.1 meV/atom and forces of 109.9 meV/Å . The ML-EFG model is assessed both by the quality of the relative orientation of the tensors and the MAE in !Q. C shows the combined distribution function (CDF) of the quaternion scalar product between the DFT and ML quaternions, q DFT • q ML . This indicates that the majority of tensors are oriented in the same direction comparing DFT to ML. The ML-EFG model has an error of 7.4 kHz on !Q, where the experimental sensitivity of 7 Li SAE is shown shaded in red, as 10 kHz for !Q. |
661cd447418a5379b0df725d | 12 | Studying timescales relevant for spin alignment measurements necessitates an efficient methodology for the evaluation of energies and forces to drive molecular dynamics over microsecond timescales. Xie et al. have recently introduced a new interatomic potential, matching the accuracy of established MLIPs but boosting the speed by one or two orders of magnitude, such that it is comparable with the computational efficiency of classical force-fields . The architecture uses a local representation of atomic environments as established by fundamental work using SOAP and Behler-Parinello symmetry functions . |
661cd447418a5379b0df725d | 13 | The energy of the system is expanded as a sum of 2-body and 3-body contributions using cubic B-splines, which combine the beneficial properties of smoothness and differentiability with the advantage of a compact support. Hence, the number of basis functions that need to be evaluated in every energy computation step is strongly limited, as a maximum of four functions can be non-zero in every segment. The low number of basis functions directly relates to a high computational efficiency . |
661cd447418a5379b0df725d | 14 | The UFP is trained using the active learning procedure shown in the workflow in Figure . The initial dataset is an existing set of LPS structures which was used to train a GAP for LPS . The UFP is trained and iteratively improved by adding structures of -and am-LPS to the training set. Structures are drawn from UFP-MD simulations, where the UFP used for each iteration is the most recent UFP obtained during the training workflow. This active learning cycle of training, UFP-MD simulation, and model evaluation is repeated iteratively until convergence of the UFP energy and force errors is achieved. Finally, the converged energy and force errors over a withheld test set are displayed in Figure 1 meV/atom and 109.9 meV/Å, respectively). These are comparable with the corresponding errors for the GAP for LPS . In addition to the iterative training procedure used to create a robust dataset, the hyperparameters specific to the UFP model were also optimized. Details are given in the Supporting Information Table . |
661cd447418a5379b0df725d | 15 | The Symmetry Adapted Gaussian Process Regression (SA-GPR) machine learning framework, combines covariant atomic descriptors with symmetry adapted kernels in order to learn tensors of any dimension with Gaussian process regression . We have previously shown that by using tensorial learning via the SA-GPR frame-work, we are able to predict quadrupolar frequencies (! Q ) for the 7 Li nucleus within the experimental sensitivity of SAE NMR . We couple the workflow for tensorial learning to the active learning procedure used for training the UFP, as shown in Figure , in order to train a model for predicting the 7 Li EFG tensors of -and am-LPS. The final set of structures from the active learning procedure for the UFP is used as the training set for validating the ML-EFG model. |
661cd447418a5379b0df725d | 16 | The final set of DFT computed 7 Li EFG tensors over structures of Li 3 PS 4 contains 166 diverse structures from the LPS UFP model, which have a total of 14,448 Li environments. The EFG tensor for each atom is calculated for all the structures using the plane-wave pseudopotential DFT code CASTEP v22 . The hyperparameters for the SA-GPR descriptor are optimized as described in the Supporting Information, using a 5-fold cross validation procedure with a test set, which is withheld from training. The resulting mean absolute error (MAE) for the test set in ! Q is 7.4 kHz, and the correlation plot is shown in Figure . It is important to note that the density of points of ! Q within the red bars is high, and thus this representation highlights the outliers as they are clearer to distinguish from the majority. |
661cd447418a5379b0df725d | 17 | In addition to evaluating the MAE in ! Q , it is also important to validate how well the ML-EFG model predicts the orientation of the 7 Li EFG tensors. Besides magnitude (C Q ) and shape (⌘), the hACF ! Q i is a sensitive measure of the orientation of one tensor at a time t m relative to another at t 0 . We use the unit quaternion q to uniquely define the orientation of each tensor . The unit quaternion is a superior metric for determining orientation over Euler angles, as it is independent of the choice of reference system. Therefore, in Figure , we show the cumulative distribution function (CDF) of the scalar product between the DFT calculated and ML-EFG predicted quaternions, q DFT • q ML . A scalar product of 1 indicates perfect alignment, and from Figure , we see that around 75% of the predicted EFG tensors are wellaligned with their DFT reference (q DFT • q ML 0.9). This is an important factor as it will reduce the noise in the hACF ! Q i, Equation 4. |
661cd447418a5379b0df725d | 18 | We finally test the ML-EFG model for size extensivity, because the system sizes included in the training set are between 200 and 256 atoms per unit cell, due to DFT performance considerations, while our target structures for -LPS and am-LPS are 384 and 576 atoms, respectively. Therefore, we calculated the EFG tensors using DFT for two structures of -and am-LPS each, extracted from the final 1 µs UFP simulations, and predicted the 7 Li EFG tensors for these four structures using the ML-EFG model (see Supplementary Information Figure ). The accuracy of the ! Q parameter for these four larger models is 9.2 kHz, which is below the experimentally known sensitivity of 7 Li SAE experiments, 10 kHz. Thus we can say with confidence that our model will have reasonable accuracy on the larger system sizes used in the final 1 µs UFP simulations. |
661cd447418a5379b0df725d | 19 | In addition to the low energy and force errors of the UFP shown in Figure , it is also important to validate the behavior of the UFP relative to high quality first principles methods. Therefore, we compare the structural models generated using the UFP with literature models generated from ab-initio molecular dynamics (AIMD). The radial distribution function (RDF) for -LPS and am-LPS in a 300 K, 1 µs simulation with the UFP is shown in the Supporting Information, Figure , in comparison with two literature references for the RDF ofand am-LPS from AIMD . The UFP simulated RDFs for both -and am-LPS show excellent agreement with AIMD. We also compare the UFP with the established method of Turbo-GAP for -LPS and am-LPS using the mean square displacement (MSD) at 500 K (see Figure in the Supporting Information). We reach a perfect agreement for the am-LPS and a deviation of a factor of five for the -LPS. The deviation can be explained with a much higher sensitivity of the MSD on the barrier height and density in the crystalline material and could potentially be improved by extending the dataset with additional nudged elastic band calculations over Li hopping events. |
661cd447418a5379b0df725d | 20 | Furthermore, we can extract the average hopping rate of Li-ions by discretizing the MSD of all independent single ion trajectories (details of the discretization procedure are given in the Supporting Information). From the discretized trajectories we calculate Li hopping rates of 2.57 ⇥ 10 5 s 1 for -LPS and 7.0 ⇥ 10 7 s 1 for am-LPS. Our results of significantly faster ion diffusion in am-LPS than in the crystalline -LPS phase are in line with our previous findings and experimental reports . Finally, as a result of using the UFP, we are able to simulate dynamics at 300 K for 1 µs. To the best of our knowledge, simulations of this length have not yet been executed using MLIPs. Typical simulation times with MLIPs are on the order of nanoseconds, reaching 100 ns at most . Additionally, most previous studies use higher temperatures in their MD runs , which induces an extrapolation error in their property prediction at room temperature. With an established methodology like the Turbo-GAP, a 1 µs MD simulation would require on the order of 1 million CPUh. With an acceleration factor of 25 over Turbo-GAP, the UFP-MD for LPS on the other hand was computationally feasible in a couple of weeks (40,000 CPUh on a single compute node). |
661cd447418a5379b0df725d | 21 | Using the UFP+ML-EFG model, we obtain the hACF ! Q i over a 1 µs simulation at 300 K run using the UFP for both -and am-LPS, as shown in Figure . The hACF ! Q i is averaged over all Li atoms in each system, and normalized to [0, 1]. 1. |
661cd447418a5379b0df725d | 22 | Firstly, and perhaps most importantly, we are simulating an infinite, pristine, single crystal, by imposing periodic boundary conditions over the unit cell of -LPS. Because SAE can only distinguish between sites with an inequivalent average local EFG , if Li hopping events only occur between sites with equivalent average EFGs (! Q (t 1 ) = !Q (t 2 )), the hACF ! Q i will not exhibit the characteristic exponential decay. While this would usually be associated with vanishing mobility (which is not the case in -LPS as shown in Figure ), it can also be due to insensitivity of SAE with respect to motion between equivalent !Q . Thus, if there are a few sets of mutually inequivalent sites with similar !Q one would obtain a partially averaged !Q , which is the weighted average between the !Q for each of these sites. A single crystal, therefore, will always be such a case, because all of the sites have the same predominant orientation throughout the simulation. A slow decay, beyond the microsecond timescale, would be dominated in a polycrystalline material by Li motion across grain boundaries of differently oriented crystalline grains. In this case, the ⌧ SAE decay could be modeled as a function of the Li diffusion coefficient and grain size distribution. |
661cd447418a5379b0df725d | 23 | Secondly, in this particular example of -LPS, there are only two crystallographically inequivalent Li sites, a tetrahedral LiS 4 site and an octahedral LiS 6 site, which posses almost identical local EFGs. We can show this by looking at a distribution of the DFT calculated ! Q values of all the crystalline -LPS structures included in the training set for our ML-EFG model, shown in the left panel of Figure . The distributions are fairly narrow and the average !Q for LiS 4 is 10.8 kHz, and for LiS 6 !Q is 13.8 kHz, a difference of less than 4 kHz. A close look at the first 250 ns of the -LPS hACF ! Q i suggests that there is a small initial decay due to the inverse jump rate between LiS 4 and LiS 6 sites, which is undetectable due to both the signal-to-noise ratio of the hACF ! Q i as a result of the overlap in ! Q between the sites, as well as the low number of Li sites (144 total) in the -LPS unit cell. This could likely be resolved in the model with a larger sampling of trajectories, but is not relevant for the observable quantities in the SAE experiment, where one would observe the residual, partially averaged coupling, shown in green. |
661cd447418a5379b0df725d | 24 | To highlight the intricate relationship between tensor shape and orientation in -LPS that leads to the very similar and narrow ! Q distributions displayed in Figure (left) we also compute a theoretical autocorrelation function hACF C Q i of the orientation-independent coupling constant, C Q , experienced by the Li ions during their motion through the crystalline model in the MD simulation. We note that this is not a directly accessible quantity in the SAE experiment . We compute this hACF C Q i in a similar fashion to that for ! Q given in Equation , |
661cd447418a5379b0df725d | 25 | and fit the resulting hACF C Q i over the stretched exponential given by Equation to extract a decay constant ⌧ and Li hopping rate ⌧ 1 . A histogram of all of the individual atomistic C Q values calculated using DFT on the -LPS training set is shown in Figure , right panel. The spread of C Q values for the LiS 6 sites is much wider than that for LiS 4 , and their averages are able to be discriminated (a 30 kHz difference). LiS 6 sites have an average CQ of 124.1 kHz, whereas LiS 4 sites have an CQ of 90.9 kHz . Thus while !Q cannot be used to distinguish these two sites, their CQ values could be a good target to understand the local structure in ideal single crystal -LPS. Using the UFP-MD, we are able to track single-atom trajectories across the simulation, and therefore can calculate a single-atom ACF C Q , for each site in the -LPS crystalline structure. In order to understand how the hACF C Q i behaves, we separate the individual single atom ACF C Q , by the Li sites at time t = 0. In Figure , we plot both the individual ACF C Q and hACF C Q i, where the individual ACF C Q are colored by the site in which the Li atom started at time t = 0. The hACF C Q i average is calculated over the 13 Li ions that experience a hop to a different site (either LiS 4 ! LiS 6 or vice versa) during the 1 µs simulation, to reduce the noise in the hACF C Q i. We show that averaging over only the sites which hop is a reasonable assumption to make by comparing these results to a 1 µs simulation at 350 K, shown in the Supporting Information Figure , in which 102 Li atoms hop during the simulation, and there is better averaging over more sites. |
661cd447418a5379b0df725d | 26 | From the top panel in Figure , we can clearly distinguish the individual ACF C Q for LiS 6 sites (green), LiS 4 sites (blue), and hopping events between the sites, as there is a steep rise (or drop) in the ACF C Q at each hopping event. Taking the average over all 13 Li sites, the hACF C Q i does exhibit an exponential decay. Fitting the hACF C Q i in Figure to Equation , we find a decay time of ⌧ = 1.19 µs, or a Li hopping rate of 8.41⇥10 5 s 1 . This is on the same order of magnitude as the Li hopping rate extracted from the MSD, 2.57⇥10 5 s 1 . Additionally, by removing the orientation dependence, and averaging over only the hopping sites, we achieve better signal to noise ratio, and can more clearly distinguish the small initial decay at (t m < 50 ns). |
661cd447418a5379b0df725d | 27 | In contrast to the -LPS hACF ! Q i, which exhibits no exponential decay, as shown in Figure , the hACF ! Q i for am-LPS shows a clear, fast exponential decay which can be fit to the Lipari-Szabo relation given in Equation 5 ( = 1.0). The decay time extracted from hACF ! Q for am-LPS is ⌧ SAE = 46 ns, which corresponds to a Li hopping rate of ⌧ 1 SAE = 2.17 ⇥ 10 7 s 1 . Comparing this with the hopping rate extracted from the MSD (7.0⇥10 7 s 1 ), we see that both methods predict the same order of magnitude hopping rates for Li at 300 K. The hopping rate extracted from ⌧ 1 SAE is a slight underestimation to the rate extracted from the MSD, however this is consistent with the fact that the hACF ! Q i is not sensitive to all ion hops that occur within the material, only those for which ! tm 6 = ! t0 , as discussed above. |
661cd447418a5379b0df725d | 28 | Previous work on Li hopping in LPS using a 100 ps AIMD simulation of am-LPS with 48 Li atoms at 600 K, predicts Li hopping rates in the range of 10 11 Hz . Their method for determining a Li hopping event involved tracking the escape time for Li atoms to leave a 3 Å radius surrounding the nearest polyanion and fitting this escape mechanism to an exponential decay function. Given the short timescale of the simulation, they were only able to access hopping events with residence times shorter than 100 ps (10 10 Hz). As the shortest ⌧ SAE = 46 ns, for real ion hops in am-LPS, this requires a simulation of at least several nanoseconds at 300 K considering the signal-to-noise ratio in the simulation to accurately estimate the hopping rate. This highlights the importance of simulating both at room temperature and for a sufficiently long simulation time, in order to achieve convergence of the Li dynamics and observe the correct motion of Li atoms within LPS. Similar inaccuracies from simple extrapolation to ambient conditions are expected for any material with broad and complex distributions of migration barriers that become progressively accessible upon temperature increase. |
661cd447418a5379b0df725d | 29 | This study pioneers the application of the latest generation of machine learning techniques to directly predict dynamical ssNMR observables at microsecond timescales from atomistic simulations. It is important to stress that an ssNMR calculation with DFT accuracy on the µs timescale would not be possible without leveraging machine learning to predict the EFG tensors. Calculating EFG tensors for the 576 atom am-LPS unit cell over a 1 µs simulation would cost roughly 22.5 million CPUh, with snapshots taken every 100 ps. The same prediction made using the ML-EFG model uses 500 CPUh. This is a factor of 45,000 speedup over DFT-calculated EFG tensors. Therefore, this is, to the best of our knowledge, the first dynamical ssNMR calculation performed at DFT level accuracy, and on an experimentally relevant timescale. |
661cd447418a5379b0df725d | 30 | By integrating first-principles methodologies, it ensures consistent multi-scaling between NMR calculations derived from DFT and predictions applied to large-scale structures. Unlike AIMD studies on Li-ion conduction and diffusivity, where high temperatures are necessary in order to promote ion motion and gather enough statistics, we are able to simulate LPS at 300 K, which is the relevant temperature for comparison with realistic experimental solid state electrolyte systems. |
661cd447418a5379b0df725d | 31 | By calculating hACF ! Q i in both -and am-LPS, we find that the decay time for Li in am-LPS at 300 K is on the order of 46 ns, while the hACF ! Q i of single-crystalline -LPS exhibits no characteristic exponential decay, and instead oscillates about an average value of hACF ! Q i. By considering the orientations of the EFG tensors during the simulations in both -LPS and am-LPS we can see more clearly the differences in behavior of the EFG tensor in these two materials. Figure shows a 2D histogram of all of the accessed angles during the full 1 µs simulation at 300 K for -and am-LPS. In the -LPS histogram (Figure left), the majority of the angles (✓, ) are clustered around either (⇡/2, 0) for LiS 4 tetrahedra or (⇡/2±⇡/6, ±⇡/4) for LiS 6 . On the other hand, there are no clear preferred values of (✓, ) for am-LPS, indicating that the Li atoms experience a wide array of environments during the 1 µs simulation. The large spread in angular distribution in the am-LPS case is what leads to the characteristic rapid decay shown in Figure , as the Li ions visit sites with all possible orientations during the full simulation, leading to loss of correlation, which is normally characteristic of SAE in glasses or polymers . Once Li atoms are in a single crystalline grain, this orientational memory loss is no longer possible, and we see slow, or non existent decay as in -LPS. |
661cd447418a5379b0df725d | 32 | We assessed the two limits of overall microstructure in the LPS fast ion conductors. The -LPS crystal represents an infinitely large fully uniform single crystal of LPS, as depicted in orange in Figure . As such, all the ! Q values in both LiS 4 and LiS 6 sites have the same predominant value (c.f Figure left), which does not vary throughout the simulation, even during Li hopping events. In addition, the mean !Q for LiS 4 and LiS 6 are only 4 kHz apart, and the spread of the individual atomic ! Q for LiS 6 is entirely contained within the distribution for LiS 4 , as presented in Figure . Therefore, we would expect a vanishingly small decay of hACF ! Q i for single crystal -LPS, in which only those two sites are accessible, and then observe a residual, partially averaged coupling throughout. However in a polycrystalline material, shown in green in Figure , where LiS 4 and LiS 6 sites are oriented along different crystal axes in neighboring grain boundaries, we are no longer limited by the predominant orientation of the ideal single crystal. In this case, we would expect lower ⌧ SAE , and a better sensitivity to inter-grain Li-ion motion for SAE. |
661cd447418a5379b0df725d | 33 | At the other extreme, we consider the bulk am-LPS, represented by the unstructured purple square in Figure , and find that hACF ! Q i decays rapidly over a period of 46 ns. In the homogeneous amorphous regime, we can see that as the amorphous PS 4 backbone changes across the simulation, Li atoms experience continually changing electronic environments, and thus we can think of the Li atoms moving in a "glass-like" ensemble of sites embedded in PS 4 environments. At a 46 ns decay rate, ⌧ SAE is outside of the range detectable by a real SAE experiment which would, at best, yield a small residual coupling b > 0 (see Equation ). In a fast ion conductor, we expect this rapid decay of the hACF ! Q i, however this is the first time we are able to accurately quantify the rate of this decay in an amorphous material, highlighting the importance of this UFP+ML-EFG approach. |
661cd447418a5379b0df725d | 34 | These two regimes (single crystal and fully amorphous), which are straightforward to simulate, are not representative of the realistic microstructure in glassceramic LPS electrolytes . All of the glass ceramic materials that are critical for building the next generation of all solid state batteries such as LISCION, LIPON, LGPS, and LPS lie within this range between fully amorphous to fully crystalline Li-ion conductors with hypothetical ⌧ SAE decay constants schematically depicted in Figure . That is, they are a mixture of glassy regions and crystalline regions (depicted as the Glass Ceramic and Polycrystalline in Figure ), in which the Li-ion conductivity across grain boundaries is often the determining factor for the quality of these super-ionic conductors. In these cases, we propose that SAE will provide a unique grain-boundary sensitive technique for understanding Liion diffusion, as the intra-grain diffusion will be at either the amorphous or crystalline limit, and therefore undetectable with SAE. |
661cd447418a5379b0df725d | 35 | Experimentally, the Grahnwehr group has observed ⌧ SAE ⇡ 30 50 ms in a polycrystalline sample of beta-LPS, which is well above the intra-grain decay rates we have predicted here . This can likely be rationalized by sufficiently fast (⌧ 1 µs) intra-grain diffusion leading to partially averaged coupling tensors, combined with long timescale inter-grain diffusion processes between the polycrystalline grains (⌧ SAE ⇡ ms). However, determining the rates and mechanisms of these processes which combine to give an experimental decay rate in the ms time scale, requires dynamical NMR crystallography and analysis techniques that allow one to unfold the various timescales and effective partially averaged interaction tensors contained in the measured data . From this point onward, we now have the capability to make such an approach, by combining dynamical ssNMR with data analysis and simulations to interpret the unfolded data in terms of atomistic processes. |
661cd447418a5379b0df725d | 36 | Beyond suggesting further work on grain-boundary simulations, we demonstrate the potential to access motion even in single pristine crystalline Li-ions, by deriving hACF C Q i and calculating a corresponding ⌧ , which does exhibit a decay at 300 K for -LPS. Furthermore, we show that the Li hopping rate predicted by ⌧ 1 from hACF C Q i is comparable with that calculated from the -LPS MSD. |
661cd447418a5379b0df725d | 37 | We are just at the beginning of this new era of NMR crystallography in which we are able to accurately model dynamical processes at the same temperatures and timescales as experiment. This workflow combining UFPs and experimental observables is a baseline on which the next generation of machine learning for materials methods can be based. We are now one step closer to bridging the gap between theory and experiment, and can tackle more dynamic in operando calculations, which were previously computationally infeasible. |
661cd447418a5379b0df725d | 38 | [58] H. Jónsson, G. Mills, and K. W. Jacobsen, Nudged elastic band method for finding minimum energy paths of transitions, in Classical and Quantum Dynamics in Condensed Phase Simulations (World Scientific, 1998). Finally, to compare the atom dynamics in the UFP versus another high quality machine learning potential for LPS, we simulated a 1 ns trajectory at 500 K for both -and am-LPS using the UFP and TurboGAP . The resulting MSDs are shown in Figure , and we find that for am-LPS the MSD is comparable between Turbo-GAP and the UFP, and for -LPS we have a five times faster transport in the TurboGAP compared to UFP. This can be explained by a insufficient barrier sampling in the approaches, as the fitting of the interatomic potentials is done using snapshots from MD simulations. Those snapshots are strongly biased towards the minima and a better estimate of the barrier height could be achieved by including nudged elastic band [58] trajectories from DFT into the training sets of both MLIPs. where ✓ is the Heaviside function and a is a threshold of square displacement. We set a to 3 Å and provide a sensitivity analysis for this parameter (Figure ). The FIG. . Mean square displacement of a 1 ns MD run of -LPS and am-LPS at 500 K The MSD for -LPS (left) and am-LPS (right) is compared between 1 ns simulations in TurboGAP and UFP in order to validate the Li diffusion behavior in the UFP model. |
661cd447418a5379b0df725d | 39 | hopping detection method, Equation S1, is run over a single Li trajectory until a hop is detected, and then repeated iteratively, using the detected hopping point as a new starting point. Also an additional filter is used which ensures a residence time of 0.5 ns to exclude jump attempts from the detection. Examples of discretized Li squared displacement trajectories of the -LPS are shown in Figure . We test the sensitivity of the calculated jump frequency from MD simulations on the selected threshold a from Equation S1 and show the result in Figure . We find a plateau between 2.8 and 3.2 Å and thus select a cutoff of 3 Å. |
661cd447418a5379b0df725d | 40 | FIG. . Sensitivity of the computed jump frequency on the selected threshold a of the absolute displacement for am-LPS By varying the threshold distance, a for computing a jump frequency we find a window in which the jump frequency is stable (between 2.8 and 3.2 Å) and use this to select the optimal threshold distance, 3.0 Å. |
6564ff0329a13c4d47215b97 | 0 | search algorithm with a focus on energy optimization. Confort incorporates a distance geometry approach to generate low-energy conformations, while MED-3DMC utilizes a Monte Carlo-based method. Multiconf-DOCK utilizes a systematic search approach for exploring ligand flexibility within the DOCK5 program. It extends multiple anchor segments stepwise and generates conformations by systematically rotating single, nonterminal, acyclic bonds at specified increments, while CONFECT employs an evolutionary algorithm. BRIKARD utilizes a knowledge-based approach, and ForceGen incorporates force field-based methods. TCG utilizes a systematic torsion angle search algorithm and Cxcalc utilizes a fragment fusion method and the Dreiding force field for the calculation and optimization of conformers. These tools aid in the exploration of potential binding modes and interactions. Finally, it's important to note that all of these methods generate conformations in the gas-phase and not solution or in the crystalline phase. |
6564ff0329a13c4d47215b97 | 1 | The primary objective of these conformation generation tools is to identify the global minima or a list of lowenergy conformers from a large ensemble of generated conformations. The accuracy, speed, and computational reliability of these tools are achieved through different algorithmic approaches. However, it is crucial to validate the results obtained from these tools with experimental findings. The validation of ligand conformations often involves comparing the generated conformers with experimentally determined structures, typically obtained from proteinbound ligand conformations extracted from the Protein Data Bank (PDB). A shortcoming of these so-called "bioactive conformers" for the validation of conformation generation software is the limited number and diversity of experimentally determined protein-ligand structures and questions surrounding whether these "bioactive" conformers represent the global minimum or local minimum or high energy structures in the conformational ensemble. Additionally, X-ray structures in the PDB represent static snapshots of molecules in crystalline states, which may not fully capture their dynamic behavior in solution or other environments. The resolution of X-ray structures is used as a quality criterion and low-resolution structures may lack precision and atomic-level details necessary for accurate conformation determination. It is crucial to consider these limitations and explore alternative validation approaches, such as benchmark datasets or comparison with other experimental data. In addition to the Protein Data Bank (PDB), another widely used validation dataset for ligand conformations is the Cambridge Structural Database (CSD). The CSD primarily consists of small organic molecule crystal structures obtained from X-ray crystallography experiments. It offers a large collection of experimentally determined structures, providing valuable insights into the three-dimensional arrangements and intermolecular interactions of small molecules in the solid state. |
6564ff0329a13c4d47215b97 | 2 | Over the past two decades, Ion Mobility-Mass Spectrometry (IM-MS) 132 has greatly advanced as an important method in metabolomics applications for the characterization of small molecules in the gas-phase. The technique of ion mobility spectrometry (IMS) measures an ions drift time through a gas-filled region (N2 or He) under the influence of an electric field, efficiently separating gas-phase molecular ions based on charge, size, and shape. IM-MS integrates diverse technologies like traveling wave (TWIMS) , drift tube (DTIM) , trapped IM (TIMS) , and differential mobility MS (DMS) , in combination with ionization methods such as matrix-assisted laser desorption ionization (MALDI), electrospray ionization (ESI), and atmospheric pressure chemical ionization (APCI). It seamlessly accommodates liquid-phase separations including capillary electrophoresis, gas chromatography, and supercritical fluid chromatography. Unlike traditional techniques like X-ray crystallography and NMR spectroscopy, IM-MS is rapid, bypassing the need for prior purification or crystallization of the target compound. The technique doesn't directly measure molecular surfaces, instead, it derives collision cross-section (CCS) values from mobility data using a mathematical model. These CCS values are key for understanding the conformational features of molecules and enable comparison with experimental values for accurate and consistent results. The term Collision Cross Section was historically associated with the hard sphere collision model. Theoretically, CCS is computed by averaging the cross-sectional area of rotation for a target molecular ion using the Mason-Schamp equation. This process relies on input atomic coordinate files derived from various sources, including X-ray scattering, NMR data, quantum chemical calculations, or molecular dynamics (MD) simulations. Three distinct computational treatments of ion-buffer gas collisions are in general use: projection approximation (PA) , exact hard sphere scattering (EHSS) 141 , and the trajectory method (TM) 141 are all employed in CCS estimation. To achieve accurate CCS predictions, it is essential to calculate all potential collision angles between a buffer gas and the target molecule. The precision of CCS prediction is contingent upon effectively sampling the correct conformational space. Consequently, the initial generation of the conformation ensemble plays a pivotal role in predicting accurate CCS values and, by extension, the correct three-dimensional structure in the gas phase. |
6564ff0329a13c4d47215b97 | 3 | Hence, in this work, we hypothesize that gas-phase IM-MS studies sample the gas-phase conformational ensemble of a molecule providing unique insights into the shape and, hence, the structure of a molecule in the gas- phase. Importantly, we are assuming the drift gas (usually N2 or He) has a minimal perturbation on the gas-phase molecular structure. Based on this hypothesis, we propose a novel approach to evaluate and compare gas-phase conformational search engines based on their ability to characterize the gas-phase conformational ensemble and identify the global minima using a quantum mechanics (QM) based workflow whose outcomes are compared against experimental IM-MS information. 9,10 Specifically, we have developed a QM-based method to calculate Collisional Cross Sections (CCS), which is an accurate indicator of the global minima for molecular structures in the gas-phase . |
6564ff0329a13c4d47215b97 | 4 | For example, we have shown (vide infra) that if you take a higher energy, non-global minimum and compute its CCS value the deviation from the experimental CCS values is increased. Our CCS calculations have been validated against experimental data, demonstrating their reliability in capturing the most stable conformations. To conduct our comparative analysis, we employed four different freely available conformational search engines: Auto3D, CREST, Balloon, and ETKDG (from RDKit). These engines utilize diverse methodologies, including force fieldbased conformation generation (ETKDG, Balloon), semi-empirical methods (CREST), and machine learning potentials (Auto3D). By generating conformations using each engine and comparing them with the ensemble and global minima validated through CCS calculations, we aimed to identify the most effective conformational search engine for accurate global minima prediction. By evaluating and comparing the performance of different engines in the gas phase, our study aims to provide valuable insights into the selection of the optimal conformational search approach for improved molecular structure determination and related applications. Moreover, the resultant data set can be used to validate other gas-phase conformational search engines. |
6564ff0329a13c4d47215b97 | 5 | In this study, we focused on 20 metabolites and employed a DFT based workflow to compute their Collisional Cross Section values. Our workflow has demonstrated good accuracy in CCS prediction, with an error rate of less than 3% compared to experiment (experimental error is ~3%). Our established workflow encompasses the following steps to predict accurate CCS values: First, the conformations of each metabolite were generated using tools contained within RDKit. The conformation of the molecule is initially generated using the ETKDG algorithm, an embedded method within RDKit, employing default settings, followed by structural optimization of the generated conformations using the MMFF94 force field. A maximum number of generated conformers is set to 1000 for the small molecules systems. Each generated conformer was then geometry optimized using the ANI QM-ML model. The optimized structures were subsequently clustered using our in-house automated clustering code AutoGraph, enabling the identification of chemically distinct conformations as centroids of the identified clusters. Geometry optimization and Mulliken atomic charge calculations were performed on representative conformations of each identified cluster using B3LYP/6-31+G(d,p) and B3LYP/6-311++G(d,p) level of theory, respectively employing a GPU enabled, in-house developed QM engine called QUICK. The CCS values were computed using the trajectory method (TM) as implemented in the HPCCS code developed by Zanotto et al. The inclusion of an unsupervised clustering method in our workflow reduces the potential for human bias and error in cluster selection, while the QM-ML model and clustering technique contribute to its computational efficiency. |
6564ff0329a13c4d47215b97 | 6 | To assess the accuracy of conformational search engines in predicting the global minima, we compared the generated conformations from Auto3D, CREST, Balloon, and ETKDG (from RDKit), with the most stable conformation determined by our QM based workflow. Conformations were ranked based on increasing relative energies, computed using the respective potential energy functions employed by each conformation generation tool. |
6564ff0329a13c4d47215b97 | 7 | We performed RMSD calculations between the generated conformations and the QM optimized most stable conformation using the LS-align algorithm, a high-throughput virtual screening atom-level structural alignment method developed by Zhang et al. The conformation with the lowest RMSD and energy values was considered the global minima for that particular molecule using the specific conformation generation engine. If no conformation matched these criteria, it was deemed that the engine failed to find the global minima for that molecule. Furthermore, we calculated the Boltzmann average CCS values using the conformations generated by the conformation search engines and compared them with experimental values. The percentage error in predicting the CCS was reported and an error range within 3% was considered indicative of a good CCS prediction as the experimental uncertainty of CCS values within 3%. System setup. In our previous study, we extensively investigated various ionization models (protonation/deprotonation) and their impact on CCS prediction accuracy for metabolites. The predicted CCS values were compared to experimental results to identify the charge model that exhibited the lowest error percentage. In the current study, focusing on finding global minima based on CCS values, we selected the protonation state that yielded the best predicted CCS values (lowest error percentage) for further analysis. For instance, in the case of the carnosine molecule, five models were considered (model 1, model 2, model 3, model 4, and model 5) with corresponding CCS errors of 9.4%, 9.9%, 8.3%, 0.1%, and 31.0%, respectively. Model 4, exhibiting the lowest error percentage, was chosen as the representative carnosine model for the present investigation. Figure presents an overview of the metabolites included, with their respective ionization sites. The protonation site is distinctly highlighted in red, while the deprotonation site is accentuated in blue. |
6564ff0329a13c4d47215b97 | 8 | In the context of open-source applications, we used the default settings provided by the developers of the methods. In the case of ETKDG (from RDKit), the conformations were generated and then optimized using the MMFF94 force field. The 'rdkit.Chem.AllChem' module was utilized to generate conformations through a Python script. The number of generated conformations was set to 1000 by invoking the 'EmbedMultipleConfs' keyword, with the RMS threshold set to 0.1 kcal mol -1 Å -1 (pruneRmsThresh = 0.1). The 'randomSeed' keyword was employed to acquire a seed for the random number generator. Following this, the generated conformations underwent optimization using the MMFF94 force field, and the resulting optimized coordinates and energy were stored for subsequent analysis. Balloon also uses energy minimization employing the MMFF94 (file name-'MMFF94.mff') force field, which is defined using the '-forcefield' ('-f') setting in Balloon, and the input and output file formats are in SDF. |
6564ff0329a13c4d47215b97 | 9 | Balloon employed a multiobjective genetic algorithm for generating ensembles of molecular conformers. The number of generated conformations was determined by the 'nconfs' switch, which was set to 1000, and the convergence criterion based on the gradient root-mean-square (rms) was set to 0.1 kcal mol -1 Å -1 . Balloon conducts conformation generation, RMSD checks, and eliminates similar conformations as described in the original publication. It is noteworthy that, despite the initial ensemble size being set at 1000 conformations, the ultimate ensemble size varied based on the number of rotatable bonds.. For CREST, conformer generation employs the GFN2-xTB method. CREST utilizes metadynamics 158 for conformation generation and writes input and output files in the xyz file format. |
6564ff0329a13c4d47215b97 | 10 | The 'ewin' keyword sets the default energy window for conformational energies at GFN2-xTB level in CREST, typically at 6 kcal/mol. The 'cluster' keyword is used to cluster the generated conformations, while the 'chrg' keyword designates the molecule's charge. Auto3D initially runs the default RDKit conformer engine ETKDG using SMILES as input for stereoisomer enumeration and 3D construction. The input command 'K=1000' generated 1000 conformations, which were subsequently filtered using a 0. |
6564ff0329a13c4d47215b97 | 11 | Conformation generation and global minima search. In this study, we examined the performance of various conformation generation engines, including Auto3D, CREST, Balloon, and ETKDG (from RDKit), in generating conformations and identifying global minima. Table provides an overview of the number of conformations generated by each engine for the selected metabolites. In the case of QM results, the conformation generation process involved using ETKDG to initially generate conformations, followed by clustering and subsequent QM geometry optimization. |
6564ff0329a13c4d47215b97 | 12 | Among the engines, Auto3D and CREST had the capability to perform clustering as part of their conformation generation process, whereas Balloon and ETKDG did not include this clustering step. Consequently, after generating conformations using Balloon and ETKDG, we applied the Autograph clustering algorithm to cluster the resulting conformational ensemble. This allowed for an analysis of the conformations and their subsequent evaluation in terms of capturing the global minima. The number of conformations generated by Balloon and ETKDG prior to the clustering step can be found in Table -S64 in the SI. The inclusion of a clustering step in Auto3D and CREST eliminated high energy conformations giving a short list of conformations to consider. On the other hand, Balloon and ETKDG produced a significantly higher number of conformations due to the lack of this pruning step. It is worth noting that the number of conformations generated by Balloon was lower than that of ETKDG. |
6564ff0329a13c4d47215b97 | 13 | To determine the global minima for each molecule, we employed a root-mean-square deviation (RMSD) matrix to compare the conformations generated by the conformation search engines with the lowest-energy QM conformation. The RMSD values for all conformations can be found in the SI specifically Table -S102. The conformations were ranked based on both RMSD and energy values, and those achieving the top rank (ranked as 1, lowest RMSD, lowest energy) in both categories were considered global minima and are highlighted in bold in Table . On the other hand, if the lowest-energy conformation did not correspond to the lowest RMSD value, it indicated that the engines failed to identify the global minima, and these instances are not highlighted. For instance, in the case of carnosine, Auto3D successfully identified the global minima with a rank of 1 out of 13 conformations, while ETKDG achieved a rank of 1 out of 9 conformations. However, CREST and Balloon were unable to find the global minima, as their lowest RMSD conformations ranked 7 out of 7 and 6 out of 10 in terms of energy, respectively. The details of the RMSD values, relative energies, and corresponding rank of Carnosine conformations are given in Table . It is important to note that the range of relative energies obtained from the conformation generation engines exhibits significant variation. Our analysis revealed that the relative energies generated by Auto3D span a wide range, while the relative energies produced by CREST are relatively compressed. For the carnosine system, all seven conformations generated by CREST exhibited relative energies within 5 kcal/mol, whereas none of the 13 conformations generated by Auto3D fell within this range. Notably, Conformation 9 (viz. Conf_9) was the second lowest in energy among the Auto3D conformations, but it had a higher energy by 15.9 kcal/mol. The highest relative energies obtained from Balloon and ETKDG were 6.3 kcal/mol and 17.8 kcal/mol, respectively. In comparison, the highest energy conformations generated by Auto3D and CREST were 31.9 kcal/mol and 5.7 kcal/mol, respectively. Detailed energy values for all the molecules can be found in the Supporting Information (Table -S102). Out of the 20 metabolites considered in this study, Auto3D successfully identified the global minima for 8 metabolites, whereas CREST detected them for 4 metabolites. Balloon and ETKDG each demonstrated success for 3 metabolites. The success rate of Auto3D in finding global minima was 40%, while CREST attained 20%. Balloon and ETKDG both achieved a 15% success rate, indicating comparatively lower performance. |
6564ff0329a13c4d47215b97 | 14 | We further evaluated the accuracy of CCS predictions for the generated conformational ensembles using all the engines, as summarized in Table . The calculated CCS values were compared with experimental CCS values, and predictions within 3% of the experimental values were considered accurate and bolded. Conversely, predictions with errors exceeding 3% were considered inaccurate and not highlighted. |
6564ff0329a13c4d47215b97 | 15 | Our results showed that out of the 20 metabolites, the QM method achieved accurate CCS predictions for 13 metabolites, resulting in a success rate of 65%. Among the conformation generation engines, Auto3D demonstrated accurate CCS predictions for 8 molecules, yielding a success rate of 40%. CREST performed well, achieving accurate CCS predictions for 9 metabolites with a success rate of 50%. However, Balloon and ETKDG exhibited lower accuracy, correctly predicting CCS values for only 5 and 6 metabolites, respectively, with success rates of 25% and 30%. The average errors in CCS predictions for the QM, Auto3D, CREST, Balloon, and ETKDG generated conformational ensembles were found to be 2.5%, 4.9%, 3.7%, 5.9%, and 6.0%, respectively. Notably, the QM method achieved the highest accuracy in CCS prediction, highlighting its superiority in capturing the conformational behavior of the metabolites. The semi-empirical-based engine CREST had a success rate of 50% in accurately predicting CCS values. However, the ML-based engine Auto3D exhibited a slightly lower accuracy rate of 40%. The force field-based engines Balloon and ETKDG yielded the lowest accuracy rates of 25% and 30%, respectively. These results underscore the importance of selecting appropriate conformation generation engines for accurate prediction of global minima and CCS values in molecular gas phase conformational ensembles. The QM method, with its ability to capture fine structural details and accurately calculate CCS values, emerges as the most reliable approach. The findings also highlight the promising performance of the semi empirical based engine CREST and the ML based engine Auto3D, while indicating the limitations of FF based tools such as Balloon and ETKDG in accurately representing the conformational space and predicting CCS values. |
6564ff0329a13c4d47215b97 | 16 | The establishment of a Gas Phase Conformational Library (GPCL) is a steps towards developing a data set for the validation of gas-phase conformational search engines. GPCL, currently encompasses the full ensembles of 20 small molecules. This library, constructed through our standard QM workflow to compute CCS values, is a freely available dataset for validating various conformational search engines. Moreover, the data set can be used to refine conformational generation methods, thereby enhancing the reliability of computational predictions. While the GPCL only contains 20 molecules it can be readily expanded using our standard workflow to generate additional members of any molecule of interest, significantly expanding the library's utility. |
6564ff0329a13c4d47215b97 | 17 | In this study, we investigated the performance of different conformation generation engines, namely Auto3D, CREST, Balloon, and ETKDG (from RDKit), in generating molecular gas phase conformational ensembles by their ability to predict experimental gas-phase collisional cross section values for 20 small molecules. We utilized a computational workflow that encompassed conformer generation, clustering, and analysis of global minima and accurate CCS prediction. The conformations were generated using the respective conformational search engines, and we compared them with the global minima obtained through QM computation that were validated against experimental CCS values. We also compared the predicted CCS values of the generated conformations with experimental values to assess their accuracy. Based on this analysis, we observed that the ML based algorithm, Auto3D achieved the highest success rate in identifying global minima, followed by CREST, ETKDG, and Balloon. In terms of CCS prediction accuracy, QM methods yielded the most accurate results, followed by CREST, Auto3D, ETKDG and Balloon. It is noteworthy that while Auto3D demonstrated a higher success rate in global minima identification, CREST exhibited relatively higher accuracy in CCS prediction among the engines considered. |
6564ff0329a13c4d47215b97 | 18 | This study provides insights into the performance of different conformation generation engines and their impact on global minima identification and accurate CCS prediction. Moreover, the findings will contribute to the development of more reliable computational workflows for conformational search and related applications in drug design. Based on our present observations conformational search tools have significant room for improvement for gas-phase ensemble prediction. To help in fostering improvements we created the open-source GPCL database, which currently contains the conformational ensembles of 20 small molecules. |
661d1fce21291e5d1de10f3e | 0 | Abstract: Bicyclic carbocycles containing a high fraction of Csp 3 have become highly attractive synthetic targets because of the multiple applications they have found in medicinal chemistry. The formal cycloaddition of bicyclobutanes (BCB) with two-or three-atom partners has recently been extensively explored for the construction of bicyclohexanes and bicycloheptanes, but applications to the synthesis of medium-sized bridged carbocycles remained more limited. We report herein the formal (4π+2σ) cycloaddition of BCB ketones with silyl dienol ethers. The reaction occurred in the presence of 5 mol% aluminium triflate as a Lewis acid catalyst. Upon acidic hydrolysis of the enol ether intermediates, rigid bicyclo [4.1.1]octanes (BCOs) diketones could be accessed in up to quantitative yields. This procedure tolerated a range of both aromatic and aliphatic substituents on both the BCB substrates and the dienes. The obtained BCO products could be functionalized through reduction and cross-coupling reactions. |
661d1fce21291e5d1de10f3e | 1 | Saturated polycyclic carbocycles have gained growing attention in both medicinal and organic chemistry. Molecules incorporating these motifs exhibit enhanced pharmacokinetic and physiochemical properties compared to more common Csp 2 -rich bioactive synthetic compounds, and have become privileged candidates for drug-discovery. The increased conformational rigidity of these polycyclic frameworks is especially important as it can lead to improved affinity to their biological targets, as demonstrated also in many bioactive natural products. Accordingly, the efficient construction of bicycloalkanes as core elements of more complex systems has become an important goal for synthetic chemists, although it demands addressing the challenges coming from their inherent complexity. In the past few years, the use of carbonyl-substituted bicyclo [1.1.0]butanes (BCBs) in strain-releasing annulations has emerged as a modular approach for the generation of bicyclic carbocycles and their heterocyclic analogs. The synthesis of bicyclo [2.1.1]hexanes (BCHex's) through the formal (2π+2σ) cycloaddition of BCBs has been extensively studied to access new bioisosteres of the benzene ring. Following on the seminal reports by the groups of Glorius and Brown, several methods have appeared that rely on radical pathways, either under light induced energy transfer (Scheme 1.A.1: Glorius, Brown, Bach ) or electron-transfer conditions (Scheme 1.A.2: Li, Procter, Wang ). Lewis acid catalysis has also proven effective to promote annulations following a polar mechanism (Scheme 1.A.3: Leitch, Studer, Glorius, Deng ). |
661d1fce21291e5d1de10f3e | 2 | As a recent expansion, the annulation of BCBs with three-atom partners has been used to obtain bicyclo[3. 1.1]heptanes (BCHeps) using the same three activation modes (Scheme 1.B: Molander, Li, Waser, Deng ). Cycloadditions of BCB affording larger saturated bicycloalkanes have however remained unexplored so far, and only one example exists, in which this kind of transformation is employed to form unsaturated thiabicyclo[5. 1.1]nonanes (Scheme 1.C; Glorius). Medium sized carbocycles and their bridged variants are abundant among both natural and pharmacologically relevant compounds. One example is bicyclo[3. 2.1]octane ([3.2.1]-BCO), which represents a conformationally rigid analog of cycloheptane. This scaffold can be found in thousands of bioactive terpenoid derivatives, and extensive research has focused on its synthesis (Scheme 1D). In comparison, bicyclo [4.1.1]octane (BCO) is rarer in nature, it has been much less studied, and the very few preparative methods that have been established so far are limited in scope and lack convergence. In a recent study, the group of Grygorenko showcased the improved lipophilicity of this unique motif and its potential function as an isosteric replacement for both aromatic and saturated monocyclic carbocycles. Furher investigations on BCO ring systems would be of great benefit in the perspective of their applications in medicinal chemistry. Nonetheless, progressing in this direction is hampered by the lack of efficient synthetic methods granting an expedient access to these scaffolds. The annulation of BCBs with four-carbon partners such as dienes appears as an attractive convergent strategy to access BCOs. However, dienes can also act as twocarbon partners, leading to the competitive formation of BCHexs. This is especially true when a radical-based mechanism in involved. In previous reports, using weakly or non-polarized dienes under photochemical conditions had resulted in the formation of the (2π+2σ) BCHex products. On the other side, the only reported transformation giving access to medium-sized bicyclic scaffolds relied on a photo-induced dearomative expansion of thiophenes. Therefore, we wondered if Lewis acid catalysis might constitute a more viable alternative. Herein, we describe the synthesis of BCO through the formal (4π+2σ) cycloaddition of BCB ketones with dienol silyl ethers under Lewis acid catalysis through the successful implementation of this strategy (Scheme 1.E). To the best of our knowledge, this is the first application of BCBs to synthesize medium-sized bridged all-carbon carbocycles, as well as the first example of a formal Diels-Alder cyclization involving a 2σ dienophile. At the start of our studies, more stable naphthoyl BCB 1a was selected as our model substrate and treated with an excess (2.2 mmol) of tert-butyl diphenylsilyl (TBDPS) dienol ether 2a in DCM and in the presence of TMS-OTf (20 mol%, the catalyst reported by Studer for BCB activation ) at room temperature. A check of the reaction after 16 hours showed the full conversion of 1a and the formation of a less polar compound (later identified as silyl enol ether 3). After methanol was added and the resulting mixture was stirred for 2 hours, we observed that 3 had been completely transformed into BCO ketone product 4aa, which could be isolated in 71% yield. Because the purification of the intermediate silyl enol ether was challenging, we focused directly on optimizing the formation of ketone 4aa. As the complete conversion of 3 to 4aa through the sole addition of MeOH was difficult to achieve, an excess of TMS-OTf was used. A screening of silyl protecting groups on the dienol ether using 20 mol% of TMS-OTf as catalyst showed that, compared to TBDPS (Table , entry 1) the smaller and less stable TBS (entry 2) and TIPS (entry 3) provided 4aa in lower yield. Ga(OTf)3the catalyst of choice in the annulation of BCB ketones with imines published by the group of Leitch led to an increased yield of over 80% (entry 4). Other Lewis acids furnished inferior results (see ESI, for details). Reducing the catalytic loading to 10 mol% did not affect the efficiency of the reaction (entry 5). On the contrary, a smaller amount of the dienol ether (1.2 instead of 2.2 equivalents) afforded a significantly diminished yield (entry 6). Al(OTf)3 was next investigated as a more sustainable alternative to Ga(OTf)3. No diminution of yield occurred when the reaction was performed using 10 mol% Al(OTf)3 (entry 7). Testing other solvents confirmed the superiority of DCM to other chlorinated (entry 8) and non-chlorinated ones (entry 9). In addition, further lowering the catalytic loading of Al(OTf)3 to 5 mol% provided the product in even higher 90% yield (entry 10); this was not the case with Ga(OTf)3 (see ESI). Finally, the influence of the silyl-deprotecting work-up after the formal cycloaddition step was investigated. For ensuring reproducibility, the scale of the process was doubled to 0.30 mmol ketone 1a. Treatment with TBAF upon solvent-switch to THF gave inferior results (entry 11) compared to the protocol involving the addition of TMS-OTf and MeOH (entry 12), which was therefore adopted as our optimal procedure. Changing TMS-OTf to methanolic HCl provided 4aa in a comparable yield (entry 13), and can be thus considered as a more costeffective alternative. |
661d1fce21291e5d1de10f3e | 3 | Reaction conditions: 0.15 mmol BCB ketone 1a (1.0 equiv), 0.33 mmol silyl dienol ether 2a-a'' (2.2 equiv.), Lewis acid (X mol%), in With an optimized protocol in hands, we then assessed the generality of our method (Scheme 3). We started by considering variations of the BCB ketone substrates. Aryl-substituted BCB ketones were initially studied (Scheme 3A). A further five-fold scale-up of the reaction to 1.5 mmol of 2a produced 4aa in 80% yield, demonstrating the excellent reproducibility of the procedure. Phenyl ketone 1b afforded BCO 4ba in 84% yield. An electron-donating methoxy substituent on the aromatic ring was also tolerated in both the para (4ca, 84% yield) and the meta (4da, 73% yield) positions. With an ortho OMe group, BCO 4ea was isolated in 57% yield. Electron-withdrawing substituents were also compatible, albeit longer reaction times were necessary: substrates having a bromine atom, a trifluoromethyl, or a nitrile in the para position of the aryl group gave BCO derivatives 4g-ia in 60-70% yield. Thiophene-containing BCB 1i gave 4ia in 70% yield. Then, BCBs with substituents on the bridgehead of the bicycle were examined (Scheme 3B). A methyl was poorly tolerated as product 4ja was obtained in only 15% yield. BCB 1k, containing a phenyl at the bridgehead carbon, was converted into 4ka in 35% yield. In the presence of more electron-poor 3,4-difluorophenyl and 4-trifluoromethyl phenyl groups, products 4la and 4am were generated in 39% and 58% yields. Finally, alkyl BCB ketones were also good starting materials (Scheme 3C): a primary n butyl, a secondary and cyclic cyclohexyl, and a tertiary t butyl groups on the carbonyl of the substrate were all tolerated, furnishing aliphatic BCO 4na, 4oa and 4pa in 59%, 77% and 57% yields, respectively. X-ray diffraction of 4pa gave a confirmation of the caged bicyclic framework of the synthesized BCO derivatives. We then turned our interest towards varying the TBDPS dienol ether in the reaction with 1a (Scheme 3D). Unsubstituted 2b and 1-methyl substituted 2c both gave corresponding BCO derivative, 4ab and 4ac, in modest yields (27% and 34%). Diene 2dcontaining methyl groups in both C1 and C3also gave a moderated yield butinterestinglyproduct 4ad was formed as a single trans diastereoisomer, as determined by X-Ray diffraction. In the case of a diene bearing a methyl group in C4, the expected BCO 4ae was not formed and only a complex mixture was observed. With one substituent in C3 position, the reaction worked consistently well with different substituents. Alkyl groups were all tolerated: benzyl-containing BCO 4af was synthesized in high 75% yield, whereas 4ag and 4ahwith a n butyl and a cyclohexyl groupswere delivered quantitatively and in 77% yield. With aryl C3-substituted dienes, readjusting the procedure was necessary: a slightly decreasing the amount of the dienol ether to 2.0 equivalents was possible, but a longer reaction time was needed, together with a larger excess of TMS-OTf during the silyl-deprotecting work-up. With diene 2i bearing an electron-rich p-anisyl group in C3, 4ai was obtained in 71% yield. Heterocyclic diene 2j gave benzofuran-substituted BCO 4aj in 61% yield. Slightly lower yields were obtained with dienol silyl ethers bearing less electron-donating aryl substituents: 4ak and 4am were accessed in 55% and 56% yields. [a] Performed on 1.5 mmol scale. [b] The reaction was run overnight. [c] Average yield over two reiterations. |
661d1fce21291e5d1de10f3e | 4 | In order to evaluate the synthetic versatility and utility of the obtained BCO diketones, their modifications were then investigated (Scheme 4). We focused on BCO 4aa, containing a naphthyl group on the carbonyl function. In this case, chemoselective functionalization is facilitated as only the carbonyl group on the bicyclooctane scaffold is enolizable. Accordingly, 4aa was smoothly converted into enol triflate 5 in 72% yield under kinetic-controlled conditions. This compound was the starting material for a series of subsequent transformations. Styrene 6 and alkene 7 were both accessed in good yields through a Suzuki cross coupling reaction and, respectively, a Pd 0 -catalyzed reduction with Bu3SnH. A Stille coupling allowed to synthesize diene 8. Refluxing the latter with DMAD followed by oxidation with DDQ permitted to forge benzene-fused product 9 quantitatively. The completely reduced, saturated skeleton of bicycle [4.1.1]octane could be accessed by catalytic hydrogenation of 10 in the presence on Li2CO3. Unfortunately, a yield higher than 50% could be obtained because of its sensitivity to overreduction. In summary, the first formal (4π+2σ) cycloaddition of BCB ketones with dienol silyl ethers has been disclosed. The reaction occured under mild conditions, using commercially available Al(OTf)3 as a Lewis acid catalyst, and represents a convenient modular method for the synthesis of uncommon biyclo [4.1.1]octane carbocycles. The latter could be generally obtained in good to very good yields, with a wide tolerance of substituents on both the substrate and the diene, including alkyl as well as electron-rich and -poor aryl groups. The obtained products were available for an array of further transformations, giving access to BCO derivatives with different fractions of Csp 3 . As the importance of biyclo [4.1.1]octanes has started emerging in the search for new bridged cycloalkanes with bioisosteric properties, we believe that our protocol for the expedient preparation of these intriguing frameworks will contribute to facilitate and accelerate research on them. |
60c73f85ee301c7b01c78902 | 0 | They also can be used to estimate various experimental observables, including solvation free energies of small molecules , binding free energies of small molecules to proteins and molecular hosts, and the on and off rate constants for noncovalent association events. Molecular simulation technologies rely on potential functions, or force fields, mathematical functions which estimate the energy of the molecular system and the forces on its atoms as a function of the atomic coordinates. The force field used in a simulation is a critical determinant of the accuracy of the results. The centrality of the force field has motivated decades of pioneering and innovative research and development. In spite of these efforts, recent studies indicate that force field issues still significantly limit the accuracy of simulations. The Open Force Field Initiative seeks a systematic approach to the continuing challenge of improving force fields, reducing the human effort required and generating new force fields that make statistically sound use of appropriate reference data. One major goal of our effort is to automate the development of new force fields given a choice of functional form and reference data. Later, we aim also to automate decisions about what functional forms to use and what reference data to fit. These capabilities will dramatically reduce the human time required to create new force fields, while also producing more accurate force fields with clear dependencies on the underlying data. Such capabilities would also support advances in force field science, such as determining what functional form achieves the best accuracy for particular applications at a specified level of computational cost. For example, a force field that explicitly treats electronic polarizability and includes fixed electric multipoles, such as AMOEBA, should be able to reach higher accuracy than a force field with fixed, atom-centered point partial charges. But how much additional accuracy do multipoles and polarizability actually provide? We cannot currently answer these questions because the question of the functional form is conflated with other issues, such as the use of different input data, different atom types, different fitting methods, and differences in the chemical intuition brought to the problem. In contrast, an automated approach would allow systematic evaluation of the benefits of an advanced functional form within a given context. |
60c73f85ee301c7b01c78902 | 1 | Although some force field parameterization tools already exist, the full process of force field development has not been automated. For example, the parameterization software ForceBalance advanced the field by automating the adjustment of force field parameters against experimental and theoretical observables with a gradient-based optimizer. However, the researcher must still address not only how to weight the components of the objective function but also the fundamental question of what atom types to use. |
60c73f85ee301c7b01c78902 | 2 | As we seek to automate parameterization, it is important to take note of where human expertise is typically employed, and one key place is in determining which chemical environments (usually treated as atom types) will be treated separately by a force field. This process of distinguishing between different chemical environments in order to assign force fields parameters we call the chemical perception. Chemical perception has been a key ingredient in building general purpose small molecule force fields. Chemical perception in current force fields largely consists of assigning atom types or fragment (nonbonded, bond, angle, torsion) types, defined using human intuition. Ideally, force field fitting should involve adjusting not only the numerical parameters of a force field, but also the chemical perception. For example, we could start a force field parameterization process with only a single type of carbon-carbon bond, but the automated process might propose adding a second bond type, thus allowing distinct parameters to be assigned to single versus double bonds. If this proposal led to improved accuracy sufficient to justify the increased number of parameters, it would become part of the force field definition. Thus, we need a way to sample not only over the numerical parameters of a force field, but also over its atom or fragment types. However, we are not aware of any existing algorithm or software tools to carry out this type of automated parameter sampling. |
60c73f85ee301c7b01c78902 | 3 | In this paper, we address this fundamental problem with a novel approach to sampling over atom or fragment types typically used in biomolecular force fields, so that these definitions can ultimately be learned automatically without a human expert. In particular, we introduce methods of sampling over hierarchical chemical perception trees. That is, we organize force field atom or fragment types into hierarchical trees, such that child types contain more specific types than parent types. We utilize the SMARTS and SMIRKS substructure definition languages to specify atom types and more general fragment types which may be associated with distinct numerical parameters. Then, we show how a Monte Carlo scheme can be used to sample over chemical perception trees defined using these languages. Both tools for sampling chemical perception trees, SMARTY (atom types) and SMIRKY (fragment types), are freely available to the community on GitHub along with Open Force Field Initiative software (). As a proof of principle for this approach, we compare the chemical complexity of sampled atom and fragment types to those in existing force fields. These algorithms set the stage for future applications in which the scoring function will be based on the agreement of simulations with experimental, quantum, or other reference data. |
60c73f85ee301c7b01c78902 | 4 | We consider two different approaches for assigning force field parameters to a molecule: direct and indirect chemical perception. Indirect chemical perception is exemplified by the traditional approach to parameter assignment (such as the AMBER and CHARMM force field families) in which, once a molecule's atoms have been typed, all other information about chemical environments (including bond orders) is discarded. All force field parameters, including valence terms, are then assigned using only the atom types and the way they are connected. Thus, in indirect chemical perception, atom types encode the information needed to assign all valence and bonded parameters. Alternatively, in direct chemical perception, parameters are assigned based on the full molecular graph-a full valence representation of the molecule including elements, connectivity and bond orders, rather than just atom types and local connectivity. This approach thus involves direct analysis of the full molecular graph, including bond orders, instead of indirect analysis through connected atom types, as in indirect chemical perception. As previously detailed, direct chemical perception allows force fields to be fully specified with far fewer numerical parameters than required with indirect chemical perception. We recently introduced a new force field format, the SMIRKS Native Open Force Field (SMIRNOFF) which uses SMIRKS patterns to allow direct assignment of force field parameters, thereby implementing direct chemical perception. This is a substantial break from indirect chemical perception which uses a graph labeled with atom types to assign parameters. SMIRNOFF instead uses direct chemical perception, using substructure searches via different SMIRKS strings to assign parameters when the target molecular substructures are encountered. Thus, the chemical perception and parameters for each force term are separate from those applied to other force terms. For example, a new set of Lennard-Jones parameters could be introduced without needing to introduce additional valence terms, or vise versa. |
60c73f85ee301c7b01c78902 | 5 | In this paper, we introduce approaches to sample chemical perception trees with both traditional atom types and SMIRNOFF fragment types. Here, we use the term chemical perception tree to describe a hierarchical classification of molecular substructures in order to assign parameters. One of our major interests is to sample over a variety of chemical perception trees to see if we can match the chemical perception used in existing force fields. We further use the term fragment type to refer to the more generalized notion of an "atom type" used by direct chemical perception -a particular substructure that would be assigned a particular parameter. The SMIRNOFF format, then, has four categories of fragment types -bond, angle, torsion, and nonbonded types -corresponding to the valence and nonbonded interaction force field parameters. |
60c73f85ee301c7b01c78902 | 6 | In order to automate sampling of chemical perception trees, a language to express atom or fragment types directly was required. We utilize the SMILES Arbitrary Target Specification (SMARTS) and SMILES Reaction Specification (SMIRKS) languages for this purpose. A SMARTS string is a chemical substructure query, where a substructure is a set of atoms connected by bonds, and both atoms and bonds are typically further characterized with "decorators" (Table ). For example, a bond may be decorated with "@" to indicate that it in a ring, and/or "-" to indicate a single bond, and detailed specifications may be constructed by the use of Boolean operators. Atoms are set apart from bonds with square brackets, for example, "[#6X4]!@[#6r5]" describes a tetrahedral carbon atom ("[#6X4]") connected by a non-ring bond ("!@") to another carbon atom which is in a five-membered ring ("[#6r5]"). SMIRKS strings provide a language similar to SMARTS but which also includes atom indexing. SMIRKS were created to allow description of reactions, but here we use only the atom indexing feature. For our purposes, we take advantage of the indexing in SMIRKS to track relevant atoms involved in fragment types such as bond, angle, or torsion types. For example, the SMARTS above could become a SMIRKS string with the addition of ":" to identify the atom indices ("[#6X4:1]!@[#6r5:2]"). Following the SMIRNOFF notation, a bond parameter involves two indexed atoms, an angle parameter three, and so on. A selection of decorators that can be used for atoms (top section) and bonds (middle section) in SMIRKS or SMARTS strings. Decorators on atoms and bonds can be combined using Boolean operators (bottom section), where the high precedence and is applied before an or operator and the low precedence and is applied after. For a complete list of decorators and documentation for SMARTS and SMIRKS see the Daylight Theory Manual. The atom and fragment type definitions used here are based on the chemical environment of each atom extending up to two bonds away. In both SMARTY and SMIRKY, we only consider the chemical environment around the primary atom and atoms one bond away (alpha) or two bonds away (beta). Moves propose changes at any of these positions. The primary atom is the atom being typed by SMARTS or all of the indexed atoms in a SMIRKS. Atoms beyond this beta position are not currently considered. For example, consider a SMARTS describing the hydroxyl oxygen in an alcohol (Figure ). Here, the oxygen is the atom to be typed (yellow), the hydrogen and carbon bonded to the oxygen are the alpha atoms (blue), and the carbon two bonds away is a beta atom (pink), as are the ring oxygen and the hydrogen atom bonded to the alpha carbon (not included in the SMARTS pattern). Including just atoms up to two bonds away leads to a wide variety of possible SMARTS or SMIRKS patterns. The number of possible SMARTS patterns that can be generated using environments including atoms only out to the beta position is on the scale of 10 16 , estimated using the number of possible atoms in one pattern and the number of SMARTS decorators available. Atom types in most present-day force fields usually depend only on atoms out to the beta position, although future force fields might require going further. Therefore, SMARTY and SMIRKY currently do not propose new atom or fragment types that involve atoms past the beta position. The carbon ("[#6]") atom is connected to another carbon ("[#6]", which is considered a beta atom (pink)) via any bond ("∼"). The oxygen has a decorator (light green) ("X2") which means it has two connected atoms. |
60c73f85ee301c7b01c78902 | 7 | Like existing atom typing schemes, both SMARTY and SMIRKY take a hierarchical approach to defining atom and fragment types. That is, the SMARTS and SMIRKS strings specifying types are listed in a specific order, and the last string that matches an atom or fragment is the one assigned ("last one wins"). For example, in Figure , HC ("[#1$(*-#6)]") would match all hydrogens bound to carbons, but then the string H1 ("[#1$(*-[#6]∼[#8])]") overrides HC on the hydrogens with one oxygen in the beta position. In the SMARTS language the "$" is used to specify neighboring atoms, in "[#1$(*-[#6]∼[#8])]" the hydrogen is connected to a carbon bonded to an oxygen. This hierarchy allows a general pattern to catch all hydrogens that are not described by more specific patterns later in the list. We call a complete, hierarchical type specification of this sort a chemical perception tree. The same approach can be used on a hierarchical list of SMIRKS patterns for fragment types. The PATTY algorithm was developed to automatically assign traditional atom types from a hierarchy, where each atom was assigned the last type matched to it. We adapted PATTY for use in SMARTY and SMIRKY. Specifically, the set of SMARTS or SMIRKS is matched to a molecule using OpenEye's OEChem Toolkit ' and then only the last pattern to match a given atom or fragment is stored. |
60c73f85ee301c7b01c78902 | 8 | In the subsections below, we describe methods of varying the SMARTS and SMIRKS strings used to define atom or fragment types, respectively, in order to sample over chemical perception trees. We first provide a general description for our Monte Carlo sampling procedure including how we sample over chemical perception trees with a scoring function based on the agreement of the sampled atom or fragment types with those of an existing force field . Next, we detail two software packages for testing this procedure. The first is SMARTY, which learns chemical perception trees in the setting of traditional indirect chemical perception, such as the atom types found in an AMBER-family force field (Section 2.2). The second is SMIRKY, which learns chemical perception trees using direct chemical perception, such as the fragment types in a SMIRNOFF-format force field. Our description of SMIRKY focuses on those aspects which differ from SMARTY (Section 2.3). Both approaches are diagrammed in Figure . We then describe how we evaluate the ability of these methods to sample chemical perception trees of the chemical complexity found in the reference force fields. This analysis mirrors our ultimate goal of using a scoring function to measure the ability of a chemical perception tree, combined with suitable numerical parameters, to replicate a set of reference experimental and/or quantum chemical data. Finally, we describe the molecule sets used and details of simulations run to test both SMARTY and SMIRKY (Section 2.4). |
60c73f85ee301c7b01c78902 | 9 | We use the Metropolis Monte Carlo (MC) algorithm to sample over chemical perception trees by making changes to a set atom or fragment types. We call this set of atom or fragment types being changed the "working types" and to be more specific we would say "working atom types" or "working fragment types". A single iteration of the algorithm comprises 1. choosing an atom or fragment type at random from the working set 2. proposing a move in which the type is either deleted (if it is not in the base set) or used as the starting point to create a new, more specific type 3. computing the change in a scoring function due to the proposed move 4. using the Metropolis criterion to either accept or reject the proposed move, where the scoring function plays the role of the energy. |
60c73f85ee301c7b01c78902 | 10 | The effective temperature used in the Metropolis accept/reject decision and the desired number of iterations are user-specified inputs. Note that, if the user-defined temperature is zero, SMARTY and SMIRKY act as strictly optimizers, only accepting moves which result in a higher total score, whereas at nonzero temperatures, it is possible for a move with a decreased score to be accepted. |
60c73f85ee301c7b01c78902 | 11 | For this proof of principle study, we developed a scoring function that quantifies the agreement of a chemical perception tree proposed in the course of MC sampling with the chemical perception assignments associated with an existing, operational force field. This scoring function compares how the working types categorize atom and fragments, with reference types from the existing force field. Our basic problem here is to determine which of our working types best corresponds to which reference type when applied to the same set of molecules. Here, in explaining the scoring function, we focus on atom types, but the same approach is also used for other fragment types arising from direct chemical perception, as considered at the end of this subsection. |
60c73f85ee301c7b01c78902 | 12 | We use a bipartite graph with a maximum weight matching to score the working types (Figure ). A bipartite graph is a graph with vertices divided into two disjoint sets, X and Y, where each edge only connects a vertex in X with a vertex in Y; that is, there are no X-X or Y-Y edges. Here, set X comprises the working atom types and set Y comprises the reference atom types. To compose a graph for scoring, we In SMARTY (on the left), there are input files (such as base types, initial atom types, and decorators), molecules (input via a molecule set file), and reference data consisting of typed molecules (parm99/parm@Frosst atom typing was used in this work). SMIRKY has similar inputs, shown in the purple area on the right, and additionally allows the user to set the decorator odds and its reference data is fragment types (here, from smirnoff99Frosst). The algorithms are represented in the green area and are available on GitHub (). Both tools begin by reading and processing the input files (top part of the green area). SMARTY (on the left) then conducts a series of moves (coral area) consisting of choosing one working atom type per iteration (icon with connected atoms), and deleting or modifying (pencil icon) this atom type, making choices made with equal probabilities (Section 2.2). SMIRKY (on the right) is similar, but samples over working fragment types (such as nonbonded types, bonds, angles, and proper and improper torsions; in the figure these are represented by two different icons with connected atoms) and uses weighted probabilities on their choices (Section 2.3). The acceptance criteria (diamond icon) for both tools are the same, using Equation 3 (Section 2.1.1). Both tools run a user-specified number of iterations and iterate over the steps in the coral area (repeat icon), then write out a final results file after all iterations are completed. (c) For each atom, the weight is incremented by one on the edge connecting that atom's working and reference atom types. In this figure, we illustrate the case for potential graph matches to hydrogen working atom type ("#1") using the AlkEthOH molecule set (Section 2.4). However, in practice this process is applied to all working atom types simultaneously. (d) Each node is then restricted to have only a single edge, such that the total weight is maximized. |
60c73f85ee301c7b01c78902 | 13 | first process a set of molecules (Section 2.4), assigning every atom a working atom type and reference atom type. The set of working atom types in the molecules become vertices in set X and the set of reference atom types in the molecules become vertices in set Y (Figure (a)). The graph is initialized by construction of an edge of zero weight between each node in X and each node in Y (Figure (b)). Then, for each atom in each molecule, we identify its working and reference atom types and increment the weight of the edge joining the corresponding set X and set Y vertices by one (Figure (c)). We then determine the set of X-Y edges that maximizes the number of atoms assigned the same working types that are also assigned the same types in the reference set. This corresponds to a maximal weight graph-matching problem. A matching set in a graph is a subset of edges that are non-adjacent; i.e., no two edges share a common vertex. Thus, determining the matching set ensures we never have the same working atom type connected by edges to two or more different reference types, and vice versa. For example, in Figure (c), we would select only one of the edges for the "#1" node. A maximal weight graph matching is one in which the sum of the weights of the retained edges is maximized. Thus, in Figure (c), we select only the edge of highest weight, here 224. More generally, a maximal weight graph match would include all possible working and reference types, such as the result for the three working types in Figure . |
60c73f85ee301c7b01c78902 | 14 | where , is the weight of the edge associated with reference atom type and , is the number of atoms in the molecule set with reference atom type . Thus, = 1 provides an assessment for how accurately the working atom type captures the chemistry of a specific reference atom type. The total score across types then is |
60c73f85ee301c7b01c78902 | 15 | The SMARTY algorithm defines its chemical perception tree using an ordered list of SMARTS strings, as described above, and manipulates these strings in to order vary and optimize this chemical perception tree using a selected scoring function. In this work, we use the graph-based scoring function defined in Section 2.1.1 to measure similarity to the atom types in a target force field. Ultimately, our initiative we will use a scoring function that reflects the ability of a force field using the working chemical perception tree to replicate experimental data. In this subsection, we describe the algorithm, including user specified inputs and move sets in SMARTS space. |
60c73f85ee301c7b01c78902 | 16 | The present SMARTY implementation takes five input files. The first is a file containing a set of SMARTS strings defining "base atom types" or base types, which will not be changed. These are typically the most generic type definitions. The second is a file containing "initial atom types," which form a superset of the base types. |
60c73f85ee301c7b01c78902 | 17 | Typically, the initial types include not only generic base types, but also some more specific types, with the generic types listed before the specific types to define a hierarchical chemical perception tree. Initial types provide an initial configuration for the simulation in the search space of types. The third is a file listing the SMARTS atom decorators which will be used during sampling (see examples in Table ). These three files are provided in a format where the first entry in each line is a complete SMARTS string or SMARTS decorator, and the second item is an informal name for the string or decorator. For example, "[#7] nitrogen" could be an entry in the initial type file, and "X4 connectivity-4" could be an entry in the decorator file. The other two input files relate to our specific test in this study, where we seek to determine how well sampled chemical perception trees can capture the typing of an existing force field (Section 2.1.1). Thus, our fourth input file provides the set of molecules to be typed in the process of evaluating a chemical perception tree, and the fifth contains the same molecules labeled with the atom types associated with the target force field. |
60c73f85ee301c7b01c78902 | 18 | After processing the user provided input, there is a preparation step before sampling can begin. The first step is to assign the base and initial atom types to the molecules via SMARTS chemical matching to substructures and to remove those base and initial types that match no atoms, in order to simplify the sampling problem. The remaining initial atom types become the working set of atom types. After the completion of this preparation phase, our atom type sampling works via the MC algorithm detailed above (Section 2.1). We next detail the specific move set used in SMARTY. |
60c73f85ee301c7b01c78902 | 19 | As illustrated in Figure , an MC move proposal either removes a non-base atom type from the working set of atom types or creates a more specific child type from an existing atom type, A. For creation of a new child, A', if the definition of A comprises only the primary atom, a decorator may be added to it; or an alpha substituent may be added. When a new substituent is added, the type of bond connecting it, single, double, triple, or aromatic, is also chosen. If A already has an alpha substituent, then A' may be created by adding a decorator to A; by adding a second alpha substituent; or by adding a beta substituent to any non-hydrogen alpha substituent. Finally, if A already has an alpha and a beta substituent, then a new decorator may be added to A, or a new alpha or beta substituent may be added. It is possible that in the future, move types might be added to allow the addition of decorations to alpha and beta substituents, but those moves are not included in our current SMARTY tests. |
60c73f85ee301c7b01c78902 | 20 | 1. All atoms in the molecule set must be assigned an atom type from the proposed list. 2. A new child, A', must match at least one atom in the molecule set. 3. A new child A' must not be a duplicate of any other atom type. 4. The parent atom type A of a new child must still match at least one atom in the molecule set, unless it is a base type. |
60c73f85ee301c7b01c78902 | 21 | Note that criterion 2 eliminates any atom type specifications that violate valence restrictions, such as a carbon with more than four bonds. All of these criteria are applied when the molecules are typed with the full chemical perception tree, so criteria 2 and 4 will only hold if types A and A' are both assigned to at least one atom. If these criteria are met, the proposed atom type set is valid and can be scored (Section 2.1.1). |
60c73f85ee301c7b01c78902 | 22 | The SMARTY implementation also offers the option of allowing proposed moves only for atom types involving a single element. For example, one might allow deletion and child creation for only carbon atom types. This elemental SMARTY sampler, SMARTY , avoids the combinatorial complexity that results when changes are allowed for all elements and thus can speed convergence to the global optimum. |
60c73f85ee301c7b01c78902 | 23 | We recently argued that direct chemical perception has major advantages over indirect chemical perception and illustrated the application of direct chemical perception via a prototype smirnoff99Frosst force field in the new SMIRNOFF format. The SMARTY algorithm (Section 2.2) is not adequate to sample over direct chemical perception trees, because it samples only over atom types, and not the independent bond, angle, The diamonds represent decisions and the rectangles are processes. We start the SMARTY move proposals with the working atom types and decide randomly with equal probability if we want to remove or add an atom type to the set. If we decide to remove, we randomly choose a working type to be removed and re-score the new set. If we decide to add, we pick a working atom type from the set and check if it has an alpha substituent. If the answer is no, we either add an alpha substituent or a decorator. If the answer is yes, we first check if the working atom type describes a hydrogen, and if yes, we add a beta substituent, if not, we either add an alpha or a beta substituent. The new atom type SMARTS created is added to the end of the list of its corresponding parent. The end result (black circle on the bottom) is a move proposal which is then evaluated via scoring function (Section 2.1.1). and torsion types used in direct chemical perception. Therefore, we have developed a second algorithm, SMIRKY, to sample over chemical perception trees corresponding to these fragment types. SMIRKY uses the same Metropolis MC method to sample over a chemical perception tree, and also uses an analogous scoring function (Section 2.1.1). The differences are the use of more general fragment types instead of atom types, and the resulting differences in the move set. SMIRKY also differs in that it uses of unequal probabilities for move proposals. We made this choice based on the unequal distribution of different SMIRKS decorators in SMIRNOFF fragment types. These unequal probabilities come from two sources -odds specified by user in the input files (Section 2.3.2) and odds specified in the SMIRKY move set (Section 2.3.3). Unlike SMARTY's elemental approach, we do not currently have a mechanism for reducing the combinatorial problem associated with sampling SMIRKS patterns by limiting the considered chemical space. We now present a new tool developed specifically to manipulate SMIRKS strings and then detail the SMIRKY input files and move set. |
60c73f85ee301c7b01c78902 | 24 | We created the ChemicalEnvironment Python object which divides a SMIRKS string into atoms connected by bonds, and stores the decorators associated with each (Figure ). This object also uses the atom indexing in the SMIRKS string to allow extraction of any indexed atom, any atom alpha or beta to an indexed atom, or any associated bond. The user can then easily modify the ChemicalEnvironment by adding neighboring atoms, removing neighboring atoms, or changing the list of decorators for a given atom or bond. Each ChemicalEnvironment is loaded and output as a SMIRKS string, so this object integrates with any other tool that can generate and interpret SMIRKS. |
60c73f85ee301c7b01c78902 | 25 | The ChemicalEnvironment object categorizes decorators on atoms and bonds based on the type of Boolean operator used to combine them; that is, the decorators are separated into OR and AND types. For example, consider "[#6X3H2,#7X2H1;A+0:1]-[#1:2]" in Figure , which is a SMIRKS pattern for a bond type, and hence has two indexed atoms. For atoms, OR types are composed of a base atom type (typically an atomic number) and a list of decorators to be combined via a logical OR (","). In this example, atom 1 has two OR types ("#6X3H2" and "#7X2H1") which are divided into OR bases ("#6" and "#7") and their corresponding decorators. For atoms, AND types are decorators that will be combined via a logical AND (";"). Our example atom 1 has two AND decorators ("A" and "+0") which apply to both the carbon and nitrogen OR types. Bonds connecting atoms can also have OR and AND decorators. When no Boolean operator is used then the decorator is considered an OR type, so the bond in the present example, "-", would be considered an OR. |
60c73f85ee301c7b01c78902 | 26 | The present SMIRKY implementation takes ten input files which allow users more customized control of probabilities while sampling. Three of these files are similar to SMARTY inputs: a file with initial fragment types (that is SMIRKS strings) defining a hierarchical chemical perception tree; a file containing molecules to be typed in the course of scoring the direct chemical perception tree; and a SMIRNOFF file which provides the reference fragment types for use in scoring. As in SMARTY, any of the initial fragment types that do not match any fragments are removed, creating a working set of fragment types for the MC algorithm. The next five files provide the atom, bond, and decorator types: OR atom types; OR and AND decorators for atoms; OR bond types; and AND decorators for bonds (Section 2.3.1). Each decorator file includes a column for the odds of proposing a given decorator in the course of the MC sampling. The final category of files allows the user to specify the odds of picking a certain atom or bond in a fragment that will be changed during the move. There are two files in this category -one for atoms and one for bonds. There are two columns in this format, one specifying if the move is to an indexed, alpha or beta atom or bond using the SMIRKS index number or the key words "alpha" or "beta." Then the second column is used to set the odds. For example, in a torsion, a user might want to make it more likely to make changes to the outside atoms (1 and 4) than to the inside atoms (2 and 3). The SMIRKS pattern (middle) represents a bond parameter "-" (gray) between two labeled atoms -a carbon (light blue) or nitrogen (light blue) atom and a hydrogen atom (light red). In this figure, we show two matches for this SMIRKS pattern on the top structure. The matches are highlighted in light blue (atom 1) and light red (atom 2) circles on the substructure (top). In the ChemicalEnvironment representation, at bottom, atom 1 (light blue rectangle), there are two ORtypes '''#6X3H2" with a carbon atom base "#6" and OR decorators "['X3, 'H2']", corresponding to a connectivity of three and a total hydrogen count of one and "#7X2H1" with nitrogen atom base "#7" and OR decorators "['X2, 'H1']" (light green). The AND decorators for the atom 1 are "['A', '+0']" (light green) corresponding to an aliphatic atom with a zero charge. In SMIRKS strings, the high precedence "and" operator is given by a semi-colon ";", so the bond described by this pattern is one between a carbon atom with connectivity three and hydrogen count two or a nitrogen atom with connectivity two and hydrogen count one that is also aliphatic with zero charge. |
60c73f85ee301c7b01c78902 | 27 | SMIRKY uses the same general move set as SMARTY; that is, a fragment type A is chosen and then either deleted or used as the starting point for a child fragment type A' (Figure ). The input odds files for SMIRKY allow the user to customize sampling for a specific fragment type, but the probabilities determining which type of move, for example adding or removing a non-indexed atom, are set internally. When creating a child fragment type, the first choice made is whether to change an atom or a bond. If an atom is chosen, then decorators on the atom can be added, swapped, or removed; a new connected atom can be added as a neighbor; or if the atom selected is not an indexed atom it can be removed (indexed atoms must be retained in order for the fragment to be fully defined). An atom can be removed from a fragment definition only if it is connected to just one other atom; the associated bond is removed at the same time. If a bond is chosen instead of an atom, either type of decorator can be added, swapped, or removed. As with SMARTY, we only consider substructures that extend to the beta position of any indexed atom. Because there are more SMIRKS decorators available for atoms than bonds, the move set is weighted to choose atom moves more often than bond moves. |
60c73f85ee301c7b01c78902 | 28 | To allow efficient construction of complex SMIRKS patterns that make chemical sense, symmetric moves are also sometimes proposed. In symmetric moves, equivalent modifications are proposed simultaneously to both outer atoms in a bond, angle, or torsion. The probability of making a symmetric move is fixed inside SMIRKY. Specifically, the frequency of symmetric bond, angle, and torsion types in smirnoff99Frosst was used to assign the probability of making symmetric moves for each fragment type by category. |
60c73f85ee301c7b01c78902 | 29 | We sought to determine whether our machinery could discover SMARTS or SMIRKS patterns that replicate the chemical complexity of types in an existing force field, thus providing a proof of principle for automating a step in force field development that has in the past been done only by hand. In order to measure chemical complexity we defined success based on the total and partial scores for the sample types compared to * -The probability of "yes" for this particular decision is 0.2, 0.6, and 0.15 for bond, angle, and torsion types respectively). |
60c73f85ee301c7b01c78902 | 30 | reference types (Section 2.1.1). A total score of 100% corresponds to patterns matching all reference atom or fragment types and would indicate complete success for a set of working atom or fragment types. However, it is not necessary that we exactly reproduce the atom typing or fragment typing of existing force fields to succeed, especially in view of the combinatorial challenge we face; it is sufficient that we sample comparable chemical complexity. Thus, achieving a high total score on average would also be acceptable, especially if we can achieve at the same time a partial score of 100% for most atom or fragment types. That is, for both SMARTY and SMIRKY, we seek to recover SMARTS or SMIRKS which will mirror the previously defined indirect or direct chemical perception from the reference force field, by separating atoms or fragments into similar types. However, the automatically generated trees do not necessarily need to encode the exact same chemical perception trees as those from the reference force field. |
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