id
stringlengths 24
24
| idx
int64 0
402
| paragraph
stringlengths 106
17.2k
|
|---|---|---|
60c743b6469df4007bf43256 | 21 | In this work, an additional 2D scan of the Ο and Ο dihedral angles of serine was found to be necessary for accurate torsional parameters for serine and threonine, which both have a polar oxygen atom at the X Ξ³ position. This followed similar protocols to those previously described, however the sidechain Ο 1 angle now had to be taken into account. Scans were performed at 30 β’ increments of Ο/Ο, for Ο 1 initially set to -60 β’ , 60 β’ and 180 β’ . This gave three 2D energy scans for the main rotamers of serine. The minimum energy structure for each Ο/Ο angle was then used to construct the overall minimum Ο/Ο potential energy surface (Section S3.1). |
60c743b6469df4007bf43256 | 22 | steepest descent algorithm. MM potential energy surfaces were computed by scanning dihedral angles in 15 β’ increments using the BOSS software. The backbone torsional parameters for all dipeptides tested, excluding serine and threonine, were fit to the alanine and glycine scans previously described. The total error for the two scans was given by: |
60c743b6469df4007bf43256 | 23 | Error Total = 0.928 Γ Error Ala + 0.072 Γ Error Gly (6) with the prefactors corresponding to the relative frequency of each amino acid in the human proteome. Preliminary testing (Section S1.1) showed that a weighting function and regularization did not significantly improve the conformations sampled during the dipeptide MD simulations and so were not used (Ξ» = 0, W = 0). |
60c743b6469df4007bf43256 | 24 | The remaining dipeptides, threonine and serine (both of which contain aliphatic hydroxyl groups in their sidechain), were assigned identical backbone parameters that were fit to reproduce the QM scans of serine. For these scans, regularization and weighting were shown to be necessary to produce dipeptide dynamics which were in agreement with experiment. |
60c743b6469df4007bf43256 | 25 | The sidechain scans for all dipeptides followed the same fitting process as the alanine/glycine backbone with no weighting or regularization used. As atom-typing is not used for the non-bonded parameter assignment in the QUBE force field, each set of sidechain torsional parameters is also residue-specific. This differs from the approach used in OPLS-AA/M in which sidechain torsional parameters with the same set of atom types are generally assigned the same parameters. |
60c743b6469df4007bf43256 | 26 | This was restricted to setting a number of torsion parameters to zero (that is, Ξ» = β) and reducing the number of scans used in the fitting process. In particular, the aspartic acid Ο/Ο distribution was improved by setting the Ο 2 torsional parameters to zero. Additionally, using only the QM energy scan with the lowest minimum energy in the fitting process was shown to result in an improvement in the MD simulations of the dipeptides for the Ο 1 torsional parameters of cysteine, methionine, serine and threonine. The need for manual input in the fitting process was also required for developing OPLS-AA/M and is likely due to the restrictive functional form of the torsional potential and the conformational dependence of the energy scans. The full set of manual changes involved is listed, along with the final torsional parameters, in Section S3.3. |
60c743b6469df4007bf43256 | 27 | As the non-bonded parameters used are specific to the system under study, they are not the same for an alanine dipeptide molecule as for the alanine pentapeptide (Ala 5 ). The alanine residue in the dipeptide is blocked by acetyl and N-methyl groups whereas the central three alanine residues in Ala 5 have neighboring alanine residues on both sides. Therefore, varying environments exist for alanine residues in the different molecules. Consequently, the parameters found for the alanine dipeptide were found to be unsuitable for MD simulations of Ala 5 (Table ). However, the use of a harmonic restraint in the fitting process resulted in torsional parameters that were sufficiently accurate for the alanine and glycine peptide simulations. Alanine and glycine backbone torsional parameters were refit to the QM energy scans with Ξ» = 0.50, no weighting was used. The optimal value used for the regularization parameter was found by minimizing the differences between simulated and experimental NMR observables for Ala 5 (Table ). We note that the J coupling error is not too sensitive to the strength of the harmonic restraint. Separate torsional parameters are used for the alanine pentapeptide and glycine tripeptide (Gly 3 ), as residue-specific parameters should result in a more accurate force field. |
60c743b6469df4007bf43256 | 28 | Alanine, glycine, serine, and proline torsional parameters are fit to available QM potential energy surfaces and are therefore residue-specific. Threonine uses torsional parameters fit to the serine torsional scan, and all other amino acid use torsional parameters fit to joint alanine/glycine energy scans. These backbone parameters are combined with the dipeptide sidechain torsional parameters to give the full QUBE protein force field parameter set. Blue is used for non-bonded terms, yellow is used for bonded terms. |
60c743b6469df4007bf43256 | 29 | Figure shows the steps required to set up a QUBE protein force field for a MD simulation. As in Section 2.1, the ONETEP linear-scaling DFT software is used to compute the ground state electron density of the five proteins, and assign the charge and Lennard-Jones parameters from the partitioned atomic electron densities. Consistent with the QUBE small molecule approach, every atom in the protein is assigned bespoke non-bonded parameters derived from the quantum mechanical electron density. To model polarization effects in the condensed phase, the electron density is computed first in vacuum, then using an implicit solvent model with a dielectric constant of 80. The iPol approach used in AMBER ff15ipq is then employed, with all non-bonded parameters set halfway between their vacuum and condensed phase values. The purpose of this approach, as well as overcoming issues associated with closing of the electronic band gap in large system sizes, is to account for electrostatics and induction in the condensed phase in an effective manner using a fixed point charge force field. Typical computational requirements for a QM calculation on a small protein (β 1000 atoms) are approximately 2000 cpuhrs. In order to provide a consistent and computationally efficient approach to assigning the non-bonded parameters, we recommend minimizing the experimental structure using a standard transferable force field in explicit water prior to the DFT calculation. In this study, we used the OPLS-AA/M force field for the initial minimization. Following non-bonded parameter assignment, bond, angle and torsion parameters were assigned as described in Section 2 based on the OPLS-AA/M atom types. For torsion and improper types not re-parameterized in this study, OPLS-AA/M parameters are retained. Table summarizes the number of bespoke non-bonded parameters for each protein studied, along with the bonded parameters that are parametrized using the dipeptide molecules as described above. All parameters, including atom-specific non-bonded parameters, are written to a CHARMM-style parameter file. The psf, pdb and inp files are provided in the Supporting Information. We note that preparation of the parameter files is fully automated, and scripts and step-by-step tutorials are available from group/QUBEMAKER. MD simulations were performed using the NAMD software, using input parameters detailed elsewhere (Section S2.1). Statistics were collected over a period of 200 ns for dipeptides and Ala 5 and Gly 3 , and 0.5 Β΅s for the proteins. All MD simulations were performed in triplicate. |
60c743b6469df4007bf43256 | 30 | The final backbone torsional parameters and associated errors in the recreation of the QM energy scans are given in Section S3.2 of the Supporting Information. For the alanine and glycine scans, the error for the QUBE force field evaluated using eq 5 is 1.25 kcal/mol compared to 0.93 kcal/mol for OPLS-AA/M, which is a reasonable level of agreement. For proline and serine, the errors remain comparable to OPLS-AA/M. |
60c743b6469df4007bf43256 | 31 | For the sidechain torsional parameters (Section S3.3), the mean error in the recreation of the QM potential energy scans for the QUBE force field is 1.29 kcal/mol, compared to 1.12 kcal/mol for OPLS-AA/M. Particularly high errors occur for both the Ο 1 and Ο 2 glutamic acid scans, and the glutamine Ο 2 scan. For glutamic acid, the error is also high for the OPLS-AA/M force field parameters, but the rotamer populations remained close to the experimental data, and this may be due to a problem with the functional form used in classical force fields. The OPLS-AA/M error in the potential energy scan for glutamine is roughly half that of the QUBE force field. However, as we will show, the accuracy of the glutamine dipeptide MD simulations is good, and so no further refinement was made to the sidechain torsional parameters in this work. |
60c743b6469df4007bf43256 | 32 | Although a low error in the reproduction of the QM potential energy surface is clearly the desired result, this does not necessarily correspond to accurate non-bonded force field parameters. The degree to which torsional parameters can improve the fit between MM and QM scans depends not only on the accuracy of the non-bonded, and bond and angle, parameters, but also on the shape of the energy difference between the QM and MM scans. |
60c743b6469df4007bf43256 | 33 | The functional form used in classical MM force fields is very restrictive. However, the energy difference between the QM and MM energy scans must be corrected by the functional form for low errors to be achieved. Therefore, although we use errors in potential energy scans as a guide to performance, they cannot be relied upon as a measure of the accuracy of a force field. Therefore, we now investigate the performance of the QUBE force field in MD simulations. |
60c743b6469df4007bf43256 | 34 | The QUBE force field achieves a root mean square (RMS) error of 0.42 Hz, which can be compared to 0.35 Hz for OPLS-AA/M. 1 Encouragingly, the error in the J couplings simulated using the QUBE force field is much lower than that of OPLS-AA (0.97 Hz) and OPLS-AA/L (0.79 Hz). With the arginine dipeptide excluded from the QUBE data, the error drops further to 0.33 Hz. Residue-specific arginine backbone torsional parameters could be computed, however given that the Ο/Ο distribution of arginine occupies the main conformations expected, this is not investigated in this work. |
60c743b6469df4007bf43256 | 35 | Figure shows the collective Ο/Ο distributions from the dipeptide MD simulations, along with the main expected protein conformational propensities. As discussed in Section S9 of the Supporting Information, it is important to consider the dihedral distributions present as well as the J coupling data. Encouragingly, the Ο/Ο distribution for the dipeptides show that the major conformations present in protein structures are sampled in the QUBE MD simulations. The ΞΆ conformation does have a slightly lower Ο angle than suggested, and there is an additional region with very low occupancy to the right of the Ξ³ conformation. |
60c743b6469df4007bf43256 | 36 | The Ο/Ο distributions for each individual dipeptide are shown in Section S4.2 of the Supporting Information. Generally, similar areas of the Ο/Ο distribution are occupied by all the dipeptides. The serine and threonine dipeptides do not sample identical regions to the other dipeptides, which is not unexpected given that they have a separate set of backbone torsional parameters. There are several dipeptides which show populations of left-handed Ξ±-helical conformation. High left-handed helical populations have previously caused problems for other force fields. However, since the occupancy of PPII and Ξ² regions always remain higher than the the populations of the left-handed Ξ±-helical region, reducing the left-handed helical population was not considered a priority in this work. The right-handed Ξ±-helical populations are small for all the dipeptides. This is in agreement with experimental results. Figure : a) The Ο/Ο distribution extracted from the dipeptide MD simulations, plotted in the form -log(p Ο,Ο ) (where p Ο,Ο is the probability of a region being occupied). The lighter regions correspond to low probability areas including conformations that are not sampled during the simulation. b) The major conformations observed in protein structures. The right-handed Ξ±-helical region is labelled as Ξ΄ and the left-handed Ξ±-helical region as Ξ΄ . |
60c743b6469df4007bf43256 | 37 | As well as the backbone conformations sampled, the sidechain rotamer populations were also analyzed. In Figure , the simulated rotamer populations are compared to experimental data taken from protein coil libraries (the data are given in the SI of Ref. 1). Given that the experimental data are not specific to dipeptides, perfect agreement is not expected. |
60c743b6469df4007bf43256 | 38 | However, populations at extreme values would cause concern and a correlation between the experimental and simulated values is favorable. Figure shows that no dipeptides have populations consisting of just one type of rotamer and there are no extremely high values (as was observed for OPLS-AA and OPLS-AA/L 1 ). The rotamer M populations are occasionally slightly lower than expected. However, given the issues previously mentioned with the experimental data used, further changes were not made to adjust the outliers. |
60c743b6469df4007bf43256 | 39 | With a MUE of 14%, QUBE performs better than both OPLS-AA and OPLS-AA/L, which have errors of 23% and 21% respectively. The error is not as low as OPLS-AA/M, which has an error of 10%, however with further empirical changes to the torsional parameters the error could likely be further reduced. Examining individual dipeptide errors, protonated histidine and aspartic acid are found to have the highest errors. The protonated histidine experimental data includes all ionization states of histidine and therefore may not be accurate, which would explain the high error. The higher error in the simulated dynamics of the aspartic acid dipeptide is more problematic and, in future versions of the QUBE force field, further changes to these sidechain torsional parameters may be considered. |
60c743b6469df4007bf43256 | 40 | Set 2 Set 3 0.90 Β± 0.03 (0.86 Β± 0.03) 4.16 Β± 0.01 (0.81 Β± 0.03) 1.51 Β± 0.02 (0.87 Β± 0.03) Figure : The Ο and Ο distributions of the central residues of the alanine pentapeptide, plotted in the form -log(p Ο,Ο ) (where p Ο,Ο is the probability of a region being occupied). The lighter regions correspond to low probability areas including conformations that are not sampled during the simulation. . The J coupling errors extracted from MD simulations of the alanine pentapeptide are shown in Table , with the Ο/Ο distribution shown in Figure and further results given in Section S5.1 of the Supporting Information. Three sets of Karplus parameters are used to evaluate the error and the values in parentheses exclude the 2 J(N, C Ξ± ) coupling term. |
60c743b6469df4007bf43256 | 41 | Issues with the 2 J(N, C Ξ± ) coupling Karplus parameters are discussed in Section S9 of the Supporting Information and elsewhere. The J coupling error for set 1 is very encouraging and is lower than both the OPLS-AA/M (1.16 Β± 0.02) and AMOEBA force field errors (0.99). The errors for sets 2 and 3 with the excluded 2 J(N, C Ξ± ) term are similar in value. |
60c743b6469df4007bf43256 | 42 | In the simulations carried out in this work, as well as the work of Amber ff15ipq and OPLS-AA/M, the low Ξ² backbone populations present result in a high 2 J(N, C Ξ± ) error for the second and third set of Karplus parameters. The pentapeptide conformation with the largest population is PPII with 62 Β± 2 % of the simulation spent in this conformation (Table ). This is similar to the conformational propensity observed for OPLS-AA/M (53.5 Β± 0.2 %). Both force fields also result in a low Ξ±-helical population, which is consistent with experimental data. 6: The Ο and Ο distribution for the glycine tetrapeptide (all residues are included) using a) the QUBE force field and b) OPLS-AA/M, plotted in the form -log(p Ο,Ο ) (where p Ο,Ο is the probability of a region being occupied). The lighter regions correspond to low probability areas including conformations that are not sampled during the simulation. |
60c743b6469df4007bf43256 | 43 | The problems associated with using the Karplus parameters for Gly 3 are discussed in Section S9 of the Supporting Information and elsewhere. Therefore, we evaluate the backbone conformations of Gly 3 through its Ο/Ο distribution alone. In Figure , the OPLS-AA/M backbone conformational distribution is compared to that obtained using the QUBE force field. A lower Ξ±-helical population is occupied by the QUBE force field, but otherwise both distributions are very similar. |
60c743b6469df4007bf43256 | 44 | The MD simulations presented here have demonstrated that the QUBE force field, and the parameterization methods used to create it, are sufficiently accurate to recreate conformational propensities of short, flexible peptides. The errors in the simulated dynamics of these molecules are comparable to OPLS-AA/M, and the Ο/Ο distributions demonstrate that the major conformations observed in protein structures are populated. Issues with the transferability of torsional parameters have already been identified from the longer peptide simulations, and are solved by applying regularization. In the following subsection, the performance of QUBE for entire proteins is evaluated to demonstrate the feasibility of applying the methodology to macromolecules and to further understand the intricacies of fitting torsional parameters to a system-specific force field. |
60c743b6469df4007bf43256 | 45 | Figure : A comparison of the QUBE and OPLS non-bonded parameters for ubiquitin. The regions circled in correspond to carbonyl carbon atoms, which are expected to be electron deficient and therefore require small A and B Lennard-Jones coefficients. Blue and dashed black lines represent lines of best fit and y = x respectively. The use of system-specific non-bonded parameters for biomolecular force fields allows for long-ranged polarization effects to be included, which is expected to improve the accuracy of the force field, particularly for measurements such as protein-ligand binding affinity that are sensitive to the electrostatic potential at the protein surface. A comparison of the QUBE and OPLS non-bonded parameters for ubiquitin is shown in Figure . Figures for the other proteins tested follow similar trends. As we have described, QUBE non-bonded parameters are derived directly from the QM partitioned electron density, and so, each atom has a unique charge and set of Lennard-Jones coefficients which depend on its environment. In contrast, the OPLS parameters are read from a library of atom types. The QUBE and OPLS charges correlate well with no clear outliers. As has previously been observed, the QUBE Lennard-Jones parameters show a far greater level of variation than OPLS (and most other force fields). |
60c743b6469df4007bf43256 | 46 | One assumption employed in the use of system-specific charges for proteins (and small molecules) is that the derived parameter set is not too dependent on the molecular conformation. To investigate this assumption, the sensitivity of the non-bonded parameters, for the GB3 protein, to the choice of input structure is investigated in Section S6.2. Ten structures were extracted from a MD simulation employing the OPLS-AA/M force field, and QUBE non-bonded parameters were computed for each snapshot. The standard deviation of the charge distribution across the ensemble is just 0.02 e, supporting previous observations that the underlying DDEC atoms-in-molecule charges are relatively independent of conformation. It is important to test whether these system-specific force field parameters translate into more accurate protein interactions and dynamics. In this regard, although the conformational preferences of the peptides tested in the previous section are promising, it is not known whether the torsional parameters will continue to be appropriate for use with proteins. As the non-bonded parameters vary with the system studied, the transferability of torsional parameters cannot be readily assumed. To assess this we begin by studying MD simulations of the proteins ubiquitin and GB3. |
60c743b6469df4007bf43256 | 47 | The J coupling errors for ubiquitin and GB3 are summarized in Table . With an overall RMSE of 1.54 Hz, the error using the QUBE force field for ubiquitin is higher than that of OPLS-AA/M, which has an RMSE of 1.12 Hz, but lower than OPLS-AA and OPLS-AA/L with errors of 1.84 Hz and 1.70 Hz respectively. 1 GB3 follows the same trend with an RMSE of 1.10 Hz for the QUBE force field, compared to the error for OPLS-AA/M of 0.90 Hz, whilst OPLS-AA and OPLS-AA/L both have an error of 1.46 Hz. 1 The J coupling results suggest that whilst the transfer of torsional parameters from dipeptides to proteins may cause some issues, the QUBE force field remains more accurate than OPLS-AA and OPLS-AA/L. This is promising when we consider that OPLS has been in development for many years with multiple iterations and parameter adjustments performed. |
60c743b6469df4007bf43256 | 48 | The 3 J(H Ξ± , H Ξ² ) coupling term is the main contributor to the J coupling error. For GB3, the 3 J(H Ξ± , H Ξ² ) error for the QUBE force field is 1.80 Hz, this is well below the errors for OPLS-AA and OPLS-AA/L of 3.71 Hz and 3.38 Hz respectively. |
60c743b6469df4007bf43256 | 49 | However, as discussed in Section S9 of the Supporting Information, the J coupling error should not be used as the only measure of force field accuracy. To further test the performance of the QUBE force field, we compared the Ο/Ο torsion angle distributions and root mean square deviation (RMSD) of the backbone C Ξ± atoms of each residue from the experimental crystal structure for five proteins (Section S7 of the Supporting Information). |
60c743b6469df4007bf43256 | 50 | The dihedral angles of the experimental structure are shown on each Ο/Ο plot and these experimental points, along with the previous data for AMBER ff15ipq (the Ο/Ο plots are given in the Supporting Information of Ref. 2) are used to evaluate the performance of the force field. Figure shows the five proteins tested, with the residue labels indicating the main regions that deviated from the crystal structure during simulation. |
60c743b6469df4007bf43256 | 51 | Figure shows the average RMSD of the C Ξ± atoms of the five proteins from the experi- The Ο/Ο distributions of GB3 (Figure ) and the RMSD per residue (Figure ) help us to further analyze the results. Residues which deviate from the experimental structure, and the results from the AMBER ff15ipq force field, also tend to have high J coupling errors. |
60c743b6469df4007bf43256 | 52 | For example, residues 8-21 have a large deviation from the experimental structure and this is reflected by high J coupling errors in this region. The backbone J coupling error, using the 2007 Karplus parameters, for residues 8-21 is 2.00 Hz which is almost double the total backbone error. This region corresponds to a Ξ²-sheet, which separates over the second half of the MD trajectory and contributes to the increased backbone RMSD. Aside from this region, the only other residues which show noticeable deviation from the crystal structure are Val39, Asp40, Gly41 and Thr55. However, the small deviations that are present in these four residues are also observed in simulations using the AMBER ff15ipq force field. Deviations between the simulated ubiquitin dynamics and experiment tend to be confined to regions without clear secondary structures. Often this is of little concern since both experimental NMR measurements and simulations with the AMBER force field also indicate flexibility in these regions (e.g. residues 7-11 and 72-74). However, deviations from the crystal structure in the disordered region between residues 54-66 is more of a concern, and contributes to the high J coupling and rising RMSD of the protein backbone over the second half of the simulation. |
60c743b6469df4007bf43256 | 53 | In contrast, Figure shows that both the villin headpiece (PDB: 2F4K) and BPTI (PDB: 5PTI) retain their experimental structures extremely well (average RMSD in the range 1-2 Γ
). The three Ξ±-helices present in the villin headpiece are retained throughout the simulations, and the Ο/Ο distributions are in excellent agreement with experiment and the AMBER force field (Figure ). Similarly, in BPTI, regions with helical or Ξ²-sheet structures retain their structure. Some small changes in structure are observed (for example, residues 10-12 in villin and 36-40 in BPTI), though these correspond to regions with no fixed secondary structure or a bend. |
60c743b6469df4007bf43256 | 54 | The two Ξ±-helices present in 1BUJ, around residue 10 and residue 30, are generally well represented with the QUBE force field. However, in regions with no structure, a bend, or a turn significant deviations from experiment are observed and the RMSD reaches extremely high values. By way of comparison, the backbone RMSD using the AMBER ff15ipq force field was 3.4 Γ
after 10Β΅s of simulation, and after 0.5 Β΅s was approximately 3 Γ
. In the AMBER ff15ipq work, the high RMSD was attributed to variability in the loop regions, which had also been observed in experimental structures. Closer examination of the Ο/Ο distributions of each residue reveal the difficulty of capturing accurate conformational preferences. For example, the NMR ensemble for Lys38 shows the presence of both Ξ²-sheet and Ξ±-helical conformations. These are also observed in MD simulations using both AMBER ff15ipq and the QUBE force field, but the proportion of each conformation is different. The ensemble of Ser66 is not well represented with AMBER ff15ipq, but with the QUBE force field all structures in the ensemble are captured to some degree, although an additional Ξ±-helical conformation is also observed. |
60c743b6469df4007bf43256 | 55 | The assumption that biomolecular force fields must be parametrized against the experimental properties of small molecules has persisted since MM simulations began and remains in all force fields under widespread use. In this work, we look to challenge this assumption by deriving system-specific non-bonded parameters, from linear-scaling QM simulations, for consistency with the QUBE small molecule force field. These non-bonded terms were used here alongside libraries of (non-bespoke) bond and angle parameters, derived using the modified Seminario method, and newly reparametrized torsional terms. |
60c743b6469df4007bf43256 | 56 | We have shown here that using system-specific non-bonded force field parameters can result in accurate conformational preferences for short peptides. Rotamer populations and simulated J couplings for the dipeptide molecules are in good agreement with experimental data and compare favorably with the latest OPLS force field. For longer peptide molecules, the problems associated with fitting torsional parameters to a system-specific force field became more apparent. Using regularization in the fitting process was shown to overcome these issues and resulted in a J coupling error of just 0.90 Β± 0.03 for the alanine pentapeptide. Further work investigating disordered peptides will ascertain how general this fix is. |
60c743b6469df4007bf43256 | 57 | The accuracy of the peptide simulations supports the use of our non-bonded and modified Seminario bonded parametrization strategies. In protein MD simulations, the RMSD of the backbone atoms relative to experimental structures remained low, below 2 Γ
, for two of the five proteins tested. The Ξ±-helices present in all of the proteins generally remained close to the experimental structures, but the Ξ²-sheets exhibited greater loss of structure, and regions with no clear structure or exhibiting a turn regularly deviated from the starting structure. |
60c743b6469df4007bf43256 | 58 | Whilst developing QUBE, manual adjustments to some torsional parameters were required. This was also required in the development of OPLS-AA/M, and we can infer from this that automatically fitting backbone and sidechain torsional parameters using dihedral energy scans is still challenging. The most obvious failure of dihedral energy scan fitting was that for a number of sidechains it was more accurate to set the torsional parameters to zero than to use the originally derived terms. This is in part due to the functional form used, with potential improvements to this discussed below, but is also due to the poor sampling of relevant structures by scanning one or two dihedral angles at a time. This problem is reduced by the iterative fitting methods used in AMBER ff14ipq and ff15ipq, 2,38 which sample the structures used for torsional parameter fitting by performing MD simulations with the current iteration of the force field. This approach will be considered in future versions of the force field. |
60c743b6469df4007bf43256 | 59 | Another potential source of error is the choice of modified Seminario method for derivation of bond and angle force constants. However, this method has been shown to accurately reproduce QM vibrational frequencies, and importantly also reproduce QM intramolecular potential energy surfaces of drug-like molecules when combined with the QUBE non-bonded and torsion parameters. There are also additional considerations involved in using a library of torsional parameters alongside system-specific non-bonded parameters. The torsional parameters are fit using one set of non-bonded parameters but are then used for a range of environment-dependent nonbonded terms. This is likely the reason for the importance of regularizations in this study. |
60c743b6469df4007bf43256 | 60 | It may be possible to address this issue by changing the functional form of the torsional component of the force field. The functional form currently used is inaccurate due to the parameter dependency on only a single dihedral angle. The coupling between torsional terms has been addressed in a number of different ways. These include the use of the CMAP term in CHARMM22, a grid based correction used to improve the backbone torsional energetics. Extending the CMAP correction so it is dependent on the Ο 1 sidechain dihedral angle has also recently been investigated. The functional form could also be improved by adding a torsion-torsion coupling term as employed in previous studies. Importantly, the flexibility of the QUBE parametrization process means that changes to the torsional parameters are not the only alterations that could be made to improve the accuracy of the benchmark validation tests studied here. It is not just protein-protein interactions that determine structure, but also interactions with the water model. In particular, the balance between electrostatic and dispersive interactions has been shown to be crucial. Interactions between the QUBE force field and the TIP3P water model may be responsible for some of the instabilities in structure that we have observed, and development of a QUBE water model may lead to improved dynamics and computed free energies of hydration. An advantage of using a parametrization scheme that depends almost entirely on QM data is that alterations to the parametrization strategy or functional form can be readily inserted into the existing workflow. There is future scope for improvement in the choice of exchange-correlation functional used to derive non-bonded parameters, for example through the use of hybrid functionals, or the choice of electron density partitioning methods, 66 or the addition of off-center charges to model electron anisotropy effects. More fundamentally, we have the opportunity to investigate improvements to the functional form of the force field itself, for example, by adding higher order dispersion terms beyond the dipole-dipole interaction or by altering the short-range repulsion term. A future QUBE polarizable force field is also envisaged and, towards this goal, the derivation of accurate atoms-in-molecule atomic polarizabilities is under investigation. As presented in the Results section, the general picture that emerges is that this first generation quantum mechanical bespoke force field is an improvement over legacy OPLS-AA and OPLS-AA/L force fields, but is out-performed by the most recent OPLS-AA/M force field for simulated dynamics of folded proteins in their native state. While we have previously shown that DDEC charges are not too dependent on small conformation changes, 28 further investigation is needed to establish the utility of QUBE for protein folding simulations. |
60c743b6469df4007bf43256 | 61 | Hence, although we have outlined our roadmap to future improvements, a natural question is: where can the QUBE protein force field be used now (especially given the higher cost of parameterization compared to transferable force fields)? Importantly, it has been shown previously that the use of system-specific force field charges leads to improvements in binding energetics of small molecules, and reproduction of the QM electrostatic potential for both small molecules 27 and proteins. Therefore, although simulated protein backbone dynamics is an important test, we envisage the QUBE small molecule and protein force field being particularly important for the study of intermolecular interactions in the condensed phase. |
60c743b6469df4007bf43256 | 62 | Indeed, QUBE was originally developed to provide, by construction, a compatible protein and small molecule force field for computer-aided drug design, where an accurate surface electrostatic potential of the protein is crucial. In this regard, the absolute binding free energies between the L99A mutant of T4 lysozyme and six benzene analogs have been recently computed using QUBE with a mean unsigned error of 0.85 kcal/mol, which compares very favorably with OPLS-AA/M (1.26 kcal/mol). Although further work is required to establish this accuracy across a significantly wider range of protein-ligand complexes, the promise of these initial biomolecular simulation results indicate a viable pathway toward improved protein dynamics and interactions using quantum mechanical bespoke force fields. |
667d75625101a2ffa8a64edf | 0 | Among the increasing wealth of degradable polymers, polythioesters are gaining interest because of enhanced mechanical properties compared to their (oxo)ester counterparts, and as degradable, sustainable materials, including for emerging biomedical applications. Polythioesters are typically prepared through anionic/catalytic ring-opening polymerization (ROP) of thiolactones (featuring cyclic -C(=O)S-). Recently, the ROP of unstrained thionolactones (cyclic -C(=S)O-) was shown to give polythioesters through S/O isomerization. Only few reports have described the synthesis of polythioesters through the cationic ring-opening polymerization (CROP) of thionolactones (which likewise involves S/O isomerization). In 2000, Endo's group observed quantitative conversions of the 7-membered monomer Ξ΅-thionocaprolactone when initiated with BF3β’Et2O. The lanthanide triflate-initiated CROP of the 5membered homologue Ξ³-thionobutyrolactone reported in 2005 by the same group, on the other hand, gave lower conversions (53-78%) and low SEC-measured molar masses (3.4-6.3 kg/mol). A screening of different cationic initiators for the same cyclic monomer and substituted derivatives by Xia et al. in 2023 showed [Et3O] + [B(C6F5)4] -to be the ideal candidate to achieve efficient polymerization and a high degree of polymer crystallinity. During the writing of this manuscript, Peng et al. reported the BF3β’Et2O-initiated CROP of the dibenzo-substituted Ξ΅thionocaprolactone dibenzo[c,e]-oxepine-5(7H)-thione (DOT). Notably, all these polymerizations were done under inert atmosphere, typically in a glovebox. In 2019, a radical approach to polythioesters was reported independently by Gutekunst and our group. DOT was shown to undergo radical ring-opening copolymerization with a variety of vinyl monomers including acrylates, acrylamides, styrene, , and maleimides. DOT-containing copolymers have since been shown to be promising for degradable latexes, networks, and adhesives, recycling of polymers, and drug delivery. However, DOT does not homopolymerize well radically, meaning that the degradation of DOT-containing copolymers into predetermined small molecules is limited to rare cases of alternating copolymerization. Polythioester homopolymers made through anionic/catalytic ROP are known to degrade in the presence of base through the backbiting of a terminal thiol (the reactive chain end) which produces a cyclic thiolactone monomer. As this depolymerization can occur under polymerization conditions, strategies such as introduction of substituents or fused rings have been used to increase the ring strain and drive the equilibrium toward the polythioester product. Capping the terminal thiol as a thioester or thioether was shown to prevent base-mediated depolymerization. There has recently been renewed interest in depolymerization in the context of the chemical recycling of polymers with the nature of the end groups playing a pivotal role. For example, in the radical polymerization arena, Anastasaki's group demonstrated the importance of the Ο-end group on the depolymerization efficiency of vinyl polymers with more labile or reactive end groups facilitating an efficient end-to-end unzipping. To the best of our knowledge, the influence of Ο-end groups on the depolymerization of cationically-made polythioesters has not been investigated. Notably, the CROP of thionolactones does not proceed via thiol(ate) end groups, but cations which are quenched during workup which provides an end-cap. |
667d75625101a2ffa8a64edf | 1 | Herein, we present the CROP of DOT. A detailed comparison of initiators and reaction conditions showed that quantitative monomer conversion and low dispersities (1.5 < Γ < 2.0) could be obtained without the need for inert atmosphere or even dry solvents. The resulting DOT homopolymers degraded quantitatively under various conditions, including through aminolysis, thiolysis or simple heating with or without solvent. The respective mechanisms are discussed with polymers showing unzipping through controlled depolymerization. Interestingly, the choice of initiator had a profound impact on the thermal stability of pDOT polymers with methyl triflate (MeOTf)-initiated polymers showing a much lower onset of thermal depolymerization. The depolymerization of pDOT produces the thiolactone isomer of DOT as sole/main degradation product making this system promising for chemical recycling. |
667d75625101a2ffa8a64edf | 2 | All chemicals were purchased from Fisher, Fluorochem and Sigma Aldrich and were used as obtained unless otherwise stated. Solvents were dried over 3 Γ
molecular sieves, whereas glassware and stir bars were dried in oven overnight at 100 Β°C. Sbenzyl-S'-propyl carbonotrithioate and S-benzyl-N,N-diethyl dithiocarbamate were synthesised following literature procedures. 1,2,3,4,5-Pentakis(carbomethoxy)cyclopentadiene (PCCP) was synthesised following the method reported by M. A. Radtke et al. The monomer DOT was synthesised as described by Bingham et al. For the purification of the products by column chromatography, Sigma silica gel Geduran Si60 (40-63 ΞΌm) was used. |
667d75625101a2ffa8a64edf | 3 | Nuclear magnetic resonance (NMR) spectroscopy was used to calculate monomer conversions and to analyse products. Spectra were recorded on a Bruker AVANCE III HD 500 MHz or 400 MHz NanoBay spectrometer. Samples were prepared by dissolving 5-30 mg solid sample 50-100 ΞΌL of liquid sample in 400-500 ΞΌL CDCl3 in 5 mm NMR tubes. The residual solvent signal (Ξ΄ = 7.26 ppm) was used as reference. Thermal gravimetric analysis (TGA) experiments were performed on a TGA Q500 (TA Instruments, New Castle, United States). A sample of 2-5 mg was loaded in the platinum pan and heated at a heating rate of 10 Β°C/min from room temperature (RT) to 800 Β°C under nitrogen atmosphere with a flow rate of 60 mL/min. Thermal decomposition temperature is defined as the temperature at which only 95% of the original mass remains. |
667d75625101a2ffa8a64edf | 4 | Differential scanning calorimetry (DSC) experiments were conducted on a DSC Q1000 (TA Instruments, New Castle, United States) that was calibrated with indium. Approximately 2 -5 mg of sample was weighed and sealed in an aluminium hermetic pan. A similar empty pan was used as the reference. The glass transition temperature (Tg) of the sample was measured using a heat-cool-heat cycle between -60 Β°C and 210 Β°C under nitrogen atmosphere at heating/cooling rates of 10 Β°C/min. The midpoint Tg is reported from the second heating. |
667d75625101a2ffa8a64edf | 5 | Modified from the work by Sanda et al. and Kottisch et al. , DOT (25-1000 equiv.) was dissolved in a suitable anhydrous solvent unless otherwise mentioned below. Stock solutions of different initiators (boron trifluoride etherate BF3β’Et2O, methyl triflate MeOTf, tin(IV) chloride SnCl4, trifluoromethanesulfonic acid TfOH, methyl ptoluenesulfonate MeOTs, PCCP) (1 equiv.) were prepared in the same solvent and they were added to DOT. The mixture was stirred at RT for different time durations mentioned in Table . For experiments under O2-free conditions, each solution was sealed with a septum and degassed for 30 mins by bubbling nitrogen gas separately. For kinetics measurements, aliquots were withdrawn in intervals and quenched with a drop of methanol followed by NMR analysis of the crude mixture in CDCl3. The polymers were purified by precipitating into ice-cold hexane-diethyl ether (1:1 by volume, approximately 20-fold excess), centrifugation and drying in vacuum. Products presented as white solids and were dissolved in THF for SEC analysis. For experiments in different temperatures, the solutions were prepared as mentioned above and kept for stirring in an ice-cold bath or a salt-ice bath maintaining the required temperatures. |
667d75625101a2ffa8a64edf | 6 | Adapted from the work by Uchiyama et al. , DOT and the RAFT agent (varying ratios, mentioned in Table ) were dissolved in a suitable anhydrous solvent, sealed with septum, and degassed for 30 mins by bubbling nitrogen gas. Separately, a stock solution of the initiator was made in the same solvent followed by degassing the same way. Then it was added to the mixture of DOT and RAFT agent. The resultant mixture was stirred at RT. For kinetics measurements, same method was followed as above. SEC analysis was done after precipitating the polymer into excess ice-cold 1:1 hexane-diethyl ether. |
667d75625101a2ffa8a64edf | 7 | PDOT (5 mg) was dissolved in THF (1 mL) followed by the addition of the degradant (1 mL) and the mixture was stirred overnight at RT. Three different amines (npropylamine, isopropyl amine, ethylamine) were tested for degradation. The amines and THF were evaporated by blowing nitrogen and the residues were analysed by SEC by dissolving them further in THF. |
667d75625101a2ffa8a64edf | 8 | PDOT (10-20 mg) was dissolved in CDCl3 (1 mL). Stock solutions of ethanethiol and DBU were prepared separately in CDCl3. All these solutions were kept sealed and degassed separately by bubbling nitrogen gas for 20 minutes. The stock solutions (2-400 % of thioester linkages calculated in pDOT) were added to the pDOT solution, and it was stirred overnight at RT. NMR analysis was done with the crude aliquots and LCMS analysis was done with the crude degradation product obtained from 400 % degradant. SEC analysis was done after removal of DBU by aqueous wash and further dissolving in THF. |
667d75625101a2ffa8a64edf | 9 | Similar method was followed as mentioned in section 2.5.2. Stock solution of 2,6lutidine was prepared in CDCl3 and added to the pDOT solution after degassing separately for 20 minutes. The solution was stirred overnight at RT and also at 50 Β°C. 1 H NMR analysis was done each time with the crude reaction mixture. |
667d75625101a2ffa8a64edf | 10 | Stock solution of potassium thioacetate (10 % of thioester linkages calculated in pDOT) was prepared in anhydrous DMF and it was added to pDOT (20 mg) solution prepared in the same solvent after degassing as mentioned in the section 2.5.2. It was sealed and stirred at RT for 2 days. 1 H NMR and SEC analysis were done after evaporating the solvent and dissolving the residue in CDCl3 and THF respectively. |
667d75625101a2ffa8a64edf | 11 | Different initiators and solvents. Our research group previously reported the radical homopolymerization of the thionolactone dibenzo[c,e]oxepine-5(7H)-thione (DOT) and found significant retardation associated with the process. After 27 days of heating with several sequential additions of the radical initiator AIBN, only 22% monomer conversion to pDOT was achieved. Herein, the cationic ring-opening homopolymerization of DOT was explored, Scheme 1. Gratifyingly, DOT reacted readily upon addition of several cationic initiators leading to the disappearance of its bright yellow colour and rapid formation of pDOT homopolymer, as observed by 1 H NMR spectroscopy, Figure . Of six initiators tested (BF3β’Et2O, MeOTf, MeOTs, TfOH, SnCl4, and PCCP) effective polymerization was observed with four (BF3β’Et2O, MeOTf, TfOH, and SnCl4). Notably, polymerizations occurred at ambient conditions at RT, without the use of a glovebox or anhydrous solvents and led to nearly 100% conversion of the monomer (Table , entries . The isolated polymer, pDOT, presented as a white solid. 1 H NMR analysis gave the same signals as the polymer obtained through radical ring-opening polymerization, see Figure . 13 C, 1 H- 13 C HSQC and 1 H- 13 C HMBC NMR spectra (Figure -S5) and FT-IR analysis (characteristic band at Ξ½ = 1656 cm -1 assigned to SC=O stretch, Figure ) of a sample made using BF3β’Et2O as initiator confirmed the expected structure of the polymer and S-O isomerization. ) and were likely due to back-biting, a common phenomenon found in cationic polymerizations . The amount of formed DOO was typically around 0-5 mol-% and was assumed to be caused by attack of water onto a cationically activated DOT monomer, although, surprisingly, our results showed little correlation between the observed amount of DOO formation and the use of anhydrous solvents. Gratifyingly, the use of BF3β’Et2O with (non-)anhydrous DCM or toluene reproducibly led to no or very low (1-2 mol-%) formation of side products. DOO and DTO, as well as the S,S-isomer dibenzo[c,e]thiepin-5(7H)-thione (DTT) were synthesised separately and subjected to react with BF3β’Et2O under similar conditions. No conversion was found for any isomer, indicating the importance of the thionolactone-thioester S-O isomerization in driving the ring-opening and that the formation of the side products, while lowering the yield, did not lead to the formation copolymers, see Scheme 1. |
667d75625101a2ffa8a64edf | 12 | SEC analysis of the aliquots during kinetics measurements and of final products gave dispersities typically around 1.5 < Γ < 2.0 with mono-or bimodal distributions, suggesting the absence of controlled polymerization under the chosen conditions. While lower dispersities are of academic appeal, the ability to produce pDOT under ambient conditions makes this system more suitable for industrial application. |
667d75625101a2ffa8a64edf | 13 | While keeping the feed ratio of [DOT]0/[I]0 constant at 50:1, the SEC-measured PMMAequivalent molecular weights, Mn, of the isolated homopolymers varied between 1.3 kgmol -1 to 13.4 kgmol -1 . The initiators MeOTf and SnCl4 generally formed polymers with lower Mn values and more side products. This observation was attributed to faster polymerization kinetics and the high sensitivity of metal chloride initiators towards the presence of water . In some cases, using anhydrous solvents helped reduce the dispersity and decelerate the reaction kinetics along with decreasing the percentage of side products (Table , entries 1-4, 7, 8). On the other hand, the initiator BF3β’Et2O was able to form polymers with reasonably high Mn values potentially because of low initiator efficiency and contributed to better monitoring of gradual polymer formation (Figure ). Considering all the factors mentioned above, BF3β’Et2O was chosen as the best initiator for further analysis. |
667d75625101a2ffa8a64edf | 14 | The mechanism of the BF3β’Et2O-initiated CROP of DOT (Scheme 2) was presumed to involve the reaction of BF3 with (adventitious) water to generate a proton as the actual initiating species, followed by activation of the C=S double bond of DOT generating a cationic species stabilised by the aromatic ring and resonance with the thionoester oxygen (Scheme 2). Based on the other ring being able to stabilise a ringopened cation, the formation of a benzylic cation intermediate through irreversible ringopening (and concurrent thionolactone-thioester isomerization) was considered likely. After attack of the next DOT monomer, propagation via benzylic cations was presumed, until termination is expected to happen through (reversible) recombination with a hydroxide anion. Influence of polymerization temperature and monomer-to-initiator ratio. BF3β’Et2O-initiated polymerization kinetics were examined at RT, 4 Β°C, and -10 Β°C in anhydrous toluene. Expectedly, the polymerization rates decreased and SECmeasured molar masses decreased with decreasing temperature, see Figure , entry 4). Dotted lines were added as a guide. All polymerization discussed above were done with an initial ratio [M]0:[I]0 of 50:1. Additional ratios of 25:1, 100:1, 200:1, and 1000:1 were trialled (Table , entries . The ratio had a strong effect on the resulting degree of polymerization with SECmeasured molar masses increasing with a decreasing initiator concentration. The series of polymers had molar masses ranging from 4.0 to 26 kg/mol with similar dispersities between 1.5 < Γ < 1.7, Figure . Notably, this range included polymers with a much greater length than the pDOT species prepared through radical polymerization (Mn = 4.9 kgmol -1 with Δ = 2.0). Interestingly, fewer to no side products were detected at lower initiator concentrations. Attempts at living cationic polymerization. We attempted to polymerize DOT through "living" cationic methods using cationic RAFT and through 1,2,3,4,5pentakis(carbomethoxy)cyclopentadiene (PCCP)-initiated/mediated polymerization. Two RAFT agents, S-benzyl-S'-propyl carbonotrithioate and S-benzyl-N,Ndiethyl dithiocarbamate were used. To the best of our knowledge neither had been used for cationic polymerizations, but were expected to be suitable for DOT based on the presumed formation of a benzylic cation, similar to the DOT monomer. BF3β’Et2O and triflic acid were used as initiators (Table , entries . While polymer products were formed with poor to moderate conversions, the SEC-measured dispersities (1.5 < Γ < 2.4) were not lower than in polymerizations without RAFT agents. Indeed, the very high SEC-measured molar mass of 50.4 kg/mol for a polymerization of DOT (1000 eq) initiated by BF3β’Et2O (1 eq) in the presence of S-benzyl-N,N-diethyl dithiocarbamate (20 eq) suggested no sharing of the cations between different chains. Unfortunately, attempted PCCP-initiation failed with no conversion of DOT to polymer observed (Table , entry 9). In an attempt to use PCCP as mediator but not initiator, a combination of PCCP and MeOTf was employed (Table , entry 25). While polymer was formed, its relatively high SEC-measured dispersity of Γ = 2.03 suggested no control. |
667d75625101a2ffa8a64edf | 15 | Polymer properties. After studying the homopolymerization behaviour of DOT, the pDOT product was characterised. At RT and at concentrations of 10 g/L, pDOT was soluble in DMF, THF, DCM, chloroform, anisole, and toluene, and insoluble in water, methanol, isopropanol, acetone, DMSO, acetonitrile, ethyl acetate, petroleum ether, and hexane. PDOT was stable for at least 18 months when stored at RT under air with samples showing no change of SEC-measured Mn after this time. A BF3β’Et2O-initiated sample (Table , entry 1) had a measured glass transition temperature of 97 Β°C (Figure ), which was slightly higher than the value of 95 Β°C reported for a radically made oligomer. The thermal stability of the polymers was analysed using TGA (Figure , S8, S9). Interestingly, the choice of initiator had an influence on the thermal stability. While BF3β’Et2O-initiated pDOT (Table , entry 4) was found to be stable until 270 Β°C, a MeOTf-initiated sample (Table , entry 8) started to decompose at 170 Β°C. The TGA profile of this MeOTf-initiated sample was similar to that of DTO (Figure ), see below for further discussion. With labile thioester linkages in every repeat unit, pDOT holds the potential for complete degradation into small molecules. Three degradation conditions were evaluated in detail: aminolysis, thiolysis, and thermal degradation in the absence of solvent. |
667d75625101a2ffa8a64edf | 16 | Anion/base-mediated degradation. Initially, aminolysis was tested as this is a main method for the degradation of radically-made DOT copolymers. Herein, three primary short-chain amines (n-propylamine, isopropylamine, ethylamine) were used in a 1:1 (vol:vol) mixture with THF at RT. For all amines, SEC analysis showed the complete disappearance of the polymer and formation of small molecules, suggesting the expected full degradation (Figure , S11A-B). NMR analysis (Figure ) confirmed the formation of small molecules including predominantly the alkylamidethiol molecule expected from quantitative aminolysis (Scheme S1). To explore thiolysis, a sample of pDOT (Table , entry 4, 8) was first treated with a 4fold excess (relative to the concentration of the thioester repeat units) of ethanethiol and DBU in CDCl3 at RT. While aminolysis typically requires a large excess of amine, the stronger nucleophilicity of thiolate anions meant that this 4-fold excess was sufficient to cause full degradation. SEC analysis (Figure ,C) of the isolated products confirmed the disappearance of the polymers and formation of small molecule products. 1 H NMR analysis confirmed the degradation through the disappearance of the characteristic broad multiplets of the benzylic protons (Ξ΄ = 3.73 and 3.94 ppm, Figure ) of DOT-DOT diads. Instead, the spectrum of the fully degraded sample showed two narrow doublets at 3.56 and 4.27 ppm, in addition to narrow, shifted aromatic signals (Figure ). These chemical shifts were similar (but not identical) to those of the cyclic thioester DTO reported in the literature. To identify this major product of the degradation, DTO was prepared separately through thermal isomerization of DOT. We found that the chemical shifts of DTO depended strongly on the NMR solvent. Gratifyingly, 1-D and 2-D NMR spectra of the decomposition product recorded in CDCl3 (Figure We considered three base/anion-mediated pathways leading to the formation of DTO as the sole degradation product of pDOT: (i) a self-immolative mechanism starting from the Ξ± end-group, in which a deprotonated thiocarboxylate attacks the adjacent benzylic position to give one molecule of DTO and releases another thiocarboxylate (Scheme 3, Pathway 1); (ii) a self-immolative degradation through backbiting of a thiol following a single thioester cleavage event (Scheme 3, Pathway 2); and (iii) a two-step process first forming an ethyl thioester-mercapto-functional biphenyl through thiolysis of two adjacent thioester linkages followed by intramolecular cyclization (Scheme 3, Pathway 3). To distinguish between these mechanisms, a series of experiments was conducted. |
667d75625101a2ffa8a64edf | 17 | First, two experiments were done to facilitate "Ξ±-depolymerization". The proposed mechanism (Scheme 3, Pathway 1) requires the presence of an Ξ± thiocarboxylic acid, as expected for BF3β’Et2O-initiated polymers (since the initiation occurs through protons formed with adventitious water). Thus, samples of BF3β’Et2O-initiated pDOT and MeOTf-initiated pDOT (which, carrying a methyl thiocarboxylate Ξ± endgroup, was not expected to undergo Ξ±-depolymerization) were treated with 2,6lutidine. This base of low nucleophilicity was expected to efficiently deprotonate thiocarboxylic acid Ξ± end-groups. However, neither polymer showed any formation of DTO or changes in the SEC-measured molecular weight distribution. Next, a sample of BF3β’Et2O-initiated pDOT was treated with 10 mol-% (relative to thioester linkages) of potassium thioacetate, a small molecular model of a thiocarboxylate Ξ± end-group. Only a negligible amount of DTO was formed. These experiments indicated that Ξ±depolymerization does not play an important role in the degradation of pDOT. The absence of Ξ± thiocarboxylate-initiated self-immolation is also confirmed by the observed stability of BF3β’Et2O-initiated pDOT samples during storage (see above). |
667d75625101a2ffa8a64edf | 18 | To distinguish between Pathways 2 (Ο depolymerization) and 3 (cyclization of small molecule fragments), samples of pDOT were treated with substoichiometric amounts of ethanethiol/DBU. When 10 mol-% of ethanethiol/DBU (relative to thioester linkages) was used, 80 mol-% conversion to DTO was found with 20 mol-% residual polythioester (Figure ) after 18 h at RT. Increasing the reaction time to 10 days did not increase the amount of formed DTO. SEC analysis showed a shift toward lower molecular weights, indicating partial degradation (Figure ). When the same intact homopolymer was treated with only 2 mol-% of ethanethiol/DBU, formation of 8 mol-% of DTO was observed (Figure ). With a shortage of reactive thiolate, the cleavage of two adjacent thioester units (mechanism iii) becomes less likely, making the backbiting mechanism (Scheme 3 , Pathway 2) more plausible. This self-immolative pathway is also supported by the lower pKa of the benzylic thiol within the polymer chain (pKa of benzyl mercaptan in water = 9.43) compared to ethanethiol (pKa in water = 10.3), making the polymeric thiolate a better leaving group than ethane thiolate. We therefore assume that the degradation of pDOT in the presence of base or anions (at least when a substoichiometric amount of thiolate is employed) starts with the transthioesterification of a random thioester within a chain, followed by selfimmolative depolymerization from the Ο end of the polymeric thiol (Scheme 3, Pathway 2). Assuming quantitative unzipping of a thiolate-terminated chain, a single thioester cleavage event should reduce the average molecular weight of the (remaining) polymer to half, since, on average, half of each chain depolymerizes, while the other (ethyl thioester Ξ±-terminated) half is presumed to remain intact until it is attacked by another thiolate from its middle. In theory, a chain of, say, 32 (= 2 5 ) repeat units should thus require 5 thiolates (5/32 = 15.6 mol-%) to achieve full degradation to DTO, while a longer chain with a DP of 128 (= 2 7 ) would degrade fully in the presence of 5.5 mol-% (= 7/128) thiolate. Applying this theory to the observed DTO formations gave an initial DP of the intact homopolymer of 23 for the degradation observed with 10 mol-% thiolate and an initial DP of 6 for the degradation observed with 2 mol-% thiolate. This discrepancy indicated that either the thiolate reagent did not react quantitatively under the employed conditions and/or that the backbiting did not depolymerize the entire half of the chain making a larger amount of thiolate necessary. Thermal degradation. Inspired by the strikingly different TGA profiles of BF3β’Et2Oand MeOTf-initiated polymers (Figure ), the thermal degradation in the absence of solvent was explored further. The thermal degradation of the MeOTf-initiated sample (Figure , grey curve) was nearly identical to a curve recorded as comparison of the small molecule DTO (Figure , green curve). We therefore hypothesized that, for the MeOTf-initiated sample, upon heating in the absence of solvent or nucleophiles, degradation to DTO took place at or below the onset of observed mass loss and that the observed decrease in mass stemmed mostly from the thermal disintegration of DTO. To investigate, samples of MeOTf-initiated pDOT (Table , entry 8) and BF3β’Et2O-initiated pDOT (Table , entry 4) were heated to 140 Β°C in air in a test-tube without solvent or additives. During heating, the fluffy white polymers gradually changed to a brown/orange colour and became denser with a sand-like appearance supporting the formation of a crystalline product. 1 H NMR analysis of the mixtures confirmed 35 mol-% degradation to DTO for the MeOTf-initiated sample after heating overnight, while a significantly lower DTO content of 6 mol-% was found in the BF3β’Et2O-initiated polymer after heating for 1 week to 140 Β°C (Table , entries 1, 2). |
667d75625101a2ffa8a64edf | 19 | Apart from the DTO degradation product and residual pDOT, only minor other signals were observed in the 1 H NMR spectrum, Figure . SEC analysis (Figure ) showed shifts toward lower observed molar masses, indicating the partial degradation of chains, as is common for a controlled depolymerization. For comparison, a sample of MeOTf-initiated pDOT was heated to 140 Β°C in DMF. Faster thermal degradation was observed with 67 mol-% DTO formed after 20 h (Figure , Table , entry 3) together with a large shift in SEC-measured molar mass (Figure ). With continuing heating, the sample degraded fully into small molecules after 3 days (Figure ), but NMR analysis (Figure ) showed the formation of multiple side products. |
667d75625101a2ffa8a64edf | 20 | Heating of dry samples to a higher temperature of 170 Β°C was trialled. After only 10 minutes of heating to this temperature, the MeOTf-initiated sample had undergone 10 mol-% degradation to DTO, while the BF3β’Et2O-initiated comparator remained intact following the same treatment (Table , entries 4, 5) These experiments confirmed the formation of DTO as main product upon heating of dry samples and the large influence of the initiator on the thermal stability. We thus hypothesised that the observed difference in thermal stability was related to the different Ο end groups (as the BF3β’Et2O-and MeOTf-initiated samples featured comparable SEC-measured Mn values of 5.2 and 8.7 kg/mol, respectively, and comparable dispersities of 1.81 and 1.66, respectively). Indeed, the breakage of an Ο end cap is typically the starting point for depolymerization. The lower thermal stability of the MeOTf-initiated polymers suggested the presence of benzyl triflate end groups compared to the less labile hydroxy end groups expected for BF3β’Et2O-initiated polymers. The presumed mechanism of this thermal degradation involved a forward-biting of thioester sulfur lone pairs starting from the Ο end group (Scheme 3, Pathway 4). Presumably, the counterion (hydroxide, triflate) or other nucleophiles (adventitious water) can interrupt the depolymerization by eliminating a cyclic DTO cation (Scheme 3, Pathway 4 right) which would explain the observation of partially degraded chains (Figure ) (as opposed to a mixture of fully degraded and intact chains). Notably, the dependence of the thermal stability on the nature of the Ο end group remarkable. While this concept has recently been demonstrated for radically-made polymers our work demonstrates the first example of a cationic initiator influencing the thermal depolymerization efficiency and offers the possibility of tuning the degradation behaviour of a, otherwise identical, material simply through the choice of initiator. |
667d75625101a2ffa8a64edf | 21 | Among the various types of ring-opening polymerization, CROP is, arguably, the least commonly used, presumably because of the typical need for strictly anhydrous and air-free conditions. Our work demonstrates that polythioesters with dispersities below Γ = 2.0 can be derived from DOT with excellent conversions under ambient conditions. The efficiency of this synthesis is presumed to lie in the involvement of stabilised benzylic cations. Notably, this approach gave access to high molar mass DOT homopolymers that are not accessible through radical ring-opening polymerization and allowed studying depolymerization mechanisms in detail. The thiolate-initiated depolymerization was shown to involve the initial cleavage of a mid-chain thioester followed by Ο-unzipping of the thiolate-terminated fragment. Thiocarboxylate Ξ±-end groups, on the other hand, were not found to play a role in the depolymerization which accounted for stability of the polymers in the presence of (non-nucleophilic) base. The thermal depolymerization was shown to originate from Ο end groups and therefore depend on the end cap provided by the initiator. This depolymerization was found to be controlled, i.e. with a gradual decrease of molar mass rather than complete unzipping of some chains, while others remained intact. Overall, these insights are expected to be helpful in the design of recyclable materials with stability during use and full degradability under tailorable conditions. |
6772757f6dde43c908c5bc64 | 0 | Progress in nanotechnology is facilitated by the development of precise synthesis methods and the detailed characterization of fine and sophisticated nanomaterials. Ligand-protected metal clusters, a representative group of nanomaterials, have been the focus of numerous studies, resulting in the establishment of precise synthesis methods and the elucidation of their properties through synergistic experimental and theoretical investigations. Among these, ligand-protected metal clusters composed of noble metal elements, such as gold (Au), silver (Ag), and copper (Cu), exhibit unique properties according to the number of constituent atoms and dopant elements, including photoluminescence (PL), magnetic properties, and catalytic activity. These characteristics have attracted significant attention in both fundamental research and practical applications. Recently, studies have also been conducted on clusters with complex structures arising from combinations of noble metal elements and main group elements. Among these, Agsulfur (Ag-S) based clusters are metal clusters with cavities capable of encapsulating various anions, and recent efforts have focused on altering the encapsulated anionic species to modulate the physicochemical properties of these clusters. Ligand-protected metal clusters often exhibit PL. Recent experimental studies have shown that phosphorescence originates in the excited triplet state. Therefore, enhancing the population of the excited triplet state of metal clusters is crucial for their application as room-temperature phosphorescent materials and triplet sensitizers. Generally, transition from the excited singlet state (Sn) to the excited triplet state (Tm) is spin-forbidden, resulting in a zero transition-moment. |
6772757f6dde43c908c5bc64 | 1 | However, studies on organic fluorescent dyes have shown that introducing heavy atoms, such as iodine (I), into the fluorophore enhances spin-orbit coupling (the internal heavy-atom effect), which increases the rate constant for intersystem crossing (ISC) from Sn to Tm, thereby improving the efficiency of phosphorescence. Similarly, encapsulating a heavy atom into Ag-S clusters may enhance the phosphorescence quantum yield. However, to date, there are limited reports on the internal heavy-atom effect of ligand-protected metal clusters. In this study, we successfully synthesized ligand-protected Ag-S clusters with central cavities encapsulating anions X z-, where X z-= S 2-(sulfide) or I -(iodide), which significantly differ in atomic number each other (Scheme 1). Single-crystal X-ray diffraction (SC-XRD) and proton nuclear magnetic resonance ( 1 H NMR) spectroscopy revealed that the resulting Ag clusters were composed of X@Ag54S20(thiolate)20(sulfonate)m, where (X, m) = (S, 12) or (I, 11) (X@Ag54). Furthermore, a comparison of the optical properties of the obtained pair of X@Ag54 (X = S or I) demonstrated that an internal heavy-atom effect occurred in these Ag-S clusters, similar to that in organic fluorescent dyes. Accordingly, the phosphorescence quantum yield was 16 times higher when S 2-was replaced by I -as the encapsulated atom (Scheme 1). Scheme 1. Enhancement of phosphorescence quantum yield by encapsulating S 2-or I -anions inside the central cavity of the Ag54S20(S t Bu)20(SO3 t Bu)m framework. |
6772757f6dde43c908c5bc64 | 2 | For the synthesis of S@Ag54, 48.6 mg (0.22 mmol) of silver trifluoroacetate (Ag(TFA)) and 10.6 mg (0.044 mmol) of copper(II) nitrate trihydrate (Cu(NO3)2β’3H2O) were dissolved in 4 mL of a mixture of acetone and acetonitrile (50/50 vol%). Then, 15 Β΅L (0.13 mmol) of tert-butanethiol ( t BuSH) was added to this solution, and the resulting mixture was transferred into a glass tube (Figure ). A cap with a small hole (Figure ) was placed on the glass tube, and the tube was left undisturbed under a fluorescent lamp for light irradiation (Figure ). Orange crude crystals of S@Ag54 were obtained after approximately one week (Figure ). The crude crystals were dissolved in chloroform, and hexane was slowly added to the upper layer. The solution was left to stand for one month, resulting in the formation of single crystals of S@Ag54 (Figure ). I@Ag54 was synthesized in the same manner as S@Ag54, except 20 mg (0.054 mmol) of tetrabutylammonium iodide (TBAI), as well as t BuSH, was added to the acetone/acetonitrile mixture of Ag(TFA)/Cu(NO3)2. Red-orange crude crystals of I@Ag54 were obtained after approximately two weeks (Figure ). The crude crystals were dissolved in chloroform, and hexane was slowly added to the upper layer. The solution was left to stand for one month, resulting in the formation of single crystals of I@Ag54 (Figure ). |
6772757f6dde43c908c5bc64 | 3 | S@Ag54 and I@Ag54 were crystallized in space groups of Fm-3 and Pa-3, respectively (Table ), and their geometric structures were determined using SC-XRD (Figures and). According to these geometric structures, the chemical compositions of S@Ag54 and I@Ag54 were X@Ag54S20(S t Bu)20(SO3 t Bu)m (X = S and I; S t Bu = tert-butanethiolate; SO3 t Bu = tert-butyl sulfonate) (hereafter, X@Ag54). Although the number of SOβ t Bu ligands in both S@Ag54 and I@Ag54 was determined to be 12 by SCXRD, the latter cluster exhibits relatively high thermal parameters for the SOβ t Bu ligands. We believe this is due to the lower occupancy of these ligands. Therefore, an attempt was made to estimate the number of SO3 t Bu ligands in I@Ag54 through 1 H NMR analysis. |
6772757f6dde43c908c5bc64 | 4 | In the 1 H NMR spectra of S@Ag54 and I@Ag54 (Figure ), the two peaks at 1.63 and 1.38 ppm can be attributed to the protons of S t Bu and SO3 t Bu, respectively. The integral values of these peaks revealed that S@Ag54 contained 12 SO3 t Bu ligands, while I@Ag54 contained 11 SO3 t Bu ligands. |
6772757f6dde43c908c5bc64 | 5 | The above chemical compositions indicate that there is a difference in the number of SO3 t Bu ligand between S@Ag54 and I@Ag54. Ligand-protected metal clusters are generally formed when the total number of valence electrons is even. In this study, SC-XRD and electrospray ionization (ESI) mass spectrometry of the low mass region showed that no TFA -, which could be a counter ion, was observed in either S@Ag54 or I@Ag54, suggesting that these clusters were neutral. In this case, because S@Ag54S20(S t Bu)20(SO3 t Bu)12 has an even number of valence electrons, I@Ag54 with the same ligand combination (I@Ag54S20(S t Bu)20(SO3 t Bu)12) should have an odd number of valence electrons. Therefore, it can be considered that I@Ag54 was formed with one fewer SO3 t Bu ligand than S@Ag54 to prevent destabilization due to the odd number of valence electrons. |
6772757f6dde43c908c5bc64 | 6 | To gain a deeper understanding of the chemical composition, we also acquired ESI mass spectra of the products. The ESI-mass spectra of both S@Ag54 and I@Ag54 contained multiple peaks attributed to ions in which AgS or ligands were adsorbed or desorbed from the clusters (e.g., , Tables and). These results confirmed that the estimation of the above chemical compositions is collect for both X@Ag54. |
6772757f6dde43c908c5bc64 | 7 | The geometric structures of X@Ag54 clusters were similar each other, with both containing an X@{Ag12S8} core (Figures 1A and 1B). In this core, the central anion X (S 2-or I -) was surrounded by 12 Ag atoms, forming an icosahedron (point group Ih) (Figure ), with 8 S atoms in a cubic arrangement surrounding this core. On the surface of the X@{Ag12S8} core, 12 S atoms formed an intermediate layer (highlighted in yellow, Figure ), which was connected to outer Ag42(S t Bu)20. |
6772757f6dde43c908c5bc64 | 8 | The 12 S atoms of the intermediate layer were bonded to 12 Ag atoms of Ag42(S t Bu)20 (X@{Ag12S8}S12[Ag42(S t Bu)20]) (highlighted in blue, Figure ). On the surface of X@{Ag12S8}S12[Ag42(S t Bu)20], the S atoms of S( t Bu) were arranged in a regular icosahedral structure with two coordination modes: ΞΌ3-S( t Bu) and ΞΌ4-S( t Bu) (Figure and). The m SO3 t Bu ligands were coordinated with 12 Ag atoms of Ag42(S t Bu)20 (highlighted in blue, Figure ), which were bonded to the S atoms of the intermediate layer, as well as 2 Ag atoms of remaining Ag30(S t Bu)20 (highlighted in red, Figure ) in the coordination mode of ΞΌ3-O3S( t Bu)-ΞΊ 3 O,OΚΉ,OΚΉΚΉ (Figure ). |
6772757f6dde43c908c5bc64 | 9 | In these structures, both the X@{Ag12S20} part and surrounding Ag42(S t Bu)20(SO3 t Bu)m shell exhibit the same Th symmetry. However, as mentioned earlier, I@Ag54 has one fewer SO3 t Bu ligand than S@Ag54. The SC-XRD results suggest that a SO3 t Bu ligand is missing from a random site, rather than a specific site, in I@Ag54. Therefore, in I@Ag54, the 12 coordination sites are randomly occupied by 11 SO3 t Bu ligands, leading to the formation of multiple structural isomers and accordingly, disorder in the geometric structure of I@Ag54. |
6772757f6dde43c908c5bc64 | 10 | These geometric structures of X@Ag54 are similar to those of previously reported clusters, such as [email protected](S t Bu)20(SO3 t Bu)12 and S@Cu54S12O6(S t Bu)20(SO3 t Bu)12. In the two previously reported clusters, the M42(S t Bu)20(SO3 t Bu)12 (M = Ag or Cu) shell, which has Th symmetry, also covers the core. However, there are two major differences between these two previously reported clusters and X@Ag54: 1) in the previously reported clusters, Ag and Cu, or only Cu, are included as metals, whereas in X@Ag54, only Ag is present as the metal of the clusters; 2) the previously reported clusters have two fewer chalcogenide ions (S 2-or O 2-) other than the central ion (18 chalcogenide ions) than X@Ag54 (20 sulfide ions). As a result, the diameter of the cavity of the M12S8 core of X@Ag54 (approximately 5.04 and 5.13 Γ
for S@Ag54 and I@Ag54, respectively; Figures and), is greater than that of the two previously reported clusters (4.94 Γ
and 4.88 Γ
). For this reason, both S 2-(ionic radius = 1.84 Γ
) and I -(ionic radius = 2.20 Γ
), were stably encapsulated inside the {M12S8} core of X@Ag54. Formation mechanism X@Ag54 contains 20 S atoms. These S atoms are considered to be produced through the reaction between Ag-S t Bu and Ag + : this reaction produces Ag2S. In this study, although only t BuSH was added as the ligand during the synthesis, in-situ produced SO3 t Bu was also included as a ligand in X@Ag54, as confirmed by SC-XRD (Figure ), 1 H NMR (Figure ), and ESI-mass spectroscopy (Figure ), in addition to X-ray photoelectron spectroscopy (XPS) (Figures and) and Fourier-transform infrared (FT-IR) absorption spectroscopy (Figure ), of the products. The catalytic oxidation of thiols by Cu 2+ (Scheme S1) is responsible for the formation of these SO3 t Bu ligands. In this reaction, Cu 2+ coordinates with RSH, which reduces Cu (Cu + ) and generates the thiyl radical (RSβ’). RSβ’ reacts with oxygen molecular (O2) and unreacted RSH in the system to produce RSO3H (Figure ). After coordinating with RSH, Cu + is oxidized to Cu 2+ by O2, returning to its original state. As these reactions proceed, SO3 t Bu is formed in the reaction solvent and coordinates with the metal cluster (Scheme S1). In these reactions, the coordination and reduction of Cu 2+ and formation of RSO3H from RSβ’ proceed with rate constants of approximately 10 8-10 M -1 s -1 , which is very fast. Moreover, these reactions are faster than the oxidation of Cu + to Cu 2+ by O2, which becomes the rate-limiting step. Indeed, when Cu(NO3)2 and t BuSH were mixed, the blue color of the solution immediately disappeared owing to the reduction of Cu 2+ to colorless Cu + , whereas this blue color took 2 days to reappear as Cu + reverted to Cu 2+ (Figure ). However, when Ag + coexisted with Cu 2+ and t BuSH, the recovery of Cu 2+ from Cu + occurred more rapidly (Figure ), with the disappearance of t BuSH confirmed by electron spin resonance (ESR) spectroscopy of the reaction solution. These results demonstrate that the presence of Ag + accelerates the rate-limiting step of RSH oxidation by Cu 2+ , thereby accelerating the formation of RSO3H. |
6772757f6dde43c908c5bc64 | 11 | Zhu et al. have reported the synthesis of [email protected](S t Bu)20(SO3 t Bu)12 containing both Ag and Cu as metals under reaction conditions similar to those used in our study. However, in our study, X@Ag54, which contains only Ag as the metal, was synthesized (Figure ). In our study, unlike the research by Zhu et al., we did not add the reducing reagents, such as borane amine complexes, into the reaction solvent. Moreover, compared to their study, we significantly reduced the amount of Cu 2+ catalyst relative to Ag + (1.260 vs 0.198 atom %). These factors likely contributed to the successful synthesis of X@Ag54 with only Ag as the metal, which enabled the encapsulation of I -. |
6772757f6dde43c908c5bc64 | 12 | In (A), the peaks on the low binding energy side (yellow) are attributed to sulfide S 2-or thiolate t BuS -, and the peaks on the high binding energy side (green) are attributed to S derived from sulfonate t BuSO3 -. Spectrum (B) indicates that the charge state of I is similar to that of I -. Spectrum (C) indicates that X@Ag54 does not include Cu. In (D), the peaks around 368 eV and 374 eV are attributed to Ag 3d5/2 and Ag 3d3/2, respectively. These spectra indicated that the oxidation state of Ag in X@Ag54 was similar to that of Ag2S and AgO. |
6772757f6dde43c908c5bc64 | 13 | The core of X@Ag54 consisted of only Ag and S and formed a central cavity, as observed in previously reported [S@Ag50S12(S t Bu)20](TFA)4. In the previously reported cluster, all the Ag atoms are in the +1 oxidation state, giving rise to a single sharp peak in both the Ag 3d3/2 and 3d5/2 regions of its XPS spectrum. In contrast, broad peaks were observed in the Ag 3d5/2 and 3d3/2 regions of the XPS spectra of X@Ag54 (Figure ). These peaks were fitted with two functions, and the position of the peak on the high-energy side was close to the position of the peak corresponding to Ag2S or AgO (Figures and, Table ). These observations indicates that Ag in X@Ag54 is in a mixed-valence state, rather than the single-valence state of Ag in [S@Ag50S12(S t Bu)20](TFA)4. In fact, there have been several reports on Ag existing in mixed-valence states. For example, bulk silver monoxide (AgO), which can be described as Ag2Oβ’Ag2O3, contains Ag in a mixed-valence state of Ag I and Ag III . Furthermore, Cu atoms in Cu-chalcogen clusters with geometric structures similar to those of X@Ag54, such as [S@Cu54S12O6(S t Bu)20(SO3 t Bu)12] and [Cu50S12(S t Bu)20(TFA)12], also exist in a mixed-valence state of Cu I and Cu II . Unlike [S@Ag50S12(S t Bu)20](TFA)4, X@Ag54 contained two types of ligands (S t Bu and SO3 t Bu), and this can be considered to cause the mixed-valence state of Ag. |
6772757f6dde43c908c5bc64 | 14 | Stability against degradation in solution was evaluated by heating X@Ag54 in toluene and tracking changes in its ultraviolet-visible (UV-vis) absorption spectrum. The results showed that 1) the stabilities of both clusters are similar, and 2) the absorption spectra of both samples in toluene can remain unchanged over 20 h of heating at 60 Β°C (Figures and). The half-life of both clusters under these degradation conditions was estimated to be approximately 200 h (Table ). |
6772757f6dde43c908c5bc64 | 15 | Stability against heat-induced dissociation was evaluated using thermogravimetric analysis (TGA). Both clusters underwent three stages of weight loss (Figures and). According to the weight of the ligands and their functional groups, the weight loss at approximately 100 Β°C is attributed to the removal of SO3 t Bu ligands (theoretical loss = 20% for S@Ag54 and 16% for I@Ag54), while the weight loss at approximately 120 Β°C is attributed to the removal of t Bu groups from S t Bu ligands (theoretical loss = 11% for both S@Ag54 and I@Ag54). The final weight loss at approximately 180 Β°C is interpreted as the removal of sulfur (theoretical loss = 6.5% for both S@Ag54 and I@Ag54). The slow weight loss at subsequent temperatures can be attributed to the desorption of sulfur or X from the remaining X@Ag54S20. The dissociation energies of Ag-SO3 t Bu and AgS-t Bu, calculated using density functional theory (DFT), were 54.2 and 57.4 kcal/mol, respectively (Table ). This should be the reason why thermal dissociation occurred in the order. |
6772757f6dde43c908c5bc64 | 16 | Stability against CID was investigated in a vacuum. Specifically, X@Ag54 was introduced into an ESI-mass spectrometer, where it collided with argon (Ar) to undergo CID. The stability of each cluster was examined by evaluating the chemical composition and ion intensity of the generated fragment ions. Mass spectra were obtained following the collision of [S@Ag54 + SO3 t Bu] 2+ and [I@Ag54 + SO3 t Bu + 2AgS] 2+ with Ar at different collision energies (Figure and 5B, Table ). |
6772757f6dde43c908c5bc64 | 17 | The parent ions of X@Ag54 dissociated as the collision energy increased. The main dissociation patterns corresponded to the radical cleavage of Ag-O3S t Bu and S-t Bu (Figure ). These dissociation patterns closely resembled those observed in the TGA curves. Furthermore, these dissociation reactions of both clusters occurred at similar collision energies (Figures and, Tables and), indicating that the stability of both clusters against CID was also similar each other. |
6772757f6dde43c908c5bc64 | 18 | In these experiments, detachment of surface ligands was the first step of degradation. It can be considered that since the difference in the kinds of the central anions (X) do not significantly affect the binding energy between surface Ag and the ligands, the two X@Ag54 clusters showed similar stability against the three factors tested in the above experiments. |
6772757f6dde43c908c5bc64 | 19 | Figure shows the PL spectra of X@Ag54 in toluene under an Ar atmosphere. To obtain strong PL, the excitation wavelength was set to 405 nm. Both cluster solutions exhibited a broad PL peak at approximately 610 nm (Figure ). Recent studies have shown that the PL of metal clusters consisting of a large number of metal atoms entails photoexcitation to generate a dark excited singlet state, which subsequently undergoes intersystem crossing (ISC) to a bright excited triplet state, resulting in phosphorescence. Because X@Ag54 also comprised a large number of metal atoms, the observed emission of X@Ag54 is likely phosphorescence. In fact, the estimated radiative lifetime of X@Ag54 was on the order of tens to hundreds of microseconds (Table ), which is significantly longer than that of fluorescent materials (β€ 1 Β΅s). The photoluminescence quantum yield (Ξ¦PL) of X@Ag54 was evaluated using a relative method, revealing that the Ξ¦PL of I@Ag54 was approximately 16 times greater than that of S@Ag54 (Table ). Because there was no significant difference in the symmetry of the geometries of the two X@Ag54 clusters, the difference in Ξ¦PL did not arise from symmetry breaking. Figure 5. (A) CID-mass spectra of (a) S@Ag54 and (b) I@Ag54 as a function of collision energy. CE indicates the collision energy. (B) Survival yield obtained from CID profiles of X@Ag54 (Figure ). Details for calculating the survival yield are provided in the Supporting Information (Section S1.8). (C) CID process of X@Ag54. However, 1) the two X@Ag54 clusters differs in the type of anion present in their internal cavities, and 2) Ξ¦PL increases with increasing atomic number of encapsulated anion. Introducing heavy halogens (heavy atoms) into aromatic dyes, such as acene-based compounds, enhances ISC from the excited singlet to the excited triplet state owing to the heavy atom effect, which increases the radiative rate constant (kr) and, consequently, Ξ¦PL. In the present system, a similar effect likely occurred for I@Ag54 to exhibit photoluminescence with high Ξ¦PL. |
6772757f6dde43c908c5bc64 | 20 | To confirm the presence of an internal heavy-atom effect, the PL decay curves of X@Ag54 in deuterated toluene were evaluated using the time-correlated single-photon counting method (Figure ). The obtained decay curves were fitted with multiple exponential decays to determine the average photoluminescence lifetimes (ΟPL) of S@Ag54 and I@Ag54, which were 106.2 and 652.9 ns, respectively (Tables and). From this fitting, the radiative rate constants (kr) of I@Ag54 and S@Ag54 were estimated to be 1.9Γ10 3 and 4.8Γ10 4 s -1 , respectively (Table ). Therefore, when X changed from S 2-to I -, kr increased by approximately 25 times. This trend is similar to the enhancement of phosphorescent parameters through the heavy atom effect in conventional fluorescent dyes. Therefore, it can be interpreted that replacing S 2-with heavier I -as X in X@Ag54 accelerated ISC via the heavy atom effect, which increases the population of the bright triplet state and kr, thereby improving the Ξ¦PL of X@Ag54. |
6772757f6dde43c908c5bc64 | 21 | The non-radiative rate constant (knr) of I@Ag54 was approximately 1/6 of that of S@Ag54 (Table ). Because I -has a larger ionic radius than S 2-, it fills a greater volume of the cavity than S 2-, and thus I@Ag54 seems to have a more rigid framework than S@Ag54. In addition, the bond enthalpies of Ag-I and Ag-S bonds are 234 and 217 kJ mol -1 , respectively, indicating that the Ag-I bond has a slightly higher bond energy than the Ag-S bond. These factors seems to accelerate the vibrational relaxation of I@Ag54 compared with that of S@Ag54, thereby reducing the non-radiative rate constant of I@Ag54 to approximately 1/6 of that of S@Ag54. |
6772757f6dde43c908c5bc64 | 22 | Finally, we discuss about the optical absorption of S@Ag54 and I@Ag54 (Figure ). Both spectra exhibited shoulder-like absorptions around 400 and 550 nm, and their overall optical absorption spectra were quite similar each other. However, upon closer inspection, the spectrum of I@Ag54 contained a more distinct shoulder-like peak at approximately 500 nm compared with the spectrum of S@Ag54. The heavy atom effect increases the oscillator strength of the spin-forbidden transition from the ground state to the triplet excited state (S0βT1), leading to the S-T absorption peak in the absorption spectrum. In fact, in the optical absorption spectrum of some ligand-protected metal clusters, absorption peak attributable to S-T transition appears with a relatively high oscillator strength at a slightly longer wavelength than the peak attributed to S0βSn transition. Therefore, we predict that the shoulder peak at approximately 500 nm in the optical absorption spectrum of X@Ag54 is derived from S-T absorption, which is promoted by the heavy atom effect (Figure ). |
6772757f6dde43c908c5bc64 | 23 | In this study, we successfully synthesized a pair of X@Ag54 clusters (X = S or I) protected by two types of ligands, thiolate and sulfonate, by adding Ag + and a catalytic amount of Cu 2+ to the reaction system. No significant difference was observed between the two X@Ag54 clusters (X = S or I) in terms of geometric structure and stability against degradation. However, notable differences were observed in their PL and optical absorption. We concluded that the differences in their optical properties are derived from the heavy atom effect. This effect enhances the oscillator strength of transitions from the spin-forbidden excited singlet state to the triplet excited state, as well as transitions from the ground singlet state to the triplet excited state. This study clearly demonstrated that incorporating heavy atoms into Ag-S clusters significantly enhances their phosphorescence quantum yield, similar to organic fluorescent dyes. These findings are expected to provide clear design guidelines for developing metal clusters as room-temperature phosphorescent materials and triplet sensitizers. |
6704530012ff75c3a1c36ad8 | 0 | Multiconfiguration nonclassical-energy functional theory (MC-NEFT) 1,2,3 is a low-cost and high-accuracy electronic structure method to recover dynamic correlations in inherently multiconfigurational species. In MC-NEFT, one starts with a multiconfigurational wave function, usually a multiconfiguration self-consistent-field (MCSCF) wave function, such as a complete active space self-consistent field (CASSCF) wave function, 4 that recovers the static correlation and typically a small portion of the dynamic correlation. Then, a nonclassical energy functional is used to calculate the energy from some properties of the multiconfigurational wave function. The use of a nonclassical energy functional greatly reduces the computational cost compared to traditional post-CASSCF methods such as second-order complete active space perturbation theory (CASPT2), multireference MΓΈller-Plesset perturbation theory, or multireference configuration interaction while having comparable or better accuracy in terms of bond dissociation energy, reaction barrier height, excitation energies, or other chemical properties. In recent years, we and coworkers have developed various versions of MC-NEFT, including multiconfiguration pair-density functional theory (MC-PDFT), multiconfiguration density-coherence functional theory (MC-DCFT), and multiconfiguration data-driven functional methods (MC-DDFMs), including hybrid versions of MC-PDFT and MC-DCFT. The ultimate goal of these theories is to achieve chemical accuracy at a cost that is affordable even for complex systems. |
6704530012ff75c3a1c36ad8 | 1 | MC-DCFT is the most recently developed version of MC-NEFT. It is motivated by the relationship of the off-diagonal elements of the one-body reduced density matrix (1-RDM) to multiconfigurational effects in electronic wave functions, and it has an advantage of only using the 1-RDM in the nonclassical energy functional, which in the context of MC-DCFT is called the density coherence (DC) functional. In contrast, the two-body reduced density matrix (2-RDM) is needed in the nonclassical energy functional of MC-PDFT. The reason why one uses the 1-RDM is that it has a physical relation to the number of unpaired electrons, but we should keep in mind that the number of unpaired electrons is an interpretive quantity that has no unique definition, which will be an important consideration in the present work. The use of only the 1-RDM not only improves the physical interpretation and reduces the computational cost, but also it simplifies the development of the theory, making it easier to extend to more complex calculations. In the present article, we present a new functional form for the DC functional and parameterize a hybrid DC functional against the same database of bond dissociation energies and reaction barrier heights as used for our previous hybrid DC functional. The new functional will be called DC24. The new functional form improves both the accuracy and the physical interpretability of the functional. |
6704530012ff75c3a1c36ad8 | 2 | The total electronic energy of hybrid MC-DCFT (HMC-DCFT) has the following form: πΈπΈ HMC-DCFT = πΈπΈ class + πππΈπΈ MC,XC + (1 -ππ)πΈπΈ DC (1) where πΈπΈ class is the classical energy from the multiconfigurational wave function, πΈπΈ MC,XC is the MCSCF exchange-correlation energy, πΈπΈ DC the nonclassical energy calculated from a DC functional, and ππ is a parameter. Details of πΈπΈ class and πΈπΈ MC,XC are given in our earlier papers on MC-DCFT; here it suffices to note that πΈπΈ class is the sum of the MCSCF kinetic energy, electron-nuclear attraction, and classical Coulomb interaction of the electronic charge distribution, and πΈπΈ MC,XC is defined such that the sum of πΈπΈ class and πΈπΈ MC,XC is the original CASSCF energy evaluated by the wave function variational principle. Next, we explain πΈπΈ DC . |
6704530012ff75c3a1c36ad8 | 3 | one may encounter points in space where ππ οΏ½ ππ (π«π«) < 0 if some of the natural orbitals have occupation numbers 0 < ππ ππ < 1. A negative effective density is not physical, and it can produce spurious results. To tackle this issue in our earlier versions of DC functionals, we set ππ οΏ½ ππ (π«π«) and β π«π« ππ οΏ½ ππ (π«π«) to zero for quadrature points r where ππ οΏ½ ππ (π«π«) < 0: |
6704530012ff75c3a1c36ad8 | 4 | This gives derivative discontinuities at points where ππ οΏ½ ππ passes through zero. While the earlier versions of DC functionals work reasonably well on a wide range of systems, the derivative discontinuities are unsatisfactory. We therefore experimented with alternative ways to define the unpaired density π·π·(π«π«) and the effective spin densities ππ οΏ½ ππ (π«π«) and ππ οΏ½ ππ (π«π«), and we present an improved scheme in this report. |
6704530012ff75c3a1c36ad8 | 5 | Then ππ οΏ½ ππ (π«π«) is defined according to eq 9 using the newly defined ππ οΏ½ ππ (π«π«). Note that eq 10 can be expanded in a series by Equation 11 agrees with eq 9 through the leading two terms in a Taylor series of the exponential, but it has continuous derivatives and is always non-negative; this is the motivation for using eq 10. |
6704530012ff75c3a1c36ad8 | 6 | In new methods 3 and 4, we use the same method as the original MC-DCFT to convert ππ(π«π«) and π·π·(π«π«) into ππ οΏ½ ππ (π«π«) and ππ οΏ½ ππ (π«π«), but we use alternative definitions of π·π·(π«π«) by taking advantage of the fact that eq 6 for the effective number of unpaired electrons is not unique. The effective number of unpaired electrons can be defined in various ways; by changing the definition of ππ(ππ), we are able to construct alternative definitions of π·π·(π«π«). |
6704530012ff75c3a1c36ad8 | 7 | New method 3: In this method, the effective number of unpaired electrons is defined by ππ(ππ) = min(ππ, 2 -ππ) (12) and ππ οΏ½ ππ (π«π«), ππ οΏ½ ππ (π«π«), and π·π·(π«π«) are defined according to eqs 2, 3, and 5 using the newly defined ππ(ππ) in eq 12. The definition of π·π·(π«π«) according to eqs 5 and 12 is equivalent to using the unpaired electron density matrix ππ of Head-Gordon. Equation 12 maintains the desirable property that a natural orbital occupancy of one indicates there is exactly one unpaired electron in the orbital. |
6704530012ff75c3a1c36ad8 | 8 | Figure compares ππ(ππ) of the original method and method 3. Since ππ(ππ) β€ ππ for ππ(ππ) under this definition, contribution of π·π·(π«π«) from each natural orbital will always be less or equal to that of ππ(π«π«). This makes π·π·(π«π«) β€ ππ(π«π«) for all points in space. However, this definition of ππ(ππ) gives discontinuities at points where ππ = 1. Generally, the potential energy surface and wave function coefficients are smooth functions (i.e. functions with continuous first derivative) of the nuclear coordinates, except at conical intersections. Because the natural orbital occupation number is a function of the nuclear coordinates, by applying the chain rule, one can show that a non-smooth ππ(ππ) can result in non-smooth wave function coefficients, and further result in nonsmooth potential energy surface. Because non-smooth ππ(ππ) may appear in regions that are not conical intersections, method 3 may lead to unphysical non-smooth potential energy surfaces. An example of where the f(n) of method 3 leads to a non-smooth potential energy surface is any trajectory path along which one of the natural orbital occupation number passes through 1. Method 4 modifies the effective number of unpaired electrons such that we obtain a smooth DC functional. |
6704530012ff75c3a1c36ad8 | 9 | Again, ππ οΏ½ ππ (π«π«), ππ οΏ½ ππ (π«π«), and π·π·(π«π«) are defined according to eqs 2, 3, and 5 using the newly defined ππ(ππ) in eq 13. New method 4 is an improvement to new method 3 to remove the discontinuity at ππ = 1. Here we simply mention two key points: (i) Equation 13 is a hyperbola that satisfies ππ(ππ) β€ min(ππ, 2 -ππ), which also makes π·π·(π«π«) β€ ππ(π«π«) for all points in space. (ii) Equation 13 has one adjustable parameter, which it is convenient to take as ππ because this is the value of ππ(ππ) at n = 1; if one sets ππ = 1, method 4 reduces to method 3. Below we will discuss the effect of the choice of ππ on the performance of the DC functional. With some trial and error, we determined that ππ = 0.96 is the most appropriate value for practical calculations in terms of accuracy and physical interpretation. |
6704530012ff75c3a1c36ad8 | 10 | Figure compares ππ(ππ) of new method 4 with ππ = 0.96 to ππ(ππ) of new method 3, and Figure compares ππ(ππ) of new method 4 with various ππ values. As ππ increases, the shape of ππ(ππ) becomes closer to that of method 3. When ππ = 0.96, the shape is almost identical to that of method 3. As ππ continue to approach 1, a perhaps-unwelcome consequence of this improvement in shape starts to occur; the gradient of ππ(ππ) changes more rapidly at ππ = 1. In the limit of ππ = 1, ππ(ππ) of method 4 would become identical to that of method 3, with a discontinuous derivative at ππ = 1. We wish to avoid discontinuous or very large derivatives because they could cause numerical problems. It is also interesting to consider the small-n behavior of eq 13. One can easily show that |
6704530012ff75c3a1c36ad8 | 11 | To test the performance of DC functionals constructed using the four methods above, we parametrized hybrid DC functionals based on the HCTH functional. We used the same procedure and the same multireference database as used to parameterize the rcHCTHh functional in our previous work. The multireference database consists of 59 bond energies and 60 reaction barrier heights calculated from CASSCF wave functions using an automatic active space selection scheme. The ma-TZVP basis set is used for all calculations. The CASSCF calculations were performed in Molpro or OpenMolcas. A Python module based on PySCF and Libxc 44 was used to perform MC-DCFT calculations. All MC-DCFT calculations are performed with a grid with 99 radial shells and 590 angular points per shell. The parameters in the DC functionals are optimized using a Python program based on PyTorch, Numpy, and Pandas. The accuracy of each functional is characterized by the mean unsigned error (MUE) of the predicted bond energies and reaction barrier heights. The MUE is calculated using all 119 data points, as in our previous work. Note that we used a slightly different grid as compared to our previous work. We therefore reparametrize the rcHCTHh functional using the new grid and label it as "original". |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.