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623497af13d4787e8992f7fb | 15 | h ω = 4.75 eV and (bottom) hω = 4.75 -0.45i eV with λ z = 0.0125 atomic units. We see evidence of strong coupling via splitting of the surfaces where the |X, 1 and |A, 0 states are resonant, when the photon energy is pure real, and we see the splitting vanish when the imaginary part of the photon energy is large compared to the interaction energy. |
623497af13d4787e8992f7fb | 16 | The two lowest-lying excited states of the NH-CQED-CIS with both photon frequency values are plotted as a function of bondlength for values between 1.3 and 2.7 Angstroms with increments of 0.1 Angstroms (see Ref. 53) in Figure . In addition to computing these polariton surfaces at the NH-CQED-CIS/cc-pVDZ level, we compute these polaritonic surfaces at the same values of the MgH+ bondlength R using a model 3-level Hamiltonian: |
623497af13d4787e8992f7fb | 17 | In Eq. 14, E X ( µ X ) and E A ( µ A ) denote the ground-state and first singlet excited-state energies (dipole moments), respectively, and µ XA denotes the transition dipole moment between state X and A. The ground-state energies and dipole moments for each value of R are calculated at the RHF/cc-pVDZ level and the excited-state energies, dipole moments, and transition dipole moments are calculated at the CIS/cc-pVDZ level (see Ref. 53). The polaritonic surfaces obtained from diagonalizing Eq. ( ) are referred to as the 'Model LP' and 'Model UP' surfaces in Figure . We see with a pure real photon energy, the |LP and |UP surfaces experience a strong splitting in the region where the |X, 1 state (the ground-state plus a photon) crosses the |A, 0 state (the first excited-state without a photon). It should be noted that the NH-CQED-CIS curves are typically slightly stabilized compared to the Model LP and UP curves. We have already seen that the CQED-RHF method can provide orbital relaxation in the presence of cavity coupling that would not be available to the Model LP and UP solutions, and the NH-CQED-CIS wavefunction also includes additional variational flexibility through the excitations coupled through the Ĥdse and Ĥep terms. It is interesting to consider when such deviations between the NH-CQED-CIS and simpler model Hamiltonian's arise; we explore this question with the MgH+ system as a function of fundamental coupling strength λ in Appendix C.. For a strongly dissipative photon, we see that both the model and CQED-CIS curves closely approximate the CIS curves for the lone molecules, which signals that this system is not in the strong-coupling regime. The loss of strong coupling in this case arises because the dissipative energy scale of the photon is significant compared to the interaction energy scale between the photon and the molecular transition . This echos a fundamental condition for strong coupling that the interaction strength g must be large compared to the dissipation energy scale hγ, specifically g > h γ 4 . If this condition is not satisfied, then the energy splitting between the interacting states vanishes. The imaginary part of the frequency giving rise to the curves shown in the bottom panel of Figure was specifically chosen so that g < h γ 4 , leading to the vanishing of the splitting that is observed in the top panel of Figure . As a final illustrative example, we examine the ground-state photon population of the MgH+ system for coupling strengths approaching the ultra-strong coupling regime, defined when the coupling energy scale is commensurate with the bare excitations in the system, e.g. g ≈ Re( ω). We define the groundstate photon occupation as |
623497af13d4787e8992f7fb | 18 | where the c coefficients are taken from the lowest root of the NH-CQED-CIS Hamiltonian matrix. We see an approximate quadratic dependence of the photon occupation in the ground-state as a function of relative coupling strengths independent of dissipa- . Photon occupations of the NH-CQED-CIS/cc-pVDZ groundstate of MgH+ at a bondlength of 2.2 Angstroms as a function of the relative coupling energy scale, g/Re( ω), and the dissipation energy scale γ. In this case, g ≈ ω 2 λ z µ z for MgH+ where λ z = 0.0125 atomic units, Re(h ω) = 4.75 eV. We see approximate quadratic scaling of the photon occupation with the relative coupling strength in the ground-state at all loss rates, in agreement with the analytical findings discussed in Ref. 6. tion energy scale (see Figure ). The results of this analysis agrees qualitatively with the analytical analysis of the groundstate populations of the ground-state wavefunctions of dissipative systems in the ultra-strong coupling regime by De Liberato in Ref. 6. An important point raised by this work is that features associated with the ultra-strong coupling regime (e.g. virtual photon occupation in the ground-state) persist even in the presence of very strong dissipation that would obscure the effects normally associated with strong-coupling (e.g. Rabi splitting) . Similar to our analysis illustrated in Figure , the exact analysis also showed photon occupation of the ground-state wavefunction increases quadratically with the relative coupling strength, where the relative coupling strength is defined as g/Re( ω), where g relates to the coupling energy scale. To determine if our NH-CQED-CIS obeys this scaling relationship for the photon occupation of the groundstate, we compute the photon occupations for the ground-state of MgH+ computed at the NH-CQED-CIS/cc-pVDZ level of theory with bondlength fixed at r = 2.2 Angstroms for relative coupling strengths g/Re( ω) in a range of values between 0 and 0.5, where in our case g ≈ ω 2 λ z µ z , where Re(h ω) = 4.75 eV throughout (resonant with the |X → |A transition at this geometry, λ z = 0.0125 atomic units, λ z ≈ 2.2 atomic units, and Im(h ω) is chosen relative to g. We emphasize this analysis involves coupling strengths that are much larger than those realized in any experiments we are aware of with molecular systems, and serve purely to analyze the behavior of our approximate NH-CQED-CIS method compared to the exact analysis provided in Ref. 6. |
623497af13d4787e8992f7fb | 19 | We combined ab initio molecular electronic Hamiltonians with a cavity quantum electrodynamics model for dissipative photonic modes and applied mean-field theories to the ground-and excited-states of resulting polaritonic systems. In particular, we developed a non-Hermitian configuration interaction singles theory for mean-field ground-and excitedstates of the molecular system strongly interacting with a photonic mode, and applied these methods to elucidating the phenomenology of paradigmatic polaritonic systems including the ground-state polaritonic structure of formaldehyde coupled to cavity modes that were shown to modify the symmetry of the ground-state wavefunction, and the polaritonic potential energy surfaces of the magnesium hydride ion coupled to a lossy photonic mode. A reference implementation of this method and the CQED-RHF method was realized using the Psi4Numpy framework which can be accessed using links provided within the text. |
623497af13d4787e8992f7fb | 20 | The orbital basis and reference determinant utilized in the NH-CQED-CIS theory results from solving the CQED-RHF equations. We start with a Hermitian version of Eq. 1 that utilizes a pure real value of ω, and following Ref. 26 and 29, we introduce a product wavefunction between an electronic Slater determinant (which in practice may be initialized using a canonical RHF wavefunction) and a zero-photon number state, |
623497af13d4787e8992f7fb | 21 | where we see that the terms involving Ĥp and Ĥep vanish, and the expectation value of Ĥe is analogous to the ordinary RHF energy. To evaluate the expectation value of Ĥdse , we can first expand Ĥdse in terms of the dipole operator (with electronic and nuclear contributions) and dipole expectation values as follows: |
623497af13d4787e8992f7fb | 22 | In the above expansion of Ĥdse we have specifically indicated that the product of electronic dipole operators contains 2electron contributions when i = j, and 1-electron quadrupole contributions when i = j. The quadrupole contributions arise from the fact that μξ (x i ) μξ (x i ) = -Qξξ (x i ). Furthermore, a one-electron term arises that contains the electronic dipole operator scaled by λ • µ nucλ • µ , where again µ will be iteratively updated during the CQED-RHF procedure. |
623497af13d4787e8992f7fb | 23 | Given the modifications to the polaritonic potential energy surfaces observed in Figure in the main text, it is interesting to consider if the ground-state potential energy surfaces can also be modified. While such modifications would be discernible from ground-state ab initio polaritonic structure methods, we suspect the onset would not be observed until the onset of ultra-strong coupling and perhaps still under special conditions like the field polarization being oriented relative to a permanent dipole moment in particular ways. Here we consider only the case of the equilibrium geometry of the ground-state of MgH+ computed at the RHF/cc-pVDZ, CQED-RHF/cc-pVDZ, and CQED-CIS/cc-pVDZ levels of theory with the same coupling parameters considered in the main text for this system, namely hω = 4.75 eV and λ = (0, 0, 0.0125 atomic units. The potential energy curves from each of these methods is shown in Figure , and we find from numerical location of the minima that the equilibrium bondlength predicted by all levels of theory is approximately 1.65 Angstroms. |
623497af13d4787e8992f7fb | 24 | In Figure of the text, we see deviations between the polaritonic surfaces computed by the NH-CQED-CIS/cc-pVDZ method and those computed by a simpler 3x3 model Hamiltonian that is parameterized by CIS/cc-pVDZ calculations of MgH+. In Figure , we explore the eigenvalues of these two approaches for the lower-and upper-polariton surfaces of MgH+ with bondlength fixed at 2.2 Angstroms coupled to a photon with energy 4.75 eV with variable values of λ z between 0 and 0.025 atomic units, which is approximately twice the value considered in Figure . We see that deviations between the model Hamiltonian and the NH-CQED-CIS results become evident when the fundamental coupling strength λ has a magnitude between 0.01 and 0.015 atomic units, which is in the range of values we considered for Figure in the main text, and that is also in line with experimentally-realized coupling strengths reported in Ref. |
676a0ce6fa469535b999990a | 0 | Crystal polymorphism, the existence of different crystal structures for the same chemical compound, is a common phenomenon in chemistry. Many compounds are known to form multiple polymorphs depending on the crystallization conditions. Different polymorphs can have different physical and chemical properties, such as density, melting point, hardness, color, stability, morphology, solubility, and bioavailability. Therefore, crystal polymorphism is an important and fascinating aspect of solid state chemistry with implications for various fields including pharmaceuticals, materials science (e.g., energetic materials, dyes and pigments, and organic electronics), and agriculture. Late-appearing polymorphs are crystalline forms that emerge unexpectedly after a long period of time or under altered production conditions. Such forms may lead to the inability to obtain a crystal form that was previously prepared for pharmaceutical or other applications, thus necessitate the redesign of the production process. They can alter the solubility, bioavailability, stability, and dissolution rate of the API, significantly impacting the quality, efficacy, and safety of pharmaceutical products. The pharmaceutical industry has suffered a few disastrous issues due to late-appearing polymorphs, leading to patent disputes, regulatory issues, and even market recalls, including the famous cases of ritonavir, rotigotine, 4 and many others. Therefore, it is crucial to identify and characterize all possible polymorphs of a given API and understand the factors that influence their formation and transformation. |
676a0ce6fa469535b999990a | 1 | The conventional process for designing a clinical formulation of a small molecule drug typically begins with experimental polymorph screening and scale-up studies. This process aims to identify and characterize the different polymorphs of the active pharmaceutical ingredient (API) and to select the most suitable one for development. However, this process can be time consuming and may miss some important low energy polymorphs due to the inability to exhaust all crystallization conditions. As such, inexhaustive polymorph screening poses serious challenges for drug development and manufacturing. |
676a0ce6fa469535b999990a | 2 | Computational polymorph prediction can complement experiments to de-risk unexpected polymorphic changes during drug development. Unlike experiments, computational methods, in principle, can enable identification of all low energy polymorphs of the API, including those that may not be easily accessible by conventional experimental methods, or that may only appear under specific isolation conditions. This can help avert discovery of new polymorphs in late stage development that could potentially affect the quality, efficacy, and safety of the drug product. Motivated by the crystal structure prediction (CSP) blind test challenge organized by CCDC, the field of computational polymorph prediction has made large leaps in the past two decades. Several studies have demonstrated the ability of computational methods to accurately predict the crystal structures of small molecules, including flexible molecules of comparable complexity to typical modern small molecule drugs. These studies have provided valuable insights and examples for the field of computational polymorph screening. However, most of these previous CSP studies have only investigated a small number of molecules to demonstrate the potential of such calculations. A large-scale validation of the proposed methods for general small molecule crystal structure prediction has yet to be reported. |
676a0ce6fa469535b999990a | 3 | In this paper, we report a novel crystal structure prediction method and demonstrate its accuracy on a large set of diverse molecules. The method integrates a novel systematic approach to search the crystal packing parameters and a hierarchical energy ranking method that balances accuracy and cost (Figure ). The new packing search method uses a divide-and-conquer strategy to break down the parameter space into subspaces based on space group symmetries. Each subspace is then searched consecutively. The energy ranking method combines molecular dynamics (MD) simulations using a classical force field (FF), structure optimization and reranking using a machine learning force field (MLFF) with long range electrostatic and dispersion interactions, and periodic density functional theory (DFT) calculations for ranking the final shortlist. The temperaturedependent stability of different polymorphs is evaluated with free energy calculations using previously established methods. Currently focused on searching crystal structures with one molecule in the asymmetric unit (ASU), corresponding to the Z'=1 search space, the method was validated on a large set of 66 molecules with 137 unique crystal structures, including all relevant molecules from the first six CCDC CSP blind tests, Target XXXI from the seventh blind test, other molecules studied by previous CSP methods, and several molecules from modern drug discovery programs. For all the molecules in this large test set, the experimentally known polymorphs are correctly predicted by our method and are ranked among the top candidate structures. For several molecules, our prediction suggests new low energy polymorphs yet to be discovered by experiment, implying potential risks that could jeopardize the development of the currently known forms of these compounds. Comparisons to the results of other computational approaches are made when feasible. |
676a0ce6fa469535b999990a | 4 | A comprehensive set of molecules for CSP method validation was compiled. The dataset is divided into three tiers following definitions established by previous CCDC CSP blind tests. The first tier consists of mostly rigid molecules up to 30 atoms. The second tier consists of small druglike molecules with around two to four rotatable bonds, and up to approximately 40 atoms. The third tier is composed of large drug-like molecules with five to ten rotatable bonds, usually containing 50 to 60 atoms. Additional tiers will be defined in the future as the complexity of CSP targets increase. The entire collection of test molecules is shown in Figure . |
676a0ce6fa469535b999990a | 5 | The dataset construction began by including all of the Z'=1 cases from the first six CCDC CSP blind tests with a few exceptions. The excluded molecules were either not drug-like or contained elements not supported by the pretrained MLFF, the charge recursive neural network (QRNN). These were Target IX, which contains iodine and resembles an organic semiconductor, and Target III, which contains boron. Targets V and VIII were able to be included by replacing bromine atoms with chlorine, for the purposes of QRNN, which were then replaced back with bromine for DFT ranking. A total of 17 molecules from the first six CCDC CSP blind tests were included. |
676a0ce6fa469535b999990a | 6 | The dataset was further enriched by molecules with previously published CSP and experimental results with relevance to small-molecule pharmaceuticals. The final dataset, comprising 66 molecules, covers a diversity of functional groups, including polar groups such as amide, urea, pyridine, sulfonamide, hydroxyl, nitro, carboxylate, cyano, nonpolar groups such as phenyl and alkane chains, and various substituted aromatic and nonaromatic rings. The functional group diversity present in the dataset requires high accuracy of the energy models across chemical space, particularly as it applies to intra-and inter-molecular interactions relevant for molecular crystal packing. |
676a0ce6fa469535b999990a | 7 | The experimental crystal structures for the molecular crystal polymorphs were obtained from the CSD 10 with a few exceptions when the crystal structure data only existed in literature, such as Form D of Cimetidine. When multiple data entries exist for a polymorph in the CSD, the most reliable one was selected. The preference was as follows: neutron diffraction studies, followed by low temperature single-crystal X-ray diffraction (XRD), and room temperature powder X-ray diffraction (PXRD) studies were considered the least reliable. When all other experimental conditions were equal across multiple entries, the crystal structure with the smallest R-factor was used. |
676a0ce6fa469535b999990a | 8 | For the 33 molecules with one target crystalline form, Figure (a) shows the final rankings of the predicted crystal structures that best match the known experimental structures using the r 2 SCAN-D3 functional. In all cases, a predicted structure with RMSDN (RMSD of a spherical cluster of N molecules following the CSD standard) better than 0.50 Å for a cluster of at least 25 molecules was sampled and ranked among the top 10 of the predicted structures. For 26 out of the 33 molecules, the best match candidate structures was ranked among the top 2. |
676a0ce6fa469535b999990a | 9 | Upon careful inspection of the top ranked predicted candidate structures, we found that some of them adopt very similar conformers and packing patterns. These structures correspond to different local minima of the quantum chemical potential energy surface at 0K, but may interconvert at room temperature since the corresponding energy barriers might be comparable to thermal fluctuation. This could be related to disordered structures and has been proposed to be one of the common reasons for the well known over-prediction problem in CSP calculations. To remove this type of non-trivial duplicate from the static landscapes, we clustered similar structures (with RMSD15 better than 1.2 Å) into a single representative structure with the lowest energy among the cluster, similar to what has been done in earlier studies. The rankings of the best matched structures after clustering are shown in Figure (a) (red bars). This improved the rankings, for example, for MK-8876, Target V, and naproxen. Figure 3(b) shows the relative energy between the candidate structure that best matches the experimental structure and the lowest energy predicted structure for each molecule in the subset of molecules with only a single experimentally known crystal structure. The blue and red bars show the results before and after clustering analysis. For most molecules, the known experimental structure corresponds to the lowest energy predicted structure using the r 2 SCAN-D3 functional, thus the relative energy is zero. For a few molecules, the relative energy is less than 0.5 kcal/mol, which is likely within the error bars of the DFT calculations. However, in two systems we observe candidate structures with significantly lower energies (1 kcal/mol) than any experimentally observed polymorph. These two molecules are GSK268499B and MK-8876. Such low energy structures indicate the possibility for stable polymorphs that are yet to be discovered by experiment. A detailed analysis for these molecules will be presented in the following section. |
676a0ce6fa469535b999990a | 10 | For molecules with multiple known experimental structures, Figure (a) and 4(b) show the rankings and relative energies of the predicted candidate structures best matching the corresponding known experimental structures after clustering. In all cases, the known experimental structures were sampled and ranked well. 80% of the candidate structures matching known experimental structures were ranked among the top 10 of the predictions with relative energies less than 1.0 kcal/mol as compared to the lowest energy predicted structures. Among this subset of molecules with multiple known experimental structures, the energy gap between the most stable known polymorph and the lowest energy predicted structure is only about 0.5 kcal/mol, which indicates that extensive experimental screening might have already identified the most stable polymorphs for these molecules. |
676a0ce6fa469535b999990a | 11 | The CSP generated energy landscape of cocaine is shown in Figure (a). The predicted structure with the lowest energy matches the experimental structure (CSD refcode COCAIN10) with a RMSD25 of 0.07 Å. Its energy is around 0.8 kcal/mol lower than the second lowest energy predicted structure using PBE-D3, which is in agreement with previously reported energy landscapes using the PBE-D functional. However, the energy gap between the known experimental structure and second lowest energy candidate structures reduces to 0.3 kcal/mol using r 2 SCAN-D3, indicating possible limitations in PBE-D3 for the purpose of high accuracy ranking. A few benchmark studies have shown that r 2 SCAN-D3 describes the energy and structure in a variety of chemical environments more accurately than PBE-D3, in particular, for hydrogen bonding and dispersion interactions that are typically present in organic molecular crystals. The top 7 predicted structures, which are within the lowest 1.8 kcal/mol energy window from our calculations, match those from a previous study within a RMSD25 of 0.2 Å. The energy gap between the known experimental structure and other top candidate structures is further increased when using the PBE0-MBD functional (Figure (e)), often considered as a more reliable method for calculating crystal lattice energies according to prior studies. The relative stabilities of the top predicted structures vary slightly as a function of temperature, but the experimental form remains the most stable at all temperatures (Figure (a) in SI). This further indicates the low likelihood of observing any additional more stable Z'=1 polymorph of cocaine. Such a CSP landscape, with the global minimum separated by about 1.0 kcal/mol from all other candidate structures, is uncommon in our experience. Most drug-like molecules we have studied have many predicted structures within 1.0 kcal/mol of the global minimum using accurate periodic DFT. |
676a0ce6fa469535b999990a | 12 | MK-2022, a GPR119 agonist, was developed by Merck & Co., Inc. for potential applications in metabolic diseases, including type-2 diabetes. A recent study used the GRACE software to predict the crystal polymorphs of this molecule and compared the prediction results with experiments. The GRACE software correctly identified a candidate structure (ranked 6 th with around 1.0 kcal/mol higher energy compared to the global minimum) matching the experimentally known polymorph for MK-2022. Our calculations also correctly predicted this experimental structure, with the lowest energy predicted structure matching experiment with an RMSD25 of 0.23 Å (Figure ). The relative stabilities of the top 5 predicted structures vary slightly as a function of temperature (Figure (h) in SI), though the rank II predicted structure has slightly lower free energy than the experimental structure at room temperature. |
676a0ce6fa469535b999990a | 13 | Olanzapine is used as an atypical antipsychotic agent for the treatment of bipolar disorder and schizophrenia. Despite having only one rotatable bond, it exhibits a high degree of polymorphism in its solid state, giving rise to about 60 known distinct solid forms including four anhydrous polymorphs, 56 crystalline solvates, and an amorphous phase. Here, we focus on the four Z'=1 anhydrous forms. Among them, only three forms I, II, and IV have been characterized as single crystals, whereas form III was concomitantly found with form II. Form III was identified by comparing the PXRD patterns of form II and a mixed phase crystal of forms II and III. The presence of form III was also detected in a combined solid state NMR and CSP study, where a CSP generated structure in the Pbca space group was identified to possess the spectra characteristics of form III. We will refer to this structure as form III* in the following discussion. |
676a0ce6fa469535b999990a | 14 | From our CSP calculations, candidate structures matching well with published structures for forms I, II and IV (RMSD26 of 0.04, 0.13 and 0.20 Å in reference to CSD structures UNOGIN03, UNOGIN04 and UNOGIN05) are sampled and ranked among the top 5 of the candidate list (Figure ). In agreement with the previous study, we find that forms I and IV are highly competitive in energy with an energy difference of only around 0.1 kcal/mol as obtained from using both the r 2 SCAN-D3 and the PBE0-MBD methods. In addition, the lattice parameters of one of the low-lying predicted structures in the Pbca space group (Rank 3) has very similar lattice parameters and structure (RMSD28 of 0.32 Å) as compared to form III* . The simulated PXRD data of our best match Pbca structure show many of the characteristic peaks which were assigned to form III (see Figure in SI). These comparisons indicate that the rank 3 predicted structure in the Pbca space group might be a putative structure of form III (Following the nomenclature in Ref. , we refer our best match Pbca structure as form III * in Figure ). |
676a0ce6fa469535b999990a | 15 | In addition to these four structures identified in earlier experimental and computational studies, our calculations also predicted a low-energy candidate structure in the P21/c space group (Rank 4 prediction). Both the putative form III* in the Pbca space group and the newly identified P21/c structure have identical 2D layers as the experimental form II, but the packing along the third dimension differs, similar to Aspirin's crystalline forms I and II. The simulated PXRD data of this P21/c structure matched better with the characteristic peaks assigned to experimental form III (Figure in SI). These results challenge the conclusion from Ref. that the experimentally observed form III corresponds to the Pbca structure, as it appears that our predicted P21/c candidate structure can better explain the experimental data. Furthermore, since the lattice parameters of the P21/c structure are very close to those of form II, it is more likely than form III* to grow together with form II. It is also possible that the experimentally observed form III might be a mixture of the predicted P21/c and Pbca candidate structures. GSK269984B GSK268499B, a drug candidate developed by GlaxoSmithKline, has been reported as an EP(1) receptor antagonist for the treatment of inflammatory pain. Previous studies combining experimental screening and CSP have concluded that form I is the most stable anhydrous crystal structure. Interestingly, form I does not possess strong intermolecular hydrogen bonding apart from intermolecular halogen bonds and pi-pi interactions, as shown in Figure (m). Instead, it contains intramolecular hydrogen bonds between the carboxylic acid proton and pyridine nitrogen. |
676a0ce6fa469535b999990a | 16 | A prior CSP study of GSK268499B predicted form I as the global minimum with other low-lying crystals possessing intermolecular hydrogen bonding. In that study, a mixed DFT intramolecular conformational energy and empirical intermolecular electrostatic and dispersion model was used to evaluate relative stability of candidate crystal structures. From our CSP calculations using accurate periodic DFT calculations, at 0K and without zero-point energies, the candidate structure matching the experimental form I (RMSD32 of 0.09 Å in reference to CSD structure BIFHOP) is ranked 9th (Figure (d)) using the r 2 SCAN-D3 method, more than 1.0 kcal/mol less stable compared to the lowest energy candidate structure. |
676a0ce6fa469535b999990a | 17 | The two lowest energy candidate structures, referred to as R1(P212121) and R2(𝑃 # ) (Figure (k) and 5(l)), both have the carboxylic acid in the cis-isomer conformation forming strong intermolecular hydrogen bonds with nearby molecules in the crystals. The intermolecular hydrogen bonding in R1(P212121) is between the carboxylic acid proton and the pyridine nitrogen from a nearby molecule, similar to the hydrogen bond networks in the rank 2 predicted structure from the prior study, whereas the R2(𝑃 # ) structure exhibits the typical bidentate hydrogen bonds between cis carboxylic acids existing in many other crystal structures with the same chemical group. Eleven molecules in our validation set contain a carboxylic acid group; among those, nine form a double hydrogen bond motif with the carboxylic acid of another molecule in at least one experimentally observed form. The remaining two cases are either zwitterionic (Gabapentin) or form another favorable double hydrogen bond involving the carboxylic acid and another polar chemical group (Ceftizoxime). All candidate structures within the 3.0 kcal/mol energy window have similar hydrogen bond networks in R1(P212121) and/or R2(𝑃 # ). |
676a0ce6fa469535b999990a | 18 | Although the experimental structure was predicted to have higher energy than a few other predicted structures at 0K, its relative stability improved substantially with increased temperature (Figure (c) in SI). At room temperature, the rank I predicted structure and the experimental structure have a free energy difference of about 0.3 kcal/mol while all other predicted structures have higher free energies. These results highlight the important role of entropy in accurately evaluating the relative stabilities of crystal structures at room temperature. |
676a0ce6fa469535b999990a | 19 | Summary of key results for a few other interesting molecules: ROY, Galunisertib, Rotigotine, MK-8876,LY-156735, Bicalutamide, XXIII, Axitinib and AZD8329, Target XXXI Among all the small organic molecules exhibiting multiple crystal polymorphs, ROY and Galunisertib have been shown to exhibit the largest number of fully characterized polymorphs. For ROY, twelve fully characterized crystal structures, Y, ON, R, OP, YN, ORP, YT04, Y04, R05, PO13, R18, and Y19, have been discovered. These polymorphs stem from a broad set of conformers responsible for their red, orange, and yellow colors. For Galunisertib, solid form screening experiments produced many solvates and ten anhydrous forms (form I -form X), with forms IV-VII found to be the most stable, having experimentally measured melting enthalpies within the margin of error of one another. Our approach correctly predicted all the known Z'=1 polymorphs for ROY and Galunisertib (Figure (a) and 6(b)). For ROY, the intramolecular torsion energies are known to be challenging for typical functionals used in periodic DFT and corrections to periodic DFT energies are needed to accurately rank order the relative stabilities of these polymorphs. The raw rankings from periodic DFT are shown in Figure with intramolecular torsion energy corrections discussed in Figure of SI. By incorporating conformer energy corrections using the ωB97X-D3/def2-TZVP functional, Y, R, YT04 and OP were correctly ranked to be the four most stable polymorphs at 0K matching experiments, although the relative stability between R and YT04 is the opposite compared to experiment by a very small energy difference. The relative stabilities changed slightly as a function of temperature but the energy gap remains small (Figure (d) in SI). |
676a0ce6fa469535b999990a | 20 | For Galunisertib, forms VIII, IX, X, were predicted to be more stable than forms V and VI according to the r 2 SCAN-D3 functional. Our second most stable candidate structure in the P212121 space group, is yet to be observed experimentally, and matches the structure reported as the global minimum in prior CSP landscapes. Using the conformer energy correction, the order of stabilities of the Z'=1 experimentally known forms remains largely unchanged (Figure ), in agreement with prior computed results. Adding room temperature free energy calculations (Figure (e) in SI) indicates that form VIII becomes less stable with increasing temperature and forms IX and X remain more stable than forms V and VI across the computed temperature range. |
676a0ce6fa469535b999990a | 21 | Rotigotine is a dopamine agonist for the treatment of Parkinson's disease and restless legs syndrome. The late appearing, more stable form II disrupted the clinical usage of its initial formulation of form I. A previous CSP study predicted another candidate structure in the P32 space group, referred to as form III in our discussion and in Figure (c), with stability between the experimentally known forms I and II. From our CSP calculations, all 3 forms are sampled and ranked well. Form II is correctly predicted to be about 2.0 kcal/mol (Figure (c)) lower in energy than form I according to the r 2 SCAN-D3 and the PBE0-MBD functionals, in agreement with the energy gap previously reported with PBE0-MBD (1.7 kcal/mol) and differential scanning calorimetry (DSC) measurements (1.8 kcal/mol). In addition to form III, we find another candidate crystal structure in the P212121 space group with stability comparable to form I. The additional P212121 crystal structure was also predicted in the prior study, although the relative energy by their computed method was slightly higher. Detailed structural and energetic comparison with the earlier CSP study is given in Figure & S9 of the SI. |
676a0ce6fa469535b999990a | 22 | The recent study by Merck & Co, Inc. also investigated the application of GRACE to predict the crystal structures of MK-8876, an HCV site NS5B site D inhibitor. The GRACE software failed in predicting the crystal structure for MK-8876 since the candidate structure matching the experimental form was ranked 2290th by the tailor-made force field and was dropped from the workflow. Our calculations correctly predicted the experimental structure, corresponding to rank 10 of the predicted structure (Figure ). The relative energy of the experimental structure of MK-8876 compared to the predicted global minimum varies between 0.1 to 1.5 kcal/mol with different DFT functionals (Figure ), and the gap increased slightly at room temperature (Figure (g) in SI), indicating the possibility for the existence of other polymorphs with competitive stability. This is in line with experimental evidence suggesting other metastable forms. LY156735, a potent and selective melatonin agonist (MA) investigated for the treatment of insomnia and circadian rhythm disorders, showed some unusual crystallization behavior among the R and S enantiomers. While the inactive enantiomer, S-MA, was found to crystallize in at least two anhydrous polymorphic forms (form 1 and 2), with form 2 about 0.7 kcal/mol more stable than form 1, the active enantiomer, R-MA, was found to crystallize only in form 1 despite extensive efforts. In addition, another racemate structure, form RS-MA, was also characterized in the prior work. A prior CSP study predicted form 2 to be more stable than form 1, with the racemate form in between. Our CSP calculations predicted all three forms and ranked them among the top ten lowest energy structures (Figure (e)). Form 2 is correctly predicted to be about 1.0 kcal/mol more stable than form 1 according to r 2 SCAN-D3 and PBE0-MBD functionals, with the energy of the racemate structure in between (Figure ). Interestingly, our calculations also suggested a few other competitive structures, some of which were also predicted in the prior study. A novel racemate candidate structure in the P21/c space group with different hydrogen bond networks was predicted to be the most stable form at 0K but became less stable at room temperature (Figure (i) in SI). These results indicate that the polymorphic landscape of this molecule is perhaps more complex than what is currently known experimentally. |
676a0ce6fa469535b999990a | 23 | Bicalutamide is an anti-androgen medication that is primarily used to treat prostate cancer. Extensive experimental studies have identified two Z'=1 forms, I and II, with form I found to be more stable. From our CSP calculations, candidate structures matching well with experimental structures for forms I and II (RMSD30 of 0.09 and 0.19 Å in reference to CSD structures JAYCES and JAYCES02) are sampled and ranked among the top 5 (Figure (f)). Form I is correctly predicted to be slightly more stable than form II according to r 2 SCAN-D3 although the relative ranking is sensitive to different DFT functionals due to the relatively small energy difference (Figure ). The relative stability between these two forms does not change significantly as a function of temperature (Figure (l) in SI). |
676a0ce6fa469535b999990a | 24 | The sixth CCDC blind test featured molecule XXIII submitted by Pfizer Inc. which was a former research compound aimed at treating Alzheimer's disease. Three Z'=1 forms (A, B, D) and two Z'=2 forms (C, E) have been experimentally characterized and their relative stabilities are strongly dependent on temperature. The thermodynamically most stable form changes over a small range of temperatures in the following way: form C below 253 K, form B in 273 -288 K, form A in 290 -294 K, and form D at 295 K and higher. Many CSP approaches in the sixth blind test predicted form B to be the most stable among the three Z'=1 polymorphs. From our CSP calculations, candidate structures that match well with published structures for the three Z'=1 forms A, B, D (RMSD30 of 0.39, 0.23, and 0.18 Å in reference to CSD structures XAFPAY, XAFPAY01, XAFPAY03, respectively) are sampled and ranked among the top 30. We find that PBE-D3 favors form B as the most stable structure, similar to previous findings, and that r 2 SCAN-D3 and PBE0-MBD favor a predicted P-1 crystal structure not discovered by experiment (Figure ). Our computed temperature dependent stabilities correctly predicted form D to be most stable above room temperature, with form A very similar in energy as compared to form D across the temperature range (Figure (j) in SI). |
676a0ce6fa469535b999990a | 25 | Pfizer's anticancer drug axitinib has 5 known neat polymorphs and 66 solvates to date. Form IV was initially targeted for development but more stable forms XXV and XLI were fortuitously discovered later during the manufacturing campaign. DSC and solubility experiments indicate the stability in this order: XLI > XXV, VI > IV > I, where the energy ordering of XXV compared to VI is uncertain. A previous CSP study ranked the relative stabilities among these forms incorrectly, with XLI predicted to have a 2.4 kcal/mol higher energy than form VI. From our CSP calculations, we correctly predicted all four Z'=1 experimentally known structures (RMSD29 within 0.13-0.29 Å in reference to CSD structures VUSDIX, VUSDIX03, VUSDIX04, VUSDIX06) among the top 20 candidate structures. Contrary to experiment, form VI was predicted to be more stable than form XLI according to the r2SCAN-D3 functional, but the energy difference decreased to within 0.2 kcal/mol using the PBE0-MBD functional. By incorporating conformer energy corrections using the ωB97X-D3/def2-TZVP functional in conjunction with r 2 SCAN-D3 crystal energies (referred to as r 2 SCAN-D3 + Δ ωB97X-D3 in Figure in SI), form XLI was correctly predicted to be the most stable form, matching experiment and a previous computational study. The temperature dependent free energy calculation indicates the stability of forms XLI and VI gets closer as temperature increases, with form XLI remaining more stable at temperatures below 200K (Fig. (m) in SI). |
676a0ce6fa469535b999990a | 26 | AZD8329 is a pharmaceutical compound under development for the potential treatment of metabolic disorders including type 2 diabetes. Among the seven known crystal forms, the Z'=1 forms I and IV have been chosen for development due to their suitable material properties. The two forms are enantiotopically related, with form IV more stable at ambient conditions and form I more stable at high-temperature. From our CSP calculations, candidate structures that match well with published structures for forms I and IV (RMSD27 of 0.23 Å and 0.64 Å, in reference to structures published in Ref. ) are sampled and ranked among the top 5 of the candidate list. Form IV is found to be more stable than form I at 0K by the r 2 SCAN-D3 functional, which is in agreement with the reported stability ordering at ambient conditions. In addition, the temperature dependent stability calculations indicate form I becomes more stable than form IV with increasing temperature, in qualitative agreement with experiments. |
676a0ce6fa469535b999990a | 27 | While this paper was under review, reports of the seventh blind test results of crystal structure prediction organized by the CCDC were published. Compound XXXI is the only molecule in this blind test that is relevant for agrochemical and pharmaceutical development and has experimental forms with only Z'=1 structures. Three experimental structures of XXXI were determined. However, Form C is a channel-type solvate containing unresolved solvent and therefore falls outside the scope of prediction. Form A contains two disorder components resulting from the flipping of the fluorinated ring, and form B was determined by competitive slurry experiments as the most stable form below 55°C with form A becoming more stable for temperatures above 55°C. |
676a0ce6fa469535b999990a | 28 | The predicted energy landscape of XXXI at 0K from our calculations and the temperature dependent relative stability between forms A and B are reported in Figure (a), (b) and (c). Our calculations correctly predicted form B and the two disordered forms of form A among the top 25 predicted structures. The temperature dependent relative stability calculations indicate that with increased temperature form A, with its two disordered structures, become more stable as compared to form B, consistent with the experimental findings that form A is more stable at temperatures higher than 55°C. However, the relative free energy difference between the two forms at room temperature is small (about 0.4 kcal/mol), within the errors of the calculations, and therefore it can not be predicted with confidence which form is more stable at room temperature. It is also interesting to note that the relative lattice energy difference (stability at 0K reported in Figure (a)) among these three structures from our calculations are consistent with the results from all groups participating in seventh blind test that used similar DFT calculations to rank order the structures (including groups 3, 20), except for group 10 who reported a different order than others. |
676a0ce6fa469535b999990a | 29 | Flupyradifurone is a systemic insecticide developed by Bayer CropScience that protects crops from sap-feeding pests like aphids and whiteflies. Flupyradifurone was approved for use in plant protection products by the EU in 2015, and extensive experimental polymorph screening was performed by Bayer during the product development. The Schrodinger team were provided with only the 2D structure of flupyradifurone and performed polymorph predictions without any experimental data. Upon completion of the presented CSP workflow, prediction results were sent to Bayer to compare with the experimental polymorph screening results. The predictions were limited to Z'=1 space due to the current limitation of the method. The predicted polymorph landscape in Z'=1 space is shown in Figure . Using r 2 SCAN-D3, flupyradifurone has a very dense energy landscape with 42 predicted structures within the lowest 2.0 kcal/mol energy window. The lowest energy predicted structure matches very well with the only known Z'=1 experimental structure Mod I (RMSD32 of 0.12Å between predicted and experimental structure as shown in Figure (e)), and simulated PXRD also agrees well with the experimental spectra (Figure (f)). In addition to Mod I, flupyradifurone also has a Z'=2 experimental structure (Mod II) that was not attempted in the current round of calculations. We also performed free energy calculations of the top predicted Z'=1 structures along with the Z'=2 experimental Mod II to obtain their relative stabilities as a function of temperature. As shown in Figure (g), according to the calculations, the lowest energy predicted structure at 0K (corresponding to experimental Mod I) is most stable at all temperatures below 400K. These results are consistent with Bayer's experimental findings that Mod II and Mod I are monotropic polymorphs with Mod I more stable at all temperatures below its melting point of 361K. |
676a0ce6fa469535b999990a | 30 | Like many other CSP approaches, we separate the sampling of molecular conformational degrees of freedom from that of the lattice degrees of freedom. To validate the conformer generation method, the CSP test set was enriched with examples from the CSD drug subset with 9 or fewer rotatable bonds from Z'=1 crystal structures. In total, the dataset consists of 430 experimental crystal conformers. The RMSD of the results from the conformer generation protocol are presented in Table in SI. The conformer generation protocol reliably samples conformations within a RMSD of 0.40 Å compared to the experimental ASU for all molecules in the Z'=1 CSP test set. Due to the exhaustive nature of our method, high quality conformers are always generated across the chemical space tested, even for large flexible molecules. |
676a0ce6fa469535b999990a | 31 | To benchmark the packing search protocol, we curated a dataset of 426 neat Z'=1 crystal polymorphs from the CSD drug subset (Table in SI). These crystals are relaxed with symmetry constrained MD using the OPLS4 force field. Good crystal similarity is achieved for the full dataset, demonstrating the accuracy of the OPLS4 in describing molecular crystal packing interactions. The crystal-relaxed ASU is then used to search for the relaxed crystal structure. For the 426 crystals used in this benchmark, a candidate structure matching experiment was generated with close to a 100% success rate (Table Force field parametrization and conformer generation costs are omitted due to minimal computational expense (tens of CPU hours at most). |
676a0ce6fa469535b999990a | 32 | In Table , we list the compute cost for each step of the polymorph prediction workflow for a representative set of molecules with increasing complexity. Our CSP workflow is significantly more computationally efficient than CPU costs reported previously by other approaches. To facilitate comparisons, we convert our GPU costs to CPU costs using a 1:10 conversion. For PF-998245, our CPU cost is 22.6K hours, whereas approximately 200K hours was reported in Ref . For rotigotine, our CPU cost is 26.5K hours whereas 125K CPU hours was reported in Ref . For XXXI, our computational cost is 93K CPU hours and 200 GPU hours, whereas most participants in the seventh blind test who successfully predicted the experimental structures used significantly more CPU hours. It should be noted that our calculations were limited to Z'=1 structure predictions, whereas these participants might have spent a lot of effort for higher Z' structure predictions, so these CPU hours might not be directly comparable. |
676a0ce6fa469535b999990a | 33 | For small or rigid molecules, the conformer pool is small and DFT relaxation takes most of the computational time. When the molecule contains more conformational degrees of freedom (ring states, nitrogen inversion centers, flexible torsions), the number of conformers increases and so does the packing search time. For very large and flexible molecules like ritonavir, the conformer and crystal packing sampling would take much more computation resources than DFT relaxation. This also poses a challenge for composite systems such as Z'>1, hydrates, salts, and cocrystals. An effort is underway to further improve the performance of the crystal packing search. These improvements include workflow optimization, pre-computing and storing the geometry dependent molecular interactions in the memory to reuse them during geometry optimizations. This type of optimizations led to orders of magnitude performance improvements in molecular docking and preliminary results suggest such optimizations could boost the performance of crystal packing search by a factor of 3-5. |
676a0ce6fa469535b999990a | 34 | The systematic and hierarchical crystal packing approach (see Method Summary section) provides a significant efficiency improvement as compared to the stochastic approach employed by other CSP methods. Most groups participating in the 7th CSP Blind Test used methods that parameterize the search space via the six unit cell lattice parameters, the six parameters for ASU location and orientation, and the conformational degrees of freedom, and search these degrees of freedom simultaneously. These methods require substantial computational effort to adequately cover the search space due to the size and complexity of the parameter space. |
676a0ce6fa469535b999990a | 35 | Alternative methods included making perturbations to existing crystal structures and choosing to accept or reject the new candidate using a Monte Carlo scheme as well as the generative adversarial network of Group 10. To manage computational cost, many participants chose to terminate their program's execution after a certain number of structures or generation attempts were made. Some participants included convergence criteria by monitoring repeated generation of the lowest energy structures or by monitoring the number of generation attempts without finding new low-energy candidates. In contrast, the method presented here efficiently covers the search space for molecular crystals using a divide-and-conquer strategy that partitions the parameter space into subspaces based on space group symmetries, eliminating the need for the convergence checks required by stochastic approaches. |
676a0ce6fa469535b999990a | 36 | We have presented the use of QRNN, a machine learned force field (MLFF), to perform structural relaxation and energy ranking of molecular crystals in our CSP workflow prior to DFT. Innovations in the successful use of machine learning methods were also demonstrated by participants in the 7th CSP Blind Test. MLFFs were developed and utilized in the CSP protocols of groups 12, 15, 16, and 23. In the second part of the seventh blind test, Group 16 demonstrated energy ranking results with system specific MLFFs comparable to accurate DFT methods. Additionally, groups 10 and 20 made use of machine learning to reduce the number of structures required to be evaluated by costly methods, such as DFT. Future developments of QRNN in our CSP workflow will include improving molecule specific fine-tuning protocols to further reduce the cost of DFT evaluations. |
676a0ce6fa469535b999990a | 37 | A disadvantage of the packing search method described here is the significant effort required to implement it. This challenge arises because the symmetry operations differ for each space group, resulting in unique intermediate cluster constructions for each space group. Our current sampling covers the top 22 most common space groups, but extending the approach to all 230 space groups would require significant effort. Although, the choice to focus efforts on only a subset of space groups was universal among participants in 7th CSP Blind Test. Although the current packing search aims for crystals of Z'=1, coverage of Z'<1 crystals is inherent to the method. This is because the point group symmetry of the ASU together with a lower symmetry space group can form a higher symmetry space group. If the corresponding lower symmetry space groups are already searched, no additional development is needed for Z'<1 systems. Extension to other complex systems such as hydrates, salts, and cocrystals, is straightforward. However, a naive implementation may present a challenge for workflow throughput. |
676a0ce6fa469535b999990a | 38 | Through careful comparison of relative stabilities across different DFT functionals for the set of molecules studied, we found the relative energies between different DFT functionals can vary by around 0.5 kcal/mol or even up to 1.0 kcal/mol in some cases, in agreement with the error estimates from previous studies. Future work on more accurate DFT methods, particularly DFT methods that more accurately describe the conformational energies could further improve the reliability of the ranking among crystals with competitive stabilities. The temperature dependent free energy calculations also improved the relative stabilities as compared to experiment in many cases. We hope the large number of predicted solid form landscapes we have provided, including experimental relative energy rankings where available, can aid in the investigation and further development of more accurate energy ranking methods, including DFT functional selection, conformer energy correction protocols, and temperature dependent free energy evaluations. |
676a0ce6fa469535b999990a | 39 | We have presented a reliable computational method with state of the art accuracy for predicting molecular crystal polymorphs validated on a large and diverse set of molecules including a blinded study. Our validations include all of the relevant molecules from the first six CCDC blind test, other molecules studied by previous computational polymorph prediction methods, and several molecules from modern drug discovery programs. Our method not only reproduces the experimentally known polymorphs, but also suggests new low energy polymorphs that have not been observed experimentally, posing potential risks to developing the currently known forms of these compounds without carefully considering these alternative low energy structures from our calculations. |
676a0ce6fa469535b999990a | 40 | Our method has several novel features and clear advantages over existing CSP methods and protocols for predicting molecular crystal polymorphs. First, our method uses a novel algorithm that systematically and efficiently explores the vast space of possible crystal packing parameters, overcoming the exponential scaling challenge of multi-parameter sampling for Monte-Carlo or other stochastic methods. Second, our method effectively balances the accuracy and throughput for candidate structures ranking by using a hierarchical approach that incorporates different levels of accuracy and computational cost, from empirical force fields to DFT calculations. Third, our method leverages the power of a pretrained, transferable MLFF which predicts the relative stability of different polymorphs with sufficient accuracy to require only a practical number of DFT calculations. The pretrained MLFF can be further customized on a per molecule basis with molecule specific DFT calculations to further improve the reliability and further decrease the number of expensive periodic DFT calculations. Considering the well documented high accuracy requirements of successful crystal structure ranking, neither of the current MLFF models used in this work are of sufficient accuracy to completely remove the need for periodic DFT refinement. |
676a0ce6fa469535b999990a | 41 | The high accuracy and reliability of our method, as demonstrated here, position it for routine crystal structure prediction in drug formulation. In the future, we plan to extend our method to support more complex and/or multi-component systems, such as co-crystals, solvates, hydrates and salts. We also plan to integrate our method with other computational tools, such as solubility, permeability, mechanical properties and crystal morphology predictions, to enable a comprehensive analysis of polymorphs in terms of their structure, stability, function, and performance. |
676a0ce6fa469535b999990a | 42 | Our CSP workflow begins by converting a molecule's bonding information to a single, canonicalized three dimensional geometry. This geometry is input to the Schrödinger Force Field Builder (FFBuilder), which examines the coverage of the OPLS4 force-field for the molecule and refits torsion parameters which are not well represented in the default training set with additional QM calculations when needed. This approach differs from other CSP approaches where customized parameters are trained specifically on one molecule or a set of molecules. The resulting parameters from our method are transferable to different chemistries and for different applications, whereas the customized parameters used in other CSP methods only have limited scope of application. More detailed discussion on the construction of OPLS4 and automated torsion parameter fitting is reported elsewhere. To generate a pool of conformers for molecular crystal packing, the molecule is fragmented, low energy ring states are determined, pyramidal nitrogens with unique inversion states are identified, and energy profiles of each flexible torsion are obtained. Sample angles for each flexible torsion are determined using a combination of simple chemical rules and automated detection of low energy regions. All combinations of the chosen torsion angles, ring states, and pyramidal nitrogen states are placed onto the molecule fragments. Fragments with low energy according to the OPLS4 force field are combined to produce a diverse pool of unrelaxed conformers. The conformers within 8 kcal/mol of the global minimum are then relaxed, combined with low-energy unrelaxed conformers, and deduplicated to produce the conformer pool. Our crystal packing search treats the sampled conformers as rigid building blocks and only targets crystals with Z'=1 currently. Molecular clusters constructed from initial guesses of unevenly distributed parameters corresponding to basic symmetry elements, such as translation, inversion, rotation, screw, and glide are minimized against these parameters. Additional symmetry elements are searched sequentially for each cluster until unit cells can be constructed for the space group under consideration. The cluster size ranges from 2 for an inversion dimer to 36 for the final representation of the 3D crystal in some space groups. For example, the P1 space group contains three translation symmetries, and we effectively search low-energy periodic structures in one, two, and three dimensions consecutively corresponding to clusters with 3, 6, and 12 molecules (Figure (a)). When multiple different symmetries exist, the search order matters. Therefore we search with different symmetry orderings for these space groups. The search scope is determined by the energy tolerance of the symmetrized clusters at each search step, and intermediate clusters with energies lower than 6 kcal/mol per molecule from the global minimum of that step are retained for the following steps. As a result, this systematic and hierarchical approach does not need a feedback loop to determine a termination point, unlike other CSP methods based on random sampling. After the packing search, the predicted crystals pass through a multi-stage energy relaxation and filtering of increasing accuracy and cost, including MD, QRNN and DFT stages where all structural degrees of freedom are fully flexible to relax. At each stage, high energy configurations are discarded. The crystal candidates first go through structural relaxation and filtering using symmetry constrained molecular dynamics with the OPLS4 force field. Then, the machine learning force field (MLFF) is used for relaxation and reranking of the remaining crystals. Following this, a coarse DFT relaxation using PBE-D3 is performed followed by more DFT evaluations with increasingly accurate settings and functionals to obtain the final energy ranking. On average, it takes about 20 GPU seconds to relax a crystal with MD, 20 CPU minutes with QRNN, and 60 CPU hours with DFT. |
676a0ce6fa469535b999990a | 43 | The temperature dependent free energy calculations uses the previously established pseudo super critical path (PSCP) and temperature replica exchanges (REMD) method. The reference state for the PSCP free energy calculation is performed at 300K, and the temperature REMD is run in the range of 100-500K under the NPT ensemble. The free energy changes along the temperatures are extrapolated to 0K, and the 0K enthalpies are corrected to be the same as the periodic DFT relative energy results. All the free energy calculations are done with Desmond on GPU with the OPLS4 force field. |
676a0ce6fa469535b999990a | 44 | The periodic DFT calculations were performed using Quantum Espresso available via Schrodinger Materials Sciences Suite. The candidate crystal structures were generated using the systematic packing search method described in the methods section of the paper, with the pseudo code in the supplementary information. The OPLS force field, Desmond, and QRNN packages are available in Schrodinger's software suite version 2024-2. |
676a0ce6fa469535b999990a | 45 | Figure Overview of the computational polymorph prediction method. The novel packing search method uses a divide-and-conquer strategy to break down the parameter space into subspaces based on space group symmetries. 3D candidate crystal structures are built step by step from low energy conformers to different sized clusters with favorable interactions following the funnel shaped energy landscape mimicking the crystal nucleation process. Each conformer can generate multiple candidate structures via different pathways (the entire sampling tree), and multiple pathways can lead to the same candidate structure (the blue colored paths generate the same candidate structure). The energy ranking method integrates a multi-stage energy relaxation and filtering process with increasing accuracy and cost, including molecular dynamics simulations using the classical force field, structure optimization and reranking using a machine learning force field (MLFF) with long range electrostatic and dispersion interactions, and periodic DFT calculations for ranking the final shortlist. For cocaine (a), the only known experimental structure is predicted to have much lower energy than all other predicted candidate structures with an energy gap of about 1.0 kcal/mol by PBD-D3 and PBE0-MBD functionals (e). For MK-2022 all functionals predict experimentally known form I to be most stable. For olanzapine, the three resolved experimental structures are predicted among the top five candidate structures with three different DFT functionals (f). For the unresolved form III, two predicted candidate structures have the spectra characteristics of form III from experiment, one corresponding to a previously identified structure in the Pbca space group (j), and one novel structure in the P21/c space group with an identical 2D layer (i). For GSK269984B, candidate structures with favorable intermolecular hydrogen bonds (k) and (l), including the typical bidentate hydrogen bonds for carboxylic acids (k), are predicted to have lower energy than the experimental structure with only intramolecular hydrogen bonds (m), indicating the possibility of other polymorphs with competitive stability yet to be discovered by experiment. ). For (a) ROY and (b) Galunisertib, molecules holding the current record for the largest number of fully characterized polymorphs, our CSP approach correctly predicted all the known Z'=1 polymorphs. For rotigotine (c), where the late appearance of the more stable form II disrupted the clinical usage of the original form I formulation, our CSP calculations correctly predicted all the experimentally known forms I and II, the candidate form III from a prior CSP study, and another novel candidate crystal in the P212121 space group with greater stability than form I. For MK-8876 (d) and MK-2202 (e), a previous CSP study using the GRACE software correctly predicted a candidate structure matching the experimentally known polymorph for MK-2022, but failed for MK-8876. Our CSP calculations correctly predicted both experimental structures with the experimental structure ranking 1st for MK-2022 and 2nd for MK-8876. For LY156735 (f), a potent and selective melatonin agonist with some unusual crystallization behavior among the R and S enantiomers, our calculations correctly predicted all three known experimental forms, and suggested a few other competitive structures, indicating the complex polymorphic landscape of this molecule may remain to be extensively explored experimentally. The predicted lowest energy structure matching the experimental Z'=1 structure of Mod I is most stable at all temperatures below 400K according to the calculations, matching experimental results that Mod I is the most stable form at all temperatures below its melting point of 361 K. |
66734173c9c6a5c07ae019a6 | 0 | It has been reported that high-fat diet loading in wild-type mice increased MGAT2 expression in the small intestine and increased MGAT activity. Furthermore, MGAT2 knockout mice showed suppressed weight gain, insulin resistance, blood cholesterol elevation, fatty liver formation, and energy consumption even under high-fat diet loading. In general, drug absorption in the gastrointestinal tract is often rate-limited by the dissolution of the drug from the dosage form. The wettability of a drug is an important property that affects its dissolution; wettability can be quantitatively evaluated by contact angle measurements. S-309309 has poor wettability, low solubility, and low stability under acidic condition, which are challenges for formulation development. Poorwettability and low-solubility drugs may not be absorbed sufficiently in the body, resulting in an ineffective blood concentration. In addition, excessive production of related substances in the body not only impairs the stability and efficacy of the drug, but also increases the risk to patient health. |
66734173c9c6a5c07ae019a6 | 1 | To evaluate the wettability of S-309309, S-309309 alone or mixed with a water-soluble polymer was compressed to form tablets and then the water contact angle of each tablet was evaluated. The results are listed in Table . The contact angle of all tablets containing S-309309 and a water-soluble polymer was significantly lower compared with that of the tablet of S-309309 alone, indicating that the wettability of the tablets was improved by including a water-soluble polymer. Talukder et al. reported the contact angles of the poorly soluble drugs ibuprofen, nifedipine, and carbamazepine with 0.5% Hydroxypropyl cellulose (HPC) solution and water. It was found that the contact angles of 0.5% HPC solution on the drug surfaces were lower than the corresponding contact angles for water. |
66734173c9c6a5c07ae019a6 | 2 | They concluded that the relatively non-ionic polymer HPC markedly lowered the surface tension of water and also allow the contact between the polymer and poor water-soluble drugs. In this study, the water contact angle of tablets prepared by mixing S-309309 and a water-soluble polymer was evaluated. The results indicated that the contact between the water-soluble polymer on the tablet surface and the media lowered the surface tension of the water droplet on the tablet surface, leading to improved wettability of the S-309309based formulations. |
66734173c9c6a5c07ae019a6 | 3 | The dissolved concentration of S-309309 in phosphate buffer (pH6.8) after 120 min was improved by mixing a water-soluble polymer, regardless of the polymer type, compared with that of S-309309 alone. Lippold et al. suggested that improved drug wettability leads to an increase of the effective surface area, which in turn results in an accelerated dissolution rate. Therefore, it was indicated that the water-soluble polymers improved the wettability of S-309309, which raised the dissolution rate of the drug and resulted in a higher S-309309 concentration in the buffer after 120 min than was the case for S-309309 alone. |
66734173c9c6a5c07ae019a6 | 4 | S-309309 has poor stability under acidic conditions; it decomposes to form compound 8 (Table ). Therefore, it is important to minimize contact between S-309309 and gastric fluid to suppress the amount of compound 8 formed in the body. We tried to encapsulate S-309309 and evaluated the effect of encapsulation on the increase of compound 8 amount in acidic solution. To prevent the decomposition of drugs in the stomach, entericcoated capsules or tablets with enteric coating are usually prepared. However, when enteric-coated formulations are used, a decrease in bioavailability is often observed. Therefore, in this study, we used a rapidly dissolving capsule considering the gastric emptying rate in the fasting state , which has a low pH. The time-dependent formation of the compound 8 amount from S-309309 capsule or unencapsulated S-309309 in hydrochloric acid solutions was evaluated (Table ). When S-309309 was encapsulated, no compound 8 was observed for 20 min, and even after 30 min, the increase of compound 8 amount was suppressed compared with the case for unencapsulated S-309309. These results suggest that encapsulating S-309309 will suppress its decomposition in the stomach. |
66734173c9c6a5c07ae019a6 | 5 | To estimate the dissolution of the designed S-309309-based formulations in the small intestine, formulations (Table ) were prepared using HPC, which increased the wettability of S-309309, and encapsulated to suppress the increase of compound 8 amount under acidic conditions. The dissolution profile of each formulation in phosphate buffer (pH 6.8) was assessed, as shown in Fig. ). In addition, the effect of HPC on the dissolution of S-309309 was evaluated. Although a lag time of up to 5 min after the start of the test was observed regardless of the presence or absence of HPC, all the capsules containing HPC showed rapid dissolution behavior compared with the capsules without HPC regardless of S-309309 dose. These results demonstrated that the wettability improvement induced by HPC accelerated the dissolution rate of S-309309. Thus, the formulations containing HPC can be expected to show better dissolution and subsequent absorption in the small intestine than the formulations without HPC. |
66734173c9c6a5c07ae019a6 | 6 | We tried to develop S-309309 formulation by simple manufacturing methods with the goals of achieving rapid dissolution of S-309309 in the small intestine and suppression of compound 8 formation in the stomach. The results suggested that the mixing S-309309 with a water-soluble polymer improved the wettability of S-309309, thereby increasing its dissolved concentration and dissolution rate. We also found that encapsulating S-309309 should suppress the increase of compound 8 amount in the stomach. These findings provide useful information for designing and developing a S-309309 formulation that is both safe and efficacious. |
66734173c9c6a5c07ae019a6 | 7 | The synthesis of S-309309 hydrate is described in the Supplementary Material. The particle sizes of S-309309 hydrate used in this study were D50 = 2.74 µm, D90 = 8.34 µm for one sample (Lot No. B1) and D50 = 3.29 µm, D90 = 10.94 µm for the other sample (Lot No. A1); the purity (quantitative value) of these samples was 99.4% and 99.6%, respectively. D50 or D90 is defined as the size value corresponding to cumulative size distribution at 50% or 90%, which represents the size of particles below which 50%, or 90% of the sample lies. HPC, hypromellose (HPMC), and povidone (PVP), which are water-soluble polymers, were purchased from Nippon Soda Co., Ltd. (Tokyo, Japan), Shin-Etsu Chemical Co., Ltd. (Tokyo), and BASF SE (Ludwigshafen, Germany), respectively. Mannitol was purchased from Roquette Frères (Lestrem, France), lowsubstituted hydroxypropyl cellulose was purchased from Shin-Etsu Chemical Co., Ltd., magnesium stearate was purchased from SpecGx LLC (St. Louis, MO), and HPMC capsules were purchased from Lonza K.K. (Sagamihara, Kanagawa, Japan). All other chemicals and solvents were analytical reagent-grade commercial products. |
66734173c9c6a5c07ae019a6 | 8 | After mixing 50.6 mg of S-309309 hydrate (as 50 mg of S-309309) with 10 mg of a watersoluble polymer (HPC, HPMC, or PVP), the flat tablets consisting of each mixture were prepared using a single tablet press equipped with a 7.5 mm diameter at a compression force of 5 kN. A drop of water (1 µL) was dropped onto the flat surface of each tablet and then the water contact angle was measured using an automatic contact angle meter (DMo-601; Kyowa Interface Science Co., Ltd. Niiza, Saitama, Japan). The control group consisted of tablets containing only S-309309, without a water-soluble polymer. |
66734173c9c6a5c07ae019a6 | 9 | The capsule with S-309309 was added to 50 mL of 0.1N hydrochloric acid in a smallvolume vessel equipped with a small paddle stirring at 50 rpm. The mixture was heated to 37 °C and then 3 mL of aliquots were withdrawn after 5, 10, 15, 20, and 30 min. Each aliquot was filtered through a 0.45-µm filter and then diluted 2 times with 100 mM carbonate buffer (pH 9.7) to inject into the UPLC system. The amount of the degradation product compound 8 was measured by UPLC at a wavelength of 267 nm using a YMC-Triart C18 ExRS column (1.9 µm, 3.0 × 100 mm) at 60°C using a column heater. The mobile phase consisted of 0.1% formic acid and acetonitrile. The separation was achieved in 35 min using the gradient program summarized in Table . The flow rate was 0.6 mL/min throughout the run. The injection volume was 10 µL. The amount of compound 8 was calculated as a percentage (%) of the total peak area of the chromatogram, which was set to 100%. |
66734173c9c6a5c07ae019a6 | 10 | S-309309 capsule formulations were composed of the common pharmaceutical excipients (mannitol, HPC, low-substituted hydroxypropyl cellulose, magnesium stearate, and HPMC capsule) without any special excipients and were manufactured by simple manufacturing processes such as mixing, and encapsulation. The formulae used are listed in Table . Dissolution tests were conducted with a dissolution apparatus (NTR-6400AC; Toyama Sangyo Co., Ltd. Osaka) following the paddle method (the United States Pharmacopeia (USP) Apparatus II) at 50 rpm and 37°C. S-309309 capsule formulations were tested in 900 mL of 200 mM phosphate buffer (pH6.8). A sinker was used for the dissolution test. Five-mL aliquots of the test solution were collected at 5, 10, 15, 20, 30, 45 and 60 min. Each aliquot was filtered through a 0.45-µm filter. The filtrate was injected into UPLC system. UPLC analysis was performed at a wavelength of 267 nm with a YMC-Triart C18 ExRS column (1.9 µm, 3.0 × 100 mm) under an isocratic condition of mobile phase (0.1% formic acid:acetonitrile, 3:2, v/v) for 5 min at 60°C using a column heater. The detection wavelength was set at 267 nm and the injection volume was 5 µL. |
66734173c9c6a5c07ae019a6 | 11 | The aqueous layer was separated and then the obtained organic solution was subsequently washed with 2% citric acid aqueous solution and 5% sodium bicarbonate/5% sodium chloride aqueous solution. Then, the obtained organic solution was concentrated under reduced pressure to 5.5 vol. By repeatedly concentrating with tetrahydrofuran multiple times, the solvent is replaced with tetrahydrofuran. The volume of solution was adjusted to 5.0 vol with tetrahydrofuran to obtain a compound 2/tetrahydrofuran solution. |
66734173c9c6a5c07ae019a6 | 12 | To a cooled (-50 °C) solution of lithium hexamethyldisilazide in tetrahydrofuran (1.2 mol/L, 2.3 equiv.) was added dropwise tert-butyl acetate (2.3 equiv.) over 0.5 h, and then the mixture was stirred for 0.5 h. A solution of chlorotriisopropoxytitanium (IV) (2.7 equiv.) dissolved in tetrahydrofuran (5.0 vol) was cooled to 5 °C, which was added dropwise to the reaction mixture over 1 h. After the reaction mixture was stirred at -50 °C for 0.5 h, the compound 2/tetrahydrofuran solution from Step 1A was added dropwise to the reaction mixture over 1 h. After stirring at -50 °C for 0.5 h, the reaction mixture was added dropwise to a solution of citric acid monohydrate (4.0 wt) dissolved in water (11 vol) at 0 °C. After separation of the aqueous layer, the obtained organic solution was washed with 5% sodium bicarbonate aqueous solution and concentrated under reduced pressure to 4.5 vol. After adding 2-methyltetrahydrofuran, the mixture was washed with 2.5% sodium chloride aqueous solution. By repeatedly concentrating with methanol multiple times, the solvent is replaced with methanol. The mixture was filtrated through activated carbon. The activated carbon was washed with methanol. The mixed filtrate was concentrated to 5.0 vol under reduced pressure to obtain a compound 3/methanol solution. |
66734173c9c6a5c07ae019a6 | 13 | To a cooled (0 °C) solution of compound 3/methanol from Step 1B was added dropwise 4 N hydrogen chloride/ethyl acetate solution (1.8 equiv.) over 1.5 h, and then the mixture was stirred at 0 °C for 1 h. After n-heptane, water, and ethyl acetate were added to the reaction mixture, the organic layer was separated. The aqueous solution was washed with n-heptane, and then the aqueous solution was adjusted to weak basic condition with 1 N sodium hydroxide aqueous solution. After ethyl acetate was added to the mixture, the aqueous layer was separated. Ethyl acetate was added to the separated aqueous layer, and then the aqueous layer was separated. The combined organic layer was washed with 2.5% sodium chloride aqueous solution, and then the mixture was filtered through activated carbon. The activated carbon was washed with ethyl acetate. The mixed filtrate was concentrated under reduced pressure to 11.5 vol, and then n-heptane (10.0 vol) was added to the mixture. A solution of (-)-10-camphorsulfonic acid (0.17 equiv.) dissolved in tetrahydrofuran (1.6 vol) was added dropwise to the mixture over 2.5 h, and then the resulting slurry was stirred at 25 °C for 1 h. After a solution of (-)-10-camphorsulfonic acid (0.49 equiv.) dissolved in tetrahydrofuran (4.4 vol) was added dropwise to the slurry over 3.5 h, n-heptane (18.0 vol) was added dropwise over 5 h. The slurry was stirred at 25 °C for 1 h and filtrated. The filtrated solid was washed with a mixture of ethyl acetate (3.0 vol) and n-heptane (6.0 vol). The obtained solid was dried under reduced pressure at 25 °C to afford compound 4 (61% yield). |
66734173c9c6a5c07ae019a6 | 14 | To a cooled (10 °C) mixture of compound 4 and tetrahydrofuran (4.0 vol) were added triethylamine (1.5 equiv.), cyanoacetic acid (1.5 equiv.), and 1-ethyl-3-(3dimethylaminopropyl) carbodiimide hydrochloride (1.5 equiv.). The mixture was stirred at 25 °C for 1 h. After 5% citric acid aqueous solution and methyl tert-butyl ether were added to the mixture, the aqueous layer was separated. The organic solution was subsequently washed with 5% sodium bicarbonate aqueous solution and 10% sodium chloride aqueous solution. By repeatedly concentrating with methanol multiple times, the solvent is replaced with methanol. The volume of solution was adjusted to 4.5 vol with methanol to obtain a compound 5/methanol solution. |
66734173c9c6a5c07ae019a6 | 15 | To a solution of compound 5/methanol from Step 2B were added methanol (6.4 vol) and 30% sodium methoxide/methanol solution (2.0 equiv.). The mixture was heated to 50 °C and stirred at 50 °C for 3 h. The reaction mixture was concentrated under reduced pressure to 7.0 vol. After water (4.6 vol) was added to the obtained concentrate, the mixture was adjusted to acidic condition with 35% hydrochloric acid. After the resulting slurry was stirred at 25 °C for 2 h, 35% hydrochloric acid (2.4 equiv.) was added to the slurry. The slurry was stirred at 25 °C for 1 h and filtrated. The filtrated solid was washed with a mixture of methanol (0.7 vol) and water (2.9 vol). The obtained solid was dried under reduced pressure at 80 °C to afford compound 6 (85% yield). Step 3 (vol, wt, and equiv. were based on the amount of compound 6) |
66734173c9c6a5c07ae019a6 | 16 | To a solution of compound 6 and isopropyl acetate (10.0 vol) was added N,Ndimethylformamide (2.0 vol) and the mixture was cooled to 5 °C. Phosphorus oxychloride (0.92 equiv.) was added dropwise to the mixture, and the mixture was stirred at 5 °C for 9 h. After cooling to 0 °C, an aqueous solution of tripotassium citrate (1.5 equiv.) dissolved in water (10.0 vol) was added dropwise to the reaction mixture at 0 °C. After the aqueous solution separated at 5 °C, the obtained organic solution was washed with 2% sodium chloride aqueous solution. The obtained organic solution was concentrated under reduced pressure to 5.0 vol. After n-heptane (0.5 vol) was added to the mixture, the resulting slurry was stirred at 25 °C for 1.5 h. Then, n-heptane (13.0 vol) was added dropwise to the slurry, and the slurry was stirred at 25 °C for 3 h and filtrated. The filtrated solid was washed with a mixture of isopropyl acetate (1.0 vol) and n-heptane (4.0 vol), and then washed with n-heptane (4.0 vol). The obtained solid was dried under reduced pressure at 60 °C to afford compound 7 (83% yield). Step 4 (vol, wt, and equiv. were based on the amount of compound 7) |
66734173c9c6a5c07ae019a6 | 17 | Anisole (18.0 vol), compound 9 (1.25 equiv.), and water (9.5 vol) were mixed and then heated to 85 °C, after which 62.5% sulfuric acid aqueous solution (6.0 equiv.) was added dropwise over 2 h. The mixture was stirred at 85 °C for 2.5 h. After the organic layer was separated, the obtained aqueous solution was washed with anisole. The aqueous solution was adjusted to weak acidic condition with 48% sodium hydroxide aqueous solution. A solution of compound 7 dissolved in 2-methyltetrahydrofuran (15.0 vol) was added dropwise to the aqueous solution. An aqueous solution of tripotassium phosphate (2.3 equiv.) dissolved in water (3.5 vol) was added dropwise to the mixture. After stirring at 25 °C for 1 h, the mixture was heated to 50 °C and then stirred for 6 h. After the aqueous layer was separated, 2-methyltetrahydrofuran (5.0 vol) and 1 N hydrochloric acid/2.5% sodium chloride aqueous solution were added to the organic solution. After the aqueous layer was separated, which was followed by the filtration through microcrystalline cellulose. The microcrystalline cellulose was washed with 2-methyltetrahydrofuran (3.0 vol). 2% sodium chloride aqueous solution was added to the mixed filtrate, and then the aqueous layer was separated, which was followed by the filtration through activated carbon. The activated was washed with 2-methyltetrahydrofuran (15.0 vol). The mixed filtrate was concentrated to 9.5 vol, and then the resulting slurry was stirred for at 25 °C 1 h. n-Heptane (15.0 vol) was added dropwise to the slurry, and then the slurry was stirred at 25 °C for 2 h and filtrated. The filtrated solid was washed with a mixture of 2methyltetrahydrofuran (1.5 vol) and n-heptane (2.5 vol), and then n-heptane (4.0 vol). |
66734173c9c6a5c07ae019a6 | 18 | Tetrahydrofuran (3.0 vol), ethyl acetate (1.5 vol), compound 8 were mixed. After the mixture was cooled to 0 °C, 52% propylphosphonic anhydride/ethyl acetate solution (2.8 equiv.) was added dropwise to the mixture. Pyridine (2.4 equiv.) was added to the mixture, and then a solution of compound 11 (1.3 equiv.) dissolved in tetrahydrofuran (3.0 vol) was added dropwise to the mixture. After stirring at 0 °C for 6 h, the reaction mixture was added dropwise to a mixture of ethyl acetate (10.0 vol) and 5% sodium bicarbonate aqueous solution (10.0 wt). After stirring at 0 °C for 1 h, the aqueous layer was separated. |
66734173c9c6a5c07ae019a6 | 19 | 25% sodium chloride solution and 7% sodium bicarbonate aqueous solution were added to the organic solution, and then the aqueous layer was separated. Methanol (5.0 vol) was added to the organic solution, which was followed by the filtration through activated carbon. The activated carbon was washed with a mixture of methanol (0.9 vol) and ethyl acetate (2.1 vol). The mixed filtrate was concentrated under reduced pressure to 9.0 vol, and then methanol (1.0 vol) and ethyl acetate (2.0 vol) were added to the concentrate. |
66b23c3f01103d79c5e84bbe | 0 | The adsorption energy of an adsorbate on the catalyst surface is crucial for determining the reactivity and selectivity of catalytic reactions. The highest catalytic activity of a material frequently resides at the optimal adsorption energy of the key reaction intermediates, according to the Sabatier principle . Therefore, developing cheap and efficient adsorption energy evaluation methods is key for accelerating catalyst discovery. Currently, high-throughput screening of catalysts relies heavily on computationally expensive simulations like density functional theory (DFT) . However, multiple adsorption sites and variable adsorbate geometries lead to numerous possible adsorption configurations and local minima on the potential energy surface . The local adsorption energy, which strongly depends on the initial structure of the simulation, might not well represent the catalytic activity. Several methods, including global optimization algorithms and "brute-force" searches , have been employed to find the most stable adsorption structures and corresponding global minimum adsorption energies (GMAE). However, the high computational cost of such DFT-based methodologies inevitably imposes limitations on their large-scale implementation, given the immense catalyst design space. |
66b23c3f01103d79c5e84bbe | 1 | Recent developments in machine learning (ML) algorithms hold great promises in approximating DFT-level accuracy with significantly higher efficiency and lower computational costs . Various ML models, such as random forests, multilayer perceptions, and graph neural networks (GNNs), have been explored to predict the adsorption energy of adsorbate-surface systems . However, several drawbacks are present in most models, which (1) can only predict local minimum adsorption energies, require specific binding information between the adsorbates and catalyst surfaces, and (3) exhibit poor generalizability limited to specific adsorbates. Recently, Ulissi et al. proposed the AdsorbML workflow , which combines heuristic search and ML potentials to accelerate the GMAE calculation. The ML potentials trained on the huge Open Catalyst 2020 (OC20) dataset achieve promising prediction accuracy and substantial speedups over DFT computations . Moreover, Margraf et al. proposed a global optimization protocol that employs on-the-fly ML potentials trained on iteratively DFT calculations to search the most stable adsorption structures. This method is versatile for various combinations of surfaces and adsorbates, significantly reducing DFT calculations as well as the reliance on prior expertise . Despite notably mitigating computational expenses relative to DFT methods, these approaches still require the exploration of a large number of initial adsorption structures and iterative calculations to obtain the GMAE values. |
66b23c3f01103d79c5e84bbe | 2 | The AdsMT is designed to capture the intricate relationships between adsorbates and the multiple adsorption sites on surfaces through the cross-attention mechanism, thereby avoiding the enumeration of adsorption configurations. To the best of our knowledge, this is the first work that directly predicts the GMAE of diverse adsorption systems without the acquisition of any site-binding information. As illustrated in Fig. , three GMAE datasets comprising diverse catalyst surfaces and adsorbates were constructed for the challenging GMAE prediction task. |
66b23c3f01103d79c5e84bbe | 3 | Our AdsMT demonstrates excellent performance in predicting GMAE, with mean absolute errors (MAE) below 0.15 eV for two of the datasets. A transfer learning strategy was also proposed to further improve AdsMT's performance on small-sized datasets. Moreover, crossattention weights are exploited to identify the most energetically favorable adsorption sites and demonstrate the intrinsic interpretability of AdsMT. The calibrated uncertainty estimation is integrated into our AdsMT for reliable GMAE prediction. Overall, AdsMT exhibits strong learning ability, generalizability, and interpretability, making it a powerful tool for fast GMAE calculations and catalyst screening. |
66b23c3f01103d79c5e84bbe | 4 | AdsMT is a multi-modal Transformer that takes periodic graph representations of catalyst surfaces and feature vectors of adsorbates as inputs to predict the GMAE of each surface/adsorbate combination without any site binding information. As depicted in Fig. , the AdsMT architecture consists of three parts: a graph encoder E G , a vector encoder E V , and a cross-modal encoder E C . In the graph encoder, the unit cell structure of each catalyst surface is modeled as a graph G with periodic invariance by self-connecting edges and radius-based edge construction (see Methods for details). The atom-wise embeddings of surfaces are output from the graph encoder and passed into the cross-modal encoder. Any geometric graph neural network, such as SchNet and GemNet , can serve as the graph encoder in the AdsMT framework. |
66b23c3f01103d79c5e84bbe | 5 | The cross-modal encoder takes atomic embeddings of surfaces and vector embeddings of adsorbates as inputs to predict the GMAE. It comprises cross-attention layer(s), self-attention layer(s), and an energy block (Fig. and). The adsorption energy primarily arises from the interaction between the catalyst surface and the adsorbate, while the resulting surface atomic displacements also influence it . Therefore, the cross-attention layer is assigned to capture the complex relationships between the adsorbate and all surface atoms, while the selfattention layer is expected to learn the interactions between atoms within the surface caused by adsorption (e.g., atomic displacements). In the first cross-attention layer (Fig. ), the concatenated matrix of adsorbate vector embeddings and surface graph embeddings is employed as the query matrix, while the concatenated matrix of atomic embeddings and depth embeddings serves as the key and value matrices. Each atomic depth vector describes the relative position (e.g., top-layer or bottom-layer) of an atom within the surface (Methods). In the self-attention layer, the stacked matrix of atom embeddings, surface graph embeddings, and adsorbate vector embeddings are set to the input query, key, and value. The aggregated output of the final selfattention layer is concatenated with the output of the last cross-attention layer, and passed into the energy block to predict the GMAE. The detailed algorithm of the cross-modal encoder is described in the Methods. AdsGT layers (c) with an edge-wise attention mechanism. d t ij and e t ij are the distance and embedding of t-th edge between atom i and j. z i is the atomic number of atom i. h l i is the atomic embedding of atom i at l-th AdsGT layer. LN and BN represent layer normalization and batch normalization, respectively. |
66b23c3f01103d79c5e84bbe | 6 | The graph encoder employed in the AdsMT model plays a pivotal role in capturing structural and chemical features of catalyst surfaces. Unfortunately, existing GNNs fail to discriminate between top-layer and bottom-layer atoms when representing a surface as a graph. Practically, only the top-layer atoms of surfaces are capable of interacting with adsorbates, rendering them inherently more important than other atoms in terms of adsorption energy. Therefore, we designed a graph transformer called AdsGT specifically for encoding surface graphs. As depicted in Fig. , a novel positional encoding method is proposed to compute the positional feature δ i for each atom based on fractional height relative to the underlying atomic plane. This approach augments the model's understanding of surface structures and differentiates between top and bottom layer atoms. Fig. shows the architecture of the AdsGT encoder, which consists of radial basis function (RBF) expansions, embeddings, and graph attention layers. Different from the conventional graph transformer like Graphormer , the AdsGT layer (Fig. ) adopts an edge-wise attention mechanism, delineated by three sequential steps: edge-wise attention coefficients calculation, edge-wise message calculation, and node update. More details about AdsGT architecture and its positional encoding are described in the Methods. We built three GMAE benchmark datasets named OCD-GMAE, Alloy-GMAE and FG-GMAE from OC20-Dense , Catalysis Hub , and 'functional groups' (FG)-dataset datasets through strict data cleaning (see Methods for details), and each data point represents a unique combination of catalyst surface and adsorbate. As shown in Fig. and Supplementary where the distances between each surface/adsorbate combination are correlated with the differences in feature space . Each surface/adsorbate combination is depicted by the smooth overlap of atomic positions (SOAP) descriptors of surfaces and RDKit descriptors of adsorbates. Fig. demonstrates that three GMAE datasets delineate separate chemical spaces, albeit with certain overlapping regions. |
66b23c3f01103d79c5e84bbe | 7 | were evaluated on the three GMAE datasets (Fig. and Supplementary To enhance the AdsMT performance under data scarcity, we implemented a transfer learning strategy that entails pre-training on data with local minimum adsorption energy (LMAE). To this end, we established OC20-LMAE, a novel dataset comprising 363,937 surface/adsorbate combinations alongside their LMAEs, derived through data cleaning of the OC20 dataset (Methods). It should be noted that both OCD-GMAE and OC20-LMAE datasets originate from the Open Catalyst Project with analogous surface and adsorbate types, which will be advantageous for transfer learning. As illustrated in Fig. , each AdsMT model undergoes initial pre-training on the OC20-LMAE, followed by fine-tuning on the GMAE datasets while selectively freezing graph encoder parameters. The efficacy of our transfer learning strategy is elucidated in Fig. and Supplementary Table -10, where AdsGT and GNNs reported in the past two years ( ) are chosen as the graph encoders for AdsMT. On the OCD-GMAE dataset, AdsMT models achieve obvious performance gains after transfer learning, resulting in all MAE reductions surpassing 0.14 eV and SR increments exceeding 7 %. Particularly, the ET encoder enables AdsMT to achieve an MAE reduction of 0.291 eV and a 9.3 % increase in SR, and the GemNet-OC encoder facilitates AdsMT to attain an MAE reduction of 0.256 eV and a 9.5 % increase in SR. The best performance of AdsMT on the OCD-GMAE was obtained after transfer learning, yielding an MAE of 0.389 eV and a SR of 22.0 %. On the contrary, transfer learning only provides slight improvements for AdsMT models on the Alloy-GMAE and FG-GMAE, likely attributable to substantial dissimilarities in catalyst surface types between these datasets and OC20-LMAE . Additionally, AdsMT already exhibits commendable predictive performance on these datasets, with MAE values below or proximal to 0.1 eV, indicating limited scope for further performance optimization. |
66b23c3f01103d79c5e84bbe | 8 | Beyond predicting adsorption energies, identifying adsorption sites holds particular importance in catalyst design and reaction mechanism studies . In this context, we explored the application of attention scores from cross-attention layers to estimate the most energetically favorable adsorption sites on catalyst surfaces. As illustrated in Fig. , the average crossattention score of each surface atom with respect to the adsorbate is computed from all attention heads of the last cross-attention layer, which implies the relative importance of each surface atom in adsorbate binding. The surface atom(s) with the highest average cross-attention score is hypothesized as the most favorable adsorption site. To assess the reliability of adsorption site identification from cross-attention scores, no information regarding adsorption structures or sites was provided to the AdsMT model during training. The trained AdsMT model is employed to suggest the optimal adsorption site for each surface/adsorbate combination and compared with the ground truth from DFT calculations. reasoning about adsorption sites on simple monometallic surfaces (e.g., FG-GMAE dataset), where the top-layer atoms are completely equivalent and have identical attention scores. Furthermore, we computed the accuracy of AdsMT models in identifying optimal adsorption sites on the Alloy-GMAE and OCD-GMAE (Supplementary Note 3). As illustrated in Fig. , the AdsMT models demonstrate commendable identification capabilities for optimal adsorption sites across both datasets, substantially surpassing the accuracy obtained through random atom selection (black dotted line). The AdsMT model adopting the ET encoder achieves the highest accuracy of 0.48 on the Alloy-GMAE dataset, while the AdsMT model with the AdsGT encoder exhibits the highest accuracy of 0.56 on the OCD-GMAE.The implementation of transfer learning was also found to improve the AdsMT's accuracy for adsorption site identification. |
66b23c3f01103d79c5e84bbe | 9 | From the practical perspective of virtual catalyst screening, it is desirable that the models can provide uncertainty estimation for their predictions, enabling researchers to evaluate the reliability of predictions and assign experimental effort more efficiently. To this end, an ensemble of independent AdsMT replicates is trained to estimate the uncertainty from the variance of individual models' predictions, which is a widely recognized method for effective uncertainty quantification. (Methods) . The AdsMT ensemble's predictions were ranked based on their uncertainty estimations (Supplementary Note 4), and the correlation between uncertainty and prediction MAE was investigated. As depicted in Supplementary Fig. predictions with lower uncertainty tend to have lower MAEs across the three GMAE datasets. |
66b23c3f01103d79c5e84bbe | 10 | Moreover, the Spearman correlation coefficients between the estimated uncertainty and prediction MAEs for the AdsMT models with different graph encoders consistently exceed 0.98 on the three GMAE datasets (Supplementary Fig. ). The results show that the AdsMT's estimated uncertainty is significantly correlated with the predicted MAE, and its predictions are highly accurate at low uncertainty levels . Furthermore, we investigated whether the AdsMT's uncertainty estimation is well-calibrated and statistically significant, thereby avoiding overconfidence or underconfidence . Sup-plementary Fig. presents the calibration curves and corresponding miscalibration areas of AdsMT models with different graph encoders on the three GMAE datasets (Supplementary Note 5-6), which is an effective approach to evaluating the calibration of uncertainty estimates . It is notable that the calibration curves of AdsMT models closely approximate the ideal diagonal line and exhibit small miscalibration areas less than 0.1. The results prove that AdsMT's uncertainty estimations are well-calibrated and scaled with errors . |
66b23c3f01103d79c5e84bbe | 11 | We have presented AdsMT, a general multi-modal transformer framework for directly predicting GMAE of chemically diverse surface-adsorbate systems without relying on any binding information. The AdsMT integrates heterogeneous input modalities of surface graphs and adsorbate feature vectors, demonstrating excellent predictive performance on two GMAE benchmark datasets. Utilizing separate input information of catalysts and adsorbates, the AdsMT could generalize predictions for unseen surface/adsorbate combinations, making it suitable for efficient virtual screening of catalysts where adsorption structures are rarely available. Moreover, AdsMT achieves a speedup of approximately eight orders of magnitude compared to DFT calculations, and four orders of magnitude faster than machine learning interatomic potentials (MLIP) combined with heuristic search (Supplementary Note 7). Such a high efficiency and low computational cost endow AdsMT with great promises for fast GMAE prediction and large-scale screening of catalysts. |
66b23c3f01103d79c5e84bbe | 12 | In terms of data scarcity, AdsMT remains poised for enhancement, as indicated by its unsatisfactory performance on the OCD-GMAE dataset. It was shown that transfer learning is effective in addressing this challenge. In future work, MLIP can be employed to acquire coarse GMAE data for model pretraining, which is much cheaper than LMAE data from DFT calculations. Moreover, it can be particularly interesting to integrate AdsMT with active learning, as it enables the iterative expansion of the training datasets towards underexplored regions of catalyst space and improves the model's reliability. |
66b23c3f01103d79c5e84bbe | 13 | The application of identifying the most advantageous adsorption sites from AdsMT's cross-attention scores is promising, despite the current accuracy is not high enough. An intriguing avenue for future research lies in incorporating adsorption site and adsorbate geometric information into model training, potentially enhancing the model's capability for GMAE prediction and adsorption site identification. Moreover, considering the surfacial atom importance for adsorption sites as a prediction target and fusing it into the loss function can be beneficial for the model to learn the complex relationship between catalyst surfaces and adsorbates. |
66b23c3f01103d79c5e84bbe | 14 | Another natural extension to this work involves combining our AdsMT with MLIP and DFT calculations for catalyst screening in specific reactions. Each catalyst crystal can generate a large number of surface structures due to varying Miller indices and absolute positions of surface planes. AdsMT can be appointed for rapid preliminary screening in huge catalyst libraries and pinpoint a small range of candidate catalyst surfaces with desired GMAE and low uncertainty. Afterwards, MLIP and DFT methods are used to calculate the precise GMAE of the candidate surfaces relative to key reaction intermediates and compared with the optimal adsorption energies according to the Sabatier principle. This strategy holds promise for significantly reducing computational costs while achieving reliable virtual catalyst screening. |
66b23c3f01103d79c5e84bbe | 15 | Three new GMAE datasets, named Alloy-GMAE, FG-GMAE and OCD-GMAE, were built from Catalysis Hub , 'functional groups' (FG)-dataset , and OC20-Dense datasets, respectively. Each of the source datasets enumerated all adsorption sites on surfaces and performed DFT calculations on various possible adsorption configurations. The data cleaning was conducted to remove abnormal adsorption structures and take the lowest adsorption energy of all conformations as the GMAE target for each surface/adsorbate combination. Each data point in the datasets represents a unique combination of catalyst surface and adsorbate. Random splitting is adopted on three datasets during the model evaluation. |
66b23c3f01103d79c5e84bbe | 16 | In addition, a similar data cleaning procedure was employed on the OC20 dataset to create a new dataset named OC20-LMAE, which comprises surface/adsorbate pairings along with their local minimum adsorption energies (LMAE). The data points with anomalies (adsorbate dissociation, surface reconstruction, etc.) are removed. The OC20-LMAE dataset contains 363,937 data points and serves as an effective resource for model pretraining. Specifically, its training set consists of 345,254 data points, while the validation set comprises 18,683 data points. Further detailed descriptions of the datasets are provided in the Supplementary Note 1. |
66b23c3f01103d79c5e84bbe | 17 | R n×k is the node feature matrix, where h i ∈ R k is the k-dimensional feature vector of atom i. E ∈ R m×k ′ is the edge feature matrix, where e t ij ∈ R k ′ is the k ′ -dimensional feature vector of t-th edge between node i and j. |
66b23c3f01103d79c5e84bbe | 18 | is the position matrix, where Ignoring periodic invariance will lead to different graph representations and energy predictions for the same surface . Different from crystals, the presence of the vacuum layer breaks the periodicity along the direction perpendicular to the surface. This means that the catalyst surfaces actually exhibit periodicity only in the a and b directions. Thus, the infinite surface structure can be represented as |
66b23c3f01103d79c5e84bbe | 19 | To encode such periodic patterns, the infinite representation of the surface is used for graph construction, and all nodes and their repeated duplicates are considered to build edges. Given a cutoff radius r c ∈ R, if there is any integer pair (k ′ 1 , k ′ 2 ), such that the Euclidean distance |
66b23c3f01103d79c5e84bbe | 20 | Positional feature: Unlike molecular graphs, the importance of each atom in the catalyst surface differs for adsorption energy prediction (Fig. ). For example, atoms at the top layers are more important, while atoms at the bottom are less important. Moreover, GNNs are unable to determine the relative heights of atoms in a surface based on a surface graph, making it impossible to distinguish between top-layer and bottom-layer atoms. To help models understand the varying importance of atoms at different relative heights (Fig. ), each atom i of a surface graph will get a positional feature δ i computed by |
66b23c3f01103d79c5e84bbe | 21 | where h is the height of the atom i and calculated by the projection length of the atom coordinate x i on the c vector. h max and h min represent the maximum and minimum heights of surface atoms, respectively. Specifically, δ i = 1 indicates that the atom i is located at the topmost layer, while δ i = 0 means that the atom i is located at the bottommost layer. Then, δ i is expanded via a set of exponential normal radial basis functions e RBF to compute the positional embedding ζ i of surface atom i: |
66b23c3f01103d79c5e84bbe | 22 | In the initialization, atomic number z i is passed to the embedding layer and summed with the positional embedding ζ i to compute the initial node embedding h 0 i . The distance d t ij of t-th edge between node i and j is expanded via a set of radial basis functions (RBF) and transformed by linear layers and Softplus activation function to obtain the edge embedding e t ij . The message passing phase follows an edge-wise attention mechanism . In the l-th (0 ≤ l ≤ L) attention layer, edge-wise attention weights α t ij and message m t ij of t-th edge between node i and j are calculated based on h l i , h l j and e t ij according to |
66b23c3f01103d79c5e84bbe | 23 | The proposed AdsMT model consists of three parts: a graph encoder E G , a vector encoder E V , and a cross-modal encoder E C . Each surface/adsorbate combination c, consisting of a surface graph G c and an adsorbate feature vector p c , is defined as the model input, and the GMAE of the combination is set as the prediction target. Surface graphs and adsorbate feature vectors are passed to the graph encoder E G and the vector encoder E V for embedding learning, respectively. Then, both embeddings are passed to the cross-modal encoder E C for the crossmodal learning and GMAE prediction. The details of these parts are as follows. |
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