Developing a Differentiable Long-Range Force Field for Proteins with E(3) Neural Network-Predicted Asymptotic Parameters.

Accurately describing long-range interactions is a significant challenge in molecular dynamics (MD) simulations of proteins. High-quality long-range potential is also an important component of the range-separated machine learning force field. This study introduces a comprehensive asymptotic parameter database encompassing atomic multipole moments, polarizabilities, and dispersion coefficients. Leveraging active learning, our database comprehensively represents protein fragments with up to 8 heavy atoms, capturing their conformational diversity with merely 78,000 data points. Additionally, the E(3) neural network (E3NN) is employed to predict the asymptotic parameters directly from the local geometry. The E3NN models demonstrate exceptional accuracy and transferability across all asymptotic parameters, achieving an R2 of 0.999 for both protein fragments and 20 amino acid dipeptide test sets. The long-range electrostatic and dispersion energies can be obtained using the E3NN-predicted parameters, with an error of 0.07 and 0.02 kcal/mol, respectively, when compared to symmetry-adapted perturbation theory (SAPT). Therefore, our force fields demonstrate the capability to accurately describe long-range interactions in proteins, paving the way for next-generation protein force fields.

Performance of point charge embedding schemes for excited states in molecular organic crystals.

Modeling excited state processes in molecular crystals is relevant for several applications. A popular approach for studying excited state molecular crystals is to use cluster models embedded in point charges. In this paper, we compare the performance of several embedding models in predicting excited states and S1-S0 optical gaps for a set of crystals from the X23 molecular crystal database. The performance of atomic charges based on ground or excited states was examined for cluster models, Ewald embedding, and self-consistent approaches. We investigated the impact of various factors, such as the level of theory, basis sets, embedding models, and the level of localization of the excitation. We consider different levels of theory, including time-dependent density functional theory and Tamm-Dancoff approximation (TDA) (DFT functionals: ωB97X-D and PBE0), CC2, complete active space self-consistent field, and CASPT2. We also explore the impact of selection of the QM region, charge leakage, and level of theory for the description of different kinds of excited states. We implemented three schemes based on distance thresholds to overcome overpolarization and charge leakage in molecular crystals. Our findings are compared against experimental data, G0W0-BSE, periodic TDA, and optimally tuned screened range-separated functionals.

Competition between ultralong organic phosphorescence and thermally activated delayed fluorescence in dichloro derivatives of 9-benzoylcarbazole.

Optoelectronic materials based on metal-free organic molecules represent a promising alternative to traditional inorganic devices. Significant attention has been devoted to the development of the third generation of OLEDs which are based on the temperature-activated delayed fluorescence (TADF) mechanism. In the last few years, several materials displaying ultra-long organic phosphorescence (UOP) have been designed using strategies such as crystal engineering and halogen functionalisation. Both TADF and UOP are controlled by the population of triplet states and the energy gaps between the singlet and triplet manifolds. In this paper, we explore the competition between TADF and UOP in the molecular crystals of three dichloro derivatives of 9H-carbazol-3-yl(phenyl)methanone. We investigate the excited state mechanisms in solution and the crystalline phase and address the effects of exciton transport and temperature on the rates of direct and reverse intersystem crossing under the Marcus-Levich-Jortner model. We also analyse how the presence of isomeric impurities and the stabilisation of charge transfer states affect these processes. Our simulations explain the different mechanisms observed for the three derivatives and highlight the role of intramolecular rotation and crystal packing in determining the energy gaps. This work contributes to a better understanding of the connection between chemical and crystalline structures that will enable the design of efficient materials.

Assessment of SAPT and Supermolecular EDA Approaches for the Development of Separable and Polarizable Force Fields.

Which is the best reference quantum chemical approach to decipher the energy components of the total interaction energy: Symmetry-Adapted Perturbation Theory (SAPT) or Supermolecular Energy Decomposition Analysis (EDA) methods? With the rise of physically motivated polarizable force fields (polFF) grounded on these procedures, the need to answer such a question becomes critical. We report a systematic and detailed assessment of three variants of SAPT (namely SAPT2, SAPT2+3, and SAPT(DFT)) and three supermolecular EDA approaches (ALMO, CSOV, and RVS). A set of challenging, strongly bound water complexes, (H2O)2, Zn2+. . .H2O, and F-. . .H2O, is used as "stress tests" for these electronic structure methods. We have developed a procedure to separate the induction energy into the polarization and charge-delocalization using an infinite-order strategy based on SAPT(DFT). This paper aims to provide not only an overview of the capabilities and limitations but also similarities of SAPT and supermolecular EDA approaches for polFF developments. Our results show that SAPT(DFT)/noS2 and ωB97X-D∥ALMO are the most accurate and reliable techniques.

A non-empirical intermolecular force-field for trinitrobenzene and its application in crystal structure prediction.

An anisotropic atom-atom distributed intermolecular force-field (DIFF) for rigid trinitrobenzene (TNB) is developed using distributed multipole moments, dipolar polarizabilities, and dispersion coefficients derived from the charge density of the isolated molecule. The short-range parameters of the force-field are fitted to first- and second-order symmetry-adapted perturbation theory dimer interaction energy calculations using the distributed density-overlap model to guide the parameterization of the short-range anisotropy. The second-order calculations are used for fitting the damping coefficients of the long-range dispersion and polarization and also for relaxing the isotropic short-range coefficients in the final model, DIFF-srL2(rel). We assess the accuracy of the unrelaxed model, DIFF-srL2(norel), and its equivalent without short-range anisotropy, DIFF-srL0(norel), as these models are easier to derive. The model potentials are contrasted with empirical models for the repulsion-dispersion fitted to organic crystal structures with multipoles of iterated stockholder atoms (ISAs), FIT(ISA,L4), and with Gaussian Distributed Analysis (GDMA) multipoles, FIT(GDMA,L4), commonly used in modeling organic crystals. The potentials are tested for their ability to model the solid state of TNB. The non-empirical models provide more reasonable relative lattice energies of the three polymorphs of TNB and propose more sensible hypothetical structures than the empirical force-field (FIT). The DIFF-srL2(rel) model successfully has the most stable structure as one of the many structures that match the coordination sphere of form III. The neglect of the conformational flexibility of the nitro-groups is a significant approximation. This methodology provides a step toward force-fields capable of representing all phases of a molecule in molecular dynamics simulations.

First-Principles Many-Body Nonadditive Polarization Energies from Monomer and Dimer Calculations Only: A Case Study on Water.

The many-body polarization energy is the major source of nonadditivity in strongly polar systems such as water. This nonadditivity is often considerable and must be included, if only in an average manner, to correctly describe the physical properties of the system. Models for the polarization energy are usually parametrized using experimental data, or theoretical estimates of the many-body effects. Here we show how many-body polarization models can be developed for water complexes using data for the monomer and dimer only using ideas recently developed in the field of intermolecular perturbation theory and state-of-the-art approaches for calculating distributed molecular properties based on the iterated stockholder atoms (ISA) algorithm. We show how these models can be calculated, and we validate their accuracy in describing the many-body nonadditive energies of a range of water clusters. We further investigate their sensitivity to the details of the polarization damping models used. We show how our very best polarization models yield many-body energies that agree with those computed with coupled-cluster methods, but at a fraction of the computational cost.

X-ray total scattering study of magic-size clusters and quantum dots of cadmium sulphide.

Four types of magic-size CdS clusters and three different CdS quantum dots have been studied using the technique of X-ray total scattering and pair distribution function analysis. We found that the CdS quantum dots could be modelled as a mixed phase of atomic structures based on the two bulk crystalline phases, which is interpreted as representing the effects of random stacking of layers. However, the results for the magic-size clusters are significantly different. On one hand, the short-range features in the pair distribution function reflect the bulk, indicating that these structures are based on the same tetrahedral coordination found in the bulk phases (and therefore excluding new types of structures such as cage-like arrangements of atoms). But on the other hand, the longer-range atomic structure clearly does not reflect the layer structures found in the bulk and the quantum dots. We compare the effect of two ligands, phenylacetic acid and oleic acid, showing that in one case the ligand has little effect on the atomic structure of the magic-size nanocluster, and in another it has a significant effect.

Charge Distributions of Nitro Groups Within Organic Explosive Crystals: Effects on Sensitivity and Modeling.

The charge distribution of NO2 groups within the crystalline polymorphs of energetic materials strongly affects their explosive properties. We use the recently introduced basis-space iterated stockholder atom partitioning of high-quality charge distributions to examine the approximations that can be made in modeling polymorphs and their physical properties, using 1,3,5-trinitroperhydro-1,3,5-triazine, trinitrotoluene, 1-3-5-trinitrobenzene, and hexanitrobenzene as exemplars. The NO2 charge distribution is strongly affected by the neighboring atoms, the rest of the molecules, and also significantly by the NO2 torsion angle within the possible variations found in observed crystal structures. Thus, the proposed correlations between the molecular electrostatic properties, such as trigger-bond potential or maxima in the electrostatic potential, and impact sensitivity will be affected by the changes in conformation that occur on crystallization. We establish the relationship between the NO2 torsion angle and the likelihood of occurrence in observed crystal structures, the conformational energy, and the charge and dipole magnitude on each atom, and how this varies with the neighboring groups. We examine the effect of analytically rotating the atomic multipole moments to model changes in torsion angle and establish that this is a viable approach for crystal structures but is not accurate enough to model the relative lattice energies. This establishes the basis of transferability of the NO2 charge distribution for realistic nonempirical model intermolecular potentials for simulating energetic materials.

Nine questions on energy decomposition analysis.

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

New Angles on Standard Force Fields: Toward a General Approach for Treating Atomic-Level Anisotropy.

Nearly all standard force fields employ the "sum-of-spheres" approximation, which models intermolecular interactions purely in terms of interatomic distances. Nonetheless, atoms in molecules can have significantly nonspherical shapes, leading to interatomic interaction energies with strong orientation dependencies. Neglecting this "atomic-level anisotropy" can lead to significant errors in predicting interaction energies. Herein, we propose a simple, transferable, and computationally efficient model (MASTIFF) whereby atomic-level orientation dependence can be incorporated into ab initio intermolecular force fields. MASTIFF includes anisotropic exchange-repulsion, charge penetration, and dispersion effects, in conjunction with a standard treatment of anisotropic long-range (multipolar) electrostatics. To validate our approach, we benchmark MASTIFF against various sum-of-spheres models over a large library of intermolecular interactions between small organic molecules. MASTIFF achieves quantitative accuracy, with respect to both high-level electronic structure theory and experiment, thus showing promise as a basis for "next-generation" force field development.

From dimers to the solid-state: Distributed intermolecular force-fields for pyridine.

An anisotropic atom-atom force-field for pyridine, using distributed atomic multipoles, polarizabilities, and dispersion coefficients and an anisotropic atom-atom repulsion model derived from symmetry-adapted perturbation theory (density functional theory) dimer calculations, is used to model pyridine crystal structures. Here we show that this distributed intermolecular force-field (DIFF) models the experimental crystal structures as accurately as modelling all but the electrostatic term with an isotropic repulsion-dispersion potential that has been fitted to experimental crystal structures. In both cases, the differences are comparable to the changes in the crystal structure with temperature, pressure, or neglect of zero-point vibrational effects. A crystal structure prediction study has been carried out, and the observed polymorphs contrasted with hypothetical thermodynamically competitive crystal structures. The DIFF model was able to identify the structure of an unreported high pressure phase of pyridine, unlike the empirically fitted potential. The DIFF model approach therefore provides a model of the underlying pair potential energy surface that we have transferred to the crystalline phase with a considerable degree of success, though the treatment of the many-body terms needs improvement and the pair potential is slightly over-binding. Furthermore, this study of a system that exhibits isotopic polymorphism highlights that the use of an empirical potential has partially absorbed temperature and zero-point motion effects as well as the intermolecular forces not explicitly represented in the functional form. This study therefore highlights the complexity in modelling crystallization phenomena from a realistic pair potential energy surface.

Multipole Moments in the Effective Fragment Potential Method.

In the effective fragment potential (EFP) method the Coulomb potential is represented using a set of multipole moments generated by the distributed multipole analysis (DMA) method. Misquitta, Stone, and Fazeli recently developed a basis space-iterated stockholder atom (BS-ISA) method to generate multipole moments. This study assesses the accuracy of the EFP interaction energies using sets of multipole moments generated from the BS-ISA method, and from several versions of the DMA method (such as analytic and numeric grid-based), with varying basis sets. Both methods lead to reasonable results, although using certain implementations of the DMA method can result in large errors. With respect to the CCSD(T)/CBS interaction energies, the mean unsigned error (MUE) of the EFP method for the S22 data set using BS-ISA-generated multipole moments and DMA-generated multipole moments (using a small basis set and the analytic DMA procedure) is 0.78 and 0.72 kcal/mol, respectively. The MUE accuracy is on the same order as MP2 and SCS-MP2. The MUEs are lower than in a previous study benchmarking the EFP method without the EFP charge transfer term, demonstrating that the charge transfer term increases the accuracy of the EFP method. Regardless of the multipole moment method used, it is likely that much of the error is due to an insufficient short-range electrostatic term (i.e., charge penetration term), as shown by comparisons with symmetry-adapted perturbation theory.

Ab Initio Atom-Atom Potentials Using CamCASP: Theory and Application to Many-Body Models for the Pyridine Dimer.

Creating accurate, analytic atom-atom potentials for small organic molecules from first principles can be a time-consuming and computationally intensive task, particularly if we also require them to include explicit polarization terms, which are essential in many systems. We describe how the CamCASP suite of programs can be used to generate such potentials using some of the most accurate electronic structure methods currently applicable. We derive the long-range terms from monomer properties and determine the short-range anisotropy parameters by a novel and robust method based on the iterated stockholder atom approach. Using these techniques, we develop distributed multipole models for the electrostatic, polarization, and dispersion interactions in the pyridine dimer and develop a series of many-body potentials for the pyridine system. Even the simplest of these potentials exhibits root mean square errors of only about 0.6 kJ mol(-1) for the low-energy pyridine dimers, significantly surpassing the best empirical potentials. Our best model is shown to support eight stable minima, four of which have not been reported before in the literature. Further, the functional form can be made systematically more elaborate so as to improve the accuracy without a significant increase in the human-time spent in their generation. We investigate the effects of anisotropy, rank of multipoles, and choice of polarizability and dispersion models.

Beyond Born-Mayer: Improved Models for Short-Range Repulsion in ab Initio Force Fields.

Short-range repulsion within intermolecular force fields is conventionally described by either Lennard-Jones (A/r(12)) or Born-Mayer (A exp(-Br)) forms. Despite their widespread use, these simple functional forms are often unable to describe the interaction energy accurately over a broad range of intermolecular distances, thus creating challenges in the development of ab initio force fields and potentially leading to decreased accuracy and transferability. Herein, we derive a novel short-range functional form based on a simple Slater-like model of overlapping atomic densities and an iterated stockholder atom (ISA) partitioning of the molecular electron density. We demonstrate that this Slater-ISA methodology yields a more accurate, transferable, and robust description of the short-range interactions at minimal additional computational cost compared to standard Lennard-Jones or Born-Mayer approaches. Finally, we show how this methodology can be adapted to yield the standard Born-Mayer functional form while still retaining many of the advantages of the Slater-ISA approach.

Molecular dynamics simulation study of various zeolitic imidazolate framework structures.

We report the results of a series of molecular dynamics simulations on a number of zinc zeolitic imidazolate framework (ZIF) structures together with some lattice dynamics calculations on ZIF-4, providing information about the flexibilities of these structures. The simulations have used a force field we developed based on ab initio calculations of clusters of ligands and metal cations. We have shown that there are instabilities of the structures of some ZIF structures at low temperatures and high pressures. A rigidity analysis based on the Rigid Unit Mode model shows considerable degree of network flexibility, including a significant elastic flexibility.

Localized overlap algorithm for unexpanded dispersion energies.

First-principles-based, linearly scaling algorithm has been developed for calculations of dispersion energies from frequency-dependent density susceptibility (FDDS) functions with account of charge-overlap effects. The transition densities in FDDSs are fitted by a set of auxiliary atom-centered functions. The terms in the dispersion energy expression involving products of such functions are computed using either the unexpanded (exact) formula or from inexpensive asymptotic expansions, depending on the location of these functions relative to the dimer configuration. This approach leads to significant savings of computational resources. In particular, for a dimer consisting of two elongated monomers with 81 atoms each in a head-to-head configuration, the most favorable case for our algorithm, a 43-fold speedup has been achieved while the approximate dispersion energy differs by less than 1% from that computed using the standard unexpanded approach. In contrast, the dispersion energy computed from the distributed asymptotic expansion differs by dozens of percent in the van der Waals minimum region. A further increase of the size of each monomer would result in only small increased costs since all the additional terms would be computed from the asymptotic expansion.

Distributed Multipoles from a Robust Basis-Space Implementation of the Iterated Stockholder Atoms Procedure.

The recently developed iterated stockholder atoms (ISA) approach of Lillestolen and Wheatley (Chem. Commun. 2008, 5909) offers a powerful method for defining atoms in a molecule. However, the real-space algorithm is known to converge very slowly, if at all. Here, we present a robust, basis-space algorithm of the ISA method and demonstrate its applicability on a variety of systems. We show that this algorithm exhibits rapid convergence (taking around 10-80 iterations) with the number of iterations needed being unrelated to the system size or basis set used. Further, we show that the multipole moments calculated using this basis-space ISA method are as good as, or better than, those obtained from Stone's distributed multipole analysis (J. Chem. Theory Comput. 2005, 1, 1128), exhibiting better convergence properties and resulting in better behaved penetration energies. This can have significant consequences in the development of intermolecular interaction models.

Charge Transfer from Regularized Symmetry-Adapted Perturbation Theory.

The charge-transfer (CT) together with the polarization energy appears at second and higher orders in symmetry-adapted perturbation theory (SAPT). At present there is no theoretically compelling way of isolating the charge-transfer energy that is simultaneously basis-set independent and applicable for arbitrary intermolecular separation. We argue that the charge-transfer can be interpreted as a tunneling phenomenon and can therefore be defined via regularized SAPT. This leads to a physically convincing, basis-independent definition of the charge-transfer energy that captures subtleties of the process, such as the asymmetry in the forward and backward charge transfer, as well as secondary transfer effects. With this definition of the charge-transfer the damping needed for polarization models can be determined with a level of confidence hitherto not possible.

High pressure ionic and molecular crystals of ammonia monohydrate within density functional theory.

A combination of first-principles density functional theory calculations and a search over structures is used to predict the stability of a proton-transfer modification of ammonia monohydrate with space group P4∕nmm. The phase diagram is calculated with the Perdew-Burke-Ernzerhof (PBE) density functional, and the effects of a semi-empirical dispersion correction, zero point motion, and finite temperature are investigated. Comparison with MP2 and coupled cluster calculations shows that the PBE functional over-stabilizes proton transfer phases because too much electronic charge moves with the proton. This over-binding is partially corrected by using the PBE0 hybrid exchange-correlation functional, which increases the enthalpy of P4∕nmm by about 0.6 eV per formula unit relative to phase I of ammonia monohydrate and shifts the transition to the proton transfer phase from the PBE pressure of 2.8 GPa to about 10 GPa. This is consistent with experiment as proton transfer phases have not been observed at pressures up to ∼9 GPa, while higher pressures have not yet been explored experimentally.

A quantitative study of the clustering of polycyclic aromatic hydrocarbons at high temperatures.

The clustering of polycyclic aromatic hydrocarbon (PAH) molecules is investigated in the context of soot particle inception and growth using an isotropic potential developed from the benchmark PAHAP potential. This potential is used to estimate equilibrium constants of dimerisation for five representative PAH molecules based on a statistical mechanics model. Molecular dynamics simulations are also performed to study the clustering of homomolecular systems at a range of temperatures. The results from both sets of calculations demonstrate that at flame temperatures pyrene (C(16)H(10)) dimerisation cannot be a key step in soot particle formation and that much larger molecules (e.g. circumcoronene, C(54)H(18)) are required to form small clusters at flame temperatures. The importance of using accurate descriptions of the intermolecular interactions is demonstrated by comparing results to those calculated with a popular literature potential with an order of magnitude variation in the level of clustering observed. By using an accurate intermolecular potential we are able to show that physical binding of PAH molecules based on van der Waals interactions alone can only be a viable soot inception mechanism if concentrations of large PAH molecules are significantly higher than currently thought.