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

Water-carbon disulfide dimers: observation of a new isomer and ab initio structure theory

The weakly bound dimer water-carbon disulfide is studied by ab initio structure theory and high-resolution infrared spectroscopy. The calculations yield three stable minima in the potential energy surface, all planar. The most stable, isomer 1, was observed previously by microwave spectroscopy. It has C2v symmetry, an S-O bond, and a linear O-S-C-S backbone. Isomer 2, the next most stable, has not been considered previously by theory or experiment. It also has C2v symmetry, but with a side-by-side structure. Isomer 3, which is slightly less stable, is side-by-side with one O-H bond pointing toward an S atom. The first gas phase water-CS2 infrared spectra are reported. For isomer 1, H2O-, HDO-, and D2O-CS2 are observed in the CS2ν1 + ν3 region, H2O-CS2 in the H2O ν2 bend region, and D2O-CS2 in the D2O ν1 and ν3 stretch regions. The latter ν3 spectrum enables an experimental determination of the A rotational parameter, which turns out to be larger than expected. The new isomer 2 is observed by means of a band in the H2O ν2 region, confirming its C2v symmetry and calculated structure.

Use of caps in the auxiliary basis set formulation of the fragment molecular orbital method

An auxiliary polarization formulation of the fragment molecular orbital (FMO) method is developed, combining a basis set correction computed for capped isolated fragments with a polarization obtained from uncapped fragments. For a set of organic and inorganic test systems, it is shown that the total energy and atomic charges are accurately reproduced with respect to full unfragmented calculations. It is demonstrated that the method is accurate for computing electronic excited states. The developed approach is applied to rank the isomers of chignolin from experimental NMR data (PDB: 1UAO) according to their relative energy. Contributions of polarization and basis set effects to pair interactions between fragments are elucidated.

Water Electric Field Induced Modulation of the Wetting of Hexagonal Boron Nitride: Insights from Multiscale Modeling of Many-Body Polarization

Understanding the behavior of water contacting two-dimensional materials, such as hexagonal boron nitride (hBN), is important in practical applications, including seawater desalination and energy harvesting. Water, being a polar solvent, can strongly polarize the hBN surface via the electric fields that it generates. However, there is a lack of molecular-level understanding about the role of polarization effects at the hBN/water interface, including its effect on the wetting properties of water. In this study, we develop a theoretical framework that introduces an all-atomistic polarizable force field to accurately model the interactions of water molecules with hBN surfaces. The force field is then utilized to self-consistently describe the water-induced polarization of hBN using the classical Drude oscillator model, including predicting the hBN-water binding energies which are found to be in excellent agreement with diffusion Monte Carlo (DMC) predictions. By carrying out molecular dynamics (MD) simulations, we demonstrate that the polarizable force field yields a water contact angle on multilayered hBN which is in close agreement with the recent experimentally reported values. Conversely, an implicit modeling of the hBN-water polarization energy utilizing a Lennard-Jones (LJ) potential, a commonly utilized approximation in previous MD simulation studies, leads to a considerably lower water contact angle. This difference in the predicted contact angles is attributed to the significant energy-entropy compensation resulting from the incorporation of polarization effects at the hBN-water interface. Our work highlights the importance of self-consistently modeling the hBN-water polarization energy and offers insights into the wetting-related interfacial phenomena of water on polarizable materials.

Benchmarking Swaths of Intermolecular Interaction Components with Symmetry-Adapted Perturbation Theory

A benchmark database for interaction energy components of various noncovalent interactions (NCIs) along their dissociation curve is one of the essential needs in theoretical chemistry, especially for the development of force fields and machine-learning methods. We utilize DFT-SAPT or SAPT(DFT) as one of the most accurate methods to generate an extensive stock of the energy components, including dispersion energies extrapolated to the complete basis set limit (CBS). Precise analyses of the created data, and benchmarking the total interaction energies against the best available CCSD(T)/CBS values, reveal different aspects of the methodology and the nature of NCIs. For example, error cancellation effects between the S2 approximation and nonexact xc-potentials occur, and large charge transfer energies in some systems, including heavy atoms, can explain the lower accuracy of DFT-SAPT. This method is perfect for neutral complexes containing light nonmetals, while other systems with heavier atoms should be treated carefully. In the last part, a representative data set for all NCIs is extracted from the original data.

Force-field-enhanced neural network interactions: from local equivariant embedding to atom-in-molecule properties and long-range effects

We introduce FENNIX (Force-Field-Enhanced Neural Network InteraXions), a hybrid approach between machine-learning and force-fields. We leverage state-of-the-art equivariant neural networks to predict local energy contributions and multiple atom-in-molecule properties that are then used as geometry-dependent parameters for physically-motivated energy terms which account for long-range electrostatics and dispersion. Using high-accuracy ab initio data (small organic molecules/dimers), we trained a first version of the model. Exhibiting accurate gas-phase energy predictions, FENNIX is transferable to the condensed phase. It is able to produce stable Molecular Dynamics simulations, including nuclear quantum effects, for water predicting accurate liquid properties. The extrapolating power of the hybrid physically-driven machine learning FENNIX approach is exemplified by computing: (i) the solvated alanine dipeptide free energy landscape; (ii) the reactive dissociation of small molecules.

Site-Specific Ionization Potentials and Electron Affinities in Large Molecular Systems at Coupled Cluster Level

A many-body expansion of ionization potentials and electron affinities is developed based on a combination of the fragment molecular orbital method and equation-of-motion coupled-cluster (EOM-CC). In addition to site-specific values, obtained as one-body properties, pair and triple corrections are added to account for nonlocal EOM-CC contributions of the molecular environment of a chromophore. The developed method is applied to carboxylic acids, alkyl cations, a protein ubiquitin (Protein Data Bank ID 1UBQ), and a nano ribbon of white graphene elucidating the effect of environment on ionization potential and electron affinity.

General Charge Transfer Dipole Model for AMOEBA-Like Force Fields

The development of highly accurate force fields is always an importance aspect in molecular modeling. In this work, we introduce a general damping-based charge transfer dipole (D-CTD) model to describe the charge transfer energy and the corresponding charge flow for H, C, N, O, P, S, F, Cl, and Br elements in common bio-organic systems. Then, two effective schemes to evaluate the charge flow from the corresponding induced dipole moment between the interacting molecules were also proposed and discussed. The potential applicability of the D-CTD model in ion-containing systems was also demonstrated in a series of ion-water complexes including Li⁺, Na⁺, K⁺, Mg²⁺, Ca²⁺, Fe²⁺, Zn²⁺, Pt²⁺, F^-, Cl^-, Br^-, and I^- ions. In general, the D-CTD model demonstrated good accuracy and good transferability in both charge transfer energy and the corresponding charge flow for a wide range of model systems. By distinguishing the intermolecular charge redistribution (charge transfer) under the influence of an external electric field from the accompanying intramolecular charge redistribution (polarization), the D-CTD model is theoretically consistent with current induced dipole-based polarizable dipole models and hence can be easily implemented and parameterized. Along with our previous work in charge penetration-corrected electrostatics, a bottom-up approach constructed water model was also proposed and demonstrated. The structure-maker and structure-breaker roles of cations and anions were also correctly reproduced using Na⁺, K⁺, Cl^-, and I^- ions in the new water model, respectively. This work demonstrates a cost-effective approach to describe the charge transfer phenomena. The water and ion models also show the feasibility of a modulated development approach for future force fields.

Force Decomposition Analysis: A Method to Decompose Intermolecular Forces into Physically Relevant Component Contributions

Computational quantum chemistry can be more than just numerical experiments when methods are specifically adapted to investigate chemical concepts. One important example is the development of energy decomposition analysis (EDA) to reveal the physical driving forces behind intermolecular interactions. In EDA, typically the interaction energy from a good-quality density functional theory (DFT) calculation is decomposed into multiple additive components that unveil permanent and induced electrostatics, Pauli repulsion, dispersion, and charge-transfer contributions to noncovalent interactions. Herein, we formulate, implement, and investigate decomposing the forces associated with intermolecular interactions into the same components. The resulting force decomposition analysis (FDA) is potentially useful as a complement to the EDA to understand chemistry, while also providing far more information than an EDA for data analysis purposes such as training physics-based force fields. We apply the FDA based on absolutely localized molecular orbitals (ALMOs) to analyze interactions of water with sodium and chloride ions as well as in the water dimer. We also analyze the forces responsible for geometric changes in carbon dioxide upon adsorption onto (and activation by) gold and silver anions. We also investigate how the force components of an EDA-based force field for water clusters, namely MB-UCB, compare to those from force decomposition analysis.

Development and Implementation of Atomically Anisotropic First-Principles Force Fields: A Benzene Case Study

π-interactions are an important motif in chemical and biochemical systems. However, due to their anisotropic electron densities and complex balance of intermolecular interactions, aromatic molecules represent an ongoing challenge for accurate and transferable force field development. Historically, ab initio force fields for aromatics have not exhibited good accuracy with respect to bulk properties or have only been used to study gas-phase dimers. Using benzene as a proof of concept, herein we show how our own ab initio MASTIFF force field incorporates an atomically anisotropic description of intermolecular interactions to yield an accurate and robust model for aromatic interactions irrespective of phase. Compared to existing models, the MASTIFF benzene force field not only is accurate for liquid phase properties but also offers transferability to the gas and solid phases. Additionally, we introduce a computationally efficient OpenMM plugin which enables customizable anisotropic intermolecular functional forms and which can be generically used in any MD simulation where a model for nonspherical atomic features is required. Overall, our results demonstrate the importance of atomic-level anisotropy in enabling next-generation ab initio force field development.

Parametrized quantum-mechanical approaches combined with the fragment molecular orbital method

Fast parameterized methods such as density-functional tight-binding (DFTB) facilitate realistic calculations of large molecular systems, which can be accelerated by the fragment molecular orbital (FMO) method. Fragmentation facilitates interaction analyses between functional parts of molecular systems. In addition to DFTB, other parameterized methods combined with FMO are also described. Applications of FMO methods to biochemical and inorganic systems are reviewed.

Protein-Ligand Binding Free-Energy Calculations with ARROW─A Purely First-Principles Parameterized Polarizable Force Field

Protein-ligand binding free-energy calculations using molecular dynamics (MD) simulations have emerged as a powerful tool for in silico drug design. Here, we present results obtained with the ARROW force field (FF)─a multipolar polarizable and physics-based model with all parameters fitted entirely to high-level ab initio quantum mechanical (QM) calculations. ARROW has already proven its ability to determine solvation free energy of arbitrary neutral compounds with unprecedented accuracy. The ARROW FF parameterization is now extended to include coverage of all amino acids including charged groups, allowing molecular simulations of a series of protein-ligand systems and prediction of their relative binding free energies. We ensure adequate sampling by applying a novel technique that is based on coupling the Hamiltonian Replica exchange (HREX) with a conformation reservoir generated via potential softening and nonequilibrium MD. ARROW provides predictions with near chemical accuracy (mean absolute error of ∼0.5 kcal/mol) for two of the three protein systems studied here (MCL1 and Thrombin). The third protein system (CDK2) reveals the difficulty in accurately describing dimer interaction energies involving polar and charged species. Overall, for all of the three protein systems studied here, ARROW FF predicts relative binding free energies of ligands with a similar accuracy level as leading nonpolarizable force fields.

Physical mechanisms of intermolecular interactions from symmetry-adapted perturbation theory

Symmetry-adapted perturbation theory (SAPT) is a method for computational studies of noncovalent interactions between molecules. This method will be discussed here from the perspective of establishing the paradigm for understanding mechanisms of intermolecular interactions. SAPT interaction energies are obtained as sums of several contributions. Each contribution possesses a clear physical interpretation as it results from some specific physical process. It also exhibits a specific dependence on the intermolecular separation R. The four major contributions are the electrostatic, induction, dispersion, and exchange energies, each due to a different mechanism, valid at any R. In addition, at large R, SAPT interaction energies are seamlessly connected with the corresponding terms in the asymptotic multipole expansion of interaction energy in inverse powers of R. Since such expansion explicitly depends on monomers' multipole moments and polarizabilities, this connection provides additional insights by rigorously relating interaction energies to monomers' properties.

Development of the Quantum-Inspired SIBFA Many-Body Polarizable Force Field: Enabling Condensed-Phase Molecular Dynamics Simulations

We present the extension of the Sum of Interactions Between Fragments Ab initio Computed (SIBFA) many-body polarizable force field to condensed-phase molecular dynamics (MD) simulations. The quantum-inspired SIBFA procedure is grounded on simplified integrals obtained from localized molecular orbital theory and achieves full separability of its intermolecular potential. It embodies long-range multipolar electrostatics (up to quadrupole) coupled to a short-range penetration correction (up to charge-quadrupole), exchange repulsion, many-body polarization, many-body charge transfer/delocalization, exchange dispersion, and dispersion (up to C10). This enables the reproduction of all energy contributions of ab initio symmetry-adapted perturbation theory (SAPT(DFT)) gas-phase reference computations. The SIBFA approach has been integrated within the Tinker-HP massively parallel MD package. To do so, all SIBFA energy gradients have been derived and the approach has been extended to enable periodic boundary conditions simulations using smooth particle mesh Ewald. This novel implementation also notably includes a computationally tractable simplification of the many-body charge transfer/delocalization contribution. As a proof of concept, we perform a first computational experiment defining a water model fitted on a limited set of SAPT(DFT) data. SIBFA is shown to enable a satisfactory reproduction of both gas-phase energetic contributions and condensed-phase properties highlighting the importance of its physically motivated functional form.

Molecular basis for the initiation of DNA primer synthesis

During the initiation of DNA replication, oligonucleotide primers are synthesized de novo by primases and are subsequently extended by replicative polymerases to complete genome duplication. The primase-polymerase (Prim-Pol) superfamily is a diverse grouping of primases, which includes replicative primases and CRISPR-associated primase-polymerases (CAPPs) involved in adaptive immunity^1-3. Although much is known about the activities of these enzymes, the precise mechanism used by primases to initiate primer synthesis has not been elucidated. Here we identify the molecular bases for the initiation of primer synthesis by CAPP and show that this mechanism is also conserved in replicative primases. The crystal structure of a primer initiation complex reveals how the incoming nucleotides are positioned within the active site, adjacent to metal cofactors and paired to the templating single-stranded DNA strand, before synthesis of the first phosphodiester bond. Furthermore, the structure of a Prim-Pol complex with double-stranded DNA shows how the enzyme subsequently extends primers in a processive polymerase mode. The structural and mechanistic studies presented here establish how Prim-Pol proteins instigate primer synthesis, revealing the requisite molecular determinants for primer synthesis within the catalytic domain. This work also establishes that the catalytic domain of Prim-Pol enzymes, including replicative primases, is sufficient to catalyse primer formation.

Polarization energies in the fragment molecular orbital method

Using isolated and polarized states of fragments, a method for computing the polarization energies in density functional theory (DFT) and density-functional tight-binding (DFTB) is developed in the framework of the fragment molecular orbital method. For DFTB, the method is extended into the use of periodic boundary conditions (PBC), for which a new component, a periodic self-polarization energy, is derived. The couplings of the polarization to other components in the pair interaction energy analysis (PIEDA) are derived for DFT and DFTB, and compared to Hartree-Fock and second-order Møller-Plesset perturbation theory (MP2). The effect of the self-consistent (DFT) and perturbative (MP2) treatment of the electron correlation on the polarization is discussed. The difference in the polarization in the bulk (PBC) and micro (cluster) solvation is elucidated.

Using atomic charges to model molecular polarization

We review different models for introducing electric polarization in force fields, with special focus on methods where polarization is modelled at the atomic charge level. While electric polarization has been included in several force fields, the common approach has been to focus on atomic dipole polarizability. Several approaches allow modelling electric polarization by using charge-flow between charge sites instead, but this has been less exploited, despite that atomic charges and charge-flow is expected to be more important than atomic dipoles and dipole polarizability. A number of challenges are required to be solved for charge-flow models to be incorporated into polarizable force fields, for example how to parameterize the models and how to make them computational efficient.

Improvement of the Gaussian Electrostatic Model by separate fitting of Coulomb and exchange-repulsion densities and implementation of a new dispersion term

The description of each separable contribution of the intermolecular interaction is a useful approach to develop polarizable force fields (polFFs). The Gaussian Electrostatic Model (GEM) is based on this approach, coupled with the use of density fitting techniques. In this work, we present the implementation and testing of two improvements of GEM: the Coulomb and exchange-repulsion energies are now computed with separate frozen molecular densities and a new dispersion formulation inspired by the Sum of Interactions Between Fragments Ab initio Computed polFF, which has been implemented to describe the dispersion and charge-transfer interactions. Thanks to the combination of GEM characteristics and these new features, we demonstrate a better agreement of the computed structural and condensed properties for water with experimental results, as well as binding energies in the gas phase with the ab initio reference compared with the previous GEM* potential. This work provides further improvements to GEM and the items that remain to be improved and the importance of the accurate reproduction for each separate contribution.

A Quantum Chemical Topology Picture of Intermolecular Electrostatic Interactions and Charge Penetration Energy

Based on the Interacting Quantum Atoms approach, we present herein a conceptual and theoretical framework of short-range electrostatic interactions, whose accurate description is still a challenging problem in molecular modeling. For all the noncovalent complexes in the S66 database, the fragment-based and atomic decomposition of the electrostatic binding energies is performed using both the charge density of the dimers and the unrelaxed densities of the monomers. This energy decomposition together with dispersion corrections gives rise to a pairwise approximation to the total binding energy. It also provides energetic descriptors at varying distance that directly address the atomic and molecular electrostatic interactions as described by point-charge or multipole-based potentials. Additionally, we propose a consistent definition of the charge penetration energy within quantum chemical topology, which is mainly characterized in terms of the intramolecular electrostatic energy. Finally, we discuss some practical implications of our results for the design and validation of electrostatic potentials.

Multimolecular complexes of the phosphodiester anion with Zn(II) or Mg(II) and water molecules-Preliminary validations of a polarizable potential by ab initio quantum chemistry

Dimethyl phosphate (DMP^- ) is a model for the phosphodiester backbone of DNA, RNA, and phospholipids. It is central for the binding of divalent cations and water along the backbone of nucleic acids. Significant polarization and charge-transfer contributions and nonadditivity come into play in the multimolecular complexes organized around phosphate. Prior to large-scale molecular dynamics (MD) with advanced polarizable potentials, it is essential to evaluate how well the values and trends of intermolecular interaction energies (ΔE) from ab initio quantum chemistry (QC) and their individual contributions are reproduced in a diversity of such complexes. These differ by the starting binding modes of a divalent cation, Zn(II), namely direct, bi- or mono-dentate to anionic and/or ester oxygens, versus through-water binding. We present first the results from automated refinements of the individual contributions of the SIBFA potential with respect to their QC counterparts using a Zn(II) or a water probe. This is followed by validations on eight relaxed multimolecular complexes of DMP^- with Zn(II) or Mg(II) and seven waters, then on sixteen complexes of DMP^- with Zn(II) and eight waters in arrangements extracted from MD or energy-minimization on a droplet of sixty-four waters. This monitors the compared evolutions of SIBFA and QC ΔE and their individual contributions in the competing arrangements. Some waters, bridging Zn(II) and DMP^- , were found to have exceptionally large dipole moments, of up to 3.8 Debye. The perspectives of extension to a flexible phosphodiester backbone are discussed in the context of the SIBFA potential for DNA and RNA.