Toward a Physically Motivated Force Field: Hydrogen Bond Directionality from a Symmetry-Adapted Perturbation Theory Perspective

Range-dependence of two-body intermolecular interactions and their energy components in molecular crystals

Routinely assessing the stability of molecular crystals with high accuracy remains an open challenge in the computational sciences. The many-body expansion decomposes computation of the crystal lattice energy into an embarrassingly parallel collection of computations over molecular dimers, trimers, and so forth, making quantum chemistry techniques tractable for many crystals of small organic molecules. By examining the range-dependence of different types of energetic contributions to the crystal lattice energy, we can glean qualitative understanding of solid-state intermolecular interactions as well as practical, exploitable reductions in the number of computations required for accurate energies. Here, we assess the range-dependent character of two-body interactions of 24 small organic molecular crystals using the physically interpretable components from symmetry-adapted perturbation theory (electrostatics, exchange repulsion, induction/polarization, and London dispersion). We also examine correlations between the convergence rates of electrostatics and London dispersion terms with molecular dipole moments and polarizabilities, to provide guidance for estimating convergence rates in other molecular crystals.

CONI-Net: Machine Learning of Separable Intermolecular Force Fields

Noncovalent interactions (NCIs) play an essential role in soft matter and biomolecular simulations. The ab initio method symmetry-adapted perturbation theory allows a precise quantitative analysis of NCIs and offers an inherent energy decomposition, enabling a deeper understanding of the nature of intermolecular interactions. However, this method is limited to small systems, for instance, dimers of molecules. Here, we present a scale-bridging approach to systematically derive an intermolecular force field from ab initio data while preserving the energy decomposition of the underlying method. We apply the model in molecular dynamics simulations of several solvents and compare two predicted thermodynamic observables-mass density and enthalpy of vaporization-to experiments and established force fields. For a data set limited to hydrocarbons, we investigate the extrapolation capabilities to molecules absent from the training set. Overall, despite the affordable moderate quality of the reference ab initio data, we find promising results. With the straightforward data set generation procedure and the lack of target data in the fitting process, we have developed a method that enables the rapid development of predictive force fields with an extra dimension of insights into the balance of NCIs.

Automated Parameterization of Quantum Mechanically Derived Force Fields for Soft Materials and Complex Fluids: Development and Validation

The reliability of molecular dynamics (MD) simulations in predicting macroscopic properties of complex fluids and soft materials, such as liquid crystals, colloidal suspensions, or polymers, relies on the accuracy of the adopted force field (FF). We present an automated protocol to derive specific and accurate FFs, fully based on ab initio quantum mechanical (QM) data. The integration of the Joyce and Picky procedures, recently proposed by our group to provide an accurate description of simple liquids, is here extended to larger molecules, capable of exhibiting more complex fluid phases. While the standard Joyce protocol is employed to parameterize the intramolecular FF term, a new automated procedure is here proposed to handle the computational cost of the QM calculations required for the parameterization of the intermolecular FF term. The latter is thus obtained by integrating the old Picky procedure with a fragmentation reconstruction method (FRM) that allows for a reliable, yet computationally feasible sampling of the intermolecular energy surface at the QM level. The whole FF parameterization protocol is tested on a benchmark liquid crystal, and the performances of the resulting quantum mechanically derived (QMD) FF were compared with those delivered by a general-purpose, transferable one, and by the third, "hybrid" FF, where only the bonded terms were refined against QM data. Lengthy atomistic MD simulations are carried out with each FF on extended 5CB systems in both isotropic and nematic phases, eventually validating the proposed protocol by comparing the resulting macroscopic properties with other computational models and with experiments. The QMD-FF yields the best performances, reproducing both phases in the correct range of temperatures and well describing their structure, dynamics, and thermodynamic properties, thus providing a clear protocol that may be explored to predict such properties on other complex fluids or soft materials.

Charting Hydrogen Bond Anisotropy

A hydrogen bond (HB) is an essential interaction in countless phenomena, regulating the chemistry of life. HBs are characterized by two features, strength and directionality, with a high degree of heterogeneity across different chemical groups. These characteristics are dependent on the electronic configuration of the atoms involved in the interaction, which, in turn, is influenced strongly by the local molecular environment. Studies based on the analysis of HB in the solid phase, such as X-ray crystallography, suffer from significant biases due to packing forces. These will tend to better describe strong HBs at the expenses of weak ones, which will be either distorted or under-represented. Using quantum mechanics (QM), we calculated interaction energies for about a hundred acceptors and donors in a rigorously defined set of geometries. We performed 180,000 independent QM calculations, covering all relevant angular components, mapping strength and directionality in a context free from external biases, with both single-site and cooperative HBs. By quantifying directionality, we show that there is no correlation with strength; therefore, these two components need to be addressed separately. Results demonstrate that there are very strong HB acceptors (e.g., dimethyl sulfoxide) with nearly isotropic interactions and weak ones (e.g., thioacetone) with a sharp directional profile. Similarly, groups can have comparable directional propensity but be very distant in the strength spectrum (e.g., thioacetone and pyridine). Results provide a new perspective on the way HB directionality is described, with implications for biophysics and molecular recognition that ultimately can influence chemical biology, protein engineering, and drug design.

Symmetry-Adapted Perturbation Theory Decomposition of the Reaction Force: Insights into Substituent Effects Involved in Hemiacetal Formation Mechanisms

The decomposition of the reaction force based on symmetry-adapted perturbation theory (SAPT) has been proposed. This approach was used to investigate the substituent effects along the reaction coordinate pathway for the hemiacetal formation mechanism between methanol and substituted aldehydes of the form CX₃CHO (X = H, F, Cl, and Br), providing a quantitative evaluation of the reaction-driving and reaction-retarding force components. Our results highlight the importance of more favorable electrostatic and induction effects in the reactions involving halogenated aldehydes that leads to lower activation energy barriers. These substituent effects are further elucidated by applying the functional-group partition of symmetry-adapted perturbation theory (F-SAPT). The results show that the reaction is largely driven by favorable direct noncovalent interactions between the CX₃ group on the aldehyde and the OH group on methanol.

Classical Pauli repulsion: An anisotropic, atomic multipole model

Pauli repulsion is a key component of any theory of intermolecular interactions. Although Pauli or exchange repulsion has its origin in the quantum mechanical nature of electrons, it is possible to describe the resulting energetic effects via a classical model in terms of the overlap of electron densities. In fact, closed shell intermolecular repulsion can be explained as a diminution of election density in the internuclear region resulting in decreased screening of nuclear charges and increased nuclear-nuclear repulsion. We provide a concise anisotropic repulsion formulation using the atomic multipoles from the Atomic Multipole Optimized Energetics for Biomolecular Applications force field to describe the electron density at each atom in a larger system. Mathematically, the proposed model consists of damped pairwise exponential multipolar repulsion interactions truncated at short range, which are suitable for use in compute-intensive biomolecular force fields and molecular dynamics simulations. Parameters for 26 atom classes encompassing most organic molecules are derived from a fit to Symmetry Adapted Perturbation Theory exchange repulsion energies for the S101 dimer database. Several applications of the multipolar Pauli repulsion model are discussed, including noble gas interactions, analysis of stationary points on the water dimer potential surface, and the directionality of several halogen bonding interactions.

Read between the Molecules: Computational Insights into Organic Semiconductors

The performance and key electronic properties of molecular organic semiconductors are dictated by the interplay between the chemistry of the molecular core and the intermolecular factors of which manipulation has inspired both experimentalists and theorists. This Perspective presents major computational challenges and modern methodological strategies to advance the field. The discussion ranges from insights and design principles at the quantum chemical level, in-depth atomistic modeling based on multiscale protocols, morphological prediction and characterization as well as energy-property maps involving data-driven analysis. A personal overview of the past achievements and future direction is also provided.

A physically grounded damped dispersion model with particle mesh Ewald summation

Accurate modeling of dispersion is critical to the goal of predictive biomolecular simulations. To achieve this accuracy, a model must be able to correctly capture both the short-range and asymptotic behavior of dispersion interactions. We present here a damped dispersion model based on the overlap of charge densities that correctly captures both regimes. The overlap damped dispersion model represents a classical physical interpretation of dispersion: the interaction between the instantaneous induced dipoles of two distinct charge distributions. This model is shown to be an excellent fit with symmetry adapted perturbation theory dispersion energy calculations, yielding an RMS error on the S101x7 database of 0.5 kcal/mol. Moreover, the damping function used in this model is wholly derived and parameterized from the electrostatic dipole-dipole interaction, making it not only physically grounded but transferable as well.

Development and Validation of Quantum Mechanically Derived Force-Fields: Thermodynamic, Structural, and Vibrational Properties of Aromatic Heterocycles

A selection of several aromatic molecules, representative of the important class of heterocyclic compounds, has been considered for testing and validating an automated Force Field (FF) parametrization protocol, based only on Quantum Mechanical data. The parametrization is carried out separately for the intra- and intermolecular contributions, employing respectively the Joyce and Picky software packages, previously implemented and refined in our research group. The whole approach is here automated and integrated with a computationally effective yet accurate method, devised very recently ( J. Chem.

THEORY

Comput., 2018, 14, 543-556) to evaluate a large number of dimer interaction energies. The resulting quantum mechanically derived FFs are then used in extensive molecular dynamics simulations, in order to evaluate a number of thermodynamic, structural, and dynamic properties of the heterocycle's gas and liquid phases. The comparison with the available experimental data is good and furnishes a validation of the presented approach, which can be confidently exploited for the design of novel and more complex materials.

Site specificity of halogen bonding involving aromatic acceptors

Based on Cambridge structural database survey and quantum chemical studies, aromatic halogen bond (XB) acceptors are found to have unique pattern of XB binding sites and rim specificity.

Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis

The importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized with respect to both the QM electronic density and the MM induced dipoles. This QM/AMOEBA model is implemented through the Q-Chem/LibEFP code interface and then applied to the evaluation of solute-solvent interaction energies for various systems ranging from the water dimer to neutral and ionic solutes (NH₃, NH₄⁺, CN^-) surrounded by increasing numbers of water molecules (up to 100). In order to analyze the resulting interaction energies, we also utilize an energy decomposition analysis (EDA) scheme which identifies contributions from permanent electrostatics, polarization, and van der Waals (vdW) interaction for the interaction between the QM solute and the solvent molecules described by AMOEBA. This facilitates a component-wise comparison against full QM calculations where the corresponding energy components are obtained via a modified version of the absolutely localized molecular orbitals (ALMO)-EDA. The results show that the present QM/AMOEBA model can yield reasonable solute-solvent interaction energies for neutral and cationic species, while further scrutiny reveals that this accuracy highly relies on the delicate balance between insufficiently favorable permanent electrostatics and softened vdW interaction. For anionic solutes where the charge penetration effect becomes more pronounced, the QM/MM interface turns out to be unbalanced. These results are consistent with and further elucidate our findings in a previous study using a slightly different QM/AMOEBA model ( Dziedzic et al. J. Chem. Phys. 2016 , 145 , 124106 ). The implications of these results for further refinement of this model are also discussed.

Physical Molecular Mechanics Method for Damped Dispersion

Damped dispersion can be a significant component of the interaction energy in many physical and chemical processes, for example, physisorption and noncovalent complexation. For physically interpreting and modeling such processes, it is convenient to have an analytic method to calculate damped dispersion that is readily applicable across the entire periodic table. Of the available methods to calculate damped dispersion energy for interacting systems with overlapping charge distributions, we select symmetry-adapted perturbation theory (SAPT) as providing a reasonable definition, and of the possible analytic forms, we choose the D3(BJ) method. However, the available parametrizations of D3(BJ) include not only damped dispersion energy but also corrections for errors in specific exchange-correlation functionals. Here we present a parametrization that provides a physical measure of damped dispersion without such density functional corrections. The method generalizes an earlier method of Pernal and co-workers to all elements from hydrogen to plutonium.

Perspective: Quantum mechanical methods in biochemistry and biophysics

In this perspective article, I discuss several research topics relevant to quantum mechanical (QM) methods in biophysical and biochemical applications. Due to the immense complexity of biological problems, the key is to develop methods that are able to strike the proper balance of computational efficiency and accuracy for the problem of interest. Therefore, in addition to the development of novel ab initio and density functional theory based QM methods for the study of reactive events that involve complex motifs such as transition metal clusters in metalloenzymes, it is equally important to develop inexpensive QM methods and advanced classical or quantal force fields to describe different physicochemical properties of biomolecules and their behaviors in complex environments. Maintaining a solid connection of these more approximate methods with rigorous QM methods is essential to their transferability and robustness. Comparison to diverse experimental observables helps validate computational models and mechanistic hypotheses as well as driving further development of computational methodologies.

Assessing Ion-Water Interactions in the AMOEBA Force Field Using Energy Decomposition Analysis of Electronic Structure Calculations

AMOEBA is a molecular mechanics force field that addresses some of the shortcomings of a fixed partial charge model, by including permanent atomic point multipoles through quadrupoles, as well as many-body polarization through the use of point inducible dipoles. In this work, we investigate how well AMOEBA formulates its non-bonded interactions, and how it implicitly incorporates quantum mechanical effects such as charge penetration (CP) and charge transfer (CT), for water-water and water-ion interactions. We find that AMOEBA's total interaction energies, as a function of distance and over angular scans for the water dimer and for a range of water-monovalent cations, agree well with an advanced density functional theory (DFT) model, whereas the water-halides and water-divalent cations show significant disagreement with the DFT result, especially in the compressed region when the two fragments overlap. We use a second-generation energy decomposition analysis (EDA) scheme based on absolutely localized molecular orbitals (ALMOs) to show that in the best cases AMOEBA relies on cancellation of errors by softening of the van der Waals (vdW) wall to balance permanent electrostatics that are too unfavorable, thereby compensating for the missing CP effect. CT, as another important stabilizing effect not explicitly taken into account in AMOEBA, is also found to be incorporated by the softened vdW interaction. For the water-halides and water-divalent cations, this compensatory approach is not as well executed by AMOEBA over all distances and angles, wherein permanent electrostatics remains too unfavorable and polarization is overdamped in the former while overestimated in the latter. We conclude that the DFT-based EDA approach can help refine a next-generation AMOEBA model that either realizes a better cancellation of errors for problematic cases like those illustrated here, or serves to guide the parametrization of explicit functional forms for short-range contributions from CP and/or CT.

Challenging Dogmas: Hydrogen Bond Revisited

Hydrogen bond directionality in the water dimer is explained on the basis of symmetry-adapted intermolecular perturbation theory which directly separates the intermolecular interaction energy into four physically interpretable components: electrostatics, exchange-repulsion, dispersion, and induction. Analysis of these four main contributions to the binding energy allows a deeper understanding of the dominant factors ruling the mutual arrangement of the two monomers. A preference for the linear configuration is shown to be due to a subtle interplay of all four energy components. While the first-order terms, electrostatic and exchange-repulsion, almost perfectly cancel each other near the equilibrium geometry of the dimer, the importance of the second- and higher-order terms, induction and dispersion, becomes evident.

A Universal and Straightforward Approach to Include Penetration Effects in Electrostatic Interaction Energy Estimation

To compensate for the lack of the explicit treatment of charge penetration in classical force fields, we propose a new charge-distribution model based on a promolecule augmented with point charges (aug-PROmol). It relies on a superposition of spherical atomic electron densities obtained for each chemical element from SCF energy optimized atomic orbitals. Atomic densities are further rescaled by partial point charges computed from fits to the molecular electrostatic potential. Aug-PROmol was tested on the S66 benchmark dataset extended to nonequilibrium geometries (J. Chem. Theory Comput., 2011, 7, 3466). The model does not need any additional parametrization other than point charges. Despite its simplicity, aug-PROmol approximates the electrostatic energy with good agreement (RMSE=0.76 kcal mol(-1) to DFT-SAPT with B3LYP/aug-cc-pVTZ).