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While the many-body expansion (MBE) and counterpoise treatments are commonly used to mitigate the high scaling of accurate ab initio methods, researchers may need to piece together tools and scripts if their primary chosen software does not support targeted features. To further modular software in quantum chemistry, the arbitrary-order, multiple-model-chemistry, counterpoise-enabled MBE implementation from Psi4 has been extracted into an independent, lightweight, and open-source Python module, QCManyBody, with new schema underpinning, application programming interface, and software integrations. The package caters to direct users by facilitating single-point and geometry optimization MBE calculations backed by popular quantum chemistry codes through the QCEngine runner and by defining a schema for requesting and reporting many-body computations. It also serves developers and integrators by providing minimal, composable, and extensible interfaces. The design and flexibility of QCManyBody are demonstrated via integrations with geomeTRIC, OptKing, Psi4, QCEngine, and the QCArchive project. [ABSTRACT FROM AUTHOR]

Symmetry-adapted perturbation theory (SAPT) is an ab initio approach that directly computes noncovalent interaction energies in terms of electrostatics, exchange repulsion, induction/polarization, and London dispersion components. Due to its high computational scaling, routine applications of even the lowest order of SAPT are typically limited to a few hundred atoms. To address this limitation, we report here the addition of electrostatic embedding to the SAPT (EE-SAPT) and ISAPT (EE-ISAPT) methods. We illustrate the embedding scheme using water trimer as a prototype example. Then, we show that EE-SAPT/EE-ISAPT can be applied for efficiently and accurately computing noncovalent interactions in large systems, including solvated dimers and protein–ligand systems. In the latter application, particular care must be taken to properly handle the quantum mechanics/molecular mechanics boundary when it cuts covalent bonds. We investigate various schemes for handling charges near this boundary and demonstrate which are most effective in the context of charge-embedded SAPT. [ABSTRACT FROM AUTHOR]

Symmetry-adapted perturbation theory (SAPT) directly computes intermolecular interaction energy in terms of electrostatics, exchange-repulsion, induction/polarization, and London dispersion components. In SAPT based on Hartree–Fock ("SAPT0") or based on density functional theory, the most time-consuming step is the computation of the dispersion terms. Previous work has explored the replacement of these expensive dispersion terms with simple damped asymptotic models. We recently examined [Schriber et al. J. Chem. Phys. 154, 234107 (2021)] the accuracy of SAPT0 when replacing its dispersion term with Grimme's popular -D3 correction, reducing the computational cost scaling from O ( N 5 ) to O ( N 3 ). That work optimized damping function parameters for SAPT0-D3/jun-cc-pVDZ using estimates of the coupled-cluster complete basis set limit [CCSD(T)/CBS] on a 8299 dimer dataset. Here, we explore the accuracy of SAPT0-D3 with additional basis sets, along with an analogous model using -D4. Damping parameters are rather insensitive to basis sets, and the resulting SAPT0-D models are more accurate on average for total interaction energies than SAPT0. Our results are surprising in several respects: (1) improvement of -D4 over -D3 is negligible for these systems, even charged systems where -D4 should, in principle, be more accurate; (2) addition of Axilrod–Teller–Muto terms for three-body dispersion does not improve error statistics for this test set; and (3) SAPT0-D is even more accurate on average for total interaction energies than the much more computationally costly density functional theory based SAPT [SAPT(DFT)] in an aug-cc-pVDZ basis. However, SAPT0 and SAPT0-D3/D4 interaction energies benefit from significant error cancellation between exchange and dispersion terms. [ABSTRACT FROM AUTHOR]

We present an efficient, open-source formulation for coupled-cluster theory through perturbative triples with domain-based local pair natural orbitals [DLPNO-CCSD(T)]. Similar to the implementation of the DLPNO-CCSD(T) method found in the ORCA package, the most expensive integral generation and contraction steps associated with the CCSD(T) method are linear-scaling. In this work, we show that the t1-transformed Hamiltonian allows for a less complex algorithm when evaluating the local CCSD(T) energy without compromising efficiency or accuracy. Our algorithm yields sub-kJ mol−1 deviations for relative energies when compared with canonical CCSD(T), with typical errors being on the order of 0.1 kcal mol−1, using our TightPNO parameters. We extensively tested and optimized our algorithm and parameters for non-covalent interactions, which have been the most difficult interaction to model for orbital (PNO)-based methods historically. To highlight the capabilities of our code, we tested it on large water clusters, as well as insulin (787 atoms). [ABSTRACT FROM AUTHOR]

Multiple algorithms exist for calculating Coulomb (J) or exchange (K) contributions to Fock-like matrices, and it is beneficial to develop a framework that allows the seamless integration and combination of different J and K construction algorithms. In Psi4, we have implemented the "CompositeJK" formalism for this purpose. CompositeJK allows for the combination of any J and K construction algorithms for any quantum chemistry method formulated in terms of J-like or K-like matrices (including, but not limited to, Hartree–Fock and density functional theory) in a highly modular and intuitive fashion, which is simple to utilize for both developers and users. Using the CompositeJK framework, Psi4 was interfaced to the sn-LinK implementation in the GauXC library, adding the first instance of noncommercial graphics processing unit (GPU) support for the construction of Fock matrix elements to Psi4. On systems with hundreds of atoms, the interface to the CPU sn-LinK implementation displays a higher performance than all the alternative JK construction methods available in Psi4, with up to x2.8 speedups compared to existing Psi4JK implementations. The GPU sn-LinK implementation, harnessing the power of GPUs, improves the observed performance gains to up to x7.0. [ABSTRACT FROM AUTHOR]

Access to accurate force-field parameters for small molecules is crucial for computational studies of their interactions with proteins. Although a number of general force fields for small molecules exist, e.g., CGenFF, GAFF, and OPLS, they do not cover all common chemical groups and their combinations. The Force Field Toolkit (ffTK) provides a comprehensive graphical interface that streamlines the development of classical parameters for small molecules directly from quantum mechanical (QM) calculations, allowing for force-field generation for almost any chemical group and validation of the fit relative to the target data. ffTK relies on supported external software for the QM calculations, but it can generate the necessary QM input files and parse and analyze the QM output. In previous ffTK versions, support for Gaussian and ORCA QM packages was implemented. Here, we add support for Psi4, an open-source QM package free for all users, thereby broadening user access to ffTK. We also compare the parameter sets obtained with the new ffTK version using Gaussian, ORCA, and Psi4 for three molecules: pyrrolidine, n-propylammonium cation, and chlorobenzene. Despite minor differences between the resulting parameter sets for each compound, most prominently in the dihedral and improper terms, we show that conformational distributions sampled in molecular dynamics simulations using these parameter sets are quite comparable. [ABSTRACT FROM AUTHOR]

Community efforts in the computational molecular sciences (CMS) are evolving toward modular, open, and interoperable interfaces that work with existing community codes to provide more functionality and composability than could be achieved with a single program. The Quantum Chemistry Common Driver and Databases (QCDB) project provides such capability through an application programming interface (API) that facilitates interoperability across multiple quantum chemistry software packages. In tandem with the Molecular Sciences Software Institute and their Quantum Chemistry Archive ecosystem, the unique functionalities of several CMS programs are integrated, including CFOUR, GAMESS, NWChem, OpenMM, Psi4, Qcore, TeraChem, and Turbomole, to provide common computational functions, i.e., energy, gradient, and Hessian computations as well as molecular properties such as atomic charges and vibrational frequency analysis. Both standard users and power users benefit from adopting these APIs as they lower the language barrier of input styles and enable a standard layout of variables and data. These designs allow end-to-end interoperable programming of complex computations and provide best practices options by default.

The focal-point approximation can be used to estimate a high-accuracy, slow quantum chemistry computation by combining several lower-accuracy, faster computations. We examine the performance of focal-point methods by combining second-order Møller–Plesset perturbation theory (MP2) with coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] for the calculation of harmonic frequencies and that of fundamental frequencies using second-order vibrational perturbation theory (VPT2). In contrast to standard CCSD(T), the focal-point CCSD(T) method approaches the complete basis set (CBS) limit with only triple-ζ basis sets for the coupled-cluster portion of the computation. The predicted harmonic and fundamental frequencies were compared with the experimental values for a set of 20 molecules containing up to six atoms. The focal-point method combining CCSD(T)/aug-cc-pV(T + d)Z with CBS-extrapolated MP2 has mean absolute errors vs experiment of only 7.3 cm−1 for the fundamental frequencies, which are essentially the same as the mean absolute error for CCSD(T) extrapolated to the CBS limit using the aug-cc-pV(Q + d)Z and aug-cc-pV(5 + d)Z basis sets. However, for H2O, the focal-point procedure requires only 3% of the computation time as the extrapolated CCSD(T) result, and the cost savings will grow for larger molecules. [ABSTRACT FROM AUTHOR]

Dimer interaction energies have been well studied in computational chemistry, but they can offer an incomplete understanding of molecular binding depending on the system. In the current study, we present a dataset of focal-point coupled-cluster interaction and deformation energies (summing to binding energies, De) of 28 organic molecular dimers. We use these highly accurate energies to evaluate ten density functional approximations for their accuracy. The best performing method (with a double-ζ basis set), B97M-D3BJ, is then used to calculate the binding energies of 104 organic dimers, and we analyze the influence of the nature and strength of interaction on deformation energies. Deformation energies can be as large as 50% of the dimer interaction energy, especially when hydrogen bonding is present. In most cases, two or more hydrogen bonds present in a dimer correspond to an interaction energy of −10 to −25 kcal mol−1, allowing a deformation energy above 1 kcal mol−1 (and up to 9.5 kcal mol−1). A lack of hydrogen bonding usually restricts the deformation energy to below 1 kcal mol−1 due to the weaker interaction energy. [ABSTRACT FROM AUTHOR]

The many-body expansion (MBE) is promising for the efficient, parallel computation of lattice energies in organic crystals. Very high accuracy should be achievable by employing coupled-cluster singles, doubles, and perturbative triples at the complete basis set limit [CCSD(T)/CBS] for the dimers, trimers, and potentially tetramers resulting from the MBE, but such a brute-force approach seems impractical for crystals of all but the smallest molecules. Here, we investigate hybrid or multi-level approaches that employ CCSD(T)/CBS only for the closest dimers and trimers and utilize much faster methods like Møller–Plesset perturbation theory (MP2) for more distant dimers and trimers. For trimers, MP2 is supplemented with the Axilrod–Teller–Muto (ATM) model of three-body dispersion. MP2(+ATM) is shown to be a very effective replacement for CCSD(T)/CBS for all but the closest dimers and trimers. A limited investigation of tetramers using CCSD(T)/CBS suggests that the four-body contribution is entirely negligible. The large set of CCSD(T)/CBS dimer and trimer data should be valuable in benchmarking approximate methods for molecular crystals and allows us to see that a literature estimate of the core-valence contribution of the closest dimers to the lattice energy using just MP2 was overbinding by 0.5 kJ mol−1, and an estimate of the three-body contribution from the closest trimers using the T0 approximation in local CCSD(T) was underbinding by 0.7 kJ mol−1. Our CCSD(T)/CBS best estimate of the 0 K lattice energy is −54.01 kJ mol−1, compared to an estimated experimental value of −55.3 ± 2.2 kJ mol−1. [ABSTRACT FROM AUTHOR]

Psi4 is an ab initio electronic structure program providing methods such as Hartree-Fock, density functional theory, configuration interaction, and coupled-cluster theory. The 1.1 release represents a major update meant to automate complex tasks, such as geometry optimization using complete-basis-set extrapolation or focal-point methods. Conversion of the top-level code to a Python module means that Psi4 can now be used in complex workflows alongside other Python tools. Several new features have been added with the aid of libraries providing easy access to techniques such as density fitting, Cholesky decomposition, and Laplace denominators. The build system has been completely rewritten to simplify interoperability with independent, reusable software components for quantum chemistry. Finally, a wide range of new theoretical methods and analyses have been added to the code base, including functional-group and open-shell symmetry adapted perturbation theory, density-fitted coupled cluster with frozen natural orbitals, orbital-optimized perturbation and coupled-cluster methods (e.g., OO-MP2 and OO-LCCD), density-fitted multiconfigurational self-consistent field, density cumulant functional theory, algebraic-diagrammatic construction excited states, improvements to the geometry optimizer, and the "X2C" approach to relativistic corrections, among many other improvements.

To study the contribution of three-body dispersion to crystal lattice energies, we compute the three-body contributions to the lattice energies for crystalline benzene, carbon dioxide, and triazine using various computational methods. We show that these contributions converge quickly as the intermolecular distances between the monomers grow. In particular, the smallest value among the three pairwise intermonomer closest-contact distances, Rmin, shows a strong correlation with the three-body contribution to the lattice energy, and, here, the largest of the closest-contact distances, Rmax, serves as a cutoff criterion to limit the number of trimers to be considered. We considered all trimers up to R max = 15 A ̊ . The trimers with R min < 4 A ̊ contribute 90.4%, 90.6%, and 93.9% of the total three-body contributions for crystalline benzene, carbon dioxide, and triazine, respectively, for the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] method. For trimers with R min > 4 A ̊ , the second-order Møller–Plesset perturbation theory (MP2) supplemented with the Axilrod–Teller–Muto (ATM) three-body dispersion correction reproduces the CCSD(T) values for the cumulative three-body contributions with errors of less than 0.1 kJ mol−1. Moreover, three-body contributions are converged within 0.15 kJ mol−1 by R max = 10 A ̊ . From these results, it appears that in molecular crystals where dispersion dominates the three-body contribution to the lattice energy, the trimers with R min > 4 A ̊ can be computed with the MP2+ATM method to reduce the computational cost, and those with R max > 10 A ̊ appear to be basically negligible. [ABSTRACT FROM AUTHOR]

Using the many-body expansion to predict crystal lattice energies (CLEs), a pleasantly parallel process, allows for flexibility in the choice of theoretical methods. Benchmark-level two-body contributions to CLEs of 23 molecular crystals have been computed using interaction energies of dimers with minimum inter-monomer separations (i.e., closest contact distances) up to 30 Å. In a search for ways to reduce the computational expense of calculating accurate CLEs, we have computed these two-body contributions with 15 different quantum chemical levels of theory and compared these energies to those computed with coupled-cluster in the complete basis set (CBS) limit. Interaction energies of the more distant dimers are easier to compute accurately and several of the methods tested are suitable as replacements for coupled-cluster through perturbative triples for all but the closest dimers. For our dataset, sub-kJ mol−1 accuracy can be obtained when calculating two-body interaction energies of dimers with separations shorter than 4 Å with coupled-cluster with single, double, and perturbative triple excitations/CBS and dimers with separations longer than 4 Å with MP2.5/aug-cc-pVDZ, among other schemes, reducing the number of dimers to be computed with coupled-cluster by as much as 98%. [ABSTRACT FROM AUTHOR]

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 by 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. [ABSTRACT FROM AUTHOR]

We report the implementation of a symmetry-adapted perturbation theory algorithm based on a density functional theory [SAPT(DFT)] description of monomers. The implementation adopts a density-fitting treatment of hybrid exchange–correlation kernels to enable the description of monomers with hybrid functionals, as in the algorithm by Bukowski, Podeszwa, and Szalewicz [Chem. Phys. Lett. 414, 111 (2005)]. We have improved the algorithm by increasing numerical stability with QR factorization and optimized the computation of the exchange–correlation kernel with its 2-index density-fitted representation. The algorithm scales as O(N5) formally and is usable for systems with up to ∼3000 basis functions, as demonstrated for the C60–buckycatcher complex with the aug-cc-pVDZ basis set. The hybrid-kernel-based SAPT(DFT) algorithm is shown to be as accurate as SAPT(DFT) implementations based on local effective exact exchange potentials obtained from the local Hartree–Fock (LHF) method while avoiding the lower-scaling [O(N4)] but iterative and sometimes hard-to-converge LHF process. The hybrid-kernel algorithm outperforms Hartree–Fock-based SAPT (SAPT0) for the S66 test set, and its accuracy is comparable to the many-body perturbation theory based SAPT2+ approach, which scales as O(N7), although SAPT2+ exhibits a more narrow distribution of errors. [ABSTRACT FROM AUTHOR]

High-level quantum chemical computations have provided significant insight into the fundamental physical nature of non-covalent interactions. These studies have focused primarily on gas-phase computations of small van der Waals dimers; however, these interactions frequently take place in complex chemical environments, such as proteins, solutions, or solids. To better understand how the chemical environment affects non-covalent interactions, we have undertaken a quantum chemical study of π–π interactions in an aqueous solution, as exemplified by T-shaped benzene dimers surrounded by 28 or 50 explicit water molecules. We report interaction energies (IEs) using second-order Møller–Plesset perturbation theory, and we apply the intramolecular and functional-group partitioning extensions of symmetry-adapted perturbation theory (ISAPT and F-SAPT, respectively) to analyze how the solvent molecules tune the π–π interactions of the solute. For complexes containing neutral monomers, even 50 explicit waters (constituting a first and partial second solvation shell) change total SAPT IEs between the two solute molecules by only tenths of a kcal mol−1, while significant changes of up to 3 kcal mol−1 of the electrostatic component are seen for the cationic pyridinium–benzene dimer. This difference between charged and neutral solutes is attributed to large non-additive three-body interactions within solvated ion-containing complexes. Overall, except for charged solutes, our quantum computations indicate that nearby solvent molecules cause very little "tuning" of the direct solute–solute interactions. This indicates that differences in binding energies between the gas phase and solution phase are primarily indirect effects of the competition between solute–solute and solute–solvent interactions. [ABSTRACT FROM AUTHOR]

Symmetry-adapted perturbation theory (SAPT) has become an invaluable tool for studying the fundamental nature of non-covalent interactions by directly computing the electrostatics, exchange (steric) repulsion, induction (polarization), and London dispersion contributions to the interaction energy using quantum mechanics. Further application of SAPT is primarily limited by its computational expense, where even its most affordable variant (SAPT0) scales as the fifth power of system size [ O ( N 5 ) ] due to the dispersion terms. The algorithmic scaling of SAPT0 is reduced from O ( N 5 ) → O ( N 4 ) by replacing these terms with the empirical D3 dispersion correction of Grimme and co-workers, forming a method that may be termed SAPT0-D3. Here, we optimize the damping parameters for the -D3 terms in SAPT0-D3 using a much larger training set than has previously been considered, namely, 8299 interaction energies computed at the complete-basis-set limit of coupled cluster through perturbative triples [CCSD(T)/CBS]. Perhaps surprisingly, with only three fitted parameters, SAPT0-D3 improves on the accuracy of SAPT0, reducing mean absolute errors from 0.61 to 0.49 kcal mol−1 over the full set of complexes. Additionally, SAPT0-D3 exhibits a nearly 2.5× speedup over conventional SAPT0 for systems with ∼300 atoms and is applied here to systems with up to 459 atoms. Finally, we have also implemented a functional group partitioning of the approach (F-SAPT0-D3) and applied it to determine important contacts in the binding of salbutamol to G-protein coupled β1-adrenergic receptor in both active and inactive forms. SAPT0-D3 capabilities have been added to the open-source Psi4 software. [ABSTRACT FROM AUTHOR]

Computation of intermolecular interactions is a challenge in drug discovery because accurate ab initio techniques are too computationally expensive to be routinely applied to drug–protein models. Classical force fields are more computationally feasible, and force fields designed to match symmetry adapted perturbation theory (SAPT) interaction energies can remain accurate in this context. Unfortunately, the application of such force fields is complicated by the laborious parameterization required for computations on new molecules. Here, we introduce the component-based machine-learned intermolecular force field (CLIFF), which combines accurate, physics-based equations for intermolecular interaction energies with machine-learning models to enable automatic parameterization. The CLIFF uses functional forms corresponding to electrostatic, exchange-repulsion, induction/polarization, and London dispersion components in SAPT. Molecule-independent parameters are fit with respect to SAPT2+(3)δMP2/aug-cc-pVTZ, and molecule-dependent atomic parameters (atomic widths, atomic multipoles, and Hirshfeld ratios) are obtained from machine learning models developed for C, N, O, H, S, F, Cl, and Br. The CLIFF achieves mean absolute errors (MAEs) no worse than 0.70 kcal mol−1 in both total and component energies across a diverse dimer test set. For the side chain–side chain interaction database derived from protein fragments, the CLIFF produces total interaction energies with an MAE of 0.27 kcal mol−1 with respect to reference data, outperforming similar and even more expensive methods. In applications to a set of model drug–protein interactions, the CLIFF is able to accurately rank-order ligand binding strengths and achieves less than 10% error with respect to SAPT reference values for most complexes. [ABSTRACT FROM AUTHOR]

Intermolecular interactions are critical to many chemical phenomena, but their accurate computation using ab initio methods is often limited by computational cost. The recent emergence of machine learning (ML) potentials may be a promising alternative. Useful ML models should not only estimate accurate interaction energies but also predict smooth and asymptotically correct potential energy surfaces. However, existing ML models are not guaranteed to obey these constraints. Indeed, systemic deficiencies are apparent in the predictions of our previous hydrogen-bond model as well as the popular ANI-1X model, which we attribute to the use of an atomic energy partition. As a solution, we propose an alternative atomic-pairwise framework specifically for intermolecular ML potentials, and we introduce AP-Net—a neural network model for interaction energies. The AP-Net model is developed using this physically motivated atomic-pairwise paradigm and also exploits the interpretability of symmetry adapted perturbation theory (SAPT). We show that in contrast to other models, AP-Net produces smooth, physically meaningful intermolecular potentials exhibiting correct asymptotic behavior. Initially trained on only a limited number of mostly hydrogen-bonded dimers, AP-Net makes accurate predictions across the chemically diverse S66x8 dataset, demonstrating significant transferability. On a test set including experimental hydrogen-bonded dimers, AP-Net predicts total interaction energies with a mean absolute error of 0.37 kcal mol−1, reducing errors by a factor of 2–5 across SAPT components from previous neural network potentials. The pairwise interaction energies of the model are physically interpretable, and an investigation of predicted electrostatic energies suggests that the model "learns" the physics of hydrogen-bonded interactions. [ABSTRACT FROM AUTHOR]

The focal-point approach, combining several quantum chemistry computations to estimate a more accurate computation at a lower expense, is effective and commonly used for energies. However, it has not yet been widely adopted for properties such as geometries. Here, we examine several focal-point methods combining Møller–Plesset perturbation theory (MP2 and MP2.5) with coupled-cluster theory through perturbative triples [CCSD(T)] for their effectiveness in geometry optimizations using a new driver for the Psi4 electronic structure program that efficiently automates the computation of composite-energy gradients. The test set consists of 94 closed-shell molecules containing first- and/or second-row elements. The focal-point methods utilized combinations of correlation-consistent basis sets cc-pV(X+d)Z and heavy-aug-cc-pV(X+d)Z (X = D, T, Q, 5, 6). Focal-point geometries were compared to those from conventional CCSD(T) using basis sets up to heavy-aug-cc-pV5Z and to geometries from explicitly correlated CCSD(T)-F12 using the cc-pVXZ-F12 (X = D, T) basis sets. All results were compared to reference geometries reported by Karton et al. [J. Chem. Phys. 145, 104101 (2016)] at the CCSD(T)/heavy-aug-cc-pV6Z level of theory. In general, focal-point methods based on an estimate of the MP2 complete-basis-set limit, with a coupled-cluster correction evaluated in a (heavy-aug-)cc-pVXZ basis, are of superior quality to conventional CCSD(T)/(heavy-aug-)cc-pV(X+1)Z and sometimes approach the errors of CCSD(T)/(heavy-aug-)cc-pV(X+2)Z. However, the focal-point methods are much faster computationally. For the benzene molecule, the gradient of such a focal-point approach requires only 4.5% of the computation time of a conventional CCSD(T)/cc-pVTZ gradient and only 0.4% of the time of a CCSD(T)/cc-pVQZ gradient. [ABSTRACT FROM AUTHOR]

Accurate prediction of intermolecular interaction energies is a fundamental challenge in electronic structure theory due to their subtle character and small magnitudes relative to total molecular energies. Symmetry adapted perturbation theory (SAPT) provides rigorous quantum mechanical means for computing such quantities directly and accurately, but for a computational cost of at least O ( N 5 ) , where N is the number of atoms. Here, we report machine learned models of SAPT components with a computational cost that scales asymptotically linearly, O (N). We use modified multi-target Behler–Parrinello neural networks and specialized intermolecular symmetry functions to address the idiosyncrasies of the intermolecular problem, achieving 1.2 kcal mol−1 mean absolute errors on a test set of hydrogen bound complexes including structural data extracted from the Cambridge Structural Database and Protein Data Bank, spanning an interaction energy range of 20 kcal mol−1. Additionally, we recover accurate predictions of the physically meaningful SAPT component energies, of which dispersion and induction/polarization were the easiest to predict and electrostatics and exchange–repulsion are the most difficult. [ABSTRACT FROM AUTHOR]

This paper presents techniques for Fock matrix construction that are designed for high performance on shared and distributed memory parallel computers when using Gaussian basis sets. Four main techniques are considered. (1) To calculate electron repulsion integrals, we demonstrate batching together the calculation of multiple shell quartets of the same angular momentum class so that the calculation of large sets of primitive integrals can be efficiently vectorized. (2) For multithreaded summation of entries into the Fock matrix, we investigate using a combination of atomic operations and thread-local copies of the Fock matrix. (3) For distributed memory parallel computers, we present a globally accessible matrix class for accessing distributed Fock and density matrices. The new matrix class introduces a batched mode for remote memory access that can reduce the synchronization cost. (4) For density fitting, we exploit both symmetry (of the Coulomb and exchange matrices) and sparsity (of 3-index tensors) and give a performance comparison of density fitting and the conventional direct calculation approach. The techniques are implemented in an open-source software library called GTFock. [ABSTRACT FROM AUTHOR]

We present an algorithm to compute the lattice energies of molecular crystals based on the many-body cluster expansion. The required computations on dimers, trimers, etc., within the crystal are independent of each other, leading to a naturally parallel approach. The algorithm exploits the long-range three-dimensional periodic order of crystals to automatically detect and avoid redundant or unnecessary computations. For this purpose, Coulomb-matrix descriptors from machine learning applications are found to be efficient in determining whether two N-mers are identical. The algorithm is implemented as an open-source Python program, CrystaLattE, that uses some of the features of the Quantum Chemistry Common Driver and Databases library. CrystaLattE is initially interfaced with the quantum chemistry package Psi4. With CrystaLattE, we have applied the fast, dispersion-corrected Hartree–Fock method HF-3c to the lattice energy of crystalline benzene. Including all 73 symmetry-unique dimers and 7130 symmetry-unique trimers that can be formed from molecules within a 15 Å cutoff from a central reference monomer, HF-3c plus an Axilrod-Teller-Muto estimate of three-body dispersion exhibits an error of only −1.0 kJ mol−1 vs the estimated 0 K experimental lattice energy of −55.3 ± 2.2 kJ mol−1. The convergence of the HF-3c two- and three-body contributions to the lattice energy as a function of intermonomer distance is examined. [ABSTRACT FROM AUTHOR]

Accurate potential energy models are necessary for reliable atomistic simulations of chemical phenomena. In the realm of biomolecular modeling, large systems like proteins comprise very many noncovalent interactions (NCIs) that can contribute to the protein's stability and structure. This work presents two high-quality chemical databases of common fragment interactions in biomolecular systems as extracted from high-resolution Protein DataBank crystal structures: 3380 sidechain-sidechain interactions and 100 backbone-backbone interactions that inaugurate the BioFragment Database (BFDb). Absolute interaction energies are generated with a computationally tractable explicitly correlated coupled cluster with perturbative triples [CCSD(T)-F12] "silver standard" (0.05 kcal/mol average error) for NCI that demands only a fraction of the cost of the conventional "gold standard," CCSD(T) at the complete basis set limit. By sampling extensively from biological environments, BFDb spans the natural diversity of protein NCI motifs and orientations. In addition to supplying a thorough assessment for lower scaling force-field (2), semi-empirical (3), density functional (244), and wavefunction (45) methods (comprising >1M interaction energies), BFDb provides interactive tools for running and manipulating the resulting large datasets and offers a valuable resource for potential energy model development and validation. [ABSTRACT FROM AUTHOR]

An efficient implementation of analytic gradients for the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method with the density-fitting (DF) approximation, denoted as DFCCSD(T), is reported. For the molecules considered, the DF approach substantially accelerates conventional CCSD(T) analytic gradients due to the reduced input/output time and the acceleration of the so-called "gradient terms": formation of particle density matrices (PDMs), computation of the generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the effective PDMs and GFM, back-transformation of the PDMs and GFM, from the molecular orbital to the atomic orbital (AO) basis, and computation of gradients in the AO basis. For the largest member of the molecular test set considered (C6H14), the computational times for analytic gradients (with the correlation-consistent polarized valence triple-ζ basis set in serial) are 106.2 [CCSD(T)] and 49.8 [DF-CCSD(T)] h, a speedup of more than 2-fold. In the evaluation of gradient terms, the DF approach completely avoids the use of four-index two-electron integrals. Similar to our previous studies on DF-second-order Møller-Plesset perturbation theory and DF-CCSD gradients, our formalism employs 2- and 3-index two-particle density matrices (TPDMs) instead of 4-index TPDMs. Errors introduced by the DF approximation are negligible for equilibrium geometries and harmonic vibrational frequencies. [ABSTRACT FROM AUTHOR]