Accurate description of intermolecular interactions involving ions using symmetry-adapted perturbation theory

Unveiling the Noncovalent Interactions between Formamide and Heteroaromatics: Microwave Spectroscopy of the Formamide Complexes with Furan and Thiophene

The noncovalent interactions between formamide (FM) and the heteroaromatic compounds (furan and thiophene) were investigated through microwave spectroscopy and theoretical calculations. Each of the investigated complexes exhibits a single rotational spectrum corresponding to the lowest energy structure predicted theoretically. In the detected structures, N-H···O and C-H···O hydrogen bonds dominate the complexation between FM and furan, resulting in a planar configuration. Conversely, a superposed configuration linked by a N-H···π hydrogen bond and C═O···π contact is observed for the FM-thiophene complex. In both cases, hydrogen bonding interactions with N-H as proton donor rank as the dominant forces, and the interaction energy of N-H···O is larger than that of N-H···π. It was found that the electrostatic component is the largest contributor to the attraction between FM and furan, while the dispersion component is the most significant attractive factor in the FM-thiophene complex. These findings highlight the distinct features of hydrogen bonding interactions of amides with heteroaromatics in the studied complexes.

Magnetic Ionic Liquids: Current Achievements and Future Perspectives with a Focus on Computational Approaches

Magnetic ionic liquids (MILs) stand out as a remarkable subclass of ionic liquids (ILs), combining the desirable features of traditional ILs with the unique ability to respond to external magnetic fields. The incorporation of paramagnetic species into their structures endows them with additional attractive features, including thermochromic behavior and luminescence. These exceptional properties position MILs as highly promising materials for diverse applications, such as gas capture, DNA extractions, and sensing technologies. The present Review synthesizes key experimental findings, offering insights into the structural, thermal, magnetic, and optical properties across various MIL families. Special emphasis is placed on unraveling the influence of different paramagnetic species on MILs' behavior and functionality. Additionally, the Review highlights recent advancements in computational approaches applied to MIL research. By leveraging molecular dynamics (MD) simulations and density functional theory (DFT) calculations, these computational techniques have provided invaluable insights into the underlying mechanisms governing MILs' behavior, facilitating accurate property predictions. In conclusion, this Review provides a comprehensive overview of the current state of research on MILs, showcasing their special properties and potential applications while highlighting the indispensable role of computational methods in unraveling the complexities of these intriguing materials. The Review concludes with a forward-looking perspective on the future directions of research in the field of magnetic ionic liquids.

Second quantization-based symmetry-adapted perturbation theory: Generalizing exchange beyond single electron pair approximation

This paper presents a general second-quantized form of a permutation operator interchanging n pairs of electrons between interacting subsystems in the framework of the symmetry-adapted perturbation theory (SAPT). We detail the procedure for constructing this operator through the consecutive multiplication of single-pair permutation operators. This generalized form of the permutation operator has enabled the derivation of universal formulas for S2n approximations of the exchange energies in the first and second order of the interaction operator. We present expressions for corrections of S4 approximations and assess its efficacy on a selection of systems anticipated to exhibit a slowly converging overlap expansion. Additionally, we outline a method to sum the overlap expansion series to infinity in second-quantization, up to the second order in V. This new approach offers an alternative to the existing formalism based on density-matrix formulations. When combined with a symbolic algebra program for automated derivations, it paves the way for advancements in SAPT theory, particularly for intricate wavefunction theories.

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.

Balance between Physical Interpretability and Energetic Predictability in Widely Used Dispersion-Corrected Density Functionals

We assess the performance of different dispersion models for several popular density functionals across a diverse set of noncovalent systems, ranging from the benzene dimer to molecular crystals. By analyzing the interaction energies and their individual components, we demonstrate that there exists variability across different systems for empirical dispersion models, which are calibrated for reproducing the interaction energies of specific systems. Thus, parameter fitting may undermine the underlying physics, as dispersion models rely on error compensation among the different components of the interaction energy. Energy decomposition analyses reveal that, the accuracy of revPBE-D3 for some aqueous systems originates from significant compensation between dispersion and charge transfer energies. However, revPBE-D3 is less accurate in describing systems where error compensation is incomplete, such as the benzene dimer. Such cases highlight the propensity for unpredictable behavior in various dispersion-corrected density functionals across a wide range of molecular systems, akin to the behavior of force fields. On the other hand, we find that SCAN-rVV10, a targeted-dispersion approach, affords significant reductions in errors associated with the lattice energies of molecular crystals, while it has limited accuracy in reproducing structural properties. Given the ubiquitous nature of noncovalent interactions and the key role of density functional theory in computational sciences, the future development of dispersion models should prioritize the faithful description of the dispersion energy, a shift that promises greater accuracy in capturing the underlying physics across diverse molecular and extended systems.

Magic Numbers and Stabilities of Photoionized Water Clusters: Computational and Experimental Characterization of the Nanosolvated Hydronium Ion

The stability and distributions of small water clusters generated in a supersonic beam expansion are interrogated by tunable vacuum ultraviolet (VUV) radiation generated at a synchrotron. Time-of-flight mass spectrometry reveals enhanced population of various protonated water clusters (H⁺(H₂O)_n) based upon ionization energy and photoionization distance from source, suggesting there are "magic" numbers below the traditional n = 21 that predominates in the literature. These intensity distributions suggest that VUV threshold photoionization (11.0-11.5 eV) of neutral water clusters close to the nozzle exit leads to a different nonequilibrium state compared to a skimmed molecular beam. This results in the appearance of a new magic number at 14. Metadynamics conformer searches coupled with modern density functional calculations are used to identify the global minimum energy structures of protonated water clusters between n = 2 and 21, as well as the manifold of low-lying metastable minima. New lowest energy structures are reported for the cases of n = 5, 6, 11, 12, 16, and 18, and special stability is identified by several measures. These theoretical results are in agreement with the experiments performed in this work in that n = 14 is shown to exhibit additional stability, based on the computed second-order stabilization energy relative to most cluster sizes, though not to the extent of the well-known n = 21 cluster. Other cluster sizes that show some additional energetic stability are n = 7, 9, 12, 17, and 19. To gain insight into the balance between ion-water and water-water interactions as a function of the cluster size, an analysis of the effective two-body interactions (which sum exactly to the total interaction energy) was performed. This analysis reveals a crossover as a function of cluster size between a water-hydronium-dominated regime for small clusters and a water-water-dominated regime for larger clusters around n = 17.

Noncovalent Interactions in Hydrated Nitrosonium Ion Clusters Mediated by Hydrogen-Bonded Water Networks

As important species in the D region of the ionosphere, hydrated nitrosonium ion clusters [NO⁺(H₂O)_n] are also archetypal and concise models to illustrate effects of different solvent shells. We have investigated noncovalent interactions in NO⁺(H₂O)₃ and NO⁺(H₂O)₄ isomers with high levels of ab initio and symmetry-adapted perturbation theory (SAPT) methods. On the basis of our computations, the exchange energies become much more repulsive, whereas the induction energies are significantly more attractive for the noncovalent interactions of NO⁺ with hydrogen-bonded water chains. Combined with analyses of the electron densities for the NO⁺(H₂O)₃ and NO⁺(H₂O)₄ isomers, we propose that the counteracting effect of the exchange and induction energies could be deemed as an index for the tendency to form the HO-NO covalent bond. Moreover, we have also found that the third-order induction terms are very important to evaluate reasonable charge transfer energies with the SAPT computations.

Electronic structure theory on modeling short-range noncovalent interactions between amino acids

While short-range noncovalent interactions (NCIs) are proving to be of importance in many chemical and biological systems, these atypical bindings happen within the so-called van der Waals envelope and pose an enormous challenge for current computational methods. We introduce SNCIAA, a database of 723 benchmark interaction energies of short-range noncovalent interactions between neutral/charged amino acids originated from protein x-ray crystal structures at the "gold standard" coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory with a mean absolute binding uncertainty less than 0.1 kcal/mol. Subsequently, a systematic assessment of commonly used computational methods, such as the second-order Møller-Plesset theory (MP2), density functional theory (DFT), symmetry-adapted perturbation theory (SAPT), composite electronic-structure methods, semiempirical approaches, and the physical-based potentials with machine learning (IPML) on SNCIAA is carried out. It is shown that the inclusion of dispersion corrections is essential even though these dimers are dominated by electrostatics, such as hydrogen bondings and salt bridges. Overall, MP2, ωB97M-V, and B3LYP+D4 turned out to be the most reliable methods for the description of short-range NCIs even in strongly attractive/repulsive complexes. SAPT is also recommended in describing short-range NCIs only if the δMP2 correction has been included. The good performance of IPML for dimers at close-equilibrium and long-range conditions is not transferable to the short-range. We expect that SNCIAA will assist the development/improvement/validation of computational methods, such as DFT, force-fields, and ML models, in describing NCIs across entire potential energy surfaces (short-, intermediate-, and long-range NCIs) on the same footing.

Understanding the Role of Intramolecular Ion-Pair Interactions in Conformational Stability Using an Ab Initio Thermodynamic Cycle

Intramolecular ion-pair interactions yield shape and functionality to many molecules. With proper orientation, these interactions overcome steric factors and are responsible for the compact structures of several peptides. In this study, we present a thermodynamic cycle based on isoelectronic and alchemical mutation to estimate the intramolecular ion-pair interaction energy. We determine these energies for 26 benchmark molecules with common ion-pair combinations and compare them with results obtained using intramolecular symmetry-adapted perturbation theory. For systems with long linkers, the ion-pair energies evaluated using both approaches deviate by less than 2.5% in the vacuum phase. The thermodynamic cycle based on density functional theory facilitates calculations of salt-bridge interactions in model tripeptides with continuum/microsolvation modeling and four large peptides: 1EJG (crambin), 1BDK (bradykinin), 1L2Y (a mini-protein with a tryptophan cage), and 1SCO (a toxin from the scorpion venom).

Benefits of hybrid QM/MM over traditional classical mechanics in pharmaceutical systems

Hybrid quantum mechanics/molecular mechanics (QM/MM) is one of the most reliable approaches for accurately modeling and studying the complex pharmaceutical discovery system. Classical mechanics has significantly accelerated the drug discovery process in the past decade. However, the current challenge is the large pool of false positives, which require extensive validation. Hybrid QM/MM is an effective solution for accurately studying ligand binding, structural mechanisms, free energy evaluation, and spectroscopic characterization. This article highlights the methodological details relevant to cost-effective hybrid QM/MM methods. This approach, combined with traditional pharmacoinformatics methods, could be a reliable strategy to balance the cost and accuracy of the calculations.

Reduced-Scaling Double Hybrid Density Functional Theory with Rapid Basis Set Convergence through Localized Pair Natural Orbital F12

Following earlier work [Mehta, N.; Martin, J. M. L. J. Chem. Theory Comput.2022, 10.1021/acs.jctc.2c00426] that showed how the slow basis set convergence of the double hybrid density functional theory can be obviated by the use of F12 explicit correlation in the GLPT2 step (second order Görling-Levy perturbation theory), we demonstrate here for the very large and chemically diverse GMTKN55 benchmark suite that the CPU time scaling of this step can be reduced (asymptotically linearized) using the localized pair natural orbital (PNO-L) approximation at negligible cost in accuracy.

Explicitly Correlated Double-Hybrid DFT: A Comprehensive Analysis of the Basis Set Convergence on the GMTKN55 Database

Double-hybrid density functional theory (DHDFT) offers a pathway to accuracy approaching composite wavefunction approaches such as G4 theory. However, the Görling–Levy second-order perturbation theory (GLPT2) term causes them to partially inherit the slow ∝L^–3 (with L the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied by introducing F12 explicit correlation: we investigate the basis set convergence of both DHDFT and DHDFT-F12 (where GLPT2 is replaced by GLPT2-F12) for the large and chemically diverse general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 DHDFs are investigated as test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12 basis sets as large as cc-pVQZ-F12. We show that F12 greatly accelerates basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12 basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPPD in orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z. Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set convergence in both the development and applications of double-hybrid functionals. Mass storage and I/O bottlenecks for larger systems can be circumvented by localized pair natural orbital approximations, which also exhibit much gentler system size scaling.

Informing geometric deep learning with electronic interactions to accelerate quantum chemistry

Predicting electronic energies, densities, and related chemical properties can facilitate the discovery of novel catalysts, medicines, and battery materials. However, existing machine learning techniques are challenged by the scarcity of training data when exploring unknown chemical spaces. We overcome this barrier by systematically incorporating knowledge of molecular electronic structure into deep learning. By developing a physics-inspired equivariant neural network, we introduce a method to learn molecular representations based on the electronic interactions among atomic orbitals. Our method, OrbNet-Equi, leverages efficient tight-binding simulations and learned mappings to recover high-fidelity physical quantities. OrbNet-Equi accurately models a wide spectrum of target properties while being several orders of magnitude faster than density functional theory. Despite only using training samples collected from readily available small-molecule libraries, OrbNet-Equi outperforms traditional semiempirical and machine learning-based methods on comprehensive downstream benchmarks that encompass diverse main-group chemical processes. Our method also describes interactions in challenging charge-transfer complexes and open-shell systems. We anticipate that the strategy presented here will help to expand opportunities for studies in chemistry and materials science, where the acquisition of experimental or reference training data is costly.

Origin of the Microsolvation Effect on the Central Barriers of SN2 Reactions

We have quantitatively analyzed the microsolvation effect on the central barriers of microsolvated bimolecular nucleophilic substitution (S_N2) reactions by means of a two-step energy decomposition procedure. According to the first energy decompositions, an obvious increase in the central barrier for a microsolvated S_N2 reaction against its unsolvated counterpart can be mainly ascribed to the fact that the interaction between the solute and the conjunct solvent becomes less attractive from the reactant complex to the transition state. On the basis of the second energy decompositions with symmetry-adapted perturbation theory, this less attractive interaction in the transition state is primarily due to the interplay of the changes in the electrostatic, exchange, and induction components. However, the contribution of the change for the dispersion component is relatively small. A distinct linear correlation has also been observed between the changes of the total interaction energies and those of the corresponding electrostatic components for the microsolvated S_N2 reactions studied in this work. Moreover, the two-step energy decomposition procedure employed in this work is expected to be extensively applied to the gas phase reactions mediated by molecules or clusters.

Optimization of the r2SCAN-3c Composite Electronic-Structure Method for Use with Slater-Type Orbital Basis Sets

The "Swiss army knife" composite density functional electronic-structure method r²SCAN-3c (J. Chem. Phys. 2021, 154, 064103) is extended and optimized for the use with Slater-type orbital basis sets. The meta generalized-gradient approximation (meta-GGA) functional r²SCAN by Furness et al. is combined with a tailor-made polarized triple-ζ Slater-type atomic orbital (STO) basis set (mTZ2P), the semiclassical London dispersion correction (D4), and a geometrical counterpoise (gCP) correction. Relativistic effects are treated explicitly with the scalar-relativistic zeroth-order regular approximation (SR-ZORA). The performance of the new implementation is assessed on eight geometry and 74 energy benchmark sets, including the extensive GMTKN55 database as well as recent sets such as ROST61 and IONPI19. In geometry optimizations, the STO-based r²SCAN-3c is either on par with or more accurate than the hybrid density functional approximation M06-2X-D3(0)/TZP. In energy calculations, the overall accuracy is similar to the original implementation of r²SCAN-3c with Gaussian-type atomic orbitals (GTO), but basic properties, intermolecular noncovalent interactions, and barrier heights are better described with the STO approach, resulting in a lower weighted mean absolute deviation (WTMAD-2(STO) = 7.15 vs 7.50 kcal mol^-1 with the original method) for the GMTKN55 database. The STO-optimized r²SCAN-3c outperforms many conventional hybrid/QZ approaches in most common applications at a fraction of their cost. The reliable, robust, and accurate r²SCAN-3c implementation with STOs is a promising alternative to the original implementation with GTOs and can be generally used for a broad field of quantum chemical problems.

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost

Hybrid or "extended" symmetry-adapted perturbation theory (XSAPT) replaces traditional SAPT's treatment of dispersion with better performing alternatives while at the same time extending two-body (dimer) SAPT to a many-body treatment of polarization using a self-consistent charge embedding procedure. The present work presents a systematic study of how XSAPT interaction energies and energy components converge with respect to the choice of Gaussian basis set. Errors can be reduced in a systematic way using correlation-consistent basis sets, with aug-cc-pVTZ results converged within <0.1 kcal/mol. Similar (if slightly less systematic) behavior is obtained using Karlsruhe basis sets at much lower cost, and we introduce new versions with limited augmentation that are even more efficient. Pople-style basis sets, which are more efficient still, often afford good results if a large number of polarization functions are included. The dispersion models used in XSAPT afford much faster basis-set convergence as compared to the perturbative description of dispersion in conventional SAPT, meaning that "compromise" basis sets (such as jun-cc-pVDZ) are no longer required and benchmark-quality results can be obtained using triple-ζ basis sets. The use of diffuse functions proves to be essential, especially for the description of hydrogen bonds. The "δ(Hartree-Fock)" correction for high-order induction can be performed in double-ζ basis sets without significant loss of accuracy, leading to a mixed-basis approach that offers 4× speedup over the existing (cubic scaling) XSAPT approach.

A DLPNO-CCSD(T) benchmarking study of intermolecular interactions of ionic liquids

The accuracy of correlation energy recovered by coupled cluster single-, double-, and perturbative triple-excitations, CCSD(T), has led to the method being considered the gold standard of computational chemistry. The application of CCSD(T) has been limited to medium-sized molecular systems due to its steep scaling with molecular size. The recent development of alternative domain-based local pair natural orbital coupled-cluster method, DLPNO-CCSD(T), has significantly broadened the range of chemical systems to which CCSD(T) level calculations can be applied. Condensed systems such as ionic liquids (ILs) have a large contribution from London dispersion forces of up to 150 kJ mol^-1 in large-scale clusters. Ionic liquids show appreciable charge transfer effects that result in the increased valence orbital delocalization over the entire ionic network, raising the question whether the application of methods based on localized orbitals is reliable for these semi-Coulombic materials. Here the performance of DLPNO-CCSD(T) is validated for the prediction of correlation interaction energies of two data sets incorporating single-ion pairs of protic and aprotic ILs. DLPNO-CCSD(T) produced results within chemical accuracy with tight parameter settings and a non-iterative treatment of triple excitations. To achieve spectroscopic accuracy of 1 kJ mol^-1 , especially for hydrogen-bonded ILs and those containing halides, the DLPNO settings had to be increased by two orders of magnitude and include the iterative treatment of triple excitations, resulting in a 2.5-fold increase in computational cost. Two new sets of parameters are put forward to produce the performance of DLPNO-CCSD(T) within chemical and spectroscopic accuracy.

Spin-component-scaled and dispersion-corrected second-order Møller-Plesset perturbation theory: A path toward chemical accuracy

Second-order Moller-Plesset perturbation theory (MP2) provides a valuable alternative to density functional theory for modeing problems in organic and biological chemistry. However, MP2 suffers from known limitations in the description...

A Benchmark Study of Quantum Mechanics and Quantum Mechanics-Molecular Mechanics Methods for Carbocation Chemistry

Carbocations play key roles in classical organic reactions and have also been implicated in several enzyme families. A hallmark of carbocation chemistry is multitudes of competing reaction pathways, and to be able to distinguish between pathways with quantum chemical calculations, it is necessary to approach chemical accuracy for relative energies between carbocations. Here, we present an extensive study of the performance of selected density functional theory (DFT) methods in describing the thermochemistry and kinetics of carbocations and their corresponding neutral alkenes both in the gas-phase and within a hybrid quantum mechanics-molecular mechanics (QM/MM) framework. The density functionals are benchmarked against accurate ab initio methods such as CBS-QB3 and DLPNO-CCSD(T). Based on the findings in the gas-phase calculations of carbocations and alkenes, the best functionals are chosen and tested further for non-covalent interactions in model systems using QM and QM/MM methods. We compute the interaction energies between a model carbocation/alkane and model π, dipole, and hydrophobic systems using DFT and QM(DFT)/MM and compare with DLPNO-CCSD(T). These latter model systems are representative of side chains of amino acids such as phenylalanine/tyrosine, tryptophan, asparagine/glutamine, serine/threonine, methionine, and other hydrophobic groups. The Lennard-Jones parameters of the QM atoms in QM(DFT)/MM calculations are modified to obtain an optimal fit with the QM energies. Finally, a selected carbocation reaction is studied in the gas phase and in implicit chloroform solvent using QM and in explicit chloroform solvent using QM/MM and umbrella sampling simulations. This study highlights the highest accuracy possible with selected density functionals and QM/MM methods but also some limitations in using QM/MM methods for carbocation systems.

Accelerating the Convergence of Self-Consistent Field Calculations Using the Many-Body Expansion

The balance between cost-effective and sufficiently accurate methods represents the proverbial "promised land" for quantum chemistry calculations. The burden thus falls upon theoretical and computational chemists to provide such alternatives to mitigate the issues that arise from the employ of finite computing resources. In this paper, we attempt to demonstrate the importance of the quality of the initial guess for the self-consistent field (SCF) calculation when considering cost reduction techniques. We broach this challenge by using the many body expansion (MBE) to yield high quality density matrices (DMs) which, in turn, are applied as an SCF initial guess. The MBE-DM approaches combined with purification schemes and distance-based cutoff schemes can serve as initial guesses to reduce the SCF cycles necessary for convergence or derive energy directly through one Fock build. To this end, four unique types of clusters including water clusters, fluoride anion water clusters, sodium cation water clusters, and ammonium-bisulfate salt clusters have been used to test the performance of MBE-DM where its truncation at three-body expansion, MBE(3)-DM, shows vast improvement for those four clusters with reductions in the number of SCF cycles up to 40% as compared with the traditional superposition of atomic densities (SAD) guess. Other types of typical initial guesses, superposition of atomic potentials (SAP) and basis set projection (BSP), perform much worse than MBE-DM and SAD. In addition, the MBE-DM shows consistency across an array of fragment types irrespective of charges, size, level of theory, and basis set selection. Through MBE(3)-DM with the distance cutoff and the average purification scheme, the energy can be obtained directly with a mere 3.2 mH of the mean absolute deviation (MAD) for (H₂O)_N=6-55 which is at least 73 times better than the energy prediction using the typical initial guesses (SAD, SAP, and BSP). The corresponding MAD per monomer is only 0.14 mH which reaches the threshold of the "dynamical accuracy". The promising results of the methods outlined in this paper not only indicate two direct routes for computational cost reduction but also lay the possible foundation for composite techniques (i.e., ab initio sampling) that make best use of near converged values as their starting point.

NENCI-2021. I. A large benchmark database of non-equilibrium non-covalent interactions emphasizing close intermolecular contacts

In this work, we present NENCI-2021, a benchmark database of ∼8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation-π and anion-π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion-π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (E_int) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The E_int values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from -38.5 to +186.8 kcal/mol, with a mean (median) E_int value of -1.06 kcal/mol (-2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent-these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation-π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the E_int values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive E_int values, and maximum errors of ±0.2-0.3 kcal/mol (i.e., ∼±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

Topology Automated Force-Field Interactions (TAFFI): A Framework for Developing Transferable Force Fields

Force-field development has undergone a revolution in the past decade with the proliferation of quantum chemistry based parametrizations and the introduction of machine learning approximations of the atomistic potential energy surface. Nevertheless, transferable force fields with broad coverage of organic chemical space remain necessary for applications in materials and chemical discovery where throughput, consistency, and computational cost are paramount. Here, we introduce a force-field development framework called Topology Automated Force-Field Interactions (TAFFI) for developing transferable force fields of varying complexity against an extensible database of quantum chemistry calculations. TAFFI formalizes the concept of atom typing and makes it the basis for generating systematic training data that maintains a one-to-one correspondence with force-field terms. This feature makes TAFFI arbitrarily extensible to new chemistries while maintaining internal consistency and transferability. As a demonstration of TAFFI, we have developed a fixed-charge force-field, TAFFI-gen, from scratch that includes coverage for common organic functional groups that is comparable to established transferable force fields. The performance of TAFFI-gen was benchmarked against OPLS and GAFF for reproducing several experimental properties of 87 organic liquids. The consistent performance of these force fields, despite their distinct origins, validates the TAFFI framework while also providing evidence of the representability limitations of fixed-charge force fields.

Exploring the Limits of Second- and Third-Order Møller-Plesset Perturbation Theories for Noncovalent Interactions: Revisiting MP2.5 and Assessing the Importance of Regularization and Reference Orbitals

This work systematically assesses the influence of reference orbitals, regularization, and scaling on the performance of second- and third-order Møller-Plesset perturbation theory wave function methods for noncovalent interactions (NCIs). Testing on 19 data sets (A24, DS14, HB15, HSG, S22, X40, HW30, NC15, S66, AlkBind12, CO2Nitrogen16, HB49, Ionic43, TA13, XB18, Bauza30, CT20, XB51, and Orel26rad) covers a wide range of different NCIs including hydrogen bonding, dispersion, and halogen bonding. Inclusion of potential energy surfaces from different hydrogen bonds and dispersion-bound complexes gauges accuracy for nonequilibrium geometries. Fifteen methods are tested. In notation where nonstandard choices of orbitals are denoted as methods:orbitals, these are MP2, κ-MP2, SCS-MP2, OOMP2, κ-OOMP2, MP3, MP2.5, MP3:OOMP2, MP2.5:OOMP2, MP3:κ-OOMP2, MP2.5:κ-OOMP2, κ-MP3:κ-OOMP2, κ-MP2.5:κ-OOMP2, MP3:ωB97X-V, and MP2.5:ωB97X-V. Furthermore, we compare these methods to the ωB97M-V and B3LYP-D3 density functionals, as well as CCSD. We find that the κ-regularization (κ = 1.45 au was used throughout) improves the energetics in almost all data sets for both MP2 (in 17 out of 19 data sets) and OOMP2 (16 out of 19). The improvement is significant (e.g., the root-mean-square deviation (RMSD) for the S66 data set is 0.29 kcal/mol for κ-OOMP2 versus 0.67 kcal/mol for MP2) and for interactions between stable closed-shell molecules, not strongly dependent on the reference orbitals. Scaled MP3 (with a factor of 0.5) using κ-OOMP2 reference orbitals (MP2.5:κ-OOMP2) provides significantly more accurate results for NCIs across all data sets with noniterative O(N⁶) scaling (S66 data set RMSD: 0.10 kcal/mol). Across the entire data set of 356 points, the improvement over standard MP2.5 is approximately a factor of 2: RMSD for MP3:κ-OOMP2 is 0.25 vs 0.50 kcal/mol for MP2.5. The use of high-quality density functional reference orbitals (ωB97X-V) also significantly improves the results of MP2.5 for NCI over a Hartree-Fock orbital reference. All our assessments and conclusions are based on the use of the medium-sized aug-cc-pVTZ basis to yield results that are directly compared against complete basis set limit reference values.

Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers

We present a formulation of the multiconfigurational (MC) wave function symmetry-adapted perturbation theory (SAPT). The method is applicable to noncovalent interactions between monomers which require a multiconfigurational description, in particular when the interacting system is strongly correlated or in an electronically excited state. SAPT(MC) is based on one- and two-particle reduced density matrices of the monomers and assumes the single-exchange approximation for the exchange energy contributions. Second-order terms are expressed through response properties from extended random phase approximation (ERPA). The dispersion components of SAPT(MC) have been introduced in our previous works [HapkaM.J. Chem. Theory Comput.2019, 15, 1016−102730525591; HapkaM.J. Chem. Theory Comput.2019, 15, 6712–672331670950]. SAPT(MC) is applied either with generalized valence bond perfect pairing (GVB) or with complete active space self-consistent field (CASSCF) treatment of the monomers. We discuss two model multireference systems: the H₂ ··· H₂ dimer in out-of-equilibrium geometries and interaction between the argon atom and excited state of ethylene. Using the C₂H₄* ··· Ar complex as an example, we examine second-order terms arising from negative transitions in the linear response function of an excited monomer. We demonstrate that the negative-transition terms must be accounted for to ensure qualitative prediction of induction and dispersion energies and develop a procedure allowing for their computation. Factors limiting the accuracy of SAPT(MC) are discussed in comparison with other second-order SAPT schemes on a data set of small single-reference dimers.

Advanced Electrostatic Model for Monovalent Ions Based on Ab Initio Energy Decomposition

Ions play important roles in the structures and functions of biomolecules. In biomolecular simulations, ions either directly interact with biomolecules or provide an ionic environment that influences electrostatic interactions of solutes. The AMOEBA+ water model has demonstrated significant advancement of the classical force field for describing molecular interactions due to its improvements on the functional forms to account for essential physics. This work expands the applicability of the AMOEBA+ model toward alkali metal (Li, Na, K, Rb, and Cs) and halogen (F, Cl, Br, and I) ions. Various quantum chemical data on ion-ion and ion-water interactions, experimental ion hydration free energies, and lattice energies of salt crystals are used in the parametrization. The final parameters are verified with other properties outside of the parametrization data, including lattice energies of additional salt crystals and ionic activity coefficients in solution. The new model captures a wide range of ion properties from the gas phase to solution phase and crystals. More importantly, AMOEBA+ provides energy components that are consistent with ab initio energy decomposition. Thus, we expect AMOEBA+ to be more general, transferable, and valuable for the interpretation of intermolecular forces in efficient classical simulations.

Benchmarking London dispersion corrected density functional theory for noncovalent ion-π interactions

The strongly attractive noncovalent interactions of charged atoms or molecules with π-systems are important binding motifs in many chemical and biological systems. These so-called ion-π interactions play a major role in enzymes, molecular recognition, and for the structure of proteins. In this work, a molecular test set termed IONPI19 is compiled for inter- and intramolecular ion-π interactions, which is well balanced between anionic and cationic systems. The IONPI19 set includes interaction energies of significantly larger molecules (up to 133 atoms) than in other ion-π test sets and covers a broad range of binding motifs. Accurate (local) coupled cluster values are provided as reference. Overall, 19 density functional approximations, including seven (meta-)GGAs, eight hybrid functionals, and four double-hybrid functionals combined with three different London dispersion corrections, are benchmarked for interaction energies. DFT results are further compared to wave function based methods such as MP2 and dispersion corrected Hartree-Fock. Also, the performance of semiempirical QM methods such as the GFNn-xTB and PMx family of methods is tested. It is shown that dispersion-uncorrected DFT underestimates ion-π interactions significantly, even though electrostatic interactions dominate the overall binding. Accordingly, the new charge dependent D4 dispersion model is found to be consistently better than the standard D3 correction. Furthermore, the functional performance trend along Jacob's ladder is generally obeyed and the reduction of the self-interaction error leads to an improvement of (double) hybrid functionals over (meta-)GGAs, even though the effect of the SIE is smaller than expected. Overall, the double-hybrids PWPB95-D4/QZ and revDSD-PBEP86-D4/QZ turned out to be the most reliable among all assessed methods for the description of ion-π interactions, which opens up new perspectives for systems where coupled cluster calculations are no longer computationally feasible.

CHAL336 Benchmark Set: How Well Do Quantum-Chemical Methods Describe Chalcogen-Bonding Interactions?

We present the CHAL336 benchmark set-the most comprehensive database for the assessment of chalcogen-bonding (CB) interactions. After careful selection of suitable systems and identification of three high-level reference methods, the set comprises 336 dimers each consisting of up to 49 atoms and covers both σ- and π-hole interactions across four categories: chalcogen-chalcogen, chalcogen-π, chalcogen-halogen, and chalcogen-nitrogen interactions. In a subsequent study of DFT methods, we re-emphasize the need for using proper London dispersion corrections when treating noncovalent interactions. We also point out that the deterioration of results and systematic overestimation of interaction energies for some dispersion-corrected DFT methods does not hint at problems with the chosen dispersion correction but is a consequence of large density-driven errors. We conclude this work by performing the most detailed DFT benchmark study for CB interactions to date. We assess 109 variations of dispersion-corrected and dispersion-uncorrected DFT methods and carry out a detailed analysis of 80 of them. Double-hybrid functionals are the most reliable approaches for CB interactions, and they should be used whenever computationally feasible. The best three double hybrids are SOS0-PBE0-2-D3(BJ), revDSD-PBEP86-D3(BJ), and B2NCPLYP-D3(BJ). The best hybrids in this study are ωB97M-V, PW6B95-D3(0), and PW6B95-D3(BJ). We do not recommend using the popular B3LYP functional nor the MP2 approach, which have both been frequently used to describe CB interactions in the past. We hope to inspire a change in computational protocols surrounding CB interactions that leads away from the commonly used, popular methods to the more robust and accurate ones recommended herein. We would also like to encourage method developers to use our set for the investigation and reduction of density-driven errors in new density functional approximations.

From Intermolecular Interaction Energies and Observable Shifts to Component Contributions and Back Again: A Tale of Variational Energy Decomposition Analysis

Quantum chemistry in the form of density functional theory (DFT) calculations is a powerful numerical experiment for predicting intermolecular interaction energies. However, no chemical insight is gained in this way beyond predictions of observables. Energy decomposition analysis (EDA) can quantitatively bridge this gap by providing values for the chemical drivers of the interactions, such as permanent electrostatics, Pauli repulsion, dispersion, and charge transfer. These energetic contributions are identified by performing DFT calculations with constraints that disable components of the interaction. This review describes the second-generation version of the absolutely localized molecular orbital EDA (ALMO-EDA-II). The effects of different physical contributions on changes in observables such as structure and vibrational frequencies upon complex formation are characterized via the adiabatic EDA. Example applications include red- versus blue-shifting hydrogen bonds; the bonding and frequency shifts of CO, N₂, and BF bound to a [Ru(II)(NH₃)₅]^{2 +} moiety; and the nature of the strongly bound complexes between pyridine and the benzene and naphthalene radical cations. Additionally, the use of ALMO-EDA-II to benchmark and guide the development of advanced force fields for molecular simulation is illustrated with the recent, very promising, MB-UCB potential.

Electrostatics, Charge Transfer, and the Nature of the Halide-Water Hydrogen Bond

Binary halide-water complexes X^-(H₂O) are examined by means of symmetry-adapted perturbation theory, using charge-constrained promolecular reference densities to extract a meaningful charge-transfer component from the induction energy. As is known, the X^-(H₂O) potential energy surface (for X = F, Cl, Br, or I) is characterized by symmetric left and right hydrogen bonds separated by a C_2v-symmetric saddle point, with a tunneling barrier height that is <2 kcal/mol except in the case of F^-(H₂O). Our analysis demonstrates that the charge-transfer energy is correspondingly small (<2 kcal/mol except for X = F), considerably smaller than the electrostatic interaction energy. Nevertheless, charge transfer plays a crucial role determining the conformational preferences of X^-(H₂O) and provides a driving force for the formation of quasi-linear X··· H-O hydrogen bonds. Charge-transfer energies correlate well with measured O-H vibrational redshifts for the halide-water complexes and also for OH^-(H₂O) and NO₂^-(H₂O), providing some indication of a general mechanism.

Nonapproximated third-order exchange induction energy in symmetry-adapted perturbation theory

The exchange terms in symmetry-adapted perturbation theory (SAPT) are normally calculated within the so-called S² or single exchange approximation, which approximates the all-electron antisymmetrizer by interchanges of at most one electron pair between the interacting molecules. This approximation is typically very accurate at the van der Waals minimum separation and at larger intermolecular distances but begins to deteriorate at short range. Nonapproximated expressions for the second-order SAPT exchange corrections have been derived some time ago by Schäffer and Jansen [Mol. Phys. 111, 2570 (2013)]. In this work, we extend Schäffer and Jansen's formalism to derive and implement a nonapproximated expression for the third-order exchange-induction correction. Numerical tests on several representative noncovalent databases show that the S² approximation underestimates the exchange-induction contributions in both second and third orders. This underestimation is very similar in relative terms, but the larger absolute values of the third-order exchange-induction effects, and their near complete cancellation with the corresponding induction energies, make the third-order errors more severe. In the worst-case scenario of interactions involving ions, the breakdown of the S² approximation can result in a qualitatively wrong, attractive character of SAPT total energies at short range {as first observed by Lao and Herbert [J. Phys. Chem. A 116, 3042 (2012)]}. As expected, the inclusion of the full third-order exchange-induction energy in place of its S²-approximated counterpart restores the correct, repulsive short-range behavior of the SAPT potential energy curves computed through the third order.

Assessing the Applicability of the Geometric Counterpoise Correction in B2PLYP/Double-ζ Calculations for Thermochemistry, Kinetics, and Noncovalent Interactions

We present a proof-of-concept study of the suitability of Kruse and Grimme’s geometric counterpoise correction (gCP) for basis set superposition errors (BSSEs) in double-hybrid density functional calculations with a double-ζ basis set. The gCP approach only requires geometrical information as an input and no orbital/density information is needed. Therefore, this correction is practically free of any additional cost. gCP is trained against the Boys and Bernardi counterpoise correction across a set of 528 noncovalently bound dimers. We investigate the suitability of the approach for the B2PLYP/def2-SVP level of theory, and reveal error compensation effects—missing London dispersion and the BSSE—associated with B2PLYP/def2-SVP calculations, and present B2PLYP-gCP-D3(BJ)/def2-SVP with the reparametrised DFT-D3(BJ) and gCP corrections as a more balanced alternative. Benchmarking results on the S66x8 benchmark set for noncovalent interactions and the GMTKN55 database for main-group thermochemistry, kinetics, and noncovalent interactions show a statistical improvement of the B2PLYP-gCP-D3(BJ) scheme over plain B2PLYP and B2PLYP-D3(BJ). B2PLYP-D3(BJ) shows significant overestimation of interaction energies, barrier heights with larger deviations from the reference values, and wrong relative stabilities in conformers, all of which can be associated with BSSE. We find that the gCP-corrected method represents a significant improvement over B2PLYP-D3(BJ), particularly for intramolecular noncovalent interactions. These findings encourage future developments of efficient double-hybrid DFT strategies that can be applied when double-hybrid calculations with large basis sets are not feasible due to system size.

Accurate Hybrid Density Functionals with UW12 Correlation

In previous work, we suggested a single-parameter hybrid functional containing a novel correlation contribution based on the Unsöld approximation, UW12. This model resembles the explicitly correlated part of MP2-F12 theory and can be written as an explicit formula in terms of the single-particle reduced density matrix. Here, we further investigate hybrid functionals containing UW12 correlation and in particular look at functionals with a large fraction of exact exchange to reduce the self-interaction error. We suggest two new hybrid functionals B-LYP-osUW12 and fB-LYP-osUW12. On the test sets we use, our best hybrid functional overall (B-LYP-osUW12) is of similar accuracy to the best double hybrids considered while eliminating the need for virtual orbitals.

Double hybrid DFT calculations with Slater type orbitals

On a comprehensive database with 1,644 datapoints, covering several aspects of main-group as well as of transition metal chemistry, we assess the performance of 60 density functional approximations (DFA), among them 36 double hybrids (DH). All calculations are performed using a Slater type orbital (STO) basis set of triple-ζ (TZ) quality and the highly efficient pair atomic resolution of the identity approach for the exchange- and Coulomb-term of the KS matrix (PARI-K and PARI-J, respectively) and for the evaluation of the MP2 energy correction (PARI-MP2). Employing the quadratic scaling SOS-AO-PARI-MP2 algorithm, DHs based on the spin-opposite-scaled (SOS) MP2 approximation are benchmarked against a database of large molecules. We evaluate the accuracy of STO/PARI calculations for B3LYP as well as for the DH B2GP-PLYP and show that the combined basis set and PARI-error is comparable to the one obtained using the well-known def2-TZVPP Gaussian-type basis set in conjunction with global density fitting. While quadruple-ζ (QZ) calculations are currently not feasible for PARI-MP2 due to numerical issues, we show that, on the TZ level, Jacob's ladder for classifying DFAs is reproduced. However, while the best DHs are more accurate than the best hybrids, the improvements are less pronounced than the ones commonly found on the QZ level. For conformers of organic molecules and noncovalent interactions where very high accuracy is required for qualitatively correct results, DHs provide only small improvements over hybrids, while they still excel in thermochemistry, kinetics, transition metal chemistry and the description of strained organic systems.

SAPT codes for calculations of intermolecular interaction energies

Symmetry-adapted perturbation theory (SAPT) is a method for calculations of intermolecular (noncovalent) interaction energies. The set of SAPT codes that is described here, the current version named SAPT2020, includes virtually all variants of SAPT developed so far, among them two-body SAPT based on perturbative, coupled cluster, and density functional theory descriptions of monomers, three-body SAPT, and two-body SAPT for some classes of open-shell monomers. The properties of systems governed by noncovalent interactions can be predicted only if potential energy surfaces (force fields) are available. SAPT is the preferred approach for generating such surfaces since it is seamlessly connected to the asymptotic expansion of interaction energy. SAPT2020 includes codes for automatic development of such surfaces, enabling generation of complete dimer surfaces with a rigid monomer approximation for dimers containing about one hundred atoms. These codes can also be used to obtain surfaces including internal degrees of freedom of monomers.

Psi4 1.4: Open-source software for high-throughput quantum chemistry

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

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.

Strength, character, and directionality of halogen bonds involving cationic halogen bond donors

Halogen bonds involving cationic halogen bond donors and anionic halogen bond acceptors have recently been recognized as being important in stabilizing the crystal structures of many salts. Theoretical characterization of these types of interactions, most importantly in terms of their directionality, has been limited. Here we generate high-quality symmetry adapted perturbation theory potential energy curves of a H₃N-C[triple bond, length as m-dash]C-Br⁺Cl^- model system in order to characterize halogen bonds involving charged species, in terms of contributions from electrostatics, exchange, induction, and dispersion, with special emphasis on analyzing contributions that are most responsible for the directionality of these interactions. It is found that, as in the case of neutral halogen bonds, exchange forces are important contributors to the directionality of charged halogen bonds, however, it is also found that induction effects, which contribute little to the stability and directionality of neutral halogen bonds, play a large role in the directionality of halogen bonds involving charged species. Potential energy curves based on the ωB97X-D/def2-TZVP/C-PCM method, which includes an implicit solvation model in order to mimic the effects of the crystal medium, are produced for both the H₃N-C[triple bond, length as m-dash]C-Br⁺Cl^- model system and for the 4-bromoaniliniumCl^- dimer, which is based on the real 4-bromoanilinium chloride salt, whose crystal structure has been determined experimentally. It is found that, within a crystal-like medium, charged halogen bond are significantly weaker than in the gas phase, having optimum interaction energies up to approximately -20 kcal mol^-1.

On the geometric dependence of the molecular dipole polarizability in water: A benchmark study of higher-order electron correlation, basis set incompleteness error, core electron effects, and zero-point vibrational contributions

In this work, we investigate how geometric changes influence the static dipole polarizability (α) of a water molecule by explicitly computing the corresponding dipole polarizability surface (DPS) across 3125 total (1625 symmetry-unique) geometries using linear response coupled cluster theory including single, double, and triple excitations (LR-CCSDT) and the doubly augmented triple-ζ basis set (d-aug-cc-pVTZ). Analytical formulae based on power series expansions of this ab initio surface are generated using linear least-squares analysis and provide highly accurate estimates of this quantity as a function of molecular geometry (i.e., bond and angle variations) in a computationally tractable manner. An additional database, which consists of 25 representative molecular geometries and incorporates a more thorough treatment of both basis sets and core electron effects, is provided as a current benchmark for this quantity and the corresponding leading-order C ₆ dispersion coefficient. This database has been utilized to assess the importance of these effects as well as the relative accuracy that can be obtained using several quantum chemical methods and a library of density functional approximations. In addition to high-level electron correlation methods (like CCSD) and our analytical least-squares formulae, we find that the SCAN0, PBE0, MN15, and B97-2 hybrid functionals yield the most accurate descriptions of the molecular polarizability tensor in H₂O. Using first-order perturbation theory, we compute the zero-point vibrational correction to α at the CCSDT/d-aug-cc-pVTZ level and find that this correction contributes approximately 3% to the isotropic (α _iso) and nearly 50% to the anisotropic (α _aniso) polarizability values. In doing so, we find that α _iso = 9.8307 bohr³, which is in excellent agreement with the experimental value of 9.83 ± 0.02 bohr³ provided by Russell and Spackman. The DPS reported herein provides a benchmark-quality quantum mechanical estimate of this fundamental quantity of interest and should find extensive use in the development (and assessment) of next-generation force fields and machine-learning based approaches for modeling water in complex condensed-phase environments.

Semi-empirical or non-empirical double-hybrid density functionals: which are more robust?

The development of non-empirical double-hybrid density functionals (DHDFs) is a very active research area with the number of approaches in this field having increased rapidly. At the same time, there is a lack of published work that provides a fair assessment and comparison between non-empirical and semi-empirical DHDFs on an equal footing. Herein, we close this gap and present a thorough analysis of both classes of DHDFs on the large GMTKN55 benchmark database for general main-group thermochemistry, kinetics, and noncovalent interactions [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184-32215]. In total, 115 variations of dispersion-corrected and -uncorrected DHDFs are tested, which will be condensed to an in-depth assessment of 31 methods: 19 non-empirical and 12 semi-empirical DHDFs. As such, our study represents the largest DHDF study ever conducted and can serve as an important benchmark informing method developers and users alike. Our results show that semi-empirical DHDFs are the most robust density functional approximations and more reliable and accurate than non-empirical ones. In fact, some non-empirical approaches are even outperformed by hybrid approaches or even dispersion-corrected and -uncorrected MP2 and SCS-MP2. SOS0-PBE0-2-D3(BJ) is the only exception and the only non-empirical DHDF that we can safely recommend for general applicability. However, it is still outperformed by six semi-empirical DHDFs, of which we would like to particularly recommend the following five: ωB97X-2-D3(BJ), DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), B2NC-PLYP-D3(BJ), and B2GPPLYP-D3(BJ). Our findings seriously question current trends in the field and they highlight that novel strategies have to be found in order to outperform the currently best density functional theory methods on the market. We hope that our study can function as an important cornerstone inspiring such a change of direction in the field.