Extensions and applications of the A24 data set of accurate interaction energies

Regularized and Opposite Spin-Scaled Functionals from Møller-Plesset Adiabatic Connection─Higher Accuracy at Lower Cost

Noncovalent interactions (NCIs) play a crucial role in biology, chemistry, material science, and everything in between. To improve pure quantum-chemical simulations of NCIs, we propose a methodology for constructing approximate correlation energies by combining an interpolation along the Møller-Plesset adiabatic connection (MP AC) with a regularization and spin-scaling strategy applied to MP2 correlation energies. This combination yields cosκos-SPL2, which exhibits superior accuracy for NCIs compared to any of the individual strategies. With the N4 formal scaling, cosκos-SPL2 is competitive or often outperforms more expensive dispersion-corrected double hybrids for NCIs. The accuracy of cosκos-SPL2 particularly shines for anionic halogen bonded complexes, where it surpasses standard dispersion-corrected DFT by a factor of 3 to 5.

Accuracy of Noncovalent Interactions Involving d-Elements by the 1-Determinant Fixed-Node Diffusion Monte Carlo Method with Effective Core Potentials

A critical assessment of effective core potential (ECP)-based single-determinant (SD) fixed-node diffusion quantum Monte Carlo (FNDMC) accuracy in prototypical noncovalent closed-shell systems involving d-elements is presented. Careful analysis of biases and elimination of possible bias sources leads to two findings of practical importance for SD FNDMC in these systems. First, in some systems (HCu:HCu, HCu:CuH), SD FNDMC reveals large biases of interaction energy differences (significantly exceeding the target 2% relative error) vs a reliable coupled-cluster CCSD(T)/CBS (complete basis set) reference. Second, the leading error of SD FNDMC with ECPs was attributed to a higher nuclear charge Z of d-group (pseudo) atoms, when compared to sp elements, in line with a previously reported finding that aggregate SD FNDMC bias tends to increase in systems with higher electronic densities. Therefore, SD FNDMC should only be used with caution in systems with a large Z.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

Toward Accurate yet Effective Computations of Rotational Spectroscopy Parameters for Biomolecule Building Blocks

The interplay of high-resolution rotational spectroscopy and quantum-chemical computations plays an invaluable role in the investigation of biomolecule building blocks in the gas phase. However, quantum-chemical methods suffer from unfavorable scaling with the dimension of the system under consideration. While a complete characterization of flexible systems requires an elaborate multi-step strategy, in this work, we demonstrate that the accuracy obtained by quantum-chemical composite approaches in the prediction of rotational spectroscopy parameters can be approached by a model based on density functional theory. Glycine and serine are employed to demonstrate that, despite its limited cost, such a model is able to predict rotational constants with an accuracy of 0.3% or better, thus paving the way toward the accurate characterization of larger flexible building blocks of biomolecules.

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.

Addressing the System-Size Dependence of the Local Approximation Error in Coupled-Cluster Calculations

Over the last two decades, the local approximation has been successfully used to extend the range of applicability of the "gold standard" singles and doubles coupled-cluster method with perturbative triples CCSD(T) to systems with hundreds of atoms. The local approximation error grows in absolute value with the increasing system size, i.e., by increasing the number of electron pairs in the system. In this study, we demonstrate that the recently introduced two-point extrapolation scheme for approaching the complete pair natural orbital (PNOs) space limit in domain-based pair natural orbital CCSD(T) calculations drastically reduces the dependence of the error on the system size, thus opening up unprecedented opportunities for the calculation of benchmark quality relative energies for large systems.

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.

junChS and junChS-F12 Models: Parameter-free Efficient yet Accurate Composite Schemes for Energies and Structures of Noncovalent Complexes

A recently developed model chemistry (denoted as junChS [Alessandrini, S.; et al. J. Chem. Theory Comput. 2020, 16, 988-1006]) has been extended to the employment of explicitly correlated (F12) methods. This led us to propose a family of effective, reliable, and parameter-free schemes for the computation of accurate interaction energies of molecular complexes ruled by noncovalent interactions. A thorough benchmark based on a wide range of interactions showed that the so-called junChS-F12 model, which employs cost-effective revDSD-PBEP86-D3(BJ) reference geometries, has an improved performance with respect to its conventional counterpart and outperforms well-known model chemistries. Without employing any empirical parameter and at an affordable computational cost, junChS-F12 reaches subchemical accuracy. Accurate characterizations of molecular complexes are usually limited to energetics. To take a step forward, the conventional and F12 composite schemes developed for interaction energies have been extended to structural determinations. A benchmark study demonstrated that the most effective option is to add MP2-F12 core-valence correlation corrections to fc-CCSD(T)-F12/jun-cc-pVTZ geometries without the need of recovering the basis set superposition error and the extrapolation to the complete basis set.

Monte Carlo MP2-F12 for Noncovalent Interactions: The C60 Dimer

A scalable stochastic algorithm is presented that can evaluate explicitly correlated (F12) second-order many-body perturbation (MP2) energies of weak, noncovalent, intermolecular interactions. It first transforms the formulas of the MP2 and F12 energy differences into a short sum of high-dimensional integrals of Green's functions in real space and imaginary time. These integrals are then evaluated by the Monte Carlo method augmented by parallel execution, redundant-walker convergence acceleration, direct-sampling autocorrelation elimination, and control-variate error reduction. By sharing electron-pair walkers across the supermolecule and its subsystems spanned by the joint basis set, the statistical uncertainty is reduced by one to 2 orders of magnitude in the MP2 binding energy corrected for the basis-set incompleteness and superposition errors. The method predicts the MP2-F12/aug-cc-pVDZ binding energy of 19.1 ± 4.0 kcal mol^-1 for the C₆₀ dimer at the center distance of 9.748 Å.

Coupled cluster benchmarks of large noncovalent complexes: The L7 dataset as well as DNA-ellipticine and buckycatcher-fullerene

In this work, benchmark binding energies for dispersion-bound complexes in the L7 dataset, the DNA-ellipticine intercalation complex, and the buckycatcher-C₆₀ complex with 120 heavy atoms using a focal-point method based on the canonical form of second-order Møller-Plesset theory (MP2) and the domain based local pair natural orbital scheme for the coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] extrapolated to the complete basis set (CBS) limit are reported. This work allows for increased confidence given the agreement with respect to values recently obtained using the local natural orbital CCSD(T) for L7 and the canonical CCSD(T)/CBS result for the coronene dimer (C2C2PD). Therefore, these results can be considered pushing the CCSD(T)/CBS binding benchmark to the hundred-atom scale. The disagreements between the two state-of-the-art methods, CCSD(T) and fixed-node diffusion Monte Carlo, are substantial with at least 2.0 (∼10%), 1.9 (∼5%), and 10.3 kcal/mol (∼25%) differences for C2C2PD in L7, DNA-ellipticine, and buckycatcher-C₆₀, respectively. Such sizable discrepancy above "chemical accuracy" for large noncovalent complexes indicates how challenging it is to obtain benchmark binding interactions for systems beyond small molecules, although the three up-to-date density functionals, PBE0+D4, ωB97M-V, and B97M-V, agree better with CCSD(T) for these large systems. In addition to reporting these values, different basis sets and various CBS extrapolation parameters for Hartree-Fock and MP2 correlation energies were tested for the first time in large noncovalent complexes with the goal of providing some indications toward optimal cost effective routes to approach the CBS limit without substantial loss in quality.

Noncovalent Interactions by the Quantum Monte Carlo Method: Strong Influence of Isotropic Jastrow Cutoff Radii

We present a paradigmatic example of a strong effect of Jastrow cutoff radii setup on the accuracy of noncovalent interaction energy differences within one-determinant Slater-Jastrow fixed-node diffusion Monte Carlo (1FNDMC) simulations using isotropic Jastrow terms and effective-core potentials. Analysis of total energies, absolute and relative errors, and local energy variance of energy differences vs the reference results suggests a simple procedure to marginalize the related biases. The presented data showcase improvements in dispersion-bounded systems within such a 1FNDMC method.

Interactions between large molecules pose a puzzle for reference quantum mechanical methods

Quantum-mechanical methods are used for understanding molecular interactions throughout the natural sciences. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are state-of-the-art trusted wavefunction methods that have been shown to yield accurate interaction energies for small organic molecules. These methods provide valuable reference information for widely-used semi-empirical and machine learning potentials, especially where experimental information is scarce. However, agreement for systems beyond small molecules is a crucial remaining milestone for cementing the benchmark accuracy of these methods. We show that CCSD(T) and DMC interaction energies are not consistent for a set of polarizable supramolecules. Whilst there is agreement for some of the complexes, in a few key systems disagreements of up to 8 kcal mol^-1 remain. These findings thus indicate that more caution is required when aiming at reproducible non-covalent interactions between extended molecules.

Dataset of noncovalent intermolecular interaction energy curves for 24 small high-spin open-shell dimers

We introduce a dataset of 24 interaction energy curves of open-shell noncovalent dimers, referred to as the O24 × 5 dataset. The dataset consists of high-spin dimers up to 11 atoms selected to assure diversity with respect to interaction types: dispersion, electrostatics, and induction. The benchmark interaction energies are obtained at the restricted open-shell CCSD(T) level of theory with complete basis set extrapolation (from aug-cc-pVQZ to aug-cc-pV5Z). We have analyzed the performance of selected wave function methods MP2, CCSD, and CCSD(T) as well as the F12a and F12b variants of coupled-cluster theory. In addition, we have tested dispersion-corrected density functional theory methods based on the PBE exchange-correlation model. The O24 × 5 dataset is a challenge to approximate methods due to the wide range of interaction energy strengths it spans. For the dispersion-dominated and mixed-type subsets, any tested method that does not include the triples contribution yields errors on the order of tens of percent. The electrostatic subset is less demanding with errors that are typically an order of magnitude smaller than the mixed and dispersion-dominated subsets.

Prototypical π-π dimers re-examined by means of high-level CCSDT(Q) composite ab initio methods

The benzene-ethene and parallel-displaced (PD) benzene-benzene dimers are the most fundamental systems involving π-π stacking interactions. Several high-level ab initio investigations calculated the binding energies of these dimers using the coupled-cluster with singles, doubles, and quasi-perturbative triple excitations [CCSD(T)] method at the complete basis set [CBS] limit using various approaches such as reduced virtual orbital spaces and/or MP2-based basis set corrections. Here, we obtain CCSDT(Q) binding energies using a Weizmann-3-type approach. In particular, we extrapolate the self-consistent field (SCF), CCSD, and (T) components using large heavy-atom augmented Gaussian basis sets [namely, SCF/jul-cc-pV{5,6}Z, CCSD/jul-cc-pV{Q,5}Z, and (T)/jul-cc-pV{T,Q}Z]. We consider post-CCSD(T) contributions up to CCSDT(Q), inner-shell, scalar-relativistic, and Born-Oppenheimer corrections. Overall, our best relativistic, all-electron CCSDT(Q) binding energies are ∆E_e,all,rel = 1.234 (benzene-ethene) and 2.550 (benzene-benzene PD), ∆H₀ = 0.949 (benzene-ethene) and 2.310 (benzene-benzene PD), and ∆H₂₉₈ = 0.130 (benzene-ethene) and 1.461 (benzene-benzene PD) kcal mol^-1. Important conclusions are reached regarding the basis set convergence of the SCF, CCSD, (T), and post-CCSD(T) components. Explicitly correlated calculations are used as a sanity check on the conventional binding energies. Overall, post-CCSD(T) contributions are destabilizing by 0.028 (benzene-ethene) and 0.058 (benzene-benzene) kcal mol^-1, and thus, they cannot be neglected if sub-chemical accuracy is sought (i.e., errors below 0.1 kcal mol^-1). CCSD(T)/aug-cc-pwCVTZ core-valence corrections increase the binding energies by 0.018 (benzene-ethene) and 0.027 (benzene-benzene PD) kcal mol^-1. Scalar-relativistic and diagonal Born-Oppenheimer corrections are negligibly small. We use our best CCSDT(Q) binding energies to evaluate the performance of MP2-based, CCSD-based, and lower-cost composite ab initio procedures for obtaining these challenging π-π stacking binding energies.

Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage

The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH₄···(H₂O)₂₀, is a stringent test for approximate methods, including density functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here, we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA), which uses approximate Kohn-Sham orbitals as its input. The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of the many-body expansion. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the many-body expansion. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.

The challenge of non-covalent interactions: theory meets experiment for reconciling accuracy and interpretation

In the past decade, many gas-phase spectroscopic investigations have focused on the understanding of the nature of weak interactions in model systems. Despite the fact that non-covalent interactions play a key role in several biological and technological processes, their characterization and interpretation are still far from being satisfactory. In this connection, integrated experimental and computational investigations can play an invaluable role. Indeed, a number of different issues relevant to unraveling the properties of bulk or solvated systems can be addressed from experimental investigations on molecular complexes. Focusing on the interaction of biological model systems with solvent molecules (e.g., water), since the hydration of the biomolecules controls their structure and mechanism of action, the study of the molecular properties of hydrated systems containing a limited number of water molecules (microsolvation) is the basis for understanding the solvation process and how structure and reactivity vary from gas phase to solution. Although hydrogen bonding is probably the most widespread interaction in nature, other emerging classes, such as halogen, chalcogen and pnicogen interactions, have attracted much attention because of the role they play in different fields. Their understanding requires, first of all, the characterization of the directionality, strength, and nature of such interactions as well as a comprehensive analysis of their competition with other non-covalent bonds. In this review, it is shown how state-of-the-art quantum-chemical computations combined with rotational spectroscopy allow for fully characterizing intermolecular interactions taking place in molecular complexes from both structural and energetic points of view. The transition from bi-molecular complex to microsolvation and then to condensed phase is shortly addressed.

Quantum Monte Carlo Study of the Water Dimer Binding Energy and Halogen-π Interactions

Halogen-π systems are involved with competition between halogen bonding and π-interaction. Using the diffusion quantum Monte Carlo (DMC) method, we compare the interaction of benzene with diatomic halogens (X₂: Cl₂/Br₂) with the typical hydrogen bonding in the water dimer, taking into account explicit correlations of up to three bodies. The benzene-Cl₂/Br₂ binding energies (13.07 ± 0.42/16.62 ± 0.02 kJ/mol) attributed to both halogen bonding and dispersion are smaller than but comparable to the typical hydrogen bonding in the water dimer binding energy (20.88 ± 0.27 kJ/mol). All of the above values are in good agreement with those from the coupled-cluster with single, double, and noniterative triple excitations (CCSD(T)) results at the complete basis set limit (benzene-Cl₂/Br₂: 12.78/16.17 kJ/mol; water dimer: 21.0 kJ/mol).

Range-separated double-hybrid density-functional theory with coupled-cluster and random-phase approximations

We construct range-separated double-hybrid (RSDH) schemes which combine coupled-cluster or random-phase approximations (RPAs) with a density functional based on a two-parameter Coulomb-attenuating-method-like decomposition of the electron-electron interaction. We find that the addition of a fraction of short-range electron-electron interaction in the wave-function part of the calculation is globally beneficial for the RSDH scheme involving a variant of the RPA with exchange terms. Even though the latter scheme is globally as accurate as the corresponding scheme employing only second-order Møller-Plesset perturbation theory for atomization energies, reaction barrier heights, and weak intermolecular interactions of small molecules, it is more accurate for the more complicated case of the benzene dimer in the stacked configuration. The present RSDH scheme employing a RPA thus represents a new member in the family of double hybrids with minimal empiricism which could be useful for general chemical applications.

Understanding non-covalent interactions in larger molecular complexes from first principles

Non-covalent interactions pervade all matter and play a fundamental role in layered materials, biological systems, and large molecular complexes. Despite this, our accumulated understanding of non-covalent interactions to date has been mainly developed in the tens-of-atoms molecular regime. This falls considerably short of the scales at which we would like to understand energy trends, structural properties, and temperature dependencies in materials where non-covalent interactions have an appreciable role. However, as more reference information is obtained beyond moderately sized molecular systems, our understanding is improving and we stand to gain pertinent insights by tackling more complex systems, such as supramolecular complexes, molecular crystals, and other soft materials. In addition, accurate reference information is needed to provide the drive for extending the predictive power of more efficient workhorse methods, such as density functional approximations that also approximate van der Waals dispersion interactions. In this perspective, we discuss the first-principles approaches that have been used to obtain reference interaction energies for beyond modestly sized molecular complexes. The methods include quantum Monte Carlo, symmetry-adapted perturbation theory, non-canonical coupled cluster theory, and approaches based on the random-phase approximation. By considering the approximations that underpin each method, the most accurate theoretical references for supramolecular complexes and molecular crystals to date are ascertained. With these, we also assess a handful of widely used exchange-correlation functionals in density functional theory. The discussion culminates in a framework for putting into perspective the accuracy of high-level wavefunction-based methods and identifying future challenges.

Testing Semiempirical Quantum Mechanical Methods on a Data Set of Interaction Energies Mapping Repulsive Contacts in Organic Molecules

Semiempirical quantum mechanical (QM) methods with corrections for noncovalent interactions provide a favorable combination of accuracy and computational efficiency that makes them a useful tool for a study of large molecular systems. It was, however, noted that the accuracy of these methods deteriorates at intermolecular distances shorter than equilibrium. In this work, we explore this issue systematically using a newly developed data set of benchmark interaction energies named R160×6. This data set maps repulsive contacts in organic molecules, and it consists of 160 model complexes for which six points along the dissociation curve are provided. Testing a wide range of semiempirical QM methods against the CCSD(T)/CBS benchmark revealed that most methods, and all the dispersion-corrected ones, underestimate the repulsion systematically. The worst cases are usually hydrogen-hydrogen contacts. The best results were obtained with PM6-D3H4 and DFTB3-D3H4, as these methods already contain a correction for the H-H repulsion, but the errors are still about twice as large as in equilibrium geometries.

Bias cancellation in one-determinant fixed-node diffusion Monte Carlo: Insights from fermionic occupation numbers

The accuracy of the fixed-node diffusion Monte Carlo (FNDMC) depends on the node location of the supplied trial state Ψ_{T}. The practical FNDMC approaches available for large systems rely on compact yet effective Ψ_{T}, most often containing an explicitly correlated single Slater determinant (SD). However, SD nodes may be better suited to one system than to another, which may possibly lead to inaccurate FNDMC energy differences. It remains a challenge how to estimate nonequivalence or appropriateness of SDs. Here we use the differences of a measure based on the Euclidean distance between the natural orbital occupation number (NOON) vector of the SD and the exact solution in the NOON vector space, which can be viewed as a measure of SD nonequivalence and as a qualitative measure of the expected degree of nondynamic-correlation-related bias in FNDMC energy differences. This is explored on a set of small noncovalent complexes and covalent bond breaking of Si_{2} vs N_{2}. It turns out that NOON-based measures well reflect the magnitude and sign of the bias present in the data available, thus providing insights into the nature of bias cancellation in SD FNDMC energy differences.

On the role of charge transfer in halogen bonding

We have quantified the energetic contribution of charge transfer to halogen bonding to be about 10% of the interaction energy.

Discovering correlated fermions using quantum Monte Carlo

It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.