C. David Sherrill

Psi4: an open-source ab initio electronic structure program

The Psi4 program is a new approach to modern quantum chemistry, encompassing Hartree–Fock and density‐functional theory to configuration interaction and coupled cluster. The program is written entirely in C++ and relies on a new infrastructure that has been designed to permit high‐efficiency computations of both standard and emerging electronic structure methods on conventional and high‐performance parallel computer architectures. Psi4 offers flexible user input built on the Python scripting language that enables both new and experienced users to make full use of the programs capabilities, and even to implement new functionality with moderate effort. To maximize its impact and usefulness, Psi4 is available through an open‐source license to the entire scientific community.

Density-functional approaches to noncovalent interactions: A comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals

A systematic study of techniques for treating noncovalent interactions within the computationally efficient density functional theory (DFT) framework is presented through comparison to benchmark-quality evaluations of binding strength compiled for molecular complexes of diverse size and nature. In particular, the efficacy of functionals deliberately crafted to encompass long-range forces, a posteriori DFT+dispersion corrections (DFT-D2 and DFT-D3), and exchange-hole dipole moment (XDM) theory is assessed against a large collection (469 energy points) of reference interaction energies at the CCSD(T) level of theory extrapolated to the estimated complete basis set limit. The established S22 [revised in J. Chem. Phys. 132, 144104 (2010)] and JSCH test sets of minimum-energy structures, as well as collections of dispersion-bound (NBC10) and hydrogen-bonded (HBC6) dissociation curves and a pairwise decomposition of a protein-ligand reaction site (HSG), comprise the chemical systems for this work. From evaluations of accuracy, consistency, and efficiency for PBE-D, BP86-D, B97-D, PBE0-D, B3LYP-D, B970-D, M05-2X, M06-2X, ωB97X-D, B2PLYP-D, XYG3, and B3LYP-XDM methodologies, it is concluded that distinct, often contrasting, groups of these elicit the best performance within the accessible double-ζ or robust triple-ζ basis set regimes and among hydrogen-bonded or dispersion-dominated complexes. For overall results, M05-2X, B97-D3, and B970-D2 yield superior values in conjunction with aug-cc-pVDZ, for a mean absolute deviation of 0.41 - 0.49 kcal/mol, and B3LYP-D3, B97-D3, ωB97X-D, and B2PLYP-D3 dominate with aug-cc-pVTZ, affording, together with XYG3/6-311+G(3df,2p), a mean absolute deviation of 0.33 - 0.38 kcal/mol.

An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene−Methane, and Benzene−H2S†

Large, correlation-consistent basis sets have been used to very closely approximate the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] complete basis set potential energy curves of several prototype nonbonded complexes, the sandwich, T-shaped, and parallel-displaced benzene dimers, the methane-benzene complex, the H2S-benzene complex, and the methane dimer. These benchmark potential energy curves are used to assess the performance of several methods for nonbonded interactions, including various spin-component-scaled second-order perturbation theory (SCS-MP2) methods, the spin-component-scaled coupled-cluster singles and doubles method (SCS-CCSD), density functional theory empirically corrected for dispersion (DFT-D), and the meta-generalized-gradient approximation functionals M05-2X and M06-2X. These approaches generally provide good results for the test set, with the SCS methods being somewhat more robust. M05-2X underbinds for the test cases considered, while the performances of DFT-D and M06-2X are similar. Density fitting, dual basis, and local correlation approximations all introduce only small errors in the interaction energies but can speed up the computations significantly, particulary when used in combination.

Assessment of the Performance of DFT and DFT-D Methods for Describing Distance Dependence of Hydrogen-Bonded Interactions.

Noncovalent interactions such as hydrogen bonds, van der Waals forces, and π-π interactions play important roles influencing the structure, stability, and dynamic properties of biomolecules including DNA and RNA base pairs. In an effort to better understand the fundamental physics of hydrogen bonding (H-bonding), we investigate the distance dependence of interaction energies in the prototype bimolecular complexes of formic acid, formamide, and formamidine. Potential energy curves along the H-bonding dissociation coordinate are examined both by establishing reference CCSD(T) interaction energies extrapolated to the complete basis set limit and by assessing the performance of the density functional methods B3LYP, PBE, PBE0, B970, PB86, M05-2X, and M06-2X and empirical dispersion corrected methods B3LYP-D3, PBE-D3, PBE0-D3, B970-D2, BP86-D3, and ωB97X-D, with basis sets 6-311++G(3df,3pd), aug-cc-pVDZ, and aug-cc-pVTZ. Although H-bonding interactions are dominated by electrostatics, it is necessary to properly account for dispersion interactions to obtain accurate energetics. In order to quantitatively probe the nature of hydrogen bonding interactions as a function of distance, we decompose the interaction energy curves into physically meaningful components with symmetry-adapted perturbation theory (SAPT). The SAPT results confirm that the contribution of dispersion and induction are significant at and near equilibrium, although electrostatics dominate. Among the DFT/DFT-D techniques, the best overall results are obtained utilizing counterpoise-corrected ωB97X-D with the aug-cc-pVDZ basis set.

Basis set consistent revision of the S22 test set of noncovalent interaction energies.

The S22 test set of interaction energies for small model complexes [Phys. Chem. Chem. Phys. 8, 1985 (2006)] has been very valuable for benchmarking new and existing methods for noncovalent interactions. However, the basis sets utilized to compute the CCSD(T) interaction energies for some of the dimers are insufficient to obtain converged results. Here we consistently extrapolate all CCSD(T)/complete basis set (CBS) interaction energies using larger basis sets for the CCSD(T) component of the computation. The revised values, which we designate S22A, represent the most accurate results to date for this set of dimers. The new values appear to be within a few hundredths of 1 kcal mol(-1) of the true CCSD(T)/CBS limit at the given geometries, but the former S22 values are off by as much as 0.6 kcal mol(-1) compared to the revised values. Because some of the most promising methods for noncovalent interactions are already achieving this level of agreement (or better) compared to the S22 data, more accurate benchmark values would clearly be helpful. The MP2, SCS-MP2, SCS-CCSD, SCS(MI)-MP2, and B2PLYP-D methods have been tested against the more accurate benchmark set. The B2PLYP-D method outperforms all other methods tested here, with a mean average deviation of only 0.12 kcal mol(-1). However, the consistent, slight underestimation of the interaction energies computed by the SCS-CCSD method (an overall mean absolute deviation and mean deviation of 0.24 and -0.23 kcal mol(-1), respectively) suggests that the SCS-CCSD method has the potential to become even more accurate with a reoptimization of its parameters for noncovalent interactions.

PSI3: An open‐source Ab Initio electronic structure package

PSI3 is a program system and development platform for ab initio molecular electronic structure computations. The package includes mature programming interfaces for parsing user input, accessing commonly used data such as basis‐set information or molecular orbital coefficients, and retrieving and storing binary data (with no software limitations on file sizes or file‐system‐sizes), especially multi‐index quantities such as electron repulsion integrals. This platform is useful for the rapid implementation of both standard quantum chemical methods, as well as the development of new models. Features that have already been implemented include Hartree‐Fock, multiconfigurational self‐consistent‐field, second‐order Møller‐Plesset perturbation theory, coupled cluster, and configuration interaction wave functions. Distinctive capabilities include the ability to employ Gaussian basis functions with arbitrary angular momentum levels; linear R12 second‐order perturbation theory; coupled cluster frequency‐dependent response properties, including dipole polarizabilities and optical rotation; and diagonal Born‐Oppenheimer corrections with correlated wave functions. This article describes the programming infrastructure and main features of the package. PSI3 is available free of charge through the open‐source, GNU General Public License.

Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O 4

We describe an alternative procedure for obtaining approximate Brueckner orbitals in ab initio electronic structure theory. Whereas approximate Brueckner orbitals have traditionally been obtained by mixing the orbitals until the coefficients of singly substituted determinants in the many-electron wave function become zero, we remove singly substituted determinants at the outset and obtain orbitals which minimize the total electronic energy. Such orbitals may be described as variational Brueckner orbitals. These two procedures yield the same set of exact Brueckner orbitals in the full configuration interaction limit but differ for truncated wave functions. We consider the simplest variant of this approach in the context of coupled-cluster theory, optimizing orbitals for the coupled-cluster doubles (CCD) model. An efficient new method is presented for solving the coupled equations defining the energy, doubles amplitudes, and orbital mixing parameters. Results for several small molecules indicate nearly iden...

Size-consistent wave functions for nondynamical correlation energy: The valence active space optimized orbital coupled-cluster doubles model

The nondynamical correlation energy may be defined as the difference between full configuration interaction within the space of all valence orbitals and a single determinant of molecular orbitals (Hartree–Fock theory). In order to describe bond breaking, diradicals, and other electronic structure problems where Hartree–Fock theory fails, a reliable description of nondynamical correlation is essential as a starting point. Unfortunately, the exact calculation of nondynamical correlation energy, as defined above, involves computational complexity that grows exponentially with molecular size and is thus unfeasible beyond systems of just two or three heavy atoms. We introduce a new hierarchy of feasible approximations to the nondynamical correlation energy based on coupled-cluster theory with variationally optimized orbitals. The simplest member of this hierarchy involves connected double excitations within the variationally optimized valence active space and may be denoted as VOO-CCD, or VOD. VOO-CCD is size-...

The Configuration Interaction Method: Advances in Highly Correlated Approaches

Abstract Highly correlated configuration interaction (CI) wavefunctions going beyond the simple singles and doubles (CISD) model space can provide very reliable potential energy surfaces, describe electronic excited states, and yield benchmark energies and molecular properties for use in calibrating more approximate methods. Unfortunately, such wavefunctions are also notoriously difficult to evaluate due to their extreme computational demands. The dimension of a full CI procedure, which represents the exact solution of the electronic Schrodinger equation for a fixed one-particle basis set, grows factorially with the number of electrons and basis functions. For very large configuration spaces, the number of CI coupling coefficients becomes prohibitively large to store on disk; these coefficients must be evaluated as needed in a so-called direct CI procedure. Work done by several groups since 1980 has focused on using Slater determinants rather than spin ( S ^ 2 ) eigenfunctions because coupling coefficients are easier to compute with the former. We review the fundamentals of the configuration interaction method and discuss various determinant-based CI algorithms. Additionally, we consider some applications of highly correlated CI methods.

Wavefunction methods for noncovalent interactions

Noncovalent interactions remain poorly understood despite their importance to supramolecular chemistry, biochemistry, and materials science. They are an ideal target for theoretical study, where interactions of interest can be probed directly, free from competing secondary interactions. However, the most popular tools of computational chemistry are not particularly reliable for noncovalent interactions. Here we review recent works in wavefunction‐based quantum chemistry techniques aimed at greater accuracy and faster computations for these systems. We describe recent developments in high‐accuracy benchmarks, a variety of recent wavefunction methods with promise for noncovalent interactions, various approximations to speed up these methods, and recent advances in wavefunction‐based symmetry‐adapted perturbation theory, which provides not only interaction energies but also their decomposition into physically meaningful components. Together, these advances are currently extending robust, accurate computations of noncovalent interactions from systems with around one dozen heavy atoms up to systems with several dozens of heavy atoms.