Communication: Efficient counterpoise corrections by a perturbative approach

We investigate the use of Hartree-Fock and density functional perturbative corrections for estimating the counterpoise correction (CPC) for interaction energies at the self-consistent field level. We test our approach using several popular basis sets on the S22 set of weakly bound systems, which can exhibit large basis set superposition errors. Our results show that the perturbative approaches typically recover over 95% of the CPC and can be up to twelve times faster to compute than the conventional methods and therefore provide an attractive alternative to calculating CPCs in the conventional way.P.M.W.G. thanks the Australian Research Council for funding (Grant Nos. DP0984806 and DP1094170) and APAC for a generous allocation of supercomputer resources. J.D. thanks the ANU/RSC for a PhD scholarship

MP2[V] – A simple approximation to second-order Møller–Plesset perturbation theory

We propose a simplified variant of the dual-basis MP2[K] scheme [J. Chem. Phys. 2011,134, 081103] that bootstraps a small-basis MP2 result to a large-basis one. This simplified method, which we call MP2[V], assumes the occupied orbitals are adequately described by the smaller basis, and, therefore, only the relaxation of the virtual orbitals is considered when shifting to the larger basis. Numerical tests on several organic reactions and noncovalent interactions show that MP2[V] yields absolute and relative energies that are in excellent agreement with the conventional large-basis MP2 calculations but in a small fraction of the time.P.M.W.G. thanks the Australian Research Council for funding (Grant Nos. DP1094170 and DP120104740) and APAC for a generous allocation of supercomputer resources. J.D. thanks the ANU/RSC for a Ph.D. scholarship

Approaching the Hartree–Fock limit by perturbative methods

We describe perturbative methods for improving finite-basis Hartree-Fock calculations toward the complete-basis limit. The best method appears to offer quadratic error reduction and preliminary numerical applications demonstrate that remarkably accurate Hartree-Fock energies can be obtained.J.D. thanks the ANU for a Ph.D. scholarship and P.M.W.G. thanks the Australian Research Council for funding Grant No. DP0771978

Hartree–Fock perturbative corrections for total and reaction energies

We have performed an assessment of the Hartree-Fock perturbative correction (HFPC) on a large and diverse set of molecules and reactions. Errors in both absolute and reaction energies with respect to converged secondary basis Hartree-Fock results are reported for a wide spectrum of primary/secondary basis set combinations. These results show that using an adequate primary basis, HFPC can accurately reproduce secondary basis energies at a substantially reduced cost. Comparisons of HFPC with the related dual basis Hartree-Fock (DBHF) scheme are also made for several molecules and target secondary basis sets. Our results indicate that HFPC is faster and more accurate than DBHF for approaching triple-zeta basis sets. For quadruple-zeta secondary basis sets, HFPC is capable of yielding more accurate energies at a marginally increased cost over DBHF.We thank the Australian Research Council for funding Grant No. DP0771978 and APAC for a generous allocation of supercomputer resources. J.D. thanks the ANU/RSC for a Ph.D. scholarship

A generalized Poisson equation and short-range self-interaction energies

We generalize the Poisson equation to attenuated Newtonian potentials. If the attenuation is at least exponential, the equation provides a local mapping between the density and its potential. We use this to derive several density functionals for the short-range self-interaction energy

Self-consistent-field calculations of core excited states

The accuracy of core excitation energies and core electron binding energies computed within a Δself-consistent-field framework is assessed. The variational collapse of the core excited state is prevented by maintaining a singly occupied core orbital using an overlap criterion called the maximum overlap method. When applied to a wide range of small organic molecules, the resulting core excitation energies are not systematically underestimated as observed in time-dependent density functional theory and agree well with experiment. The accuracy of this approach for core excited states is illustrated by the calculation of the pre-edge features in x-ray absorption spectra of plastocyanin, which shows that accurate results can be achieved with Δself-consistent-field calculations when used in conjunction with uncontracted basis functions.N.A.B. is grateful to the ANU for a 2007 Visiting Fellowship

Extracting atoms from molecular electron densities via integral equations

The observation that a molecular electron density is close to the superposition of its constituent atoms leads naturally to the idea of modeling a density by a sum of nuclear-centered, spherically symmetric functions. The functions that are optimal in a least-squares sense are known as Stewart atoms. Previous attempts to construct Stewart atoms by expanding them in an auxiliary basis have been thwarted by slow convergence with respect to the size of the auxiliary basis used. We present a method for constructing Stewart atoms via convolution integrals which bypasses the need for an auxiliary basis, and is able to produce highly accurate approximations to Stewart atoms.ATBG is grateful for funding and support from QCHEM Inc

Software for the frontiers of quantum chemistry : An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design.This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.Peer reviewe

Communication: Hartree-Fock description of excited states of H₂

Hartree-Fock (HF) theory is most often applied to study the electronic ground states of molecular systems. However, with the advent of numerical techniques for locating higher solutions of the self-consistent field equations, it is now possible to examine the extent to which such mean-field solutions are useful approximations to electronic excited states. In this Communication, we use the maximum overlap method to locate 11 low-energy solutions of the HF equation for the H2 molecule and we find that, with only one exception, these yield surprisingly accurate models for the low-lying excited states of this molecule. This finding suggests that the HF solutions could be useful first-order approximations for correlated excited state wavefunctions

Resolutions of the Coulomb operator

We discuss a generalization of the resolution of the identity by considering one-body resolutions of two-body operators, with particular emphasis on the Coulomb operator. We introduce a set of functions that are orthonormal with respect to 1∕r₁₂ and propose that the resulting “resolution of the Coulomb operator,” r₁₂⁻¹=∣ϕi><ϕi∣, may be useful for the treatment of large systems due to the separation of two-body interactions. We validate our approach by using it to compute the Coulomb energy of large systems of point charges