Computation of molecular Hartree–Fock Wigner intracules

Combining Wave Function Methods with Density Functional Theory for Excited States

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.

Computation and interpretation of molecular Omega intracules

The Omega intracule is a three-dimensional function that describes the relative positions, momenta, and directions of motion of pairs of electrons in a system. In this paper, we describe the computation of the Omega intracule for a molecular system whose electronic wave function is expanded in a Gaussian basis set. This is followed by implementation details and numerical tests. Finally, we use the Omega intracules of a number of small systems to illustrate the power of this function to extract simple physical insights from complicated wave functions.

Intracule functional models: I. Angle-corrected correlation kernels

We explore the merits of applying a simple angle-dependent correction to the correlation kernel within the framework of Hartree-Fock-Wigner theory. Based on numerical results for the first eighteen atoms, we conclude that such a correction offers a significant improvement over the action kernel that we and others have explored previously.

Application of Wigner and Husimi intracule based electron correlation models to excited states

A new approach to the electron correlation problem based on phase space intracules derived from the Wigner distribution is applied to excited states. The computed electron correlation energy reduces the mean absolute error in the prediction of the excitation energies of 55 atomic excited states from 0.65 eV for unrestricted Hartree-Fock to 0.32 eV. This compares favorably to a mean absolute deviation of 0.52 eV for second order Moller-Plesset perturbation theory and 0.35 eV for the Lee-Yang-Parr functional. An analogous correlation model based on the Husimi distribution is developed. Predicted correlation energies and excitation energies from this model are significantly worse than for the Wigner intracule based model. Alternative correlation kernels may be more suitable for the Husimi intracule based approach.

Analysis of multiconfigurational wave functions in terms of hole-particle distributions

A detailed study of hole-particle distributions in many-electron molecular systems is presented, based on a representation of the high-order density matrices obtained by an operator technique reminiscent of Bogolyubov's quantum statistical operator theory. A rigorous definition of density matrices of arbitrary order is given for a composite system of holes and particles. Particular attention is focused on the description of mixed hole-particle distributions. The main results are given as the functionals of excitation operators (generators) that are used in the conventional configuration interaction (CI) and coupled cluster (CC) theories. Local atomic occupation numbers for holes and particles are introduced to provide a measure of the participation of specific atoms in the electron correlation processes. The corresponding total occupations--as well as the hole-hole, particle-particle, and hole-particle mean distances--provide a useful and physically intuitive description of electron correlation. Suitable computational schemes for numerical evaluation of the above characteristics within full CI and typical CC approaches are presented. The insights one can gain with the developed approach into the peculiarities and nuances of the hole-particle picture in typical electronic processes such as excitation and molecular dissociation are illustrated with specific computations on small molecules and closed-shell atoms.

A family of intracules, a conjecture and the electron correlation problem

We present a radical approach to the calculation of electron correlation energies. Unlike conventional methods based on Hartree-Fock or density functional theory, it is based on the two-electron phase-space information in the Omega intracule, a three-dimensional function derived from the Wigner distribution. Our formula for the correlation energy is isomorphic to the Hartree-Fock energy expression but requires a new type of four-index integral. Preliminary results, obtained using a model that is based on the known correlation energies of small atoms, are encouraging.

Advances in methods and algorithms in a modern quantum chemistry program package

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

Atomic and molecular intracules for excited states

Intracules in position space, momentum space and phase space have been calculated for low-lying excited states of the He atom, Be atom, formaldehyde and butadiene. The phase-space intracules (Wigner intracules) provide significantly more information than the position- and momentum-space intracules, particularly for the Be atom. Exchange effects are investigated through the differences between corresponding singlet and triplet states.