Ewa Pastorczak

Ensemble density variational methods with self- and ghost-interaction-corrected functionals.

Ensemble density functional theory (DFT) offers a way of predicting excited-states energies of atomic and molecular systems without referring to a density response function. Despite a significant theoretical work, practical applications of the proposed approximations have been scarce and they do not allow for a fair judgement of the potential usefulness of ensemble DFT with available functionals. In the paper, we investigate two forms of ensemble density functionals formulated within ensemble DFT framework: the Gross, Oliveira, and Kohn (GOK) functional proposed by Gross et al. [Phys. Rev. A 37, 2809 (1988)] alongside the orbital-dependent eDFT form of the functional introduced by Nagy [J. Phys. B 34, 2363 (2001)] (the acronym eDFT proposed in analogy to eHF--ensemble Hartree-Fock method). Local and semi-local ground-state density functionals are employed in both approaches. Approximate ensemble density functionals contain not only spurious self-interaction but also the so-called ghost-interaction which has no counterpart in the ground-state DFT. We propose how to correct the GOK functional for both kinds of interactions in approximations that go beyond the exact-exchange functional. Numerical applications lead to a conclusion that functionals free of the ghost-interaction by construction, i.e., eDFT, yield much more reliable results than approximate self- and ghost-interaction-corrected GOK functional. Additionally, local density functional corrected for self-interaction employed in the eDFT framework yields excitations energies of the accuracy comparable to that of the uncorrected semi-local eDFT functional.

A minimalistic approach to static and dynamic electron correlations: Amending generalized valence bond method with extended random phase approximation correlation correction

A perfect-pairing generalized valence bond (GVB) approximation is known to be one of the simplest approximations, which allows one to capture the essence of static correlation in molecular systems. In spite of its attractive feature of being relatively computationally efficient, this approximation misses a large portion of dynamic correlation and does not offer sufficient accuracy to be generally useful for studying electronic structure of molecules. We propose to correct the GVB model and alleviate some of its deficiencies by amending it with the correlation energy correction derived from the recently formulated extended random phase approximation (ERPA). On the examples of systems of diverse electronic structures, we show that the resulting ERPA-GVB method greatly improves upon the GVB model. ERPA-GVB recovers most of the electron correlation and it yields energy barrier heights of excellent accuracy. Thanks to a balanced treatment of static and dynamic correlation, ERPA-GVB stays reliable when one moves from systems dominated by dynamic electron correlation to those for which the static correlation comes into play.

Perspective: Found in translation: Quantum chemical tools for grasping non-covalent interactions

Todays quantum chemistry methods are extremely powerful but rely upon complex quantities such as the massively multidimensional wavefunction or even the simpler electron density. Consequently, chemical insight and a chemists intuition are often lost in this complexity leaving the results obtained difficult to rationalize. To handle this overabundance of information, computational chemists have developed tools and methodologies that assist in composing a more intuitive picture that permits better understanding of the intricacies of chemical behavior. In particular, the fundamental comprehension of phenomena governed by non-covalent interactions is not easily achieved in terms of either the total wavefunction or the total electron density, but can be accomplished using more informative quantities. This perspective provides an overview of these tools and methods that have been specifically developed or used to analyze, identify, quantify, and visualize non-covalent interactions. These include the quantitative energy decomposition analysis schemes and the more qualitative class of approaches such as the Non-covalent Interaction index, the Density Overlap Region Indicator, or quantum theory of atoms in molecules. Aside from the enhanced knowledge gained from these schemes, their strengths, limitations, as well as a roadmap for expanding their capabilities are emphasized.

Electronic Excited States from the Adiabatic-Connection Formalism with Complete Active Space Wave Functions

It is demonstrated how the recently proposed multireference adiabatic-connection (AC) approximation for electron correlation energy ( Pernal , K. Electron Correlation from the Adiabatic Connection for Multireference Wave Functions . Phys. Rev. Lett. 2018 , 120 , 013001 ) can be extended to predicting correlation energy in excited states of molecules. It is the first successful application of the AC approach to computing excited-states energies of molecules using a complete active space (CAS) wave function as a reference. The unique feature of the AC-CAS approach with respect to popular methods such as CASPT2 and NEVPT2 is that it requires only one- and two-particle reduced density matrices, making it possible to efficiently treat large spaces of active electrons. Application of the simpler variant of AC, the AC0, which is based on the first-order expansion of the AC integrand at the uncorrelated system limit, to excited states yields excitation energies with accuracy rivaling that of the NEVPT2 method but at greatly reduced computational cost.

Correlation Energy from the Adiabatic Connection Formalism for Complete Active Space Wave Functions

Recently, the adiabatic connection (AC) formula for the electron correlation energy has been proposed for a broad class of multireference wave functions (Pernal, K. Electron Correlation from the Adiabatic Connection for Multireference Wave Functions. Phys. Rev. Lett. 2018, 120, 013001). We show that the AC formula used together with the extended random phase approximation (ERPA) can be efficiently applied to complete active space (CAS) wave functions to recover the remaining electron correlation. Unlike most of the perturbation theory approaches, the proposed AC-CAS method does not require construction of higher than two-electron reduced density matrices, which offers an immediate computational saving. In addition, we show that typically the AC-CAS systematically reduces the errors of both the absolute value of energy and of the energy differences (energy barrier) upon enlarging active spaces for electrons and orbitals. AC-CAS consistently gains in accuracy from including more active electrons. We also propose and study that the performance of the AC0 approach resulting from the first-order expansion of the AC integrand at the coupling constant equal to 0. AC0 avoids solving the full ERPA eigenequation, replacing it with small-dimension eigenproblems, while retaining good accuracy of the AC-CAS method. Low computational cost, compared to AC-CAS or perturbational approaches, makes AC0 the most efficient ab initio approach to capturing electron correlation for the CAS wave functions.

Intricacies of van der Waals interactions in systems with elongated bonds revealed by electron-groups embedding and high-level coupled-cluster approaches.

Noncovalent interactions between molecules with stretched intramonomer covalent bonds are a fascinating, yet little studied area. This shortage of information stems largely from the inability of most of the commonly used computational quantum chemistry methods to accurately describe weak long-range and strong nondynamic correlations at the same time. In this work, we propose a geminal-based approach, abbreviated as EERPA-GVB, capable of describing such systems in a robust manner using relatively inexpensive computational steps. By examining a few van der Waals complexes, we demonstrate that the elongation of one or more intramolecular covalent bonds leads to an enhanced attraction between the monomers. We show that this increase in attraction occurs as the electron density characterizing intramolecular covalent bonds depletes and migrates toward the region between the monomers. As the covalent intramonomer bonds continue to stretch, the intermolecular interaction potential passes through a minimum and eventually goes up. The findings resulting from our EERPA-GVB calculations are supported and further elucidated by the symmetry-adapted perturbation theory and coupled-cluster (CC) computations using methods that are as sophisticated as the CC approach with a full treatment of singly, doubly, and triply excited clusters.