Symmetry-adapted formulation of the combined G-particle-hole hypervirial equation and Hermitian operator method

Abstract

High accuracy energies of low-lying excited states, in molecular systems, have been determined by means of a procedure which combines the G-particle-hole Hypervirial (GHV) equation method [Alcoba et al. Int. J. Quantum Chem. 109:3178 (2009)] and the Hermitian Operator (HO) one [Bouten et al. Nucl. Phys. A 202:127 (1973)]. This paper reports a suitable strategy to introduce the point group symmetry within the framework of the combined GHV-HO method, what leads to an improvement of the computational efficiency. The resulting symmetry-adapted formulation has been applied to illustrate the computer timings and the hardware requirements in selected chemical systems of several geometries.

Unraveling the Band Gap Trend in the Narrowest Graphene Nanoribbons from the Spin-Adapted Excited-Spectra Reduced Density Matrix Method

“…Previous studies have shown that the ground and excited states of oligobenzenes become more strongly correlated as the length of the oligomers grow. − In this work, we compute the trend in the vertical singlet–triplet gap of the acene (AC) and phenacene (PA) chains using the stable excited-spectra reduced density matrix (ES-RDM) method in ref . Strong electron correlation is captured through the calculation of the ground-state 2-RDM from the variational 2-RDM (v2-RDM) method. − We compare the ES-RDM results with other single-excitation theories like configuration interaction singles (CIS) and time-dependent density functional theory (TD-DFT), which are known to underestimate band gaps, as well as the recent experimental reports on oligobenzenes. − , The ES-RDM calculations reveal that the band gap in acenes decays exponentially with chain length to a finite asymptotic value, which is in good agreement with a recent experiment . The calculations do not show the band gap oscillation as reported in some previous studies. , Finally, in contrast to the decay of the band gap of acenes, the band gap of phenacenes is fairly constant with chain length, reflecting significant differences in the degree of electron correlation detected in the acene and phenacene chains.…”

Symmetry-adapted formulation of the hybrid treatment resulting from the G-particle-hole Hypervirial equation and equations of motion methods: a procedure for modeling solids

“…The aim of this work is to further improve the efficiency of the combined GHV-EOM method by using point group symmetry. Following recent treatments carried out within the framework of the GHV method [21,22], a symmetry-related analysis of the matrices and matrix operations involved in the EOM method is performed. This analysis allows one to formulate a symmetry-adapted version of the combined GHV-EOM algorithm for Abelian groups, which leads to significant computational savings in both floating-point operations and memory storage.…”

Excited-State Spectra of Strongly Correlated Molecules from a Reduced-Density-Matrix Approach

“…In this Letter, we improve a theory for the computation of excited-state spectra from any ground-state two-electron reduced density matrix (2-RDM). − In the excited-spectra RDM theory known as the Hermitian operator method, − ,, the excited-state energies are computed in the space of p-electron transitions from the correlated ground-state wave function from a knowledge of only the 2 p -RDM. Previous work developed and applied the theory for p = 1 to small molecular systems with accurate results, ,,, but applications to both larger and more correlated molecules were hindered by ill-conditioning of the effective eigenvalue problem.…”

“…In this Letter, we present a Hamiltonian-shifted regularization of a family of excited-spectra RDM-based methods for computing excited-state energies from knowledge of ground-state RDMs. In particular, we focus on a specific ES-2RDM-based method with Hermitian single-particle transition operators, also known as the Hermitian operator method. − , The Hamiltonian-shifted regularization removes the singularities of the generalized eigenvalue equation that are not well-treated by the traditional deflation method. The 2-RDM method is explored through its application to a set of strongly correlated molecules including hydrogen and n -acene chains, a nickel dithiolate dianion, and a conjugated dye.…”