Ground- and Excited-State Dipole Moments and Oscillator Strengths of Full Configuration Interaction Quality.

We report ground- and excited-state dipole moments and oscillator strengths (computed in different "gauges" or representations) of full configuration interaction (FCI) quality using the selected configuration interaction method known as Configuration Interaction using a Perturbative Selection made Iteratively (CIPSI). Thanks to a set encompassing 35 ground- and excited-state properties computed in 11 small molecules, the present near-FCI estimates allow us to assess the accuracy of high-order coupled-cluster (CC) calculations including up to quadruple excitations. In particular, we show that incrementing the excitation degree of the CC expansion (from CC with singles and doubles (CCSD) to CC with singles, doubles, and triples (CCSDT) or from CCSDT to CC with singles, doubles, triples, and quadruples (CCSDTQ)) reduces the average error with respect to the near-FCI reference values by approximately 1 order of magnitude.

Connections between many-body perturbation and coupled-cluster theories.

Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] to show connections between the Bethe-Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe-Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method are also put forward. The present work allows us to easily transfer key developments and the general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks.

Spectroscopic properties of open shell diatomic molecules using Piris natural orbital functionals.

Spectroscopic properties such as equilibrium distances, vibrational constants, rotational constants, dissociation energies, and excitation energies are calculated for nine heteronuclear diatomic molecules (PH, NF, NH, NO, CS, AlF, ClF, BeO and CF) using an interactive pair model (PNOF7s), that has been generalized for spin multiplet states, and its second order perturbation variant, NOF-MP2, which was also generalized for multiplets. The results obtained are compared with Complete Active Space (CASSCF) and Complete Active Space Perturbation Theory (CASPT2). It is shown that the potential energy curves provided by the PNOF functional for open shell diatomic molecules are in acceptable agreement with those from CASSCF and CASPT2. The spectroscopic constants depending at most on the second derivative of the potential energy are in good agreement with experiment, while those requiring the evaluation of the third and fourth derivatives show larger deviations from experiment and from those predicted by CASPT2. Thus, it is shown that the PNOF functional extension to multiplets is an alternative approach in predicting spectroscopic constants of molecules where static correlation plays an important role, like the open shell heteronuclear diatomic molecules studied in this work.

Natural orbital functional for spin-polarized periodic systems.

Natural orbital functional theory is considered for systems with one or more unpaired electrons. An extension of the Piris natural orbital functional (PNOF) based on electron pairing approach is presented, specifically, we extend the independent pair model, PNOF5, and the interactive pair model PNOF7 to describe spin-uncompensated systems. An explicit form for the two-electron cumulant of high-spin cases is only taken into account, so that singly occupied orbitals with the same spin are solely considered. The rest of the electron pairs with opposite spins remain paired. The reconstructed two-particle reduced density matrix fulfills certain N-representability necessary conditions, as well as guarantees the conservation of the total spin. The theory is applied to model systems with strong non-dynamic (static) electron correlation, namely, the one-dimensional Hubbard model with periodic boundary conditions and hydrogen rings. For the latter, PNOF7 compares well with exact diagonalization results so the model presented here is able to provide a correct description of the strong-correlation effects.