New Single- and Multi-Reference Coupled-Cluster Methods for High Accuracy Calculations of Ground and Excited States

P. Piecuch, Michigan State University (Principal Investigator)

This proposal describes a continuing effort to develop, disseminate, and apply new gen­erations of ab ini­tio electronic structure approaches and computer codes exploiting the exponential wave function ansatz of coupled-cluster (CC) theory, which enable precise modeling of mo­lecular processes and prop­erties relevant to energy science, including, but not limited to, com­bustion, ca­talysis, photochemis­try, and harnessing light to drive and control chemical reactivity. The emphasis is on meth­ods that offer high accuracy, ease of use, and lower com­putational costs com­pared to other ap­proaches that aim at similar precision, so that one can study complex molecular prob­lems with dozens or hun­dreds of at­oms, in addition to smaller systems, in a predictive and sys­tematically improvable manner, sup­porting ongoing experiments or in the absence of experimental information. The proposed new effort concentrates on (i) a novel CC formalism, abbreviated as CC(P;Q), and its extension to the electronically excited and open-shell states via the equation-of-motion (EOM) methodology, including states that display a substan­tial multireference character, in which the previously ex­ploited stochastic configuration interaction (CI) Quantum Monte Carlo (QMC) propagations in the many-electron Hilbert space, used to identify the dominant higher–than–doubly excited de­terminants for the inclusion in the initial steps of the CC(P;Q) algorithm, are replaced by the selected CI approach ab­breviated as CIPSI; (ii) externally corrected CC (ec-CC) methods using the three- and four-body clusters ex­tracted from se­lected CI (e.g., CIPSI) runs and correcting the resulting energies for the missing many-electron corre­lation effects with the help of moment expansions similar to those defining the CC(P;Q) theories, along with the utilization of the selected-CI-driven ec-CC frame­work in formu­lating a new type of multireference CC technique, in which the relatively inex­pensive sequences of Hamiltonian diagonaliza­tions provide the desired multi­configurational reference states; and (iii) devel­opment of a new type of the adap­tive, self-correcting, “black-box” CC(P;Q) methodol­ogy, which will allow one to converge the high-level CC and EOMCC energetics in single- as well as mul­tireference situations at the small frac­tion of the computational effort and without having to rely on non-CC concepts. We will continue our work toward the de­velopment of semi-stochastic CC(P;Q) theo­ries, especially their extensions to excited and open-shell states, the cluster-analysis-driven FCIQMC framework aimed at recovering the exact, full CI, energetics in weakly as well as strongly correlated systems, new generations of approximate coupled-pair methods that can handle larger numbers of strongly correlated electrons with an ease of a single-reference CC computation, and extending the single and double elec­tron-attachment and ionization EOMCC meth­odologies to the triple elec­tron-at­tachment and triple ioniza­tion cases, which can be use­ful in studies of triradicals and inorganic chromo­phores, of interest in solar energy con­ver­sion schemes, which emerge out of d³ electronic configurations. We will also enrich the previously developed linear scal­ing, local correlation CC codes ex­ploiting the cluster-in-molecule framework, and their multi-level ex­tensions allowing one to mix dif­fer­ent levels of electronic structure theory in a single computation, which can take advantage of mod­ern, mas­sively par­allel com­puter plat­forms, by the active-space CC and CC(P;Q) op­tions. Among the pro­posed appli­ca­tions are radi­cal-radical reac­tions rele­vant to com­bustion, singlet–triplet gaps and elec­tronic excita­tion spectra of poly­acenes, elec­tronic structure of chains, rings, and three-dimensional lattices of hydro­gen atoms that can be used to model metal-insulator transitions, and computational studies of super pho­toreagents.