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 planned research 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.

In its first part, the planned new effort focuses on the powerful quantum-mechanical many-body methodology known as CC(P;Q), which is designed to target the nearly exact or exact high levels of the CC and equation-of-motion CC (EOMCC) theories at tiny fractions of the computational costs, even in challenging multiconfigurational situations characterized by large and nonperturbative higher–than–two-body cluster and EOM exci­tation amplitudes, where conventional perturbative approximations fail or struggle. This will enable the PI’s group to (i) further advance and conclude their foundational work on the selected-configuration-interaction-driven and adaptive, self-improving, CC(P;Q) approaches, especially their extensions to excited electronic states relevant to photochemistry, and (ii) test and apply new types of the approximate coupled-pair methods merged with the CC(P;Q) ideas, designed to handle strongly correlated systems characterized by the entanglement of larger numbers of electrons, for which conventional single- and multireference CC hierarchies fail or become inapplicable. The second part of the planned effort focuses on the double ionization potential (DIP) and double electron-attachment (DEA) EOMCC approaches with full and active-space treatments of 4-hole–2-particle (4h-2p) and 4-particle–2-hole (4p-2h) excitations and three-body clusters and the similarly high-level IP-EOMCC and EA-EOMCC methods with up to 3h-2p and 3p-2h excitations and singly, doubly, and triply excited clusters in the underlying CC computations for single ionization and electron attachment, alongside the CC(P;Q)-inspired noniterative corrections to the lower-order IP- and EA-EOMCC methods to capture the missing electron correlation effects in radical species in a robust manner. Among the planned applications are singlet–triplet gaps in biradical species and polyacenes, electronic excitation spectra of radicals, and reactivity of small organic molecules enabled by strong-field ionizing laser pulses.

The planned approaches address some of the most important challenges of modern electronic structure theory, including the development of practical and system­atically improvable com­putational schemes aimed at an accurate description of chemical reaction pathways and molecular electronic exci­tations in the gas and condensed phases, and strongly correlated materials. The methods will find use in a wide variety of molec­ular applications relevant to energy science and continue to be shared at no cost with the community via the GAMESS package and established open-source mechanisms, such as GitHub. The planned research will provide excellent train­ing ex­peri­ences in the forefront physical sciences for members of the PI's group.