Quantum Cluster Theory for the Polarizable Continuum Model (PCM)

Dielectric continuum methods for quantum chemistry

“…These ideas have been extended beyond their perturbation theory origins and represent the available options for self‐consistency in any calculation that combines an SCRF method with a quantum‐chemical model that requires a post‐SCF calculation, 582,586,587,615,636–640 including TDDFT 586 . An alternative pictorial representation of the simplest method (PTE) and most complete scheme (PTED) is provided in Figure 10b, which furnishes a flowchart for an excited‐state calculation indicating which densities are used to construct the various reaction‐field operators .…”

“…A general LR‐PCM formulation has been given by Cammi et al ., 618,645 and specific formulations for different excited‐state methods are available as well, including for TDDFT and other single‐excitation theories, 644–648 following on earlier implementations of the coupled‐perturbed SCF + PCM procedure for response properties; 216,649 for multiconfigurational SCF wave functions; 98 for ADC; 599,641 and for the GW /Bethe‐Salpeter equation formalism 650 . Finally, LR‐PCM has been implemented for coupled‐cluster theory, 651–655 based on the coupled‐cluster response formalism 637 …”

“…48 This nomenclature derives from efforts to use perturbation theory to include correlation in the ground-state calculation (e.g., MP2 + SCRF), [632][633][634][635] where one must decide whether (and how) electron correlation should be included in the density that is used to polarize the continuum. The same notation has been adopted for PCM calculations using nonperturbative models such as coupled-cluster theory, 636,637 and is used here in a discussion that is formulated specifically with excited-state calculations in mind. As illustrated in Figure 10a, the PTE scheme involves self-consistent solution of the SCF + SCRF problem followed by a single-shot post-SCF calculation using solvent-polarized MOs.…”

“…650 Finally, LR-PCM has been implemented for coupled-cluster theory, [651][652][653][654][655] based on the coupled-cluster response formalism. 637 For isolated-molecule quantum chemistry, the LR formalism for excitation energies is generally equivalent to solving the corresponding Schrödinger equation, 656 but the LR-and SS-PCM formalisms are not equivalent. 618,657 The general form of the LR-PCM result for excitation energies is 618…”