How Much Dispersion Energy Is Included in the Multiconfigurational Interaction Energy?

Abstract

We demonstrate how to quantify the amount of dispersion interaction recovered by supermolecular calculations with the multiconfigurational self-consistent field (MCSCF) wave functions. For this purpose, we present a rigorous derivation which connects the portion of dispersion interaction captured by the assumed wave function model—the residual dispersion interaction—with the size of the active space. Based on the obtained expression for the residual dispersion contribution, we propose a dispersion correction for the MCSCF that avoids correlation double counting. Numerical demonstration for model four-electron dimers in both ground and excited states described with the complete active space self-consistent field (CASSCF) reference serves as a proof-of-concept for the method. Accurate results, largely independent of the size of the active space, are obtained. For many-electron systems, routine CASSCF interaction energy calculations recover a tiny fraction of the full second-order dispersion energy. We found that the residual dispersion is non-negligible only for purely dispersion-bound complexes.

Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers

“…In Figure 3 , we compare SAPT(CAS) interaction energy curves with supermolecular CAS(2,3) results and a coupled-cluster benchmark. As it has been rigorously shown in ref ( 99 ), supermolecular CAS interaction energy misses dispersion contributions if active orbitals are assigned only to one monomer, which is the case here. The CAS+DISP curves in Figure 3 represent CAS interaction energy supplemented with the dispersion component taken from SAPT(CAS) calculations, E DISP (2) = E disp (2) + E exch–disp (2) .…”

“…To illustrate this, we have presented interaction energy curves obtained in a hybrid approach, which recovers induction terms up to infinite order in V̂ . Indeed, a combination of supermolecular CASSCF and second-order dispersion energy from SAPT(CAS) calculations, which we refer to as the CAS+DISP approach, 99 outperforms SAPT for the π → π* state and remains in excellent agreement with the coupled-cluster reference.…”

“…The δ HF component was added to the SAPT interaction energy provided that the ratio of the sum of the induction and exchange–induction energies to the total interaction energy was larger than 12.5%, in agreement with the criterion selected in ref ( 98 ). Note that in Section 4.3 error statistics for total interaction energies are reported for the S 2 subset of the TK21 data set, which excludes six largest dimers (see refs ( 87 ) and ( 99 )).…”

Symmetry-adapted perturbation theory based on multiconfigurational wave function description of monomers

“…As it has been rigorously shown in Ref. 104, supermolecular CAS interaction energy misses dispersion contributions if active orbitals are assigned only to one monomer, which is the case here. The CAS+DISP curves in Figure 3 represent CAS interaction energy supplemented with the dispersion component taken from SAPT(CAS) calculations, E…”

“…To illustrate this, we have presented interaction energy curves obtained in a hybrid approach which recovers induction terms up to infinite order in V . Indeed, a combination of supermolecular CASSCF and second-order dispersion energy from SAPT(CAS) calculations, which we refer to as the CAS+DISP approach, 104 outperforms SAPT for the π → π * state, and remains in excellent agreement with the coupled-cluster reference.…”