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.
Highlights
Calculations of the intermolecular interaction energy typically involve the supermolecular approach
A given wave function theory (WFT) approximation is useful in describing interactions either if it accounts for highorder components in the intermolecular interaction operator or when it is reasonably accurate in the lowest orders and it is known which higher-order components are missing
The HF energy contains electrostatic, exchange, and induction interaction energy components and has been rigorously shown to miss the second-order dispersion component.[5]. In spite of this deficiency, the supermolecular HF result can be corrected for the dispersion energy which leads to a low-cost hybrid approach.[6−8] The accuracy of the hybrid approach can be significantly improved by including intramonomer correlation effects in a perturbative manner which is known as the HFDc(1) method.[8,9]
Summary
Calculations of the intermolecular interaction energy typically involve the supermolecular approach. A representative example from the first group are the coupled cluster (CC) methods[3,4] which predict interaction energies with high accuracy when effects of single, double, and triple excitations are accounted for. The HF energy contains electrostatic, exchange, and induction interaction energy components and has been rigorously shown to miss the second-order dispersion component.[5] In spite of this deficiency, the supermolecular HF result can be corrected for the dispersion energy which leads to a low-cost hybrid approach.[6−8] The accuracy of the hybrid approach can be significantly improved by including intramonomer correlation effects in a perturbative manner which is known as the HFDc(1) method.[8,9]
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