Triple electron-electron-proton excitations and second-order approximations in nuclear-electronic orbital coupled cluster methods

TL;DR

This paper develops and tests advanced coupled cluster methods within the nuclear-electronic orbital framework, emphasizing the importance of triple electron-electron-proton excitations for accurately modeling nuclear quantum effects.

Contribution

It introduces a NEO-CCSD(eep) method with triple excitations and a scaled-opposite-spin NEO-CC2 approximation, enhancing accuracy and computational efficiency.

Findings

NEO-CCSD(eep) yields highly accurate proton densities and affinities.

Scaled-opposite-spin NEO-CC2 achieves near NEO-CCSD(eep) accuracy.

The methods enable efficient modeling of nuclear quantum effects in large systems.

Abstract

The accurate description of nuclear quantum effects, such as zero-point energy, is important for modeling a wide range of chemical and biological processes. Within the nuclear-electronic orbital (NEO) approach, such effects are incorporated in a computationally efficient way by treating electrons and select nuclei, typically protons, quantum mechanically with molecular orbital techniques. Herein, we implement and test a NEO coupled cluster method that explicitly includes the triple electron-proton excitations, where two electrons and one proton are excited simultaneously. Our calculations show that this NEO-CCSD(eep) method provides highly accurate proton densities and proton affinities, outperforming any previously studied NEO method. These examples highlight the importance of the triple electron-electron-proton excitations for an accurate description of nuclear quantum effects. Additionally, we also implement and test the second-order approximate coupled cluster with singles and doubles (NEO-CC2) method, as well as its scaled-opposite-spin (SOS) versions. The NEO-SOS$'$-CC2 method, which scales the electron-proton correlation energy as well as the opposite-spin and same-spin components of the electron-electron correlation energy, achieves nearly the same accuracy as the NEO-CCSD(eep) method for the properties studied. Because of its low computational cost, this method will enable a wide range of chemical and photochemical applications for large molecular systems. This work sets the stage for a wide range of developments and applications within the NEO framework.