TY - JOUR
T1 - Reduced explicitly correlated Hartree-Fock approach within the nuclear-electronic orbital framework
T2 - Theoretical formulation
AU - Sirjoosingh, Andrew
AU - Pak, Michael V.
AU - Swalina, Chet
AU - Hammes-Schiffer, Sharon
N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2013/7/21
Y1 - 2013/7/21
N2 - The nuclear-electronic orbital (NEO) method treats electrons and select nuclei quantum mechanically on the same level to extend beyond the Born-Oppenheimer approximation. Electron-nucleus dynamical correlation has been found to be highly significant due to the attractive Coulomb interaction. The explicitly correlated Hartree-Fock (NEO-XCHF) approach includes explicit electron-nucleus correlation with Gaussian-type geminal functions during the variational optimization of the nuclear-electronic wavefunction. Although accurate for small model systems, the NEO-XCHF method is computationally impractical for larger chemical systems. In this paper, we develop the reduced explicitly correlated Hartree-Fock approach, denoted NEO-RXCHF, where only select electronic orbitals are explicitly correlated to the nuclear orbitals. By explicitly correlating only the relevant electronic orbitals to the nuclear orbitals, the NEO-RXCHF approach avoids problems that can arise when all electronic orbitals are explicitly correlated to the nuclear orbitals in the same manner. We examine three different NEO-RXCHF methods that differ in the treatment of the exchange between the geminal-coupled electronic orbitals and the other electronic orbitals: NEO-RXCHF-fe is fully antisymmetric with respect to exchange of all electronic coordinates and includes all electronic exchange terms; NEO-RXCHF-ne neglects the exchange between the geminal-coupled electronic orbitals and the other electronic orbitals; and NEO-RXCHF-ae includes approximate exchange terms between the geminal-coupled electronic orbitals and the other electronic orbitals. The latter two NEO-RXCHF methods offer substantial computational savings over the NEO-XCHF approach. The NEO-RXCHF approach is applicable to a wide range of chemical systems that exhibit non-Born-Oppenheimer effects between electrons and nuclei, as well as positron-containing molecular systems.
AB - The nuclear-electronic orbital (NEO) method treats electrons and select nuclei quantum mechanically on the same level to extend beyond the Born-Oppenheimer approximation. Electron-nucleus dynamical correlation has been found to be highly significant due to the attractive Coulomb interaction. The explicitly correlated Hartree-Fock (NEO-XCHF) approach includes explicit electron-nucleus correlation with Gaussian-type geminal functions during the variational optimization of the nuclear-electronic wavefunction. Although accurate for small model systems, the NEO-XCHF method is computationally impractical for larger chemical systems. In this paper, we develop the reduced explicitly correlated Hartree-Fock approach, denoted NEO-RXCHF, where only select electronic orbitals are explicitly correlated to the nuclear orbitals. By explicitly correlating only the relevant electronic orbitals to the nuclear orbitals, the NEO-RXCHF approach avoids problems that can arise when all electronic orbitals are explicitly correlated to the nuclear orbitals in the same manner. We examine three different NEO-RXCHF methods that differ in the treatment of the exchange between the geminal-coupled electronic orbitals and the other electronic orbitals: NEO-RXCHF-fe is fully antisymmetric with respect to exchange of all electronic coordinates and includes all electronic exchange terms; NEO-RXCHF-ne neglects the exchange between the geminal-coupled electronic orbitals and the other electronic orbitals; and NEO-RXCHF-ae includes approximate exchange terms between the geminal-coupled electronic orbitals and the other electronic orbitals. The latter two NEO-RXCHF methods offer substantial computational savings over the NEO-XCHF approach. The NEO-RXCHF approach is applicable to a wide range of chemical systems that exhibit non-Born-Oppenheimer effects between electrons and nuclei, as well as positron-containing molecular systems.
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U2 - 10.1063/1.4812257
DO - 10.1063/1.4812257
M3 - Article
AN - SCOPUS:84903362389
SN - 0021-9606
VL - 139
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 3
M1 - 034102
ER -