title: Alternative wavefunction ansatz for including explicit electron-proton correlation in the nuclear-electronic orbital approach.
abstract: The nuclear-electronic orbital (NEO) approach treats specified nuclei quantum mechanically on the same level as the electrons with molecular orbital techniques. The explicitly correlated Hartree-Fock (NEO-XCHF) approach was developed to incorporate electron-nucleus dynamical correlation directly into the variational optimization of the nuclear-electronic wavefunction. In the original version of this approach, the Hartree-Fock wavefunction is multiplied by (1+Ĝ), where Ĝ is a geminal operator expressed as a sum of Gaussian type geminal functions that depend on the electron-proton distance. Herein, a new wavefunction ansatz is proposed to avoid the computation of five- and six-particle integrals and to simplify the computation of the lower dimensional integrals involving the geminal functions. In the new ansatz, denoted NEO-XCHF2, the Hartree-Fock wavefunction is multiplied by √(1+Ĝ) rather than (1+Ĝ). Although the NEO-XCHF2 ansatz eliminates the integrals that are quadratic in the geminal functions, it introduces terms in the kinetic energy integrals with no known analytical solution. A truncated expansion scheme is devised to approximate these problematic terms. An alternative hybrid approach, in which the kinetic energy terms are calculated with the original NEO-XCHF ansatz and the potential energy terms are calculated with the NEO-XCHF2 ansatz, is also implemented. Applications to a series of model systems with up to four electrons provide validation for the NEO-XCHF2 approach and the treatments of the kinetic energy terms.
authors.affiliation: Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
authors.forename: Chaehyuk
authors.initials: C
authors.lastname: Ko
authors.forename: Michael V
authors.initials: MV
authors.lastname: Pak
authors.forename: Chet
authors.initials: C
authors.lastname: Swalina
authors.forename: Sharon
authors.initials: S
authors.lastname: Hammes-Schiffer