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 $(1 + \hat G)$(1+Ĝ), where $\hat G$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 $\sqrt {1 + \hat G} $1+Ĝ rather than $(1 + \hat G)$(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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 03, 2011
- Source ID
- 10.1063/1.3611054
Entities
People
- Chaehyuk Ko
- Chet Swalina
- Michael V. Pak
- Sharon Hammes-Schiffer
Organizations
- Air Force Office of Scientific Research
- Pennsylvania State University