### Abstract

The density matrix formulation of the nuclear-electronic orbital explicitly correlated Hartree-Fock (NEO-XCHF) approach for including electron-proton correlation in mixed nuclear-electronic wave functions is presented. This approach is based on a general ansatz for the nuclear-electronic wave function that includes explicit dependence on the nuclear-electronic distances with Gaussian-type geminal functions. The NEO-XCHF approach is extended to treat multielectron, multiproton systems and to describe a broader class of systems that require a more general form of the wave function, such as open-shell and multireference wave functions. General expressions are derived for the one-particle and two-particle densities, as well as the total energy. In addition, expressions for the total energy and Fock matrices in an atomic orbital basis are derived for the special case of a closed-shell electronic system. The resulting Hartree-Fock-Roothaan equations can be solved iteratively to self consistency. An advantage of the density matrix representation is that it facilitates the development of approximate NEO-XCHF methods in which specified high-order density terms are neglected to decrease the computational expense. Another advantage of the density matrix representation is that it provides the foundation for the development of electron-proton functionals within the framework of density functional theory, thereby enabling a consistent treatment of both electron-electron and electron-proton correlation in a computationally practical manner.

Original language | English (US) |
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Article number | 204101 |

Journal | Journal of Chemical Physics |

Volume | 129 |

Issue number | 20 |

DOIs | |

State | Published - Dec 10 2008 |

Externally published | Yes |

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

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## Cite this

*Journal of Chemical Physics*,

*129*(20), [204101]. https://doi.org/10.1063/1.2998312