TY - JOUR

T1 - Density matrix formulation of the nuclear-electronic orbital approach with explicit electron-proton correlation

AU - Chakraborty, Arindam

AU - Hammes-Schiffer, Sharon

N1 - Funding Information:
We thank Michael V. Pak for numerous insightful discussions. We gratefully acknowledge the support of AFOSR Grant No. FA9550-07-1-0143 and NSF Grant No. CHE-07-49646.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

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U2 - 10.1063/1.2998312

DO - 10.1063/1.2998312

M3 - Article

C2 - 19045846

AN - SCOPUS:57149135271

SN - 0021-9606

VL - 129

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 20

M1 - 204101

ER -