TY - JOUR

T1 - Properties of the exact universal functional in multicomponent density functional theory

AU - Chakraborty, Arindam

AU - Pak, Michael V.

AU - Hammes-Schiffer, Sharon

N1 - Funding Information:
We thank Kieron Burke for helpful discussions. We gratefully acknowledge the support of the AFOSR under Grant No. FA9550-07-1-0143.

PY - 2009

Y1 - 2009

N2 - Multicomponent density functional theory has been developed to treat systems with more than one type of quantum particle, such as electrons and nuclei, in an external potential. The existence of the exact universal multicomponent density functional in terms of the one-particle densities for each type of quantum particle has been proven. In the present paper, a number of important mathematical properties of the exact universal multicomponent density functional are derived. The expression relating the electron-proton pair density to the one-particle densities leads to an inequality for the potential energy component of the electron-proton correlation functional under well-defined conditions. General inequalities for the kinetic energy correlation functionals and the total electron-proton correlation functional are also derived. The coordinate scaling analysis leads to mathematical inequalities describing the effect of scaled densities on the kinetic, potential, and total energy functionals. The adiabatic connection formula defines the exact electron-proton functional in terms of an adiabatic scaling parameter that smoothly connects the noninteracting system with the fully interacting system. The virial expression provides the relation between the exact kinetic and potential energy functionals for the ground state densities of multicomponent systems. These mathematical relationships provide insight into the fundamental properties of the exact universal multicomponent density functional and serve as a guide for the development of approximate electron-proton density functionals.

AB - Multicomponent density functional theory has been developed to treat systems with more than one type of quantum particle, such as electrons and nuclei, in an external potential. The existence of the exact universal multicomponent density functional in terms of the one-particle densities for each type of quantum particle has been proven. In the present paper, a number of important mathematical properties of the exact universal multicomponent density functional are derived. The expression relating the electron-proton pair density to the one-particle densities leads to an inequality for the potential energy component of the electron-proton correlation functional under well-defined conditions. General inequalities for the kinetic energy correlation functionals and the total electron-proton correlation functional are also derived. The coordinate scaling analysis leads to mathematical inequalities describing the effect of scaled densities on the kinetic, potential, and total energy functionals. The adiabatic connection formula defines the exact electron-proton functional in terms of an adiabatic scaling parameter that smoothly connects the noninteracting system with the fully interacting system. The virial expression provides the relation between the exact kinetic and potential energy functionals for the ground state densities of multicomponent systems. These mathematical relationships provide insight into the fundamental properties of the exact universal multicomponent density functional and serve as a guide for the development of approximate electron-proton density functionals.

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U2 - 10.1063/1.3236844

DO - 10.1063/1.3236844

M3 - Article

C2 - 19791860

AN - SCOPUS:70349624432

SN - 0021-9606

VL - 131

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 12

M1 - 124115

ER -