Non‐Born–Oppenheimer density functional theory of molecular systems

It is shown that the Hohenberg–Kohn–Levy density functional theory of molecular structure is not restricted by the Born–Oppenheimer approximation. The existence of the corresponding ground‐state density functionals for the case of the exact nonadiabatic, nonrelativistic, field‐free Hamiltonian of a molecular system, in terms of the one‐particle electronic and nuclear densities, is proven and the associated Euler equations are discussed. Extensions to the case of the system in an external electric field and to the bound excited states, are briefly examined. As an example the non‐Born–Oppenheimer Hartree–Fock theory of Thomas is discussed from the density functional viewpoint. Possible applications of the theory in the analysis of molecular structure and chemical reactivity are identified.

[1]  H. W. Joy,et al.  Protonic Structure of Molecules. II. Methodology, Center-of-Mass Transformation, and the Structure of Methane, Ammonia, and Water , 1970 .

[2]  T. Gilbert.  Hohenberg--Kohn theorem for nonlocal external potentials , 1975 .

[3]  A K Theophilou,et al.  The energy density functional formalism for excited states , 1979 .

[4]  B. Sutcliffe,et al.  Molecular structure and the born—Oppenheimer approximation , 1977 .

[5]  R. Parr,et al.  Electronegativity: The density functional viewpoint , 1978 .

[6]  J. MacDonald,et al.  On the Modified Ritz Variation Method , 1934 .

[7]  S. Valone,et al.  Consequences of extending 1‐matrix energy functionals from pure–state representable to all ensemble representable 1 matrices , 1980 .

[8]  R. Kalia,et al.  Surface structure of electron-hole drops in germanium and silicon , 1977 .

[9]  I. Thomas.  Protonic Structure of Molecules. I. Ammonia Molecules , 1969 .

[10]  L. Lathouwers.  Generator-coordinate theory of molecular spectra , 1978 .

[11]  J. Katriel.  An alternative interpretation of Theophilou's extension of the Hohenberg-Kohn theorem to excited states , 1980 .

[12]  M. Levy,et al.  Rigorous and approximate relations between expectation values of atoms , 1980 .

[13]  M. Levy.  Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[14]  R. Parr,et al.  Elementary properties of an energy functional of the first‐order reduced density matrix , 1978 .

[15]  Bound excited states in density-functional theory , 1981 .

[16]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[17]  I. Thomas.  Photoprotonic Effect in Hydrides , 1972 .

[18]  R. Parr,et al.  Electronegativities of the elements from simple .CHI..alpha. theory , 1980 .