Non-Born–Oppenheimer density functional theory of molecular systems

Abstract

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.

Limitations of density functional theory in application to degenerate states

“…Formally this limitation can be eliminated by introducing the nuclear wave function and nuclear density. In the work of Capitani and colleagues 17 the so-called non-Born᎐Oppenheimer situation in DFT is considered by introducing the nuclear density that is treated on the same level as the electronic density, assuming that the total wave function is multiplicative with respect to the electronic and nuclear coordinates. In somewhat dif-Ž .…”

“…the full adiabatic FA approximations assume the multiplicative form of the wave function; in the CA approximation the electronic function is independent of nuclear coordinates, while in the FA case the electronic function contains the nuclear coordinates as parameters. From this point of view this article 17 deals with the CA approximation. As seen from the discussion below, if the nuclear coordinates are included explicitly, the difference between the CA and FA approximations is significant in the DFT formulation.…”

Cornell Fuel Cell Institute: Materials Discovery to Enable Fuel Cell Technologies

“…Figure 19 shows the power of this approach to capture screening and chemical solvation effects, showing how chloride ions remain on the oxygen-terminated surface of Cr 2 O 3 in contact with a solution whereas hydrous oxide bonds are destabilized by dielectric screening and the protons come off into the solution. The formalism works by extending the combination of Mermin's nonzero temperature 125 and Capitani's mixed species formulation of density functional theory 126 to prove that the free energy of a system of nuclei and electrons (i.e., the material surface, including any chemisorbed species) in equilibrium with a solvent environment is given exactly by the following variational principle where n(r) is the quantum and thermodynamically averaged electron density of the surface at position r, N(r,s) is the likewise averaged density of the nuclei of atomic species s of the solvent at position r, F KS is the traditional electronic-structure Kohn-Sham density functional for the surface or solute under study while in isolation, A liq is the so-called "classical" continuum density-functional theory of the solvent system while in isolation, and U is the coupling between …”

Molecular grand-canonical ensemble density functional theory and exploration of chemical space

“…Over the last few decades, several proposals for a multicomponent ͑MC͒ non-BornOppenheimer DFT, wherein electrons and nuclei are treated on the same footing, have been presented. [41][42][43][44] In particular, Capitani, Nalewajski, and Parr 41 ͑CNP͒ proved a multicomponent version of the Hohenberg-Kohn theorem, 17 thereby establishing the existence of an energy density functional of electronic and nuclear densities whose minimum is the ground state equilibrium geometry of the total Hamiltonian of a system of N e electrons and N ␣ nuclei of type ␣. This theory was later revisited by Kreibich and Gross 43 who noted that the densities used by CNP as the basis of their MC-DFT must necessarily be constant for all isolated atoms, molecules, and solids due to the translational invariance of the Hamiltonian; they presented a MC-DFT based on densities describing the internal properties of a system.…”