Electron Density Distribution of a Single Hydrogen Perturbation in a Metal Lattice

Abstract

The electronic structure of hydrogen centres stored in a metal crystal is described by a microscopic theory based on a functional energy difference method. That formalism works in a suitably chosen tensor product space built on a physical quasi-particle vacuum state. A transformation back to a bare Fock space representation is shown. This transformation operator divides the functional eigenvalue equation into a difference of two Schrödinger problems. The resulting state vectors can be used to calculate the electronic density distribution of a hydrogen excess electron in a metal lattice. The density function is obtained in a higher order approximation which considers the influence of three-particle correlations. A numerical solution is discussed for the case of a single hydrogen centre in a magnesium crystal. The plot shows that the excess electron is mainly localized in the surroundings of the corresponding hydrogen core. But with increasing host lattice extension there is more and more a non-vanishing probability to find the hydrogen electron dipped into the Fermi sea of metal electrons.