A Higher Order Approximation for the Electronic Structure of Hydrogen in Metals

Abstract

A functional energy difference method based on first principles is used to calculate the elec tronic contribution to the storage energy of hydrogen im purities in metals. That electronic problem is treated in a higher order approxim ation which means considering the coupling between one-electron wavefunctions and three-particle amplitudes. A formalism is presented to eliminate all higher order correlations and to reduce the whole system to a one-particle Schrö dinger equation with the help o f a suitable G reen's function. The resulting one-electron eigen value problem contains some logarithmic singularities due to the fact that there is no gap between occupied and unoccupied electron states in the band structure of a metal. In an electron gas model a convergent theory is reached by an im provem ent of the G reen's function leading to a screening of the long-range Coulom b potentials. The result is a complicated non-linear algebraic eigenvalue equation which is solved numerically for the special case of a single hydrogen perturbation in a magnesium crystal. The solution shows the influence of higher order electron correlations on the electronic energy eigenvalue of an interstitial hydrogen centre plot as a func tion of host lattice distortions.