An embedding scheme for the Dirac equation

TL;DR

This paper introduces an embedding scheme for the Dirac Hamiltonian that simplifies the calculation of eigenstates in a specified region by replacing the rest of the system with an effective potential derived from Green functions.

Contribution

The paper develops a novel embedding method for the Dirac equation that explicitly incorporates the effects of the surrounding region via Green functions, enabling localized solutions.

Findings

Successfully applied to hydrogen atom in a spherical cavity.

Demonstrated effectiveness on Au/Ag/Au sandwich structure.

Provides a practical approach for relativistic quantum calculations.

Abstract

An embedding scheme is developed for the Dirac Hamiltonian H. Dividing space into regions I and II separated by surface S, an expression is derived for the expectation value of H which makes explicit reference to a trial function defined in I alone, with all details of region II replaced by an effective potential acting on S and which is related to the Green function of region II. Stationary solutions provide approximations to the eigenstates of H within I. The Green function for the embedded Hamiltonian is equal to the Green function for the entire system in region I. Application of the method is illustrated for the problem of a hydrogen atom in a spherical cavity and an Au(001)/Ag/Au(001) sandwich structure using basis sets that satisfy kinetic balance.