Self-consistent solution of Kohn-Sham equations for infinitely extended systems with inhomogeneous electron gas

摘要

The density functional approach in the Kohn-Sham approximation is widely usedto study properties of many-electron systems. Due to the nonlinearity of theKohn-Sham equations, the general self-consistence searching method involvesiterations with alternate solving of the Poisson and Schr\"{o}dinger equations.One of problems of such an approach is that the charge distribution renewed bymeans of the Schr\"{o}dinger equation solution does not conform to boundaryconditions of Poisson equation for Coulomb potential. The resulting instabilityor even divergence of iterations manifests itself most appreciably in the caseof infinitely extended systems. The published attempts to deal with thisproblem are reduced in fact to abandoning the original iterative method andreplacing it with some approximate calculation scheme, which is usuallysemi-empirical and does not permit to evaluate the extent of deviation from theexact solution. In this work, we realize the iterative scheme of solving theKohn-Sham equations for extended systems with inhomogeneous electron gas, whichis based on eliminating the long-range character of Coulomb interaction as thecause of tight coupling between charge distribution and boundary conditions.The suggested algorithm is employed to calculate energy spectrum,self-consistent potential, and electrostatic capacitance of the semi-infinitedegenerate electron gas bounded by infinitely high barrier, as well as the workfunction and surface energy of simple metals in the jellium model. Thedifference between self-consistent Hartree solutions and those taking intoaccount the exchange-correlation interaction is analyzed. The case study of themetal-semiconductor tunnel contact shows this method being applied to aninfinitely extended system where the steady-state current can flow.