Selfconsistent solution of the KohnSham equations for systems with inhomogeneous electron gas
Abstract
The gas of the interacted electrons is usually described within KohnSham approximation by the set of Poisson and Schrödinger equations with an effective potential for the singleparticle wave functions. The solution of these equations should give the selfconsistent electron density distribution and Coulomb potential those can only be obtained using manystep iteration procedure. The well known difficulty in this task is that the wave functions obtained after every iteration step give the distribution of electron density which is not corresponded to the boundary conditions for the Coulomb potential. As a result, either it is impossible to obtain the solution for the next iteration step or some parameters of the system are to be changed, for example, the density of the positive charge. The last way is disagreed with the EulerLagrange variational derivation of the selfconsistent equations. We propose new converging iterative scheme for solving KohnSham and Poisson equations, where we do not need to modify parameters of the system. This procedure was tested for two tasks: 1. Semiinfinite electron gas bounded by infinite potential barrier. This model allows to simulate the behavior of the electron density near a semiconductorinsulator interface. The quantum corrections to the capacity of the barrier structure are calculated. 2. Semiinfinite electron gas which is bounded by selfconsistent potential barrier within the famous LangKohn jellium model of the metal surface. The new converging calculations give the results which are different from the nonselfconsistent ones obtained by Lang and Kohn and have the better agreement with the experimental data.
 Publication:

arXiv eprints
 Pub Date:
 September 2002
 arXiv:
 arXiv:condmat/0209335
 Bibcode:
 2002cond.mat..9335S
 Keywords:

 Condensed Matter  Materials Science;
 Condensed Matter  Statistical Mechanics
 EPrint:
 6 pages, 4 figures, reported on the International Conference of Theoretical Physics (TH2002), July 2227, 2002, Paris, France