Electronic structure of thin films by the self-consistent numerical-basis-set linear combination of atomic orbitals method: Ni(001)

We present the self-consistent numerical-basis-set linear combination of atomic orbitals (LCAO) discrete variational method for treating the electronic structure of thin films. As in the case of bulk solids, this method provides for thin films accurate solutions of the one-particle local density equations with a non-muffintin potential. Hamiltonian and overlap matrix elements are evaluated accurately by means of a three-dimensional numerical Diophantine integration scheme. Application of this method is made to the self-consistent solution of one-, three-, and five-layer Ni(001) unsupported films. The LCAO Bloch basis set consists of valence orbitals ($3d$, $4s$, and $4p$ states for transition metals) orthogonalized to the frozen-core wave functions. The self-consistent potential is obtained iteratively within the superposition of overlapping spherical atomic charge density model with the atomic configurations treated as adjustable parameters. Thus the crystal Coulomb potential is constructed as a superposition of overlapping spherically symmetric atomic potentials and, correspondingly, the local density Kohn-Sham ($\alpha =\frac{2}{3}$) potential is determined from a superposition of atomic charge densities. At each iteration in the self-consistency procedure, the crystal charge density is evaluated using a sampling of 15 independent $k$ points in $\left(\frac{1}{8}\right)\mathrm{th}$ of the irreducible two-dimensional Brillouin zone. The total density of states (DOS) and projected local DOS (by layer plane) are calculated using an analytic linear energy triangle method (presented as an Appendix) generalized from the tetrahedron scheme for bulk systems. Distinct differences are obtained between the surface and central plane local DOS. The central plane DOS is found to converge rapidly to the DOS of bulk paramagnetic Ni obtained by Wang and Callaway. Unlike the result of earlier non-self-consistent calculations, only a very small surplus charge (0.03 electron/atom) is found on the surface planes—in agreement with jellium model calculations.