Three-Center Tight-Binding Together with Multipolar Auxiliary Functions

We present an ab initio tight-binding
method that allows to improve
on the effective potential and minimal basis approximations employed
in semiempirical calculations. Three-center expansions are used to
evaluate the zeroth-order Hamiltonian matrix elements and repulsive
energy terms in the spirit of the Horsfield method. Self-consistency
is handled by expanding atomic orbital products in an auxiliary basis
following the work of Giese and York, combined with a two-center expansion
of the exchange–correlation kernels. Together with nonminimal
main basis sets (double-ζ plus polarization), we show that the
resulting method trades a modest amount of accuracy for a significant
gain in speed, compared to that of numerical atomic orbital density
functional theory, in calculations on small molecules, bulk compounds,
and metal nanoclusters.