Efficient solution of Poissonrsquo;s equation in linear combination of atomic orbitals (LCAO) electronic structure calculations

摘要

An accurate and efficient method is described for the evaluation of electrostatic contributions in LCAO electronic structure calculations. The charge density thinsp;rgr;(r) is decomposed into thinsp;rgr;(1)(r), a component whose rapid variation near any nucleus reproduces that of thinsp;rgr;(r) to a very good approximation, and a remainder density dgr;rgr;(r)equiv;rgr;(r)minus;rgr;(1)(r), which is thereby guaranteed to be slowly varying in space. The power of the decomposition resides in the fact that thinsp;rgr;(1)(r) can be expressed exactly as a sum of onehyphen;center densities, without the use of any fit procedure. Because thinsp;rgr;(1)(r) is a sum of onehyphen;center multipolar densities, the Hartree potential is a function with a simple onehyphen;dimensional integral representation, and its matrix elements can be obtained by performing onehyphen;dimensional integrals over it. Since dgr;rgr;(r) is spatially slowly varying, the Hartree potential to which it corresponds and the matrix elements of this potential can accurately be evaluated on a relatively coarse coordinate space mesh, using fast Fourier transforms. The method is illustrated via molecular structure calculations for N2and NH3. The calculations are accurate to a few percent when the required integrals over dgr;rgr;(r) and dgr;V(r) are performed on a mesh of spacing 0.4 a.u. The Nndash;N bond length and stretch frequency are found to equal 2.10 a.u. and 2.3times;103cmminus;1, respectively. The equilibrium Nndash;H bond length and Hndash;Nndash;H angle are calculated to be 1.93 a.u. and 105deg;, respectively, while the NH3inversion barrier turns out to equal 0.25 eV. These results are in good agreement with earlier calculations.