Numerical SCF method for the calculation of static polarizabilities and hyperpolarizabilities for atoms, He through Ne

Abstract

The static polarizabilities and hyperpolarizabilities for the ground states of first row atoms, helium through neon, have been calculated solving the SCF equations of an atom in an electric field by numerical integration of coupled one dimensional differential equations using the Numerov method in matrix form. The calculated polarizabilities agree within 2% with the values obtained by basis function methods. Heretofore only the hyperpolarizabilities of helium, lithium, beryllium, and neon have been calculated. For helium the hyperpolarizability is in good agreement with previous calculations, whereas for beryllium and neon the values obtained by basis function methods are scattered and significantly lower than the values we obtain. Comparison with experimental results for neon indicates that the Numerical Hartree Fock (NHF) method leads to a better representation of polarized orbitals than the use of basis function methods, which require tedious nonlinear optimization of large basis sets.