The Hartree-Fock Method for Atoms: A Numerical Approach

1s2s ¹S 1sns accurate asymptotic form atomic properties boundary condition boundary value problem Brillouin's theorem holds computed configuration state functions contribution convergence core correlation energy correlation function defined derived determined differential equation effect EMCHF equivalent electrons error exact example expansion first-order correction Froese Fischer grid points Hartree Hartree-Fock approximation Hartree-Fock equations hydrogenic included integral interaction inverse iteration ionization potential iteration Kinetic Energy linear combination matrix element MCHF approximation MCHF calculation mixing coefficients nonorthogonal obtained off-diagonal energy parameters orthogonal orthogonal transformation P(nl pair pair-correlation energy pair-correlation function perturbation theory Phys Potential Energy procedure quantum numbers r₁ radial functions Ratio replacements secular equations Simpson's rule single-configuration solution spin stationary system of equations Table 2-3-continued tion Total Energy total wavefunction transformation two-electron variable variational vector Y₁ Z-dependent zero zero-order