Hylleraas Method for Many-Electron Atoms.I.The Hamiltonian

摘要

A general expression for the nonrelativistic Hamiltonian for n-electron atoms with the fixed nucleus approximation is derived in a straightforward manner using the chain rule.The kinetic energy part is transformed into the mutually independent distance coordinates r_i,r_(ij),and the polar angles thetha_v,and phi_i.This form of the Hamiltonian is very appropriate for calculating integrals using Slater orbitals,not only of states of S symmetry,but also of states with higher angular momentum,as P states.As a first step in a study of the Hylleraas method for five-electron systems,variational calculations on the ~2P ground state of boron atom are performed without any interelectronic distances.The orbital exponents are optimized.The single-term reference wave function leads to an energy of -24.498369 atomic units(a.u.) with a virial factor of eta = 2.0000000009,which coincides with the Hartree-Fock energy -24.498369 a.u.A 150-term wave function expansion leads to an energy of -24.541246 a.u.,with a factor of T) = 1.9999999912,which represents 28% of the correlation energy.