Hylleraas method for many‐electron atoms. I. The Hamiltonian

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 ri, rij, and the polar angles θi, and φi. 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 distance. 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 η = 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 η = 1.9999999912, which represents 28% of the correlation energy.