Hylleraas method for many‐electron atoms
Hylleraas method for many‐electron atoms. I. The Hamiltonian
María Belén Ruiz
María Belén Ruiz
Abstract
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. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
Hylleraas method for many‐electron atoms. II. Integrals over wave functions with one interelectronic coordinate
Abstract
A procedure is proposed to evaluate matrix elements containing r linked with angular functions. Using this procedure, the different types of two-, three-, and four-electron radial and angular integrals that appear in a five-electron atom, in the case of only one rij coordinate per basis function, are written in a compact form, separated in radial coordinates of one electron. The general formulas with which to obtain the integrals for powers ν ≥ 1 are developed, based on the orthogonality of the Legendre polynomials. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
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