Removal of core orbitals in ‘valence orbital only’ calculations

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Abstract
Examination is made of inner (core) and outer-shell (valence) separation in molecular orbital calculations. Assuming a set of simple Slater type functions, pseudo-potentials are examined which approximate the formation of a valence set of basis functions which are orthogonal and non-interacting with the core, and which simulate the core in ‘valence-orbital only’ calculations. The simplest form of this potential is , where Δαi is the overlap between valence orbital i and core orbital α and F αα, the diagonal element of the Fock matrix for core orbital α, is estimated from atomic X-ray terms or fitted empirically from model diatomic calculations. Errors introduced by dropping explicit consideration of core orbitals in the formation of the Fock matrix elements for valence orbitals are not small, but can be compensated for in adjustments of F αα in approximate formulations. The total energy is examined and it is found that the ‘valence-orbital only’ energy gives a rather accurate description of the system energy after sufficient concern is taken with the core. Model calculations on the atoms Li to Cl show that truly simple valence methods can approximate the full atomic energy within ±0·10 per cent. N2 is examined at all levels of approximation. The valence-orbital only calculations on N2 and N show a bonding energy of 1·16 eV compared with 1·19 eV from the full minimal basis set calculations.