Cluster expansion of the wavefunction. Pseudo-orbital theory based on the SAC expansion and its application to the spin density of open-shell systems

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Abstract
We have studied the pseudo‐orbital theory, which is based on the symmetry‐adapted‐cluster (SAC) expansion of an exact wavefunction proposed previously, in comparison with the conventional open‐shell orbital theories, and applied it to the calculations of the spin densities of the first‐row atoms, Li(2S), Li(2P), Be+(2S), B2+(2S), B(2P), C(3P), N(4S), O(3P), and F(2P). We have started from the RHF reference wavefunction and considered mainly the spin‐polarization excitation operator and its self‐consistency effect. This pseudo‐orbital theory corresponds to an extension of the UHF and spin‐extended HF (SEHF) theories, and yet it is free from the theoretical defects found previously for these theories. The relative magnitudes of the calculated spin densities are predicted to be in the order of the UHF or SEHF, present, and first‐order (FO) CI in the decreasing order. This sequence has been confirmed in the calculated spin densities for the first‐row atoms. For the three‐electron atoms the present theory gives an excellent agreement with experiment, and for boron through fluorine the present results are fairly better than those of the UHF and SEHF theories and reasonable within the orbital theoretic approach. The calculated energies are also satisfactory when the angular correlation is included within the pseudo‐orbital theory.