New type of wave function for Li, Be+, and B++

A recently developed method for electronic wave functions has been applied to Li, Be+, and B++. This method, the G1 method, leads to much better energies than does the Hartree-Fock (HF) method (for Li the G1 energy is -7.447560 as compared to the HF energy of -7.432727); however, the independent-particle interpretation is retained. A significant difference is that although the HF valence orbital has a node (being orthogonal to the core orbital), none of the three G1 orbitals has a node. The valence G1 orbital satisfies the cusp condition at the nucleus, has a minimum in the core region, and outside the core region is very similar to the HF valence orbital. The G1 wave function has the form of a paired-electron wave function but strong orthogonality is not imposed. Since the resulting orbitals have significant overlaps and since the energy is made much worse by imposing strong orthogonality, it appears that strong orthogonality is a significant constraint for orbital-type paired-electron wave functions (such as in the extended valence bond method). Since the G1 wave function is nearly at the radial limit and does not include instantaneous correlation among the electrons, the dynamic correlation is essentially all due to angular correlation just as for two electron atoms and ions. Since the G1 valence orbitals need not be orthogonal to the core orbitals, the use of this method for solids could eliminate these problems in band-structure calculations which are due to the orthogonality conditions inherent in the HF method.