O(4) and U(3) symmetry breaking in the second row of the periodic table

Abstract

An analysis of O(4) and U(3) symmetry classified states and their contribution to configuration mixing between 3s ²-3p ^n-2 and 3p ⁿ functions is made through a global group-theoretical study of second-row atoms (Na, Mg, Al, Si, P, S, Cl, Ar) and their ions. This permits us to estimate the amount of symmetry breaking due to electronic repulsions in these systems. The O(4) eigenstates give consistently better overlaps with the exact intrashell (3s-3p) functions than U(3), which is striking if one remembers that the results for first-row atoms are exactly the opposite. This ‘partial recovery of O(4) symmetry’ is consistent with the tendency of O(4) to improve with the number of electrons and may prove to be useful. However, if we introduce innershell effects the O(4) scheme is spoiled and in fact it is U(3) which gives a better approximation to unrestricted Hartree-Fock functions for 3s-3p complexes. These results are discussed and analysed with regard to their future possibilities.