The spin-coupled valence bond theory of molecular electronic structure. I. Basic theory and application to the ² Σ ⁺ states of BeH

The spin-coupled valence bond theory of molecular electronic structure is developed, according to which the single configuration spin-coupled theory is reformulated so as to yield both ground and excited orbitals. These orbitals are subsequently used to generate v.b. structures, the Hamiltonian matrix of which is diagonalized as in the conventional v.b. method. The fundamental feature of the excited spin-coupled orbitals is that, except those with the highest energy, they retain the characteristic distorted atomic form of the ground state orbitals, and correspondingly possess negative orbital energies. This leads to compact and rapidly convergent wavefunctions for the ground and lower-lying excited states, thus overcoming one of the basic drawbacks of the original v.b. theory. The theory is applied to the $^2\Sigma^+$ states of BeH by using 53, 71 and 80 structures of this kind. Very good convergence is found for the lowest six states, and the total energy of the ground state is below that given by a very large m.o.c.i. calculation. The present theory is thus a powerful and flexible alternative to m.o.c.i. calculations but using about an order of magnitude fewer functions.