Direct minimization of the energy functional in the LCAO-MO density matrix formalism

The previously proposed method of direct energy minimization by a gradient approach is here applied to the separated electronic pair functions (strongly orthogonal geminals). The minimization of the energy is achieved by an alternate iterative procedure in which the geminal occupation coefficients are optimized making each geminal self-consistent in the field of the others and the orbital forms are directly optimized using a sequence of orthogonal transformations of an arbitrary orthonormal basis set. The method is tested on H₂, He₂, LiH, NH₃ and H₂O molecules.

Possible generalizations of the formalism to other geminal models are briefly presented.