Abstract: A method and apparatus analyze chemical compounds from molecular geometric data of a chemical compound. Localized molecular orbitals are used to form a density matrix and a Fock matrix. The method and apparatus performs an annihilation process on the Fock matrix to interactively eliminate the interaction of each bonding orbital with each non-bonding orbital, i.e., .psi.F.psi.*, where .psi. is a bonding orbital, F is a corresponding member of the Fock matrix and .psi.* is an antibonding orbital. The annihilation process involves a simple diagonalization of a 2.times.2 matrix and replaces the very lengthy calculation of diagonalizing the Fock matrix, as is done in the related art. To further speed up the process, the method and apparatus of the present invention determine which of the bonding orbitals and antibonding orbitals cannot interact using interatomic distances. The interaction for these bonding orbitals and antibonding orbitals is not eliminated in the annihilation process.