Localized Orbitals. I. σ Bonds

This paper presents a method for the delineation of a set of truly localized orbitals and uses a nonunitary transformation to convert the localized orbitals into equivalent orbitals which are suitable for molecular quantum-mechanical calculations. The localized orbitals, which are suitable for describing polyatomic molecules including large nonplanar ones, are generated on the premise that the atomic orbitals used in the construction of two-center one- or two-electron bonds should be such that, when overlap is totally neglected, each atomic orbital has the same calculated value of angular momentum about its bond axis. The non-unitary transformation is derived from the modification in the form of the general orthonormality conditions upon a change from overlap metric 1 to a realistic overlap matrix Δ. This approach is applied to methane, ammonia, and water to calculate the equivalent orbitals. System energies and dipole moments are also calculated, and these and the equivalent orbitals are compared with the results of reported SCF calculations. The close values of the energies show that this approach may be used for realistic calculations. It also has an advantage over SCF techniques in that extension to extremely complicated molecular systems is possible. Further, the orbitals used herein are particularly useful for chemists since they are couched in terms of localized-bond characteristics alone.