Self-consistent-field wavefunctions for complex molecules. The approximation of partial retention of diatomic differential overlap

A new approach, based on partial retention of diatomic differential overlap over an orthogonalized basis, is described for approximating LCAO SCF molecular orbital wavefunctions at the minimum basis set level for closed‐shell molecules containing hydrogen and first‐row atoms. The SCF equations are solved explicitly, retaining all one‐electron integrals and approximating two‐electron Coulomb integrals, hybrid integrals, and exchange integrals of the forms ${\mathrm{(i}}_{\mathrm{A}}{j}_{\mathrm{A}}{\mathrm{|\hspace{0.17em}i}}_{\mathrm{A}}{j}_{\mathrm{A}})$ and ${\mathrm{(i}}_{\mathrm{A}}{j}_{\mathrm{B}}{\mathrm{\hspace{0.17em}|\hspace{0.17em}j}}_{\mathrm{A}}{j}_{\mathrm{B}})$ for centers A and B. Single‐center averaging processes otherwise required for rotational invariance are avoided by the use of local atomic‐centered axes which are unique in anisotropic environments. The result is accuracy comparable to that of much more elaborate methods such as STO‐3G, in computing times only moderately longer than for simpler methods based on neglect of differential overlap such as CNDO and INDO. Both unparameterized and parameterized methods are reported. Comparison of parameterized results with ab initio SCF results for a large number of molecules indicates that F‐matrix elements are given to standard deviations of 0.007 a.u., density matrix elements to 0.007 electrons, orbital populations and atomic charges to 0.01 or 0.02 electrons, orbital energies to 0.01 a.u., and total energies to 0.03 a.u. Optimal geometries and computed force constants also agree well with reference SCF results. Computing times in seconds for the IBM 360/91 are ${\text{0.2+0.006N}}^2{\text{+0.00015N}}^3{\text{+0.0000012N}}^4$ for molecules with minimum basis sets of 2–64 atomic orbitals (N).