A procedure for constructing a highly localized and symmetrical bond orbital basis set

A procedure for constructing a highly localized and symmetrical bond orbita l basis set with the pi systems separated off from the sigma frameworks has been developed. It is a four - step procedure: (1) over the opened - shell localized fragment molecular orbital (FMO) basis set [Phi (k), Phi (i), Ph i (j)]where Phi (i) is an element of doubly occ. and vacant sigma FMOs, Phi (j) is an element of piFMOs, and Phi (k) is an element of singly occ. FMOs , the conditional RHF computations provide each of the FUL and DSI degrees electronic states of a molecule, such as norbornadiene with a set of the cl osed - shell FMOs; (2) the symmetrical MOs, Phi (l ')degrees = Sigma a(kl ' ) Phi (k) (k = 1,2,..., N-s) which have delocalized over the whole molecule , in the DSI degrees substitutes for the unsymmetrical Phi (l) = Sigma a(kl )Phi (k) in FUL state, and those together with other two groups of the unsy mmetrical FMOs, Phi (m) = Sigma a(jm) Phi (j) and Phi (n) = Sigma a(in) Phi (i) in the FUL state formed a closed - shell FMO basis set [Phi (n), Phi ( m), Phi (l ')degrees] in which each of FMOs Phi (n) and Phi (m) is still lo calized on its corresponding fragment; (3) based on the basis set [Phi (n), Phi (m), Phi (l ')degrees], the conditional RHF computation for molecule i s performed under the following constraint: all F-ij = 0.0 and S-ij = 0.0 ( i satisfies j, i is an element of fragment P, j is an element of fragment Q , and P satisfies Q) except for those between Phi (l ')degrees. It provides a molecule, such as norbornadiene, with a highly localized and symmetrical FMO basis set [Phi (n ') , Phi (m ') , Phi (l ') ]; (4) each of the FMOs P hi (n ') , Phi (m ') and Phi (l ') is concentrated on a specific atom or tw o neighboring atoms using the Perkin procedure at last, and it has correct orbital occupancy.