π和σ体系彻底分离的高度定域的键轨道基组的建立

高度定域的、对称的、键轨道基组的建立是一个多步的计算程序：(1)以定域片断轨道[φk，φi，φj]为基，对分子作有条件的RHF运算，算得FUL和DSI°态的片断分子轨道[Φ°l',Φ°n,Φ°m]和[Φl,Φn,Φm]。在基组[φk，φi，φj]中，φi∈双占据和空σ片断分子轨道(FMOs)组，φj∈πFMO组，φk∈单占据σFMO组，它们都精确地定域在各自的片断内；(2)利用Φ°l'与Φ°l间的重叠积分值(Sl'l>0.5)，可以从DSI°态中，自动地选出Ns个对称的、由单占据轨道线性组合而成的分子轨道Φ°l'=Σakl'φk(k=1,2,…,Ns),接着，用Φ°l'取代FUL态中同类的、非对称轨道组Φl=Σaklφk(k=1,2,…,Ns);(3)以上述新的轨道组[Φ°l',Φn,Φm]为基(其中,Φ°l'∈DSI°态，它们离域于整个分子；双占据及空σFMO组Φm和πFMO组Φm属于FUL态)，按FUL态的条件，再次对分子作有条件的RHF运算，从中得到一组对称的、闭壳层正则FMOs，而且每一个FMO均有正确的电子占据数；(4)利用Perkin原理，将第3步所得的正则FMO组定域成一个对称的键轨道基组[Φl',Φn',Φm']。在这个基组中，π体系Φm'与σ构架Φn'是彻底分离的，而且这两个轨道组始终精确地定域在各自的片断内。

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

A procedure for constructing a highly localized and symmetrical bond orbital basis set with the πsystems separated off from the σ frameworks has been developed. It is a four - step procedure: (1) over the opened - shell localized fragment molecular orbital (FMO) basis set [φk，φi，φj] where φi ∈ doubly occ. and vacant σFMOs, φj ∈πFMOs, and φk∈ singly occ. FMOs, the conditional RHF computations provide each of the FUL and DSI°electronic states of a molecule, such as norbornadiene with a set of the closed - shell FMOs; (2) the symmetrical MOs ,Φ°l' = Σakl'φk(k=1,2, …,Ns) which have delocalized over the whole molecule, in the DSI° substitutes for the unsymmetrical Φl= Σaklφk in FUL state, and those together with other two groups of the unsymmetrical FMOs, Φm= Σajmφj and Φn= Σ ainφi in the FUL state formed a closed - shell FMO basis set [Φn,Φm, Φ°l'] in which each of FOMs Φn and Φm is still localized on its corresponding fragment; (3) based on the basis set [Φn,Φm, Φ°l'], the conditional RHF computation for molecule is performed under the following constraint: all Fij=0.0 and Sij=0.0(i≠j, i∈fragment Q, and P≠Q) execpt for those between Φ°l'. It provides a molecule, such as norbornadiene, with a highly localized and symmetrical FMO basis set [ Φn', Φm', Φl']; (4) each of the FMOs Φn', Φm' and Φl' is concentrated on a specific atom or two neighboring atoms using the Perkin procedure at last, and it has correct orbital occupancy.