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[Фk，Фi，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[Ф0l，Ф0n，Ф0m]和[Фl，Фn，Фm].在基组[Фk，Фi，φj]中，Фi∈双占据和空σ片断分子轨道(FMOs)组，φi∈πFMO组，Фk∈单占据σFMO组，它们都精确地定域在各自的片断内；(2)利用Ф0l与Фl间的重叠积分值(Sll>O.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Ф0l=∑akФk(k=1，2，…，Ns).接着，用Ф0l取代FUL态中同类的、非对称轨道组Фl=∑aldФk(k=1，2，…，Ns)；(3)以上述新的轨道组[Ф0l，Фn，Фm]为基(其中，Ф0l∈DSI0态，它们离域于整个分子；双占据及空σFMO组Фn和πFMO组Фm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[Фl′，Фn′Фm′].在这个基组中，π体系Фm′与σ构架Фn′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 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, φ0l′= ∑ akl′ φk ( k = 1,2,…, Ns) which have delocalized over the whole molecule, in the DSI° substitutes for the unsymmetrical Фl = ∑aklφk in FUL state, and those together with other two groups of the unsymmetrical FMOs, Фm= ∑ajmφj and Ф′n = ∑ainφi in the FUL state formed a closed-shell FMO basis set [Фn, Фm,Ф0l′ ] in which each of FMOs Фn and Фm is still localized On its corresponding fragment;(3) based on the basis set [ Фn, Фm, Ф0l′ ], the conditional RHF computation for molecule is performed under the following constraint: all Fij =0.0 and Sij =0.0( i ≠ j, i ∈ fragment P, j∈ fragment Q, and P ≠ Q )except for those between Ф0l′. It provides a molecule, such as norbornadiene, with a highly localized and symmetrical FMO basis set [Фb′, Фm′ ,Ф1′ ]; (4)each of the FMOs Фn′, Фm′ and Ф1′ is concentrated on a specific atom or two neighboring atoms using the Perkin procedure at last, and it has correct orbital occupancy.
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