片断分子的建立和正则轨道的定域化

The formation of fragment molecules and the localization of canonical molecular orbitals

为了研究共轭分子的芳香性,我们建立了新的作用能分解法。该方法的核心是为任何一个共轭分子提供一个π和σ体系彻底分离的轨道基组{Φ_m^(P-π),Φ_l^(P-σ),Φ_t^P}。为此,放射形环炔烃分子(D_(3h)对称的)必须分割成3个乙炔片断(A,C,E)和3个乙烯片断(B,D,F),它的{Φ_m^(P-π),Φ_l^(P-σ),Φ_t^P}是由6个片断的轨道基组{ψ_k^(P-π),ψ_n^(P-σ),φ_s^('P)}(P=A,B,…,F)叠加而成。FMP-L和FMP-R(P=A,B,…,F)是片断P的两个片断分子,设它们C-H_R键的键长分别是r_R(P)和r_L(P)。在定域化后,单占据轨道φ_s^('P)和参考氢原子H_R占据轨道φ_h^('H)的总电子数∑q_(?)(P)+∑q_h(P)总是正确的,与r_R(P)和r_L(P)的取值无关。但是,{φ_s^('P)的空间取向取决于r_L(P)和r_R(P)的值。在片断A和B中,R_V(A)=(-V/T)=1.95153+0.50869*r_R^V(A),R_V(B)=1.94556+0.54823*r_R^V(B),设R_V=2,则r_R^V(A)=0.09528nm,r_R^V(B)=0.09930nm。另外,有条件地优化FMP-R可算得:r_R^O(A)=0.10658nm,r_R^O(B)=0.10888nm。当r_R^V(P)和r_R^O(P)确定后,可得到;q_S^V(A)=6.05124-56.5228*r_L^V(A),q_S^V(B)=5.17915-47.0804*r_L^V(B);q_S^O(A)=5.81883-49.0924*r_L^O(A),q_S^O(B)=4.70043-39.0818*r_L^O(B)。然后设q_S(P)=q_h(P)=(1/4)(∑q_S(P)+∑q_h(P)),可得到:r_L^V(A)=0.08937nm,r_L^V(B)=0.08678nm;r_L^O(A)=0.09816nm,r_L^O(B)=0.09297nm,再由r_R^V(P)和r_L^V(P)计算的{Φ_m^(P-π),Φ_l^(P-σ),Φ_t^P}中,每一对成键单占据轨道Φ_t^P的电子占据数Q_t比较均匀合理,它的12个单占据轨道的电子总占据数为∑Q_t=12.3。另外,在由{Φ_m^(P-π),Φ_l^(P-σ),Φ_t^P}~V算得的FUL态中,轨道分布也是更好地满足FUL态的基本特征。所以r_R^V(P)和r_L^V(P)比r_R^O(P)和r_L^O(P)更为合理。

A new program for energy partition has been developed to quantify aromaticity, and its sub-program, a multi-step procedure, provides an aromatic compound with a LFMO (localized fragment molecular orbital) basis set, in which the ∏ and (?) systems have been separated out thoroughly. Accordingly, a redialene molecule (C_(12)H_6, D_(3h)) has to be dissected into three - C ≡ C - fragments (A, C ,E) and three - C = C - fragments(B, D, F), and its results from the superposition of six fragment MO (molecular orbital) basis sets (P=A,B, … , F). The localization of canonical MO basis set is simplified due to the formation of fragment molecules FMP- L, and it ensures that total electronic occupancy Σq_i, a sum of Σq_s (P) for all singly occupied fragment MOs (?)_S('P) and Σq_h (P) for the singly occupied fragment MOs of all referential hydrogen atoms H_R, is always correct. After the localization, the conditional RHF computation based on the fragment molecule FMP-R is to separate the Σ and (?) systems out thoroughly. It is necessary to determine the lengths r_L(P) and r_R(P) of the bond C-H_R in FMP-L and FMP-R because these lengths have a great effect on the orientation of the singly occupied (?)_S^('P). There are two methods of determining r_R(P). The first one is based on the linear function: R_v(A)=(-V/T)=1.95153+0.50869 * r_R^V(A), R_v(B)=1.94556+0.54823 * r_R^V (B). When R_v = 2, r_R^V(A)=0.09528nm, r_R^V(B)=0.09930nm. Secondly, r_R^O(A)=0.10658nm and r_R^O(B)=0.10888nm, are obtained from the conditional geometry optimization of FMP-R at B3LYP/6-311G ** . As soon as the values of r_R (P) are deter- mined, the following linear relationships between q_3 (P) for a specific (?)_S^('P) and the length r_L (P) are found : (i) q_3~V (A) = 6.05124 - 56.5228 * r_L^V(A), q_3~V(B) = 5.17915 - 47.0804 * r_L^V(B); (ii) q_S^O(A) = 5.81883 - 49.0924 * r_L^O(A), q_3~O(B) = 4.70043 - 39.0818 * r_L_O(B). Setting of q_3(P) = (1/4) (Σq_3(P) + Σq_h(P)) provides FMP-L with r_L^V(A) = 0.08937nm,r_L^V(B) = 0.08678 nm; r_L^O(A) = 0.09816nm, r_L^O(B) = 0.09297 nm. Two basis sets, denoted as correspond to two groups of the bond lengths ( r_L^V (P) and r_L^V (B)) and ( r_L^O (P) and r_R^O (B)). On the basis of the features of the FUL state obtained from the conditional RHF computation, over, for molecule, the values of r_L^V(p) and r_L^V(p) are more reasonable than those of r_L^O(P) and r_R^O(P).