【摘要】 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。更多还原

【Abstract】 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 (C₁₂H₆, 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 q₃ （P） for a specific （?）_S^’P and the length r_L （P） are found : （i） q₃^V （A） = 6.05124 - 56.5228 * r_L^V（A）, q₃^V（B） = 5.17915 - 47.0804 * r_L^V（B）; （ii） q_S^O（A） = 5.81883 - 49.0924 * r_L^O（A）, q₃^O（B） = 4.70043 - 39.0818 * r_LO（B）. Setting of q₃（P） = （1/4） （Σq₃（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）.更多还原