Schuurman Michael S, Yarkony David R
Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA.
J Phys Chem B. 2006 Sep 28;110(38):19031-9. doi: 10.1021/jp0607216.
Second-order degenerate perturbation theory, in conjunction with the group homomorphism method for describing a similarity transformation, are used to characterize the subspace of two-state conical intersections contained in the branching space of a three-state conical intersection. It is shown by explicit calculation, using the lowest three-state conical intersection of (CH)3N2, that a second-order treatment yields highly accurate absolute energies, even at significant distances from the reference point of three-state intersection. The excellent agreement between the second order and ab initio results depends on the average energy component, which is computed using 5 first-order terms and 15 second-order terms. The second-order absolute energy change over the range rho = 0.0-0.3 au, where rho is the distance from the three-state conical intersection in the branching space coordinates, is approximately 6500 and 9500 cm(-1) for the E(1=2) and E(2=3) seams, respectively, with the maximum ab initio energy deviation from degeneracy of 200 cm(-1) occurring at rho = 0.3 au. The characteristic parameters gIJ and hIJ are also predicted to great accuracy, even at large rho, with the error growing to only 10-15% at rho = 0.3 au.
二阶简并微扰理论，结合用于描述相似变换的群同态方法，被用于刻画包含在三态锥形交叉分支空间中的两态锥形交叉子空间。通过对(CH)3N2的最低三态锥形交叉进行显式计算表明，即使在距三态交叉参考点有显著距离时，二阶处理也能产生高度精确的绝对能量。二阶结果与从头算结果之间的出色一致性取决于平均能量分量，该分量使用5个一阶项和15个二阶项进行计算。在分支空间坐标中，从三态锥形交叉起算的距离rho在0.0 - 0.3原子单位范围内，对于E(1 = 2)和E(2 = 3)接缝，二阶绝对能量变化分别约为6500和9500厘米^(-1)，在rho = 0.3原子单位时，从头算能量与简并的最大偏差为200厘米^(-1)。即使在rho较大时，特征参数gIJ和hIJ也能被高精度预测，在rho = 0.3原子单位时误差仅增长到10 - 15%。
