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您好，笛卡尔坐标、内坐标和简征坐标之间的变换关系如下：
Firstly, the Duschinsky effect, or mode mixing of the initial and final electronic states, is expressed as
Q′ = JQ + K (1)
where the Q and Q′ are the normal coordinates of the two electronic states, respectively, and the matrix J and column vector K define the linear transformation. To obtain the matrix J and vector K in Equation (1), in terms of Cartesian coordinates displacements approach,the general linear transformation of an arbitrary distortion X can be written:
X′ = ZX + R (2)
where X and X′ are distortions expressed as Cartesian displacements from the equilibrium geometries of the initial and final electronic states, respectively. R = Req – R′eq is the change in equilibrium geometry between the initial and final electronic states in Cartesian coordinates centered on the molecular center of mass, and Z is a rotation matrix. In a conventional normal–mode analysis, the Cartesian displacements, X, is transformed to internal coordinates, S, and then to normal coordinates, Q, and visa versa, by the B and L matrices. That is S=BX and S=LQ. After several substitutions, the relation to relate Q to Q′ are obtained
Q′ = (L′-1B′) [ZM-1 (L-1B)†Q + R]. (3)
where the superscript “†” indicates the transpose of the matrix. Equation (3), substituted back into equation (1) gives expressions for J and K:
J = (L′-1B′) ZM-1 (L-1B)† and K = (L′-1B′) R |
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发表于 Post on 2015-3-20 08:51:50
我正在做荧光激发光谱振动分析，要考虑FC、FCHT、HT、和Duschinsky effect！ 但是我理解Duschinsky effect，我也是用FCclasses做的哦！如果可以的话，麻烦各位大侠和我说说Duschinsky effect效应的理解和解释及做法！还有就是需要扫描势能面，看S0态和S1态的势能曲线有没有发生变化！我在小*虫里找到这么句话：Duschinsky rotation是分子激发态的势能函数相对于基态势能函数的转动，只是转动，形状没有改变。要是相撞也改变了，那就是adiabatic近似了。做势能曲线扫描，是要看形状有没有发生变化！
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发表于 Post on 2015-3-20 12:07:23
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