恩，好的，谢谢Sob老师，有点心急了！我多找找，多看看这方面的文章！作者Author: jliang 时间: 2015-3-23 10:30
Sob老师对“内坐标”、"简正坐标"和“笛卡尔坐标”怎么区分解释的很清楚。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
上面就是利用笛卡尔坐标处理振动模混合效应的方法。
