任意阶力常数矩阵F的近似计算

Appoximate Calculation of Arbitrary Order Matrix F of Vibrational Force Constants

以L矩阵是下三角矩阵的近似^([1,2])为出发点,得到了求解F矩阵元的通式和均方振幅矩阵元的通式。简谐近似下,研究分子微振动问题,要解Wilson矩阵方程^([3]):GFL=L∧(1)及Cyvin矩阵方程^([4]):∑G^(-1)L=L∆(2)式中,G是与振动动能有关的矩阵;F是与振动势能有关的力常数矩阵;L是GF矩阵的本征矢矩阵,∧是GF矩阵的本征值对角矩阵,对角元λ_(k)=4π^(2)c^(2)v_(k)^(2),v_(k)为振动波数;∑是均方程振幅矩阵,⊿为对角矩阵,对角元δ为在正则坐标下,每个正则振动振幅的均方值,δ_(k)=h/8π^(2)cv^(2)-coth(hcv_(K)/2KT).

Applying the approximation assuming matrix L to be lower triangular, the general expressions determining arbitrary order matrix elements of the quadratic force constants and the meansquare amplitudes have been obtained.