运用线性量子变换理论和定态微扰论求解线型多原子分子振动的一般方法

The general approach to solve linear polyatomic molecular vibration utilizing linear quantum transformation theory and stationary state perturbation theory

采用键长伸缩和垂直键轴位移为内坐标,多维耦合谐振子、势函数中超过二次幂的项分别为零级近似和微扰的线型多原子分子振动模型,运用广义线性量子变换理论和定态微扰论对线型多原子分子振动进行了普遍求解,将线型多原子分子简谐振动能量本征值和态的求解转化成正定和半正定矩阵的对角化问题,微扰矩阵元、能量和波函数各级修正的计算转换到多维无耦合谐振子的本征表象中进行.并以CO2分子为例进行了具体求解.

The vibrational model of linear polyatomic molecule is adopted, choosing atomic displacements along and perpendicular to bond axis as the internal coordinates, multidimensional coupling oscillators and outstripping quadratic power terms of the potential function, respectively, as zero order approximation and perturbation. The vibration of linear polyatomic molecule are generally solved utilizing general linear quantum transfor- mation theory and stationary state perturbation theory. Finding the solution of the oscillator＇ s eigenvalue and state for linear polyatomic molecule is changed into the diagonalization of semi-positive and positive definite matrices. Perturbation matrix elements, all of the different levels energy and perturbation corrects of wave function are calculated in the representation of multidimensional non-coupling oscillators. And as a example CO2 molecule is particularly solved.