取代苯体系的二阶非线性光学性质:动力学李代数方法

提出了一种动力学李代数方法来研究取代苯体系的非线性光学性质. 对于给定的PPP模型(Pariser-Parr-Pople)哈密顿量, 生成了一个动力学李代数. 依据这些代数元构造出演化算子作为群参数的函数, 通过求解一组非线性微分方程能够得到这些群参数. 再按照统计力学中的密度算子公式给出取代苯分子体系偶极矩的统计平均值. 于是导出二阶极化率的表达式. 与其他量子力学计算结果比较, 表明这种动力学李代数方法在预言有机共轭分子的非线性光学性质上同样有用.

Second Order Optical Nonlinearity in Substituted Benzene Systems: a Dynamical Lie Algebraic Treatment

The dynamical Lie algebraic (DLA) formulation is used to describe the nonlinear optical process for the model system of substituted benzenes in a Pariser-Parr-Pople(PPP) Hamiltonian. It is shown how to generate the dynamical Lie algebra for the given Hamiltonian, and then the evolution operator for the system is expressed as a function of group parameters in terms of the elements of the dynamical algebra. The group parameters can be determined with a set of coupled nonlinear differential equations. The statistical average of the molecular electronic polarization can be determined according to the density operator formalism in statistical mechanics, and the hyperpolarizability of the molecules is thus obtained readily. An expression for the hyperpolarizabilities of the di,substituted benzenes as a function of the on-site energy is derived. Compared with other quantum calculations, DLA method appears to provide an effective method for the calculation of the hyperpolarizability of conjugated organic molecules.