物理化学学报 >> 2005, Vol. 21 >> Issue (11): 1319-1323.doi: 10.3866/PKU.WHXB20051126

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取代苯体系的二阶非线性光学性质:动力学李代数方法

吴爱玲; 赵显; 关大任; 易希璋   

  1. 山东大学威海分校空间科学与应用物理系, 山东 威海 264209; 山东大学晶体材料国家重点实验室, 济南, 250100; 山东大学理论化学研究所, 济南 250100
  • 收稿日期:2005-03-18 修回日期:2005-07-06 发布日期:2005-11-15
  • 通讯作者: 吴爱玲 E-mail:ailingwu@sdu.edu.cn

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

WU Ai-ling; ZHAO Xian; GUAN Da-ren; YI Xi-zhang   

  1. Department of Space Science and Applied Physics, Shandong University at Weihai, Weihai 264209; State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100; Institute of Theoretical Chemistry, Shandong University, Jinan 250100
  • Received:2005-03-18 Revised:2005-07-06 Published:2005-11-15
  • Contact: WU Ai-ling E-mail:ailingwu@sdu.edu.cn

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摘要： 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.

关键词: 动力学李代数方法, 二阶非线性光学性质, 统计力学, 取代苯体系

Abstract: 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.

Key words: Dynamical Lie algebraic method, Second-order optical nonlinearity, Statistical mechanics, Substituted benzene system