苯衍生物二阶非线性光学性质的量子化学研究

本文采用引入外场微扰的CNDO/S—CI方法,计算了一系列苯衍生物的分子二阶非线性光学系数,探讨了取代基的电子性质、取代位置及取代基数目对分子二阶非线性光学系数的影响.结果表明;取代基的供电能力越强,分子的二阶非线性光学系数越大.D,A对位二取代苯和1—D,2.4—A,A三取代苯具有较高的非线性光学效应,苯衍生物中取代基数目为3时分子具有最佳的非线性光学效应.文中还对上述结论给出了初步的理论解释.     

含1,3-方酸苯螺旋共轭分子的设计及其电子光谱和非线性光学性质的理论研究

以量子化学半经验方法PM3优化构型为基础,利用INDO/CI方法研究了嵌入1,3-方酸的苯螺旋共轭分子的电子光谱,同时利用INDO/CI-SOS程序计算了它们的二阶非线性光学系数β_ijk和β_μ值,从而探索分子结构与电子光谱及非线性光学性质的关系.理论计算结果表明:在苯螺旋共轭分子中适当地嵌入方酸后,其二阶非线性光学系数增大.与苯螺旋共轭分子和1,3-方酸的比较表明,方酸环处于左端的体系有很好的二阶非线性光学性质,可能成为较好的光学材料.     

5,12-二硫杂-7,14-二氮杂-5,7,12,14-四氢并五苯及其相关化合物二阶非线性光学性质的理论研究

在ZINDO方法基础上,按完全态求和(SOS)公式编制了计算分子二阶非线性光学系数β_ijk、β_u的程序.研究了不同取代基在5,12-二硫杂-7,14-二氮杂-5,7,12,14-四氢并五苯侧环取代衍生物及相关化合物的结构、光谱和二阶非线性光学性质。结果表明:侧环上取代推、拉电于基团对增大二阶光学非线性都有利;分子共平面,共轭作用强,对增大二阶光学非线性有利.     

氮杂联苯乙烯系列衍生物的二阶非线性光学性质的理论研究

新型高非线性光学活性生色团分子的设计与探索已成为近来工作的焦点 [1] .化学家们 [2～ 9]研究了大量具有π电子结构和有分子内电子转移的有机化合物如推拉苯乙烯、 Schiff碱、偶氮苯、取代吡啶、噻吩乙烯等体系的二阶非线性光学特性 ,发现这些推拉共轭体系的共轭链长增加均导致二阶非线性极化率 β增大 ,紫外光谱红移 ,透明性降低 .本文研究推拉氮杂苯乙烯及二苯乙烯系列衍生物的二阶非线性光学性质 .结果表明 ,对于苯乙烯和二苯乙烯衍生物 ,引入嘧啶环既提高了二阶非线性光学系数 ,又不影响材料的透明性 ,是很有前途的二阶非线性光学候…     

准线型四原子分子高激发振动能级的动力学李代数方法

近几年来 ,人们用李代数方法处理了许多问题 [1～ 5] ,在此基础上 ,我们利用动力学李代数方法研究了准线型四原子分子高激发振动态 ,把分子的 Hamiltonian展开成 Casimir算子与 Majorana算子之和[6,7] ,然后进行代数处理 ,从而得到了代数 Hamiltonian的本征值 .1　基本理论四原子分子有 3个键 ,所满足的对称群为 G=U1(4) U2 (4) U3 (4) ,处理分子问题时 ,一般要考Fig.1　 The bond coordinates of fulminic acid(HCNO)虑键与键之间的耦合 ,为了方便 ,首先让键 1与键 2耦合 ,然后再与键 3耦合 (图 1 ) .这种耦合方式可记为 (1 2 ) 3 …     

六元环硼氮烷对称取代方酸的电子光谱和非线性光学性质的DFT研究

用量子化学密度泛函理论B3LYP方法,在6-31G(d)水平上对环硼氮烷和苯基对称取代方酸进行几何构型优化.以此为基础,利用TD-DFT方法得到方酸衍生物的UV-Vis吸收光谱.进一步引入外电场,用有限场(FF/DFT-B3LYP)方法探讨了各体系的三阶非线性光学性质(NLO).计算结果显示,对称环硼氮烷取代的方酸衍生物性质不同于苯环取代,取代位置对电荷分布、分子轨道特征和非线性光学性质的影响很大.氮原子与方酸相连时对提高方酸体系的三阶非线性光学性质十分有效,其NLO系数可达2.3808×10^-24C·m.     

苯并噻二嗪衍生物电子结构和非线性光学性质的研究

运用量子化学PM3方法，对苯并噻二嗪几种衍生物的几何构型、电子结构和前线分子轨道成分进行了分析，研究了电荷分布规律。同时，基于体系中电子转移的特点，利用有限场FF方法探讨了其非线性光学性质的变化。结果表明，苯并噻二嗪分子具有较好的二阶非线性光学性质，并可能成为一类良好的光学材料。     

有机及金属有机苯乙炔树状分子体系的非线性光学性质的理论研究

应用密度泛函理论研究了一系列有机及金属有机苯乙炔树状分子的激发态性质和非线性光学性质。计算的电子吸收光谱显示这些树状分子均在低能区域有一个最强的吸收;此外,金属有机体系的吸收光谱和有机体系相比发生了明显的红移。响应性质的计算结果表明共轭体系的扩展和金属有机基团的引入都使得苯乙炔树状分子的非线性光学极化率显著增加,尤其是含Ru体系,其β和γ值呈数量级增长。对于有机体系和含Pd体系,发生在共轭体系内部的π→π*电荷跃迁是产生分子一阶和二阶超极化率的主要原因。而含Ru体系相当大的非线性响应则主要起源于Ru的轨道到共轭体系的π*的跃迁,同时与Ru相邻的C≡C到共轭体系的π→π*跃迁起着辅助贡献。     

推、拉电子基团对水杨醛缩胺分子电子结构和非线性光学性质的影响

采用量子化学半经验FF／PM3方法,讨论了水杨醛缩苯胺分子中两苯环的对位被推、拉电子基团取代后,体系电子结构和非线性光学性质的变化,考查了分子电子结构对非线性光学性质影响的微观本质,得到的具有给体－共轭桥键－受体型结构的水杨醛缩苯胺分子应显示良好的非线光学性质。     

N-取代螺旋共轭化合物非线性光学性质的理论研究

以量子化学半经验AM1方法优化几何构型为基础，采用FF／AMl和INDO-SOS方法计算了N-取代螺旋共轭化合物的非线性光学系数，讨论了N原子不同取代位置对螺旋共轭体系结构、电子光谱、非线性光学系数的影响．计算结果表明，N杂原子的引入可改善体系的非线性光学性质，所设计的分子具有较大的二阶非线性光学系数和较好的透明性．     

Dynamic Lie algebraic formulation of second‐order optical nonlinearity for substituted benzenes

A dynamic Lie algebraic (DLA) formulation is applied to the study of nonlinear optical properties of the substituted benzenes. We have described the generation of the dynamic Lie algebra for the model Hamiltonian used in the present study. In terms of these elements of the dynamic algebra we express the evolution operator as a function of the group parameters, which can be determined by means of solving a system of coupled nonlinear differential equations. Thus, in terms of the density matrix operator formalism in statistical mechanics we obtain the statistical averages of the electric polarization and then derive readily an expression for the hyperpolarizability of the paradisubstituted benzenes. Comparisons with experimental observations and other quantum calculations of the hyperpolarizabilities for the paradisubstituted benzenes are made qualitatively and quantitatively. These results imply that the DLA method appears useful in describing the nonlinear optical phenomena in the substituted benzene molecules. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 335–343, 2003     

反应碰撞的动力学李代数描述

提出一种李代数方法描述分子反应碰撞问题．给出了含有主要动力学参量的S-矩阵元、分子碰撞跃迁几率以及反应体系能量统计平均值随时间演化的解析表达式．讨论了一个简单排斥势场中的原子-双原子分子共线反应体系，以阐明这种新方法的要点。     

Statistical mechanics of energy transfer in gas–surface scattering: A dynamical Lie algebraic approach

The dynamical Lie algebraic (DLA) method is used to describe statistical mechanics of energy transfer in rotationally inelastic molecule–surface scattering. Statistical average values of an observable for the scattering system are calculated in terms of density operator formalism in statistical mechanics. Employing a cubic expansion procedure of molecule–surface interaction potential leads to generation of a dynamical Lie algebra. Thus these statistical average values as a function of the group parameters can be obtained analytically in this formulation. The group parameters can be found from solving a set of coupled nonlinear differential equations. The DLA method, which has no need for determination of transition probabilities in advance as made routinely in the calculation, offers an efficient alternative to the method for computing the statistical average values. This method is much less computationally intensive because most of calculations can be analytically carried out. The average final rotational energies and their dependence on the main dynamic variables and the average interaction potential are presented for the rotationally inelastic scattering of NO molecules from a flat, static Ag(111) surface. Direct comparison is made between the predictions of this model calculation and experiment. The model reproduces well the degree of rotational excitation and correlation between the average final translational and the average rotational energies. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Statistical mechanics in rotationally inelastic scattering of molecules from surface within the dynamical Lie algebraic method

The dynamical Lie algebraic (DLA) method of Alhassid and Levine [Phys. Rev. A 18 (1978) 89] is applied to statistical mechanics in rotationally inelastic scattering of molecules from surfaces. Specifically, the method is generalized to include the motion of surface atoms, i.e., phonons. For given Hamiltonian and initial state, the set of constraints required to obtain the solution of the motion equations is determined by an algebraic procedure. It is furthermore found possible to derive the motion equations for the mean values of the constraints. Application of the method to the scattering of NO molecules from a Pt(1 1 1) surface is made. The mean values of the final energies of NO molecules scattered from the surface obtained using the DLA method are in good agreement with experimental results in qualitative trends. The DLA method thus appears to have a wide range of validity for describing the statistical mechanics of the gas-surface scattering.     

将A-L理论推广到无限维李代数

为使由Alhassid与Levine所提出的动力学李代数方法（简称A－L理论）能适用于更多的散射体系，在h(∞)中引入了有效集合C（有限维）的概念．按照微扰理论的意义，C中的代数元所对应的群参量是较低次微扰的结果，而不属于C的代数元所对应的群参量则相当于较高次做扰所产生的修正结果．因此可以近似地利用C来代替h(∞)．这样，不仅简化了计算程序并且对于很多具有现实意义的散射过程的计算成为可能．     

Application of the Lie algebraic approach to diffractionally and rotationally inelastic molecule–surface scattering

The Lie algebraic approach of Alhassid and Levine [Phys. Rev. A 18 , 89 (1978)] is applied to the molecule–surface scattering. Specially, the diffractionally and rotationally inelastic scattering of a diatomic molecule from a solid surface is dealt with. Within the framework of the close-coupling method, we construct a Hamiltonian for the scattering system and use it to generate a dynamical algebra h₆. By solving equations of motion for the group parameters, the scattering wave functions near the surface are obtained. Computed transition probabilities of diffractively and rotationally inelastic scattering of H₂ from LiF(001) surface with the use of Lie algebraic method are seen to agree well with the coupled-channel calculations. The Lie algebraic method thus appears to have a wide range of validity for describing the dynamics of gas–surface scattering. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 981–989, 1997     

Algebraic approach to electronic spectroscopy and dynamics

Lie algebra, Zassenhaus, and parameter differentiation techniques are utilized to break up the exponential of a bilinear Hamiltonian operator into a product of noncommuting exponential operators by the virtue of the theory of Wei and Norman [J. Math. Phys. 4, 575 (1963); Proc. Am. Math. Soc., 15, 327 (1964)]. There are about three different ways to find the Zassenhaus exponents, namely, binomial expansion, Suzuki formula, and q-exponential transformation. A fourth, and most reliable method, is provided. Since linearly displaced and distorted (curvature change upon excitation/emission) Hamiltonian and spin-boson Hamiltonian may be classified as bilinear Hamiltonians, the presented algebraic algorithm (exponential operator disentanglement exploiting six-dimensional Lie algebra case) should be useful in spin-boson problems. The linearly displaced and distorted Hamiltonian exponential is only treated here. While the spin-boson model is used here only as a demonstration of the idea, the herein approach is more general and powerful than the specific example treated. The optical linear dipole moment correlation function is algebraically derived using the above mentioned methods and coherent states. Coherent states are eigenvectors of the bosonic lowering operator a and not of the raising operator a(+). While exp(a(+)) translates coherent states, exp(a(+)a(+)) operation on coherent states has always been a challenge, as a(+) has no eigenvectors. Three approaches, and the results, of that operation are provided. Linear absorption spectra are derived, calculated, and discussed. The linear dipole moment correlation function for the pure quadratic coupling case is expressed in terms of Legendre polynomials to better show the even vibronic transitions in the absorption spectrum. Comparison of the present line shapes to those calculated by other methods is provided. Franck-Condon factors for both linear and quadratic couplings are exactly accounted for by the herein calculated linear absorption spectra. This new methodology should easily pave the way to calculating the four-point correlation function, F(tau(1),tau(2),tau(3),tau(4)), of which the optical nonlinear response function may be procured, as evaluating F(tau(1),tau(2),tau(3),tau(4)) is only evaluating the optical linear dipole moment correlation function iteratively over different time intervals, which should allow calculating various optical nonlinear temporal/spectral signals.     

Calculation of the nonlinear optical properties of molecules

A finite-field method for the calculation of polarizabilities and hyperpolarizabilities is developed based on both an energy expansion and a dipole moment expansion. This procedure is implemented in the MOPAC semiempirical program. Values and components of the dipole moment (μ), polarizability (α), first hyperpolarizability (β), and second hyperpolarizability (γ) are calculated as an extension of the usual MOPAC run. Applications to benzene and substituted benzenes are shown as test cases utilizing both MNDO and AM1 Hamiltonians.