高激发振动态氰化氢分子的解离研究

运用李代数陪集空间方法，结合莫尔斯（Morse）振子的解离特点研究了具有多重共振的高 激发振动态氰化氢（HCN）分子的解离.结果表明，分子振动模之间的共振（主要是体系的高 次共振）作用，有助于化学键的解离，共振的作用导致H—C键解离能量的降低. 关键词： 高激发振动态 共振 解离     

用李代数方法构造四原子分子的势能面

把李代数方法得到的四原子分子的代数Hamiltonian，利用相干态经典化之后并找到一个新的变换，将分子的键角引入，而得到四原子分子的势能面.由该势能面计算得到的解离能与力常数与其他方法给出的一致.     

分子高激发振动态的理论研究

简要综述了分子高激发振动态的理论研究方法和研究进展.介绍了李代数方法在高激发振动态能级的归属和分类、分子高激发振动态动力学以及分子内振动能量弛豫和分子解离等方面的应用.随后,作者对分子高激发振动态研究领域今后的发展方向作了展望.     

红外场对双原子分子振动布居影响的李代数方法研究

采用李代数方法研究双原子分子在红外场中的振动跃迁,给出了体系跃迁概率的解析表达,并讨论了红外场的频率、光强和脉冲持续时间分别对NaCl和LiH分子振动基态和第一振动激发态上粒子数布居的影响. 关键词： 李代数方法 红外场 振动布居 双原子分子     

HOCl分子高激发振动态的动力学势研究

通过研究HOCl分子高激发振动态的动力学势, 明确了该体系的动力学特点. 研究表明, 在O-Cl伸缩模式和H-O-Cl弯曲模式间存在2:1 Fermi共振的动力学模型下, H-O伸缩振动模式对于上述两种振动模式的动力学势有显著影响, 且这种影响随Polyad数呈现有规律的变化. 作为定量研究, 还研究了Polyad数为24时该分子体系的动力学势与各能级的相空间轨迹. 分析表明, 相空间轨迹与动力学势中的动力学不动点有很好的对应关系. 此外, 将该Polyad数下的动力学势中的能级按照相空间轨迹的作用量积分进行分类, 明确了这些能级所处的量子环境.     

李代数方法在分子振动光谱研究中的应用

通过对动力学对称性的介绍,引出构造分子体系Hamiltonian的方法,并介绍李代数方法处理分子"振动-振动耦合"、"振动-转动耦合"Hamiltonian的一般步骤.还以HCO分子体系为例,说明如何选取特定的群链来构造Hamiltonian,并论证了对于该体系群链的唯一性.最后还对一些李代数方法在分子光谱中的其他应用(例如局域模,多原子分子的振转光谱研究)作了初步的介绍,并对于这一方法的不足和局限性做了论述.     

推广的一类Lie代数及其相关的一族可积系统

对已知的Lie代数An-1作直接推广得到一类新的Lie代数gl(n,C).为应用方便，本文只考虑Lie代数gl(3,C)情形.构造了gl(3,C)的一个子代数，通过对阶数的规定，得到了一类新的loop代数.作为其应用，设计了一个新的等谱问题，得到了一个新的Lax对.利用屠格式获得了一族新的可积系统，具有双Hamilton结构,且是Liouville可积系.作为该方程族的约化情形，得到了新的耦合广义Schrdinger方程. 关键词： Lie代数 可积系 Hamilton结构     

Analysis of vibrational spectra of nano-bio molecules： Application to metalloporphrins

In this paper, we have applied the Lie algebraic model to nano-bio molecules to determine the vibrational spectra of different stretching and bending vibrational modes. The determined vibrational energy levels by the Lie algebraic model are compared with the experimental data. The results from the theoretical mode[ are consistent with the experimental data. The vibrational energy levels are clustering in the excited states.     

量子变换的李代数方法

利用李代数生成元构成幺正算符,对耦合玻色体系给出了一种简单的对角化方法.     

Na2分子部分电子态的完全振动能谱和离解能的精确研究

对于大多数双原子分子的电子态，用现代实验方法或精确的量子理论方法往往可以获得含m个振动能级的能谱子集合［Ev］，而不易得到包含最高振动能级在内的所有高振动量子态能级的完全振动能谱{Ev}.鉴于Na2分子电子态的振动能谱和分子离解能De在实际研究和应用中的重要性，使用基于微扰理论的代数方法（AM），获得了Na2分子一些电子态的振动光谱常数和完全振动能谱；使用基于AM的代数能量方法（AEM）获得了这些电子态的正确离解能.研究结果表明：AM方法能从少数精确的实验能级获得精确的分子振动光谱常数集合和正确的完全振动能谱{Ev}，AEM方法获得的分子离解能比由文献发表的振动光谱常数计算得到的近似离解能值更准确，对于难以获得分子离解能的那些电子激发态，AEM方法能给出合理的离解能数据. 关键词： Na2分子 代数方法 振动能级 离解能 电子激发态     

Studies on heteronuclear diatomic molecular dissociation energies using algebraic energy method

The algebraic energy method (AEM) is applied to the study of molecular dissociation energy $D_e$ for 11 heteronuclear diatomic electronic states: $a^3\Sigma^+$ state of NaK, $X^2\Sigma^+$ state of XeBr, $X^2\Sigma^+$ state of HgI, $X^1\Sigma^+$ state of LiH, $A^3\Pi(1)$ state of ICl, $X^1\Sigma^+$ state of CsH, $A(^3\Pi_1)$ and $B0^+(^3\Pi)$ states of ClF, $2^1\Pi$ state of KRb, $X^1\Sigma^+$ state of CO, and $c^3\Sigma^+$ state of NaK molecule. The results show that the values of $D_e$ computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable $D_e$ within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature.     

Calculation of the vibronic spectra and structure of methylstyrene in the excited state by the parametric method

Calculations of the excited-state structure and of the absorption and radiation spectra of trans-β-methylstyrene are performed by the parametric method for models of the first and second approximations. Only three of the parameters, being constant in a series of related compounds, are used for molecular fragments. In the calculation, the main regularities observed in electronic spectra are reproduced, and an analysis and interpretation of their fine vibrational structure are carried out. The use of the model of the second approximation with a single additional parameter allows more accurate reproduction of angular deformations of the molecule under excitation and of the characteristic changes observed in the low-frequency spectral region in the series of diphenyl polyenes, stilbene, styrene, and methylstyrene molecules. It is shown that the parameters of the second approximation (just as of the first one) possess the transference property in the homological series of molecules. In modeling complex molecules in excited states and their vibronic spectra, the parametric method is more efficient than the ab initio one. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 2, pp. 148–153, March–April, 2000.     

Enhanced dissociation of H2+ into highly excited states by UV pulses

We theoretically study the dissociation of H₂⁺ by UV laser pulses as a function of the photon energy ω of the pulse. Our results show that pronounced enhancements of the dissociation into highly excited electronic states can be achieved at some critical ω. This is found to be attributed to a consecutively resonant excitation mechanism where the population is first transferred to the first excited state by absorbing one photon and then to higher states by absorbing another one or more photons at the same internuclear distance. This study indicates that the strong coupling between the lowest two states of H₂⁺ can significantly affect the dissociation through higher lying states.     

Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out.     

On the study of unitary representations of the twisted Heisenberg-Virasoro algebra via highest weight modules over affine Lie algebras

In this paper, we first construct an analogue of the Sugawara operators for the twisted Heisenberg-Virasoro algebra. By using these operators, we show that every integrable highest weight module over an affine Lie algebra can be viewed as a unitary representation of the twisted Heisenberg-Virasoro algebra. As a by-product of our constructions, we give the unitary representations of the twisted Heisenberg-Virasoro algebra which have the central charges appearing in [1]. Our approach to obtain these central charges is different with that of [1].     

碱金属双原子分子部分电子态的完全振动能谱和离解能

对大多数双原子分子电子态的高阶振动能谱,现代实验方法和量子力学理论计算都难以得到较精确的振动能级.文中应用基于二阶微扰理论的代数方法(AM)以及计算双原子分子离解能的新表达式研究了碱金属双原子分子Li₂的3³Σ⁺_g,1³Δ_g和2³Π_g,Na₂的B¹Π_u以及K₂的4¹Σ⁺_g电子态的完全振动能谱{E_υ^AM}和离解能,理论计算结果不仅与已有的实验值相符,而且还给出了实验尚未得到的高阶振动能级.这些结果为碱金属双原子分子精确振动能谱和离解能的科学研究提供了重要数据. 关键词： 碱金属分子 高阶振动能级 离解能 代数方法     

碱金属氢化物双原子分子部分电子态的完全振动能谱和分子离解能的精确研究

应用作者建立的基于微扰理论能级表达式的代数方法，研究了碱金属氢化物双原子分子⁶LiH，⁷LiH，NaH，KH，RbH和CsH的A¹Σ⁺电子态的完全振动能谱{E_υ}，并应用基于代数方法的代数能量方法分别研究了以上各分子电子态的离解能.得到了这些电子态的精确的振动光谱常数和包括接近分子离解极限在内的完全振动能谱以及正确的理论离解能，从而为许多需要这些双原子分子的精确振动光谱的科学研究提供了必要的数据. 关键词： 碱金属氢化物 代数方法 振动能级 离解能     

双原子分子振动能谱与离解能的精确研究

代数方法(AM)的建立解决了实验方法和精确量子力学理论方法难以获得双原子分子的包含最高振动能级在内的所有高阶振动能级的精确数值这一问题.基于LeRoy与Bernstein的工作,孙卫国等又建立了精确计算双原子分子离解能的新解析表达式.应用新公式和代数方法(AM),研究了一些双原子分子部分电子态的振动能谱和分子离解能,获得了与实验值符合非常好的理论结果.该方法在理论上提供了获得双原子分子完全振动能谱和精确分子离解能的物理新方法.     

Search for and elimination of dependences between vibrational coordinates in modeling spectra of large molecules

We have investigated an algorithm allowing us to reliably identify an arbitrary number of complex linear dependences between vibrational coordinates in a molecular model of very high dimensionality. These dependences are eliminated in the step for diagonalization of the kinetic part of the vibrational Hamiltonian. We have carried out computer experiments allowing us to propose optimal rules for designing appropriate computer programs for working with a vibrational Hamiltonian of very high dimensionality. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 561–565, September–October, 2006.