由非绝热相关获得的形式量子数及其在高激发振动态的经典解释

我们利用非绝热相关方法 ,通过关闭所有的振动模式间的耦合项并追溯到零级本征态 ,以得到体系的形式量子数 ,将形式量子数对高激发振动态的能级谱图进行归属 ,并重构本征能级图谱 ,使本征能级以有序的方式排列。这有助于对高激发振动态的能级进行分类和归属。形式量子数是体现高激发振动态的重要特征 ,是高激发振动态的近似运动守恒量。我们将多维陪集相空间的经典方法应用于高激发态的研究 ,发现形式量子数对应的李雅普诺夫指数为零或最小 ,并且它对应于较大的相空间密度     

辛和非辛算法求解薛定谔方程误差分析

在哈密尔顿体系下,提出气体声波传播的一种新的谐振子模型,并引入群论确定气体声波传播过程中的分子振动模式、能级简并.新模型将气动声学声传播问题与分子振动关联起来。由于发展高效的薛定谔方程的数值计算方法,有利于联系分子的性质来解释声的传播.本文从此出发,用二阶有限差分格式和生成函数法构造的二阶辛格式分别计算一维定态谐振子势场和含时谐振子势场的薛定谔方程,分析了数值解的误差以及传播能量误差.结果表明辛算法具有明显的优势.     

Ne-Xe体系势能曲线和光谱研究

本论文对Ne-Xe体系的势能曲线和束缚态能级作了系统的研究.采用耦合簇CCSD(T)方法和超分子近似,以及aug-cc-PVXZ(X=T,Q,5)基组,计算了Ne-Xe体系的相互作用势,并采用三种方案外推得到基底限值,给出了不同基底和外推方法下的势能曲线平衡位置和势阱深度.计算了Ne-Xe体系振转能级和各同位素基振动态的纯转动跃迁频率,及相应的光谱常数,并与实验结果进行了比较.     

分子高激发振动态的动力学特性研究

运用经典哈密顿代数方法,结合单摆的运动特点表示两个化学键之间的振动耦合.对水分子高激发态下两个氧氢键(O—H)伸缩振动动力学的研究结果表明,靠近分界线的中间能级的相空间中较易出现混沌轨道,而较高或较低能级的相空间中则具有比较规则的周期运动 关键词： 高激发振动 共振 混沌     

液相硝基甲烷分子振动特性的相干反斯托克斯拉曼散射光谱

构建时间分辨相干反斯托克斯拉曼散射（CARS）光谱系统,从微观层次研究硝基甲烷的分子相干振动动力学特性.实验中采用超连续白光作为斯托克斯光,通过调整斯托克斯光的时间延迟,得到不同振动模式的CARS光谱.通过对振动弛豫曲线的拟合,获得硝基甲烷分子不同振动模式的振动失相时间.结果表明C–H键伸缩振动比C–N键伸缩振动更容易受热声子的影响.在热加载下,硝基甲烷分子的C–H键有望首先被激发并引起初始化学反应.     

Murrell-Sorbie势分子体系振-转能级结构

对双原子分子体系内部相互作用势作了物理分析与比较,引用Murrell-Sorbie势.然后应用泰勒微扰理论.将M-S势函数泰勒展开,并取至4次方项,建立了相应的定态薛定谔方程.然后用三维谐振子势能量表象的径向矩阵对角元的简要形式,简易有效地求得一级微扰能量,进而获得双原子分子体系振-转能级的解析形式.其某些低能级和光谱的理论值与实验结果相符.     

乙炔分子的振动模型

乙炔分子振动不仅有经典力学的教学意义,对其分子振动信息的检测和分析还可直接应用于乙炔的浓度检测、光谱分析等。本文通过引入直线型三原子分子振动模型中的角簧概念,并在该三原子分子振动模型的基础上作进一步延伸,建立了乙炔分子振动的一个模型。并讨论了乙炔分子伸缩和弯曲两种振动模式,由此计算出乙炔分子在伸缩以及弯曲振动模式下分别对应的本征振动频率,并采用多组实验数据进行验证,模型预测结果与文献实验数据吻合较好。     

粒子在 Hénon-Heiles势中的逃逸动力学模拟

利用庞加莱截面和相空间轨迹方法对粒子在Hénon-Heiles势中的逃逸动力学进行了模拟.粒子的动力学性质敏感地依赖于粒子的能量.数值计算表明当能量很小时,粒子的运动是规则的;随着能量的增加,粒子的运动开始出现混沌.当能量增加到鞍点能Es时,几乎所有的相空间轨迹都是混沌的.当粒子的能量E>Es,粒子可以越过势阱发生逃逸.对于给定的大于Es的能量, 我们画出了粒子的逃逸-时间曲线和逃逸轨迹.我们的研究对于研究混沌传输和逃逸动力学具有一定的参考价值.     

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.     

基于臭氧分子体系的动力学研究

在李代数动力学群得到Hamiltonian的基础上,通过求解正则运动方程.对固定键角近似下臭氧分子体系相空间的庞加莱截面、KAM环面以及振动体系的能量属性进行了研究,获得了有关臭氧分子振动体系丰富的动力学信息.     

Local modes of silane within the framework of stretching vibrational polyads

We define stretching relative equilibria (RE) of silane and other similar tetrahedral molecules in terms of the dynamical polyad symmetry which assumes the resonance condition 1:1 between the two stretching vibrational modes ν₁ and ν₃ of the molecule. Exploiting symmetry and topology arguments and reducing the dimension of the classical mechanical system, we find these RE. One of them, with local symmetry C_3v and minimal energy within a polyad, corresponds to the local modes. We give the upper energy limit of the local mode localization within a polyad.     

Bending localization of nitrous oxide under anharmonicity and Fermi coupling: the dynamical potential approach

This paper studies the vibrational nonlinear dynamics of nitrous oxide with Fermi coupling between the symmetric stretching and bending coordinates by classical dynamical potential approach.This is a global approach in the sense that the overall dynamics is evidenced by the classical nonlinear variables such as the fixed points and the focus are on a set of levels instead of individual ones.The dynamics of nitrous oxide is demonstrated to be not so much dependent on the excitation energy.Moreover,the localized bending mode is shown to be ubiquitous in all the energy range studied.     

Dynamical potential approach to dissociation of H--C bond in HCO highly excited vibration

The highly excited vibrational levels of HCO in the electronic ground state, \tilde {X}¹A',are employed to determine the coefficients of an algebraic Hamiltonian, by which the dynamical potential is derived and shown to be very useful for interpreting the intramolecular vibrational relaxation (IVR) which operates via the HCO bending motion. The IVR inhibits the dissociation of H atom and enhances the stochastic degree of dynamical character. This approach is from a global viewpoint on a series of levels classified by the polyad number which is a constant of motion in a certain dynamical domain. In this way, the seemingly complicated level structure shows very regular picture, dynamically.     

Intramolecular vibrational dynamical barrier due to extremely irrational couplings

The intramolecular vibrational dynamics due to extremely irrational couplings is demonstrated by contrast to the resonance couplings, for the three-mode case of H分子物理学 分子内振动弛豫 甚高频无理耦合 共鸣 振动动力学intramolecular vibrational relaxation, extremely irrational couplings, resonanceProject supported by the National Natural Science Foundation of China (Grant No~20373030) and the Foundation for Key Program of Ministry of Education, China (Grant No~306020) and the Specialized Research Fund for the Doctoral Program of Higher Educatio2007-03-04The intramolecular vibrational dynamics due to extremely irrational couplings is demonstrated by contrast to the resonance couplings, for the three-mode case of H2O as an example. The extremely irrational couplings are shown to impose such strong hindrance to intramolecular vibrational relaxation （IVR） that they act as barriers. They restrict the direct action/energy transfer between the two stretching modes, though they allow the transfer between a stretching and a bending modes. In contrast, the resonance is more mediated by the bending mode and leads to chaotic IVR. It is also shown that there is a region in the dynamical space in which resonance and extremely irrational couplings coexist.     

Global dynamical analysis of vibrational manifolds of HOCl and HOBr under anharmonicity and Fermi resonance: the dynamical potential approach

The vibrational dynamics of HOCl and HOBr between bending and OCl/OBr stretching coordinates with anharmonicity and Fermi coupling is studied with the classical dynamical potential approach. The quantal vibrational dynamics is mostly mapped out by the classical nonlinear variables such as fixed points, except for the state energies, which are quantized. This approach is global in the sense that the focus is on a set of levels instead of individual ones. The dynamics of HOBr is demonstrated to be less complicated. The localized modes along the OCl/OBr stretching coordinates are also shown to have O--Br bonds more prone to dissociation.     

High-order harmonic generation of CO_2 with different vibrational modes in an intense laser field

We apply the strong-field Lewenstein model to demonstrate the high-order harmonic generation of CO_2 with three vibrational modes(balance vibration,bending vibration,and stretching vibration) driven by an intense laser field.The results show that the intensity of harmonic spectra is sensitive to molecular vibrational modes,and the high harmonic efficiency with stretching vibrational mode is the strongest.The underlying physical mechanism of the harmonic emission can be well explained by the corresponding ionization yield and the time-frequency analysis.Finally,we demonstrate the attosecond pulse generation with different vibrational modes and an isolated attosecond pulse with a duration of about 112 as is generated.     

Zero-point vibration of hydrogen adsorbed on Si and Pt surfaces

Hydrogen atoms adsorbed on Si(111) and Pt(111) were investigated by nuclear reaction analysis (NRA) using 1H(15N,alphagamma)12C. From measurements of the NRA spectrum at normal and tilted ion incidences the zero-point vibrational energies of H on Si(111) in the perpendicular and parallel directions were found to be 123.4+/-4.6 and 44.6+/-6.2 meV, respectively, which are consistent with harmonic potentials. The zero-point energies obtained for Pt(111)-H were 80.8+/-3.9 and 62.1+/-6.0 meV for perpendicular and parallel directions, respectively. These results indicate that the stretching mode is harmonic, while the bending mode is strongly anharmonic.     

不同初始振动态下D2O在B带的态-态光解动力学

利用高精度的非绝热从头算势能面,采用量子实波包方法研究了D₂O在3个不同初始振动态(0,1,0)、(1,0,0)和(0,0,1)下光激发到~B态解离过程的态-态量子动力学．结果表明,由于初始振动波函数的形状不同,从不同振动态产生的吸收光谱、产物分布和产物分支比具有不同的动力学特性．弯曲振动态(010)的吸收谱呈现出两波瓣的形状且中间具有较浅的极小值,其基态产物OD( ~X)在高能量区域会出现轻微的振动态反转现象．所有初始振动态得到的激发态产物OD(_?)的振-转态分布都随能量的变化出现强烈的震荡,这是由于受到了激发态势能面上长寿命共振态的影响．反对称伸缩振动态(0,0,1)在高能量区域具有较大的产物分支比OD(_?)/OD( ~X),表明绝热通道在某些情形下是主要的解离通道．     

Time-dependent local-to-normal mode transition in triatomic molecules

Time-evolution of the vibrational states of two interacting harmonic oscillators in the local mode scheme is presented. A local-to-normal mode transition (LNT) is identified and studied from temporal perspective through time-dependent frequencies of the oscillators. The LNT is established as a polyad-breaking phenomenon from the local standpoint for the stretching degrees of freedom in a triatomic molecule. This study is carried out in the algebraic representation of bosonic operators. The dynamics of the states are determined via the solutions of the corresponding nonlinear Ermakov equation and a local time-dependent polyad is obtained as a tool to identify the LNT. Applications of this formalism to H₂O, CO₂, O₃ and NO₂ molecules in the adiabatic, sudden and linear regime are considered.