运用线性量子变换理论和定态微扰论求解线型多原子分子振动的一般方法

采用键长伸缩和垂直键轴位移为内坐标,多维耦合谐振子、势函数中超过二次幂的项分别为零级近似和微扰的线型多原子分子振动模型,运用广义线性量子变换理论和定态微扰论对线型多原子分子振动进行了普遍求解,将线型多原子分子简谐振动能量本征值和态的求解转化成正定和半正定矩阵的对角化问题,微扰矩阵元、能量和波函数各级修正的计算转换到多维无耦合谐振子的本征表象中进行.并以CO2分子为例进行了具体求解.     

Characteristic features of electronic and vibrational spectra of free polyatomic molecules

The functional relationships between the basic characteristics of individual bands of electronic and vibrational spectra of free polyatomic molecules are ascertained. These basic characteristics are the position of the maximum of an individual electronic-vibrational band, the rate of the temperature shift of the maximum of a band, the half-width of a homogeneously or heterogeneously broadened electronic-vibrational band, the rate of the temperature variation of the half-width of a band, the asymmetry parameter of a heterogeneously broadened band, and the conditions for symmetric or asymmetric distribution of the intensity over the contour of a spectral band. The interrelations between the basic spectral characteristics result from the sequential mechanism of formation and broadening of individual bands of electronic and vibrational spectra of free polyatomic molecules. It is shown that the investigation of the basic spectral characteristics of electronic-vibrational bands and their interrelations allows one to elucidate the nature of the internal motion determining the optical properties of polyatomic molecules.     

Algorithm for solving the inverse vibronic problem on the basis of SVL fluorescence spectra

Computer methods whereby the inverse vibronic problem is solved on the basis of resonance fluorescence spectra with the use of modern quantum-mechanical methods for constructing structuraldynamic models of polyatomic molecules are discussed. An algorithm is proposed for solving the inverse vibronic problem according to resonance fluorescence spectra under laser excitation, and the corresponding calculation programs are constructed. The initial program data are acquired by means of an original software package which implements the scaling of quantum-mechanical force fields in two electronic states. The Duschinsky matrix and the initial matrix of shifts in normal coordinates caused by electron excitation are calculated in the Cartesian and natural vibrational coordinates. The program data are taken from quantum-molecular models based on calculations performed via ab initio modern quantum-mechanical methods and density functional theory. The algorithm is tested through the calculation of a model molecular system.     

A new formulation of the quantum problem in the theory of spectra of polyatomic molecules

A new approach to calculate energy levels and wave functions of polyatomic molecules with a definite geometric structure of the system assumed from the very beginning has been suggested. The effect of nuclear vibrations has been taken into account explicitly when separating variables in the Hamiltonian of the electronic state problem. The problem of the energy matrix formation has been discussed. It has been shown that some common patterns in higher-order vibrational spectra and in vibronic spectra can be explained without using concepts of anharmonism and changing the potential well parameters for an electron-excited state as compared to those for the ground state.     

On the Validity of Several Methods of Calculation of Vibronic Energy Relaxation Rates

Different approximation methods of calculation of the rates of vibronic energy relaxation are studied and compared with an exact one. The molecular vibrations are described by harmonic oscillators, the positions of equilibrium of which are assumed to be different in different electronic states. The finite line widths of the vibronic states are taken into account. It is found that the approximation methods provide too small values of the relaxation rates, particularly as the coupling strength becomes weak.     

低振动激发HeI2分子振动预离解寿命和终转动态分布

用含时黄金规则波包法，对ＨｅＩ２分子在低初始振动激发（ｖ＜１２）态下振动预离解动力学作了全维量子力学计算。所预言的总衰变宽度和寿命与谱线宽和皮秒时间分解的实时态－态测量外推数据符合得相当好。计算的总衰变宽度对初始振动态ｖ是敏感的并呈现一种非线性关系。结果表明低振动激发ＨｅＩ２分子衰变模式仍应是量子力学的。除终态相互作用对决定终转动分布有重要作用以外，首次发现，低振动激发态的初始特性也能显著影响终转动态分布。用Ｉ２的转动常数对ｖ的关系合理地解释了这个独特现象     

The Dushinsky effect and sum rules for vibronic transitions in polyatomic molecules

A method is presented for analyzing, in terms of sum rules, the intensity distribution among the vibronic bands in electronic spectra of polyatomic molecules, taking into account the rotation of the excited-state normal coordinates relative to those of the ground state (the Dushinsky effect). In the harmonic oscillator approximation, a quantitative criterion for the occurrence of the Dushinsky effect is obtained. The existence of this effect leads to non-product formulas for probabilities of the joint excitation of different vibrational modes. Expressions are obtained for the mean number of quanta excited in a given mode, and for its standard deviation, as well as for the correlation coefficients. The proposed method does not require a complete vibrational analysis of the spectrum of interest. As an example, the calculation of the correlation coefficient for the 3700-Å band system of the absorption spectrum of SO₂ is given.     

On the stability of parameters of molecular models in the parametric method of the theory of vibronic spectra

We have studied the stability of the system of parameters used in the parametric method of the theory of vibronic spectra of polyatomic molecules with respect to whether the initial structural-dynamic model of the ground state of a molecule is formed either by the fragmentary method or by direct quantum-chemical calculation. Modeling of excited states and spectra of the stilbene-h ₁₂ and stilbene-d ₁₂ molecules showed that, although the initial models of the ground states are significantly different, calculated changes in the geometry that occur upon excitation and electronic-vibrational spectra of the models are close and quantitatively agree with experiment. This indicates that the parameters of the method are stable and are applicable for performing predictive calculations of vibronic spectra based on models of the ground states created by different methods. We show that the fragmentary method has a considerable advantage, since models created by this method take into account the continuity of the structure in series of related compounds and calculations can be easily performed for molecules of arbitrarily high complexity. We show that direct quantum-chemical calculations are important in the case of molecules with unknown structural-dynamic models of fragments in the ground states.     

Lost topological (Berry) phase factor in electronic structure calculations. Example: the ozone molecule

It is shown that standard computations of electronic structures of polyatomic systems that yield the global minimum configuration and vibrational frequencies may be faulty if the symmetry of this configuration is lower than the highest possible one and the origin of this distortion, which is always due to the Jahn-Teller effect, is neglected; this may lead, in particular, to the loss of the Berry phase factor that changes the vibronic energy level spectrum and which we show to be present even when there are no apparent conical intersections. The general case and the ozone molecule are analyzed.     

Modeling of the time-resolved vibronic spectra of polyatomic molecules: The formulation of the problem and analysis of kinetic equations

A semiempirical parametric method is proposed for modeling three-dimensional (time-resolved) vibronic spectra of polyatomic molecules. The method is based on the use of the fragment approach in the formation of molecular models for excited electronic states and parametrization of these molecular fragments by modeling conventional (one-dimensional) absorption and fluorescence spectra of polyatomic molecules. All matrix elements that are required for calculations of the spectra can be found by the methods developed. The time dependences of the populations of a great number (>10³) of vibronic levels can be most conveniently found by using the iterative numerical method of integration of kinetic equations. Convenient numerical algorithms and specialized software for PC are developed. Computer experiments showed the possibility of the real-time modeling three-dimensional spectra of polyatomic molecules containing several tens of atoms.     

Mechanism of angular momentum exchange between molecules and Laguerre-Gaussian beams

We derive the interaction Hamiltonian between a diatomic molecule and a Laguerre-Gaussian beam under the assumption of a small spread of the center of mass wave function of the molecule in comparison with the beam waist. Considering the dynamical variables of the center of mass, vibrational, rotational, and electronic motion, we show that, within the electronic dipole approximation, the orbital angular momentum of the field couples with the rotational and electronic motion. The changes in the transition probabilities and selection rules induced by the field orbital angular momentum and the applicability of the derived interaction mechanisms for polyatomic molecules are discussed.     

Study of the protoporphyrin luminescence under selective laser excitation

The structural luminescence spectra of protoporphyrin IX solid solutions in ethanol and hydrochloric acid were obtained under selective laser excitation in the region of the inhomogeneouly broadened pure electronic and vibronic bands at T = 3.8 K. The dependence of the excitation selectivity on the excitation frequency was investigated. The vibrational frequencies of protoporphyrin IX were obtained in the ground and excited electronic states when the excitation frequency has been scanned in the region of pure electronic and vibronic bands, respectively. A universal apparatus is described for the investigation of the absorption and luminescence spectra of polyatomic molecules in the temperature range from 3.5 to 300 K under the dye laser excitation tunable in the spectral region 265–365 nm, 435–730 nm, detection of spectra in the region 300–900 nm with a polychromator and silicon intensified image detector and processing of the spectral information with an optical spectrum analyser controlled with a microcomputer.     

T1uhg Jahn-Teller系统中的频率约化矩阵

在研究C₆₀的电声相互作用中,最重要的应是T_1u电子态与h_{g< /sub>振动模式的偶合,俗称作T1uhg Jahn-Teller(JT)系统.线 性的T1uhg JT系统的势能面上只有势槽的存在,而当非线性耦合 项加入后,势能面将被扭曲成具有Ｄ3d或Ｄ5d对称性的势阱.在振 动频率的各向同性假设下,势阱中h 关键词： 60分子')" href="#">Ｃ60分子 “杨-太勒”系统 ?pik-Pryce方法}     

Molecular Rydberg transitions: The lowest-energy Rydberg transitions of s-type in CH3X and CD3X,X = Cl,Br, and I

The absorption spectra associated with transitions to the lowest-energy s-type Rydberg states of CH₃X and CD₃X, X = Cl, Br, and I, have been measured and analyzed. The spectra of the bromides and iodides consist, individually, of four electronic origins of s-excitation type. The vibrational frequency of a given normal mode is more or less identical in all four excited states of any one molecule; and the excited state/ground state ratios of the frequencies of any given normal vibrational mode are essentially identical for all four molecules (i.e., for 16 states, four for each of two bromides and two iodides). The spectra of the chlorides are amenable to a number of different vibronic analyses, none of them unique; these analyses are discussed.     

Improvement of the parametric method of the theory of vibronic spectra of polyatomic molecules: Absorption spectra and the structure of butadiene, hexatriene, and octatetraene in the excited state

The structure of the excited states and absorption spectra of butadiene, hexatriene, and octatetraene are calculated by the parametric method of the theory of vibronic spectra using models of the first-and second-order approximations. It is shown that these molecular models adequately reflect the molecular structure and allow one to predict quantitatively the shape and fine vibrational structure of the absorption spectra. When passing to the second-order approximation, only two additional (angular) parameters are used. These parameters are transferable in the series of polyenes. Compared to the first-order approximation model, the second-order approximation model more accurately takes into account the angular deformations of polyenes upon their excitation and describes the intensity distribution in the vibrational spectrum, including weak lines. In addition, the calculations also quantitatively predict spectral variations in the molecular series. The parametric method is more efficient for modeling polyatomic molecules in the excited states and their vibrational spectra compared to other semiempirical and ab initio methods.     

用飞秒离子产率谱和光电子影像解析振动波包动力学

时间分辨光电离是揭示多原子分子激发态动力学的一种强有力的实验方法.根据收集信号的种类,可以采用不同的测量方法:时间分辨离子产率谱(TR-IYS)和时间分辨光电子成像(TR-PEI).本文综述介绍了光电离测量与电子结构的基本概念,以及在实验上区分不同几何结构之间的振荡波包运动的几个重要研究工作,并举例说明飞秒TR-IYS和TR-PEI是如何被用来探测激发态势能面上相干振动波包的演化过程.     

Relaxation Processes at High Levels of Vibrational Excitation of Polyatomic Molecules in the Ground Electronic State

By the spectral and kinetic characteristics of the luminescence of vapors of polyatomic molecules (anthracene, anthraquinone, fluorenone) initiated by selective IR multiphoton excitation (IR MPE) of molecules in the ground electronic state S ₀ the relaxation processes proceeding under vibrational excitation of molecules to energies exceeding the energies of the lower excited electronic states have been investigated. The changes in the spectral and kinetic characteristics with increasing CO₂ laser energy density and vapor P _v and foreign gas pressure P _FG are analyzed. They are similar to the characteristics obtained for normal fluorescence of these molecules with changing vibrational energy E _vib content. On the basis of experimental data and model calculations it has been concluded that at the laser radiation densities used in the case of IR MPE the molecules reach energies considerably exceeding the energies of the electronic levels. It is shown that a nonadiabatic connection between the electronic states leads to the population of mixed electronic states isoenergetic to the vibrational levels of the ground electronic state and to emission of delayed luminescence spectrally identical to the normal luminescence of these molecules. It has been found that when high vibrational levels are populated, new relaxation channels, such as reverse electron relaxation, emission from high vibrational levels of the ground electronic state, and multiquantum vibrational energy transfer at collisions leading to a rapid establishment of vibrational equilibrium become important.     

凝聚相中血卟啉分子的激光选择激发

用脉冲染料激光器在77K对血卟啉在乙醇和HCl溶液中的电子振动带和0—0跃迁带进行激光选择激发,得到了有振动结构的荧光光谱,发现其对激发波长有明显的选择性。在冷凝的乙醇溶液中,HPD的荧光出现四种不同的特征,在选择激发下给出更好的分辨。认为它可能与异构现象有关。