Determination of the anion O-3 geometry by Franck-Condon simulations of its photoelectron spectrum

A theoretical method to calculate multidimensional Franck-Condon factors including Duschinsky effects is described and used to simulate the photoelectron spectroscopy of the anion O-3. Geometry optimization and harmonic vibrational frequency calculations have been performed on the (X～)1A1 state of O3 and (X～)2B1 state of O-3. Franck-Condon analyses and spectral simulation were carried out on the first photoelectron band of O-3. The theoretical spectrum obtained by employing CCSD(T)/6-311+G(2d,p) values are in excellent agreement with the observed one. In addition, the equilibrium geometry parameters, re(OO)= 0.135 5±0.000 5 nm and θe(O-O-O) =114.5±0.5°, of the (X～)2B1 state of O-3, are derived by employing an iterative Franck-Condon analysis procedure in the spectral simulation.     

S3分子的几何结构: 分子轨道从头算和Franck-Condon分析

在考虑Dusehinsky效应情况下,给出了多维Franck-Condon因子的理论计算公式;利用分子轨道从头算,完成了S3分子的(～X)1A1态和S-3分子的(～X)2B1态的几何结构优化和谐振频率分析,模拟了S-3的光电子能谱.在光谱模拟中,利用迭代Franck-Condon分析,得到了S3分子的(～X)1A1态的几何构型参数:r(SS)=1.94±0.02 (°A)和∠((S-S-S)=117.35±0.05°.由所得的S3分子的键角对Nimols等人得的结果[J.Phys.Chem.1986.90:2574]给出一个新的解释.     

A time-optimal setting of a dynamic object on an ellipsoid surface in multidimensional space

The technique of searching for optimal control, which makes it possible to transfer a dynamic object from an arbitrary point of the phase space onto the surface of an arbitrary multidimensional ellipsoid in the shortest time, is developed.     

On the vibronic theory of resonance Raman scattering

Resonance Raman excitation profiles of totally symmetric vibrational modes are investigated using a model that analytically includes the complete subspace of Franck-Condon active vibrations associated with each intermediate electronic state. This model is used to fit data obtained in resonance with the Soret band of cytochrome c. The excitation profiles are asymmetric and peak distinctively to the blue of the Soret absorption maximum. Large damping factors and/or inhomogeneous site distributions by themselves cannot account for the observed data. The theoretical results imply that the excited state lifetime associated with the Soret band of ferrocytochrome c has a lower limit on the order of 50 fs and that, compared to the ferrous form, the ferric cytochrome has a larger x-y splitting and a shorter lifetime.In constrast to the large multidimensional heme system, we also present the results of a simple model calculation applicable to smaller molecules. A two dimensional subspace is explored, where Raman Franck-Condon (RFC) and Franck-Condon (FC) factors are calculated for different potential energy surface parameters. Under certain conditions the RFC based scattering profiles of one vibration are strongly coupled to the FC based behaviour of the other vibration. Rather complex profiles are then predicted even for the simple two- dimensional case.     

A Generalized Talmi-Moshinsky Transformation for 1D Harmonic Oscillator Functions and Interaction Matrix Elements

A generalized Talmi-Moshinsky transformation relating one-dimensional harmonic oscillator product states with different sets of Jacobian coordinates is derived for systems composed of an arbitrary number of particles with arbitrary masses. With the help of our method the multidimensional integral which must be performed to evaluate an N-particle matrix element can be transformed into a sum of products of one-dimensional integrals.     

Exact Green's function of the equations of quantum mechanics in an electromagnetic field. I

An exact Green's function of the Cauchy problem in arbitrary (nonparallel) stationary homogeneous electrical and magnetic fields is constructed for the Klein-Gordon-Fock and Dirac equations and for the Pauli equation in arbitrary nonstationary fields, on the basis of a single approach using the method of the canonical Maslov operator (extension of the WKB method to the multidimensional case) and a Fock idea about the proper time in relativitic mechanics.     

Locally exact modifications of discrete gradient schemes

Locally exact integrators preserve linearization of the original system at every point. We construct energy-preserving locally exact discrete gradient schemes for arbitrary multidimensional canonical Hamiltonian systems by modifying classical discrete gradient schemes. Modifications of this kind are found for any discrete gradient.     

The roles of vibronic coupling and the Duschinsky effect in resonance Raman scattering

In most vibronic treatments of resonance Raman scattering it is assumed that the normal coordinates of electronically excited states are not rotated relative to those of the ground state, i.e., the Duschinsky effect is neglected. In the present paper this assumption is critically examined for the case of resonance Raman scattering by a non-totally symmetric vibrational mode. For consistency also the second-order Herzberg-Teller coupling is considered. It is shown that these second-order couplings introduce asymmetry in the excitation profile of appearance similar to that due to nonadiabatic coupling. Also it is shown that even small rotations give rise to noticeable effects in the polarization dispersion curve. Analytical formulas for the Franck-Condon factors and for the Raman tensor (valid for an arbitrary number of normal modes) for the case of small rotations are given, and illustrative calculations of excitation and polarization dispersion curves for a two mode system are presented and discussed.     

Supersymmetric origin of equivalent quantum systems

The previously established equivalence of certain multidimensional quantum hamiltonians is shown to be a consequence of the supersymmetry in quantum mechanics. Thereby the supersymmetric quantum mechanics can serve as a regular source of equivalent quantum systems in arbitrary space dimensions.     

Stability of Multidimensional Solitary Waves for Cubic-Quintic Nonlinearity

We show analytically that in the presence of cubic and quintic nonlinearities above a certain critical power, multidimensional optical solitary waves could propagate stably in bulk media. To investigate the stability an analytical expression for the solitary-wave fields with an arbitrary transverse dimension is derived through the combined use of Galerkin’s method and self-consistent-field approximation.     

Intramolecular charge transfer state and unusual fluorescence from an upper excited singlet of a nonplanar derivative of p-cyano-N,N-dimethylaniline

The TICT (twisted internal charge transfer state) fluorescence of 4-cyano-2,6,N,N-tetramethylaniline (CTMA) was found in the vapour phase. The dipole moments of excited Franck-Condon and Franck-Condon twisted ground states were estimated from the solvent shifts of absorption and fluorescence. The near-equality of excited Franck-Condon and relaxed TICT state dipole moments is discussed. The fluorescence from an upper excited singlet state is found and its mechanism is explained.     

Model studies on the systematics and interpolation of Franck-Condon factor arrays

A simple harmonic oscillator approximation is used to derive approximate algebraic expressions for low vibrational quantum number Franck-Condon factors for band systems for which molecular data are sparse. These simple expressions involve a transition parameter u which is characteristic of the electronic transition involved. The expressions provide Franck-Condon factors which agree quite well with RKR values when these are available. The formulae are used to explain quantitatively the dependence on u of the systematic properties of Franck-Condon factor arrays and to provide a method for their interpolation. The formulae are also used to describe quantitatively the dependence on u of the gross appearance of molecular band systems in emission and absorption.     

Resonance Raman investigation of the short-time dynamics of the ultraviolet photodissociation of bromoform

We report ultraviolet resonance Raman spectra of bromoform (CHBr₃) in cyclohexane solution. The resonance Raman spectra show significant intensity in the overtones of the nominal Br-C-Br symmetric bend (v ₆), the nominal H-C-Br asymmetric bend (v3), the nominal Br-C-Br symmetric stretch (v ₂) and the nominal Br-C-Br asymmetric stretch (v ₅) vibrational modes suggesting that the short-time photodissociation dynamics have noticeable multidimensional character. The lack of strong combination bands between several of the Franck-Condon active modes suggests that more than one electronic transition contribute to the resonance Raman spectra. We briefly discuss the ultraviolet short-time photodissociation dynamics of bromoform and the potential implications for the secondary photodissociation reactions of the initially formed CHBr₂ radical.     

Exact evaluation of the multidimensional Franck–Condon integrals based on the contour integral method

Adopting a different method from the Sharp–Rosenstock generating function method and the Doktorov coherent state method, a closed form expression for the Franck–Condon integrals between arbitrary multidimensional harmonic oscillators is derived exactly under the Duschinsky mixing effects on the base of the contour integral form expression of Hermite polynomials. In addition, an analytical expression for the calculation of the four-mode Franck–Condon factors is presented.     

双原子分子电子能量损失谱的解谱方法

介绍一种双原子分子电子能量损失谱的解谱方法,在利用已知的双原子分子光谱信息及理论计算的Franck-Condon(FC)因子的基础上,通过二次函数调整整个电子态振动强度的轮廓,减少拟合过程中的待定参数个数,降低对FC因子精确性的要求,提高拟合的精度和可信度.用Mathematica语言编写基于以上方法的数据处理程序,改进算法,提高了软件的运行效率.利用该软件处理氢分子的电子能量损失谱,得到氢分子不同电子态的振动跃迁的截面信息,所得结果与以前的实验结果符合很好.     

Riccati-Type Equations, Generalised WZNW Equations, and Multidimensional Toda Systems

We associate to an arbitrary ℤ-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer–Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given. Received: 3 August 1998 / Accepted: 21 December 1998     

Super-sensitivity in Dynamics of Ising Model with Transverse Field: From Perspective of Franck-Condon Principle

We study the role of Franck-Condon (F-C) principle in the dynamics of a central spin system, which is coupled to an Ising chain in transverse field. The transition process of energy levels caused by the excited central spin is studied to manifest the quantum critical effect through the Franck-Condon principle. The super-sensitivity of this quantum critical system is demonstrated clearly from the properties of Franck-Condon factors. We analytically show how spin numbers, coupling strength and order parameter of the Ising chain sensitively effect on the energy level populations in dynamical evolution near the critical point. This super-sensitivity and criticality are explicitly displayed in absorption spectrum.     

On the resolvent of elliptic operators with distant perturbations in the space

A multidimensional matrix operator of general form is considered, which need not be symmetric, with finitely many distant perturbations that are described by arbitrary abstract localized operators. We study the behavior of the resolvent of the perturbed operator as the distances between domains at which the perturbations are localized tend to infinity. An explicit formula for the resolvent of the perturbed operator is obtained; it is used to obtain a complete asymptotic expansion of the resolvent.     

Mode coupling between two connected multimode parabolic-index optical waveguides

Both a displacement of axis and a change in the refractive index distribution function cause mode coupling to occur between two multimode parabolic-index optical waveguides. This coupling is investigated by the coherent states method and the method of the dynamical symmetry group. Expressions for the mode coupling coefficients are obtained and their relationship to the Franck-Condon factors is emphasized. Recurrence relations for the mode overlap integrals and sum rules for the mode coupling coefficients are presented. An analogue of the Franck-Condon principle for the mode coupling coefficients is formulated. A simple geometric method for finding the most intensively coupled modes is also proposed.     

轴对称渐变型类周期慢波结构的色散特性

 运用场匹配法和傅里叶级数理论，提出一种原则上可数值求解任意轴对称渐变型类周期慢波结构色散特性的方法。采用该方法编制了计算渐变型波纹波导和渐变型盘荷波导色散曲线的Matlab程序，详细分析并讨论了这两类典型渐变型类周期慢波结构的色散特性。数值计算结果与多维全电磁模拟软件模拟结果的数据吻合度较高，验证了该数值算法的可靠性。另外，该方法具有较强的普适性和扩展性，也可退化到任意轴对称周期慢波结构色散特性的求解，为慢波结构的设计提供一种简单有效的途径。