Variational Calculation of Energies of Highly Excited Rovibrational States of CO2

Accurate variational calculations of energies of highly excited rovibrational states of ¹²C¹⁶O₂ using a Lanczos recursion are presented. In a first step, we use experimental rovibrational transition frequencies to determine by a least-square fitting procedure a potential energy surface for the CO₂ molecule. This potential energy surface is expressed as a multidimensional power series expansion in the normal coordinates. It is then used to determine all the rovibrational energies for symmetry e levels up to a rotational number J=200, a vibrational energy of 13 000 cm⁻¹, and a vibrational angular momentum l=13.     

Semiempirical study of perturbations of the Landé g factors of the electronic-vibrational-rotational levels of hydrogen: I. Theory

Theoretical analysis of perturbations of the Landé g factors of the electronic-vibrational-rotational levels of a diatomic molecule is performed for the case of interactions between electronic states whose number is arbitrary finite and that are not limited by the smallness of the parameter describing these interactions, with regard for the interaction of rovibrational states with an arbitrary finite number of vibrational-rotational levels of individual perturbing electronic states. The spin-multiplet interaction between rovibrational states was disregarded. As a result of general consideration, formulas are obtained for the g factors of rovibrational levels for the following cases: (i) mutual perturbation of a pair of levels; (ii) an nl complex of terms; and (iii) the interaction between an arbitrary number of vibrational-rotational levels of electronic states (whose number is also not limited) considered in the first order of the perturbation theory. The formulas obtained are given in the form of dependences on differences in observed (perturbed) values of rovibrational terms and matrix elements of vibrational wave functions dependent on the internuclear distance, which, in turn, are matrix elements of the electron wave functions of different operators that take into account the interaction between the electrons and nuclei of a molecule. The possibilities of using the obtained expressions in semiempirical study of perturbations and of determining the absolute dependences of the g factors of rovibrational levels of the electronic states of diatomic molecules (in particular, the hydrogen molecule) on the vibrational and rotational quantum numbers are analyzed.     

An angular singularity-free method for the dynamics of the rovibrational motion of diatomic molecules

An angular singularity-free method for the dynamics of the rovibrational motion of diatomic molecules has been proposed. The present method is based on a formulation that the orientation of a diatomic molecule is expressed by the Cartesian coordinates of the unit vector parallel to the molecular axis. In this light, the present method can be considered as a modification of a method proposed for the rigid rotational motion to the rovibrational motion. Illustrations of the present method have been performed for the classical dynamics of the rovibrational motion of a diatomic molecule, and for the semiclassical dynamics of the collision between an atom and a diatomic molecule, including comparisons with other conventional methods. It is concluded that the present method is free from angular singularity, and that the present method is superior to other conventional methods in view of computational efficiency.     

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.     

Thermodynamic properties and the approximate solutions of the Schrödinger equation with the shifted Deng–Fan potential model

With the introduction of a new improved approximation scheme (Pekeris-type approximation) to deal with the centrifugal term, the energy eigenvalues and the wave functions of the Schrödinger equation of the shifted Deng–Fan molecular potential are obtained, via the asymptotic iteration method. Rotational–vibrational energy eigenvalues of some diatomic molecules are presented, these results are in good agreement with other results in the literature. For these selected diatomic molecules, energy eigenvalues obtained are in much better agreement with the results obtained from the rotating Morse potential model for moderate values of rotational and vibrational quantum numbers. Furthermore, thermodynamic properties such as the vibrational mean U, specific heat C, free energy F and entropy S for the pure vibrational state in the classical limit for these energy eigenvalues are studied.     

Application of the Padé approximations to calculation of rotational energies of a triatomic linear molecule

A possibility of applying the Padé approximations to calculation of rotational-level energies of degenerate vibrational states is studied for linear molecules with various quantum numbers of the vibrational angular momentum 1. The calculations of rotational energy levels for the CO ₂ molecule show that the Padé form has a better predictability as compared to a power series. Spectroscopic constants of the Padé approximations for the vibrational states (04⁰0, 04²0, 04⁴0), (14⁰0, 14²0, 14⁴0), (15¹0, 15³0, 15⁵0), and (06⁰0, 06²0, 06⁴0, 06⁶0) for the CO ₂ molecule are determined. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 54–57, September, 2006.     

Energy transfer processes in linear triatomic molecule-solid surface collisions

The semiclassical stochastic trajectory method is extended to the study of rotational and vibrational transitions for linear triatomic molecules colliding with non-rigid solid surfaces. Rotational and vibrational motion are treated by quantum mechanics, translational motion by classical mechanics, and surface atom motion by the classical generalized Langevin equation. Self-consistent coupling of all motions is enforced via Ehrenfest's theorem. Calculations of the kinetic energy and gas temperature dependence of trapping probabilities, vibrational relaxation probabilities and final vibrational state distributions are presented for the CO₂-Ag(111) system at surface temperatures of 0 and 600 K. The trapping probabilities are greatly enhanced by the rotational motion and also vary to some degree with the initial vibrational state of the CO₂. Total vibrationally inelastic probabilities are on the order of 10⁻² for a single collision event with an initial state (00°1). For the initial state (01¹0) these are much larger, ~ 10⁻¹, due to the nature of bending mode motion. In conjunction with the large trapping probabilities, the mechanism of vibration to vibration, rotation, translation, phonon energy transfer can provide vibration relaxation probabilities in the range of those measured experimentally. A pseudo-selection rule for conservation of vibrational angular momentum is found.     

Electronic recoil effects in high-energy photoelectron spectroscopy

It is shown that the recoil energy imparted to the residual ion by the outgoing fast photoelectron leads to noticeable modifications of X-ray excited photoelectron spectra of molecules containing light atoms. The vibrational band envelopes may differ considerably from those predicted by the Franck-Condon principle. Al Kα excited valence electron bands are shown to exhibit, in addition to the translational recoil energy of the molecule, energy shifts of up to several tenth of an eV due to recoil-induced vibrational and rotational excitation. This effect has to be kept in mind when ionization potentials are determined from ESCA spectra. The recoil-induced vibrational and rotational excitation depends on the orbital quantum numbers of the ionized electron. Simple formulae for the shift of the centroid and the broadening of the band due to recoil effects are given for the special case of diatomic molecules.     

Atom-pair formulation of the rotational and vibrational motions of molecules

We have expressed the angular momentum and the internal kinetic energy of a molecule (a system of point masses) in terms of atom-pair contributions, paralleling the use of pairwise additive potential energy functions. The partitioning of the internal kinetic energy into rotational and vibrational contributions is then made following the analysis of Jellinek, J., and Li, D. H., 1989, 98, Phys. Rev. Lett., 62, 241. The resulting expressions contain pair position and velocity variables whose redundancy may be removed by transformation to Jacobi vector coordinates. These expressions should prove especially useful for describing the internal motions of clusters of like atoms.     

Polarized fluorescence of jet-cooled molecular iodine

The degree of polarized fluorescence of molecular iodine ¹²⁷I₂ cooled in a supersonic jet under rotationally selective excitation in the electronic transition B ³Π_0u ⁺-X ¹Σ _g ⁺ has been measured and calculated. It was found that the interaction of the angular momentum of the molecule with the nuclear spins of iodine atoms leads to a considerable depolarizing effect. This effect is most pronounced for small rotational quantum numbers of the angular momentum that are comparable with the total nuclear spin of the iodine molecule, which is equal to 5.     

Rotational structures of long-range diatomic molecules

We present a systematic understanding of the rotational structure of a long-range (vibrationally highly-excited) diatomic molecule. For example, we show that depending on a quantum defect, the least-bound vibrational state of a diatomic molecule with -C _n /r ⁿ (n > 2) asymptotic interaction can have only 1, 2, and up to a maximum of n-2 rotational levels. A classification scheme of diatomic molecules is proposed, in which each class has a distinctive rotational structure and corresponds to different atom-atom scattering properties above the dissociation limit.Received: 15 June 2004, Published online: 28 September 2004PACS: 33.15.Mt Rotation, vibration, and vibration-rotation constants - 34.10. + x General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.) - 03.75.Nt Other Bose-Einstein condensation phenomena - 03.75.Ss Degenerate Fermi gases     

Nuclear–nuclear correlation function from non-Born–Oppenheimer calculations of diatomic rovibrational states with total angular momentum equal to two (N = 2). Charge asymmetry in HD

The HD molecule in rovibrational states where the total angular momentum quantum number is equal to two (N = 2) is characterised with quantum mechanical calculations without assuming the Born–Oppenheimer (BO) approximation. Explicitly correlated all-particle Gaussian functions are used in the calculations. The convergence of the total non-BO energies of the considered states with the basis set size is analysed. The calculations of the averaged interparticle distances demonstrate the asymmetry of the electronic charge distribution. The algorithm to calculate the nuclear–nuclear correlation function for the N = 2 states is derived and implemented. Plots of this function for different rovibrational states provide a visual representation of the molecular structure.     

用代数方法精确研究HF分子B1Σ的振转能谱

基于代数方法(algebraic method)可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事实,又提出了一种新的代数方法(algebraic method 2)来精确研究双原子分子电子态的振转能谱和转动常数. 以HF分子的B¹Σ电子态为例,应用algebraic method 2方法研究了该电子态的振动量子数从ν=0到ν=10的所有振转能谱,获得了与实验值符合得非常好的理论结果. 关键词： 代数方法 双原子分子 振转能级     

Observation of rotational energy transfer in iodine by two-photon time delayed spectroscopy

The temporal evolution for individual rovibrational levels of the B state of the iodine molecule is observed by two-photon delayed spectroscopy. In particular the rotational energy transfer (RET) process due to collisions of the molecules in the B state with molecules in the ground state is studied. Thermal averaged rate constants for pairs of rotational levels of the v=27 vibrational state are measured. The results are discussed in terms of the dynamics of the collision process and numerical fits to the most important parametric fitting laws for RET are presented.     

Quantum monodromy and molecular spectroscopy

Monodromy (or once round) is a classical property of integrable dynamical systems in two or more degrees of freedom, which imposes a characteristic pattern on the quantum mechanical eigenvalue distribution. This article explains the connection by showing how the presence of an isolated critical point of the Hamiltonian leads to a classical action function that is multi-valued with respect to energy and angular momentum. Consequently, by the Bohr correspondence principle between actions and quantum numbers, there can be no uniquely defined global system of quantum numbers. Implications for the interpretation of highly excited molecular spectra are brought out by reference to quasi-linear molecules, which transfer one degree of freedom from rotational to vibrational motion during the excitation process. Emphasis is placed on the simplest examples, while a brief resumé of the wide scope of the quantum monodromy phenomenon is given in the final section.     

The stereodynamic properties of the F+HO(v,j) → HF+O reaction on~1 A' and ~3A' potential energy surfaces by quasi-classical trajectory calculations:Initial excitation effect(v=1-3, j=0 and v= 0, j=1-3)

The stereodynamic properties of the F ＋ HO （v, j） reaction are explored by quasi-classical trajectory （QCT） calculations performed on the 1At and 3At potential energy surfaces （PESs）. Based on the polarization-dependent differential cross sections （PDDCSs） and the angular distributions of the product angular momentum with the reactant at different values of initial v or j, the results show that the product scattering and product polarization have strong links with initial vibrationalrotational numbers of v and j. The significant manifestation of the normal DCSs is that the forward scattering gradually becomes predominant with the initial vibrational excitation increasing, and the scattering angle of the HF product taking place on the 3At potential energy surface is found to be more sensitive to the initial value of v. The product orientation and alignment are strongly dependent on the initial rovibrational excitation effect. With enhancement in the initial rovibrational excitation effect, there is an overall decrease in the product orientation as well as in the product alignment either perpendicular to the reagent relative velocity vector k or along the direction of the y axis, for which the initial rotational excitation effect is much more noticeable than the vibrational excitation effect. Moreover, the initial rovibrational excitation effect on the product polarization is more pronounced for the 3At potential energy surface than for the 1At potential energy surface.     

News Release

The forms of the dependences on the vibrational and rotational quantum numbers in the series representation of the vibration-rotational energies of diatomic molecules are discussed. It is concluded that the most convenient forms for diatomic molecules in ^lσ electronic states are (v+1/2) and (J+1/2)² respectively.     

反应物分子初始振动激发对O+HCl→OH+Cl反应的立体动力学性质的影响

在Peterson的高精度从头计算势能面上,运用准经典轨线方法讨论了反应物分子初始振动激发对O+HCl→OH+Cl反应的立体动力学性质的影响.反映两矢量k-j′相关的P(θr)函数的分布说明产物的转动角动量j′在垂直于反应物相对速度矢量k的方向上的排列取向程度随着初始反应物振动量子数的增加而增加;反映三矢量k-k′-j′相关的极角分布函数P(r)显示产物的转动角动量有比较弱的定向效应,且随着初始振动量子数的增加,这种弱的定向效应由沿Y轴负向变为沿Y轴正向.说明反应物分子的初始振动激发有利于增强产物分子的转动排列取向效应,但对产物分子P(r)分布的影响则不明显.