Stretch Motion Research Articles

The influence of excited-state vibrations on fragment state distributions: The photodissociation of NOCl on T1(1 3A″)

NO V,R distributions are reported following photodissociation of jet-cooled NOCl from selected vibrational levels of the T1(1 3A″) state. By varying the photolysis wavelength while monitoring selected rovibrational levels of NO, a photofragment yield spectrum showing the same diffuse vibrational structure as the absorption spectrum is obtained. NO rotational distributions are obtained at photolysis wavelengths corresponding to peaks in the absorption spectrum. We find that the NO stretching vibrations of T1 evolve adiabatically into NO vibrational excitations [i.e., excitation of v1 quanta of the T1 NO stretch yields predominantly NO(v″=v1) ]. The NO rotational distributions depend only on the number of T1 bending quanta, v3. The shapes of the distributions reflect the number of nodes in the bending wave functions, and similar rotational distributions are obtained following excitation of vibronic levels with equal number of ν3 quanta, but different number of ν1 quanta (v1=0–2). We also find that the excited NO(2Π3/2) state is much more populated than the lower NO(2Π1/2) state, and the widths of the absorption features increase with increasing number of ν3 quanta, but decrease with increasing ν1 excitation. The results are explained in terms of a model in which the bending and NO stretch motions in the excited state are largely uncoupled. In order to explain the multimodal rotational distributions, we calculate separately the components of the NO rotational excitation that derive from the angular momentum inherent in the bending wave function and the angular anisotropy in the potential-energy surface. We find, using the momentum representation of the harmonic oscillator, that the rotational distributions map the bending wave functions and exhibit minima for v3>0. In addition, a unidirectional torque generated by the angular anisotropy in the potential causes shifts in the distributions calculated by the pure Franck–Condon model that are bending level dependent. The observation that the absorption linewidth decreases with increasing NO stretch excitation in the parent T1 state may be a manifestation of the energy mismatch between the frequency of the NO stretch in NOCl and free NO; the increased mismatch with increasing stretch quantum number results in slower dissociation.

Theoretical14N nuclear quadrupole coupling surface for ammonia

A property surface has been calculated by SCF theory for the variation with symmetric stretch and inversion motions of the electric-field gradient at the nitrogen centre in ammonia. The SCF calculations in a polarised basis overestimate the value of qzz in the ground state of 14NH3 by 9%. On introduction of a single scaling factor, vibrational averaging using empirical non-rigid-invertor wavefunctions gives satisfactory reproduction of experimental data for low vibrational states of symmetric isotopomers.

Theoretical and computational studies of highly vibrationally excited acetylene

A consistent interpretation of the intramolecular vibrational dynamics of highly excited acetylene on the ground potential energy surface is proposed. Classical trajectory computations in the time domain (and their Fourier transform) and quantum-algebraic computations of the spectrum provide a picture which is in accord with the results of an analysis of the experimental stimulated emission pumping. A separation of time scales suggested by the algebraic Hamiltonian is verified in the classical simulations. There are four distinct, nested relaxation stages following the initial state preparation, each corresponding to energy exchange amongst a bigger subset of states. Initially (<1 ps) only the two CH stretch motions are effectively coupled. It is suggested that the two CH quanta states (which are primarily local mode in character) are responsible for the broad features in the spectra at ≈26000 cm −1. Next the CH stretches and the (Franck-Condon) excited CC stretch share energy. This stage is yet to be identified in the spectrum. By ≈ 10 ps, the CH trans bend excitation is also fully coupled, resulting in the “clumps” in the experimental spectrum. Finally, by about 15 ps there is complete relaxation corresponding to a concerted orbiting motion of the H atoms about the CC bond with a wide frequency band centered at ≈6 cm −1.

The first absorption band for H2O: Interpretation of the absorption spectrum using time dependent pictures

We examine the relation between photodissociation dynamics and the form of the total absorption spectrum for H2O in the first absorption band. Application of an exact time dependent formalism gives a direct and intuitive relation between molecular motion and spectral features. We show that the series of weak structures on top of the broad continuum is due to symmetric stretch motion in the excited state. The spacing between the structures is, essentially, given by the frequency associated with this motion. In addition, we present some excited state eigenfunctions, which provide a direct connection between the structured spectrum, the final product distributions, and the dynamics.

Frequency shifts in inelastic electron tunnelling spectroscopy of adsorbed species

The authors discuss two mechanisms which cause significant changes of mode frequencies when inelastic electron tunnelling is used to study spectra of adsorbed species. One, already well known, results from the presence of the top metal electrode in the tunnelling structure; the other results from the electric field that is applied during measurement. By analysing a simple model, they show that the applied electric field changes frequencies by the same mechanism (one depending primarily on anharmonicity of the inter-atomic potentials) as that which has previously been used to explain the top-electrode effects. The model gives a good quantitative explanation for the frequency shifts observed in the O-H stretch motion of adsorbed hydroxyl groups.

Non-adiabatic inelastic scattering and intra-molecular vibrational excitation at metal surfaces

Considering as energy transfer mechanism the formation of electron-hole pairs, the inelastic scattering of a diatomic molecule from a metal surface is investigated on a purely quantum mechanical basis. The coupling of an adsorbate level to the surface is treated in an Anderson-Newns-like model which neglects correlation and spin effects. The centre-of-mass (CM) motion and the stretch motion are coupled via the interaction with the metal electrons. The model does not include a mechanical translational-vibrational coupling for a rigid surface. The stretch frequency of the diatomic molecule is assumed to be independent of the molecule-surface separation. The vibrating diatomic molecule approaches the surface in an upright orientation. For the CM-potential energy curve a More-type shape plus van der Waals tail was assumed. The Born-Oppenheimer core wave functions are obtained using a variational spline interpolation (VSI). The non-adiabatic transition matrix elements are evaluated in an improved quantum sudden approximation which incorporates many-particle aspects. Sticking probabilities, vibrational excitation probabilities and angular distributions for the inelastically scattered molecule are given. The dependence of the results on the parameters of the model are discussed. Agreement with the experimentally observed trends for NO scattered from a silver surface can only be obtained for weak electronic coupling. Considering only a single adorbital and neglecting spin degeneracy vibrational excitation probabilities of the order of 10 −3 are predicted for substrate temperatures between 100 and 1000 K. This is nearly an order of magnitude smaller than found in experiment, but including spin effects and several adorbitals on the gas molecule might lead to larger probabilities.

Vibrational excitation and inelastic scattering of CO from a Cu(100) surface via electron-hole pair formation

Considering as energy transfer mechanism the formation of electron - hole pairs the inelastic scattering of a CO molecule from a Cu(100) surface is investigated on a purely quantum mechanical basis. The electronic coupling of the diatomic to the metal surface is treated within a model Hamiltonian approach including correlation and spin effects. The centre-of-mass (CM) motion and the stretch motion are coupled via the interaction with the metal electrons. The model does not include a mechanical translational - vibrational coupling for a rigid surface, because the stretch frequency is assumed to be independent of the molecule - surface separation. The CO molecule approaches the surface in an upright orientation. The adiabatic potential energy curve for the CM - motion is calculated from the electronic Hamiltonian and exhibits a long - range tail giving rise to a physisorption minimum separated by a barrier from the chemisorption minimum. Tunnel effects are found to be important, because elastic scattering is negligible and inelastic probabilities are determined by branch ratios. Sticking probabilities, vibrational excitation probabilities and angular distributions for the inelastically scattered molecule are calculated and discussed with respect to available experimental evidence.

Laser-induced thickness stretch motion of a transversely constrainedirradiated slab

This paper is concerned with the dynamic response of a transversely constrained, but arbitrarily thick slab due to a Holobeam model 630-Q Nd pulsed laser irradiation normal to the surface of the slab. The laser beam is assumed to be Gaussian in space and time. The laser beam energy density is adjusted to cause heating of the slab, but to avoid phase change (melting) of the slab material. The initial thickness stretch motion occurs in a time period that is very small compared to the gross motion of the thick slab with edges far away from the laser beam effective diameter. Hence, during the initial stages of the thickness stretch motion, the transversely constrained irradiated slab is considered a one-dimensional problem through the thickness with a uniform laser irradiation over the effective laser beam diameter. Solutions are obtained for the time-dependent deformation and stress fields through the thickness of the slab within the framework of classical uncoupled dynamic thermoelasticity theory and classical methods in boundary value problems. The plots confirm a wave nature of deflections that various points through the thickness are undisturbed until the wave reaches the points. Also, interesting observations are made regarding sign reversals of the deflections and stresses that are useful for the designers.

On the Optic Vibrational Modes in Amorphous Arsenic

AbstractThe Raman, infrared, and inelastic neutron spectra on bulk amorphous arsenic are reviewed and compared. The main peak in the polarized Raman spectra does not correspond to a maximum in the neutron density of states and some kind of vibrational selection rules is observed. This behaviour is interpreted in terms of a simple continuous random network model for the a‐As structure in which symmetric stretch (SS) motions, highly correlated through the network, exhibit high Raman activity.

Coupling between the nickel—carbon and carbon—oxygen stretch motion in NiCO

Linear-combination-of-Gaussian-type-orbital (LCGTO) X-alpha calculations are performed on NiCO for various linear Ni-CO and NiC-O bond distances. The basis sets used are moderately large, approximately double zeta, and thus are fairly accurate within the X-alpha approximation. The electronic structure and equilibrium bond distances are consistent with recent CI calculations, indicating a much stronger Ni-CO bond than occurs in Ni(CO)4. The calculations agree to within 100/cm with the experimentally observed NiC-O stretch frequency. The Ni-CO stretch is predicted to occur at 656/cm, although at an intensity that is 640 times less. Compared with experimental results for CO adsorbed on single crystal Ni(100), the computed vibrational frequencies and intensities are less appropriate than the relevant experimental values for Ni(CO)4. This is interpreted to mean that an accurate description of the electronic structure of the nickel atom participating directly in the surface bond requires proper accounting of the bonds to its other nearest neighbors.

On the overtone-combination spectra of XY2 molecules

It is well known that overtone and combination features in the infrared spectra of YXY molecules arise from several different effects: (1) anharmonicity in the individual stretch and bend motions; (2) nonlinear dependence of the electronic-ground-state dipole moment (μ) on the stretch and bend displacements (r, ?, and ϑ); and (3) coupling of stretches and bend via nonseparable terms in the many-dimensional potential energy (V). In order to unambiguously sort out these contributions it is necessary to know the r, ?, and ϑ dependence of both μ and V from which follow the vibrational eigenstates, line positions, and oscillator strengths. In this paper we discuss general criteria for separability of the nuclear potential energy with respect to stretch and bend motions. Preference for ’’local’’ versus ’’normal’’ coordinates is shown to derive from the atomic mass differences and bonding types. The infrared spectrum of the HOH molecule is treated in detail, since a great deal of information is already available concerning its V (r, ?, ϑ) and μ (r, ?, ϑ). First we obtain the vibrational eigenstates and use them to study the breakdown of separability with increasing energy. Then we compare the relative intensities of neighboring overtone and combination states and account for them in terms of ’’electrical’’ (μ) and ’’vibrational’’ (V) anharmonicity.

Correlated excitations and Raman scattering in glasses

The dominant Raman line in $A{X}_{2}$ tetrahedral glasses is demonstrated to be caused by correlated symmetric stretch motions of the bridging $X$ atoms. Using a bond-polarizability model and the central-force model of Sen and Thorpe, we derive simple analytic forms for Raman spectra. We show that correlations may cause qualitative changes in the polarized spectrum leading to a peak at the edge of a band of vibrational states, whereas the depolarized spectrum is less affected and mimics the density of states. Both features are clearly observed in Ge${\mathrm{O}}_{2}$ and explain features in many other glasses. The same reasoning leads to a prediction of unusual spectral features in electronic spectra of disordered solids which may be observable in angular-dependent photoemission.

On the use of mass scaled cluster coordinates to describe polyatomic molecule reaction dynamics: Application to O + CS 2 → SO + CS

We explore the use of mass scaled cluster coordinates to describe polyatomic molecule reaction dynamics. These coordinates provide the natural extension to polyatomic systems of the familiar atom—diatom model of “rolling a marble” on a skewed and scaled potential surface in that they reduce the kinetic energy of an arbitrary system to one equivalent to that of a single mass point moving in 3 N - 3 dimensions. For any given number of atoms, usually several distinct types of mass scaled cluster coordinates can be introduced, all of which are interrelated by orthogonal transformations, and many of which are convenient for describing trajectory motion in one or more arrangement channels. We illustrate these points by an application to the collinear O + CS 2 → SO + CS reaction. For this system, the reagent to product coordinate transformation is conveniently described in terms of two Euler angles α and β, for which β is analogous to the atom—diatom skew angle, and α determines how the reagent vibrational normal modes relate to the product degrees of freedom. Examination of trajectory behavior indicates that the rather small value of π - α (21.7°) leads to a rather clean correlation between CS 2 asymmetric stretch motion and product CS vibrational motion, and between CS 2 symmetric stretch and a combination of SO stretch and product translation. This explains why symmetric stretch mode excitation enhances the O + CS 2 reaction rate more efficiently than asymmetric stretch mode excitation. We also find for O + CS 2 (and many other reactions for which the unbroken bond does not significantly change its length during the reaction) that the reagent and product segments of the minimum energy path are coplanar. This means that a natural partitioning of the reaction dynamics exists in which motions parallel to this plane tend to be active in promoting the reaction whereas motions perpendicular tend to be inactive. A study of trajectory motions and product state energy partitioning for O + CS 2 confirms this.

Infrared and Raman spectrum of CaUO 4: New data and interpretations

New Raman and i.r. data on CaUO 4, including isotopic and solid solutions frequencies, are presented and interpreted with the support of a group theoretical analysis and a normal coordinate treatment. The oxygen atoms only are allowed to move during the four Raman-active modes, all of which have been observed. The vibrational behaviour of the Ca 1- x Sr x UO 4 solid solutions suggests that two of these modes are conveniently described by internal motions of the uranyl group, viz. symmetric stretch (696 cm −1) and librational (340 cm −1) motions. Similarly, solid solution frequencies and 40Ca- 44Ca isotopic shifts lead to a satisfactory assignment of the five observed (against six predicted) i.r. frequencies: internal motions of the uranyl ion (696 and 366 cm −1 for the antisymmetric stretching, and bending respectively), translations of the Ca ++ ion (305 and 165 −1), and translation of the oxygen (435 cm −1). Most of these assignments do not agree with those previously proposed. The non-reproducibility of some i.r. frequencies is also discussed.

A higher order theory for extensional motion of laminated composites

A refined laminated plate theory is developed which is applicable to fiber reinforced composite materials under impact loading. In addition to the usual bending and extensional motion, the theory also includes the first symmetric thickness shear and thickness stretch motions as well as the first antisymmetric thickness shear mode. The governing equations reveal that unsymmetrically laminated plates display a coupling phenomenon between all of the deformation modes present in the theory. The frequency spectra for laminates representative of current fibrous composites are derived from the plate theory for one-dimensional wave propagation and compared to exact solutions obtained from dynamic elasticity theory. The higher order theory yields improved results for extensional motion compared to those of existing laminated plate theories.

A direct test of the vibrationally adiabatic theory of chemical reactions

The adiabaticity assumption of the vibrationally adiabatic theory of chemical reactions in the zero-curvature approximation is directly tested for the collinear H + H 2 reaction against calculations using exact wavefunctions. It is found that the symmetric stretch motion of the transition state is adiabatic to within 10% for total energies E ranging from 0.51 eV to 0.72 eV. For E below the zero-point energy of this symmetric stretch motion non-adiabaticity is substantial and is probably due to tunneling. For E above the first excited vibrational state energy of this symmetric stretch motion the adiabaticity assumption breaks down completely.