Degenerate Bending Mode Research Articles

Six-dimensional calculation of intermolecular states in molecule-large molecule complexes by filter diagonalization: Benzene–H2O

We present an approach toward the dynamically exact calculation of intermolecular states in molecule-large molecule complexes. The approach employs an intermolecular Hamiltonian specifically formulated with the case of molecule-large molecule complexes in mind. In addition, it makes use of filter diagonalization techniques to diagonalize that Hamiltonian. The approach is applied to the calculation of J=0 intermolecular states below about 110 cm−1 in the benzene–H2O complex. The results of the calculation are interpreted in terms of five internal rotation states, a doubly degenerate bending mode and a singly degenerate stretching mode, the latter two modes involving the relative translation of the monomer moieties in the complex. The internal rotation states are discussed in the context of the two-dimensional, free internal rotation/water in-plane torsion model of Pribble et al. [J. Chem. Phys. 103, 531 (1995)]. It is shown that that model is largely successful in identifying the important features of the low-energy benzene–H2O states that involve rotation and/or libration of water. It is also shown, though, that multimode couplings can have major effects on the detailed nature of the intermolecular level structure of the species.

Infrared transition intensities in acetylene: An algebraic approach

The two-dimensional algebraic model for degenerate bending modes has been extended to include interaction terms with stretching modes and to provide a detailed description of the dipole operator for linear molecules. An algebraic mixed model is used to investigate, for the first time, the absolute infrared intensities in 12C2H2 up to 10 000 cm−1. Intensities of hitherto unmeasured vibrational bands are also given.

Intensities of infrared transitions in the two-dimensional algebraic model

In a previous paper,Reference 1 the Lie algebraic method was applied to two-dimensional problems, with special attention to the vibrational analysis of degenerate bending modes of linear molecules. This paper completes the two-dimensional algebraic model with the study of infrared transition intensities, whose theoretical aspects were only hinted at in the previous work.

Near-infrared band of the nitrate radical NO3 observed by diode laser spectroscopy

We have analyzed the near-infrared band of NO3 observed at 7602 cm−1 by using diode laser spectroscopy. Most of the spectral lines were recorded using source-frequency modulation. Zeeman modulation was found useful in selectively detecting some Q branch lines, which provided us with a clue to the assignment of the observed spectra. The band satisfied selection rules for a parallel band and was thus ascribed to a 2A1″–2A2′ vibronic component associated with the 2E′′–X̃ 2A2′ electronic transition, namely, to a transition from the ground vibronic state to the A1″ vibronic state resulting from excitation of the degenerate in-plane bending mode in the 2E′′ electronically excited state manifold. The band was almost free of perturbations, except for some K=6 lines. The least-squares analysis of 581 assigned lines led to molecular parameters of the upper state, where ground-state parameters were fixed to those obtained from the infrared study previously reported [K. Kawaguchi, E. Hirota, T. Ishiwata, and I. Tanaka, J. Chem. Phys. 93, 951 (1990)]. The upper-state B rotational constant gave the effective N–O distance of 1.271 Å, which is to be compared with 1.240 Å in the ground vibronic state. The εbb spin–rotation interaction constant of the upper state was close in magnitude to that in the ground vibronic state, but of opposite sign. This observation indicates that the spin–rotation interaction is primarily caused by that between the 2E′′ excited and the ground electronic states.

IR–rf double resonance studies of dipole moments in the ν1+ν4 and ν1+ν5 states of acetylene-d

Infrared laser–radio frequency double resonance spectroscopy has been used to observe transitions across J=1 ℓ-type doublets in vibrational states of monodeuterated acetylene, HCCD, that have both the C-H stretch and one degenerate bending mode excited. Electric dipole moments and ℓ doublings have been measured for the ν1+ν4 and ν1+ν5 states, giving: μ14=−0.046 44(3) D, qℓ(14)=132.289(6) MHz, μ15=+0.031 26(2) D, and qℓ(15)=107.263(4) MHz.

Vibrational Magnetic Dipole Moment of Acetylene in the ν5 Mode

The sign and approximate magnitude of the gyromagnetic ratio for the ν5 doubly degenerate bending mode of acetylene are determined by use of rotationally resolved magnetic dichroism measurement of transitions to the singly excited vibrational state. By analysis of the J-dependence of the apparent g-value for this transition, the vibrational g-factor was determined from the experimental spectrum by moment analysis to be gv = 0.48(25). This is the first such determination of gv in a degenerate state of a linear molecule using MVCD and the first determination of gv for the ν5 mode in acetylene. Simulated MVCD spectra based on the accepted ground state rotational g-value and this determination of gv agree with the observed intensity pattern, confirming the analysis.

Three-dimensional modelling of processes in the fast-axial-flow CO2 laser

The previously developed three temperature approximation for the analysis of the processes in the industrial fast-axial-flow CO2 laser is applied to the general three-dimensional (3D) modelling of the compressible flow in the laser cavity. The 3D geometrical representation and the compressible flow formulation allowed us to describe the realistic flow pattern and the distribution of the laser parameters. Our model predicts the development of the velocity profile along the laser from one which is near parabolic due to turbulent jet impingement, to one which is representative of a turbulent pipe flow. The translational temperature, T, the vibrational temperature of the symmetric stretch mode of CO2 T1, (almost equal to the vibrational temperature of the double degenerate bending mode of CO2, T2), the vibrational temperature of the asymmetric stretch mode of CO2, T3, and the vibrational temperature of N2, T4, are shown to increase along the laser axis except under the inlet openings, with T reaching about 360 K, T1 approximately=T2 reaching about 400 K, and T3 and T4 reaching about 3000 K. The values of T and flow velocities away from the inlet openings coincide within the accuracy of about 10% to those predicted by the 2D model. The average values of T3 and T4 (about 2500 K) seem to be in better agreement with experimental observations than those predicted by the 2D model. The predicted population inversion reaches its maximum value of about 5*1020 m-3 inside the recirculation zones between the inlet openings. We believe that our approach to the modelling of the processes in the CO2 laser may have a wide range of scientific and industrial applications far beyond the particular type of laser discussed in this paper.

Intramolecular vibrational redistribution of energy in the stimulated emission pumping spectrum of acetylene

Using a combination of low resolution dispersed Ã→X̃ fluorescence spectra and high resolution stimulated emission pumping, we have spectroscopically identified the first stages of vibrational energy flow in the highly vibrationally excited acetylene prepared by Ã→X̃ emission over the energy range 5 000–18 000 cm−1. A detailed study of the stimulated emission pumping (SEP) spectrum of acetylene in the EVIB=7000 cm−1 region, in which we report spectroscopic constants and rovibrational term values for 12 vibrational levels, has conclusively shown that Darling–Dennison resonance between the cis and trans degenerate bending vibrations is the first step in the redistribution of vibrational energy from the initially excited Franck–Condon bright CC stretch and trans-bend vibrational combination levels. This allows an extension of our prior dispersed fluorescence (DF) assignments which suggested the crucial role of Darling–Dennison coupling between the cis and trans bends in IVR [J. Chem. Phys. 95, 6336 (1991)]. We prove that the symmetric CH stretch vibration, previously thought to play a crucial role in the redistribution of vibrational energy, is Franck–Condon inactive. We have also shown that vibrational-l-resonance among the states with excitation of both degenerate bending modes, when combined with a Fermi resonance which couples CC stretch/trans/cis-bend excited states to the antisymmetric CH stretch, determines the subsequent flow of vibrational energy after the Darling–Dennison bending resonance. These resonances all scale with vibrational excitation in nearly the simple manner expected for the lowest order anharmonic terms in the Hamiltonian, which allows the prediction of the fastest processes at high energy from a detailed study of the high resolution spectrum at lower energy. We find some interesting rules for vibrational energy flow in the short time dynamics: (i) CC stretch excitation is necessary for stretch–bend coupling; (ii) if V2″ and V4″ are the quantum numbers of the initially excited bright state, and vb″ = v4″ + v5″ is the total bending quantum number of a state coupled to that bright state, then V4″ ≥ vb″ ≥ (V4″–2V2″); (iii) the total stretch quantum number ns″ = (v1″ + v2″ + v3″) is also conserved by the short time dynamics. These are severe and well characterized restrictions on the range of quantum numbers accessible to the initial bright state during the first stages of intramolecular vibrational redistribution of energy.

Van der Waals rovibration levels and the high resolution spectrum of the argon–benzene dimer

The van der Waals vibrations of Ar–benzene are calculated from two different intermolecular potentials, which are analytic fits to the same ab initio potential. The rovibrational Hamiltonian was derived earlier; the wave functions of the large amplitude vibrations are expanded in products of harmonic oscillator functions. The rotational structure of each van der Waals state is obtained from perturbation theory, as well as from variational calculations of the complete rovibrational states for J=0, 1, and 2. The degenerate bending modes and combinations have a large vibrational angular momentum; for their rotational structure it is important to include all first, second, and higher order rovibrational (Coriolis) coupling. The calculated vibrational frequencies, the information about rovibrational coupling, and the PI(C6v) selection rules for van der Waals transitions, in combination with the vibronic 601 transition on the benzene monomer, lead to a partially new assignment of the three van der Waals sidebands observed in high resolution UV spectra.

The millimeter-wave rotational spectrum of tertiary butyl isocyanide

The millimeter-wave rotational spectrum of tertiary butyl isocyanide, (CH 3) 3CNC, was measured in the ground state and in the first excited state of the doubly degenerate CNC bending mode v β . Accurate spectroscopic constants for both states have been determined from frequency measurements spanning the range 146–333 GHz. The results are compared with those for tertiary butyl cyanide, for which improved ground state sextic distortion constants are reported. The experimental quartic centrifugal distortion constants and the Coriolis coupling constant ξ β are well reproduced by a rudimentary force field calculation. Coriolis coupling constants for bending modes of linear segments attached to symmetric top C 3 v molecules based on a tetrahedrally substituted carbon atom are compared and factors responsible for changes in their values are identified and discussed.

Microwave spectrum, average structure and dipole moment of 1-chloropropyne, CH3C ? CCl

The microwave spectrum of 1-chloropropyne, CH3C CCl, has been reinvestigated in the frequency range 8–41 GHz. Previous ambiguities in the ground-state centrifugal distortion constants have been removed. Microwave data for ten isotopomers have been used to calculate the zero-point average structure after the necessary vibrational corrections:r(CC)= 1.201(2)A, r(C—C)= 1.461(1)A, r(C—Cl)= 1.643(2)A, ∠HCH = 108.4(2)°, r(C—H)= 1.103(5)AThe ground-state dipole moment has been determined to be 1.409(3) D (1D ≈ 3.335 64 × 10–30C m) from Stark-effect measurements. The vibrational satellite series from the lowest degenerate bending mode ν10 has been assigned. For V10= 1/-type doubling has been measured, giving q10= 2.029 (5) MHz which gives the wavenumber of ν10 to be 184(8) cm–1.

Vibrationally highly excited acetylene as studied by dispersed fluorescence and stimulated emission pumping spectroscopy: Vibrational assignment of the feature states

The dispersed fluorescence (DF) and stimulated emission pumping (SEP) spectra of acetylene originating from single rovibronic levels of the à 1Au state were measured with resolutions of 30 and 0.5 cm−1, respectively, in order to examine the vibrational level structure of the electronic ground X̃ 1Σ+g state. The SEP spectra revealed that the number of vibrational levels under each peak in the DF spectra increases with vibrational energy from a single vibrational level below 8000 cm−1 to as many as ten vibrational levels above 16 500 cm−1. Taking account of the fact that a peak in the DF spectrum in the high energy region is composed of more than one level, a DF peak is called a feature state (or a feature). In the DF spectra from two trans-bending levels (v3=2 and 3) of the à state a total of 140 DF features between 5 700 and 21 200 cm−1 were detected and long progressions in the trans bend (v″4=6 –18) and CC stretch (v■2=0 –6) were identified. Below 14 000 cm−1, 26 out of the 50 observed features were unambiguously assigned to these two modes and represented by a second order anharmonic expansion within the ∼20 cm−1 experimental error. At least three additional trans-bend progressions built on excitation in third vibrational mode were identified. Possible assignments of the third mode to the CH stretch (ν″1) and the cis bend (ν■5) are compared. The Darling–Dennison (DD) resonance between the two degenerate bending modes (trans and cis) was proposed as a mechanism to lend Franck–Condon (FC) intensity to the ν″5 mode. The vibrational analysis of the DF features shows that the DF features correspond to the zero-order FC bright basis states. Each feature represents a group of levels which share the character of a zero-order FC bright level. Above 14 000 cm−1, characteristic groups of DF features with a width of around 300 cm−1 appear in the DF spectra originating from both v3=2 and v′3=3. The relative intensity patterns within each group of features in the two DF spectra are nearly identical. Three anharmonic resonances, including the DD resonance, are proposed as a plausible mechanism which splits a single FC bright state into several DF features. The SEP measurement revealed that a single DF feature splits further into several features with widths around 0.5 cm−1. The characteristic nested level structure identified in the DF and SEP spectra are explained in terms of a stepwise energy flow via a series of anharmonic resonances from the initially excited CC stretch/trans-bend vibrations to the remaining vibrational modes.

Structural phase transition in the ordered fluorides MIIZrF6 (MII=Co,Zn). II. Brillouin and Raman scattering study

For pt.I see ibid., vol.2, p.7373 (1990). The first-order ferroelastic Fm3m to or from R3 structural phase transition occurring in ordered MIIZrF6 fluorides (MII=Co,Zr) is studied by means of Brillouin and Raman scattering experiments. The Brillouin data obtained with a CoZrF6 single crystal show that the elastic constant C44 does not change in the cubic phase, when the transition temperature (Tc=272+or-1 K) is approached from above. The Raman spectra of CoZrF6 and ZnZrF6 in the cubic phase are consistent with group-theoretical predictions; in the rhombohedral phase, the spectra exhibit a splitting of the nu 5 triply degenerate bending mode of the MII(Zr)F6 octahedra and show the existence of two soft rotatory modes of these octahedra. From these results and group-theoretical considerations, it is concluded that the phase transition can be considered as improper ferroelastic, driven by octahedra rotations; possibly, an intermediate behaviour between true displacing and order-disorder regimes takes place in these materials.

Quantum theory and collisional propensity rules for rotationally inelastic collisions between polyatomic molecules (NH3 and CO2) and an uncorrugated surface

We present the general quantum theory of collisions of a symmetric top molecule with an uncorrugated surface. The similarities between the description of collisions of a molecule with a structureless atom and a flat surface allow us to exploit earlier gas-phase results. We then derive several collisional propensity rules: (1) In experiments in which both inversion states in the initial J,K doublets of para-NH3 are equally populated, both inversion states of all collisionally excited levels must also be equally populated. If, however, the initial inversion level can be state selected, then unequal populations will be observed in collisionally excited inversion doublets. (2) For transitions from the J=0 level of ortho-NH3 into rotational levels of the K=3 stack, a strong propensity will exist toward conservation of the inversion symmetry for transitions into levels with J′ odd, but toward a change in the inversion symmetry for transitions into levels with J′ even. (3) If the odd terms in the angular expansion of the potential dominate, then for transitions out of rotational levels with J>0 in the K=0 stack of ortho-NH3 into rotational levels of the K=3 stack, a strong propensity will exist toward population of the upper level of the inversion doublet if the initial state has even J, and toward population of the lower level if the initial state has odd J. Using the similarities between the wave functions of a symmetric top and those of a linear polyatomic molecule with degenerate bending modes, we derived several propensity rules for the specific case of collisions of CO2 (0000) with an uncorrugated surface. In collisions which excite the low-lying (0110) bending vibration, if the initial rotational quantum number is small, then we predict that the probability of transition into a final state with J′ odd will be much larger than for transition into a final state with J′ even.

Relationship between least-squares-surface and celles-darling's hyperspherical coordinates

The Carrington-Miller reaction-surface approach to a nearly collinear reaction in a triatomic system is used to substantiate the bending-corrected rotating linear model of Walker and Hayes. To avoid couplings between mutually perpendicular bending vibrations the change of variables suggested by Carrington and Miller is slightly modified by describing overall rotation of the triatomic by means of the body-fixed frame with the polar angle of the double degenerate bending mode used as the third Euler angle. It is proved that axes of the frame defined in such a way are directed along the principal axes of the triatomic and that the appropriate parameterization of the collinear reaction surface leads to Celles-Darling's hyperspherical coordinates ξ,η,χ.

Copper trimer: a revised assignment of the upper state of the 5397 Å system

In light of recent fluorescence spectra obtained for the 5397 Å system of Cu 3, this system is reassigned as à 2A 1-X̃ 2E'. This assignment explains the observed bands without the need to invoke vibronic or Coriolis perturbations. It also accounts for the anomalous pattern of linewidths observed for the higher vibronic levels of the à 2A 1 state as unresolved splittings of the multiply excited doubly degenerate bending mode. The implications for the analysis of the ground state potential energy surfaces are discussed.

High-energy overtone spectroscopy of some deuterated methanes

High-energy overtone photoacoustic spectroscopy of gas phase CHD3 (ΔvCH=5,6, and 7), CH2D2, CH3D, and CH4 (ΔvCH=6) is reported. The overtone and combination bands of CHD3 display partially resolved rotational structure with laser limited linewidths (∼0.5 cm−1). A combination sum analysis is used to generate excited state rotational constants B′. We present an analysis of the Fermi resonances of CHD3 which indicates strong interactions of the CH stretch with degenerate bending modes. The relative intensities of the Fermi interacting states are in agreement with those calculated from an analysis based on frequency shifts and a two or three level model. However, the rotational B′ constants are not explained by such simple models indicating further interactions with states as yet unobserved. An upper limit of 10 cm−1 is estimated for the splitting of the ‖6,0〉± local mode states for CH2D2, giving support to a description based on the local mode picture. For CH3D and CH4 the spectra are apparently congested by overlapping overtone and combination bands and perhaps other mechanisms not identified in this work. Generally, our results emphasize the importance of the interactions of CH stretching with CH bending motions.

Densities of vibrational states of given symmetry species. Linear molecules and rovibrational states of nonlinear molecules

A simple statistical expression is given for the density of states of any symmetry species for linear molecules. Molecules with one and two pairs of doubly degenerate bending modes are considered. The results of our previous paper for vibrational states of nonlinear molecules are also extended to include density of rotational-vibrational states by symmetry species. The various expressions are tested by comparing with exact counts of states.

ChemInform Abstract: THE ROTATIONAL SPECTRUM AND MOLECULAR STRUCTURE OF THE BENZENE‐HYDROGEN CHLORIDE COMPLEX

The microwave spectrum of the weakly bound complex benzene–HCl was studied in the gas phase using Fourier transform microwave spectroscopy carried out in a Fabry–Perot cavity with a pulsed supersonic nozzle as the molecular source. Several R‐branch a‐dipole transitions have been observed for benzene–H 35Cl, benzene–D 35Cl, benzene–H 37Cl, and benzene(d6)–H 35Cl. The spectrum was characteristic of a symmetric top, indicating that the time averaged displacement of the H and Cl atoms from the benzene C6 axis is zero. Deuterium substitution of HCl demonstrated that the acidic proton lies between the Cl atom and the benzene ring. The chlorine nuclear quadrupole coupling constant χClaa, was measured for all four isotopic species and is interpreted in terms of a projection of the chlorine quadrupole coupling constant in free HCl, averaged over two degenerate vibrational ground state bending modes involving the angles between the benzene C6 axis and the HCl bond axis. The spectroscopic constants for benzene–HCl are: aNumbers in parentheses represent one standard deviation in the fit.

The rotational spectrum and molecular structure of the benzene–hydrogen chloride complex

The microwave spectrum of the weakly bound complex benzene–HCl was studied in the gas phase using Fourier transform microwave spectroscopy carried out in a Fabry–Perot cavity with a pulsed supersonic nozzle as the molecular source. Several R-branch a-dipole transitions have been observed for benzene–H 35Cl, benzene–D 35Cl, benzene–H 37Cl, and benzene(d6)–H 35Cl. The spectrum was characteristic of a symmetric top, indicating that the time averaged displacement of the H and Cl atoms from the benzene C6 axis is zero. Deuterium substitution of HCl demonstrated that the acidic proton lies between the Cl atom and the benzene ring. The chlorine nuclear quadrupole coupling constant χClaa, was measured for all four isotopic species and is interpreted in terms of a projection of the chlorine quadrupole coupling constant in free HCl, averaged over two degenerate vibrational ground state bending modes involving the angles between the benzene C6 axis and the HCl bond axis. The spectroscopic constants for benzene–HCl are: aNumbers in parentheses represent one standard deviation in the fit.