Vibrational Transition Probabilities Research Articles

Semiclassical algebraic description of inelastic collisions

An algebraic semiclassical approach to the calculation of vibrational transition probabilities in inelastic collisions between molecules is presented. Translational motion is treated classically, while vibrational motion is described quantum mechanically using the generalized coherent state of a proper Lie algebra. This leads to a set of linear differential equations for the parameters of the coherent state, coupled to the classical Hamilton equations. Use is also made of a time dependent canonical transformation to simplify the algebraic structure. Two examples are treated explicitly: colinear collision of an atom and a diatom and a diatom–diatom collision. Good agreement with the exact quantum results is found.

Vibrational state resolved measurements of differential cross sections for H++O2 charge transfer collisions

Vibrational state-to-state charge transfer cross sections have been obtained for H++O2 collisions at Ecm =23.0 eV in a differential scattering experiment by measuring the product H atom energy distribution in the range 0°≤θ≤11°. The results show a strong dependence of the distribution of vibrational transition probabilities P(O2, v=0→O+2, v″) on the scattering angle. At very low angles (θ≲2°) we find a strongly enhanced contribution of the more resonant states v″=3–6 compared to a Franck–Condon distribution, which is peaked at v″=1 and, on the other hand, at moderate angles of about θ=4° comes very close to the measured spectra. At even larger angles increasing deviations from the Franck–Condon distribution towards larger excitation of higher vibrational states are observed. An explanation of these and the related results for the nonexchange collisions leading to neutral O2 vibrational excitation is given in terms of the underlying potential energy surfaces.

Vibrational excitation of the OH molecule by proton (H+) impact in the presence of an infrared laser beam: a non-perturbative technique

The general theory of vibrational excitation of a diatomic OH molecule due to collision with a proton (H+) in the presence of an infrared laser beam, using the quasi-energy approach (non-perturbative) is presented. The vibrational transition probability and the excitation cross section are calculated for different field intensities and the effect of the collision on the radiative excitation process is investigated by changing the various collision parameters and using different values of the molecular field detunings.

Interaction of electromagnetic field with the OH radical: A non-perturbative approach

A non-perturbative approach for the study of the interaction of a hydroxyl (OH) radical with infra-red radiation is presented. The dressed states and vibrational transition probability of OH radical are defined by a quasi-energy approach (non-perturbative).

Angularly resolved vibrational excitation in Na2–He collisions

We report angle-resolved measurements of vi=0 → vf=1 vibrational transitions in Na2–He collisions at an energy of 90 meV. The agreement with calculated cross sections using an ab initio surface is good, both in the angular variation of the cross section as well as with respect to its magnitude relative to the vibrationally elastic process. The calculated (vi=0, ji=0) → (vf=1, jf ) differential cross sections are discussed in some more detail. They show structure, in addition to the rainbow oscillations, related to the fact that the vibrational transition probability vanishes for a specific approach angle.

Franck-condon analysis on photoelectron spectra of the methyl radical and its deuterated species

The vibrational fine structure observed in the first photoelectron bands of the methyl radical and its deuterated species is attributed mainly to excitations of the out-of-plane vibration and are well reproduced by invoking a potential function of the form V(q) = q 2 2 + σ q 4 for the neutral ground state and a harmonic oscillator potential for the ionic state. The results of calculations support the planarity of both the methyl radical and its ion. In addition, the effect of anhannonicity on vibrational energy spacings and transition probabilities due to the presence of the quartic terms is investigated.

The geometry of ethylene in the ground ionic state

Franck—Condon analyses were carried out on the first photoelectron band of ethylene to deduce the CC bond length, the CH bond length and the HCH bond angle in the ground ionic state 1 B 3u|to be 1.42 ± 0.01 Å, 1.09 ± 0.01 Å and 120 ± 1° respectively. These structructural parameters have values close to those previously obtained in the 1 B 3u Rydberg state (see ref. 10). With regard to the vibrational energies of the torsional mode of ethylene and its deuterated species in the 2 B 3u and 1 B 3u Rydberg states, they were analysed by using a one-deminsional potential function constructed from the harmonic oscillator term perturbed by a Gaussian barrier. The equilibrium torsional angles of ethylene thus obtained are found to be 28° and 25°, respectively, in the 2 B 3u and 1 B 3u states. In addition, the observed vibrational intensity distributions of the torsional mode accompanying electronic transitions from the ground state to the two 2 B 3u and 1 B 3u states are well reproduced by the proposed potential. Moreover, it is found that these vibrational transition probabilities are sensitive to the magnitude of the barrier heights, the shape of the potentials and the frequency changes upon electronic transitions and thus should be useful in providing structural information about the molecules under study.

Time-of-flight spectroscopy of high-overtone mode-selective vibrational excitation of CF4 and SF6 in collisions with H+(D+) at energies between 10 and 28 eV

Time-of-flight spectra for H+(D+)–CF4 and SF6 collisions have been measured with an improved resolution and at higher collision energies (10≤Elab ≤28 eV) compared to earlier work. In the low energy region (≤13 eV) new distinct peaks are resolved for both molecules corresponding to small contributions from the second infrared active ν4 mode in addition to the dominant ν3 mode observed previously. Reexamination of experimental vibrational transition probabilities reveals an almost perfect agreement with a Poisson distribution for both modes up to the n=6 overtone transition of ν3. A simple straight line theory is used to calculate the energy transfer in small angle scattering from the long-range potential in good agreement with a full classical trajectory calculation. With this theory dipole moment derivatives can be determined directly from the observed energy transfers and are found to agree well with previous infrared measurements. At larger collision energies (≥16 eV) an additional low intensity vibrational distribution is identified in the high energy loss tail of the spectra which can be attributed to small impact parameter collisions which probe the repulsive region of the potential. The observed energy transfers are also in good agreement with trajectory calculations indicating that the forced oscillator model is also applicable in the repulsive potential region for the present systems. A closer examination of the high energy loss tail reveals resolved structure which has been assigned to discrete states of the ν3 mode in CF4 up to the n=14 overtone. These new results demonstrate that H+(D+) energy loss scattering can provide spectroscopic information not readily available from other experiments.

Theory of Vibrational Relaxation of R 2★ Centres in Rare‐Gas Solids. Application to Ne 2★

AbstractA tunnel mechanism of vibrational relaxation is proposed for a class of emission centres which are characterized by a weak coupling to the crystalline environment and have vibrational quanta considerably exceeding phonon energies. For such kind of centres, e.g. for R centres in solidified rare gases, a new relaxation channel, connected with the anharmonicity of vibrations, appears. The theory is applied to the centre Ne in solid Ne: a direct calculation of the probabilities of vibrational transitions is carried out.

Experimental rovibrational populations of CO up to ν = 40 from doppler-limited fourier spectra of the sequences Δν = 1, 2 and 3 emitted by a laser type source

High-resolution emission Fourier spectra have been recorded from a CON 2HeO 2 mixture excited by dc discharge and cooled by liquid nitrogen. Intensities of all the observed rovibrational lines belonging to sequences Δν = 1, 2 and 3 of 12C 16O and 13C 16O, and Δν = 1 of 12C 16O, have been measured. The data treatment is described. Accurate determination of the rotational distribution and of the vibrational populations of the three isotopic species is performed. The Δν = 2 and 3 vibrational radiative transition probabilities, versus the Δν = 1 ones, are also given, up to ν = 40.

Collisions of polyatomic molecules with solid surfaces: A semiclassical stochastic trajectory approach

The semiclassical stochastic trajectory method is extended to the study of vibrational excitation and relaxation of polyatomic molecules in collisions with nonrigid solid surfaces. The technique involves a quantum-mechanical treatment of the molecular vibrational modes and a classical treatment of the translational and surface motion. Surface temperature effects are incorporated in the method through use of the generalized Langevin equation. The sudden approximation is used to treat the molecular rotational motion. Calculations of vibrational transition probabilities are reported for the collisions of CO2 with a Pt(111) surface, and these probabilities, when relatively small, are found to be quite sensitive to surface temperature. The results are relevant to recent experiments on the excitation and relaxation of the vibrational modes of CO2 in collisions with surfaces.

Semiclassical stochastic trajectory treatment of the scattering of molecules from (non-rigid, structured) solid surfaces

In this paper, we use a semiclassical stochastic trajectory (SST) dynamical formulation to investigate the scattering of a molecule from a non-rigid and structured solid surface. State-to-state rotational and vibrational transition probabilities have been calculated for H2 colliding with a solid whose phonon structure is modeled by that of Pt(111). Several different surface temperatures and four interaction potentials with various corrugations were considered. We found that the degeneracy summed and averaged transition probabilities were insensitive to both temperature and corrugation and were dominated by the Δ m = 0 transition. The amount of energy transfer from H2 to a solid surface was negligible compared with the initial kinetic energy of 0.1 eV while the fraction of kinetic-to-rotational energy transfer could be as large as 0.22. We have tested the validity of a decoupling approximation in which a molecular internal state is not coupled to other states with different magnetic quantum numbers m. The decoupling approximation was found to yield accurate results in this system.

N2 W 3Δu–A 3Σ+u emission in the near-infrared luminescence spectrum of N2-doped solid argon and krypton

The near-infrared emission spectrum of N2 diluted in rare-gas matrices exhibits a variety of new emission lines featuring different linewidths and decay times. One vibrational v″ progression of lines characterized by widths of 25 cm−1 and by decay times of 70 μs in Ar and of 60 μs in Kr is assigned to the forbidden electronic transition W 3Δu (v′)–A 3∑+u (v″=0–4). Selectively unrelaxed initial states v′=4 in 14N2 and v′=3 in 15N2 are observed, and the resistance of these particular levels against radiationless relaxation is attributed to bottlenecks in the cascade of internal conversion processes among the vibrational levels of the A, B, B′, and W electronic states. The assignments are based on isotope shift measurements and on quantitative estimates of allowed and induced vibrational and electronic radiative transition probabilities. The relative efficiency of multiphonon relaxation in different rare-gas matrices is discussed in the light of these and of other comparable measurements.

T-V and V–V energy transfer in collinear collision of two diatomic molecules. An application of label variable classical mechanics

The label variable classical mechanics method has been applied to the calculation of vibrational transition probabilities for T-V and V–V energy transfer in the collinear collision of two identical molecules where quantum resonance plays a crucial role. The results show that this very simple practical approach can handle the phase problem surprisingly well.

Relative band strengths from the study of intensity distribution in the A-X system of CrO

Relative integrated intensities are measured for ten bands in the vibrational structure of the astrophysically significant A 5π−X 5π system of CrO by the technique of photographic photometry. Vibrational transition probabilities are computed using the revised molecular constants of the electronic states. Using these results, the variation of electronic transition moment with the internuclear separation is found to be R e ( r) = const. × (1−0.398 r) in the range 1.60 A ̊ < r < 1.72 A ̊ . A smoothed array of band strengths is presented.

Multireference-CI calculations of radiative transition probabilities in C−2

Electronic transition moment functions for the dipole allowed transitions among the X 2∑+g, A 2Πu, and B 2∑+u states of C−2 have been calculated from highly correlated MCSCF-SCEP wave functions. Vibrational band transition probabilities for all bound–bound transitions have been evaluated, and radiative lifetimes of bound vibrational levels are obtained. For the B 2∑+u, v′=0 state, the calculated lifetime of 76.5 ns is in excellent agreement with recent experimental values. Strong emission from the A 2Πu state in the infrared spectral region is predicted.

PNO-CEPA and MCSCF-SCEP calculations of transition probabilities in OH, HF+, and HCl+

Electronic transition moment functions for the A 2Σ+–X2Π transitions in OH, HF+, and HCl+ have been calculated using RHF, PNO-CI, PNO-CEPA, MCSCF, and MCSCF-SCEP wave functions. The vibrational band transition probabilities are obtained, and the resulting radiative lifetimes are compared with measured values. For OH and HCl+ the deviations are smaller than 10%, but the theoretical lifetimes for HF+ are larger by about 300% than the experimental values. For the electronic ground states of HF+ and HCl+ vibrational transition probabilities have been calculated from MCSCF-SCEP dipole moment functions. Both ions are predicted to be excellent absorbers and emitters in the infrared spectral region.

Use of Ehrenfest's principle for inelastic collisions

By combining Ehrenfest's principle with optimised wavefunctions, closed equations of motion are obtained for mean values of observable quantities. Quantum-mechanical trajectories for average position and momentum of a particle are studied together with their corresponding fluctuations. The method is applied to the Landau-Teller model for the collinear atom-diatomic-molecule collision. Energy transfer and vibrational transition probabilities are extracted from the collision-induced trajectories. A comparison with coupled-channel results demonstrates the high accuracy of the proposed method.

Determination of the dipole moment function of an ozone molecule on the basis of vibrational transition probabilities

Analytical relationships are obtained that connect the vibrational transition moments to molecular and electrooptical parameters. On the basis of experimental data on vibrational band intensities, coefficients of the expansions of the dipole moment function of O3 are determined by using the above-mentioned expressions.

A new semiclassical approach to the molecular dynamics: Label variable classical mechanics

A new semiclassical approach to molecular collision dynamics is developed. In this approach the state of a system is described by a unit vector in Hilbert space. By choosing a reference unit vector and a continuous mapping, a correspondence between the vector in Hilbert space and the point in a label space is established, i.e., the vector in Hilbert space is parametrized or labeled by complex variables. It is shown that the label variables formally obey classical mechanics. Thus, the time evolution of the vectors in Hilbert space, i.e., the evolution of the states of the system, can be determined by calculating the evolution of the label variables classically. To illustrate this idea, the formalism for calculating the vibrational transition probability in the collinear collision A+BC is presented, and a demonstrative calculation for the collinear Secrest–Johnson model of He+H2 vibrationally inelastic scattering has been carried out. The comparison with the exact quantum results shows that the agreement is encouragingly good.