Vibrational Transition Probabilities Research Articles

Multi-temperature vibrational energy relaxation rates in CO2

Rates of vibrational energy relaxation in carbon dioxide are studied in the framework of the three-temperature kinetic-theory approach. Vibrational–translational transitions in the bending mode and inter-mode exchange of vibrational quanta are considered. In the zero-order approximation of the generalized Chapman–Enskog method, the energy relaxation rates in the coupled symmetric–bending and asymmetric modes are expressed in terms of thermodynamic forces similar to chemical reaction affinities, and a compact representation for the vibrational energy production rates is proposed. Linearized theory is developed, and analytical ratios of linearized relaxation rates to those defined by the original Landau–Teller (LT) theory are obtained. The relaxation rates are calculated using the Schwartz–Slawsky–Herzfeld (SSH) and forced harmonic oscillator models for the vibrational energy transition probabilities in the temperature range 200 K–10 000 K. For inter-mode exchanges, using the SSH theory yields significantly underpredicted relaxation rates. The ranges of applicability for the LT formula and linearized theory are estimated; the original LT formula for inter-mode vibrational energy exchanges is not capable of accounting for the excitation of both vibrational modes; linearized models yield better results. Possible steps for improving the numerically efficient LT model are proposed.

Radiative lifetimes of vibrational levels and transition probabilities of spontaneous emissions of the six lowest-lying triplet states of AlN radical.

The potential energy curves of 23 states of AlN radical are calculated to accurately determine the first several lowest-lying singlet and triplet states. The calculations are done using the CASSCF method, which is followed by the valence internally contracted MRCI approach. The rotationless radiative lifetimes of the vibrational levels are approximately 10-7-10-8 s for the C3Π, D3Π, and E3Δ states, 101-10-4 s for the A3Σ- state, and 10-4-10-5 s for the B3Σ+ state. The origins of the vibronic bands and the radiative lifetimes agree well with the available experimental and other theoretical results. The Einstein coefficients of many vibronic emissions are large for the C3Π-X3Π, C3Π-A3Σ-, D3Π-X3Π, D3Π-A3Σ-, and E3Δ-X3Π transitions and therefore, these transitions are strong. The emissions of the E3Δ-D3Π system are so weak that it is difficult to measure them through spectroscopy. The spectral distribution of the vibronic emissions is evaluated for the transitions of 12 pairs of states. In terms of the radiative lifetimes and transition probabilities obtained here, several spectroscopic routines for observing these states via spectroscopy are proposed.

Direct Shocks in Vibrationally Nonequilibrium Diatomic Gases at Various Distances from Critical Cross-Section of Nozzle

The high-temperature diatomic gas flows are considered in expanding nozzles under the conditions of a disturbance of the equilibrium distribution over vibrational levels of the molecules. The investigation of such flows is bound up with the problem of the inversion of the vibrational populations in the active mediums of molecular lasers. Under diverse values of the pressure overfall on coming out of the nozzle the shock waves can arise at various distances from critical cross-section. Under these conditions the research of the molecular distributions over vibrational levels behind such shocks acquires special significance. Relaxation processes behind a shock-wave front in a vibrationally nonequilibrium gas have been analyzed previously using differential equations for the vibrational populations. In our paper a shock wave is modeled by a thin transient layer between two vibrationally nonequilibrium quasi-stationary states. Generalized conditions of dynamic consistency are derived. The methods of kinetic theory are used. This approach does not allow one to determine the vibrational populations behind a shock wave at various distances from its front. However, it enables one to find the velocity of the gas, the total number of molecules in unit volume, the gas temperature and the temperature, called by Treanor the temperature of the 1st vibrational level, directly behind a shock wave (outside the relaxation zone). The knowledge of these values allows one to determine all parameters of interest using the kinetic theory methods. An advantage of this approach is that the considerably less number of equations is used and the need to know the probabilities of different vibrational transitions is eliminated. Earlier it was shown that the inversion of vibrational populations decreases when the flows pass through a shock wave. In present paper we note two competing factors. The further direct shock is from critical cross-section of the nozzle, the more the nonequilibrium degree of vibrational distributions and the inversion of vibrational populations are. In connection with that the intensity of a shock wave increases. It leads to a decrease of the vibrational nonequilibrium and the inversion of vibrational populations.

Algebraic methods applied to the study of energy transfer in anharmonic systems

We make use of two different methodologies to study the transition probabilities in a molecular anharmonic system in the presence of an external perturbation. For the first method, we use a series expansion of the displacement coordinate keeping up to fourth order terms; for the second method we use a deformed algebra to approximate the anharmonic Hamiltonian via a harmonic oscillator's Hamiltonian written in terms of deformed operators. We evaluate vibrational transition probabilities as a function of the collision energy and compare the results obtained with the two approaches.

Electronic states and spectra of BiTe

NIR/VIS emission spectra of the bismuth telluride radical, BiTe, were measured in the 3600–20 000 cm −1 region with a Fourier-transform spectrometer. BiTe was produced by reaction of bismuth and tellurium vapors and excited by energy transfer from metastable oxygen O 2( a 1Δ g) in a fast-flow system. The spectrum of BiTe was found to be markedly different from those of the previously studied BiO, BiS and BiSe radicals. The A 2 4Π 1/2 → X 1 2Π 1/2 transition which forms the most prominent and extended band system in these molecules was not observed for BiTe, and the X 2 2Π 3/2 → X 1 2Π 1/2 fine structure transition shows up with a different structure and at much lower wavenumbers than in the spectra of the lighter bismuth chalcogenides. The only common feature is the C 1 4Σ − 1/2 → X 1 2Π 1/2 system which is found in the range 16 500–19 000 cm −1 similar to the three other molecules. Besides the X 2 → X 1 and C 1 → X 1 systems, seven other transitions show up by short Δ ν = 0 sequences only. With help of the data derived from the analyses of the X 2 → X 1 and C 1 → X 1 systems and theoretical predictions of electronic and vibrational energies and transition probabilities of the strongest transitions of BiTe by Lingott et al. [7] the spectra were assigned to the transitions C 1 4Σ − 1/2 → X 2 2Π 3/2, C 1 4Σ − 1/2 → A 2 4Π 1/2, A 4 4Π 1/2 → A 2 4Π 1/2, A 4 4Π 1/2 → X 2 2Π 3/2, B 1 2Π 1/2 → A 2 4Π 1/2, B 1 2Π 1/2 → A 1 4Π 3/2, and B 2 2Π 3/2 → X 2 2Π 3/2.

Quantum dynamics manipulation using optimal control theory in the presence of laser field noise

We discuss recent advances in optimal control theory (OCT) related to the investigation of the impact of control field noise on controllability of quantum dynamics. Two numerical methods, the gradient method and the iteration method, are paid particular attention. We analyze the problem of designing noisy control fields to maximize the vibrational transition probability in diatomic quantum systems, e.g. the HF and OH molecules. White noise is used as an additive random variable in the amplitude of the control field. It is demonstrated that the convergence is faster in the presence of noise and population transfer is increased by 0.04% for small values of noise compared to the field amplitude.

Quantum dynamics of vibrational excitations and vibrational charge transfer processes in H+ + O2 collisions at collision energy 23 eV

Quantum mechanical study of vibrational state-resolved differential cross sections and transition probabilities for both the elastic/inelastic and the charge transfer processes have been carried out in the H+ + O2 collisions at the experimental collision energy of 23 eV. The quantum dynamics has been performed within the vibrational close-coupling rotational infinite-order sudden approximation framework employing our newly obtained quasi-diabatic potential energy surfaces corresponding to the ground and the first excited electronic states which have been computed using ab initio procedures and Dunning’s correlation consistent-polarized valence triple zeta basis set at the multireference configuration interaction level of accuracy. The present theoretical results for elastic/inelastic processes provide an overall agreement with the available state-selected experimental data, whereas the results for the charge transfer channel show some variance in comparison with those of experiments and are similar to the earlier theoretical results obtained using model effective potential based on projected valence bond method and using semi-empirical diatomics-in-molecules potential. The possible reason for discrepancies and the likely ways to improve the results are discussed in terms of the inclusion of higher excited electronic states into the dynamics calculation.

Quasiclassical predictions of final vibrational state distributions in reactive and nonreactive collisions

The validity of quasiclassical and semiclassical trajectory methods for predicting state-to-state vibrational transition probabilities in collisions of atoms with diatomic molecules is discussed with special emphasis on tests against accurate quantum calculations for He + H2, H + Cl2, and I + H2 collisions.

Calculation of radiative transition probabilities and radiative recombination rate coefficients for H2, OH, H 2 + and OH+ molecules

A method is presented to calculate the radiative transition probabilities and the radiative recombination rate coefficients between electronic molecular states. Total transition probabilities are determined from vibrational transition probabilities without considering the detailed rotational structure of the molecular electronic states. Radiative recombination rate coefficients are obtained from the computation of vibrational photo-ionisation cross sections. Concerning spontaneous emission, Lyman (B → X) and Werner (C → X) band systems of H2 and Meinel (A → X), (B → A) and (B → X) band systems of OH are investigated. For radiative recombination, transitions between H 2 + (X) and H2(X), and between OH+(X, a, A, b, and c) and OH(X) are considered. Transition probabilities and recombination rate coefficients are calculated as a function of temperature in the range 1500–15 000 K.

Modeling of a Vibrational Transition Collisional Model for Diatomic Molecules (1st Report, Vibrational Transition Probability)

The direct simulation Monte Carlo (DSMC) method is widely used for simulating rarefied gas flows, and in most cases, the phenomenological model with a local equilibrium assumption is chosen as a collision model. Since most collisions in the rarefied gas regime are binary ones, to make the vibrational transitional collision model for the DSMC method without the local equilibrium assumption, binary collision processes of diatomic molecules were analyzed. The semiclassical approach, in which the vibrational motion is treated quantum mechanically and other degrees of freedom are investigated with the classical mechanics, was introduced. The scheme was verified using the vibrational transition rate coefficient comparing with the empirical relation and the existent numerical results. The transition probability was obtained as a function of the initial translational and rotational energy. From collinear collisions, the transition probability can be described with a simple function of the relative translational energy. The total rotational energy of collisional pairs is appeared to be important for general collisions with rotational energies.

Molecular parameters for the gas phase molecules SbO and SbP

Franck-Condon factors and r-centroids, which are very closely related to relative vibrational transition probabilities, were evaluated by the numerical integration procedure for the bands of the A2?3/2 - X2?3/2, C2? - X2?3/2 and D2? - X2? systems of the isotopic SbO molecule and for the B1? - X1?+ system of the isotopic SbP molecule, using a suitable potential.

Analytical control of small molecules by intense laser pulses in an algebraic model

In this paper, we study the laser-pulse control of vibrational excitation for small molecules by employing an algebraic model. The analytical expression for the vibrational transition probability is obtained by using an algebraic approach. Selective vibrational excitation of diatomic and linear triatomic molecules are achieved. The influence of laser pulse frequencies and shapes on the control are studied.

Study on infrared multiphoton excitation of the linear triatomic molecule by the Lie-algebra approach

Infrared multiphoton vibrational excitation of the linear triatomic molecule has been studied using the quadratic anharmonic Lie-algebra model, unitary transformations, and Magnus approximation. An explicit Lie-algebra expression for the vibrational transition probability is obtained by using a Lie-algebra approach. The infrared multiphoton vibrational excitation of the DCN molecule is discussed as an example.

Lie algebraic approach to multiphoton selective excitation of linear triatomic molecules in intense infrared laser fields

The multiphoton selective excitation of linear triatomic molecules is studied by using a Lie algebraic approach. The vibrational transition probability and the long-time averaged vibrational transition probability, which are functions of external field frequency and time for HCN and DCN molecules, are discussed. The selective vibrational excitation of the target states in chirped and shaped infrared laser fields is obtained as well.

Molecular parameters for the band systems A, B-X of AuH and A-X of AuD

Franck-Condon factors (vibrational transition probabilities) and r-centroids have been evaluated by a numerical integration procedure for the bands of A 0+g - X 1S+, B 0+g - X 1S+ systems of AuH and A 0+ - X 1S+ system of AuD molecules using a suitable potential. The physical and astrophysical significances of our evaluated Franck-Condon factors and r-centroids have also been discussed, which would be helpful in the prediction of the presence of AuH and AuD molecules in various celestial bodies.

Franck-Condon factors and r-centroids for certain band systems of astrophysical molecules SrF and ScF

The Franck-Condon factors and r-centroids, which are very closely related to vibrational transition probabilities, have been evaluated by the more reliable numerical integration procedure for the bands of B2∑+ − X2∑+, F2∑+ − X2∑+ systems of SrF and C1∑+ − X1∑+, G1Π − X1∑+ systems of ScF molecules of astrophysical interest, using a suitable potential.

Fine-tuning molecular acoustic models: sensitivity of the predicted attenuation to the Lennard–Jones parameters

In a previous paper [Y. Dain and R. M. Lueptow, J. Acoust. Soc. Am. 109, 1955 (2001)], a model of acoustic attenuation due to vibration-translation and vibration-vibration relaxation in multiple polyatomic gas mixtures was developed. In this paper, the model is improved by treating binary molecular collisions via fully pairwise vibrational transition probabilities. The sensitivity of the model to small variations in the Lennard-Jones parameters--collision diameter (sigma) and potential depth (epsilon)--is investigated for nitrogen-water-methane mixtures. For a N2(98.97%)-H2O(338 ppm)-CH4(1%) test mixture, the transition probabilities and acoustic absorption curves are much more sensitive to sigma than they are to epsilon. Additionally, when the 1% methane is replaced by nitrogen, the resulting mixture [N2(99.97%)-H2O(338 ppm)] becomes considerably more sensitive to changes of sigma(water). The current model minimizes the underprediction of the acoustic absorption peak magnitudes reported by S. G. Ejakov et al. [J. Acoust. Soc. Am. 113, 1871 (2003)].

Atomic oxygen profiles (80–94 km) derived from Wind Imaging Interferometer/Upper Atmospheric Research Satellite measurements of the hydroxyl airglow: 1. Validation of technique

The use of satellite measurements of the hydroxyl airglow volume emission rate profile to infer the atomic oxygen profile of the mesopause region is complicated by uncertainties as to the collision de‐excitation mechanism and the vibration transition probabilities that are needed for the analysis. In this paper, we demonstrate that the shape of the derived atomic oxygen profiles is, to a large extent, independent of the choice of these factors. We use data from two nights of observation from the Wind Imaging Interferometer (WINDII) instrument onboard Upper Atmospheric Research Satellite (UARS) where the instrument observed the hydroxyl emission and the oxygen greenline emission on alternate orbits. The comparison between the derived atomic oxygen profiles from the two emissions is difficult because the region of overlap of good quality data lies in between the peaks and is small (about 4 km). Also, the altitude of the good overlap is not fixed but is a function of both latitude and local time and may lie anywhere in the altitude range from 88 to 94 km because the heights of the emission layers also change. We have adopted a technique of doing the comparison only at certain altitude/local time combinations depending on where the best data exists. The hydroxyl parameter set that used Goldman transition probabilities and a sudden death quenching model best fit the greenline derived atomic oxygen and will be used to complete a full atomic oxygen climatology from 80 to 110 km.

Non-equilibrium dissociation rates in expanding flows

In this Letter, non-equilibrium dissociation rates in expanding gas flows are studied taking into account state-to-state vibrational–chemical kinetics. A comparison of the results obtained in the state-to-state approach with the ones based on the quasi-stationary two-temperature vibrational distributions for harmonic and anharmonic oscillators and on the thermal equilibrium one-temperature distribution is presented. The influence of vibrational energy transition probabilities and nozzle profiles on vibrational level populations and dissociation rates is also discussed.

Franck-Condon factors and r-centroids for certain band systems pf astrophysical molecule BeF

The Franck-Condon factors and r-centroids, which are very closely related to vibrational transition probabilities, have been evaluated by the more reliable numerical integration procedure for the bands of B 2 Σ+ - X 2 Σ+, C 2Σ+ - X 2 Σ+ andC 2 Σ+ - A 2 Πr systems of the astrophysical molecule BeF, using a suitable potential.