Vibrational Transition Probabilities Research Articles

Theoretical Determination of Vibrational Transition Probabilities in Diatomic Molecules

Vibrational transition probabilities in diatomic molecules are given by the square of off-diagonal matrix elements of the molecular dipole-moment function M (R). Taken separately, neither ab initio molecular calculations nor molecular beam studies of the vibrational dependence of the electric dipole moment provide enough information about M (R) to determine uniquely these off-diagonal matrix elements. We develop a method to combine the available experimental and theoretical information about M (R) so as to yield a maximum of precision in the transition amplitudes. The method invokes the linear programming algorithm. As a numerical application we present and compare with experiment results for various vibration-rotation transitions in the LiH and KF molecules.

Effects of an Attractive Well Potential on the Atom–Diatomic Molecule Collinear Collision

The effect on the vibrational transition probability of an attractive well in the interaction potential for the collinear collision of an atom with a diatomic oscillator is investigated. Two forms of the potential are considered. For a square barrier potential, a square well introduces sharp resonances in the transition probability. It is shown that the position of these resonances may be predicted by a simple formula. For a ``soft'' Morse interaction potential no resonances are observed. It is shown in this case that the transition probability is determined more by the slope of the potential at the classical turning point than by the presence or absence of an attractive well.

Semiclassical Transition Probabilities for Collinear Diatom—Diatom Collisions

The semiclassical model of Heidrich, Wilson, and Rapp is extended to include translation—vibration transition probabilities for the collinear collision of diatomic molecules. The results for H2–H2 collisions are compared with quantum mechanical results and found to be in good agreement.

Vacuum-Ultraviolet Excitation Cross Sections by Electron Impact on NO

Absolute excitation functions were measured for the NO+ A 1Π −X 1Σ+ molecular band system, the nitrogen 1200–, 1243–, and 1493–Å multiplets, and oxygen 1304–Å multiplet. Excitation was by electron impact on NO from threshold to ·250 eV. At 100 eV the excitation cross section for the NO+ A—X system is 9.7 × 10–18 cm2 while the cross sections for the nitrogen and oxygen multiplets are: N, 1200 Å − 4.8 × 10–18 cm2; N, 1243 Å–0.89 × 10–18 cm2; N, 1493 Å–1.5× 10–18 cm2; and O, 1304 Å–1.1× 10–18 cm2. From the vibrational intensity distribution of the A—X system, the variation of electronic transition moment with r centroid was determined and this result used to calculate an array of vibrational transition probabilities. In addition, cross sections were measured at 100 eV only for the N 1135–, N 1745–, O 1152–, and O 1218–Å multiplets. Cross sections for these multiplets are: N, 1135 Å – 1.6× 10–18 cm2; N, 1745 Å–0.87× 10–18 cm2; O, 1152 Å–0.85× 10–18 cm2; and O, 1218 Å–0.39× 10–18 cm2.

Calculation of Transition Probabilities for Collinear Atom—Diatom Collisions with Nonpairwise Interactions

Vibrational transition probabilities are calculated for a model collinear atom—diatom collision. The collision is that of an O atom with an N2 molecule. The interaction is 0.3 that of the corresponding triatomic, N2O. The calculation is done in the close coupling approximation which is briefly discussed. The results show many Feshbach resonances which influence the ground-state elastic probability, P11, less and less as the number of open channels increases.

A Comparison of vibrational transition probabilities for penning ionization and photoionization of no to the X 1σ + state of no +

A Comparison of vibrational transition probabilities for penning ionization and photoionization of no to the X 1σ + state of no +

Semiclassical Transition Probabilities (S Matrix) of Vibrational—Translational Energy Transfer

Uniformized coordinates and an integral expression for the semiclassical S matrix, derived elsewhere, are described and applied to vibrational transition probabilities. The expression obeys microscopic reversibility. The numerical results are compared with the exact quantum mechanical results of Secrest and Johnson.

Master Equation for the Dissociation of a Dilute Diatomic Gas. V. Effect of Energy-level Spacing

Our previous vibration–dissociation coupling calculations for H2 have been repeated for D2. Closer spacing of the vibrational energy levels in D2 leads to increased translation–vibration transition probabilities, and the effect of this is to increase the rate of recombination by the vibrational mechanism at all temperatures. These numerical experiments also clarify two other issues: (i) that the position of the bottleneck does not necessarily occur at that level above which direct collisional dissociation can take place rapidly, and (ii) that there is no simple correspondence between the position of the bottleneck and the Arrhenius temperature coefficient for dissociation.

Scmielassical Calculation of the Vibrational Transition Probabilities of Diatomic Molecules in Collision. The Effect of Vibrational Anharmonicity

Abstract The multi-state semiclassical method proposed by Sharp and Rapp for calculating the vibrational transition probabilities of harmonic oscillators in collision was extended to Morse oscillators. Model calculations have been carried out for the excitation of a vibrational ground-state hydrogen molecule colliding with a helium atom at varying relative velocity. It has been shown that the Morse oscillator model gives greater transition probabilities than the corresponding harmonic oscillator model.

Collision of an Atom and a Diatomic. The Adiabatic Approximation

The adiabatic approximation is used to compute vibrational transition probabilities for the collision of an atom and a diatomic molecule in one dimension. The accuracy of the results is evaluated in terms of a parameter β, which is proportional to the period of the oscillator divided by the length of the collision. It is seen that for small β, the error in adiabatic transition probabilities approaches zero, and that the approximation is accurate over a physically interesting range of β.

The Master Equation for the Dissociation of a Dilute Diatomic Gas. IV. The Bottleneck Phenomenon

Once the initial transients have died out, the rate constant for the dissociation or recombination of a dilute diatomic gas bears the same kind of relationship to individual translation–vibration transition probabilities as does the conductance of a generalized resistance network to the individual resistance components. Thus, it is not possible to single out any one transition which "controls" the rate of dissociation or recombination.

Infrared Emission of OH in the Fundamental and First Overtone Bands

The infrared vibration–rotation spectrum of the hydroxyl radical produced by the reaction of hydrogen atoms and ozone has been recorded. The intensity of individual lines in the fundamental sequence was found to be considerably weaker than was previously predicted. The intensity of lines in the fundamental sequence is compared with the intensity of the first overtone lines to obtain ratios of the vibrational transition probabilities. These ratios are used to remove the ambiguity of the OH dipole moment function associated with previously unknown intensities of the fundamental bands. A complete set of relative transition probabilities is given. An equilibrium flux calculation using atmospheric data is performed using the derived transition probabilities to obtain the vibrational distribution of OH at formation.

Quantum Vibrational Transition Probabilities in Atom–Diatomic Molecule Collisions. V Effects of Mass and Well Depth

The method of Cheung and Wilson is used to investigate the dependence of vibrational transition probabilities on atomic masses and on the well parameters of the intermolecular potential. The presence of a well in the intermolecular potential causes quite large changes in the transition probabilities, as do changes in the masses of the colliding particles. Difficulties in using this method on systems having certain unfavorable mass ratios had been noted earlier; a procedure is presented in which these difficulties are overcome.

Vibrational Excitation in a Morse Oscillator

Vibrational excitation in the system He+H2 is studied theoretically by considering H2 as a rotating Morse oscillator. The anharmonicity of molecular vibration is found to have only a small effect on the 0 → 1 transitions. Vibrational transition probabilities are also found to be insensitive to the rotational energy of the diatom. Following the approach of Mies and Shuler, based on the modified wavenumber approximation, three-dimensional transition probabilities are calculated from one-dimensional results and the steric factor is obtained as a function of the collision energy.

Dependence of vibrational transition probabilities on the orientation angle in the three-dimensional BC + A collission

The dependence of vibrational transition probabilities on molecular orientation in the three-dimensional BC + A collision at high velocities has been investigated. For O 2 + Ar collisions calculation of the 0 → 1 vibrational transition probability shows that the collinear orientation is very inefficient for vibrational transitions above the collision velocity of about 10 6 cm/sec when the impact parameter is greater than the Lennard-Jones parameter (i.e., b ⪢ σ). When b < σ, it is also very inefficient for velocities lower than this value. At higher collision velocities, the perpendicular orientation with nonzero impact parameter becomes efficient for vibrational energy transfer.

Classical S Matrix: Numerical Application to Inelastic Collisions

A previously developed semiclassical theory of molecular collisions based on exact classical mechanics is applied to the linear atom–diatom collision (vibrational excitation). Classical, semiclassical, and uniform semiclassical results for individual vibrational transition probabilities corresponding to the H2+He system are presented and compared to the exact quantum mechanical results of Secrest and Johnson. The purely classical results (the classical limit of the exact quantum mechanical transition probability) are seen to be accurate only in an average sense; the semiclassical and uniform semiclassical results, which contain interference effects omitted by the classical treatment, are in excellent agreement (within a few percent) with the exact quantum transition probabilities. An integral representation for the S-matrix elements is also developed which, although it involves only classical quantities, appears to have a region of validity beyond that of the semiclassical or uniform semiclassical expressions themselves. The general conclusion seems to be that the dynamics of these inelastic collisions is basically classical, with all quantum mechanical structure being of a rather simple interference nature.

Quantum Vibrational Transition Probabilities in Diatomic–Diatomic-Molecule Collisions

Collinear collisions of diatomic molecules (harmonic oscillators) are examined by means of the method of Cheung and Wilson, and the dependence of the vibrational transition probabilities on incident relative translational energy, atomic masses, and intermolecular interaction potential is ascertained. Vibration–vibration transfer processes are found to be significant but not necessarily dominant, and the matching of the vibration frequencies of the colliding molecules does not appear to be an important factor in vibration–vibration transfer. Certain mass ratios lead to computational difficulties with this method.

Vibrational Excitation in Collisions Involving Oxygen Ion Beams

Inelastic energy losses in the collisions of O+ and O2+ ions with neutral molecules have been studied in a beam apparatus designed to direct mass-analyzed low-energy ion beams onto target molecules and scan the energy, mass, and angular distributions of charged reaction products. Maxima in the scattered ion intensities are observed in the O+–O2 and O2+–Ar systems which are energetically displaced from the centroids of elastically scattered ions by amounts corresponding to known vibrational energy spacings in the respective diatomic species. Vibrational transition probabilities obtained from the inelastic energy loss data show multiquantum transitions to be more important as the reactant ion kinetic energy is increased from 10 to 20 eV. For a given reactant ion kinetic energy, higher vibrational transitions predominate at larger scattering angles. The velocity dependences of these transitions are in reasonable accord with calculations that employ a semiclassical impact parameter treatment to estimate collisional energy transfer and time-dependent wavefunctions to evaluate vibrational transition probabilities for a forced harmonic oscillator model.

Vibrational transition probabilities for the (A-X) system of BF molecule

The intensity distribution for the bands of the A-X system of the BF mole and the variation of electronic transition moment with internuclear separation has been obtained with the aid of Franck-Condon factors, r-centroids and visually estimated intensities. It has been found that Re(r¯υ′υ″) varies with r¯υ′υ″ according to Re(r¯υ′υ″ = constant × exp(0.205r) over the range 1.20Å<r < 1.45Å

Calculation of Transition Probabilities for Collinear Atom–Diatom and Diatom–Diatom Collisions with Lennard-Jones Interaction

Numerical integration of the close coupled scattering equations is performed to obtain vibrational transition probabilities for three models of the electronically adiabatic H2–H2 collision. All three models use a Lennard-Jones interaction potential between the nearest atoms in the collision partners. The results are analyzed for some insight into the vibrational excitation process, including the effects of anharmonicities in the molecular vibration and of the internal structure (or lack of it) in one of the molecules. Conclusions are drawn on the value of similar model calculations. Among them is the conclusion that the replacement of earlier and simpler models of the interaction potential by the Lennard-Jones potential adds very little realism for all the complication it introduces.