Relative Vibrational Transition Probabilities Research Articles

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.

Franck-condon factors and -centroids for certain band systems of astrophysical molecular ions CN+ and N+2

The Franck-Condon factors and r-centroids, which are very closelyrelated to relative vibrational transition probabilities, have beenevaluated by the more reliable numerical integration procedure forthe bands of c1 Σ - a1 Σ and f1 Σ - a1 Σ systems of CN+ and C2 Σ+u- X2 Σ+g and D2 Πg- A2 Πu systems of N+2 molecular ions of astrophysical interest,using a suitable potential.

Excitational, vibrational, and rotational temperatures in Nd:YAG and XeCl Laser-Induced plasmas

Laser-induced plasmas formed on graphite by a Nd:YAG laser at 1064 nm and by a XeCl laser at 308 nm were analyzed spectroscopically to determine vibrational, rotational, and excitation temperatures. For determination of vibrational and rotational temperature, the emission of the CN radical in the region between 385.1 and 388.3 nm was used to construct Boltzmann plots. Relative vibrational transition probabilities were calculated. For determination of excitation temperature, a small amount of lead or iron was added to the graphite target and Boltzmann plots were constructed using transition probabilities found in the literature.

Quantitative Laser-Induced Fluorescence Spectroscopy of the CF A2Σ+−X2Π Transition: Electronic Transition Dipole Moment Function and Predissociation

Several previously unmeasured aspects of the quantitative spectroscopy of the CF A2Σ+−X2Π transition have been investigated experimentally. Ground state CF radicals were prepared in an rf discharge chamber and laser-induced fluorescence (LIF) was excited on the A−X transition. Relative vibrational transition probabilities were deduced from dispersed fluorescence spectra emitted by CF A2Σ+ (v‘ = 0 and 1), from which the form of the electronic transition dipole moment function, Re(r), could be assessed. Reasonable agreement was found with a previous ab initio prediction of a moderate decline in Re(r) over the relevant, fairly limited range of internuclear distances sampled by the experiment. Weak fluorescence has also been detected for the first time from the heavily predissociated v‘ = 2 level. A rotationally-resolved LIF excitation spectrum was obtained. Lower and upper limits on the v‘ = 2 fluorescence lifetime were estimated to be 0.4 and 2 ns, respectively. There is a weak, if any, decline in the v‘ = ...

Transition probabilities in OH A 2Σ +-X 2Π i: bands with ν' = 0 and 1, ν″ = 0 TO 4

Experimental results for relative vibrational band transition probabilities for ν' = 0 and 1, and ν″ = 0 to 4 in the A-X electronic system of OH are presented. The measurements, part of a larger set involving ν' = 0 to 4 and ν″ = 0 to 6, were made using spectrally dispersed laser-induced fluorescence (LIF) in the burnt gases of a flame. These Einstein coefficients will be usefull in dynamics experiments for quantitative LIF determinations of OH radical concentrations in high ν″.

Relative vibrational transition probabilities in the (B 3 π g−A 3Σ u + ) system of nitrogen for Hulbert-Hirschfelder oscillator model

Hulbert-Hirschfelder (h-h) potential function has been used to obtain the relative vibrational transition probabilities for the observed bands of the first positive system of nitrogen molecule. The vibrational wavefunctions have been calculated by solving the Schrodinger equation by the method due to Langer, at low vibrational quanta and by thewkb method at high vibrational quanta. It is established that theh-h potential is superior to the often used Morse potential function for the transition under consideration.

Spectral absorption coefficients for the fundamental and first overtone vibration-rotation bands of CN

A previous measurement of the transition moment of the fundamental vibration-rotation band of CN is combined with theoretical calculations of relative vibrational transition probabilities in order to compute absorption coefficients for the CN fundamental and first-overtone bands. Line strengths for 121 lines in each branch of all fundamental and first-overtone bands with upper-transition states not greater than 6 are calculated for temperatures of 2000, 3000, and 4000 K; these line strengths are presented as averaged over 8-kayser intervals. The relative vibrational transition moments are placed on an absolute scale, and the wavenumbers of the band origins and heads are given

Franck-Condon factors and r centroids for the B-X and C-X systems of the MgF molecule

Arrays of Franck-Condon factors (qνprimeν−or+) and r centroids (rνprimeν−or+), which are closely related to relative vibrational transition probabilities, have been computed upon a Morse model for the B - X and C - X systems of the MgF molecule. This molecule is of importance to astrophysicists as it occurs in the spectra of sunspots. The r centroids for a given (νprime, ν−or+) band have been found to decrease smoothly with increase of corresponding wavelength λνprimeν−or+. The value of Δr identical with rνprime + 1,ν−or+ + 1 -rνprimeν−or+ in a sequence has also been found to remain constant. The computed values of the r centroids indicate that the potentials are neither very anharmonic nor very wide.

Photoelectron spectra and ionic structure of carbon dioxide, carbon disulphide and sulphur dioxide

Photoelectron spectra of carbon dioxide, carbon disulphide and sulphur dioxide excited by 584 Å radiation have been measured at a resolution of 20 mV over the whole energy range. Ionization potentials, vibration frequencies of the ions and relative vibrational transition probabilities are presented for carbon dioxide and carbon disulphide and are used to derived structural information about the ionic states. A vibrational analysis of the photoelectron spectrum of sulphur dioxide leads to estimates of the ionic geometry in different states and to the conclusion that dπ bonding is effective in one of the 4 b 2 or 1 a 2 orbitals.

Measurement of Threshold Electrons in the Photoionization of H2 and D2*

Measurements of electrons produced in the photoionization of H2 and D2 are reported. The experimental technique employs a differential electron-energy analyzer to detect photoelectrons produced with nearly zero initial kinetic energy (≲0.1 eV). By varying the photon energy a spectrum of “threshold” photoelectrons is recorded exhibiting the vibrational structure of the H2+ and D2+ ions. From these spectra values of I(H2), I(D2), ωe(H2+), ωe(D2+), ωexe(H2+), and ωexe(D2+) are derived. In favorable cases the relative vibrational transition probabilities are also reported and compared with theoretical predictions as well as with other experiments. Some disagreements are noted in comparing the results obtained by this method with theoretical Franck–Condon factors based on potential curves appropriate to nonrotating molecules. It is suggested that the vibration–rotation interaction should be taken into account in calculations pertaining to electronic transitions in light molecules.

Measurement of Threshold Electrons in the Photoionization of Ar, Kr, and Xe

Measurements of electrons produced in the photoionization of H2 and D2 are reported. The experimental technique employs a differential electron‐energy analyzer to detect photoelectrons produced with nearly zero initial kinetic energy (≲0.1 eV). By varying the photon energy a spectrum of “threshold” photoelectrons is recorded exhibiting the vibrational structure of the H2+ and D2+ ions. From these spectra values of I(H2), I(D2), ωe(H2+), ωe(D2+), ωexe(H2+), and ωexe(D2+) are derived. In favorable cases the relative vibrational transition probabilities are also reported and compared with theoretical predictions as well as with other experiments. Some disagreements are noted in comparing the results obtained by this method with theoretical Franck–Condon factors based on potential curves appropriate to nonrotating molecules. It is suggested that the vibration–rotation interaction should be taken into account in calculations pertaining to electronic transitions in light molecules.

Determination of O +2 first negative system relative vibrational transition probabilities

A calculation of O +4 2Σ − g→ 4Π u system r-centroids and a determination of relative vibrational transition probabilities are given.

The forbidden bands of a'− X system of nitrogen

Relative vibrational transition probabilities and r-centroids for the a' 1∑ − u − X 1∑ + g system of nitrogen have been calculated by assuming Morse potentials for the two states. The transition probabilities have been calculated by the method suggested by Fraser and Jarmain (1953) and Jarmain and Fraser (1953). For calculating the r-centroids, the method given by Nicholls (1965) has been employed. Some discussion regarding appearance of the bands of this system and the electronic transition moment has been given.

Vibrational transition probabilities andrcentroids for the C-X system of N2+

Relative vibrational transition probabilities for 36 bands of the C-X system of the N2+ molecule have been calculated by using the method suggested by Jarmain and Fraser in 1953. These values have been compared with the Franck-Condon factors calculated by Nicholls in 1962. With the assumption of the Morse function for the two states, the r centroids for these bands have been determined.

Vibrational transition probabilities of the first positive system of N 2

Relative vibrational transition probabilities for the first positive system of N 2 have been calculated by the method of Fraser and Jarmain using refined molecular constants of Dieke and Heath, and from the intensity values of Turner and Nicholls using the wavelenghts of the band heads given by Dieke and Heath. A comparison between the present values and the corresponding values of Turner and Nicholls and also the Franck-Condon factors of Zare et al. shows that the present values agree better with the Franck-Condon factors of Zare et al. The variation of electronic transition moment with internuclear distance has been discussed.

A method for calculating vibrational transition probabilities

Relative vibrational transition probabilities for diatomic molecules can be calculated by methods utilizing band intensity observations or by methods not requiring such data. To date the latter class has been represented solely by the linear dipole moment function approximation. In this paper a second such method is developed. It makes use of the wave function expansion technique of Trischka and Salwen. Its critical assumption is the approximate equivalence of the Morse and simple harmonic potentials in the region about the potential minimum. This assumption is sufficient to remove all ambiguity in the relative signs of the matrix elements of the dipole moment. Further, it provides a relation through which the relative magnitudes of the matrix elements can be calculated. It is shown that this method is equivalent to using Morse eigenfunctions with a dipole moment function which departs from linearity in a manner that is qualitatively correct, at least in the region of the equilibrium configuration. The method is compared extensively with the linear approximation and with experiment. Insofar as the limited intensity data now available can show, it is generally superior to the linear approximation. The method can be of use in deriving Taylor coefficients for the expansion of the dipole moment function and in obtaining vibration-rotation interaction parameters. It also provides a new method for obtaining absolute values of transition probabilities. The experimental data required for this are values of the permanent dipole moment in two different vibrational levels. The procedure is illustrated by the calculation of the fundamental band strength of lithium hydride. The linear approximation and the present method are compared briefly with two methods which require intensity data. These are the quadratic and cubic approximations to the dipole moment function. It is suggested that the extent and the accuracy of the intensity data presently available is not sufficient for these methods to be of general use. Relative transition probabilities calculated by the present method are tabulated for all bands with v′ ≦ 9 for OH, HCl, and CO. The computational procedure used is outlined. It is not suitable for hand calculation but can be programmed for a high-speed computing machine with relative ease. On a large machine about one minute is required to compute the entire contents of each table.

THE OH NIGHTGLOW EMISSION

Abstract The several determinations of the relative vibrational transition probabilities for the OH vibration-rotation bands are examined. The discrepancies in the results may be attributed to their strong dependence on the observed intensities. More recent intensity measurements of the airglow, which are better suited for such a determination, indicate that terms of order higher than the first, in the usual dipole moment expansion, can he neglected. To represent the laboratory measurements, however, the higher order terms are necessary. The principal characteristics of the hydroxyl nightglow emission are reviewed. The emission rate shows a summer minimum and a winter maximum. Most of the spectroscopically determined gas temperatures exhibit a similar trend except that the amplitude of their seasonal variations shows a more distinct increase with the latitude. A comparison of the spectroscopic temperatures with the temperature profiles and emission altitudes obtained with rockets indicates that either the...

Intensity Measurements on the CO+Comet Tail, and the BO and Molecular Band Systems

Relative band intensities of the comet tail system (A2Π-X2Σ) of CO+ and of the α(A2Π-X2Σ) and β(B2Σ-X2Σ) systems of BO have been measured photoelectrically. They have been interpreted with the aid of Franck-Condon factors qν'νdouble prime and r-centroids rν'νdouble prime to show the variation of electronic transition moment Re(r) with internuclear separation r and thereby to give `smoothed' arrays of relative vibrational transition probabilities pν'νdouble prime and intensities at infinite temperature Iinfinity. The isotope effect on the Franck-Condon factors and intensities in the case of 10BO and 11BO band systems has been examined.

Transition probability parameters of molecular spectra arising from combustion processes

The dependence of intensity distributions in molecular spectra upon ( a) source conditions and (b) molecular constants (particularly transition probabilities) is discussed briefly. Knowledge of transition probabilities is essential to the interpretation of spectral intensities in terms of source conditions. Arrays of Franck-Condon factors q v′v″, which are closely related to relative vibrational transition probabilities. p v′v″, have been computed upon a Morse model and are presented for a comprehensive range of band systems of significance in combustion processes for the molecules C 2, CN, B 2, BO, BH, BN, OH, O 2, NO, PbO. Where available, values of smoothed relative vibrational transition probabilities p v′v″ and band intensities at infinite temperature I ∞r′r″ are also given.

Intensity Measurements on the O2+ Second Negative, CO ngstr m and Third Positive and NO and Molecular Band Systems

Relative band intensities of the Second Negative system of O2+, the Angstrom and Third Positive systems of CO, and the γ and β systems of NO have been measured. They have been interpreted with the aid of the Franck-Condon factors q ν' νdouble prime and the r-centroids r ν' νdouble prime to show the variation of the electronic transition moment Re(r) with internuclear separation r. Arrays of the relative vibrational transition probabilities p ν' νdouble prime and the intensities Iinfinity at infinite temperature have thereby been derived for these systems.