Variation Of Electronic Transition Moment Research Articles

On the electronic transition moment variation and the r-centroid approximation in interpretation of spectral intensities of diatomic molecules

Klemsdal's recent paper on this topic ( JQSRT 13, 517, 1973) has stimulated the comments, (a) that molecular intensity measurements are by no means uniformly reliable and should be interpreted accordingly, (b) the mathematical basis of the r-Centroid approximation is well understood and is related to the existence (or non-existence) of a well developed uncancelled local peak on the vibrational wavefunction product. Contrary to his comments, it has been shown to hold very well for 10 5 bands so far studied.

A shock tube determination of the CN ground state dissociation energy and the CN violet electronic transition moment

The CN ground state ( X 2∑ +) dissociation energy and the electronic transition moment of the CN violet B 2∑ + − X 2∑ + bands have been simultaneously determined from spectral emission measurements behind incident shock waves. The unshocked test gases were composed of various CO 2-CO-N 2-Ar mixtures, and the temperatures behind the incident shocks ranged from 3500 to 8000°K. The dissociation energy was determined to be 7.89 eV with a statistical precision of ±0.02 eV; a conservative estimate of the absolute error was ±0.13 eV. The value obtained for the Δυ = 0 sequence electronic transition moment was 0.90 ± 0.14, corresponding to an electronic absorption f-number of 0.035 ± 0.005 at a wavelength of 3860 Å. The electronic transition moment variation with internuclear separation was also measured.

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.

Electronic transition moment variation in D1Π-X1Σ system of SnO molecule and determination of the effective vibrational temperature

The D1 Pi -X1 Sigma (3200-4000 AA) system of SnO is excited in a vertical arc source. Relative band intensities are measured using the technique of photographic photometry and interpreted with the aid of Franck-Condon factors qv'v. It is found that the electronic transition moment varies as Re(r)=const (1-1.119r+0.356r2) where 1.8<or=r<or=2.2 AA and taking this variation into account, smoothed transition probabilities, Einstein coefficients and the oscillator strengths are calculated. A straight line plot of lg Sigma vI/v4 against G'(v') for v'=0, 1, 2, 3,... is made and the effective vibrational temperature is estimated as 1100 K.

Electronic transition-moment variation in the B1 − X1Σ+ system of PbO and determination of the effective vibrational temperature

The B1 − X 1 Σ + (4200–5000 Å) system of PbO was excited in a vertical copper arc. Relative intensities of the bands were measured by using the photographic technique. The data were interpreted through appropriate use of Franck-Condon factors ( q v′ v″ ) and r-centroids ( r v′v″ ). It was found that the electronic transition moment varies as R e ( r) = const. (1−0.5408 r) for 2.02 ≤ r ≤ 2.148. A straight line plot of log ∑ υ″ logI υ′υ″ em V 4 against G′(v′) for v′ = 0, 1, 2, 3, 4, was made and the effective vibrational temperature has been calculated from the slope of this line to be 2240°K.

Absolute oscillator strength of the (0.0) band of the gamma system of nitric oxide by the hook method

The hook method has been adapted for molecular spectra to allow a determination of the absolute oscillator strength of a band from measurements on a single hook near the band head. For the A2 Sigma +-X2II system of nitric oxide, the value f00=(3.64+or-0.05)*10-4 was obtained, in good agreement with previous measurements on the integrated absorption at high pressures. The behaviour of f00 as a function of pressure was investigated at pressures up to 7 atm of nitric oxide and 35 atm of argon, but no variation was found. The relation between f00 and the latest experimental value for the lifetime of the v'=0 vibrational level is discussed, using recent measurements for the variation of electronic transition moment with r centroid; the inconsistencies between these three sets of measurement prove to be considerably larger than the apparent experimental errors.

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

Electronic transition moment variation in CN violet band system

A possible cause for the large variation of Re(r) in the CN violet band system as obtained by the use of peak intensity data from a carbon arc source is examined. The desirability of extending the intensity measurements to cover other sources of excitation is also discussed.

The problem of the uniqueness of the Re(r$\nu$$prime$$\nu$$prime$$prime$) function for the (A 2$\Sigma$-X 2$\Sigma$) system of AlO

The validity of semi-theoretical expressions for the electronic transition moment variation with reference to the AlO (A 2Σ-X 2Σ) band system has been examined from the basic assumptions on which the expressions are built and other studies, and it is shown that none of the expressions can be a unique function for the system.

Variation of electronic transition moment in some band systems of the N 2 molecule

The variation of the electronic transition moment with the internuclear separation has been studied in the first positive, the second positive and the Vegard-Kaplan band systems of N 2 by using the Franck-Condon factors based on the Rydberg-Klein-Rees potential energy curves. The “smoothed” relative band strengths and the relative intensities at infinite temperature have also been reported for these band systems.

Transition probability parameters of the band systems of CO +

Franck-Condon factors and r-centroids have been computed for the comet-tail, the first negative and the Baldet-Johnson systems of CO + by using the vibrational wave functions appropriate to the RKR potential energy curves. The variation of electronic transition moment with the internuclear separation, the smoothed relative band strengths and the relative intensities at infinite temperature, have been calculated for the comet-tail bands. The Einstein A coefficients, the absolute band strengths and the band oscillator strengths have also been presented for these bands.

Electronic transition moment variation of the CN violet system

The eye estimates of the intensities for the CN violet system obtained by LeBlanc and Tanaka to high vibrational quantum numbers in a discharge through a mixture of acetylene and active nitrogen have been used to derive the variation of the electronic transition moments. The nature of the vibrational excitation has been examined and it has been shown that the variation in the electronic transition moments to higher quantum numbers is very significant and that the vibrational excitation is not of the Boltzmann type.

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 theoretical study of the O2x3 g-- B3 u-photodissociation continuum

Franck-Condon densities qν,vn = [vertical line][integral operator]ψν(r)ψvn(r) dr[vertical line]2 for vn = 0 in the O2 Schumann-Runge photodissociation continuum have been calculated for realistic Klein-Dunham potentials. They are combined with measured values of absorption coefficient to study the variation of electronic transition moment in the continuum. For comparison, Franck-Condon factors have similarly been used in conjunction with measured oscillator strengths to show the behaviour of the transition moment for the vn = 0 progression of bands. It appears probable that the transition moment is continuous through the dissociation limit.

Determination of re, the Difference between the Equilibrium Internuclear Distances in the Two Electronic States of a Diatomic Molecule, from Intensities of Vibrational Bands

A method for determining the value of re' - re, the difference between the equilibrium internuclear distance of two electronic states involved in a band system, from the intensity of vibrational bands is discussed. The value of Δre ≡ re' - re thus obtained can be used to give the value of equilibrium internuclear distance for any one of the two states involved provided the same is known for the other. The method consists of equating the Jarmain - Fraser theoretical expression for the ratio of the squares of the overlap integrals of the two bands having the same v' value to the ratio of their I/ν4 values, and solving it for Δre = re' - re. In some cases, where the variation of electronic transition moment is large, the values of Δre obtained in this way may be unexpectedly divergent among themselves. In such cases the pair of bands used for estimating Δre should be selected in such a way that the individual members should have the same r-centroid, rather than the same v' values.

Electronic Transition Moment Variation in Schumann-Runge Band System of O2Molecule

The r-centroids for some of the bands of v' = 0, 1 and 2 progressions have been reported. Utilizing the experimental intensity data of Treanor and Wurster, the variation of electronic transition moment in this system has been studied following the methods of Nicholls and Jarmain, and of Schuler. It has been found that, in the range 1.51 Å < r < 1.71 Å, the variation of the electronic transition moment is represented by the following equation: Re(r) = const (1-0.555r).

Electronic transition moment variation in (B1 Σ→X1 Σ) bands of BeO

Accurate integrated intensity data of the bands of BeO (B1Σ→X1Σ) system has been obtained experimentally by the technique of photographic photometry. With the use of Franck-Condon factors andr-centroids for the bands available from the work of the authors reported in papers elsewhere, the relation of electronic transition moment Re with internuclear separationr, has been evolved. The vibrational transition probabilities have been corrected for the resulting variation of Re withr. These corrected values have been examined in relation to those under assumptions of constancy of Re in conjunction with (i) mechanical anharmonicity and also (ii) mechanical harmonicity.