Browsing by Author "D.C. Jain"

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A method for obtaining the vibrational wave functions appropriate to the true potential energy curves of diatomic molecules
(1962) D.C. Jain; P. Sah
A method has been suggested for obtaining the vibrational wave functions appropriate to the true U(r) curves of diatomic molecules by the application of the Wentzel-Kramers-Brillouin (WKB) method. It consists in dividing the true U(r) curve into a number of segments and determining a quadratic expression in r, representing the U(r) curve, for each segment. These quadratic expressions are then used for evaluating the phase integrals. For checking the accuracy of the wave functions thus obtained, the Morse wave functions of a number of vibrational levels of various molecular electronic states, computed by the WKB method, have been compared with their exact Morse wave functions and the agreement has been found to be quite good. The proposed method has been applied to obtain the true wave functions of the fourth and sixth vibrational levels of the A3IIg state of C2 and of the zeroth, first and tenth vibrational levels of the A1Σ+ state of RbH. The general shape and anharmonicity of these wave functions are observed to be as expected from the nature of their true U(r) curves. Further, the deviation of the true wave functions of the fourth and sixth vibrational levels of the A 3IIg state of C2 from the exact Morse wave functions has been found to be large in comparison with the error in the WKB wave functions.
Franck-Condon factors and r-centroids for the triplet band system of CO molecule
(1961) N.L. Singh; D.C. Jain
It has been verified that the Morse potential function is a good approximation for the representation of the potential energy curves of d 3π and a3π electronic states of the CO molecule. The Franck-Condon factors for the triplet band system have been computed by the direct method of numerical integration of the Morse wave functions. The r-centroids for this band system have been calculated by (i) the direct method of numerical integration and (ii) the quadratic equation method of Nicholls and Jarmain. A close agreement is obtained between the values of r-centroids evaluated by both the methods. Assuming that the electronic transition moment is approximately constant, the relative population of the vibrational levels of the d3π state of the CO molecule has been calculated using Herman and Rakotoarijimy's experimental data on the relative intensity measurement of the triplet bands developed in the presence of xenon.
Potential-energy curves of the excited states of alkali hydride molecules
(1963) D.C. Jain; P. Sah
The potential-energy curves of the excited states of NaH and KH have been obtained by the Rydberg-Klein-Rees method as described by Singh and Jain. The simple-harmonic curves and ionic curves for LiH, NaH, KH, and RbH have also been calculated. It has been found that the potential-energy curves mostly agree with Mulliken's findings as to the anomalous behavior of the excited states of alkali hydrides.
Relative intensities in the triplet system of CO bands
(1961) N.L. Singh; D.C. Jain
[No abstract available]
The Rydberg-Klein-Rees method of constructing the true potential energy curves of diatomic molecules
(1962) N.L. Singh; D.C. Jain
Alternative simplified expressions have been deduced for f and g involved in the calculation of the true potential energy curves of such electronic states of diatomic molecules whose vibrational terms cannot be adequately represented by a quadratic in v + . These expressions have been used in calculating the true potential curve of the B3II0u+ state of 79Br81Br molecule and the results show a close agreement with those obtained by Rees (1947). The true potential energy curve of the A1Σ+ state of LiH molecule has also been calculated by the present method and the results are found to agree quite well with those obtained by Fallon, Vanderslice and Mason (1960).
The true potential energy curves of the excited states of LiH and RbH molecules
(1962) N.L. Singh; D.C. Jain
The true potential energy curves of the excited states of LiH and RbH molecules have been obtained by the Rydberg-Klein-Rees method. An analytical method has been developed for evaluating the phase integral. On the application of this method to a number of vibrational levels, it has been observed that the true potential energy curves satisfy the quantization condition very well. In the case of RbH, the phase integrals have been evaluated by a graphical method as well.