Calculation of Franck-Condon Factors for a Number of Band Systems of Diatomic Molecules Using Hua Potential

Document Type : Research Article

Authors

Department of Chemistry, Kharazmi (Tarbiat Moallem) University, Tehran, I.R. IRAN

Abstract

This work deals with the calculation of Franck-Condon factors using Hua potential function for the first time. The advantages of this function have been mentioned, and the numerical methods are used to obtain Franck-Condon factors for the following band systems: Agreement between the values of this work and those obtained from other works is quite good that verifies the reliability of the present calculations.  

Keywords

Main Subjects


[1] Islampour R., Electronic Spectral Line Shape of a Polyatomic Molecule, Chem. Phys. 133, p. 425 (1989).
[2] Islampour R., Lin S.H., Effect of Anharmonicity on intramolecular Electron Transfer Rates, Chem. Phys. Lett. 179, p. 147 (1991).
[3] Islampour R., Alden R.G., Wu G.Y.C., Lin S.H., Effect of Temperature, Energy Gap and Distortion of Potential Surfaces on Photoinduced Intramolecular Electron Transfer, J. Phys. Chem., 97, p. 6793 (1993).
[4] Morse P.M., Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels, Phys. Rev., 34, p. 57 (1929).
[5] Kratzer A., Die Ultraroten Rotationsspektren der Halogenwasserstoffe, Z. Phys., 3, p. 289 (1920).
[6] Hua W., Four-Parameter Exactly Solvable Potential for Diatomic Molecules, Phys. Rev. A., 42, p. 2524 (1990).
[7] Hua W., Four-Parameter Potential and its Bound-State Matrix Elements, J. Phys. B., 23, p. 2521 (1990).
[8] Royapp A.T., Suri V., MCDonough J.R., Comparison of Empirical Closed-Form Functions for Fitting Diatomic Interaction Potentials of Ground State First- and Second-Row Diatomics, J. Molecular Structure., 787, p. 209 (2006).
[9] Huber K.P., Herzberg G., “Molecular Spectra and Molecular Structure  , Constants of Diatomic Molecules”, New York, Van Nostrand, (1979); see also http://webbook.nist.gov/chemistry/form-ser.html
[10] Struve W.S., “Fundamentals of Molecular Spectroscopy”, John Wiley & Sons, p. 137 (1989).
[11] Hessel M.M., Vidal C.R., The  Band System of the Li2 Molecule, J. Chem. Phys., 70, p. 4439 (1979).
[12] Palma A., Rivas-silva J.F., Durand J.S., Sandoval L., Algebraic Approximation to the Franck-Condon Factors for the Morse Oscillator, Int. J. Quantum Chem., 41, p. 811 (1992).
[13] Ley-Koo E., Mateos-Cortes S., Villa-Torres G., Vibrational Levels and Franck-Condon Factors of Diatomic Molecules via Morse Potential in a Box, Int. J. Quantum Chem., 56, p. 175 (1995).
[14] Kusch P., Hessel M.M., An analysis of the  Band System of Li2, J. Chem. Phys., 67, p. 586 (1977).
[15] Waldenstrom S., Razi Naqvi K., Exact Analytic Formula for Calculating Franck-Condon Factors Using the Kratzer Potential, J. Chem. Phys., 87(6), p. 3563 (1987).
[16] Sharp C.M., The Computation of Franck-Condon Factors, r-Centroids and Associated Quantities in the Electronic Transitions of Diatomic Molecules, Astron. Astrophys. Suppl. Ser., 55, p. 33 (1984).
[17] Melendez F.J., Sandoval L., Palma A., Franck-Condon Factors for Diatomic Molecules with Anharmonic Corrections, J. Molecular Structure (Theochem), 580, p. 91 (2002).
[18] Chakraborty B., Pan Y.K., Franck-Condon Factors for the Transitions N2   and CN, -, Theoret. Chim. Acta (Berl.), 18, p. 162, (1970).
[19] Zare R.N., Larson E.O., Berg R.A., Franck-Condon Factors for Electronic Band Systems of Molecular Nitrogen, J. Mol. Spectrosc., 15, p. 117 (1965).
[20] Jarmain W.R., Nicholls R.W., Vibrational Transition Probabilities to High Quantum Numbers for the Nitrogen First and Second Positive Band Systems, Can. J. Phys. 32, p. 201 (1954).
[21] Matsumoto A., Iwamoto K., Analytical Formula for Franck-Condon Factors Involving the Morse Potential, J. Quant. Spectrosc. Radiat. Trans., 50, p. 103, (1993).
[22] Nicholls R.W., Laboratory Astrophysics, J. Quant. Spectrosc. Radiat. Trans., 2, p. 433 (1962).