Volume 167, number 3 CHEMICAL PHYSICS LETTERS 23 March 1990 zyxwvut A SIMPLE METHOD TO DETERMINE BOND LENGTHS AND EXCITED STATE SURFACES FROM ELECTRONIC-VIBRATIONAL SPECTRA Soo-Y. LEE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Department of Chemistry National University O fSingapore, Kent Ridge,S.0511 Singapore and Choy-Heng LA1 Department of Physics, National University of Singapore, Kent Ridge, S.05 I1 Singapore Received 24 November 1989 A fast and efficient method using the spectral moments of an electronic-vibrational spectrum is described to determine the harmonic and Morse potential tits to the excited state potential in the Franck-Condon region. Some of the drawbacks of the Franck-Condon least-squares fitting procedure are overcome by the moment method. The method is applied to some diatomics of current interest, spanning a wide range of bond length change in the electronic transition. The accuracy of the results suggests that the spectral moment method can be a replacement for the traditional and still popular Franck-Condon analysis. zyxwvutsrqpon 1. Introduction Franck-Condon (FC) analysis which is an itera- tive, least-squares fitting procedure is the best-known and most widely used method to determine excited state potential energy surface from an electronic-vi- brational spectrum. The procedure makes use of the eigenvalues and eigenfunctions typically of the har- monic and Morse potentials. It is aided by the avail- ability of overlap integrals for displaced harmonic oscillators in closed form [ 11, and numerous nu- merical methods for evaluating similar integrals for displaced Morse oscillators [ 21. The best fit har- monic or Morse potential is often interpreted as an expansion of the actual excited state potential about its minimum. However, when this minimum falls in the tail end of the FC region, such an interpretation is inappropriate [ 31. Moreover, when the harmonic approximation is made, symmetry prevents discrim- inating between bond lengthening or bond shorten- ing, and additional information of the excited state electronic structure has to be used. Other procedures such as the semiclassical Rydberg-Klein-Rees (RKR) method [4] for diatomics do not have to assume harmonic or Morse potentials. But, unfor- tunately, many molecules of interest do not give suf- ficient spectroscopic data to enable accurate RKR potentials to be constructed. Basis set methods, such as the recent discrete variable representation (DVR) approach of Light and coworkers [ 51 optimizes the potential energy surface by minimizing the differ- ence between the experimental and calculated vi- bronic spectra. They can also be classified as FC analysis. Like the RKR method, basis set methods require the observation of a large set of energy levels. Unfortunately, most molecules give limited lines or diffuse spectra which render such methods inapplicable. The purpose of this paper is to present a simple method that has the same accuracy, and yet can overcome most of the problems associated with FC analysis. The method presented below, uses spectral moments to determine parameters for assumed forms of the excited state potential. Both harmonic and Morse potentials are considered. The simplicity of the approach, and the good quality of the results ob- tained for a wide range of diatomics indicates that the spectral momenf method is a good alternative, if 0009-2614/90/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland ) 255