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Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method

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Title Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method
 
Creator GHOSH, S
DIXIT, MK
BHATTACHARYYA, SP
TEMBE, BL
 
Subject Upper-Division Undergraduate
Graduate Education/Research
Physical Chemistry
Computer-Based Learning
Computational Chemistry
Molecular Properties/Structure
Quantum Chemistry
Spectroscopy
N-N
MOLECULES
PRINCIPLE
SYSTEM
TRANSITIONS
CHEMISTRY
NITROGEN
 
Description Franck Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian.(FGH) method for computing the vibrational wave functions and the corresponding energy values for different electronic states of diatomics is outlined. For these computations, the Morse potential energy forms are used for constructing and diagonalizing the molecular Hamiltonians. Once the vibrational wave functions for the ground and the excited states are known, the vibrational overlap integrals are calculated by using the formula integral psi* (nu '')psi(nu ') d tau(r upsilon) where d tau(n) is the volume element for nuclear coordinate, nu ' and nu '' are the vibrational quantum numbers in the ground and exited electronic states, and psi(nu ') and psi(nu '') denote the vibrational wave functions. The effects of the changes in the location, height, and the nature of the excited state electronic energy curve (relative to the ground state) on the FCFs have been evaluated. The method is also illustrated for N-2 and O-2. This method can be effectively used for introducing the FCFs to the students of undergraduate molecular spectroscopy course and also for post-graduate students.
 
Publisher AMER CHEMICAL SOC
 
Date 2014-10-16T13:35:33Z
2014-10-16T13:35:33Z
2013
 
Type Article
 
Identifier JOURNAL OF CHEMICAL EDUCATION, 90(11)1463-1471
0021-9584
1938-1328
http://dx.doi.org/10.1021/ed4002199
http://dspace.library.iitb.ac.in/jspui/handle/100/15680
 
Language en