Energy Randomisation. How Much of Rotational Phase Space Is Explored? How Long Does It Take? Page: 8 of 30
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II. Method
(a) Basis functions
The basis functions are the product of vibrational and rotational parts11:
InJKy) = on)I JKy) . (2)
The vibrational functions, CD), are random vectors determined implicitly by the
selection of the vibrational coupling matrix elements from a Gaussian
distribution. The rotational functions, IJKy), are modified1 Wang symmetric
rigid rotor wave functions:
IJKy) = 2Y2 ei(K-Y)/2(IJK)+(-1)YIJ -K)) for K> 0 (3)
=JK) for K =0
The label y is 0 or 1 for the symmetric or asymmetric combinations of the
symmetric rotor functions respectively. For each J, there are 2J+1 rotational
functions IJKy).
One of the basis functions, IsJK'y'), is designated as the bright state.
Throughout the paper, the vibrational label s and the single-primed quantum
numbers K'and Yare used to designate the bright state.
(b) Random matrix calculations
The calculations for 1-butyne and ethanol used the previously
determined1 I coupling parameters (Table 1). The bright-bath coupling8
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Perry, D. S.; Bethardy, G. A.; Davis, M. J. & Go, J. Energy Randomisation. How Much of Rotational Phase Space Is Explored? How Long Does It Take?, article, December 1995; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc668965/m1/8/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.