Vibrational isotope effect of linear and planar molecules: Deuterated bromoethenes |
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Authors: | Tomislav P. Živković |
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Affiliation: | (1) Ruer Bokovi Institute, P.O.B. 180, HR-10002 Zagreb, Croatia |
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Abstract: | Linear (planar) molecules A and B which are identical except for isotopic substitutions at the atomic sites are considered. Stretching (bending, out-of-plane) frequencies k and normal modes k of the isotopically perturbed molecule B are expressed in terms of stretching (bending, out-of-plane) frequencies i and the corresponding normal modes i of the unperturbed molecule A. Complete specification of the unperturbed normal modes is not required. All that is needed are stretching (bending, out-of-plane) amplitudes |i of the normal modes i at those sites that are affected by isotopic substitution. The rule which interlaces frequencies k of molecule A with frequencies i of molecule B is derived. Given two isotopic molecules A and B that differ by a single isotopic substitution at site , the inversion relation is derived. This relation expresses unperturbed stretching (bending, out-of-plane) amplitudes at the site in terms of stretching (bending, out-of-plane) frequencies of molecules A and B. As an example, out-of-plane vibrations of deuterated bromoethene were considered. In the simplest method 12 out-of-plane frequencies of four polydeuterated bromoethenes were calculated from 12 out-of-plane frequencies of bromoethene and three monodeuterated bromoethenes. Standard deviation of thus calculated frequencies from experimental frequencies is =2.74 cm–1. In another method, 15 out-of-plane frequencies of four polydeuterated bromoethenes and selected monodeuterated bromoethene are calculated from 9 out-of-plane frequencies of bromoethene and the remaining two monodeuterated bromoethenes. Depending on which monodeuterated bromoethene is selected (1-, cis- or trans-), standard deviation of thus obtained frequencies from experimental frequencies is 1=2.84 cm–1, c=2.96 cm–1 and t=2.72 cm–1. |
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Keywords: | vibrational isotope effect harmonic approximation stretching and bending vibrations out-of-plane vibrations deuterated bromoethenes |
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