“…The Lagrangian eqnations for the system may now be written as (17) As is well known, eq 18 and 19 lead to the following secular equations for the determination of the normal frequencies of vibrfLtion of the coordinates qz: or, (22) (23 ) where A= 47r z p 2(v= normal frequency). In the present method, in which 8;2 rather than G;2 is computed, it is convenient to convert eq 22 to the secular equation of a single matrix, in the form (24) In practice, F22 is diagonal, or nearly so, and therefore easily reciprocated.…”
Section: Frequencies Of Semirigid Moleculesmentioning
confidence: 99%
“…Several workers have reported Raman sp ectra [1~" A, 15,16,17,18] and infrared spectra [19,20,21,22,23] for ethylbenzene. The lowest observed frequ encies in the Raman spectrum of I'thylbenzene, are, approximately, 154, 305 (weak)…”
It is shown t hat in normal coo rdi nate calculati ons of t he vibrations of moleculcs it is so metimes adva ntagco lls to calculatc the kin etic-e ncrgy matrix, r at her t ha n t he l'?ciprocal k inetic-energy m atri x. E xp li cit formulas are give n fo r t he elemen ts of the klllCtlC-energy matrix. Illustrative calculalions are given for p ropane, toluene, a nd ethy lbenzene . A se mi e mpiri cal assig nm e nt of t he v ibration frequencies of ethylbe nezene is made on t he basis of these calculations and the spectroscopi c data.
“…The Lagrangian eqnations for the system may now be written as (17) As is well known, eq 18 and 19 lead to the following secular equations for the determination of the normal frequencies of vibrfLtion of the coordinates qz: or, (22) (23 ) where A= 47r z p 2(v= normal frequency). In the present method, in which 8;2 rather than G;2 is computed, it is convenient to convert eq 22 to the secular equation of a single matrix, in the form (24) In practice, F22 is diagonal, or nearly so, and therefore easily reciprocated.…”
Section: Frequencies Of Semirigid Moleculesmentioning
confidence: 99%
“…Several workers have reported Raman sp ectra [1~" A, 15,16,17,18] and infrared spectra [19,20,21,22,23] for ethylbenzene. The lowest observed frequ encies in the Raman spectrum of I'thylbenzene, are, approximately, 154, 305 (weak)…”
It is shown t hat in normal coo rdi nate calculati ons of t he vibrations of moleculcs it is so metimes adva ntagco lls to calculatc the kin etic-e ncrgy matrix, r at her t ha n t he l'?ciprocal k inetic-energy m atri x. E xp li cit formulas are give n fo r t he elemen ts of the klllCtlC-energy matrix. Illustrative calculalions are given for p ropane, toluene, a nd ethy lbenzene . A se mi e mpiri cal assig nm e nt of t he v ibration frequencies of ethylbe nezene is made on t he basis of these calculations and the spectroscopi c data.
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