Adiabatic Internal Modes from Experimental Frequencies

ADIABATIC INTERNAL MODES FROM EXPERIMENTAL FREQUENCIES 

Ab initio frequencies of normal vibrational modes and, by this also, adiabatic frequencies suffer from the harmonic approximation used in the calculation. Even when applying efficient scaling procedures, there is no guarantee that ab initio frequencies accurately reproduce the exact fundamental frequencies of the experiment. Therefore, one has to ask whether the adiabatic internal frequencies might not be much more meaningful if they would be based on experimental frequencies rather than frequencies calculated within the harmonic approximation. 

An adiabatic mode analysis of measured vibrational spectra is possible with a simple perturbation theory approach that was already published in the sixties [44]. The basic equation of vibrational spectroscopy (compare with Eq. 19) can be written in matrix form according to Eq. (74) 

Once the experimental frequencies are known, it is possible to derive an improved version of Eq. (74) for the experimental situation utilizing the calculated D  

the experimental situation is described by a change AF of the force constant matrix and AA in the square of the frequencies relative to the calculated force constant matrix and frequencies at some level of ab initio theory. Since AA is known from the differences between experimental and calculated frequencies, it is straightforward to calculate AF and the true force constant matrix. Once the true force constant matrix is determined, one can apply the adiabatic mode analysis in the same way as it is applied for calculated vibrational spectra. 

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ADIABATIC INTERNAL MODES FROM EXPERIMENTAL FREQUENCIES... 

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