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6975811 
Journal Article 
Vibrational isotope effect by the low rank perturbation method Case study: out-of-plane vibrations of benzene (H,D)-isotopomers 
Zivkovic, TP; , 
2009 
Yes 
Journal of Mathematical Chemistry
ISSN: 0259-9791
EISSN: 1572-8897 
SPRINGER 
NEW YORK 
1060-1101 
WOS:000264527700016 
Mathematical formalism of the Low Rank Perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic approximation with a standard assumption that force field does not change under isotopic substitutions. A pair of two n-atom isotopic molecules A and B which are identical except for isotopic substitutions at rho atomic sites is considered. In the LRP approach vibrational frequencies omega(k) and normal modes vertical bar Psi(k)> of the isotopomer B are expressed in terms of the vibrational frequencies nu(i) and normal modes vertical bar Phi(i)> of the parent molecule A. In those relations complete specification of the normal modes vertical bar Phi(i)> is not required. Only amplitudes at sites tau affected by the isotopic substitutions and in the coordinate direction s (s = x, y, z) are needed. Out-of-plane vibrations of the (H, D)-benzene isotopomers are considered. Standard error of the LRP frequencies with respect to the DFT frequencies is on average Delta approximate to 0.48 cm(-1). This error is due to the uncertainty of the input data (+/- 0.5 cm(-1)) and in the absence of those uncertainties and in the harmonic approximation it should disappear. In comparing with experiment, one finds that LRP frequencies reproduces experimental frequencies of (H, D)-benzene isotopomers better (Delta(LRP)approximate to 4.74 cm(-1)) than scaled DFT frequencies (Delta(DFT)approximate to 6.79 cm(-1)) which are designed to minimize (by frequency scaling technique) this error. In addition, LRP is conceptually and numerically simple and it also provides a new insight in the vibrational isotope effect in the harmonic approximation.