An investigation into the limitations of the harmonic approximation in the calculation of vibrational isotopic shifts

Comparisons between theoretical predictions and experimental measurements of vibrational fundamentals and isotopic shifts represent a method for the identification of new molecular species. For molecules with near-lying vibrational fundamentals, experimental and theoretical factors complicate the interpretation of isotopic spectra where isotopic shift measurements are recorded. Experimentally, a large number of absorptions in a small region of the spectrum are observed. Theoretically, two factors affect the calculation of isotopic shifts in the harmonic approximation: (i) the sensitivity of the calculations due to the interaction of vibrational fundamentals and (ii) the sensitivity of the calculations due to the anharmonicity of the interaction potential. The study of vibrational spectra of long carbon chains exhibits these problems.;The present work is an investigation of the theoretical issues that affect the calculations. As a consequence of this investigation, two theoretical methods were developed in the framework of perturbation theory in order to aid in the interpretation of isotopic spectra of homonuclear molecules. Both theoretical methods are presented in this work. The first method, called the isotopic deperturbation method, is introduced in order to aid dealing with the complications regarding the sensitivity of simulated spectra due to the interactions of vibrational fundamentals. The second method is introduced here in order to estimate the anharmonicity of vibrational fundamentals from isotopic shift measurements.;The isotopic deperturbation method is applied to the infrared isotopic spectra of linear Cn (n = 3 - 12, 15, 18) and confirms our hypothesis regarding the high sensitivity of the isotopic shift calculation for molecules with near-lying vibrational fundamentals. The method to calculate anharmonic contributions is applied to the experimental spectra of linear carbon chains C2n+1 , n=1-5 as well as to cyclic C6 and C8; the results are compared with the calculated anharmonicity using a density functional theory (DFT) perturbative approach and existing calculations in the literature.