$(C_5H_5)_2Zr(OCN)_2$ infrared spectrum calculation and constraints on the laser intensity imposed by applicability of laser assisted retardation of condensation method(SILARC) for zirconium isotopes separation

Lennard-Jones potential parameters and infrared absorption spectra of the $(C_5H_5)_2Zr(OCN)_2$ molecule(DZDC), proposed for the separation of zirconium isotopes by the method of selective retardation of condensation in overcooled gas flow(SILARC), were calculated by the quantum-chemical package Gaussian09 at the Hartree-Fock approximation level in the cc-pVTZ basis set for all atoms unless zirconium, for which LANL2DZ basis set has been used. Totally 75 fundamental modes with the strongest one at $2549\rm cm^{-1}$, that range from $30\rm cm^{-1}$ to $3410\rm cm^{-1}$, have been evaluated. It has been observed that the largest isotopic shift between $^{90}Zr$ and $^{91}Zr$ isotopologues $\Delta\tilde\lambda\approx1.22\rm cm^{-1}$ corresponds to the 17th fundamental mode $\tilde\lambda_{calc}=372.22\rm cm^{-1}$. By surveying experimental data on infrared absorption spectra of DZDC in KBr disk, we found that absorption peak at $\tilde\lambda_{exp}=740\rm cm^{-1}$, can be identified with the first overtone of this mode. In order to show, that it is indeed so but not just a coincidence, since $\tilde\lambda_{exp}\approx 2\tilde\lambda_{calc}$, a new formula, which relates photo-absorption cross sections, corresponding to fundamental mode and its first overtone vibrations, via first and second derivatives of the dipole moment, has been derived. The discrepancy of values, derived from the experimental data and calculated one is not more than 30%, which can be explained by the uncertainty related to the absence of published data on sample preparation. Absorption line, corresponding to $740\rm cm^{-1}$, can be resonantly excited by Raman-shifted CO2 laser. Constraints on the laser intensity, associated with applicability of the SILARC method, have been derived. Upper and lower limits of laser intensity are inversely proportional to characteristic time of excitation loss, and proportional either to dissociation threshold or absorbed photon respectively. Dissociation threshold has been evaluated by Gaussian09, and characteristic time of excitation loss corresponds to the inverse rate of dimer formation. Dimer formation rate has been calculated from the Lennard-Jones potential parameters.