Abstract: First-principle density functional theory, at DND basis set level, was used to optimize the structure ofα-[XMo12O40]n－(X=P, Si, Ge). The optimized structure parameters coincide with those obtained by X-ray diffraction. Based on the optimized structure, frequency analyses were carried out by non-empirical method for the first time. In general, the agreement between the experimental vibrational spectra and the calculated values, on both the frequencies and intensities, is good. The assignment for all of the 22 infrared (IR) active and 44 Raman active frequencies is carried out and compared with that obtained by empirical methods. At the same time, a number of previously reported assignments have been conformed or clarified. In addition, the characteristic group frequencies of IR spectra forα-[XMo12O40]n－(X=P, Si, Ge) obey the P >Si >Ge rule, whereas those of Raman spectra are not the case. Meanwhile, a rational interpretation is offered.

Key words: Heteropolyanions, Infrared active, Raman active, Frequency analysis, Density Functional Theory(DFT)