This work aims to provide reliable benchmark data on the accuracy of harmonic and anharmonic vibrational frequencies computed with the B2PLYP double-hybrid density functional method. The exchange-correlation contributions required for the B2PLYP analytical second derivatives are presented here, which allow for the effective calculation of harmonic frequency as well as cubic and semidiagonal quartic force fields. The latter, in turn, are necessary to compute the anharmonic vibrational frequencies with the perturbative approach (VPT2). The quality of harmonic vibrational frequencies computed in conjunction with basis sets of double- to quadruple-ζ quality has been checked against reference data from the F38 benchmark set. Then, for an additional set of small closed- and open-shell systems, both harmonic frequencies and anharmonic contributions computed at the B2PLYP/N07D and the B2PLYP/aug-cc-pVTZ levels have been compared to their CCSD(T) counterparts. Moreover, for selected medium-size molecules (furan, pyrrole, thiophene, uracil, anisole, phenol, and pyridine), anharmonic frequencies have been compared to well established experimental results. Such benchmark studies have shown that the B2PLYP/N07D model provides good quality harmonic frequencies and describes correctly anharmonic contributions, the latter being of similar accuracy to their B3LYP/N07D counterparts, but obtained at significantly larger computational cost. Additionally, increased accuracy can be obtained by adopting hybrid models where the B2PLYP/N07D anharmonic contributions are combined with harmonic frequencies computed with more accurate quantum mechanical (QM) approaches or by B2PLYP with larger basis sets. This work confirmed also that most of the recently developed density functionals are significantly less suited for vibrational computations, while the B2PLYP method can be recommended for spectroscopic studies where a good accuracy of vibrational properties is required.

The subtle interplay of several different effects makes the interpretation and analysis of experimental spectra in terms of structural and dynamic characteristics a very challenging task. In this context, theoretical studies can be very helpful, and this is the reason behind the rapid evolution of computational spectroscopy from a highly specialized research field toward a versatile and widespread tool. However, in the case of vibrational spectra of large molecular systems, the most popular approach still relies on a harmonic treatment, because of the difficulty to explore the multidimensional anharmonic potential energy surface. These can be overcome considering that, in many cases, the vibrational transitions are well localized and only some of them are observed experimentally. To this aim, the procedure for the simulation of vibrational spectra of large molecular systems beyond the harmonic approximation is discussed. The quality of system-specific reduced dimensional anharmonic approaches is first validated by comparison with computations taking into account all modes simultaneously for anisole and glycine. Next, the approach is applied to two larger systems, namely glycine adsorbed on a silicon surface and chlorophyll-a in solution, and the results are compared with experimental data showing significant improvement over the standard harmonic approximation. Our results show that properly tailored reduced dimension anharmonic approaches stand as feasible routes for state-of-the-art computational spectroscopy studies and allow to take into account both anharmonic and environmental effects on the spectra even for relatively large molecular systems.

The analysis and interpretation of the vibrational spectra of complex (bio)molecular systems, such as polypeptides and proteins, requires support from quantum-chemical calculations. Such calculations are currently restricted to the harmonic approximation. Here, we show how one of the main bottlenecks in such calculations, the evaluation of the potential energy surface, can be overcome by using localized modes instead of the commonly employed normal modes. We apply such local vibrational self-consistent field (L-VSCF) and vibrational configuration interaction (L-VCI) calculations to a cyclic water tetramer and a helical hexa-alanine peptide. The results show that the use of localized modes is equivalent to the commonly used normal modes, but offers several advantages. First, a faster convergence with respect to the excitation level is observed in L-VCI calculations. Second, the localized modes provide a reduced representation of the couplings between modes that show a regular coupling pattern. This can be used to disregard a significant number of small two-mode potentials a priori. Several such reduced coupling approximations are explored, and we show that the number of single-point calculations required to evaluate the potential energy surface can be significantly reduced without introducing noticeable errors in the resulting vibrational spectra.