Quantum DFT and DF-DFT study of vibrational spectra of sulfuric acid, sulfuric acid monohydrate, formic acid and its cyclic dimer

Rigorous theoretical treatment of vibrational frequencies is critically important for the interpretation of unassigned experimental vibrational spectra and accurate determination of thermodynamic properties of molecular clusters. IR spectra of trans monomers of sulfuric and acetic acids, sulfuric acid monohydrate and cyclic dimer of the formic acid have been studied using DFT and DF-DFT methods using BLYP, B3LYP and PW91 with 12 different Pople and Dunning basis sets. New data for above-mentioned structures have been reported, scaling factors have been calculated and a comprehensive analysis of the performance of BLYP, B3LYP and PW91 methods has been performed. Comparison of the obtained results with experiments shows that results of pure PW91 and BLYP are better than predictions of well-established hybrid B3LYP method. Our analysis shows on the existence of the considerable difference in scaling factors weighted to high and low frequencies. In the case of formic acid dimer, the deviation the predicted low frequencies from the experimental data is considerable that leads to quite large (∼6-7 kcal mol−1) uncertainties in the absolute values of the cluster Gibbs free energy. In order to determine an efficient computational strategy that comprises accuracy and reasonable computational costs, the effect of density fitting (DF) and basis set superposition error (BSSE) on the vibration frequencies has been investigated. We found that application of the DF that substantially (2.5-3.5 times) increases the performance of pure PW91 and BLYP methods gives excellent results, which are very close to those of conventional DFT. This suggests that DF-DFT is a viable low-cost alternative to conventional DFT in predicting vibrational spectra. It has been found that while vibrational spectra obtained using the counterpoise correction (CP) for the BSSE do not deviate much from uncorrected ones, the difference in absorption intensities between corrected and uncorrected spectra obtained using small and medium-sized basis sets is considerable. This suggests that application of DF-DFT uncorrected for the BSSE with large basis sets is a more efficient strategy of predicting vibrational spectra than the application of conventional DFT with small basis sets.