Neural network consistent empirical physical formula construction for DFT based nonlinear vibrational spectra intensities of N-(2-methylphenyl) and N-(3-methylphenyl) methanesulfonamides

Vibrational intensities are both experimentally measured and theoretically estimated important physical quantities which are directly related to distributions of the electric charges in a molecule. In this paper, as a novel approach, by a layered feedforward neural network (LFNN), empirical physical formulas (EPFs) were constructed for density functional theory (DFT) vibrational spectra intensities of N-(2-methylphenyl) and N-(3-methylphenyl) methanesulfonamides. The spectral data was obtained from our previous study. Although the DFT spectral data was inherently extremely difficult-to-fit (sparse frequency intervals, highly nonlinear and sharply fluctuating intensities), still the optimally constructed LFFN-EPFs succeeded in fitting this data to medium and higher level of satisfaction. Moreover, LFNN–EPFs test set (i.e. yet-to-be measured experimental data) intensity predictions were also moderate to higher level. This briefly means that the general tendency of the intensity data was consistently estimated by the LFNN to an acceptable degree. In conclusion, provided that vibrational spectral data measured over sufficiently dense frequency intervals are available for any unknown molecule of significant complexity, suitable LFNN–EPFs can be constructed. Then, by various mathematical tools such as differentiation, integration, minimization, these vibrational LFNN–EPFs can be used to estimate the electronic charge distributions of the molecule. Moreover, these estimations can be compared and combined with those of theoretical DFT atomic polar tensor calculations to contribute to the identification of the molecule.

► Density functional theory vibrational intensities were estimated by neural networks.
► The intensities were obtained for N-(2 and 3 methylphenyl) methanesulfonamides.
► A novel neural network empirical physical formulas for intensities were constructed.
► These formulas can be used in theoretical atomic polar tensor calculations.
► These empirical formulas may help to estimate unknown molecule charge distributions.