Molecules-in-molecules fragment-based method for the evaluation of Raman spectra of large molecules

We present the first implementation of the evaluation Raman spectra of large molecules using the molecules-in-molecules (MIM) fragment-based method (MIM-Raman). Molecular fragments and associated overlapping subsystems are constructed by cutting the C–C bonds in the large molecule based on the connectivity information and a number-based fragmentation scheme. After saturating the dangling bonds with hydrogen link-atoms, independent energy and Raman frequency calculations are performed on each subsystem. Subsequently, link-atom-related forces, Hessian and polarisability derivative matrix elements are projected back onto the corresponding host and supporting atoms through the Jacobian projection method. In the two-layer model (MIM2), the long-range interactions, absent in the single layer model (MIM1), are taken into account through a second layer at a lower level of theory. The MIM-Raman method is benchmarked on a set of large linear and cage molecules. The MIM extrapolated energy and Raman spectra are compared with the full calculations at B3LYP/6-311G(d,p) or B3LYP/6-311+G(d,p) levels of theory. The benchmark analysis of 21 molecules at MIM2 show an accuracy improvement of 85% in energies, 74% in Raman frequencies and 66% in intensities over MIM1. The implementation and benchmark analysis validates the MIM-Raman model for exploring Raman spectra of large molecules in the future.