The experimental and computational vibrational study for three different manganese(II) oxalates hydrates was explored. The elucidation of IR and Raman spectra were discussed based on their structural singularity; in the same way, they establish some interesting relations between them in the field of computational and statistical approaches. The density functional theory (DFT) computational approach was conducted for accurate prediction and interpretation of the intermolecular effects based on experimental and calculated IR and Raman spectra in the solid-state data in combination with multivariate statistical technique. The proposed computational scheme was also explored for the case of the isolated-molecule model. The goals of the study were to access the accuracy of the proposed procedure for solid-state calculations along with electron calculations for the isolated molecules and to reveal the similarities within the groups of objects by the cluster analysis (CA) techniques and two-way CA for the data. The presented simulation procedure should be very valuable for exploring and to classify other oxalate compounds.