Using the Hessian of a QM vibrational frequency analysis I have derived bonded force constant terms for bond angle and bond stretch (length). Dihedrals were fitted using very similar structures with existing values, compatible with force field derived from the Hessian. LJ parameters were fitted from similar structures and then adjusted until the molecule of interest (an organic solvent) to reproduce the experimental density. Partial charges via the RESP RED server. 

The comparison between the magnitude of the force constants for specific bonded atom pairs can be justified by studying the Laplacian bond order. e.g., why one particular C-C force constant is different to another C-C can be seen by the bond order. This, however, is still at the QM level. 

Validating QM derived force constants at the molecular dynamics (mechanical force field level) level is a little harder. I have measured the angle and bond length deviation over time and they compare extremely well to the angle and bond length of the optimised QM structure. Likewise, once adjusting the necessary LJ parameters, I am now extremely close to the experimental density of my molecule. The RMSD of the structure is also extremely stable. Thus, the bonded terms have not deviated away from what the structure at the QM level looks like and I am able to replicate experimental properties.

I wanted then to compare the vibrational frequencies at the mechanical (MD) level to the vibrational frequencies at the QM level. So, I took my structure, removed electrostatic and LJ terms and performed normal analysis using Gromacs (i.e., perform energy min to < 0.001, then switch to nm - normal mode). This will return a Hessian which can be piped into gmx nmeig to gave the wavenumber and frequency. I've  compared these to the QM one, only addressing wave numbers where the frequency is greater than 10 cm^-1. Sadly, they are very different (see attached image). 

Any suggestions as to why they are different? Or alternative means of validating force constants derived from QM data using MD models?

Thanks