Since it is not currently feasible to derive accurate QM Hessian matrices for entire proteins, we have used the modified Seminario method to compute a complete set of bond and angle parameters for the twenty naturally occurring amino acids. This work focuses on the remaining component of the force field, namely the re-fitting of key torsional parameters that describe the backbone and sidechain dynamics of an amino acid. The methods and validation tests broadly follow the approaches employed in the development of OPLS-AA/M, the latest OPLS force field. Torsional parameters are fit by minimizing the differences between multiple QM and MM potential energy scans of dipeptide backbone and sidechain dihedral angles. Our overall goal is to test the extent to which bespoke non-bonded parameters may be combined with libraries of bonded parameters to produce a protein force field that is compatible with our QUBE small molecule force field for use in computer-aided drug design applications.