Energies, geometries, and harmonic frequencies of the chemical species in the HCN < = > HNC isomerization including the transition state are computed with the parametric variational two-electron reduced density matrix (2-RDM) method. The parametric 2-RDM method parametrizes the 2-RDM with single- and double-excitation coefficients to be both size-consistent and nearly N-representable [DePrince, A. E., III; Mazziotti, D. A. Phys. Rev. A 2007, 73, 042501.]. With the inclusion of the zero-point energies of both species, the energy of HNC relative to HCN in a polarized valence triple-zeta basis set is 14.2 kcal/mol, which agrees with the experimental value of 14.8 +/- 2 kcal/mol. The present calculations provide the first assessment of the method for computing harmonic frequencies from a molecular geometry optimization. Bond lengths, angles, and harmonic frequencies are also computed for HF, CO, and H2O.