| Abstract
| - A systematic exploration of the importance of cross terms in the Ni(II) porphine force field is reported.Several force fields of varying complexity were generated using a modification of the Hessian-biased singularvalue decomposition (HBFF-SVD) approach originally developed by Goddard et al. The X-ray crystal structure,a B3LYP/6-31G(d,p) Hessian matrix, and experimental vibrational frequencies were used. The diagonal-onlyforce field is inadequate for reproducing experimental frequencies. As anticipated, inclusion of 1,2 and 1,3cross terms significantly improves results (total rms error 14.6 cm-1; in-plane rms error = 12.0 cm-1). Thelonger range terms in a complete, in-plane, force field improve performance dramatically (in-plane rms error= 4.8 cm-1). A total of 83 long range interaction constants have values ≥10 kcal/(mol geom-unit), and 5 aregreater than 20 kcal/(mol geom-unit). For example, 1,6- and 1,9-(Cα−Cm)−(Cα−Cm) stretch−stretch, 1,4-(Cα−N)−(Cα−Cm), and 1,4-(Cβ−Cβ)−(Cα−N−Cα) stretch−bend interactions are large and positive. Couplingin- and out-of-plane motions (TORX) enhances out-of-plane accuracy. Though isotopomer data were omittedfrom the optimization, the HBFF-SVD force fields reproduce these data with high fidelity. Finally, the HBFF-SVD force fields are compared in detail to previous normal-mode analysis and scaled quantum mechanicsstudies of Ni porphine.
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