Derivation of Class II Force Fields. III. Characterization of a Quantum Force Field for Alkanes

Abstract

AbstractRecently, a quantum mechanical Class II force field (QMFF) was derived from a fit of HF/6–31G* ab initio energy and energy derivative data for alkanes, and a comparison of this quantum force field and the ab initio energy and energy derivatives was presented. In this work, the quantum force field is further evaluated with regard to its accuracy, and, more importantly, transferability. A detailed comparison between structures, frequencies, and energies calculated from quantum mechanics and from the classical analytical form is given for a set of molecules selected from both those used in the original training set and molecules selected from outside the training set. None of these properties were used directly in the original derivation of the force field. In order to assess the importance of anharmonic and coupling interactions that occur in and contribute to molecular energy surfaces, the results are compared to a diagonal quadratic force field. It is demonstrated that the QMFF functional form is capable of calculating the ab initio bond lengths, bond angles, torsion angles, and conformational energy differences to an rms accuracy of 0.003 Å, 0.4°, 1.2°, and 1.0 kcal/mol, respectively. This compares quite well to corresponding deviations of 0.006 Å, 0.8 Å, 2.3°, and 3.3 kcal/mol for a harmonic diagonal force field. Excluding three‐ or four‐membered rings, the QMFF rms frequency deviations were 24 cm−1, which again is much better than the ˜100 cm−1 deviations for the harmonic diagonal force field. Larger average rms frequency deviations of 36 and 71 cm−1 were found with QMFF for molecules with three‐ and four‐membered rings. An in‐depth analysis of C‐H and C‐C bond length, H‐C‐H, H‐C‐C, and C‐C‐C bond angle, and C‐C‐C‐C torsion angle deviations is also presented, along with a similar characterization of frequency deviations in C‐H stretching, C‐C stretching, C‐C‐C bending, and torsion modes. It is concluded from these results that the use of quantum energy surfaces allows us to derive a (Class II) functional form which is not only more accurate, but also more transferable than previous generation force fields.