Derivation of class II force fields: V. Quantum force field for amides, peptides, and related compounds

As the field of biomolecular structure advances, there is an ever-growing need for accurate modeling of molecular energy surfaces to simulate and predict the properties of these important systems. To address this need, a second generation amide force field for use in simulations of small organics as well as proteins and peptides has been derived. The critical question of what accuracy can be expected from calculations in general, and with this class II force field in particular, is addressed for structural, dynamic, and energetic properties. The force field is derived from a recent methodology we have developed that involves the systematic use of quantum mechanical observables. Systematic ab initio calculations were carried out for numerous configurations of 17 amide and related compounds. Relative energies and first and second derivatives of the energy of 638 structures of these compounds resulted in 140,970 ab initio quantum mechanical observables. The class II peptide quantum mechanical force field (QMFF), containing 732 force constants and reference values, was parameterized against these observables. A major objective of this work is to help establish the role of anharmonicity and coupling in improving the accuracy of molecular force fields, as these terms have not yet become an agreed upon standard in the ever more extensive simulations being used to probe biomolecular properties. This has been addressed by deriving a class I harmonic diagonal force field (HDFF), which was fit to the same energy surface as the QMFF, thus providing an opportunity to quantify the effects of these coupling and anharmonic contributions. Both force field representations are assessed in terms of their ability to fit the observables. They have also been tested by calculating the properties of 11 stationary states of these amide molecules. Optimized structures, vibrational frequencies, and conformational energies obtained from the quantum calculations and from both the QMFF and the HDFF are compared. Several strained and derivatized compounds including urea, formylformamide, and butyrolactam are included in these tests to assess the range of applicability (transferability) of the force fields. It was found that the class II coupled anharmonic force field reproduced the structures, energies, and vibrational frequencies significantly more faithfully than the class I harmonic diagonal force field. An important measure, rms energy deviation, was found to be 1.06 kcal/mol with the class II force field, and 2.30 kcal/mol with the harmonic diagonal force field. These deviations represent the error in relative configurational energy differences for strained and distorted structures calculated with the force fields compared with quantum mechanics. This provides a measure of the accuracy that might be expected in applications where strain may be important such as calculating the energy of a system as it approaches a (rotational) barrier, in ligand binding to a protein, or effects of introducing substituents into a molecule that may induce strain. Similar results were found for structural properties. Protein dynamics is becoming of ever-increasing interest, and, to simulate dynamic properties accurately, the dynamic behavior of model compounds needs to be well accounted for. To this end, the ability of the class I and class II force fields to reproduce the vibrational frequencies obtained from the quantum energy surface was assessed. An rms deviation of 43 cm−1 was achieved with the coupled anharmonic force field, as compared to 105 cm−1 with the harmonic diagonal force field. Thus, the analysis presented here of the class II force field for the amide functional group demonstrates that the incorporation of anharmonicity and coupling terms in the force field significantly improves the accuracy and transferability with regard to the simulation of structural, energetic, and dynamic properties of amides. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 430–458, 1998