I. Introduction
The 4.1 release of AMBER includes a new parameter file (parm94.dat) and new residue files (all_nuc94.in, all_amino94.in, all_aminont94.in, and all_aminoct94.in) which contain the parameters developed for our second generation force field. The new force field employs an approach to atomic charge fitting which is a modification of the original "standard ESP" (ElectroStatic Potential fit) approach. The new approach still involves a least squares fit of the atom centered charges so that the classical potential reproduces the quantum mechanical potential. With the new approach, however, hyperbolic restraints are applied during the fit to the charges in order to attenuate the charges on buried atoms which are statistically ill-determined. The new approach is called "RESP," for "Restrained ElectroStatic Potential fitting."
II. Two-Stage Restrained ESP (RESP) Fitting
The new charge model includes another major modification - a two-stage fit. This approach allows for the fitting of equivalent charges on certain atoms which are equivalent when the molecule is freely rotating, but are not equivalent within a static conformation. These equivalent charges are fit during the second stage of the fit, in the presence of the charges which were determined for the other atoms during the first stage.
With the previously used standard ESP method, such equivalent atoms were typically averaged "a posteriori," or after the fit. This approach often resulted in a significant change in the molecular dipole moment.
Methyl hydrogens are the atoms most typically included in the second stage fit. The methyl carbon is included as well in order to provide a sufficient number of degrees of freedom (in this case "1" since if q(C)= x then q(H)= -x/3).
The need for refitting methyl hydrogens during a second stage fit was made obvious by the example of methanol. When the three methyl hydrogens were constrained to have the same charge during a one stage fit, the charge on the oxygen was significantly reduced over its value in an unconstrained fit.
The restraint applied during the second stage of the fitting is twice as strong as that applied during the first stage (0.0010 vs. 0.0005). The motivation behind this choice was that nonpolar groups were being refit in the second stage and those atoms should have small charges in order to decrease their conformational dependence. The more the charges vary with conformation, the more the resulting conformational energies are subject to variation. Such behavior is not only undesirable from the standpoint of general reproducibility of results, but also from the standpoint that any dihedral parameters which are optimized are coupled to the charge set used.
Because the stronger restraint was applied in the second stage, the decision was also made to refit methylene groups during that stage. Second stage refitting has not been applied to polar atoms, such as the two oxygens in 1,2-ethane diol which are inequivalent when that molecule is in a conformation other than the one with highest symmetry (tTt). Similarly, second stage refitting has not been applied to amino hydrogens. Tests showed that constraining them to have the same charge during the first stage did not change their value much when compared to an unconstrained fit.
It should be emphasized that the two-stage model as described above is based on refitting only nonpolar groups during the second stage. In cases where a second stage refitting of polar atoms is thought to be necessary, then the second stage should also employ the weaker restraint and a third stage refitting employed with the stronger restraint for nonpolar groups. The best way to determine the ideal values of nonpolar charges is to carry out a fit with no restraint or with the weak restraint and with *no* constraints of equivalent atoms.
This new approach is clearly more complicated than the previous charge model and involves more subjective decisions. We have therefore provided a number of demos which we hope will serve as useful guides.
III. Multiple Conformation Fitting
Ideally, the new charge model also includes the use of multiple conformations of a given molecule in the charge fit. The amino acid charges which were derived for the new force field were fit to two conformations of each amino acid. Specifically, the extended (C5/beta-sheet) and alpha-helical conformations were applied to the backbones. The side chain torsions were then assigned so that a given torsion had a different orientation in the extended and in the alpha-helical conformation. This strategy was based on earlier results obtained with propylamine, which showed that a two-conformation fit was nearly as good as a five-conformation fit, as long as all of the primary dihedrals were varied between the two conformations. Primary dihedrals can be defined as ones where both terminal atoms are either heavy atoms or polar hydrogens.
The combined use of two-stage fitting and multiple conformation fitting requires even more decisions in terms of which atoms should be constrained to be equivalent at what times. For the example of propylamine, the best approach was found to be to constrain all corresponding heavy atoms and the amino hydrogens to be equivalent between the different conformations in the first stage. The corresponding methyl and methylene atoms were constrained to be equivalent between conformations (for the carbons and hydrogens) and within conformations (only for the hydrogens) during the second stage of the fit.
The first stage of the fit then resulted in three different charges for the carbons (C-alpha, C-beta, and C-gamma) and 7 times the number of different conformations charges for the hydrogens. That is, every hydrogen was allowed to have a different charge. One common mistake would be simply to make each atom be equivalent between all conformations, e.g. the first methyl hydrogen across all conformations and the second methyl hydrogen across all conformations, etc. However, because the conformations are different, there is no reason that individual hydrogens in a methyl group should correspond to individual hydrogens in that same methyl group in a different conformation of the molecule, based on the numbering.
IV. Conclusion
In summary, the new Two-Stage Multiple conformation RESP charge model has been shown to perform quite well in the calculation of interaction energies, free energies of solvation, and conformational energies. The new method involves more subjective decisions than the previously used standard ESP method, however. When in doubt, it is useful to carry out the charge fit in two or more different ways, in order to compare the effects of different constraints.