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Extending the Amber Force Field

Deriving Implicitly Polarized Charges in mdgx: Introduction

This tutorial will guide users through the process of creating Implicitly Polarized Charges (IPolQ) for their molecules. Implicitly polarized charges are intended to approximate the correct mean field electron density of a molecule in a condensed phase medium, which is to say the best fixed partial charge distribution if explicit polarization (Drude oscillators, fluctuating charges, inducible multipoles) is not in the simulation. The solvent environment for us has always been water, although other solvents or environments are also fair game. The IPolQ method, first published in 2013, is intended as a successor to charge sets developed from vacuum phase Hartree-Fock / 6-31G* calculations. This tutorial is written with lots of detail, but the purpose is not to dissuade beginners. Each operation in the tutorial should be simple by itself; the details are provided to help readers see the broader context, understand the control they have over their simulations, answer frequently asked questions, and hopefully prevent new users from taking wrong turns.

Stage 1: The molecule in many guises
Stage 2: QM with and without the time-averaged solvent density
Stage 3: Fitting charges
Stage 4: Iterate to convergence

Because the HF / 6-31G* method is known to over-polarize charges in some contexts, it relies on a fortuitous cancellation of errors to deliver results. IPolQ starts from a set of assumptions about the nature of the molecule and a detailed representation of the electrostatic field due to the condensed phase medium. This new method is not without approximations, and as we show in the supporting information to the 2013 publication one of these approximations (governing the way in which the energy penalty for polarizing the molecule prevents excessive charge redistribution) breaks down fairly quickly. However, the thrust of the idea remains correct: molecules in a polar condensed solvent should respond to the electrostatic field of that solvent by increasing the charge separation of their polar groups. The IPolQ method incorporates a time-averaged portrait of the charge density in the surrounding matter, which is a step up from vacuum phase quantum calculations, and this treatment permits higher levels of quantum theory to directly account for effects such as electron correlation.

The extended IPolQ scheme, published in 2014, adds the advantage of deriving charges for a molecule in vacuum as well, then expressing the IPolQ charges as a perturbation of the vacuum phase charges. This adds utility when fitting other parameters for the molecule's bonds, bond angles, and dihedrals: these parameters are typically fitted to gas-phase quantum data, and the charge set used in fitting the parameters should match. The IPolQ framework for developing a complete force field is then to fit bonded parameters in the context of vacuum phase charges and pair these with the IPolQ charges in actual simulations. This fulfills the approximation that the bonded parameters are largely unaffected by changes in the charge state, and that the consequences of dunking the molecule in a polar medium (water) are primarily electrostatic. Philosophically, this is a superior position in force field development. In practice, we have observed the results to be promising. Our published and forthcoming results show that it is important to have a polarized charge set, but the nuance of deriving bonded parameters in the context of a corresponding vacuum phase charge set is a minor advantage. Parameters derived using the traditional HF / 6-31G* workflow probably suffer slightly from the mismatch of phases at different stages in the calculation, but they appear on the whole seaworthy.

This tutorial will take the case of glycerol, a small, water-soluble molecule with several polar groups of its own and many rotatable bonds. This tutorial will make use of the mdgx program within AmberTools, and the ORCA quantum chemistry package available free to academics here. mdgx also supports the Gaussian package for its IPolQ calculations, and links to other packages may be added in the future. mdgx has an on-board manual that lists all keywords relevant to its various modules: in the case of this tutorial users can run ${AMBERHOME}/bin/mdgx (-IPOLQ, -CONFIGS, -FITQ) at any time to see the relevant documentation. Because of glycerol's size, the quantum calculations will run quickly, but if this were an actual fitting additional MD would be needed to obtain convergent charge densities. More conformations might be warranted to ensure that the charges do not depend strictly on certain rotations of each hydroxyl group, but given the symmetry of the molecule and the fact that conformations which have one hydroxyl group make a hydrogen bond to another on the same molecule are likely to be invalid, the handful of conformations that will be created in this tutorial are probably sufficient. For feature requests, questions about this tutorial, or further advice on force field development, users may contact Dave Cerutti directly at dscerutti<at>gmail<dot>com.

Publications relevant to the IPolQ scheme include:
- D.S. Cerutti, J.E. Rice, W.C. Swope, and D.A. Case. (2013) "Derivation of Fixed Partial Charges for Amino Acids Accommodating a Specific Water Model and Implicit Polarization." J. Phys. Chem. B 117: 2328-2338. link
- D.S. Cerutti, W.C. Swope, J.E. Rice, and D.A. Case. (2014) "ff14ipq: A Self-Consistent Force Field for Condensed-Phase Simulations of Proteins." J. Chem. Theory Comput. 10: 4515-4534. link
- K.T. Debiec, D.S. Cerutti, L.R. Baker, A.M. Gronenborn, D.A. Case, and L.T. Chong. (2016) "Further along the Road Less Traveled: AMBER ff15ipq, an Original Protein Force Field Built on a Self-Consistent Physical Model." J. Chem. Theory Comput. 12: 3926-3947. link

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