Journal of Computer-Aided Molecular Design

, Volume 33, Issue 2, pp 205–264 | Cite as

Force field development phase II: Relaxation of physics-based criteria… or inclusion of more rigorous physics into the representation of molecular energetics

  • A. T. HaglerEmail author


In the previous paper, we reviewed the origins of energy based calculations, and the early science of FF development. The initial efforts spanning the period from roughly the early 1970s to the mid to late 1990s saw the development of methodologies and philosophies of the derivation of FFs. The use of Cartesian coordinates, derivation of the H-bond potential, different functional forms including diagonal quadratic expressions, coupled valence FFs, functional form of combination rules, and out of plane angles, were all investigated in this period. The use of conformational energetics, vibrational frequencies, crystal structure and energetics, liquid properties, and ab initio data were all described to one degree or another in deriving and validating both the FF functional forms and force constants. Here we discuss the advances made since in improving the rigor and robustness of these initial FFs. The inability of the simple quadratic diagonal FF to accurately describe biomolecular energetics over a large domain of molecular structure, and intermolecular configurations, was pointed out in numerous studies. Two main approaches have been taken to overcome this problem. The first involves the introduction of error functions, either exploiting torsion terms or introducing explicit 2-D error correction grids. The results and remaining challenges of these functional forms is examined. The second approach has been to improve the representation of the physics of intra and intermolecular interactions. The latter involves including descriptions of polarizability, charge flux aka geometry dependent charges, more accurate representations of spatial electron density such as multipole moments, anisotropic nonbond potentials, nonbond and polarization flux, among others. These effects, though not as extensively studied, likely hold the key to achieving the rigorous reproduction of structural and energetic properties long sought in biomolecular simulations, and are surveyed here. In addition, the quality of training and validation observables are evaluated. The necessity of including an ample set of energetic and crystal observables is emphasized, and the inadequacy of free energy as a criterion for FF reliability discussed. Finally, in light of the results of applications of the two approaches to FF development, we propose a “recipe” of terms describing the physics of inter and intramolecular interactions whose inclusion in FFs would significantly improve our understanding of the energetics and dynamics of biomolecular systems resulting from molecular dynamics and other energy based simulations.


Force fields Force field derivation Potential functions Van der Waals Hydrogen bond Drug discovery Molecular dynamics Molecular mechanics Protein simulation Molecular simulation Nonbond interactions Combination rules Polarizability Charge flux Nonbond flux Polarizability flux Free energy Coupling terms Cross terms AMBER CHARMM OPLS GAFF AMOEBA SDFF CFF VFF Consistent force field Electrostatics Multipole moments Anisotropic nonbond potentials Quantum derivative fitting QDF 







Assisted model building with energy refinement


Atomic multipole optimized energetics for biomolecular applications


Absoluter unsigned error


Bond charge correction


Ben Naim–Stillinger




Critical assessment of protein structure prediction


Consistent force field


Chemistry at HARvard Macromolecular Mechanics


Charges from electrostatic potentials using a grid-based method


Charge equilibration method


Grid based energy correction map


Complete neglect of differential overlap


Condensed-phase optimized molecular potentials for atomistic simulation studies


Consistent valence force field


Density functional theory


Distributed multipole analysis


Valence double-zeta plus polarization


Empirical conformational energy program for peptides


Extended Hückel theory


Electrostatic potential


Empirical valence bond


Free energy perturbation


Force field


Fluctuating charges


Forster resonance energy transfer


General AMBER force field




GROningen MOlecular Simulation


human Cathepsin L


Hartree–Fock self-consistent-field




Intrinsically disordered protein


Linear combination of atomic orbitals




Oxygen lone pair


Monte Carlo


Momany, Carruthers, McGuire, and Scheraga force field




Molecular dynamics


MDL drug data report


Molecular Design Limited


Molecular electrostatic potentials


Molecular mechanics


Merck molecular force field




Optimized potential for liquid simulations


OPLS all atom


OPLS-AA/L OPLS all atom FF (L for LMP2)


Perturbative configuration interaction using localized orbitals


Protein data base


Potential Energy Function Consortium (Biosym)


Potential of mean force


Polarizable water model (3)


Polyproline II conformation


Quantum chemistry program exchange


Quantum derivative fitting


Charge dependent polarizability


Quantum mechanics


Restrained electrostatic potential


Root mean square


Root mean square deviation


Root mean square error


Statistical assessment of the modeling of proteins and ligands (competition)


Small angle X-ray scattering


Self-consistent field-linear combination of atomic–molecular orbital


Spectroscopically determined force fields (for macromolecules)


Sum of interactions between fragments ab initio (computed)


Simple point charge (water model)


Four point water model replacing Ben-Naim Stillinger (BNS) model


Slater-type atomic orbitals


Simple water model with negative Drude polarization


Transferable intermolecular potential three point




Triple-zeta plus valence polarization (basis set)




Urey Bradley force field


Van der Waals


Valence force field





We would like to thank Drs. Mike Gilson, Sam Krimm, Alex MacKerell, Benoit Roux, Pengyu Ren, Jay Ponder, Ken Dill, Kim Palmo, Pnina Dauber-Osguthorpe, for reading parts of manuscript and helpful discussions and Dr. Ruth Sharon for reading and help with editing. We also thank Eitan Hagler for help with the figures, Martha Obermeier for help with proofing and referee 1 who made many helpful suggestions including the addition of the effect of methodology in FF derivation. Special thanks to the editor, Dr. Terry Stouch for his invitation to write this perspective, encouragement, and endless patience.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of MassachusettsAmherstUSA
  2. 2.Valis PharmaSan DiegoUSA

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