Journal of Computer-Aided Molecular Design

, Volume 33, Issue 2, pp 133–203 | Cite as

Biomolecular force fields: where have we been, where are we now, where do we need to go and how do we get there?

  • Pnina Dauber-Osguthorpe
  • A. T. HaglerEmail author


In this perspective, we review the theory and methodology of the derivation of force fields (FFs), and their validity, for molecular simulations, from their inception in the second half of the twentieth century to the improved representations at the end of the century. We examine the representations of the physics embodied in various force fields, their accuracy and deficiencies. The early days in the 1950s and 60s saw FFs first introduced to analyze vibrational spectra. The advent of computers was soon followed by the first molecular mechanics machine calculations. From the very first papers it was recognized that the accuracy with which the FFs represented the physics was critical if meaningful calculated structural and thermodynamic properties were to be achieved. We discuss the rigorous methodology formulated by Lifson, and later Allinger to derive molecular FFs, not only obtain optimal parameters but also uncover deficiencies in the representation of the physics and improve the functional form to account for this physics. In this context, the known coupling between valence coordinates and the importance of coupling terms to describe the physics of this coupling is evaluated. Early simplified, truncated FFs introduced to allow simulations of macromolecular systems are reviewed and their subsequent improvement assessed. We examine in some depth: the basis of the reformulation of the H-bond to its current description; the early introduction of QM in FF development methodology to calculate partial charges and rotational barriers; the powerful and abundant information provided by crystal structure and energetic observables to derive and test all aspects of a FF including both nonbond and intramolecular functional forms; the combined use of QM, along with crystallography and lattice energy calculations to derive rotational barriers about ɸ and ψ; the development and results of methodologies to derive “QM FFs” by sampling the QM energy surface, either by calculating energies at hundreds of configurations, or by describing the energy surface by energies, first and second derivatives sampled over the surface; and the use of the latter to probe the validity of the representations of the physics, reveal flaws and assess improved functional forms. Research demonstrating significant effects of the flaws in the use of the improper torsion angle to represent out of plane deformations, and the standard Lorentz–Berthelot combining rules for nonbonded interactions, and the more accurate descriptions presented are also reviewed. Finally, we discuss the thorough studies involved in deriving the 2nd generation all-atom versions of the CHARMm, AMBER and OPLS FFs, and how the extensive set of observables used in these studies allowed, in the spirit of Lifson, a characterization of both the abilities, but more importantly the deficiencies in the diagonal 12-6-1 FFs used. The significant contribution made by the extensive set of observables compiled in these papers as a basis to test improved forms is noted. In the following paper, we discuss the progress in improving the FFs and representations of the physics that have been investigated in the years following the research described above.


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 Quantum derivative fitting QDF 







Assisted model building with energy refinement


Atomic multipole optimized energetics for biomolecular applications


Ben Naim–Stillinger


Consistent force field


Chemistry at HARvard Macromolecular Mechanics


Complete neglect of differential overlap


Condensed-phase optimized molecular potentials for atomistic simulation studies


Consistent valence force field


Density functional theory


Empirical conformational energy program for peptides


Extended Huckel theory


Force field


Fluctuating charges




GROningen MOlecular Simulation




Linear combination of atomic orbitals




Least squares


Monte Carlo


Momany, Carruthers, McGuire, and Scheraga Force Field




Molecular dynamics


MDL drug data report


Molecular design limited


Molecular mechanics


Merck molecular force field




Optimized potential for liquid simulations


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


Perturbative configuration interaction using localized orbitals


Protein data base


Potential energy function consortium (Biosym)


Quantum chemistry program exchange


Quantum derivative fitting


Charge dependent polarizability


Quantum mechanics


Restrained electrostatic potential


Root mean square


Root mean square deviation


Self-consistent field-linear combination of atomic-molecular orbital (wave function)


Spectroscopically determined force fields (for macromolecules)


Simple point charge (water model)


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


Slater-type atomic orbitals


Transferable intermolecular potential (functions for water, alcohols and ethers)






van der Waals


Valence force field





We would like to thank Dr. Mike Gilson, for reading parts of the manuscript and helpful discussions and Dr. Ruth Sharon for reading, discussing and valuable help with editing. We also thank Eitan Hagler for help with the figures. 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.Art Pearl StudiosNewlynUK
  3. 3.Valis PharmaSan DiegoUSA

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