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Molecular Modeling and Simulation: An Interdisciplinary Guide pp 265–298Cite as

Force Fields

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Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 21))

Abstract

In this chapter, we discuss only basic functional expressions of the potential energy function, emphasizing the simple forms typically used for biomolecules. For biomolecular systems, computational speed is premium, and the use of more complex terms (higher-order expansions, cross terms, etc.), as employed for accurate modeling of smaller systems, is not practical. The next chapter discusses important topics related to this computational complexity of the nonbonded terms: spherical cutoff techniques, fast electrostatic evaluation techniques (Ewald and fast multipoles), and implicit solvation alternatives.

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Notes

  1. 1.

    Essentially, vibrational spectra can be computed from molecular dynamics simulations by transforming time-dependent properties, such as velocity autocorrelation functions, into the frequency domain using Fourier transforms. See [1089], for example, for the precise procedure.

  2. 2.

    The simulation-derived peak heights can, at best, reproduce frequency values corresponding to the force field parameters, not the experimental values, though the latter often serve as a reference. For example, the bond stretching force constant used for O–H water bonds may be physically unrealistic, so an unnatural spectral peak may emerge from simulations using unconstrained O–H bonds. (The peak is absent if these bonds are constrained).

  3. 3.

    UV spectroscopy measures wavelengths just beyond the violet end of the visible spectrum, that is, with λ < 400 nm.

  4. 4.

    Goodman et al. [472] refer to the barrier origin as “the Bermuda Triangle of electronic theory”, reflecting a complex interdependence among three factors: electronic repulsion, relaxation mechanisms, and valence forces.

  5. 5.

    Charles Augustin de Coulomb (1736–1806) was a French physicist who formulated around 1785 the famous inverse square law, now named after him. This result was anticipated 20 years earlier by Joseph Priestly, one of the discoverers of oxygen and author of a comprehensive book on electricity.

  6. 6.

    The electrostatic energy is typically expressed as the sum over pairwise interactions between hydrodynamic DNA beads separated by segments of length l 0 as: \([{(\nu {l}_{0})}^{2}/\epsilon ]\,\sum\limits_{i<j}[\exp (-\kappa {r}_{ij})/{r}_{ij}]\), where ν is an effective linear charge density of the DNA, ε is the dielectric constant of water, and 1 ∕ κ is the Debye length at the monovalent salt concentration c s , given in Molar units (\(\kappa \approx 0.33\sqrt{{c}_{s}}\) inverse Ångstrom units at room temperature for 1:1 electrolyte solutions).

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Schlick, T. (2010). Force Fields. In: Molecular Modeling and Simulation: An Interdisciplinary Guide. Interdisciplinary Applied Mathematics, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6351-2_9

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