Nonbonded interaction potentials

Lennard-Jones potential As two atoms approach one another there is the attraction due to London dispersion forces and eventually a van der Waals repulsion as the interatomic distance r gets smaller than the equilibrium distance. A well-known potential energy function to describe this behavior is the Lennard-Jones (6-12) potential (LJ). The LJ (6-12) potential represents the attractive part as r-6-dependent whereas the repulsive part is represented by an r n term. Another often used nonbonded interaction potential is the Buckingham potential which uses a similar distance dependence for the attractive part as the LJ (6-12) potential but where the repulsive part is represented by an exponential function. 

Murtola T, Karttunen M, Vattulainen U (2009) Chem Phys 131 055101 Villa A, Peter C, van der Vegt NFA (2010) Transferability of nonbonded interaction potentials for coarse grained simulations benzene in water. J Chem Theory Comput 6 2434-2444... 

In this section, we present a detailed discussion of methods relevant to counterion simulations of DNA. Electrostatic interactions dominate all energies involving the DNA and ions. The largest systems simulated to date typically require truncation of nonbonded interaction potentials at around ISA. Abrupt truncation of the potential has the adverse effect of creating an artificial boundary. In an MD simulation, the abrupt truncation produces a discontinuity in force because the first derivative of the interaction potential at the cutoff radius is infinity. Computer programs simply set the forces at the boundary to be zero instead of large values to represent infinity. 

Most of the methods proposed include a van der Waals term for describing nonbonded interactions between atoms in the two regions. This is usually represented by a Leonard-Jones 6-12 potential of the form... 

United atom force fields (see United versus All Atom Force Fields on page 28) are sometimes used for biomolecules to decrease the number of nonbonded interactions and the computation time. Another reason for using a simplified potential is to reduce the dimensionality of the potential energy surface. This, in turn, allows for more samples of the surface. 

HyperChem also provides a shifting potential for terminating nonbonded interactions (equation 15). 

In an attempt to remedy truncation problems, a shifting potential multiplies the nonbonded electrostatic potential by a function that goes to zero. That is, the potential is shifted to zero at the cutoff Roff. Unlike the switching function, the shifted potential does not apply to van der Waals interactions. 

The above potential describes the monopole-monopole interactions of atomic charges Q and Qj a distance Ry apart. Normally these charge interactions are computed only for nonbonded atoms and once again the interactions might be treated differently from the more normal nonbonded interactions (1-5 relationship or more). The dielectric constant 8 used in the calculation is sometimes scaled or made distance-dependent, as described in the next section. 

OPES (Optimized Potentials for Liquid Simulations) is based on a force field developed by the research group of Bill Jorgensen now at Yale University and previously at Purdue University. Like AMBER, the OPLS force field is designed for calculations on proteins and nucleic acids. It introduces nonbonded interaction parameters that have been carefully developed from extensive Monte Carlo liquid simulations of small molecules. These nonbonded interactions have been added to the bonding interactions of AMBERto produce anew force field that is expected to be better than AMBER at describing simulations where the solvent is explic-... 

SH Bryant, CE Lawrence. The frequency of lon-pair substructures m proteins is quantitatively related to electrostatic potential A statistical model for nonbonded interactions. Proteins 9 108-119, 1991. 

The nonbonded potential can be described by an atom-atom interaction potential of the form used in eqs. (3.1) and (3.2). 

The potential L/nb is used for nonbonded interactions between the indicated EVB atoms, while f/ b is used for nonbonded interactions between all other atoms, as long as the corresponding atoms are not bonded to each other or to a common atom. 

Potential functions induced-dipole terms, 84-85 minimization, 113-116 nonbonded interactions, 84-85 Potential of mean force, 43, 144 Potential surfaces, 1,6-11, 85, 87-88, 85 for amide hydrolysis, 176-181,178,179, 217-220, 218... 

Fig. 7.5 Illustration of how dispersion forces affect gauche (G) conformations. Compared to structures with gauche forms devoid of dispersion forces (i.e., HF-optimized), structures with gauche forms subject to dispersion forces (MP2 optimized) contract in such a way that the 1. ..5 nonbonded interactions in an attractive part of the van der Waals potential are shortened. Thus, in GG-pentane (shown above), MP2-optimized torsional angles are contracted by several degrees compared to the HF-optimized geometry, causing a reduction in the 1...5 nonbonded distances by several tenths of an A. For additional details and the numerical values see R. F. Frey, M. Cao, S. Q. Newton, and L. Schafer, J. Mol. Struct. 285 (1993) 99.

Fig. 2.5. Possible applications of a coupling parameter, A, in free energy calculations, (a) and (b) correspond, respectively, to simple and coupled modifications of torsional degrees of freedom, involved in the study of conformational equilibria (c) represents an intramolecular, end-to-end reaction coordinate that may be used, for instance, to model the folding of a short peptide (d) symbolizes the alteration of selected nonbonded interactions to estimate relative free energies, in the spirit of site-directed mutagenesis experiments (e) is a simple distance separating chemical species that can be employed in potential of mean force (PMF) calculations and (f) corresponds to the annihilation of selected nonbonded interactions for the estimation of e.g., free energies of solvation. In the examples (a), (b), and (e), the coupling parameter, A, is not independent of the Cartesian coordinates, x. Appropriate metric tensor correction should be considered through a relevant transformation into generalized coordinates...

The revalues are distances between atoms separated by a chain of three (four) or more bonds (Section 2.1.5.). Mainly because of the introduction of the nonbonded interactions, Eq. (8) and (9) no longer represent simple harmonic force fields. We therefore denote the constants of these expressions as potential constants and not as force constants. In principle, all the constants of the force fields (2), (3), (4), (8), and (9) are different, as indicated by different indices (V FFF , U f/BFF , v = vibrational (understood in the sense of standard vibrational-spectroscopic computational techniques)). In what follows we shall be primarily concerned with force fields of the type of Eq. (8) which we therefore formulate with the simplest symbols. 

Terms representing these interactions essentially make up the difference between the traditional force fields of vibrational spectroscopy and those described here. They are therefore responsible for the fact that in many cases spectroscopic force constants cannot be transferred to the calculation of geometries and enthalpies (Section 2.3.). As an example, angle deformation potential constants derived for force fields which involve nonbonded interactions often deviate considerably from the respective spectroscopic constants (7, 7 9, 21, 22). Nonbonded interactions strongly influence molecular geometries, vibrational frequencies, and enthalpies. They are a decisive factor for the transferability of force fields between systems of different strain (Section 2.3.). 

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