Morse potential Force Field

For each pair of interacting atoms (/r is their reduced mass), three parameters are needed D, (depth of the potential energy minimum, k (force constant of the par-tictilar bond), and l(, (reference bond length). The Morse ftinction will correctly allow the bond to dissociate, but has the disadvantage that it is computationally very expensive. Moreover, force fields arc normally not parameterized to handle bond dissociation. To circumvent these disadvantages, the Morse function is replaced by a simple harmonic potential, which describes bond stretching by Hooke s law (Eq. (20)). 

FIGURE 6.2 Hannonic, cubic, and Morse potential curves used to describe the energy due to bond stretching in molecular mechanics force fields. 

In light of the differences between a Morse and a harmonic potential, why do force fields use the harmonic potential First, the harmonic potential is faster to compute and easier to parameterize than the Morse function. The two functions are similar at the potential minimum, so they provide similar values for equilibrium structures. As computer resources expand and as simulations of thermal motion (See Molecular Dynamics , page 69) become more popular, the Morse function may be used more often. 

Many other useful forms have been proposed (Steele and Lippincott, 1962) and their parameters were related to spectroscopic constants as will be given for the Morse potential by Eq. (1.14). Quite often, the potential V(r) is expanded as a power series in the displacement from equilibrium (force field method)... 

For these vibrations, the quantization scheme of Section 4.2 can be carried over without any modification (Iachello and Oss, 1991a). The potentials in each stretching coordinate 5 are in an anharmonic force field approximation represented by Morse potentials. The boson operators (Ot,xt) correspond to the quantization of anharmonic Morse oscillators, with classical Hamiltonian... 

Demiralp E, Cagin T, Goddard WA(1999) Morse stretch potential charge equilibrium force field for ceramics Application to the quartz-stishovite phase transition and to silica glass. Phys Rev l tt 82 1708-1711 Dewar MJS (1977) Ground states of molecules. The MNDO method. Approximations and parameters. J Am Chem Soc 99 4899-4907... 

These potential energy terms and their attendant empirical parameters define the force field (FF). More complicated FFs which use different and/or more complex functional forms are also possible. For example, the simple harmonic oscillator expression for bond stretching can be replaced by a Morse function, Euorse (3), or additional FF terms may be added such as the stretch-bend cross terms, Estb, (4) used in the Merck molecular force field (MMFF) (7-10) which may be useful for better describing vibrations and conformational energies. 

The Lennard-Jones potential continues to be used in many force fields, particularly those targeted for use in large systems, e.g., biomolecular force fields. In more general force fields targeted at molecules of small to medium size, slightly more complicated functional forms, arguably having more physical justification, tend to be used (computational times for small molecules are so short dial the efficiency of the Lennard-Jones potential is of little consequence). Such forms include the Morse potential [Eq. (2.5)] and the Hill potential... 

COSMIC [181] method uses only harmonic potential with respect to displacements in the diagonal force fields. Neither improper torsion nor cross terms are included. The nonbonding interactions are the sum of van der Waals interactions represented by the Morse potential and the charge-based Coulomb energy. 

DREIDING [183] is an all-purpose organic or bio-organic molecular force field. It has been most widely used for large biomolecular systems. It uses either harmonic or Morse potential for the bond stretching, and the second power polynomials in... 

ESFF has been designed to be universal [187]. The Morse potential is employed for bond stretching, the potential quadratic in the cosine of the valence angles for their bending and the harmonic potential for the out of plane force field. The 6-9 with the charge based electrostatic potential is used for nonbonding interactions. No cross terms are involved. 

This form was originally proposed by Nike tic and Rasmussen (NR) in their version of the CFF force field [79]. The NR potential can be characterized as a softer potential than the Morse one in the following sense. Two potentials are both three-parametric so that a one-to-one correspondence can be established between them by proclaiming the potentials of the two forms to be equivalent if the well depth, minimum position, and elasticity constants Knr and KM expressed through the a, 6, and c parameters of the NR potential eq. (4.117) or the D0 and a parameters of the Morse potential, respectively, coincide ... 

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