Molecular modelling Morse function

In an effort to understand silicon surface diffusion, NoorBatcha, Raff and Thompson have employed molecular dynamics to model the motion of single silicon atoms on the Si(001) and Si(lll)surfaces. Morse functions are used for the pair forces, with the parameters being determined by the heat of sublimation. Because different forces were used for the diffusing and substrate atoms, the incorporation of gas-phase species into the crystal could not be directly modeled. Nonetheless, they were able to explore the characteristics of adsorption and diffusion for single atoms. 

In molecular mechanics bond stretching is sometimes modeled using a Morse function (Eq. 3.13)[7() where a describes the curvature and D the depth of the potential function (Fig. 3.6). 

Simultaneously, de Vos Burchart and van de Graaf constructed a molecular mechanics force field for modeling silicate structures. The Si-0 bond potential was described by a Morse function, whereas a Urey-Bradley term... 

The best description of a bond stretch is a Morse function but, as this is computationally expensive, a simpler harmonic function is usually used in molecular modelling. Many force fields use extra terms in the equation to improve the accuracy of the function which, at its simplest, has the form ... 

A quadratic function defines a symmetric parabola and therefore cannot exactly reproduce the true relationship between the distortion of a bond length or valence angle and the energy needed to effect that distortion. However, a central assumption in the application of simple molecular mechanics models is that distortions from ideal values are small and in such cases it is only necessary that the potential energy function be realistic in the region of the ideal value. This is shown in Fig. 17.8.1, where a quadratic curve is compared to a Morse potential that is believed to more accurately reflect the relationship between bond length distortion and energy cost. 

Berend and Benson s classical treatment of V-V transfer [81] employs a two-dimensional collision model of a pair of diatomics with identical Morse interaction potentials between each pair of atoms. The Morse range parameter a was determined from experimental data for the N2-N2 T-V process. In-all, six functions are employed, one between each pair of atoms (Figure 3.5). Molecule CD, oriented at an angle / relative to its velocity vector, collides with molecule AB, with impact parameter b. Molecule AB is taken to be oriented parallel to the velocity vector of CD. The instantaneous angle between the molecular axis of AB and the line joining the centers of mass is denoted t). Cross sections for the reactions... 

The atomistic methods usually employ atoms, molecules or their group and can be classified into three main categories, namely the quantum mechanics (QM), molecular dynamics (MD) and Monte Carlo (MC). Other atomistic modeling techniques such as tight bonding molecular dynamics (TBMD), local density (LD), dissipative particle dynamics (DPD), lattice Boltzmann (LB), Brownian dynamics (BD), time-dependent Ginzbuig-Lanau method, Morse potential function model, and modified Morse potential fimction model were also applied afterwards. 

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