Basic Equations Used in Molecular Dynamics Calculations

Basic Equations Used in Molecular Dynamics Calculations 

The basis of MD calculations in solvation is pairwise interaction equations between the ion and the water molecule. The form of these equations depends greatly upon the water molecule model chosen there are several possibilities. 

For example, suppose one can choose a rigid three-point-charge model of water with an internal geometry of 109.47° and 100 pm for the HOH angle and OH distance, respectively. The interaction energy involves a Lennard-Jones 6-12 potential for electrostatic interactions between water-water and ion-water pairs, (/pair a nonadditive polarization energy, C/pg, and a term that includes exchange repulsion for ion-water and water-water pairs, 

An iterative approach is often taken to solve the equations. Iteration may be continued until the difference in the induced dipole for successive calculations is 0 to 0.1 D. Typically one uses a system of, say, 215 waters for one ion in a cubic cell with an 1860-pm side. The time step is 1 fs. Coulombic interactions may be cut off at as little as 800 pm. Each set of calculations involves computer software (the cost of which may be very high) and various mathematical procedures to solve the equations of motion. 

An example of an Li-0 radial distribution function (calculated by MD) is shown in Fig. 2.56. From such calculations one can obtain relaxation features of the rotational and translational motion of the neighboring waters and find the effect of Li or F , for example. 

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