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Wednesday, May 13, 2015

Gold and Lennard-Jones potential

sigma=2.637 Angström
[T. HALICIOGLU and G. M. POUND: Calculation of Potential Energy Parameters ; phys. stat. sol. (a) 30, 619 (1975) ]

Lennard-Jones potential:

A = 4εσ6 and B = 4εσ12 

Using the continuous approach, where the atoms at discrete locations on the mol- ecule are averaged over a surface, the molecular interatomic energy is obtained by calculating integrals over the surfaces of each molecule, given by
 where η1 and η2 represent the mean surface density of atoms on each molecule. Further, we may define the integral In in the form of

and therefore, E = η1η2(AI3 + BI6).
The Lennard-Jones parameters for gold nanoparticles are taken from the work

of Pu et al. [Q. Pu, Y. Leng, X. Zhao, P.T. Cummings, Molecular simulations of stretching gold nanowires in solvents. Nanotechnology 18, 424007 (2007)], who use 
ε = 0.039kcal mol1 and σ = 2.934Å 
corresponding to A = 7.2465eV ×6 and B = 4,622.6273eV ×12

From the fact that gold adopts a face-centred cubic (fcc) crystal structure, the triangular arrangement is employed to determine a mean surface density of gold nanoparticles. Assuming that each atom of gold is coordinated with six other atoms, the area of a unit cell is given by A= 3d2/2Å2 where d denotes the equilibrium spacing which can be obtained as d = 21/6σ = 3.2933Å. Consequently, the mean surface density η of the gold layers is taken to be 1/A= 0.1065Å2. 


example of NVT equilibration in LAMMPS

All the simulation was carried out in the NVT ensemble.
The initial equilibration was done by heating the system from 20 K to 300 K with discrete steps of 20 K/50 ps.
After the equilibration, the systems were run at a temperature of 300 K for additional 5 ns.
Dynamics of transfer, and variance in distributions  were analyzed by heating equilibrated systems from 300 K to 400 K followed by cooling from 400 K to 300 K in discrete steps of 10 K/ 200 ps.
For accurate analyses at each temperature, the last snapshot from the heating cycles were run for more than 2 ns and data collected in the equilibrated phase as seen through block averages of
total energy.
All simulations were carried out using the LAMMPS simulation package.
The equations of motion were integrated using the velocity-Verlet algorithm using a time step
of 1 fs. For NVT ensembles, a Nosé-Hoover thermostat with a damping time of 100 fs
was used to maintain the temperature of the system.