I want to tabulate the Finnis and Sinclair potential in LAMMPS setfl format.
As far as my knowledge, for LAMMPS, we need to provide a look-up table and LAMMPS will pick up the appropriate values for V®, rho® and F(rho) from this table by interpolation.
Now, Rho (i) = Sum over j [ ( r_ij -d ) ] ^ 2.
Rho is maximum at r = 0 and for d=4.400224 (taken from the F&S paper), the maximum value of Rho is 19.3619730879893 (Rho_Max) . So, in LAMMPS EAM table, we will tabulate F from Rho=0 to Rho= i*dRho where dRho = (Rho_max - 0)/dN (dN= number of grid points)
But, this spatial variation of Rho around site i is due to 1 atom only whose distance varies from 0 to d.
In real situation, the site i will be surrounded by many atoms (e.g. in equilibrium case, 8+6 = 14 atoms) and the density at site i will be much higher than Rho_max= 19.361973.
Now, the corresponding F(rho) is tabulated only for Rho values ranging from 0 to Rho_Max at ‘Nrho’ number of grid points where, dRho = ( Rho_Max - 0 )/Nrho.
In that case, how do LAMMPS pick up the correct value from the look up table when the effective Rho at an atomic position is more than Rho_Max ?