## Input

To run a CAC simulation, one may create/modify cac.in, in which the commands provide all input parameters for a CAC simulation.

The cac.in file, along with the potential files (embed.tab, pair.tab, and edens.tab for the EAM potential; lj.para for the LJ potential), are read by the Fortran CAC code to run the CAC simulation.

The potential files for some FCC metals are provided in the potentials directory.

### EAM potential

The EAM formulations for potential energy $E$ and the force on atom $k$, $\mathbf{f}_k$, are

$E = \frac{1}{2}\sum_i\sum_{j \atop j\neq i} V_{ij}(r_{ij}) + \sum_i F(\bar{\rho}_i)$

$\mathbf{f}_k = \sum_{j \atop j \neq k}\left[\frac{\partial V_{kj}(r_{kj})}{\partial r_{kj}}+\left(\frac{\partial F(\bar{\rho}_k)}{\partial \bar{\rho}_k}+\frac{\partial F(\bar{\rho}_j)}{\partial \bar{\rho}_j}\right)\frac{\partial \rho_{kj}(r_{kj})}{\partial r_{kj}}\right]\frac{\mathbf{r}_{kj}}{r_{kj}}$

where

$\bar{\rho}_i = \sum_{j \atop j \neq i} \rho_{ij}(r_{ij})$

Note that the force formulation above only holds for monatomic pure materials.

The first line of each *.tab file is

N first_val last_val


where N is a positive integer that equals the number of data pair (each line starting from the second line), first_val and last_val are non-negative real numbers suggesting the first and the last datum in the first column (starting from the second line), respectively.

• In embed.tab, the first column is the unitless host electron energy $\bar{\rho}$; the second column is the embedded energy $F$, in eV.
• In pair.tab, the first column is the interatomic distance $r$, in Angstrom; the second column is the pair potential $V$, in eV.
• In edens.tab, the first column is the interatomic distance $r$, in Angstrom; the second column is the unitless local electron density $\rho$.

For example, the first few lines of potentials/eam/Ag/williams/edens.tab are

3000 0.5018316703334310 5.995011000293092
0.5018316703334310       8.9800288540000004E-002
0.5036633406668621       9.0604138970000001E-002
0.5054950110002930       9.1404200869999990E-002
0.5073266813337241       9.2200486049999988E-002


In CAC simulations, an approximation is introduced to calculate the host electron density $\bar{\rho}$ of the integration points in the coarse-grained domain. For more information, read chapter 3 of Shuozhi Xu's Ph.D. dissertation.

The readers may find EAM potential files in these database:

Note that most of these files do not have the format that suits the CAC simulation.

### LJ potential

The LJ formulation for potential energy is

$E = \frac{1}{2}\sum_i\sum_{j\neq i} 4\epsilon \left[ \left( \frac{\sigma}{r^{ij}} \right)^{12} - \left( \frac{\sigma}{r^{ij}} \right)^6 \right]$

where $\epsilon$ and $\sigma$ are two parameters. In the PyCAC code, the interatomic force, not the energy, is shifted such that the force goes continuously to zero at the cut-off distance $r_\mathrm{c}$, i.e., if $r < r_\mathrm{c}$, $f = f(r) - f(r_\mathrm{c})$; otherwise, $f = 0$.

In lj.para, a blank line or a line with the "#" character in column one (a comment line) is ignored; three positive real numbers ($\epsilon$, $\sigma$, and $r_\mathrm{c}$) and one non-negative real number ($r_0$) are given in any sequence, where $r_0$ is a place holder that should always be 0.0 for the LJ potential. Note that for the EAM potential, $r_0$ equals the minimum interatomic distance, i.e., the smaller first_val given in pair.tab and edens.tab.

For example, potentials/lj/Cu/kluge/lj.para reads

# parameters for the LJ potential

epsilon   0.167
sigma     2.315
rcmin     0.
rcoff     5.38784


where epsilon = $\epsilon$, sigma = $\sigma$, rcmin = $r_0$, and rcoff = $r_\mathrm{c}$.

### Other files

When boolean_restart = t, a cac_in.restart file needs to be provided. This file is renamed from one of the cac_out_#.restart files, where # is a positive integer.

When restart_group_number > 0, or boolean_restart_refine = t and refine_style = group, one or more group_in_*.id files need to be provided, where * is a positive integer. These files are renamed from group_out_*_#.id files, which are created automatically when the total number of groups > 0. Note that if the # here does not match that in the cac_out_#.restart file, the information of the restart group may be incorrect.

When modify_number > 0 and at least one of the modify_style = add_atom, one or more LAMMPS data files lmp_*.dat need to be provided, where * is the id of the current modify command in cac.in.