Coulomb potential (Ewald or short/screened)¶

Coulomb potential requires a parameter file in.params.Coulomb. Parameters required in the file are different depending on charges and terms entries.

Fixed charges given in the input¶

The basic format (fixed charges to be specified) of in.params.Coulomb is the following,

charges  fixed
  Si   1.0
  O   -2.0
interactions
  Si  Si
  Si  O
  O   O
terms  short

sigma  2.5

In this format, black lines are neglected. There are some keywords:

charges : fixed or variable (or qeq) -- Followed by the lines of species charges, e.g., \(q_1 = 1.0\) and \(q_2 = -2.0\).
interactions (optional) -- Followed by the pairs of species. If not specified, all the interactions are taken into account.
terms : full, long or short/screened_cut -- Either full Ewald terms, long-range term only, short-range term only, or short-term with smooth cutoff.
sigma -- Width of the Gaussian charge distribution, which is related to the accuracy in case of Ewald method.

Fixed charges computed assuming charge neutrality¶

If charges fixed_bvs is given, the charges on species are computed using their formal charges and principal quantum numbers as given by Adams and Rao¹. For example, the following in.params.Coulomb file is for Li-La-Zr-O system with species charges computed using their approach.

terms   screened_cut
charges   fixed_bvs 
   O       -2.0   0.66    2
   Li       1.0   1.28    2
   La       3.0   2.07    6
   Zr       4.0   1.75    5

fbvs   1.000

interactions 
   O   O
   Li  Li
   Li  La
   Li  Zr
   La  La
   La  Zr
   Zr  Zr

The meanings of entries in the four lines just below the charges entry are in the order:

species
formal charge
ionic radius used below to determine
principal quantum number

And fbvs is \(f\) parameter for \(r_\mathrm{AB} = f\times (r_\mathrm{A} +r_\mathrm{B})\), which is the distance parameter between species A and B used in complementary error function in screened Coulomb potential as,

\[\phi_\mathrm{AB}(r_{ij}) = k\frac{q_i q_j}{r_{ij}} \mathrm{erfc} \left( \frac{r_{ij}}{r_\mathrm{AB}}\right)\]

The paper² describes how to optimize the ionic radii parameters, where all the principal quantum numbers are set to 1 in order to use formal charges for species.

Variable charge or QEq¶

Coulomb potential can treat variable charge or QEq by specifying variable or qeq to the charges keyword as shown below.

charges  variable
  Si  4.7695    8.7893    0.0   0.0  2.4
  O   7.5405    15.8067   0.0  -1.2  0.0
interactions
  Si  Si
  Si  O
  O   O
terms   screened_cut
sigma   2.5
chgopt_method   damping
codmp_method    damping
fdamp_codmp     0.7
conv_eps_qeq      1.0d-8
nstp_codmp      100
dt_codmp        0.005
qmass_codmp     0.002
qtot_codmp      0.0

Here, charges variable requires some following lines that have

name,  chi,  Jii,  E0,  qlow,  qup

name: name of the chemical species
chi: electronegativity of the species (eV)
Jii: hardness of the species (eV)
E0: atomic energy (eV)
qlow: lower limit of the charge of the species
qup: upper limit of the charge of the species

And the meanings of the other parameters are listed below:

chgopt_method: The method of charge optimization: damping or FIRE. And the codmp pre/postfix indicates that the variables are related to chgopt_method==damping.The FIRE is known to be efficient, but it is sometimes unstable.
fdamp_codmp: Damping factor multiplied to velocities of charges every step in damping MD. (default: 0.7d0)
conv_eps_qeq: Convergence criterion of energy difference (eV/atom) from the previous step or one step before the previous step. The difference from the step before the previous step is used because sometimes charges oscillate and do not converge otherwise. (Default: 1.0d-8)
nstp_codmp: Max number of steps for damping MD. (Default: 100)
dt_codmp: Time interval for damping MD in fs. (Default: 0.005)
qmass_codmp: Mass of charge in the unit of proton mass. (Default: 0.002)
qtot_codmp: Total charge of the system in the unit of \(e\). (Default: 0.0)

Adams, S. & Rao, R. P. High power lithium ion battery materials by computational design. Phys. Status Solidi 208, 1746–1753 (2011). ↩
Kobayashi, R., Miyaji, Y., Nakano, K. & Nakayama, M. High-throughput production of force-fields for solid-state electrolyte materials. APL Materials 8, 081111 (2020) ↩