Ziegler–Biersack–Littmark (ZBL)¶

Description¶

The zbl_compute_force operator computes the universal ZBL screened nuclear repulsion, which describes high-energy, short-distance collisions between atoms:

\[ E_{ij}(r) = \frac{1}{4\pi\varepsilon_0} \frac{Z_i Z_j e^2}{r} \, \phi\!\left(\frac{r}{a}\right) + S(r) \quad \text{for} \quad r<r_c \]

with the screening function

\[ \phi(x) = 0.18175\,e^{-3.19980x} + 0.50986\,e^{-0.94229x} + 0.28022\,e^{-0.40290x} + 0.02817\,e^{-0.20162x} \]

and the screening length (in Å)

\[ a = \frac{0.46850}{Z_i^{0.23} + Z_j^{0.23}} \]

\(S(r)\) is a switching function that brings the energy and its first and second derivatives smoothly to zero between an inner cutoff \(r_1\) and the outer cutoff \(r_c\). With \(t = r - r_1\):

\[ S(r) = \begin{cases} C & r \le r_1 \\ \dfrac{A}{3}t^3 + \dfrac{B}{4}t^4 + C & r_1 < r < r_c \end{cases} \]

where \(A\), \(B\) and \(C\) are computed from the value and the first two derivatives of the unscreened ZBL term at \(r_c\).

The atomic numbers \(Z_i\) and \(Z_j\) are not potential parameters: they are taken from the z property of each species (see the species block).

Parameter	Units	Description
`r1`	distance	Inner cutoff, where the switching function starts
`rc`	distance	Outer cutoff, where energy and forces reach zero
`rcut`	distance	Cutoff radius of the pair potential (use `rc`)

YAML syntax¶

zbl_compute_force:
  rcut: VALUE UNITS
  parameters: { r1: VALUE UNITS , rc: VALUE UNITS }

VALUE = Physical value of the intended parameter.
UNITS = Units of the provided value that will be passed to the conversion helper for internal units conversion.

Usage examples¶

Systems with a single atomic specy

species:
  - Ta: { mass: 180.95 Da , z: 73 , charge: 0.0 e- }

# Default variant
zbl_compute_force:
  parameters: { r1: 4.0 ang , rc: 4.8 ang }
  rcut: 4.8 ang

# Symetric variant
zbl_compute_force_symetric:
  parameters: { r1: 4.0 ang , rc: 4.8 ang }
  rcut: 4.8 ang

Systems with multiple atomic species

species:
  - In: { mass: 114.818 Da , z: 49 , charge: 0.0 e- }
  - P:  { mass: 30.974 Da  , z: 15 , charge: 0.0 e- }

zbl_multi_force:
  rcut: 4.2 ang
  common_parameters: { r1: 3.0 ang , rc: 4.2 ang }
  parameters:
    - { type_a: In , type_b: In , rcut: 4.2 ang , parameters: { r1: 3.0 ang , rc: 4.2 ang } }
    - { type_a: In , type_b: P  , rcut: 4.2 ang , parameters: { r1: 3.0 ang , rc: 4.2 ang } }
    - { type_a: P  , type_b: P  , rcut: 4.2 ang , parameters: { r1: 3.0 ang , rc: 4.2 ang } }

Tip

ZBL is typically added to a machine-learning potential (for example SNAP) to handle very short interatomic distances. List both operators in compute_force.