List of Potential Forms¶
- Born-Mayer (bornmayer)
- Buckingham (buck)
- Buckingham-4 (buck4)
- Constant (constant)
- Coulomb (coul)
- Exponential (exponential)
- Exponential Spline (exp_spline)
- Hydrogen Bond 12-10 (hbnd)
- Lennard-Jones 12-6 (lj)
- Morse (morse)
- Polynomial (polynomial)
- Square Root (sqrt)
- Tang-Toennies (tang_toennies)
- Zero (zero)
- Ziegler-Biersack-Littmark (zbl)
Key to features:
The Features field in the following potential description may contain the following values:
- potential-form - can be used in the
[Pair]
,[EAM-Embed]
and[EAM-Density]
sections of a potable input file. - potential-function - can also be used as a function in sections of input files that accept mathematical expressions.
- deriv - potential form provides an analytical derivative with respect to separation.
- deriv2 - provides an analytical second derivative with respect to separation.
Born-Mayer (bornmayer)¶
potable signature: | |
---|---|
as.bornmayer \(A\) \(\rho\) | |
Features: | potential-form, potential-function, deriv, deriv2 |
See also
Buckingham (buck)¶
Potential form due to R.A. Buckingham [Buckingham1938]
potable signature: | |
---|---|
as.buck \(A\) \(\rho\) \(C\) |
|
Features: | potential-form, potential-function, deriv, deriv2. |
Buckingham-4 (buck4)¶
Four-range Buckingham potential due to B. Vessal et al. [Vessal1989], [Vessal1993].
In other words this is a Buckingham potential in which the Born-Mayer component acts at small separations and the disprsion term acts at larger separation. These two parts are linked by a fifth then third order polynomial (with a minimum formed in the spline at \(r_\text{min}\)).
The spline parameters (\(a_{0\ldots 5}\) and \(b_{0\ldots 3}\)) are subject to the constraints that \(V(r_{ij})\), first and second derivatives must be equal at the boundary points and the function must have a stationary point at \(r_{min}\). The spline coefficients are automatically calculated by this potential-form.
Note
Due to the complexity of calculating the spline-coefficients this potential form does not have an equivalent in the atsim.potentials.potentialfunctions module.
potable signature: | |
---|---|
as.buck4 \(A\) \(\rho\) \(C\) \(r_\text{detach}\) \(r_\text{min}\) \(r_\text{attach}\) |
|
Features: | potential-form, deriv, deriv2 |
See also
Constant (constant)¶
Potential form that always evaluates to a constant value.
potable signature: | |
---|---|
as.constant C |
|
Features: | potential-form, potential-function, deriv, deriv2 |
Coulomb (coul)¶
Electrostatic interaction between two point charges.
Note
Constant value appropriate for \(r_{ij}\) in angstroms and energy in eV.
potable signature: | |
---|---|
as.coul \(q_i\) \(q_j\) |
|
Features: | potential-form, potential-function, deriv, deriv2 |
Exponential (exponential)¶
General exponential form.
potable signature: | |
---|---|
as.exponential \(A\) \(n\) |
|
Features: | potential-form, potential-function, deriv, deriv2 |
Exponential Spline (exp_spline)¶
Exponential spline function (as used in splining routines).
\[V(r_{ij}) = \exp \left( B_0 + B_1 r_{ij} + B_2 r_{ij}^2 + B_3 r_{ij}^3 + B_4 r_{ij}^4 + B_5 r_{ij}^5 \right) + C\]
Where \(B_0\), \(B_1\), \(B_2\), \(B_3\), \(B_4\), \(B_5\), \(C\) are spline coefficients.
potable signature: | |
---|---|
as.exp_spline \(B_0\) \(B_1\) \(B_2\) \(B_3\) \(B_4\) \(B_5\) \(C\) |
|
Features: | potential-form, potential-function, deriv, deriv2 |
See also
Hydrogen Bond 12-10 (hbnd)¶
portable signature: | |
---|---|
as.hbnd \(A\) \(B\) |
|
Features: | potential-form, potential-function, deriv, deriv2 |
Lennard-Jones 12-6 (lj)¶
Potential form first proposed by John Lennard-Jones in 1924 [Lennard-Jones1924].
\(\epsilon\) defines depth of potential well and \(\sigma\) is the separation at which \(V(r_{ij})\) is zero.
potable signature: | |
---|---|
as.lj \(\epsilon\) \(\sigma\) |
|
Features: | potential-form, potential-function, deriv, deriv2 |
See also
Morse (morse)¶
\(-D\) is the potential well depth at an equilibrium separation of \(r_*\).
potable signature: | |
---|---|
as.morse \(\gamma\) \(r_*\) \(D\) |
|
Features: | potential-form, potential-function, deriv, deriv2 |
See also
Polynomial (polynomial)¶
Polynomial of arbitrary order.
This function accepts a variable number of arguments which are \(C_0, C_1, \dots, C_n\) respectively.
potable signatures: | |
---|---|
as.polynomial \(C_0 ... C_n\) |
|
Features: | potential-form, potential-function, deriv, deriv2 |
Square Root (sqrt)¶
Potential function is:
potable signature: | |
---|---|
as.sqrt \(G\) |
|
Features: | potential-form, potential-function, deriv, deriv2 |
Tang-Toennies (tang_toennies)¶
This potential form was derived to describe the Van der Waal’s interactions between the noble gases (He to Rn) by Tang and Toennies [Tang2003].
This has the following form:
Where:
potable signature: | |
---|---|
as.tang_toennies \(A\) \(b\) \(C_6\) \(C_8\) \(C_{10}\) |
|
Features: | potential-form, potential-function, deriv, deriv2 |
Zero (zero)¶
Potential form which returns zero for all separations.
potable signature: | |
---|---|
as.zero |
|
Features: | potential-form, potential-function, deriv, deriv2 |
Ziegler-Biersack-Littmark (zbl)¶
Ziegler-Biersack-Littmark screened nuclear repulsion for describing high energy interactions [Ziegler2015].
Where \(Z_i\) and \(Z_j\) are the atomic numbers of two species.
potable signature: | |
---|---|
as.zbl \(Z_i\) \(Z_j\) |
|
Features: | potential-form, potential-function, deriv, deriv2 |