atsim.potentials.potentialforms¶
Functions representing different potential forms.
The functions contained herein are function factories returning a function that takes separation as its sole argument.
See List of Potential Forms for descriptions of these potential forms.
Module Contents¶
Functions¶
potential(func) |
Decorator for callables that should be tagged as potential-forms or potential-functions |
is_potential(obj) |
Identifies if an object is a potential-form or potential-function |
buck4(A, rho, C, r_detach, r_min, r_attach) |
Returns a potential form describing the four-range Buckingham potential. |
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atsim.potentials.potentialforms.potential(func)[source]¶ Decorator for callables that should be tagged as potential-forms or potential-functions
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atsim.potentials.potentialforms.is_potential(obj)[source]¶ Identifies if an object is a potential-form or potential-function
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atsim.potentials.potentialforms.buck4(A, rho, C, r_detach, r_min, r_attach)[source]¶ Returns a potential form describing the four-range Buckingham potential.
The potential form is:
\[\begin{split}V(r_{ij}) = \begin{cases} A \exp(-r_{ij}/\rho) , & 0 \leq r_{ij} \leq r_\text{detach}\\ a_0 + a_1 r_{ij} +a_2 r_{ij}^2+a_3 r_{ij}^3+a_4 r_{ij}^4+a_5 r_{ij}^5, & r_\text{detach} < r_{ij} < r_\text{min}\\ b_0 +b_1 *r_{ij}+b_2*r_{ij}^2+b_3*r_{ij}^3 , & r_\text{min} \leq r_{ij} < r_\text{attach}\\ -\frac{C}{r_{ij}^6} , & r_{ij} \geq r_\text{attach}\\ \end{cases}\end{split}\]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 \(r_ ext{min}\)).
The spline parameters 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.
See also
atsim.potentials.Buck4_Splineatsim.potentials.Buck4_SplinePotential
Note
Due to the complexity of calculating the spline-coefficients this potential form does not have an equivalent in the atsim.potentials.potentialfunctions module.
Parameters: - A – A potential parameter.
- rho – potential parameter.
- C – C parameter.
- r_detach – Separation where spline starts.
- r_min – Location of stationary point.
- r_attach – End of splined region.
Returns: Splined potential.