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Modify the expresion of Tersoff Potential to include Tersoff/shift

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Wengen Ouyang
2020-12-17 11:08:00 +02:00
parent a01b376391
commit a1b7d263c2
1 changed files with 4 additions and 3 deletions
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7
doc/src/pair_tersoff.rst
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@ -55,7 +55,7 @@ The *tersoff* style computes a 3-body Tersoff potential
.. math::
E & = \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\
V_{ij} & = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] \\
V_{ij} & = f_C(r_{ij} + \delta) \left[ f_R(r_{ij} + \delta) + b_{ij} f_A(r_{ij} + delta) \right] \\
f_C(r) & = \left\{ \begin{array} {r@{\quad:\quad}l}
1 & r < R - D \\
\frac{1}{2} - \frac{1}{2} \sin \left( \frac{\pi}{2} \frac{r-R}{D} \right) &
@ -65,14 +65,15 @@ The *tersoff* style computes a 3-body Tersoff potential
f_R(r) & = A \exp (-\lambda_1 r) \\
f_A(r) & = -B \exp (-\lambda_2 r) \\
b_{ij} & = \left( 1 + \beta^n {\zeta_{ij}}^n \right)^{-\frac{1}{2n}} \\
\zeta_{ij} & = \sum_{k \neq i,j} f_C(r_{ik}) g(\theta_{ijk})
\zeta_{ij} & = \sum_{k \neq i,j} f_C(r_{ik} + \delta) g \left[ \theta_{ijk}(r_{ij} + \delta, r_{ik} + \delta) \right]
\exp \left[ {\lambda_3}^m (r_{ij} - r_{ik})^m \right] \\
g(\theta) & = \gamma_{ijk} \left( 1 + \frac{c^2}{d^2} -
\frac{c^2}{\left[ d^2 + (\cos \theta - \cos \theta_0)^2\right]} \right)
where :math:`f_R` is a two-body term and :math:`f_A` includes three-body
interactions. The summations in the formula are over all neighbors
J and K of atom I within a cutoff distance = R + D.
J and K of atom I within a cutoff distance = R + D. math:`\delta` is
non-zero only for *tersoff/shift* style.
The *tersoff/table* style uses tabulated forms for the two-body,
environment and angular functions. Linear interpolation is performed