Tersoff

class hoomd.md.many_body.Tersoff(nlist, default_r_cut=None)

Bases: Triplet

Tersoff force.

Parameters:

The Tersoff potential is a bond-order potential based on the Morse potential that accounts for the weakening of individual bonds with increasing coordination number. It does this by computing a modifier to the attractive term of the potential. The modifier contains the effects of third-bodies on the bond energies. The potential also includes a smoothing function around the cutoff. The implemented smoothing function is exponential in nature as opposed to the sinusoid used by J. Tersoff 1988.

Tersoff computes the Tersoff three-body force on every particle in the simulation state. Despite the fact that the Tersoff potential accounts for the effects of third bodies, the species of the third body is irrelevant. It can thus use type-pair parameters similar to those of the pair potentials:

\[U_{ij}(r) = \frac{1}{2} f_C(r_{ij}) \left[f_R(r_{ij}) + b_{ij}f_A(r_{ij})\right]\]

where

\[ \begin{align}\begin{aligned}f_R(r) = A_1e^{\lambda_1(r_D-r)}\\f_A(r) = A_2e^{\lambda_2(r_D-r)}\end{aligned}\end{align} \]
\[\begin{split}f_C(r) = \begin{cases} 1 & r < r_{\mathrm{cut}} - r_{CT} \\ \exp \left[-\alpha\frac{x(r)^3}{x(r)^3 - 1} \right] & r_{\mathrm{cut}} - r_{CT} < r < r_{\mathrm{cut}} \\ 0 & r > r_{\mathrm{cut}} \end{cases}\end{split}\]
\[b_{ij} = (1 + \gamma^n\chi_{ij}^n)^{\frac{-1}{2n}}\]

In the definition of \(f_C(r)\), there is a quantity \(x(r)\), which is defined as

\[x(r) = \frac{r - (r_{\mathrm{cut}} - r_{CT})}{r_{CT}}\]

which ensures continuity between the different regions of the potential. In the definition of \(b_{ij}\), there is a quantity \(\chi_{ij}\) which is defined as

\[ \begin{align}\begin{aligned}\chi_{ij} = \sum_{k \neq i,j} f_C(r_{ik}) \cdot e^{\lambda_3^3 |r_{ij} - r_{ik}|^3} \cdot g(\theta_{ijk})\\g(\theta_{ijk}) = 1 + \frac{c^2}{d^2} - \frac{c^2}{d^2 + |m - \cos(\theta_{ijk})|^2}\end{aligned}\end{align} \]

Example:

nl = md.nlist.Cell()
tersoff = md.many_body.Tersoff(default_r_cut=1.3, nlist=nl)
tersoff.params[('A', 'B')] = dict(magnitudes=(2.0, 1.0), lambda3=5.0)

Members inherited from AutotunedObject:

property kernel_parameters

Kernel parameters. Read more...

property is_tuning_complete

Check if kernel parameter tuning is complete. Read more...

tune_kernel_parameters()

Start tuning kernel parameters. Read more...

Members inherited from Force:

additional_energy

Additional energy term. Read more...

additional_virial

Additional virial tensor term \(W_\mathrm{additional}\). Read more...

cpu_local_force_arrays

Local force arrays on the CPU. Read more...

energies

Energy contribution \(U_i\) from each particle. Read more...

energy

The potential energy \(U\) of the system from this force. Read more...

forces

The force \(\vec{F}_i\) applied to each particle. Read more...

gpu_local_force_arrays

Local force arrays on the GPU. Read more...

torques

The torque \(\vec{\tau}_i\) applied to each particle. Read more...

virials

Virial tensor contribution \(W_i\) from each particle. Read more...

Members inherited from Triplet:

r_cut

Cuttoff radius beyond which the energy and force are 0. Read more...

nlist

Neighbor list used to compute the triplet potential. Read more...

Members defined in Tersoff:

params

The Tersoff potential parameters. The dictionary has the following keys:

  • magnitudes (tuple[float, float]) - \((A_1, A_2)\) - Magnitudes of the repulsive and attractive terms (default: (1.0, 1.0)) \([\mathrm{energy}]\)

  • exp_factors (tuple[float, float]) - \((\lambda_1, \lambda_2)\) - exponential factors of the repulsive and attractive terms (default: 2.0) \([\mathrm{length}^{-1}]\)

  • lambda3 (float) - \(\lambda_3\) - exponential factor in \(\chi_{ij}\) (default: 0.0) \([\mathrm{length}^{-1}]\)

  • dimer_r (float) - \(r_D\) - length shift in attractive and repulsive terms (default: 1.5) \([\mathrm{length}]\)

  • cutoff_thickness (float) - \(r_{CT}\) - distance which defines the different regions of the potential (default: 0.2) \([\mathrm{length}]\)

  • alpha (float) - \(\alpha\) - decay rate of the cutoff term \(f_C(r)\) (default: 3.0) \([\mathrm{dimensionless}]\)

  • n (float) - \(n\) - power in \(b_{ij}\) (default: 0.0) \([\mathrm{dimensionless}]\)

  • gamma (float) - \(\gamma\) - coefficient in \(b_{ij}\) (default: 0.0) \([\mathrm{dimensionless}]\)

  • c (float) - \(c\) - coefficient in \(g(\theta)\) (default: 0.0) \([\mathrm{dimensionless}]\)

  • d (float) - \(d\) - coefficient in \(g(\theta)\) (default: 1.0) \([\mathrm{dimensionless}]\)

  • m (float) - \(m\) - coefficient in \(g(\theta)\) (default: 0.0) \([\mathrm{dimensionless}]\)

Type: TypeParameter [tuple [particle_type, particle_type], dict]