# angle_style cosine/shift/exp command¶

Accelerator Variants: cosine/shift/exp/omp

## Syntax¶

angle_style cosine/shift/exp


## Examples¶

angle_style cosine/shift/exp
angle_coeff * 10.0 45.0 2.0


## Description¶

The cosine/shift/exp angle style uses the potential

$E = -U_{\text{min}} \frac{e^{-a U(\theta,\theta_0)}-1}{e^a-1} \quad \text{with} \quad U(\theta,\theta_0) = -0.5 \left(1+\cos(\theta-\theta_0) \right)$

where $$U_{\text{min}}$$, $$\theta$$, and $$a$$ are defined for each angle type.

The potential is bounded between $$[-U_{\text{min}}, 0]$$ and the minimum is located at the angle $$\theta_0$$. The a parameter can be both positive or negative and is used to control the spring constant at the equilibrium.

The spring constant is given by $$k = A \exp(A) U_{\text{min}} / [2 (\exp(a)-1)]$$. For $$a > 3$$, $$\frac{k}{U_{\text{min}}} = \frac{a}{2}$$ to better than 5% relative error. For negative values of the $$a$$ parameter, the spring constant is essentially zero, and anharmonic terms takes over. The potential is furthermore well behaved in the limit $$a \rightarrow 0$$, where it has been implemented to linear order in $$a$$ for $$a < 0.001$$. In this limit the potential reduces to the cosineshifted potential.

The following coefficients must be defined for each angle type via the angle_coeff command as in the example above, or in the data file or restart files read by the read_data or read_restart commands:

• $$U_min$$ (energy)

• $$\theta$$ (angle)

• $$A$$ (real number)

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Speed packages doc page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Speed packages page for more instructions on how to use the accelerated styles effectively.

## Restrictions¶

This angle style can only be used if LAMMPS was built with the EXTRA-MOLECULE package. See the Build package doc page for more info.

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