$$\renewcommand{\AA}{\text{Å}}$$

# angle_style lepton command

Accelerator Variants: lepton/omp

## Syntax

angle_style style args
• style = lepton

• args = optional arguments

args = auto_offset or no_offset
auto_offset = offset the potential energy so that the value at theta0 is 0.0 (default)
no_offset = do not offset the potential energy

## Examples

angle_style lepton
angle_style lepton no_offset

angle_coeff  1  120.0  "k*theta^2; k=250.0"
angle_coeff  2   90.0  "k2*theta^2 + k3*theta^3 + k4*theta^4; k2=300.0; k3=-100.0; k4=50.0"
angle_coeff  3  109.47 "k*theta^2; k=350.0"

## Description

New in version 8Feb2023.

Angle style lepton computes angular interactions between three atoms with a custom potential function. The potential function must be provided as an expression string using “theta” as the angle variable relative to the reference angle $$\theta_0$$ which is provided as an angle coefficient. For example “200.0*theta^2” represents a harmonic angle potential with a force constant K of 200.0 energy units:

$U_{angle,i} = K (\theta_i - \theta_0)^2 = K \theta^2 \qquad \theta = \theta_i - \theta_0$

Changed in version 7Feb2024.

By default the potential energy U is shifted so that the value U is 0.0 for $theta = theta_0$. This is equivalent to using the optional keyword auto_offset. When using the keyword no_offset instead, the potential energy is not shifted.

The Lepton library, that the lepton angle style interfaces with, evaluates this expression string at run time to compute the pairwise energy. It also creates an analytical representation of the first derivative of this expression with respect to “theta” and then uses that to compute the force between the angle atoms as defined by the topology data.

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:

• Lepton expression (energy units)

• $$\theta_0$$ (degrees)

The Lepton expression must be either enclosed in quotes or must not contain any whitespace so that LAMMPS recognizes it as a single keyword. More on valid Lepton expressions below. The $$\theta_0$$ coefficient is the “equilibrium angle”. It is entered in degrees, but internally converted to radians. Thus the expression must assume “theta” is in radians. The potential energy function in the Lepton expression is shifted in such a way, that the potential energy is 0 for a angle $$\theta_i == \theta_0$$.

## Lepton expression syntax and features

Lepton supports the following operators in expressions:

 + Add - Subtract * Multiply / Divide ^ Power

The following mathematical functions are available:

 sqrt(x) Square root exp(x) Exponential log(x) Natural logarithm sin(x) Sine (angle in radians) cos(x) Cosine (angle in radians) sec(x) Secant (angle in radians) csc(x) Cosecant (angle in radians) tan(x) Tangent (angle in radians) cot(x) Cotangent (angle in radians) asin(x) Inverse sine (in radians) acos(x) Inverse cosine (in radians) atan(x) Inverse tangent (in radians) sinh(x) Hyperbolic sine cosh(x) Hyperbolic cosine tanh(x) Hyperbolic tangent erf(x) Error function erfc(x) Complementary Error function abs(x) Absolute value min(x,y) Minimum of two values max(x,y) Maximum of two values delta(x) delta(x) is 1 for x = 0, otherwise 0 step(x) step(x) is 0 for x < 0, otherwise 1

Numbers may be given in either decimal or exponential form. All of the following are valid numbers: 5, -3.1, 1e6, and 3.12e-2.

As an extension to the standard Lepton syntax, it is also possible to use LAMMPS variables in the format “v_name”. Before evaluating the expression, “v_name” will be replaced with the value of the variable “name”. This is compatible with all kinds of scalar variables, but not with vectors, arrays, local, or per-atom variables. If necessary, a custom scalar variable needs to be defined that can access the desired (single) item from a non-scalar variable. As an example, the following lines will instruct LAMMPS to ramp the force constant for a harmonic bond from 100.0 to 200.0 during the next run:

variable fconst equal ramp(100.0, 200)
bond_style lepton
bond_coeff 1 1.5 "v_fconst * (r^2)"

An expression may be followed by definitions for intermediate values that appear in the expression. A semicolon “;” is used as a delimiter between value definitions. For example, the expression:

a^2+a*b+b^2; a=a1+a2; b=b1+b2

is exactly equivalent to

(a1+a2)^2+(a1+a2)*(b1+b2)+(b1+b2)^2

The definition of an intermediate value may itself involve other intermediate values. Whitespace and quotation characters (’'’ and ‘”’) are ignored. All uses of a value must appear before that value’s definition. For efficiency reasons, the expression string is parsed, optimized, and then stored in an internal, pre-parsed representation for evaluation.

Evaluating a Lepton expression is typically between 2.5 and 5 times slower than the corresponding compiled and optimized C++ code. If additional speed or GPU acceleration (via GPU or KOKKOS) is required, the interaction can be represented as a table. Suitable table files can be created either internally using the pair_write or bond_write command or through the Python scripts in the tools/tabulate folder.

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

## Restrictions

This angle style is part of the LEPTON package and only enabled if LAMMPS was built with this package. See the Build package page for more info.

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