Struct Torsion 

pub struct Torsion;

Periodic torsion potential for dihedral angles.

Physics

Models the rotational barrier around a bond axis using a periodic cosine function.

• Formula: $$ E = \frac{1}{2} V [1 - \cos(n(\phi - \phi_0))] $$
• Derivative Factor (diff): $$ T = \frac{dE}{d\phi} = \frac{1}{2} V \cdot n \cdot \sin(n(\phi - \phi_0)) $$

Parameters

• v_half: Half barrier height $V_{half} = V/2$.
• n: Periodicity/multiplicity.
• cos_n_phi0: $\cos_{n\phi_0}$, pre-computed phase cosine.
• sin_n_phi0: $\sin_{n\phi_0}$, pre-computed phase sine.

Pre-computation

Use Torsion::precompute to convert physical constants into optimized parameters: $(V, n, \phi_0°) \to (V/2, n, \cos_{n\phi_0}, \sin_{n\phi_0})$.

Inputs

• cos_phi: Cosine of the dihedral angle $\cos\phi$.
• sin_phi: Sine of the dihedral angle $\sin\phi$.

Implementation Notes

• Uses optimized closed-form formulas for common periodicities ($n = 1, 2, 3$).
• Falls back to Chebyshev recurrence for higher periodicities.
• All intermediate calculations are shared between energy and torque computations.
• Branchless and panic-free.

Implementations

impl Torsion

pub fn precompute<T: Real>(v_barrier: T, n: u8, phi0_deg: T) -> (T, u8, T, T)

Pre-computes optimized kernel parameters from physical constants.

Input

• v_barrier: Total barrier height $V$.
• n: Periodicity/multiplicity.
• phi0_deg: Equilibrium dihedral angle $\phi_0$ in degrees.

Output

Returns (v_half, n, cos_n_phi0, sin_n_phi0):

• v_half: Half barrier height $V/2$.
• n: Periodicity (passed through).
• cos_n_phi0: $\cos_{n\phi_0}$, pre-computed phase cosine.
• sin_n_phi0: $\sin_{n\phi_0}$, pre-computed phase sine.

Computation

$$ V_{half} = V / 2, \quad n\phi_0 = n \cdot \phi_0 \cdot \pi / 180 $$ $$ \cos_{n\phi_0} = \cos(n\phi_0), \quad \sin_{n\phi_0} = \sin(n\phi_0) $$

Trait Implementations

impl Clone for Torsion

fn clone(&self) -> Torsion

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Torsion

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for Torsion

fn default() -> Torsion

Returns the “default value” for a type.

impl<T: Real> TorsionKernel<T> for Torsion

fn energy( cos_phi: T, sin_phi: T, (v_half, n, cos_n_phi0, sin_n_phi0): Self::Params, ) -> T

Computes only the potential energy.

Formula

$$ E = V_{half} [1 - (\cos(n\phi) \cos_{n\phi_0} + \sin(n\phi) \sin_{n\phi_0})] $$

fn diff( cos_phi: T, sin_phi: T, (v_half, n, cos_n_phi0, sin_n_phi0): Self::Params, ) -> T

Computes only the torque $T$.

Formula

$$ T = V_{half} \cdot n \cdot (\sin(n\phi) \cos_{n\phi_0} - \cos(n\phi) \sin_{n\phi_0}) $$

This factor allows computing forces via the chain rule: $$ \vec{F} = -T \cdot \nabla \phi $$

fn compute( cos_phi: T, sin_phi: T, (v_half, n, cos_n_phi0, sin_n_phi0): Self::Params, ) -> EnergyDiff<T>

Computes both energy and torque efficiently.

This method reuses intermediate calculations to minimize operations.

type Params = (T, u8, T, T)

Associated constants/parameters required by the potential (e.g., $V, n$).

impl Copy for Torsion