Struct CosineHarmonic 

pub struct CosineHarmonic;

Cosine Harmonic potential for bond angles.

Physics

Models the angle bending energy using a simple harmonic approximation on the cosine of the angle.

• Formula: $$ E = \frac{1}{2} C (\cos\theta - \cos\theta_0)^2 $$
• Derivative Factor (diff): $$ \Gamma = \frac{dE}{d(\cos\theta)} = C (\cos\theta - \cos\theta_0) $$

Parameters

• k_half: Half force constant $C_{half} = C/2$.
• cos0: The cosine of the equilibrium angle $\cos\theta_0$.

Inputs

• cos_theta: Cosine of the bond angle $\theta_{ijk}$.

Implementation Notes

• Pure polynomial evaluation; no acos, sin, or sqrt required.
• All intermediate calculations are shared between energy and force computations.
• Branchless and panic-free.

Trait Implementations

impl<T: Real> AngleKernel<T> for CosineHarmonic

fn energy(cos_theta: T, (k_half, cos0): Self::Params) -> T

Computes only the potential energy.

Formula

$$ E = C_{half} (\Delta)^2, \quad \text{where } \Delta = \cos\theta - \cos\theta_0 $$

fn diff(cos_theta: T, (k_half, cos0): Self::Params) -> T

Computes only the derivative factor $\Gamma$.

Formula

$$ \Gamma = 2 C_{half} (\cos\theta - \cos\theta_0) $$

This factor allows computing forces via the chain rule: $$ \vec{F} = -\Gamma \cdot \nabla (\cos\theta) $$

fn compute(cos_theta: T, (k_half, cos0): Self::Params) -> EnergyDiff<T>

Computes both energy and derivative factor efficiently.

This method reuses intermediate calculations to minimize operations.

type Params = (T, T)

Associated constants/parameters required by the potential (e.g., $k, \theta_0$).

impl Clone for CosineHarmonic

fn clone(&self) -> CosineHarmonic

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for CosineHarmonic

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

Formats the value using the given formatter.

impl Default for CosineHarmonic

fn default() -> CosineHarmonic

Returns the “default value” for a type.

impl Copy for CosineHarmonic