Struct ThetaHarmonic 

pub struct ThetaHarmonic;

Theta Harmonic potential for bond angles.

Physics

Models the angle bending energy using a harmonic approximation directly on the angle $\theta$ (in radians).

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

Parameters

• k_half: Half force constant $K_{half} = K/2$.
• theta0: The equilibrium angle $\theta_0$ in radians.

Inputs

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

Implementation Notes

• Uses k_half to save one multiplication in the energy step.
• Handles $\theta=0$ and $\theta=\pi$ analytically using L’Hopital’s rule.
• Needs a single acos call for angle calculation.

Trait Implementations

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

fn energy(cos_theta: T, (k_half, theta0): Self::Params) -> T

Computes only the potential energy.

Formula

$$ E = K_{half} (\theta - \theta_0)^2 $$

fn diff(cos_theta: T, (k_half, theta0): Self::Params) -> T

Computes only the derivative factor $\Gamma$.

Formula

$$ \Gamma = -2 K_{half} \frac{\theta - \theta_0}{\sin\theta} $$

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

fn compute(cos_theta: T, (k_half, theta0): 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 ThetaHarmonic

fn clone(&self) -> ThetaHarmonic

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for ThetaHarmonic

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

Formats the value using the given formatter.

impl Default for ThetaHarmonic

fn default() -> ThetaHarmonic

Returns the “default value” for a type.

impl Copy for ThetaHarmonic