Struct PlanarInversion 

pub struct PlanarInversion;

Planar inversion potential for sp² centers.

Physics

Models planarity for sp² hybridized atoms (e.g., aromatic carbons, carbonyl groups). The central atom $I$ is bonded to three neighbors $J, K, L$, and the potential penalizes any out-of-plane displacement.

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

Parameters

• c_half: Half force constant $C_{half} = C/2$.

Inputs

• cos_psi: Cosine of the out-of-plane angle $\psi$.

Implementation Notes

• Optimized for $\cos\psi_0 = 0$: avoids one subtraction per evaluation.
• Pure polynomial evaluation; no trigonometric functions required.
• All intermediate calculations are shared between energy and force computations.
• Branchless and panic-free.
• DREIDING convention: force constant $C = K_{inv}/3$ (split among three permutations).

Trait Implementations

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

fn energy(cos_psi: T, c_half: Self::Params) -> T

Computes only the potential energy.

Formula

$$ E = C_{half} \cos^2\psi $$

fn diff(cos_psi: T, c_half: Self::Params) -> T

Computes only the derivative factor $\Gamma$.

Formula

$$ \Gamma = 2 C_{half} \cos\psi $$

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

fn compute(cos_psi: T, c_half: Self::Params) -> EnergyDiff<T>

Computes both energy and derivative factor efficiently.

This method reuses intermediate calculations to minimize operations.

type Params = T

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

impl Clone for PlanarInversion

fn clone(&self) -> PlanarInversion

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for PlanarInversion

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

Formats the value using the given formatter.

impl Default for PlanarInversion

fn default() -> PlanarInversion

Returns the “default value” for a type.

impl Copy for PlanarInversion