Struct HydrogenBond 

pub struct HydrogenBond<const N: usize>;

DREIDING Hydrogen Bond potential (12-10).

Physics

Models the explicit hydrogen bonding interaction (typically D-H…A) using a specific 12-10 Radial potential modulated by a $\cos^N\theta$ Angular term. Standard DREIDING uses $N=4$.

• Formula: $$ E = D_{hb} \left[ 5 \left(\frac{R_{hb}}{r}\right)^{12} - 6 \left(\frac{R_{hb}}{r}\right)^{10} \right] \cos^N \theta $$
• Derivative Factor (Radial): $$ D_{rad} = - \frac{1}{r} \frac{\partial E}{\partial r} = \frac{60 D_{hb}}{r^2} \left[ \left(\frac{R_{hb}}{r}\right)^{12} - \left(\frac{R_{hb}}{r}\right)^{10} \right] \cos^N \theta $$
• Derivative Factor (Angular): $$ D_{ang} = \frac{\partial E}{\partial (\cos\theta)} = N \cdot E_{rad} \cos^{N-1} \theta $$

Parameters

• d_hb: The energy well depth $D_{hb}$.
• r_hb_sq: The squared equilibrium distance $R_{hb}^2$.
• N: The cosine power exponent (const generic).

Inputs

• r_sq: Squared distance $r^2$ between Donor (D) and Acceptor (A).
• cos_theta: Cosine of the angle $\theta_{DHA}$ (at Hydrogen).

Implementation Notes

• Cutoff: If $\cos\theta \le 0$, energy and forces represent 0.
• Optimization: Uses $s = (R_{hb}/r)^2$ recurrence to compute $r^{-10}$ and $r^{-12}$ efficiently.
• Generics: Uses const N: usize to unroll power calculations at compile time.

Trait Implementations

impl<const N: usize> Clone for HydrogenBond<N>

fn clone(&self) -> HydrogenBond<N>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const N: usize> Debug for HydrogenBond<N>

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

Formats the value using the given formatter.

impl<const N: usize> Default for HydrogenBond<N>

fn default() -> HydrogenBond<N>

Returns the “default value” for a type.

impl<T: Real, const N: usize> HybridKernel<T> for HydrogenBond<N>

fn energy(r_sq: T, cos_theta: T, (d_hb, r_hb_sq): Self::Params) -> T

Computes only the potential energy.

Formula

$$ E = D_{hb} (5s^6 - 6s^5) \cos^N \theta, \quad \text{where } s = (R_{hb}/r)^2 $$

fn diff(r_sq: T, cos_theta: T, (d_hb, r_hb_sq): Self::Params) -> (T, T)

Computes only the derivative factors.

Formula

$$ D_{rad} = \frac{60 D_{hb}}{r^2} (s^6 - s^5) \cos^N \theta, \quad \text{where } s = (R_{hb}/r)^2 $$ $$ D_{ang} = N E_{rad} \cos^{N-1} \theta $$

• force_factor_rad ($D_{rad}$): Used to compute the central force along the D-A axis: $ \vec{F}_{rad} = -D_{rad} \cdot \vec{r}_{DA} $
• force_factor_ang ($D_{ang}$): Used to compute torque-like forces on the D-H-A angle via the Wilson B-matrix gradient chain rule: $ \vec{F}_i = -D_{ang} \cdot \nabla_i (\cos\theta) $

fn compute( r_sq: T, cos_theta: T, (d_hb, r_hb_sq): Self::Params, ) -> HybridEnergyDiff<T>

Computes both energy and derivative factors efficiently.

This method reuses intermediate calculations to minimize operations.

type Params = (T, T)

Associated constants/parameters required by the potential.

impl<const N: usize> Copy for HydrogenBond<N>