Struct LennardJones 

pub struct LennardJones;

Lennard-Jones 12-6 potential for Van der Waals interactions.

Physics

Models the short-range repulsion and long-range attraction between non-bonded atoms.

• Formula: $$ E = D_0 \left[ \left( \frac{R_0}{r} \right)^{12} - 2 \left( \frac{R_0}{r} \right)^6 \right] $$
• Derivative Factor (diff): $$ D = -\frac{1}{r} \frac{dE}{dr} = \frac{12 D_0}{r^2} \left[ \left( \frac{R_0}{r} \right)^{12} - \left( \frac{R_0}{r} \right)^6 \right] $$

Parameters

• d0: The energy well depth $D_0$.
• r0_sq: The squared equilibrium distance $R_0^2$.

Inputs

• r_sq: Squared distance $r^2$ between two atoms.

Implementation Notes

• This implementation avoids sqrt entirely by operating on squared distances.
• The power chain s -> s3 -> s6 is used for efficient calculation of $r^{-6}$ and $r^{-12}$ terms.
• All intermediate calculations are shared between energy and force computations.
• Branchless and panic-free.

Trait Implementations

impl Clone for LennardJones

fn clone(&self) -> LennardJones

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for LennardJones

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

Formats the value using the given formatter.

impl Default for LennardJones

fn default() -> LennardJones

Returns the “default value” for a type.

impl<T: Real> PairKernel<T> for LennardJones

fn energy(r_sq: T, (d0, r0_sq): Self::Params) -> T

Computes only the potential energy.

Formula

$$ E = D_0 (s^6 - 2s^3), \quad \text{where } s = (R_0/r)^2 $$

fn diff(r_sq: T, (d0, r0_sq): Self::Params) -> T

Computes only the force pre-factor $D$.

Formula

$$ D = \frac{12 D_0}{r^2} (s^6 - s^3), \quad \text{where } s = (R_0/r)^2 $$

This factor is defined such that the force vector can be computed by a single vector multiplication: $\vec{F} = -D \cdot \vec{r}$.

fn compute(r_sq: T, (d0, r0_sq): Self::Params) -> EnergyDiff<T>

Computes both energy and force pre-factor efficiently.

This method reuses intermediate calculations to minimize operations.

type Params = (T, T)

Associated constants/parameters required by the potential (e.g., $k, r_0$).

impl Copy for LennardJones