Struct Buckingham 

pub struct Buckingham;

Buckingham (Exponential-6) potential for Van der Waals interactions.

Physics

Models short-range repulsion exponentially and long-range attraction with an $r^{-6}$ term, providing a more physically accurate repulsion wall than Lennard-Jones.

• Formula: $$ E = D_0 \left[ \frac{6}{\zeta-6} \exp\left(\zeta(1 - \frac{r}{R_0})\right) - \frac{\zeta}{\zeta-6} \left(\frac{R_0}{r}\right)^6 \right] $$
• Derivative Factor (diff): $$ D = -\frac{1}{r} \frac{dE}{dr} = \frac{6\zeta D_0}{r(\zeta-6)R_0} \left[ \exp\left(\zeta(1 - \frac{r}{R_0})\right) - \left(\frac{R_0}{r}\right)^7 \right] $$

Parameters

For computational efficiency, the physical parameters ($D_0, R_0, \zeta$) are pre-computed into the standard Buckingham form ($A, B, C$):

• a: The repulsion pre-factor $A = \frac{6 D_0}{\zeta-6} e^{\zeta}$.
• b: The repulsion decay constant $B = \zeta / R_0$.
• c: The attraction pre-factor $C = \frac{\zeta D_0 R_0^6}{\zeta-6}$.
• r_fusion_sq: The squared distance threshold for regularization.

Inputs

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

Implementation Notes

• The kernel operates on the computationally efficient $A, B, C$ form.
• A branchless regularization is applied for $r^2 < r_{fusion}^2$ using a mathematical mask to prevent energy collapse at very short distances, ensuring numerical stability.
• Requires one sqrt and one exp call, making it computationally more demanding than LJ.
• Power chain inv_r2 -> inv_r6 -> inv_r8 is used for the attractive term.

Trait Implementations

impl Clone for Buckingham

fn clone(&self) -> Buckingham

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Buckingham

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

Formats the value using the given formatter.

impl Default for Buckingham

fn default() -> Buckingham

Returns the “default value” for a type.

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

fn energy(r_sq: T, (a, b, c, r_fusion_sq): Self::Params) -> T

Computes only the potential energy.

Formula

$$ E = A e^{-B r} - C / r^6 $$

fn diff(r_sq: T, (a, b, c, r_fusion_sq): Self::Params) -> T

Computes only the force pre-factor $D$.

Formula

$$ D = \frac{A B e^{-B r}}{r} - \frac{6 C}{r^8} $$

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, (a, b, c, r_fusion_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, T, T)

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

impl Copy for Buckingham