occ::mults::ShortRangeInteraction Class Reference

Class for computing short-range pairwise interactions. More...

#include <short_range.h>

Classes
struct	AnisotropicResult
	Result from anisotropic repulsion computation. More...
struct	EnergyAndDerivatives
	Result structure containing energy and derivatives. More...
struct	ForceAndHessian
	Result structure containing forces and Hessian for both sites. More...

Static Public Member Functions
static AnisotropicResult	anisotropic_repulsion (const Vec3 &pos_a, const Vec3 &pos_b, const Vec3 &axis_a, const Vec3 &axis_b, const AnisotropicRepulsionParams &params)
	Compute anisotropic Born-Mayer repulsion energy, forces, and axis torques.
static double	lennard_jones_energy (double r, const LennardJonesParams &params)
	Compute Lennard-Jones energy: V(r) = 4ε[(σ/r)^12 - (σ/r)^6].
static double	lennard_jones_derivative (double r, const LennardJonesParams &params)
	Compute first derivative: dV/dr = 24ε/r[(σ/r)^6 - 2(σ/r)^12].
static double	lennard_jones_second_derivative (double r, const LennardJonesParams &params)
	Compute second derivative: d²V/dr² = 24ε/r²[26(σ/r)^12 - 7(σ/r)^6].
static EnergyAndDerivatives	lennard_jones_all (double r, const LennardJonesParams &params)
	Compute Lennard-Jones energy and both derivatives (more efficient).
static double	buckingham_energy (double r, const BuckinghamParams &params)
	Compute Buckingham energy: V(r) = A*exp(-B*r) - C/r^6.
static double	buckingham_derivative (double r, const BuckinghamParams &params)
	Compute first derivative: dV/dr = -A*B*exp(-B*r) + 6C/r^7.
static double	buckingham_second_derivative (double r, const BuckinghamParams &params)
	Compute second derivative: d²V/dr² = A*B²*exp(-B*r) - 42C/r^8.
static EnergyAndDerivatives	buckingham_all (double r, const BuckinghamParams &params)
	Compute Buckingham energy and both derivatives (more efficient).
static Vec3	derivative_to_force (double dE_dr, const Vec3 &r_vec)
	Convert radial derivative to force vector.
static ForceAndHessian	compute_force_hessian (const Vec3 &r_A, const Vec3 &r_B, double dE_dr, double d2E_dr2)
	Compute force vectors and Hessian matrices for both sites.

Detailed Description

Class for computing short-range pairwise interactions.

Provides implementations of Lennard-Jones and Buckingham potentials with analytical first and second derivatives. These are commonly used in molecular mechanics and molecular dynamics simulations.

All functions are static and thread-safe. The class provides:

• Individual energy/derivative calculations
• Combined calculations (more efficient when all are needed)
• Transformation from scalar derivatives to vector forces and Hessians

Usage example:

Vec3 r_A(0, 0, 0);
Vec3 r_B(3.5, 0, 0);  // 3.5 Angstrom separation
 
// Lennard-Jones for Ar-Ar
LennardJonesParams lj_params{.epsilon = 0.238, .sigma = 3.40};
 
// Compute energy and derivatives
auto result = ShortRangeInteraction::lennard_jones_all(
    (r_B - r_A).norm(), lj_params);
 
// Convert to forces and Hessian
auto forces = ShortRangeInteraction::compute_force_hessian(
    r_A, r_B, result.first_derivative, result.second_derivative);

Member Function Documentation

anisotropic_repulsion()

static AnisotropicResult occ::mults::ShortRangeInteraction::anisotropic_repulsion ( const Vec3 &  pos_a, const Vec3 &  pos_b, const Vec3 &  axis_a, const Vec3 &  axis_b, const AnisotropicRepulsionParams &  params  )

static

Compute anisotropic Born-Mayer repulsion energy, forces, and axis torques.

Parameters

pos_a	Position of site A
pos_b	Position of site B
axis_a	Unit z-axis of site A in lab frame (zero = isotropic for this site)
axis_b	Unit z-axis of site B in lab frame (zero = isotropic for this site)
params	Anisotropic repulsion parameters

Returns

AnisotropicResult with energy, forces, and axis torques

buckingham_all()

static EnergyAndDerivatives occ::mults::ShortRangeInteraction::buckingham_all ( double  r, const BuckinghamParams &  params  )

static

Compute Buckingham energy and both derivatives (more efficient).

This is more efficient than calling the individual functions when all quantities are needed, as it reuses intermediate calculations.

Parameters

r	Distance between sites (must be > 0)
params	Buckingham parameters (A, B, C)

Returns

Structure containing energy, first derivative, and second derivative

buckingham_derivative()

static double occ::mults::ShortRangeInteraction::buckingham_derivative ( double  r, const BuckinghamParams &  params  )

static

Compute first derivative: dV/dr = -A*B*exp(-B*r) + 6C/r^7.

Parameters

r	Distance between sites (must be > 0)
params	Buckingham parameters (A, B, C)

Returns

First derivative dV/dr

buckingham_energy()

static double occ::mults::ShortRangeInteraction::buckingham_energy ( double  r, const BuckinghamParams &  params  )

static

Compute Buckingham energy: V(r) = A*exp(-B*r) - C/r^6.

Parameters

r	Distance between sites (must be > 0)
params	Buckingham parameters (A, B, C)

Returns

Energy in same units as A

buckingham_second_derivative()

static double occ::mults::ShortRangeInteraction::buckingham_second_derivative ( double  r, const BuckinghamParams &  params  )

static

Compute second derivative: d²V/dr² = A*B²*exp(-B*r) - 42C/r^8.

Parameters

r	Distance between sites (must be > 0)
params	Buckingham parameters (A, B, C)

Returns

Second derivative d²V/dr²

compute_force_hessian()

static ForceAndHessian occ::mults::ShortRangeInteraction::compute_force_hessian ( const Vec3 &  r_A, const Vec3 &  r_B, double  dE_dr, double  d2E_dr2  )

static

Compute force vectors and Hessian matrices for both sites.

For a central potential V(r) between sites A and B, computes:

• Forces: F_A = -(dV/dr) * (r_vec/r), F_B = -F_A
• Hessians: H_ij = d²V/dx_i dx_j

The Hessian for a central potential has two terms:

1. Curvature term: (d²V/dr²) * (r_i/r) * (r_j/r)
2. Angular term: (dV/dr/r) * [δ_ij - (r_i/r)(r_j/r)]

The resulting Hessian satisfies:

• H_AB = -H_AA (from symmetry)
• H_BB = H_AA (from symmetry)
• H_AA + H_AB + H_BA + H_BB = 0 (translational invariance)

Parameters

r_A	Position of site A
r_B	Position of site B
dE_dr	First derivative dV/dr
d2E_dr2	Second derivative d²V/dr²

Returns

Structure containing forces and Hessians

derivative_to_force()

static Vec3 occ::mults::ShortRangeInteraction::derivative_to_force ( double  dE_dr, const Vec3 &  r_vec  )

static

Convert radial derivative to force vector.

For a central potential V(r), the force on site A is: F_A = -(dV/dr) * (r_vec/r) where r_vec = r_B - r_A

Parameters

dE_dr	First derivative dV/dr (scalar)
r_vec	Displacement vector r_B - r_A

Returns

Force vector on site A (force on B is -F_A)

lennard_jones_all()

static EnergyAndDerivatives occ::mults::ShortRangeInteraction::lennard_jones_all ( double  r, const LennardJonesParams &  params  )

static

Compute Lennard-Jones energy and both derivatives (more efficient).

This is more efficient than calling the individual functions when all quantities are needed, as it reuses intermediate calculations.

Parameters

r	Distance between sites (must be > 0)
params	Lennard-Jones parameters (ε, σ)

Returns

Structure containing energy, first derivative, and second derivative

lennard_jones_derivative()

static double occ::mults::ShortRangeInteraction::lennard_jones_derivative ( double  r, const LennardJonesParams &  params  )

static

Compute first derivative: dV/dr = 24ε/r[(σ/r)^6 - 2(σ/r)^12].

Parameters

r	Distance between sites (must be > 0)
params	Lennard-Jones parameters (ε, σ)

Returns

First derivative dV/dr

lennard_jones_energy()

static double occ::mults::ShortRangeInteraction::lennard_jones_energy ( double  r, const LennardJonesParams &  params  )

static

Compute Lennard-Jones energy: V(r) = 4ε[(σ/r)^12 - (σ/r)^6].

Parameters

r	Distance between sites (must be > 0)
params	Lennard-Jones parameters (ε, σ)

Returns

Energy in same units as epsilon

lennard_jones_second_derivative()

static double occ::mults::ShortRangeInteraction::lennard_jones_second_derivative ( double  r, const LennardJonesParams &  params  )

static

Compute second derivative: d²V/dr² = 24ε/r²[26(σ/r)^12 - 7(σ/r)^6].

Parameters

r	Distance between sites (must be > 0)
params	Lennard-Jones parameters (ε, σ)

Returns

Second derivative d²V/dr²

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The documentation for this class was generated from the following file:

• /home/runner/work/occ/occ/include/occ/mults/short_range.h