# BondThreeBody

class BondThreeBody

A three body bond is defined by three sites, 0 - 1 - 2. The relative vector r01 = r0 - r1 points from r1 to r0. The relative vector r21 = r2 - r1 points from r1 to r2.

Angle Property minimum_degrees sets the energy to NEAR_INFINITY at smaller angles.

For random bond angles:

In three dimensions, $$P(\theta) \propto \sin\theta\exp[-\beta U(\theta)]$$

In two dimensions, $$P(\theta) \propto \theta\exp[-\beta U(\theta)]$$

For branches involving the placement of two sites with three angles:

anchor2 -> 1         1(a2)
mobile1 -> 2         |
mobile2 -> 3         4(a1)  t143(angle)
anchor1 -> 4       /   \L34(distance)
2(m1)     3(m2, the site to be placed in this function)
t243(branch_angle)


This generic branch algorithm picks two points randomly on the surface of a unit sphere and accepts or rejects based on the bond energies of all three angles. If the bonds are relatively stiff, then this method is inefficient, and is overridden by special cases such as RigidAngle and AngleHarmonic. For AngleHarmonic, the Jacobian-Gaussian algorithm is used.

Public Functions

virtual double energy(const Position &ri, const Position &rj, const Position &rk, const Bond &angle) const

Return the energy of interaction between ri, rj and rk.

virtual double energy(const double radians, const Bond &angle) const = 0

Return the energy of interaction given an angle in radians.

virtual double random_angle_radians(const Angle &angle, const double beta, const int dimension, Random *random) const

Return one angle to form an angle bond.

virtual void random_branch(const Angle &a2a1m1, const Angle &a2a1m2, const Angle &m1a1m2, const double beta, const bool is_position_held, double *radians_a2a1m1, double *radians_a2a1m2, double *radians_m1a1m2, Random *random, double *ln_met, const Position *const a1, const Position *const a2, const Position *const m1, const Position *const m2) const

Return three random angles to form a branch.