# Bond Module¶

The bond module allows for the computation of bonds as defined by a map. Depending on the coordinate system desired, either a two or three dimensional array is supplied, with each element containing the bond index mapped to the pair geometry of that element. The user provides a list of indices to track, so that not all bond indices contained in the bond map need to be tracked in computation.

The bond module is designed to take in arrays using the same coordinate systems in the PMFT Module in freud.

Note

The coordinate system in which the calculation is performed is not the same as the coordinate system in which particle positions and orientations should be supplied. Only certain coordinate systems are available for certain particle positions and orientations:

• 2D particle coordinates (position: [$$x$$, $$y$$, $$0$$], orientation: $$\theta$$):
• $$X$$, $$Y$$
• $$X$$, $$Y$$, $$\theta_2$$
• $$r$$, $$\theta_1$$, $$\theta_2$$
• 3D particle coordinates:
• $$X$$, $$Y$$, $$Z$$

## Bonding Analysis¶

class freud.bond.BondingAnalysis(num_particles, num_bonds)

Analyze the bond lifetimes and flux present in the system.

Module author: Eric Harper <harperic@umich.edu>

Parameters: num_particles (unsigned int) – number of particles over which to calculate bonds num_bonds – number of bonds to track
bond_lifetimes

compute(self, frame_0, frame_1)

Calculates the changes in bonding states from one frame to the next.

Parameters: frame_0 (numpy.ndarray, shape=($$N_{particles}$$, $$N_{bonds}$$), dtype= numpy.uint32) – current/previous bonding frame (as output from BondingR12 modules) frame_1 (numpy.ndarray, shape=($$N_{particles}$$, $$N_{bonds}$$), dtype= numpy.uint32) – next/current bonding frame (as output from BondingR12 modules)
getBondLifetimes(self)

Returns: lifetime of bonds numpy.ndarray, shape=($$N_{particles}$$, varying), dtype= numpy.uint32
getNumBonds(self)

Get number of bonds tracked

Returns: number of bonds unsigned int
getNumFrames(self)

Get number of frames calculated

Returns: number of frames unsigned int
getNumParticles(self)

Get number of particles being tracked

Returns: number of particles unsigned int
getOverallLifetimes(self)

Returns: lifetime of bonds numpy.ndarray, shape=($$N_{particles}$$, varying), dtype= numpy.uint32
getTransitionMatrix(self)

The transition matrix :return: transition matrix :rtype: numpy.ndarray

initialize(self, frame_0)

Calculates the changes in bonding states from one frame to the next.

Parameters: frame_0 (numpy.ndarray, shape=($$N_{particles}$$, $$N_{bonds}$$), dtype= numpy.uint32) – first bonding frame (as output from BondingR12 modules)
num_bonds

Get number of bonds being tracked

num_frames

Get number of frames calculated

num_particles

Get number of particles being tracked

overall_lifetimes

transition_matrix

The transition matrix

## Coordinate System: $$x$$, $$y$$¶

class freud.bond.BondingXY2D(x_max, y_max, bond_map, bond_list)

Compute the bonds each particle in the system.

For each particle in the system determine which other particles are in which bonding sites.

Module author: Eric Harper <harperic@umich.edu>

Parameters: x_max (float) – maximum x distance at which to search for bonds y_max (float) – maximum y distance at which to search for bonds bond_map (numpy.ndarray) – 3D array containing the bond index for each x, y coordinate bond_list (numpy.ndarray) – list containing the bond indices to be tracked bond_list[i] = bond_index
bonds

The particle bonds

box

Get the box used in the calculation

compute(self, box, ref_points, ref_orientations, points, orientations, nlist=None)

Calculates the correlation function and adds to the current histogram.

Parameters: box (freud.box.Box()) – simulation box ref_points (numpy.ndarray, shape=($$N_{particles}$$, 3), dtype= numpy.float32) – points to calculate the bonding ref_orientations (numpy.ndarray, shape=($$N_{particles}$$), dtype= numpy.float32) – orientations as angles to use in computation points (numpy.ndarray, shape=($$N_{particles}$$, 3), dtype= numpy.float32) – points to calculate the bonding orientations (numpy.ndarray, shape=($$N_{particles}$$), dtype= numpy.float32) – orientations as angles to use in computation nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds
getBonds(self)

Return the particle bonds

Returns: particle bonds numpy.ndarray
getBox(self)

Get the box used in the calculation

Returns: freud Box freud.box.Box()
getListMap(self)

Get the dict used to map list idx to bond idx

Returns: list_map dict
>>> list_idx = list_map[bond_idx]

getRevListMap(self)

Get the dict used to map list idx to bond idx

Returns: list_map dict
>>> bond_idx = list_map[list_idx]

list_map

Get the dict used to map list idx to bond idx

rev_list_map

Get the dict used to map list idx to bond idx

## Coordinate System: $$x$$, $$y$$, $$\theta_2$$¶

class freud.bond.BondingXYT(x_max, y_max, bond_map, bond_list)

Compute the bonds each particle in the system.

For each particle in the system determine which other particles are in which bonding sites.

Module author: Eric Harper <harperic@umich.edu>

Parameters: x_max (float) – maximum x distance at which to search for bonds y_max (float) – maximum y distance at which to search for bonds bond_map (numpy.ndarray) – 3D array containing the bond index for each x, y coordinate bond_list (numpy.ndarray) – list containing the bond indices to be tracked bond_list[i] = bond_index
bonds

The particle bonds

box

Get the box used in the calculation

compute(self, box, ref_points, ref_orientations, points, orientations, nlist=None)

Calculates the correlation function and adds to the current histogram.

Parameters: box (freud.box.Box()) – simulation box ref_points (numpy.ndarray, shape=($$N_{particles}$$, 3), dtype= numpy.float32) – points to calculate the bonding ref_orientations (numpy.ndarray, shape=($$N_{particles}$$), dtype= numpy.float32) – orientations as angles to use in computation points (numpy.ndarray, shape=($$N_{particles}$$, 3), dtype= numpy.float32) – points to calculate the bonding orientations (numpy.ndarray, shape=($$N_{particles}$$), dtype= numpy.float32) – orientations as angles to use in computation nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds
getBonds(self)

Return the particle bonds

Returns: particle bonds numpy.ndarray
getBox(self)

Get the box used in the calculation

Returns: freud Box freud.box.Box()
getListMap(self)

Get the dict used to map list idx to bond idx

Returns: list_map dict
>>> list_idx = list_map[bond_idx]

getRevListMap(self)

Get the dict used to map list idx to bond idx

Returns: list_map dict
>>> bond_idx = list_map[list_idx]

list_map

Get the dict used to map list idx to bond idx

rev_list_map

Get the dict used to map list idx to bond idx

## Coordinate System: $$r$$, $$\theta_1$$, $$\theta_2$$¶

class freud.bond.BondingR12(r_max, bond_map, bond_list)

Compute the bonds each particle in the system.

For each particle in the system determine which other particles are in which bonding sites.

Module author: Eric Harper <harperic@umich.edu>

Parameters: r_max (float) – distance to search for bonds bond_map (numpy.ndarray) – 3D array containing the bond index for each r, t2, t1 coordinate bond_list (numpy.ndarray) – list containing the bond indices to be tracked bond_list[i] = bond_index
bonds

The particle bonds

box

Get the box used in the calculation

compute(self, box, ref_points, ref_orientations, points, orientations, nlist=None)

Calculates the correlation function and adds to the current histogram.

Parameters: box (freud.box.Box()) – simulation box ref_points (numpy.ndarray, shape=($$N_{particles}$$, 3), dtype= numpy.float32) – points to calculate the bonding ref_orientations (numpy.ndarray, shape=($$N_{particles}$$), dtype= numpy.float32) – orientations as angles to use in computation points (numpy.ndarray, shape=($$N_{particles}$$, 3), dtype= numpy.float32) – points to calculate the bonding orientations (numpy.ndarray, shape=($$N_{particles}$$), dtype= numpy.float32) – orientations as angles to use in computation nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds
getBonds(self)

Return the particle bonds

Returns: particle bonds numpy.ndarray
getBox(self)

Get the box used in the calculation

Returns: freud Box freud.box.Box()
getListMap(self)

Get the dict used to map list idx to bond idx

Returns: list_map dict
>>> list_idx = list_map[bond_idx]

getRevListMap(self)

Get the dict used to map list idx to bond idx

Returns: list_map dict
>>> bond_idx = list_map[list_idx]

list_map

Get the dict used to map list idx to bond idx

rev_list_map

Get the dict used to map list idx to bond idx

## Coordinate System: $$x$$, $$y$$, $$z$$¶

class freud.bond.BondingXYZ(x_max, y_max, z_max, bond_map, bond_list)

Compute the bonds each particle in the system.

For each particle in the system determine which other particles are in which bonding sites.

Module author: Eric Harper <harperic@umich.edu>

Parameters: x_max (float) – maximum x distance at which to search for bonds y_max (float) – maximum y distance at which to search for bonds z_max (float) – maximum z distance at which to search for bonds bond_map (numpy.ndarray) – 3D array containing the bond index for each x, y, z coordinate bond_list (numpy.ndarray) – list containing the bond indices to be tracked bond_list[i] = bond_index
bonds

The particle bonds

box

Get the box used in the calculation

compute(self, box, ref_points, ref_orientations, points, orientations, nlist=None)

Calculates the correlation function and adds to the current histogram.

Parameters: box (freud.box.Box()) – simulation box ref_points (numpy.ndarray, shape=($$N_{particles}$$, 3), dtype= numpy.float32) – points to calculate the bonding ref_orientations (numpy.ndarray, shape=($$N_{particles}$$, 4), dtype= numpy.float32) – orientations as quaternions to use in computation points (numpy.ndarray, shape=($$N_{particles}$$, 3), dtype= numpy.float32) – points to calculate the bonding orientations (numpy.ndarray, shape=($$N_{particles}$$, 4), dtype= numpy.float32) – orientations as quaternions to use in computation nlist (freud.locality.NeighborList) – freud.locality.NeighborList object to use to find bonds
getBonds(self)

Return the particle bonds

Returns: particle bonds numpy.ndarray
getBox(self)

Get the box used in the calculation

Returns: freud Box freud.box.Box()
getListMap(self)

Get the dict used to map list idx to bond idx

Returns: list_map dict
>>> list_idx = list_map[bond_idx]

getRevListMap(self)

Get the dict used to map list idx to bond idx

Returns: list_map dict
>>> bond_idx = list_map[list_idx]

list_map

Get the dict used to map list idx to bond idx

rev_list_map

Get the dict used to map list idx to bond idx