Bond Module¶

The bond modules 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 bonding 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 bonds as calculated by freud’s Bonding modules.

Determines 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¶: return – lifetime of bonds :rtype: numpy.ndarray, shape=(\(N_{particles}\), varying), dtype= numpy.uint32

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
Return type:	`numpy.ndarray`, shape=(\(N_{particles}\), varying), dtype= `numpy.uint32`

getNumBonds(self)¶

Get number of bonds tracked

Returns:	number of bonds
Return type:	unsigned int

getNumFrames(self)¶

Get number of frames calculated

Returns:	number of frames
Return type:	unsigned int

getNumParticles(self)¶

Get number of particles being tracked

Returns:	number of particles
Return type:	unsigned int

getOverallLifetimes(self)¶

Returns:	lifetime of bonds
Return type:	`numpy.ndarray`, shape=(\(N_{particles}\), varying), dtype= `numpy.uint32`

getTransitionMatrix(self)¶

Returns:	transition matrix
Return type:	`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

Returns:	number of bonds
Return type:	unsigned int

num_frames¶

Get number of frames calculated

Returns:	number of frames
Return type:	unsigned int

num_particles¶

Get number of particles being tracked

Returns:	number of particles
Return type:	unsigned int

overall_lifetimes¶: return – lifetime of bonds :rtype: numpy.ndarray, shape=(\(N_{particles}\), varying), dtype= numpy.uint32

transition_matrix¶: return – transition matrix :rtype: numpy.ndarray

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¶: return – particle bonds :rtype: numpy.ndarray

box¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

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)¶

Returns:	particle bonds
Return type:	`numpy.ndarray`

getBox(self)¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

getListMap(self)¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> list_idx = list_map[bond_idx]

getRevListMap(self)¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> bond_idx = list_map[list_idx]

list_map¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> list_idx = list_map[bond_idx]

rev_list_map¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> bond_idx = list_map[list_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¶: return – particle bonds :rtype: numpy.ndarray

box¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

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)¶

Returns:	particle bonds
Return type:	`numpy.ndarray`

getBox(self)¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

getListMap(self)¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> list_idx = list_map[bond_idx]

getRevListMap(self)¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> bond_idx = list_map[list_idx]

list_map¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> list_idx = list_map[bond_idx]

rev_list_map¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> bond_idx = list_map[list_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¶: return – particle bonds :rtype: numpy.ndarray

box¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

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)¶

Returns:	particle bonds
Return type:	`numpy.ndarray`

getBox(self)¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

getListMap(self)¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> list_idx = list_map[bond_idx]

getRevListMap(self)¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> bond_idx = list_map[list_idx]

list_map¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> list_idx = list_map[bond_idx]

rev_list_map¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> bond_idx = list_map[list_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¶: return – particle bonds :rtype: numpy.ndarray

box¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

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)¶

Returns:	particle bonds
Return type:	`numpy.ndarray`

getBox(self)¶

Get the box used in the calculation

Returns:	freud Box
Return type:	`freud.box.Box()`

getListMap(self)¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> list_idx = list_map[bond_idx]

getRevListMap(self)¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> bond_idx = list_map[list_idx]

list_map¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> list_idx = list_map[bond_idx]

rev_list_map¶

Get the dict used to map list idx to bond idx

Returns:	list_map
Return type:	dict

>>> bond_idx = list_map[list_idx]