Classes/routines for pair potentials (analphipy.potential)

Classes/routines for pair potentials (`analphipy.potential`)#

Classes:

`Generic`(phi_func[, dphidr_func, r_min, ...])	Class to define potential using callables.
`Analytic`()	Base class for defining analytic potentials.
`LennardJones`([sig, eps])	Lennard-Jones potential.
`LennardJonesNM`([n, m, sig, eps])	Generalized Lennard-Jones potential
`Yukawa`([z, sig, eps])	Hard core Yukawa potential
`HardSphere`([sig])	Hard-sphere pair potential
`SquareWell`([sig, eps, lam])	Square-well pair potential
`CubicTable`(bounds, phi_table[, phi_left, ...])	Cubic interpolation table potential.

Functions:

factory(potential_name[, rcut, lfs, cut])

Factory function to construct Phi object by name.

class analphipy.potential.Generic(phi_func, dphidr_func=None, *, r_min=None, phi_min=None, segments=None)[source]#

Bases: PhiBase

Class to define potential using callables.

Parameters:

r_min – The description is missing.
phi_min – The description is missing.
segments – The description is missing.

Attributes:

`phi_func`	Function \(\phi(r)\)
`dphidr_func`	Function \(d\phi(r)/dr\)

Methods:

`phi`(r)	Pair potential.
`dphidr`(r)	Derivative of pair potential.

phi_func#: Function \(\phi(r)\)

dphidr_func#: Function \(d\phi(r)/dr\)

phi(r)[source]#

Pair potential.

Parameters:: r (array-like) – pair separation
Returns:: phi (ndarray) – Evaluated pair potential.

dphidr(r)[source]#

Derivative of pair potential.

This returns the value of \(d \phi(r) / dr\)

Parameters:: r (array-like) – pair separation
Returns:: dphidr (ndarray) – Pair potential values.

class analphipy.potential.Analytic[source]#

Bases: PhiBase

Base class for defining analytic potentials.

Parameters:

r_min (float) – The description is missing.
phi_min (float) – The description is missing.
segments (Sequence[float]) – The description is missing.

Notes

Specific subclasses should set values for r_min, phi_min, and segments, as well as forms for phi and dphidr.

Attributes:

`r_min`	Position of minimum in \(\phi(r)\)
`phi_min`	Value of `phi` at minimum.
`segments`	Integration limits.

r_min#: Position of minimum in \(\phi(r)\)

phi_min#: Value of phi at minimum.

segments#: Integration limits.

class analphipy.potential.LennardJones(sig=1.0, eps=1.0)[source]#

Bases: Analytic

Lennard-Jones potential.

\[\phi(r) = 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6\right]\]

Notes

Specific subclasses should set values for r_min, phi_min, and segments, as well as forms for phi and dphidr.

Attributes:

`sig`	Length parameter \(\sigma\)
`eps`	Energy parameter \(\epsilon\)

Methods:

`phi`(r)	Pair potential.
`dphidr`(r)	Calculate phi and dphi (=-1/r dphi/dr) at particular r.

sig#: Length parameter \(\sigma\)

eps#: Energy parameter \(\epsilon\)

phi(r)[source]#

Pair potential.

Parameters:: r (array-like) – pair separation
Returns:: phi (ndarray) – Evaluated pair potential.

dphidr(r)[source]#

Calculate phi and dphi (=-1/r dphi/dr) at particular r.

Parameters:: r (array-like) – pair separation
Returns:: dphidr (ndarray) – Pair potential values.

class analphipy.potential.LennardJonesNM(n=12, m=6, sig=1.0, eps=1.0)[source]#

Bases: Analytic

Generalized Lennard-Jones potential

\[\phi(r) = \epsilon \frac{n}{n-m} \left( \frac{n}{m} \right) ^{m / (n-m)} \left[ \left(\frac{\sigma}{r}\right)^n - \left(\frac{\sigma}{r}\right)^m\right]\]

Notes

with parameters n=12 and m=6, this is equivalent to LennardJones.

Attributes:

`n`	`n` parameter
`m`	`m` parameter
`sig`	Length parameter
`eps`	Energy parameter

Methods:

`phi`(r)	Pair potential.
`dphidr`(r)	Derivative of pair potential.

n#: n parameter

m#: m parameter

sig#: Length parameter

eps#: Energy parameter

phi(r)[source]#

Pair potential.

Parameters:: r (array-like) – pair separation
Returns:: phi (ndarray) – Evaluated pair potential.

dphidr(r)[source]#

Derivative of pair potential.

This returns the value of \(d \phi(r) / dr\)

Parameters:: r (array-like) – pair separation
Returns:: dphidr (ndarray) – Pair potential values.

class analphipy.potential.Yukawa(z=1.0, sig=1.0, eps=1.0)[source]#

Bases: Analytic

Hard core Yukawa potential

\[\begin{split}\phi(r) = \begin{cases} \infty & r \leq \sigma \\ -\epsilon \frac{\sigma}{r} \exp\left[-z (r/\sigma - 1) \right] & r > \sigma \end{cases}\end{split}\]

Notes

Specific subclasses should set values for r_min, phi_min, and segments, as well as forms for phi and dphidr.

Attributes:

`z`	Interaction parameter
`sig`	Length parameter
`eps`	Energy parameter

Methods:

phi(r)

Pair potential.

z#: Interaction parameter

sig#: Length parameter

eps#: Energy parameter

phi(r)[source]#

Pair potential.

Parameters:: r (array-like) – pair separation
Returns:: phi (ndarray) – Evaluated pair potential.

class analphipy.potential.HardSphere(sig=1.0)[source]#

Bases: Analytic

Hard-sphere pair potential

\[\begin{split}\phi(r) = \begin{cases} \infty & r \leq \sigma \\ 0 & r > \sigma \end{cases}\end{split}\]

Notes

Specific subclasses should set values for r_min, phi_min, and segments, as well as forms for phi and dphidr.

Attributes:

sig

Length parameter

Methods:

phi(r)

Pair potential.

sig#: Length parameter

phi(r)[source]#

Pair potential.

Parameters:: r (array-like) – pair separation
Returns:: phi (ndarray) – Evaluated pair potential.

class analphipy.potential.SquareWell(sig=1.0, eps=1.0, lam=1.5)[source]#

Bases: Analytic

Square-well pair potential

\[\begin{split}\phi(r) = \begin{cases} \infty & r \leq \sigma \\ \epsilon & \sigma < r \leq \lambda \sigma \\ 0 & r > \lambda \sigma \end{cases}\end{split}\]

Notes

Specific subclasses should set values for r_min, phi_min, and segments, as well as forms for phi and dphidr.

Attributes:

`sig`	Length parameter.
`eps`	Energy parameter.
`lam`	Well width parameter.

Methods:

phi(r)

Pair potential.

sig#: Length parameter.

eps#: Energy parameter.

lam#: Well width parameter.

phi(r)[source]#

Pair potential.

Parameters:: r (array-like) – pair separation
Returns:: phi (ndarray) – Evaluated pair potential.

class analphipy.potential.CubicTable(bounds, phi_table, phi_left=inf, phi_right=0.0, dphi_left=inf, dphi_right=0.0, *, r_min=None, phi_min=None, segments=None)[source]#

Bases: PhiBase

Cubic interpolation table potential.

Parameters:

r_min – The description is missing.
phi_min – The description is missing.
segments (sequence of float, optional) – Integration segments. Defaults to sqrt(bounds).

Attributes:

`bounds`	Minimum and maximum values of squared pair separation \(r^2\)
`phi_table`	Values of potential evaluated on even grid of \(r^2\) values.
`phi_left`	value of phi at left bound (r < bounds[0])
`phi_right`	value of phi at right bound (r > bounds[1])
`dphi_left`	value of dphi at left bound
`dphi_right`	value of dphi at right bound
`size`	Size of the array (less 1).
`smin`	Minimum value of s = r**2.
`smax`	Maximum value of s = r**2.
`rsq_table`	Value of `r**2` where potential is defined.
`r_table`	Values of `r` where potential is defined.

Methods:

`from_phi`(phi, rmin, rmax, ds, **kws)	Create object from callable pair potential function.
`phidphi`(r)	Values of phi and dphi at r.
`phi`(r)	Pair potential.
`dphidr`(r)	Derivative of pair potential.

bounds#: Minimum and maximum values of squared pair separation \(r^2\)

phi_table#: Values of potential evaluated on even grid of \(r^2\) values.

phi_left#: value of phi at left bound (r < bounds[0])

phi_right#: value of phi at right bound (r > bounds[1])

dphi_left#: value of dphi at left bound

dphi_right#: value of dphi at right bound

classmethod from_phi(phi, rmin, rmax, ds, **kws)[source]#

Create object from callable pair potential function.

This will evaluate phi at even spacing in s = r**2 space.

Parameters:

phi (callable()) – pair potential function
rmin (float) – minimum pair separation r to evaluate at.
rmax (float) – Maximum pair separation r to evaluate at.
ds (float) – spaceing in s = r ** 2.
**kws – Extra arguments to constructor.

Returns:

table (CubicTable)

property size#: Size of the array (less 1).

property smin#: Minimum value of s = r**2.

property smax#: Maximum value of s = r**2.

phidphi(r)[source]#: Values of phi and dphi at r.

phi(r)[source]#

Pair potential.

Parameters:: r (array-like) – pair separation
Returns:: phi (ndarray) – Evaluated pair potential.

dphidr(r)[source]#

Derivative of pair potential.

This returns the value of \(d \phi(r) / dr\)

Parameters:: r (array-like) – pair separation
Returns:: dphidr (ndarray) – Pair potential values.

property rsq_table#: Value of r**2 where potential is defined.

property r_table#: Values of r where potential is defined.

analphipy.potential.factory(potential_name, rcut=None, lfs=False, cut=False, **kws)[source]#

Factory function to construct Phi object by name.

Parameters:

potential_name ({lj, nm, sw, hs, yk}) – Name of potential.
rcut (float, optional) – if passed, Construct either and ‘lfs’ or ‘cut’ version of the potential.
lfs (bool, default False) – If True, construct a linear force shifted potential analphipy.base_potential.PhiLFS.
cut (bool, default False) – If True, construct a cut potential analphipy.base_potential.PhiCut.

Returns:

phi (analphipy.base_potential.PhiBase subclass) – output potential energy class.

Classes/routines for pair potentials (analphipy.potential)

Contents

Classes/routines for pair potentials (analphipy.potential)#

Classes/routines for pair potentials (`analphipy.potential`)#