# CoulombSPME¶

class CoulombSPME(r_cut=None, accuracy=None, g=None, cellratio=None, i_degree=None, interlaced=None, bonded_mode=None)

Constructor of the Coulomb solver.

Parameters: r_cut (PhysicalQuantity of type length) – The cutoff radius for the real-space interactions. accuracy (float) – The desired accuracy with respect to the energy. If this value is set and is positive, the values for g, cellratio, i_degree and interlaced are set automatically. g (float) – The splitting coefficient G in the SPME method. cellratio (int) – The number of discretization points in each direction. Must be a power of two. i_degree (int) – The order of the interpolation. interlaced (bool) – Flag to switch interlaced calculation on/off. bonded_mode – Either CoulombSPME.evaluateAll or CoulombSPME.evaluate4. If evaluateAll is chosen, interactions between all particles - even those that are connected by bonds - are evaluated, using the sigma and epsilon parameters. If evaluate4 is chosen, interactions between particles that are connected by a path of bonds of length less than four are omitted.
getAllParameterNames()

Return the names of all used parameters as a list.

getAllParameters()

Return all parameters of this potential and their current values as a <parameterName / parameterValue> dictionary.

static getDefaults()

Get the default parameters of this potential and return them in form of a dictionary of <parameter name, default value> key-value pairs.

getInteractionMode()

Return the currently used interaction mode.

getParameter(parameterName)

Get the current value of the parameter parameterName.

setAccuracy(accuracy)

Set the desired accuracy.

Parameters: accuracy (float) – The desired accuracy with respect to the energy. If this value is set and is positive, the values for g, cellratio, i_degree and interlaced are set automatically.
setBondedMode(bonded_mode)

Set the way how particles that are connected by bonds are treated.

Parameters: bonded_mode – Either self.evaluateAll or self.evaluate4. If evaluateAll is chosen, interactions between all particles - even those that are connected by bonds - are evaluated, using the sigma and epsilon parameters. If evaluate4 is chosen, interactions between particles that are connected by a path of bonds of length less than four are omitted.
setCellRatio(cellratio)

Sets the number of discretization points in each direction.

Parameters: cellratio (int) – The number of discretization points in each direction. Must be a power of two.
setCutoff(r_cut)

Set the real-space cutoff radius of the Coulomb solver.

Parameters: r_cut (PhysicalQuantity of type length) – The cutoff radius for the real-space interactions.
setG(g)

Set the splitting coefficient G.

Parameters: g (float) – The splitting coefficient G in the SPME method.
setInterlaced(interlaced)

Switch interlaced calculations on or off.

Parameters: interlaced (bool) – Flag to switch interlaced calculation on/off.
setInterpolationOrder(i_degree)

Set the order of the interpolation.

Parameters: i_degree (int) – The order of the interpolation.
setParameter(parameterName, value)

Set the parameter parameterName to the given value.

Parameters: parameterName (str) – The name of the parameter that will be modified. value – The new value that will be assigned to the parameter parameterName.

## Usage Examples¶

Define a potential for Quartz by adding particle types and interaction functions to the TremoloXPotentialSet.

# -------------------------------------------------------------
# Set up a SiO2 Quartz crystal
# -------------------------------------------------------------

# Set up lattice
lattice = Hexagonal(4.916*Angstrom, 5.4054*Angstrom)

# Define elements
elements = [Silicon, Silicon, Silicon, Oxygen, Oxygen, Oxygen, Oxygen, Oxygen,
Oxygen]

# Define coordinates
fractional_coordinates = [[ 0.4697,  0.0000,  0.0000    ],
[ 0.0000,  0.4697,  0.66666667],
[ 0.5303,  0.5303,  0.33333333],
[ 0.4135,  0.2669,  0.1191    ],
[ 0.2669,  0.4135,  0.547567  ],
[ 0.7331,  0.1466,  0.785767  ],
[ 0.5865,  0.8534,  0.214233  ],
[ 0.8534,  0.5865,  0.452433  ],
[ 0.1466,  0.7331,  0.8809    ]]

# Set up configuration
bulk_configuration = BulkConfiguration(
bravais_lattice=lattice,
elements=elements,
fractional_coordinates=fractional_coordinates
)

# -------------------------------------------------------------
# Calculator
# -------------------------------------------------------------

# Create the Pedone_2006Fe2 potential by hand, by adding the individual components

potentialSet = TremoloXPotentialSet(name='Pedone_2006Fe2')

# Add the particle types to the potential set

# Add the pair potentials to the potential set
potentialSet.addPotential(MorsePotential('Si', 'O', r_0=2.1*Angstrom, k=2.0067*1/Ang, E_0=0.340554*eV, r_i=6.0*Angstrom, r_cut=7.5*Angstrom))
potentialSet.addPotential(MorsePotential('O', 'O', r_0=3.618701*Angstrom, k=1.379316*1/Ang, E_0=0.042395*eV, r_i=6.0*Angstrom, r_cut=7.5*Angstrom))

# Add the coulomb solver to the potential set
potentialSet.setCoulombSolver(CoulombSPME(r_cut=9.0*Angstrom, accuracy=1.0e-06))

# Create the calculator from the potential set
calculator = TremoloXCalculator(parameters=potentialSet)

bulk_configuration.setCalculator(calculator)
bulk_configuration.update()



## Notes¶

This smooth-particle-mesh-ewald (SPME) solver [EPB+95] provides an efficient method to calculate the long-range electrostatic interactions between particles with partial charges, as defined in ParticleType.

The CoulombSPME solver works only for periodic systems, i.e. BulkConfiguration.

Essentially, the method evaluates a screened, short-range part of the electrostatic interactions as a pair-wise sum in real space, whereas the remaining long-range contributions are calculated in reciprocal space.

When using bonded force fields the bonded_mode parameter can be used to modify how this potential acts between atoms that are connected by less than 4 bonds. If CoulombSolver.evaluateAll (or “mode_bondless”) is chosen, the potential acts between all selected atoms independent of the bonds between them. If CoulombSolver.evaluate4 (or “mode_14”) is chosen, the potential is switched off for all atoms that are connected via one, two, or three consecutive bonds.

 [EPB+95] U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen. A smooth particle mesh Ewald method. J. Chem. Phys., 1995. doi:10.1063/1.470117.