# CustomManyParticleForce¶

class OpenMM::CustomManyParticleForce

This class supports a wide variety of nonbonded N-particle interactions, where N is user specified. The interaction energy is determined by an arbitrary, user specified algebraic expression that is evaluated for every possible set of N particles in the system. It may depend on the positions of the individual particles, the distances between pairs of particles, the angles formed by sets of three particles, and the dihedral angles formed by sets of four particles.

Be aware that the cost of evaluating an N-particle interaction increases very rapidly with N. Values larger than N=3 are rarely used.

We refer to a set of particles for which the energy is being evaluated as p1, p2, p3, etc. The energy expression may depend on the following variables and functions:

• x1, y1, z1, x2, y2, z2, etc.: The x, y, and z coordinates of the particle positions. For example, x1 is the x coordinate of particle p1, and y3 is the y coordinate of particle p3.
• distance(p1, p2): the distance between particles p1 and p2 (where “p1” and “p2” may be replaced by the names of whichever particles you want to calculate the distance between).
• angle(p1, p2, p3): the angle formed by the three specified particles.
• dihedral(p1, p2, p3, p4): the dihedral angle formed by the four specified particles.
• arbitrary global and per-particle parameters that you define.

To use this class, create a CustomManyParticleForce() object, passing an algebraic expression to the constructor that defines the interaction energy of each set of particles. Then call addPerParticleParameter() to define per-particle parameters, and addGlobalParameter() to define global parameters. The values of per-particle parameters are specified as part of the system definition, while values of global parameters may be modified during a simulation by calling Context::setParameter().

Next, call addParticle() once for each particle in the System to set the values of its per-particle parameters. The number of particles for which you set parameters must be exactly equal to the number of particles in the System, or else an exception will be thrown when you try to create a Context. After a particle has been added, you can modify its parameters by calling setParticleParameters(). This will have no effect on Contexts that already exist unless you call updateParametersInContext().

Multi-particle interactions can be very expensive to evaluate, so they are usually used with a cutoff distance. The exact interpretation of the cutoff depends on the permutation mode, as discussed below. CustomManyParticleForce() also lets you specify “exclusions”, particular pairs of particles whose interactions should be omitted from force and energy calculations. This is most often used for particles that are bonded to each other. If you specify a pair of particles as an exclusion,

As an example, the following code creates a CustomManyParticleForce() that implements an Axilrod-Teller potential. This is an interaction between three particles that depends on all three distances and angles formed by the particles.

CustomManyParticleForce* force = new CustomManyParticleForce(3,
"C*(1+3*cos(theta1)*cos(theta2)*cos(theta3))/(r12*r13*r23)^3;"
"theta1=angle(p1,p2,p3); theta2=angle(p2,p3,p1); theta3=angle(p3,p1,p2);"
"r12=distance(p1,p2); r13=distance(p1,p3); r23=distance(p2,p3)");
force->setPermutationMode(CustomManyParticleForce::SinglePermutation);


This force depends on one parameter, C. The following code defines it as a global parameter:

force->addGlobalParameter("C", 1.0);


Notice that the expression is symmetric with respect to the particles. It only depends on the products cos(theta1)*cos(theta2)*cos(theta3) and r12*r13*r23, both of which are unchanged if the labels p1, p2, and p3 are permuted. This is required because we specified SinglePermutation as the permutation mode. (This is the default, so we did not really need to set it, but doing so makes the example clearer.) In this mode, the expression is only evaluated once for each set of particles. No guarantee is made about which particle will be identified as p1, p2, etc. Therefore, the energy

Not all many-particle interactions work this way. Another common pattern is for the expression to describe an interaction between one central particle and other nearby particles. An example of this is the 3-particle piece of the Stillinger-Weber potential:

CustomManyParticleForce* force = new CustomManyParticleForce(3,
"L*eps*(cos(theta1)+1/3)^2*exp(sigma*gamma/(r12-a*sigma))*exp(sigma*gamma/(r13-a*sigma));"
"r12 = distance(p1,p2); r13 = distance(p1,p3); theta1 = angle(p3,p1,p2)");
force->setPermutationMode(CustomManyParticleForce::UniqueCentralParticle);


When the permutation mode is set to UniqueCentralParticle, particle p1 is treated as the central particle. For a set of N particles, the expression is evaluated N times, once with each particle as p1. The expression can therefore treat p1 differently from the other particles. Notice that it is still symmetric with respect to p2 and p3, however. There is no guarantee about how those labels will be assigned to particles.

Distance cutoffs are applied in different ways depending on the permutation mode. In SinglePermutation mode, every particle in the set must be within the cutoff distance of every other particle. If

Another common situation is that some particles are fundamentally different from others, causing the expression to be inherently non-symmetric. An example would be a water model that involves three particles, two of which

A particle type is an integer that you specify when you call addParticle(). (If you omit the argument, it defaults to 0.) For the water model, you could specify 0 for all oxygen atoms and 1 for all hydrogen atoms. You can then call setTypeFilter() to specify the list of allowed types for each of the N particles involved in an interaction:

set<int> oxygenTypes, hydrogenTypes;
oxygenTypes.insert(0);
hydrogenTypes.insert(1);
force->setTypeFilter(0, oxygenTypes);
force->setTypeFilter(1, hydrogenTypes);
force->setTypeFilter(2, hydrogenTypes);


This specifies that of the three particles in an interaction, p1 must be oxygen while p2 and p3 must be hydrogen. The energy expression will only be evaluated for triplets of particles that satisfy those requirements. It will still only be evaluated once for each triplet, so it must still be symmetric with respect to p2 and p3.

Expressions may involve the operators + (add), - (subtract), * (multiply), / (divide), and ^ (power), and the following functions: sqrt, exp, log, sin, cos, sec, csc, tan, cot, asin, acos, atan, sinh, cosh, tanh, erf, erfc, min, max, abs, floor, ceil, step, delta, select. All trigonometric functions are defined in radians, and log is the natural logarithm. step(x) = 0 if x is less than 0, 1 otherwise. delta(x) = 1 if x is 0, 0 otherwise. select(x,y,z) = z if x = 0, y otherwise. The names of per-particle parameters have the suffix “1”, “2”, etc. appended to them to indicate the values for the multiple interacting particles. For example, if you define a per-particle parameter called “charge”, then the variable “charge2” is the charge of particle p2. As seen above, the expression may also involve intermediate quantities that are defined following the main expression, using ”;” as a separator.

In addition, you can call addTabulatedFunction() to define a new function based on tabulated values. You specify the function by creating a TabulatedFunction object. That function can then appear in the expression.

Methods

 CustomManyParticleForce() Create a CustomManyParticleForce(). ~CustomManyParticleForce() getNumParticlesPerSet() Get the number of particles in each set for which the energy is evaluated getNumParticles() Get the number of particles for which force field parameters have been defined. getNumExclusions() Get the number of particle pairs whose interactions should be excluded. getNumPerParticleParameters() Get the number of per-particle parameters that the interaction depends on. getNumGlobalParameters() Get the number of global parameters that the interaction depends on. getNumTabulatedFunctions() Get the number of tabulated functions that have been defined. getEnergyFunction() Get the algebraic expression that gives the interaction energy of each bond setEnergyFunction() Set the algebraic expression that gives the interaction energy of each bond getNonbondedMethod() Get the method used for handling long range nonbonded interactions. setNonbondedMethod() Set the method used for handling long range nonbonded interactions. getPermutationMode() Get the mode that selects which permutations of a set of particles to evaluate the interaction for. setPermutationMode() Set the mode that selects which permutations of a set of particles to evaluate the interaction for. getCutoffDistance() Get the cutoff distance (in nm) being used for nonbonded interactions. setCutoffDistance() Set the cutoff distance (in nm) being used for nonbonded interactions. addPerParticleParameter() Add a new per-particle parameter that the interaction may depend on. getPerParticleParameterName() Get the name of a per-particle parameter. setPerParticleParameterName() Set the name of a per-particle parameter. addGlobalParameter() Add a new global parameter that the interaction may depend on. getGlobalParameterName() Get the name of a global parameter. setGlobalParameterName() Set the name of a global parameter. getGlobalParameterDefaultValue() Get the default value of a global parameter. setGlobalParameterDefaultValue() Set the default value of a global parameter. addParticle() Add the nonbonded force parameters for a particle. getParticleParameters() Get the nonbonded force parameters for a particle. setParticleParameters() Set the nonbonded force parameters for a particle. addExclusion() Add a particle pair to the list of interactions that should be excluded. getExclusionParticles() Get the particles in a pair whose interaction should be excluded. setExclusionParticles() Set the particles in a pair whose interaction should be excluded. createExclusionsFromBonds() Identify exclusions based on the molecular topology. getTypeFilter() Get the allowed particle types for one of the particles involved in the interaction. setTypeFilter() Set the allowed particle types for one of the particles involved in the interaction. addTabulatedFunction() Add a tabulated function that may appear in the energy expression. getTabulatedFunction() Get a const reference to a tabulated function that may appear in the energy expression. getTabulatedFunction() Get a reference to a tabulated function that may appear in the energy expression. getTabulatedFunctionName() Get the name of a tabulated function that may appear in the energy expression. updateParametersInContext() Update the per-particle parameters in a Context to match those stored in this Force object. usesPeriodicBoundaryConditions() Returns whether or not this force makes use of periodic boundary conditions.

Enum: NonbondedMethod

 NoCutoff No cutoff is applied to nonbonded interactions. The full set of interactions is computed exactly. This necessarily means that periodic boundary conditions cannot be used. This is the default. CutoffNonPeriodic Interactions are ignored if any two particles are further apart than the cutoff distance. CutoffPeriodic Periodic boundary conditions are used, so that each particle interacts only with the nearest periodic copy of each other particle. Interactions are ignored if any two particles are further apart than the cutoff distance.

Enum: PermutationMode

 SinglePermutation For any set of particles, the interaction is evaluated only once for a single permutation of the particles. There is no guarantee about which permutation will be used (aside from the requirement to satisfy type filters), so the expression must be symmetric. If cutoffs are used, then every particle in the set must be within the cutoff distance of every other particle. UniqueCentralParticle The interaction is treated as an interaction between one central particle (p1) and various other nearby particles (p2, p3, ...). For a set of N particles it will be evaluated N times, once with each particle as p1. The expression must be symmetric with respect to the other particles, but may treat p1 differently. If cutoffs are used, then every particle must be within the cutoff distance of p1.
CustomManyParticleForce(int particlesPerSet, const std::string &energy)

Create a CustomManyParticleForce().

• particlesPerSet – the number of particles in each set for which the energy is evaluated
• energy – an algebraic expression giving the interaction energy of each triplet as a function of particle positions, inter-particle distances, angles, and any global and per-particle parameters
~CustomManyParticleForce()
int getNumParticlesPerSet() const

Get the number of particles in each set for which the energy is evaluated

int getNumParticles() const

Get the number of particles for which force field parameters have been defined.

int getNumExclusions() const

Get the number of particle pairs whose interactions should be excluded.

int getNumPerParticleParameters() const

Get the number of per-particle parameters that the interaction depends on.

int getNumGlobalParameters() const

Get the number of global parameters that the interaction depends on.

int getNumTabulatedFunctions() const

Get the number of tabulated functions that have been defined.

const std::string &getEnergyFunction() const

Get the algebraic expression that gives the interaction energy of each bond

void setEnergyFunction(const std::string &energy)

Set the algebraic expression that gives the interaction energy of each bond

NonbondedMethod getNonbondedMethod() const

Get the method used for handling long range nonbonded interactions.

void setNonbondedMethod(NonbondedMethod method)

Set the method used for handling long range nonbonded interactions.

PermutationMode getPermutationMode() const

Get the mode that selects which permutations of a set of particles to evaluate the interaction for.

void setPermutationMode(PermutationMode mode)

Set the mode that selects which permutations of a set of particles to evaluate the interaction for.

double getCutoffDistance() const

Get the cutoff distance (in nm) being used for nonbonded interactions. If the NonbondedMethod in use is NoCutoff, this value will have no effect.

Returns: the cutoff distance, measured in nm
void setCutoffDistance(double distance)

Set the cutoff distance (in nm) being used for nonbonded interactions. If the NonbondedMethod in use is NoCutoff, this value will have no effect.

• distance – the cutoff distance, measured in nm
int addPerParticleParameter(const std::string &name)

Add a new per-particle parameter that the interaction may depend on.

• name – the name of the parameter
Returns: the index of the parameter that was added
const std::string &getPerParticleParameterName(int index) const

Get the name of a per-particle parameter.

• index – the index of the parameter for which to get the name
Returns: the parameter name
void setPerParticleParameterName(int index, const std::string &name)

Set the name of a per-particle parameter.

• index – the index of the parameter for which to set the name
• name – the name of the parameter
int addGlobalParameter(const std::string &name, double defaultValue)

Add a new global parameter that the interaction may depend on.

• name – the name of the parameter
• defaultValue – the default value of the parameter
Returns: the index of the parameter that was added
const std::string &getGlobalParameterName(int index) const

Get the name of a global parameter.

• index – the index of the parameter for which to get the name
Returns: the parameter name
void setGlobalParameterName(int index, const std::string &name)

Set the name of a global parameter.

• index – the index of the parameter for which to set the name
• name – the name of the parameter
double getGlobalParameterDefaultValue(int index) const

Get the default value of a global parameter.

• index – the index of the parameter for which to get the default value
Returns: the parameter default value
void setGlobalParameterDefaultValue(int index, double defaultValue)

Set the default value of a global parameter.

• index – the index of the parameter for which to set the default value
• defaultValue – the default value of the parameter
int addParticle(const std::vector<double> &parameters = std::vector< double >(), int type = 0)

Add the nonbonded force parameters for a particle. This should be called once for each particle in the System. When it is called for the i’th time, it specifies the parameters for the i’th particle.

• parameters – the list of parameters for the new particle
• type – the type of the new particle
Returns: the index of the particle that was added
void getParticleParameters(int index, std::vector<double> &parameters, int &type) const

Get the nonbonded force parameters for a particle.

• index – the index of the particle for which to get parameters
• parameters – [out] the list of parameters for the specified particle
• type – [out] the type of the specified particle
void setParticleParameters(int index, const std::vector<double> &parameters, int type)

Set the nonbonded force parameters for a particle.

• index – the index of the particle for which to set parameters
• parameters – the list of parameters for the specified particle
• type – the type of the specified particle
int addExclusion(int particle1, int particle2)

Add a particle pair to the list of interactions that should be excluded.

In many cases, you can use createExclusionsFromBonds() rather than adding each exclusion explicitly.

• particle1 – the index of the first particle in the pair
• particle2 – the index of the second particle in the pair
Returns: the index of the exclusion that was added
void getExclusionParticles(int index, int &particle1, int &particle2) const

Get the particles in a pair whose interaction should be excluded.

• index – the index of the exclusion for which to get particle indices
• particle1 – [out] the index of the first particle in the pair
• particle2 – [out] the index of the second particle in the pair
void setExclusionParticles(int index, int particle1, int particle2)

Set the particles in a pair whose interaction should be excluded.

• index – the index of the exclusion for which to set particle indices
• particle1 – the index of the first particle in the pair
• particle2 – the index of the second particle in the pair
void createExclusionsFromBonds(const std::vector<std::pair<int, int>> &bonds, int bondCutoff)

Identify exclusions based on the molecular topology. Particles which are separated by up to a specified number of bonds are added as exclusions.

• bonds – the set of bonds based on which to construct exclusions. Each element specifies the indices of two particles that are bonded to each other.
• bondCutoff – pairs of particles that are separated by this many bonds or fewer are added to the list of exclusions
void getTypeFilter(int index, std::set<int> &types) const

Get the allowed particle types for one of the particles involved in the interaction. If this an empty set (the default), no filter is applied and all interactions are evaluated regardless of the type of the specified particle.

void setTypeFilter(int index, const std::set<int> &types)

Set the allowed particle types for one of the particles involved in the interaction. If this an empty set (the default), no filter is applied and all interactions are evaluated regardless of the type of the specified particle.

int addTabulatedFunction(const std::string &name, TabulatedFunction *function)

Add a tabulated function that may appear in the energy expression.

Returns: the index of the function that was added
const TabulatedFunction &getTabulatedFunction(int index) const

Get a const reference to a tabulated function that may appear in the energy expression.

• index – the index of the function to get
Returns: the TabulatedFunction object defining the function
TabulatedFunction &getTabulatedFunction(int index)

Get a reference to a tabulated function that may appear in the energy expression.

• index – the index of the function to get
Returns: the TabulatedFunction object defining the function
const std::string &getTabulatedFunctionName(int index) const

Get the name of a tabulated function that may appear in the energy expression.

• index – the index of the function to get
Returns: the name of the function as it appears in expressions
void updateParametersInContext(Context &context)

Update the per-particle parameters in a Context to match those stored in this Force object. This method provides an efficient method to update certain parameters in an existing Context without needing to reinitialize it. Simply call setParticleParameters() to modify this object’s parameters, then call updateParametersInContext() to copy them over to the Context.

This method has several limitations. The only information it updates is the values of per-particle parameters. All other aspects of the Force (the energy function, nonbonded method, cutoff distance, etc.) are unaffected and can only be changed by reinitializing the Context. Also, this method cannot be used to add new particles, only to change the parameters of existing ones.

bool usesPeriodicBoundaryConditions() const

Returns whether or not this force makes use of periodic boundary conditions.

Returns: true if force uses PBC and false otherwise