# md.compute

Overview

 HarmonicAveragedThermodynamicQuantities Compute harmonic averaged thermodynamic properties of particles. ThermodynamicQuantities Compute thermodynamic properties of a subset of the system.

Details

Compute properties of molecular dynamics simulations.

The MD compute classes compute instantaneous properties of the simulation state and provide results as loggable quantities for use with hoomd.logging.Logger or by direct access via the Python API.

class hoomd.md.compute.HarmonicAveragedThermodynamicQuantities(filter, kT, harmonic_pressure=0)

Bases: Compute

Compute harmonic averaged thermodynamic properties of particles.

Parameters
• filter (hoomd.filter.filter_like) – Particle filter to compute thermodynamic properties for.

• kT (float) – Temperature of the system $$[\mathrm{energy}]$$.

• harmonic_pressure (float) – Harmonic contribution to the pressure $$[\mathrm{pressure}]$$. If omitted, the HMA pressure can still be computed, but will be similar in precision to the conventional pressure.

HarmonicAveragedThermodynamicQuantities acts on a given subset of particles and calculates harmonically mapped average (HMA) properties of those particles when requested. HMA computes properties more precisely (with less variance) for atomic crystals in NVT simulations. The presence of diffusion (vacancy hopping, etc.) will prevent HMA from providing improvement. HMA tracks displacements from the lattice positions, which are saved either during first call to Simulation.run or when the compute is first added to the simulation, whichever occurs last.

Note

HarmonicAveragedThermodynamicQuantities is an implementation of the methods section of Sabry G. Moustafa, Andrew J. Schultz, and David A. Kofke. (2015). “Very fast averaging of thermal properties of crystals by molecular simulation”. Phys. Rev. E 92, 043303 doi:10.1103/PhysRevE.92.043303

Examples:

hma = hoomd.compute.HarmonicAveragedThermodynamicQuantities(
filter=hoomd.filter.Type('A'), kT=1.0)

filter

Subset of particles compute thermodynamic properties for.

Type

hoomd.filter.filter_like

kT

Temperature of the system $$[\mathrm{energy}]$$.

Type

float

harmonic_pressure

Harmonic contribution to the pressure $$[\mathrm{pressure}]$$.

Type

float

property potential_energy

Average potential energy $$[\mathrm{energy}]$$.

(Loggable: category=”scalar”)

property pressure

Average pressure $$[\mathrm{pressure}]$$.

(Loggable: category=”scalar”)

class hoomd.md.compute.ThermodynamicQuantities(filter)

Bases: Compute

Compute thermodynamic properties of a subset of the system.

Parameters

filter (hoomd.filter) – Particle filter to compute thermodynamic properties for.

ThermodynamicQuantities acts on a subset of particles in the system and calculates thermodynamic properties of those particles. Add a ThermodynamicQuantities instance to a logger to save these quantities to a file, see hoomd.logging.Logger for more details.

Note

For compatibility with hoomd.md.constrain.Rigid, ThermodynamicQuantities performs all sums $$\sum_{i \in \mathrm{filter}}$$ over free particles and rigid body centers - ignoring constituent particles to avoid double counting.

Examples:

f = filter.Type('A')
compute.ThermodynamicQuantities(filter=f)

property degrees_of_freedom

Number of degrees of freedom in the subset $$N_{\mathrm{dof}}$$.

$N_\mathrm{dof} = N_\mathrm{dof, translational} + N_\mathrm{dof, rotational}$

hoomd.State.update_group_dof describes when $$N_{\mathrm{dof}}$$ is updated.

(Loggable: category=”scalar”)

property kinetic_energy

Total kinetic energy $$K$$ of the subset $$[\mathrm{energy}]$$.

$K = K_\mathrm{rotational} + K_\mathrm{translational}$

(Loggable: category=”scalar”)

property kinetic_temperature

Instantaneous thermal energy $$kT_k$$ of the subset $$[\mathrm{energy}]$$.

$kT_k = 2 \cdot \frac{K}{N_{\mathrm{dof}}}$

(Loggable: category=”scalar”)

property num_particles

Number of particles $$N$$ in the subset.

(Loggable: category=”scalar”)

property potential_energy

Potential energy $$U$$ that the subset contributes to the system $$[\mathrm{energy}]$$.

$U = U_{\mathrm{net},\mathrm{additional}} + \sum_{i \in \mathrm{filter}} U_{\mathrm{net},i},$

where the net energy terms are computed by hoomd.md.Integrator over all of the forces in hoomd.md.Integrator.forces.

(Loggable: category=”scalar”)

property pressure

Instantaneous pressure $$P$$ of the subset $$[\mathrm{pressure}]$$.

$P = \frac{ 2 \cdot K_{\mathrm{translational}} + W_\mathrm{isotropic} }{D \cdot V},$

where $$D$$ is the dimensionality of the system, $$V$$ is the volume of the simulation box (or area in 2D), and $$W_\mathrm{isotropic}$$ is the isotropic virial:

$\begin{split}W_\mathrm{isotropic} = & \frac{1}{D} \left( W_{\mathrm{net},\mathrm{additional}}^{xx} + W_{\mathrm{net},\mathrm{additional}}^{yy} + W_{\mathrm{net},\mathrm{additional}}^{zz} \right) \\ + & \frac{1}{D} \sum_{i \in \mathrm{filter}} \left( W_\mathrm{{net},i}^{xx} + W_\mathrm{{net},i}^{yy} + W_\mathrm{{net},i}^{zz} \right)\end{split}$

where the net virial terms are computed by hoomd.md.Integrator over all of the forces in hoomd.md.Integrator.forces and $$W^{zz}=0$$ in 2D simulations.

(Loggable: category=”scalar”)

property pressure_tensor

Instantaneous pressure tensor of the subset $$[\mathrm{pressure}]$$.

The six components of the pressure tensor are given in the order: ($$P^{xx}$$, $$P^{xy}$$, $$P^{xz}$$, $$P^{yy}$$, $$P^{yz}$$, $$P^{zz}$$):

$P^{kl} = \frac{1}{V} \left( W_{\mathrm{net},\mathrm{additional}}^{kl} + \sum_{i \in \mathrm{filter}} m_i \cdot v_i^k \cdot v_i^l + W_{\mathrm{net},i}^{kl} \right),$

where the net virial terms are computed by hoomd.md.Integrator over all of the forces in hoomd.md.Integrator.forces, $$v_i^k$$ is the k-th component of the velocity of particle $$i$$ and $$V$$ is the total simulation box volume (or area in 2D).

(Loggable: category=”sequence”)

property rotational_degrees_of_freedom

Number of rotational degrees of freedom in the subset $$N_\mathrm{dof, rotational}$$.

Integration methods (hoomd.md.methods) determine the number of degrees of freedom they give to each particle. Each integration method operates on a subset of the system $$\mathrm{filter}_m$$ that may be distinct from the subset from the subset given to ThermodynamicQuantities.

When hoomd.md.Integrator.integrate_rotational_dof is False, $$N_\mathrm{dof, rotational} = 0$$. When it is True, the given degrees of freedom depend on the dimensionality of the system.

In 2D:

$N_\mathrm{dof, rotational} = \sum_{m \in \mathrm{methods}} \; \sum_{i \in \mathrm{filter} \cup \mathrm{filter}_m} \left[ I_{z,i} > 0 \right]$

where $$I$$ is the particles’s moment of inertia.

In 3D:

$N_\mathrm{dof, rotational} = \sum_{m \in \mathrm{methods}} \; \sum_{i \in \mathrm{filter} \cup \mathrm{filter}_m} \left[ I_{x,i} > 0 \right] + \left[ I_{y,i} > 0 \right] + \left[ I_{z,i} > 0 \right]$

hoomd.State.update_group_dof describes when $$N_{\mathrm{dof, rotational}}$$ is updated.

(Loggable: category=”scalar”)

property rotational_kinetic_energy

Rotational kinetic energy $$K_\mathrm{rotational}$$ of the subset $$[\mathrm{energy}]$$.

\begin{align}\begin{aligned}\begin{split}K_\mathrm{rotational,d} = \frac{1}{2} \sum_{i \in \mathrm{filter}} \begin{cases} \frac{L_{d,i}^2}{I_{d,i}} & I^d_i > 0 \\ 0 & I^d_i = 0 \end{cases}\end{split}\\K_\mathrm{rotational} = K_\mathrm{rotational,x} + K_\mathrm{rotational,y} + K_\mathrm{rotational,z}\end{aligned}\end{align}

$$I$$ is the moment of inertia and $$L$$ is the angular momentum in the (diagonal) reference frame of the particle.

(Loggable: category=”scalar”)

property translational_degrees_of_freedom

Number of translational degrees of freedom in the subset $$N_{\mathrm{dof, translational}}$$.

When using a single integration method on all particles that is momentum conserving, the center of mass motion is conserved and the number of translational degrees of freedom is:

$N_\mathrm{dof, translational} = DN - D\frac{N}{N_\mathrm{particles}} - N_\mathrm{constraints}(\mathrm{filter})$

where $$D$$ is the dimensionality of the system and $$N_\mathrm{constraints}(\mathrm{filter})$$ is the number of degrees of freedom removed by constraints (hoomd.md.constrain) in the subset. The fraction $$\frac{N}{N_\mathrm{particles}}$$ distributes the momentum conservation constraint evenly when ThermodynamicQuantities is applied to multiple subsets.

When using multiple integration methods, a single integration method on fewer than all particles, or a single integration method that is not momentum conserving, hoomd.md.Integrator assumes that linear momentum is not conserved and counts the center of mass motion in the degrees of freedom:

$N_{\mathrm{dof, translational}} = DN - N_\mathrm{constraints}(\mathrm{filter})$

(Loggable: category=”scalar”)

property translational_kinetic_energy

Translational kinetic energy $$K_{\mathrm{translational}}$$ of the subset $$[\mathrm{energy}]$$.

$K_\mathrm{translational} = \frac{1}{2} \sum_{i \in \mathrm{filter}} m_i v_i^2$

(Loggable: category=”scalar”)

property volume

Volume $$V$$ of the simulation box (area in 2D) $$[\mathrm{length}^{D}]$$.

(Loggable: category=”scalar”)