Hard particle Monte Carlo

HPMC performs hard particle Monte Carlo simulations of a variety of classes of shapes.


HPMC implements hard particle Monte Carlo in HOOMD-blue.


The following quantities are provided by the integrator for use in HOOMD-blue’s hoomd.analyze.log.

  • hpmc_sweep - Number of sweeps completed since the start of the MC integrator

  • hpmc_translate_acceptance - Fraction of translation moves accepted (averaged only over the last time step)

  • hpmc_rotate_acceptance - Fraction of rotation moves accepted (averaged only over the last time step)

  • hpmc_d - Maximum move displacement

  • hpmc_a - Maximum rotation move

  • hpmc_move_ratio - Probability of making a translation move (1- P(rotate move))

  • hpmc_overlap_count - Count of the number of particle-particle overlaps in the current system configuration

With non-interacting depletants, the following log quantities are available:

  • hpmc_fugacity_**type** - The current value of the depletant fugacity for a given type (in units of density, volume^-1)

  • hpmc_insert_count - Number of depletants inserted per colloid

With patch energies defined, the following quantities are available: - hpmc_patch_energy - The potential energy of the system resulting from the patch interaction. - hpmc_patch_rcut - The cutoff radius in the patch energy interaction.

compute.free_volume provides the following loggable quantities: - hpmc_free_volume - The free volume estimate in the simulation box obtained by MC sampling (in volume units)

update.boxmc provides the following loggable quantities:

  • hpmc_boxmc_trial_count - Number of box changes attempted since the start of the boxmc updater

  • hpmc_boxmc_volume_acceptance - Fraction of volume/length change trials accepted (averaged from the start of the last run)

  • hpmc_boxmc_ln_volume_acceptance - Fraction of log(volume) change trials accepted (averaged from the start of the last run)

  • hpmc_boxmc_shear_acceptance - Fraction of shear trials accepted (averaged from the start of the last run)

  • hpmc_boxmc_aspect_acceptance - Fraction of aspect trials accepted (averaged from the start of the last run)

  • hpmc_boxmc_betaP Current value of the \(\beta p\) value of the boxmc updater

update.muvt provides the following loggable quantities.

  • hpmc_muvt_insert_acceptance - Fraction of particle insertions accepted (averaged from start of run)

  • hpmc_muvt_remove_acceptance - Fraction of particle removals accepted (averaged from start of run)

  • hpmc_muvt_volume_acceptance - Fraction of particle removals accepted (averaged from start of run)

update.clusters() provides the following loggable quantities.

  • hpmc_clusters_moves - Fraction of cluster moves divided by the number of particles

  • hpmc_clusters_pivot_acceptance - Fraction of pivot moves accepted

  • hpmc_clusters_reflection_acceptance - Fraction of reflection moves accepted

  • hpmc_clusters_swap_acceptance - Fraction of swap moves accepted

  • hpmc_clusters_avg_size - Average cluster size

Timestep definition

HOOMD-blue started as an MD code where timestep has a clear meaning. MC simulations are run for timesteps. In exact terms, this means different things on the CPU and GPU and something slightly different when using MPI. The behavior is approximately normalized so that user scripts do not need to drastically change run() lengths when switching from one execution resource to another.

In the GPU implementation, one trial move is applied to a number of randomly chosen particles in each cell during one timestep. The number of selected particles is nselect*ceil(avg particles per cell) where nselect is a user-chosen parameter. The default value of nselect is 4, which achieves optimal performance for a wide variety of benchmarks. Detailed balance is obeyed at the level of a timestep. In short: One timestep is NOT equal to one sweep, but is approximately nselect sweeps, which is an overestimation.

In the single-threaded CPU implementation, one trial move is applied nselect times to each of the N particles during one timestep. In parallel MPI runs, one trial moves is applied nselect times to each particle in the active region. There is a small strip of inactive region near the boundaries between MPI ranks in the domain decomposition. The trial moves are performed in a shuffled order so detailed balance is obeyed at the level of a timestep. In short: One timestep is approximately nselect sweeps (N trial moves). In single-threaded runs, the approximation is exact, but it is slightly underestimated in MPI parallel runs.

To approximate a fair comparison of dynamics between CPU and GPU timesteps, log the hpmc_sweep quantity to get the number sweeps completed so far at each logged timestep.

See J. A. Anderson et. al. 2016 for design and implementation details.


HPMC supports integration with implicit depletants. Depletants are shapes that do not interact between themselves, but have a finite excluded volume with respect to other particles (the colloids). Their ideal gas nature makes it possible to randomly insert depletants into the overlap regions between the colloids, according to a Poisson point process to sample from the grand-canonical ensemble. This insertion is efficiently performed in parallel on the CPU, using TBB when it is enabled (see Installation Guide), or on the GPU.

Details on the depletant capability are documented in J. Glaser et al. 2015, and Glaser, to be published (2019).

Since release 3.0 HOOMD-blue supports quermass integration, which is a method to define the excluded volume of the colloids independently from that of the test particles. Every colloid is swept by a sphere of constant radius r_sweep (see hoomd.hpmc.integrate.mode_hpmc.set_params()), similar to implicit depletants with a spherical depletant. However, the test particle (or mixture thereof) now intersects the region of intersection between the sphere-swept colloids, as illustrated below. The name ‘Quermass integration’ of the method emphasizes the fact that test particles of arbitrary shape and in particular, convex test particles of arbitrary geometric measures (volume, surface area, integrated mean and Gaussian curvature – the four Minkowski measures in three dimensions) can be used to realize a free energy functional that depends on the corresponding measures of the system of particles in a general way. The coefficients can have any sign, e.g. negative coefficients are realized by negative test particle fugacities (see hoomd.hpmc.integrate.mode_hpmc.set_fugacity()).

Cell list schematic


hoomd.hpmc is stable. When upgrading from version 2.x to 2.y (y > x), existing job scripts that follow documented interfaces for functions and classes will not require any modifications. Maintainer: Joshua A. Anderson