Bibliography

Key references behind the methods that mcpy implements.

Hybrid Grand Canonical Monte Carlo

Senftle, T. P., Janik, M. J., van Duin, A. C. T. A ReaxFF investigation of hydride formation in palladium nanoclusters via Monte Carlo and molecular dynamics simulations. The Journal of Physical Chemistry C, 118 (9), 4967-4981 (2014). doi:10.1021/jp411015a.

The hybrid scheme, in which every trial insertion or deletion is relaxed before the acceptance test, is the basis of the GCMC loop in GrandCanonicalEnsemble.

GCMC for surface phase diagrams

Wexler, R. B., Qiu, T., Rappe, A. M. Automatic prediction of surface phase diagrams using ab initio grand canonical Monte Carlo. The Journal of Physical Chemistry C, 123 (4), 2321-2328 (2019). doi:10.1021/acs.jpcc.8b11093.

Grand-canonical sampling restricted to a region near the surface, the approach of the slab examples (GCMC on Ag(111) with a machine-learned potential).

Replica exchange and parallel tempering

Geyer, C. J. Markov chain Monte Carlo maximum likelihood. In: Computing Science and Statistics, Proceedings of the 23rd Symposium on the Interface, pp. 156-163. Interface Foundation of North America (1991).

Hukushima, K., Nemoto, K. Exchange Monte Carlo method and application to spin glass simulations. Journal of the Physical Society of Japan, 65 (6), 1604-1608 (1996). doi:10.1143/JPSJ.65.1604.

The swap acceptance rule of ReplicaExchange and BatchedReplicaExchange is the parallel-tempering (exchange Monte Carlo) criterion of these papers, in the general form of Yan and de Pablo (below).

Swendsen, R. H., Wang, J.-S. Replica Monte Carlo simulation of spin-glasses. Physical Review Letters, 57 (21), 2607-2609 (1986). doi:10.1103/PhysRevLett.57.2607.

The original replica Monte Carlo method, a precursor of replica exchange.

Yan, Q., de Pablo, J. J. Hyper-parallel tempering Monte Carlo: Application to the Lennard-Jones fluid and the restricted primitive model. Journal of Chemical Physics, 111 (21), 9509-9516 (1999). doi:10.1063/1.480282.

The swap rule of both replica-exchange drivers is the hyper-parallel tempering rule of this paper. It covers a temperature ladder, a chemical-potential ladder, and a ladder with one mu per temperature rung.

Atomic Simulation Environment

Larsen, A. H., Mortensen, J. J., Blomqvist, J., et al. The atomic simulation environment: a Python library for working with atoms. Journal of Physics: Condensed Matter, 29 (27), 273002 (2017). doi:10.1088/1361-648X/aa680e.

mcpy is built directly on ASE: every configuration is an ase.Atoms object, and any ASE-compatible calculator can drive the sampling.

MACE

Batatia, I., Kovács, D. P., Simm, G. N. C., Ortner, C., Csányi, G. MACE: Higher order equivariant message passing neural networks for fast and accurate force fields. NeurIPS 2022. arXiv:2206.07697.

The machine-learned potential of the GPU examples and the tutorial.

Thesis

Farris, R. Development and Application of Advanced Computational Methods for Predicting the Structure and Properties of Nanoparticles. PhD thesis, Universitat de Barcelona (2025). hdl:10803/697698.

The doctoral work in which mcpy was developed; the exclusion-radius calibration (Calibrating species_radii) follows it.