1.1. Cluster expansion method and thermodynamic calculations using CLUPAN¶

• Evaluation of effective cluster interactions (ECI) using the cluster expansion (CE) method.
• Calculation of energies for structures using ECI.
• Monte Carlo simulations using ECI.
• Free energy calculation based on thermodynamics integration combined with Monte Carlo simulations.
• Iterative procedure to perform the CE.

See [CE1] to find the details of the procedure.

1.2. Framework of CLUPAN¶

CLUPAN is composed of the following programs.

main programs

• Searching for symmetrically-independent structures

  • mkposcar

• Searching for symmetrically-independent clusters

  • cluster

• Calculating correlation functions of a structure

  • correlation

• Estimating ECIs using the least-squares method

  • lsf, wlsf

• Optimizing cluster set using the genetic algorithm and the simulated annealing

  • gasa, wgasa

• Searching for DFT structures that improves the estimated ECIs

  • search_poscar

• Searching for ground state structures using the ECIs

  • gss

• Performing Monte Carlo simulations using the ECIs

  • cmc, gcmc

• estimating the grand potential using the thermodynamic integration

  • ti

sub programs

• Evaluating the variance of correlation functions and the correlation between correlation functions of two clusters

  • statistic

• Calculating the mean variance of the predicted energy

  • variance_energy

• Generating VARIANCE and MEAN files required in search_poscar_variance

  • variance_stpop

• Estimating the grand potential using the low temperature expansion

  • lte

1.3. Examples of calculations by using CLUPAN¶

Predicting cation disordering in spinel oxides [CE2]

Exploring stable structures in tin oxides [CE3]