Welcome to Pycasino

Welcome to the Pycasino documentation.

Pycasino is a Python implementation of the Casino quantum Monte Carlo program. It supports VMC and DMC energy calculations and wavefunction optimisation for molecules with Gaussian or Slater-type orbital basis sets.

Pycasino is based on Numba for JIT-compiled inner loops and mpi4py for MPI parallelisation.

User guide

• Installation
  • Python version
  • Dependencies
  • Virtual environments
  • Install Pycasino
  • Developing
• Quick start
  • Prerequisites
  • Example: VMC energy for helium
  • Running the calculation
  • Workflow: optimization then DMC
• Tutorial
  • Supported configuration files and their contents
    • Input files are supported
    • Input parameters supported
      • General keywords
      • VMC keywords
      • Optimization keywords
      • DMC keywords
      • WFN definition keywords
      • Cusp correction keywords
      • Pseudopotential keywords
    • Configs read/write
  • Wavefunction
    • Summary of Methods
    • value
    • coulomb
    • nonlocal_potential
    • kinetic_energy
    • energy
    • drift_velocity
    • drift_kinetic_energy
    • value_parameters_d1
    • kinetic_energy_parameters_d1
    • nonlocal_energy_parameters_d1
    • energy_parameters_d1
  • Cusp correction
    • Physical motivation
    • Correction scheme
    • Choice of the correction radius
    • Enabling cusp correction
    • Initialisation
    • Properties
    • References
  • Slater determinant
    • Summary of Methods
    • value matrix
    • gradient matrix
    • laplacian matrix
    • hessian matrix
    • tressian matrix
    • value
    • gradient
    • laplacian
    • hessian
    • tressian
      • Implementation
    • tressian_dot
  • Jastrow
    • Cusp conditions
    • Summary of Methods
    • u-term
    • chi-term
    • f-term
    • u-term gradient
    • chi-term gradient
    • f-term gradient
    • u-term laplacian
    • chi-term laplacian
    • f-term laplacian
    • References
  • Backflow
    • Backflow and nodal surfaces
    • Summary of Methods
    • eta-term
    • mu-term
    • phi-term
    • kappa-term
    • omega-term
    • eta-term gradient
    • mu-term gradient
    • phi-term gradient
    • omega-term gradient
    • eta-term laplacian
    • mu-term laplacian
    • phi-term laplacian
    • omega-term laplacian
    • References
  • Pfaffian pairing wave function
    • Motivation: nodal topology beyond backflow
    • The Pfaffian form
    • Pairing functions in explicit form
    • Evaluation
    • The geminal wave function in Pycasino
    • Optimization strategy
    • Implementation plan
    • Open questions
    • References
  • Variational Monte Carlo
    • Notation
    • What is accepted
    • Stage I: averaging over the proposal
    • Stage II: averaging along the chain
    • Interchanging the two stages
    • approximate_step_size
    • Cost of the interchange
    • Range of validity
    • Pseudopotentials and the electron gas
    • EBES
      • What the measurement says
    • DBDS
    • acceptance_ratio
    • optimize_vmc_step
      • What the columns test
    • vmc_corr_graph
      • The correlation time and the diffusion constant peak in different places
      • Which optimum is the efficiency depends on the decorrelation period
      • How long the decorrelation loop should be
      • What the correlation times measure
    • References
  • Diffusion Monte Carlo
    • Summary of Methods
    • drift_diffusion
    • limiting_velocity
    • branching_energy
    • branching
    • t_move
    • load_balancing
    • random_step
    • random_walk
    • References
• MPI parallelisation
  • Installation
  • Running with MPI
  • Memory model
  • Choosing the number of ranks
  • Combining MPI with Numba threading

Release notes

• Changelog
  • v 0.4.0 (in progress)
  • v 0.3.0 (2025-10-30)
  • v 0.2.0 (2024-10-30)
  • v 0.1.0 (2023-10-30)