Overview

The FRIES_bin directory contains source code for several different methods within the FCI-FRI/FCIQMC framework as applied to different types of systems.

Input Files

Molecular Systems

Executables that perform calculations on molecular systems (fciqmc_mol.c, frimulti_mol.c, frisys_mol.c) use the output from a Hartree-Fock calculation to calculate Hamiltonian matrix elements. The hf_path input argument specifies the path to the directory that contains these files. The HF orbitals must be ordered the same in the eris.txt, hcore.txt, and symm.txt files. These files must be named and formatted as follows:

• eris.txt: Contains the two-electron integrals \( \langle i j || a b \rangle \), where \( i \), \( j \), \( a \), and \( b \) denote orbitals. The \( M^4 \) integrals are stored in .csv format ordered by the \( i \), \( j \), \( a \), and \( b \) indices, where \( b \) is the least significant index and \( i \) is the most significant.
• hcore.txt: Contains the one-electron integrals \( \langle i | \hat{h} | a \rangle \), stored in .csv format analogously to the two-electron integrals
• symm.txt: Contains the irrep of each orbital in the HF basis, one on each line, encoded as described here.
• sys_params.txt: Contains parameters describing the system. See examples for formatting
  • n_elec: The total number of electrons in the system
  • n_frozen: Number of core electrons to freeze in the calculation. The orbitals with the lowest indices, as determined by the ordering in the above files, will be frozen.
  • eps: The value of \( \varepsilon \) (the imaginary time step) to use to evolve the solution vector during the calculation
  • hf_energy: The HF electronic energy of the system, in Hartrees (optional, but useful for accelerating convergence)

Lattice Systems

Code for running calculations on the Hubbard model (fciqmc_hh.c and frisys_hh.c) use the parameters in the file at the path specified by the params_path input argument. See the examples for an example format of this file. The parameters are as follows:

• n_elec: The total number of electrons in the system
• lat_len: The number of lattice sites along one dimension
• n_dim: The number of dimensions in the lattice
• eps: The value of \( \varepsilon \) (the imaginary time step) to use to evolve the solution vector during the calculation
• U: The on-site repulsion energy, in units of \( t \) (the kinetic energy hoping term)
• hf_energy: The HF electronic energy of the system, in Hartrees (optional, but useful for accelerating convergence)

Output Files

All executables produce the following files in the directory specified by the result_dir input parameter:

• projnum.txt: A list of the values \( \langle \phi_\text{T} | \hat{H} | \psi^{(i)} \rangle \) calculated at each iteration in the trajectory, where \( \phi_\text{T} \) is the trial wave function
• projden.txt: A list of the values \( \langle \phi_\text{T} | \psi^{(i)} \rangle \) calculated at each iteration
• S.txt: The value of the energy shift after every 10 iterations in the trajectory
• params.txt: A summary of the input parameters for this calculation

Executables for FCIQMC calculations produce these additional output files:

• N.txt: The number of walkers after each iteration
• nnonz.txt: The number of nonzero vector elements after each iteration

Executables for FCI-FRI calculations produce one additional output file:

• norm.txt: The vector one-norm calculated after each iteration