Monte Carlo Configuration Interaction

MCCI computes energy estimates by an iterative process, starting from a set of CSFs (which initially may be a single CSF). In each step, additional CSFs are randomly generated by single and double excitations relative to the CSFs in the trial vector. The CI matrix diagonalization problem is solved on the subspace defined by the resulting expanded vector. This vector is then screened or 'pruned' by removing CSFs whose associated coefficient in the CI eigenvector has a magnitude lower than a given threshold. This pruned vector serves as trial vector for the generation of a new set of randomly generated CSFs in a subsequent cycle, and this sequence is repeated until convergence in the energy and CI vector length is reached. This scheme makes it possible to gradually increase the amount of correlation that the program will find, by gradually decreasing the CSF inclusion threshold, while keeping the computations tractable.

Compile Instructions

The provided Makefile assumes the availability of an MPI-enabled Fortran 90 compiler under the name 'mpif90'. This can be changed manually, but the user needs to check that all the flags used in the Makefile are supported by the other compiler.

If the compiler is changed, please note that the system clock called in the subroutine gen_seed.f90 may also need to be changed, depending on the behaviour of the system_clock standard subroutine on the platform used.

Keywords for the mcci.in file

ieig              =  Eigenvalue to be calculated. Each eigenvalue in each irrep begins with ieig=1 
                     i.e. ieig=1 is lowest energy eigenvalue in an irrep, ieig=2 is first excitation in an irrep, ... 
n_up              =  Number of spin up (alpha) electrons
n_dn              =  Number of spin down (beta) electrons
cmin              =  Coefficient threshold:  Defines the minimum value of CSF's coefficient to be kept following
                     a matrix diagonalization, i.e. the "pruning threshold"
s                 =  Spin ( units of h_bar ) (principle case M_s=S)
maxtry            =  The maximum number of cycles (branch, diagonalization, prune) that should be performed
mo_up(:)          =  Molecular orbital indices for up (alpha) electrons
mo_dn(:)          =  Molecular orbital indices for down (beta) electrons
lmin              =  Minimum vector length- branch will always generate lmin CSFs
npfull            =  A "full prune" step will be performed every npfull cycles
lkeep             =  Configurations to keep throughout a calculation. The first lkeep CSFs will not be pruned.
hmin              =  H matrix threshold- elements of the H matrix with absolute values below hmin are not stored
davidson_stop     =  Maximum number of iterations before stopping for convergence in the Davidson algorithm
bmin              =  Minimum vector boost (used to adjust Monte Carlo sample size in early stages of a calculation)
bmax              =  Maximum vector boost (used to adjust Monte Carlo sample size in early stages of a calculation)
frac              =  Branching ratio: number of new CSFs / number of CSFs in current CI vector
conv_thresh_e     =  Energy convergence: change in energy between npfull cycles is less that conv_thresh_e after ncheck tests
conv_thresh_l     =  Vector convergencer: change in vector length between npfull cycles is less than conv_thresh_l for ncheck tests 
                     (Note, the number of tests, n, is defined by the keyword conv_history)
restart           = .TRUE. or .FALSE. If this is set to true, then, a calculation will be 
                     restarted from a previous calculation and civ_in must be present (i.e. previous runs civ_out file 
                     should be renamed to civ_in).  If set to false, a calculation will begin from the CSF with
                     occupations define in mcci.in
test              = .TRUE. or .FALSE. Debugging flag
time              = .TRUE. or .FALSE. Timing information, general
time_all          = .TRUE. or .FALSE. Timing information, detailed
nobrnch_first     = .TRUE. or .FALSE. No branching in the first step
nodiag            = .TRUE. or .FALSE. Used for collecting CSFs only (No matrix diagonalisation is peformed during cycles)
i_want_conv       = .TRUE. or .FALSE. Stop mcci by using convergence criteria.
npfull_conv       = .TRUE. or .FALSE. Convergence test only in npfull steps
conv_average      =  Number of npfull steps to be averaged for convergence
conv_history      =  Window of npfull steps to be include in convergence checking
frozen_doubly     =  Indices of orbitals to be frozen (i.e. no excitations are allowed from these molecular orbitals 
                     during the CI calculation). Note frozen orbitals must be doubly occupied.
mo_active         =  Orbital lists of active orbitals, includes all occupied and (initially) unoccupied orbitals to include 
                     in the CI calculations. Note excludes frozen_doubly and all inactive virtual orbitals
lref              =  Branch (i.e. generate new CSFs) relative to only the first lref CSFs in a CI vector

Example: setting up a calculation in a higher symmetry

From the original control file that is obtained from the geometry relaxed system, note the numbers for the occupied symmetries, e.g.

A1 1-7
A2 1-3
B1 1-9
B2 1-2

Then run eiger -a and go as high up in energy as required and note the numbers of orbitals that you want to run for mpgrad. Make sure to leave no gaps between representations.

Then change A1 - B2 for the new symmetries and run mpgrad_ints twice.

To fill this into mcci, we only need to look at the latest version of the control file.

Fill in the n_up and n_down as required. Then we must label the symmetry representations in correct order, so if have:

MPGRAD control     MCCI counting

A1 1-10            1-10
A2 1-5             11-16
B1 1-15            17-...
B2 1-4             .......

The general rule is: for the first representation it stays as is, for the following :

(#orbitals) + (#electrons) -1

And when filling in the mcci.in file , the same rule applies.