pconf - configuration interaction

The parallel program pconf performs the configuration interaction method in the CI space defined by the list of configurations contained in the CONF.INP input file created by the add program. It takes the CONF.DAT, CONF.GNT, CONF.INT, and CONF.INP files as input. In addition, pconf can also take in the SGC.CON and SCRC.CON files, which contain one- and two-electron effective radial integrals, respectively.

Here is a summary of the input and output files used in pconf.

Input Files:

HFD.DAT - basis set radial orbitals \(\phi_{nlj}\) and radial derivatives of the orbitals \(\partial_r\phi_{nlj}\)
CONF.DAT - basis set radial orbitals \(\phi_{nlj}\) and functions \(\chi_{nlj}=h_\text{HF}^r\phi_{nlj}\), where \(h_\text{HF}^r\) is the radial part of the Dirac-Fock operator
CONF.GNT - relativistic Gaunt coefficients produced by pbasc
CONF.INT - relativistic Coulomb coefficients produced by pbasc
SGC.CON (optional) - one-electron effective radial integrals of the MBPT/all-order corrections
SCRC.CON (optional) - two-electron effective radial integrals of the MBPT/all-order corrections
CONF.INP - list of relativistic configurations and user defined parameters

Output Files:

CONF.DET - basis set of determinants
CONFp.HIJ - list of matrix elements of the Hamiltonian (generated only if Kw = 1 in ci.in)
CONFp.JJJ - list of matrix elements of the operator \(J^2\) (generated only if Kw = 1 in ci.in)
CONF.XIJ - quantum numbers, eigenvalues and eigenvectors of the Hamiltonian
CONF.ENG - tables of calculated quantum numbers \(J_i\) and energy eigenvalues \(E_i\) calculated each time CONF.XIJ is constructed during the Davidson procedure
CONF.LVL - tables of top contributing configurations for each energy level calculated each time CONF.XIJ is constructed during the Davidson procedure
CONF.RES - results of pconf program
CONF.WGT - table of configuration weights (generated only if KWeights = 1 in ci.in)
FINAL.RES - final table of quantum numbers \(J_i\) and energy eigenvalues \(E_i\)
LEVELS.RES - final table of top contributing configurations for each energy level
CONFSTR.RES - list of top contributing configurations along with their atomic term symbol for each energy level
progress.conf - binary file recording Davidson iteration progress (used to resume interrupted runs)

Additional output files when kCSF = 1:

CSF.LOG - log of the \(J^2\) matrix diagonalization used to construct the CSF basis
CONF.WFS - CSF wave functions used internally when transforming back to the determinant basis

The keyword parameters in CONF.INP are case-insensitive. The following is a sample of the head of a CONF.INP for calculating the even-parity states of \(\text{Ir}^{17+}\). Here, we include 481 relativistic configurations in the CI space, and 1132 relativistic configurations in the PT space (if conf_pt is to be used after pconf).

  Ir17+_even            # ion_parity
  Z = 77.0              # atomic number
 Am =193.0              # atomic weight
  J =  2.0              # total angular momentum
 Jm =  2.0              # angular momentum projection
 Nso=  14               # number of closed core shells
 Nc = 481               # number of relativistic configurations
 Kv =   4               # Kv = (3 - use projections, 4 - no projections)
 Nlv= 5                 # number of energy levels
 Ne =  14               # number of valence electrons
 Kl4=   1               # Kl4 = (1 - initial approx. from energy matrix, 2 - initial approx. from CONF.XIJ file)
 Nc4=  28               # number of relativistic configurations in initial approximation
Crt4=  0.0001           # cutoff criteria for davidson convergence
kout= 0                 # key for level of output (0 - low detail output, 1 - detailed output)
Ncpt=  1132             # number of relativistic configurations in PT block (used in conf_pt)
Cut0= 0.0001            # cutoff criteria for davidson convergence
N_it=  100              # number of davidson iterations
Kbrt= 1                 # key for Breit (0 - Coulomb, 1 - Gaunt, 2 - Full Breit)
Gnuc= 1.07              # gyromagnetic ratio
k_is= 0                 # isotope shift (0 - off, 1 - VS, 2 - SMS, 3 - NMS, 4 - MS)
c_is= 0.0               # isotope shift scaling factor
     0.1002     0.2002    -0.2102     0.2104     0.3002    -0.3102
     0.3104    -0.3204     0.3206     0.4002    -0.4102     0.4104
    -0.4204     0.4206
   1
   1-0.4306     0.4308
   2
   2-0.4306     0.4306     0.5002
   3-0.4305     0.4307     0.5002
   4-0.4304     0.4308     0.5002
   3
   5-0.4305     0.4308    -0.5101
   6-0.4305     0.4308     0.5101
   7-0.4306     0.4307    -0.5101
   8-0.4306     0.4307     0.5101
   :

Note

The first 5 columns up to the ‘=’ sign are fixed, and the program will give an error if there are any discrepancies here.

Note

The list of core shells are fixed to have a maximum of 6 shells per row.

In addition to the input files listed above, pconf also requires the file ci.in, which contains a list of key-value pairs defining the CI computation:

Kl     = (0,1,2,3,4) - calculation mode
Ksig   = (0,1,2)     - MBPT corrections to include
Kdsig  = (0,1)       - energy dependence of Sigma
Kw     = (0,1)       - write Hamiltonian matrix to disk
KLSJ   = (0,1)       - calculate LSJ decomposition
KXIJ   = N           - write CONF.XIJ every N Davidson iterations (default: 10)
KWeights = (0,1)     - write configuration weights to CONF.WGT (default: 0)
MaxNd0 = N           - maximum number of determinants in initial approximation (default: 3000)
kCSF   = (0,1)       - use CSF basis for diagonalization (default: 0)

The value of Kl can take the following values:

Kl = 0 - start a new CI calculation
Kl = 1 - continue a previous CI calculation
Kl = 2 - start a new CI calculation, including corrections from SGC.CON
Kl = 3 - continue a previous CI calculation, adding new configurations
Kl = 4 - estimate memory requirements and exit without running the full calculation

Note

Note that for Kl=1,3 to work, the file CONFp.HIJ must have been successfully written with Kw=1 in the original run. CONFp.HIJ stores the previous Hamiltonian matrix, which must be read to continue a CI calculation. However, this file can be as big as 1 TB or more for large systems, so it should not be used unless the user has exceptional available computational resources.

The value of Ksig can take the following values:

Ksig = 0 - pure CI
Ksig = 1 - include one-electron MBPT/all-order corrections from SGC.CON
Ksig = 2 - include one-electron corrections from SGC.CON and two-electron screening corrections from SCRC.CON

The value of Kdsig can take the following values:

Kdsig = 0 - automatic approximation of the energy dependence of the operator \(\Sigma(E)\)
Kdsig = 1 - manually specify the energy \(E_\mathrm{val}\) to treat the energy dependence of \(\Sigma(E)\)

The value of Kw can take the following values:

Kw = 0 - do not write the files CONFp.HIJ and CONFp.JJJ
Kw = 1 - write the files CONFp.HIJ and CONFp.JJJ

The value of KLSJ can take the following values:

KLSJ = 0 - do not calculate \(\langle S^2 \rangle\), \(\langle L^2 \rangle\), or form approximate terms for each energy level
KLSJ = 1 - calculate \(\langle S^2 \rangle\), \(\langle L^2 \rangle\), and form approximate term symbols for each energy level

The value of kCSF can take the following values:

kCSF = 0 - use the standard determinant basis (default)
kCSF = 1 - use a symmetry-adapted CSF (configuration state function) basis

When kCSF = 1, pconf first constructs the CSF basis by diagonalizing the \(J^2\) matrix within each relativistic configuration block and selecting eigenstates with the correct total angular momentum. The Hamiltonian is then formed and diagonalized in this CSF basis, which is smaller than the full determinant space and can significantly reduce computation time for large calculations. After diagonalization, the wave functions are transformed back to the determinant basis before writing CONF.XIJ.

Bitstring Determinants

When forming the Hamiltonian matrix, pconf can represent each determinant as a packed bitstring rather than as a list of orbital indices. This can speed up the determinant comparison step during Hamiltonian construction. pconf automatically uses the bitstring representation when it reduces total memory usage (i.e., when the number of valence electrons is large enough relative to the number of basis orbitals). The bitstring representation is not available when kCSF = 1.

The automatic selection can be overridden with the environment variable CONF_USE_BIT_DET:

export CONF_USE_BIT_DET=TRUE   # force bitstring representation
export CONF_USE_BIT_DET=FALSE  # disable bitstring representation

Double-Precision Integrals

By default, the two-electron radial integrals read from CONF.INT are stored in single precision to reduce memory usage, while the Hamiltonian matrix elements are always stored in double precision. To store the two-electron integrals in double precision as well, compile with the CMake option:

cmake -DUSE_DP_INTEGRALS=ON ..

This is only necessary for isotope shift calculations, where higher numerical precision is required. This option also affects pbasc, which writes CONF.INT, so both programs must be compiled consistently with the same setting.

After reading the keys from ci.in, the pconf program reads the general parameters and the list of configurations from the CONF.INP file. Next, the information about the basis set is read from CONF.DAT, relativistic Gaunt coefficients are read from CONF.GNT, radial integrals are read from CONF.INT, and optionally, effective radial integrals are read from SGC.CON and SCRC.CON.

Having read all required input files, the pconf program forms a list of determinants from the list of relativistic configurations and writes them to the file CONF.DET. With the list of determinants, it forms the Hamiltonian matrix and then the matrix of the operator \(J^2\). The construction of the Hamiltonian matrix is the most time-consuming part of the pconf program.

After the matrices are constructed, the pconf program enters the Davidson iterative procedure, where the Hamiltonian is diagonalized to obtain a specified number of low-lying energy eigenvalues and eigenvectors. The progress of the Davidson iterative procedure is written in the CONF.PRG file at each iteration. At selected intervals before the final iteration, the eigenvalues and eigenvectors are saved to CONF.XIJ (controlled by KXIJ). Each time CONF.XIJ is written on disk, a table of the energy levels is appended to the file CONF.ENG, and tables of the top contributing configurations for each level are appended to CONF.LVL.

Once the Davidson iterative procedure has converged, the final eigenvalues and eigenvectors are saved once again to CONF.XIJ, the final energy table is saved to FINAL.RES, the final list of the top contributing configurations for each level is saved to LEVELS.RES, and the configurations along with their atomic term symbol is written to CONFSTR.RES.

If polarizability calculations are required, the Hamiltonian matrix elements will have to be written to the file CONFp.HIJ``by setting the key ``Kw=1 in ci.in. Note that depending on the size of the Hamiltonian, this file could take up hundreds of GB to over 1 TB. By default, Kw=0 is set to not write the Hamiltonian to disk. As a reference, polarizability calculations have typically been done with Hamiltonian sizes of up to 4 million determinants.

Running pconf

To run pconf, run the command:

mpirun -n <nprocs> pconf