8 Data for Conventional Table-CI Diagonalisation

Data input controlling the diagonalisation of the final CI Hamiltonian is introduced by the DIAG directive. The process of extrapolation to zero selection threshold involves the diagonalisation module solving not just one, but several secular problems corresponding to a range of selection thresholds. The number of so called `extrapolation passes' is specified by the EXTRAP directive. In default, the module will generate NROOT eigenvectors of the CI matrix on each pass, where NROOT is the number of roots specified by the ROOTS directive at selection time. Thus the solutions of the zero-order Hamiltonian will be used through a maximum overlap criterion in deriving the final CI eigenvectors. Additional data may be specified to override this default and provide various convergence and printing controls.

8.1 DIAG

The DIAG directive comprises a single data line read to the variables TEXT, TEXTF and TEXTB using format (3A)

• TEXT should be set to the character string DIAG
• TEXTF is an optional parameter that may be used to control the quantity of printed output produced by the module. Valid settings include the strings,
  • NOPRINT, to suppress the major part of the output from the module;
  • IPRINT, to produce an intermediate level of output;
  • FPRINT, to produce output suitable for debugging purposes.
• TEXTB is an optional parameter that should be set to the string BYPASS if the user wishes to bypass DIAG processing. Such usage is typically associated with restarting Table-CI calculations.

8.2 EXTRAP

This directive consists of one line read to variables TEXT, MAXE using format (A,I).

• TEXT should be set to the character string EXTRAP.
• MAXE specifies the maximum number of extrapolation cycles to be carried out by the Davidson diagonalizer.

The directive may be omitted, when MAXE will take the default value 2.

8.3 ACCURACY

This directive may be used to define the diagonalisation thresholds for the extrapolation passes and for the final secular problem (at the threshold T_min), and consists of a single line read to variables TEXT, THRESH0, THRESHF using format (A,2F).

• TEXT should be set to the character string ACCURACY or DTHRESH;
• THRESH0: On the NEXTRP extrapolation passes, the diagonalization is converged to a threshold THRESH0;
• THRESHF: On the final diagonalisation, solving the secular problem corresponding to the threshold T_min, the diagonalization is converged to a threshold THRESHF.

The THRESH directive may be omitted, when THRESH0 will be set to 0.005 and THRESHF to 0.001.

Example

Assuming the default selection thresholds (T_min=10, T_inc=10) and the default number of extrapolation passes (NEXTRP=2), then presenting the data line

           ACCURACY 0.005 0.0005

will result in a diagonalisation threshold of 0.005 for the two extrapolation passes (corresponding to solving the secular problem at selection thresholds of 20 and 30 microhartree), and a threshold of 0.0005 for the final secular problem, that corresponding to the 10 microhartree selection.

8.4 MAXD

This directive consists of one line read to variables TEXT, MAXD using format (A,I).

• TEXT should be set to the character string MAXD.
• MAXD specifies the maximum number of iterative cycles to be carried out by the Davidson diagonalizer.

The directive may be omitted, when MAXD will take the default value 50.

8.5 TRIAL

This directive may be used to define a trial CI wavefunction by diagonalising a sub-Hamiltonian obtained by sampling the diagonal elements of the CI-Hamiltonian, and selecting the lowest energy terms. The directive may be used to define the number of such elements to be included in the sub-Hamiltonian, and is read to the variables TEXT, NTRIAL using format (A,I).

• TEXT should be set to the character string TRIAL;
• NTRIAL should be set to the number of lowest-energy configurations in the CI list to be used in constructing the sub-Hamiltonian.

The TRIAL directive may be omitted, when NTRIAL will be set to the maximum allowed value of 80.

8.6 PRINT

The PRINT directive may be used to control the printing of CI coefficients and weights throughout the extrapolation passes and in the final analysis. This directive consists of a single data line read to variables TEXT, PTHR, PTHRCC, IFLAG using format (A,2F,I).

• TEXT should be set to the character string PRINT.
• CI coefficients less than PTHR in absolute magnitude will not be printed during the extrapolation passes.
• CI weights (coefficients²) less than PTHRCC in absolute magnitude will not be printed in the final analysis of the CI wavefunctions.
• IFLAG may be used to control the printing of the CI wavefunctions in the event that the diagonalisation does not converge. Setting IFLAG=1 will cause a detailed print of the CI vectors corresponding to each root.

This directive may be omitted, when the defaults PTHR=0.05 and PTHRCC=0.002 will be taken.