24 Semi-direct Table-CI - Using Default Options

In order to simplify the process of configuration specification and data preparation, the semi-direct module now provides a set of default options that require little or no data input. While these defaults are not expected to cover most in-depth requirements, they do provide a starting point for users, and a route to subsequent, more extensive calculations. To illustrate this default working of the module, we consider below a number of example calculations.

24.1 Calculations on the Formaldehyde Ground State

A Semi-direct Table-CI calculation is to performed on the formaldehyde molecule in a TZVP basis. Given the following data sequence:

          TITLE
          H2CO - TZVP X1A1 DEFAULT TABLE-CI OPTIONS
          ZMAT ANGSTROM
          C
          O 1 1.203
          H 1 1.099 2 121.8
          H 1 1.099 2 121.8 3 180.0
          END
          BASIS TZVP
          RUNTYPE CI
          MRDCI DIRECT
          ENTER

then the calculation undertaken will be based on the following;

1. Integral transformation will use the set of orbitals from section 1, the integer specified on the ENTER directive i.e. the closed shell SCF orbitals.
2. The table-ci data base will be generated rather than restored from a pre-existing table-ci data set.
3. The symmetry, spin and number of active electrons will be taken from the corresponding SCF wavefunction. In the present case this involves:
   • A CI wavefunction of A₁ symmetry (i.e. SYMMETRY 1).
   • A singlet CI wavefunction (i.e. SPIN 1).
   • The number of active electrons in the CI will be set to be those involved in the SCF calculation (i.e. CNTRL 16).
4. Singly excited configurations with respect to each of the default reference configurations (SINGLES ALL) will be included, regardless of their computed energy lowerings.
5. The set of reference configurations to be employed will include the SCF configuration, plus those generated from this configuration by including (i) for each symmetry IRREP, the doubly excited configuration arising from excitation of the highest occupied DOMO of that symmetry to the lowest virtual orbital (VMO) of the same symmetry, and (ii) the lowest singly excited configuration, again arising from the highest occupied DOMO to the lowest VMO of the same symmetry. In the present example, this will correspond to the SCF configuration, the double and single excitation arising from the DOMO 5a₁ to VMO 6a₁, the double and single excitation arising from the DOMO 1b₁ to VMO 2b₁, and the double and single excitation arising from the DOMO 2b₂ to VMO 3b₂. No reference configurations will be included involving orbitals of a₂ symmetry given the absence of such orbitals involved in the occupied manifold. This results in a total reference set of 7 functions, as shown thus in the job output:

      numbers of open shells and corresponding main configurations
   
     0             1   2   3   4   5  28  37  38      ..   SCF configuration
     0             1   2   3   4   6  28  37  38      ..   5a1 -> 6a1 double
     2             5   6   1   2   3   4  28  37  38  ..   5a1 -> 6a1 single
     0             1   2   3   4   5  29  37  38      ..   1b1 -> 2b1 double
     2            28  29   1   2   3   4   5  37  38  ..   1b1 -> 2b1 single
     0             1   2   3   4   5  28  37  39      ..   2b2 -> 3b2 double
     2            38  39   1   2   3   4   5  28  37  ..   2b2 -> 3b2 single
   

6. The default selection process subsequently undertaken is equivalent to the following ROOTS and THRESH directives.

             THRESH 10 10
             ROOTS 1
   

   Thus this default selection process involves construction of an explicit zero-order Hamiltonian H₀ (over the reference functions described above) followed by perturbative selection of configurations with respect to the lowest root of H₀. The minimum threshold to be used in selection (T_min) is 10 micro-Hartree, with an increment of 10 uH to be used in defining the higher-threshold case to be solved in the process of extrapolation [1].

7. In default the module will, having solved the secular problem for the lowest root of the CI secular problem, generate the spinfree natural orbitals from the associated CI eigenfunction.

The sequence of data lines defining the Semi-direct Table-CI calculation is terminated by the ENTER directive. Note at this stage that the full data specification corresponding to the defaults generated from the above data file is as follows:

          TITLE
          H2CO - TZVP - EXPLICIT DATA FOR DEFAULT MRDCI SETTINGS
          SUPER OFF NOSYM
          ZMAT ANGSTROM
          C
          O 1 1.203
          H 1 1.099 2 121.8
          H 1 1.099 2 121.8 3 180.0
          END
          BASIS TZVP
          RUNTYPE CI
          ACTIVE
          1 TO 52 END
          MRDCI DIRECT
          TABLE
          SELECT
          CNTRL 16
          SPIN 1
          SYMM 1
          SINGLES ALL
          CONF
            0     1   2   3   4   5  28  37  38
            0     1   2   3   4   6  28  37  38
            2     5   6   1   2   3   4  28  37  38
            0     1   2   3   4   5  29  37  38
            2    28  29   1   2   3   4   5  37  38
            0     1   2   3   4   5  28  37  39
            2    38  39   1   2   3   4   5  28  37
          END
          THRESH 10 10
          ROOTS 1
          CI
          NATORB
          CIVEC 1
          ENTER

24.2 Calculations on the Formaldehyde Cations

Let us now consider a Semi-direct Table-CI calculation on the ²B₂ state of H₂CO⁺, again using default options available within the module. A valid data sequence for performing such a calculation is shown below, where we are still performing all the computation in a single job.

          TITLE
          H2CO+ 2B2 TZVP - DEFAULT MRDCI SETTINGS  -113.06446075
          MULT 2
          CHARGE 1
          ZMAT ANGSTROM
          C
          O 1 1.203
          H 1 1.099 2 121.8
          H 1 1.099 2 121.8 3 180.0
          END
          BASIS TZVP
          RUNTYPE CI
          MRDCI DIRECT
          ENTER

Considering the changes to the closed-shell run, the following points should be noted:

• The set of vectors used in the Table-CI transformation will be restored from the default eigenvector section of the Dumpfile (given that no section is specified on the ENTER directive). This will be section 5, the section used to store the energy-ordered canonicalised orbitals from the open-shell SCF calculation.
• The symmetry and spin of the CI wavefunction will be deduced from the preceding SCF calculation i.e. a CI wavefunction of B₂ symmetry (corresponding to SYMMETRY 3). and a doublet CI wavefunction (corresponding to SPIN 2).
• The number of active electrons in the CI will be set to be those involved in the SCF calculation (i.e. CNTRL 15).
• Singly excited configurations with respect to each of the default reference configurations (SINGLES ALL) will be included, regardless of their computed energy lowerings.
• The set of reference configurations to be employed will follow the same algorithm used in the closed shell case above i.e. the SCF configuration, plus those generated from this configuration by including (i) for each symmetry IRREP, the doubly excited configuration arising from excitation of the highest occupied DOMO of that symmetry to the lowest virtual orbital (VMO) of the same symmetry, and (ii) the lowest singly excited configuration, again arising from the highest occupied DOMO to the lowest VMO of the same symmetry. In the present example, this will correspond to the SCF configuration, the double and single excitation arising from the DOMO 5a₁ to VMO 6a₁, the double and single excitation arising from the DOMO 1b₁ to VMO 2b₁, and the double and single excitation arising from the DOMO 1b₂ to VMO 3b₂. Note that the DOMO involved in the latter configurations is now the 1b₂ given that the 2b₂ is now singly occupied, and again the absence of excitations involving a₂ MOs given the absence of such orbitals involved in the occupied manifold. This again results in a total reference set of 7 functions, as shown thus in the job output:

     numbers of open shells and corresponding main configurations
  
    1    38   1   2   3   4   5  28  37          ..   SCF configuration
    1    38   1   2   3   4   6  28  37          ..   5a1 -> 6a1 double
    3     5   6  38   1   2   3   4  28  37      ..   5a1 -> 6a1 single
    1    38   1   2   3   4   5  29  37          ..   1b1 -> 2b1 double
    3    28  29  38   1   2   3   4   5  37      ..   1b1 -> 2b1 single
    1    38   1   2   3   4   5  28  39          ..   1b2 -> 3b2 double
    3    37  38  39   1   2   3   4   5  28      ..   1b2 -> 3b2 single
  

The sequence of data lines defining the Semi-direct Table-CI calculation is again terminated by the ENTER directive. Note at this stage that the full data specification corresponding to the defaults generated from the above data file is as follows

          TITLE
          H2CO+ 2B2 TZVP - EXPLICIT DATA FOR DEFAULTS
          MULT 2
          CHARGE 1
          SUPER OFF NOSYM
          ZMAT ANGSTROM
          C
          O 1 1.203
          H 1 1.099 2 121.8
          H 1 1.099 2 121.8 3 180.0
          END
          BASIS TZVP
          RUNTYPE CI
          OPEN 1 1
          ACTIVE
          1 TO 52 END
          MRDCI DIRECT
          TABLE
          SELECT
          CNTRL 15
          SPIN 2
          SYMM 3
          SINGLES ALL
          CONF
          1    38   1   2   3   4   5  28  37
          1    38   1   2   3   4   6  28  37
          3     5   6  38   1   2   3   4  28  37
          1    38   1   2   3   4   5  29  37
          3    28  29  38   1   2   3   4   5  37
          1    38   1   2   3   4   5  28  39
          3    37  38  39   1   2   3   4   5  28
          END
          THRESH 10 10
          ROOTS 1
          CI
          NATORB
          CIVEC 1
          VECTORS ATOMS
          ENTER 4 5

Let us now consider a Semi-direct Table-CI calculation on the ²B₁ state of H₂CO⁺, again using default options available within the module. A valid data sequence for performing such a calculation is shown below, where we are still performing all the computation in a single job.

          TITLE
          H2CO+ 2B1 TZVP - DEFAULT MRDCI SETTINGS 
          MULT 2
          CHARGE 1
          ZMAT ANGSTROM
          C
          O 1 1.203
          H 1 1.099 2 121.8
          H 1 1.099 2 121.8 3 180.0
          END
          BASIS TZVP
          RUNTYPE CI
          MRDCI DIRECT
          SWAP
          7 8
          END
          ENTER

Considering the changes to the closed-shell run, the following points should be noted:

• The OPEN directive is now present, specified prior to the Table-CI data.
• In the absence of section specification on the ENTER directive, the set of vectors used in the Table-CI transformation will be restored from the default open-shell SCF section containing the energy ordered eigenvectors (section 5). The SWAP directive is to generate initial starting MOs for the B₁ state.
• The symmetry and spin of the CI wavefunction will be deduced from the preceding SCF calculation i.e. a CI wavefunction of B₁ symmetry (corresponding to SYMMETRY 2). and a doublet CI wavefunction (corresponding to SPIN 2).
• The number of active electrons in the CI will be set to be those involved in the SCF calculation (i.e. CNTRL 15).
• Singly excited configurations with respect to each of the default reference configurations (SINGLES ALL) will be included, regardless of their computed energy lowerings.
• The set of reference configurations to be employed will be generated using the same algorithm used in the open shell case above i.e. the SCF configuration, plus those generated from this configuration by including (i) for each symmetry IRREP, the doubly excited configuration arising from excitation of the highest occupied DOMO of that symmetry to the lowest virtual orbital (VMO) of the same symmetry, and (ii) the lowest singly excited configuration, again arising from the highest occupied DOMO to the lowest VMO of the same symmetry. In the present example, this will correspond to the SCF configuration, the double and single excitation arising from the DOMO 5a₁ to VMO 6a₁, and the double and single excitation arising from the DOMO 2b₂ to VMO 3b₂. Note that there no excitations involving a₂ or b₁ MOS, given the absence of such orbitals in the doubly occupied manifold. This now results in a total reference set of just 5 functions, as shown thus in the job output:

     numbers of open shells and corresponding main configurations
  
    1            28   1   2   3   4   5  37  38       ..   SCF configuration
    1            28   1   2   3   4   6  37  38       ..   5a1 -> 6a1 double
    3             5   6  28   1   2   3   4  37  38   ..   5a1 -> 6a1 single
    1            28   1   2   3   4   5  37  39       ..   2b2 -> 3b2 double
    3            28  38  39   1   2   3   4   5  37   ..   2b2 -> 3b2 single
  

The sequence of data lines defining the Semi-direct Table-CI calculation is again terminated by the ENTER directive. Note that the full data specification corresponding to the defaults generated from the above data file is as follows

          TITLE
          H2CO+ 2B1 TZVP - EXPLICIT DATA FOR DEFAULTS
          MULT 2
          CHARGE 1
          SUPER OFF NOSYM
          ZMAT ANGSTROM
          C
          O 1 1.203
          H 1 1.099 2 121.8
          H 1 1.099 2 121.8 3 180.0
          END
          BASIS TZVP
          RUNTYPE CI
          OPEN 1 1
          ACTIVE
          1 TO 52 END
          MRDCI DIRECT
          TABLE
          SELECT
          CNTRL 15
          SPIN 2
          SYMM 2
          SINGLES ALL
          CONF
          1    28   1   2   3   4   5  37  38
          1    28   1   2   3   4   6  37  38
          3     5   6  28   1   2   3   4  37  38
          1    28   1   2   3   4   5  37  39
          3    28  38  39   1   2   3   4   5  37
          END
          THRESH 10 10
          ROOTS 1
          CI
          NATORB
          CIVEC 1
          VECTORS ATOMS
          SWAP
          7 8
          END
          ENTER 4 5