26 Coupled-Cluster Calculations

Coupled-cluster (CC) calculations [41] are performed under control of the RUNTYPE CI specification, with data input characterising the nature of the CI introduced by a data line with the character string CCSD as the first four characters of the first data field. Termination of this data is accomplished by presenting a valid Class 2 directive, such as VECTORS. Before detailing example data files for performing CC calculations on the X¹A₁ state of formaldehyde, we mention some general points on conducting such calculations.

1. RUNTYPE CI represents a combination of tasks, requesting integral generation, SCF, integral transformation and, finally, the coupled-cluster calculation itself. While in simple cases it may be feasible to perform all steps in a single calculation, it will often be necessary to break up the calculation into multiple jobs, driving through each of the tasks under control of the appropriate RUNTYPE directive, with use made of the BYPASS directive in the latter stages of the computation. We illustrate this point below.

2. Several direct-access files will be generated under RUNTYPE CI processing. For coupled-cluster calculations, these include:
   • the Mainfile (ED2) and Dumpfile (ED3).
   • the semi-transformed (ED4) and transformed (ED6) integral files.
   • the Scratch file (ED7).
   • temporary files for sorting transformed integrals (the Sortfile)

   Any restart jobs will require ED6 being saved, in addition to the Dumpfile (ED3) and Mainfile (ED2).

3. In addition to the direct-access files above, the coupled cluster module uses a variety of conventional unformatted FORTRAN data sets.

4. As mentioned above, generation of a valid Mainfile for subsequent use in the integral transformation routines requires the data line

             SUPER OFF NOSYM
   

   in the SCF run.

A CC calculation is to to be performed on the H₂CO molecule. Before detailing the data requirements, let us again consider the mechanisms for restricting the scale of the all-electron computation, since this will often be required in coupled-cluster treatments. The user will typically wish to

• `freeze' inner-shell orbitals, performing a `valence-only' coupled-cluster calculation.
• discard certain virtual orbitals from the coupled cluster calculation, typically the high-energy inner-shell complement orbitals.

The CORE and ACTIVE directives of the transformation module are provided for controlling the final subset of orbitals for inclusion in the CC. The freezing of core , or inner-shell, orbitals is achieved by nominating the sequence nos. of those orbitals to be frozen under control of the CORE directive. The discarding of orbitals is performed under control of the ACTIVE directive, which specifies the sequence nos. of the active set of orbitals to appear in the CC. Turning to the H₂CO calculation, the following data sequence would be required to freeze the two inner shell and two lowest valence SCF-MOs while retaining all virtual orbitals in the subsequent coupled-cluster treatment:

          TITLE
          H2CO - TZVP - VALENCE CCSD / CCSD  ENERGY = -114.2600151982
          SUPER OFF NOSYM
          NOPRINT
          ZMATRIX 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
          ACTIVE\3 TO 50 END\CORE\1 TO 2\END
          RUNTYPE CI\CCSD 48 6 6
          CCTH 10
          CCIT 30
          ENTER

The following points should be noted:

• both ACTIVE and CORE are control directives of the integral transformation module. As such they should be presented in the data stream prior to the specification of the coupled-cluster data i.e., before the CCSD data line.

• The nature of the coupled cluster calculation is determined by the data line commencing with the character string CCSD. In this case a singles+doubles calculation is performed [42,43]. Inclusion of the triples component to the correlation energy [44,45] is requested by presenting the character string CCSD(T) (see below). The additional three integers, define in order
  • NACT, the number of active orbitals in the calculation (48 in this case)
  • NALPHA, the number of $\alpha$-electrons (6 in this example, the four highest doubly occupied SCF MOs).
  • NBETA, the number of $\beta$-electrons (again 6 in the closed shell molecule) example
  Note that the values of NACT, NALPHA and NBETA reflect the impact of CORE and ACTIVE - had we been considering an all-electron calculation, the integer values would have been 52, 8 and 8 respectively.

• The set of molecular orbitals to be used in the transformation and subsequent CC calculation are restored from the default section (section 1) associated with the closed-shell SCF module.

• Two additional directives, CCIT and CCTH, may be used to control convergence of the iterative CCSD procedure:
  • CCIT: This directive consists of a single data line, read to variables TEXT, MXCCIT using format (A,I), where TEXT should be set to the character string CCIT. MXCCIT is an integer used to specify the maximum number of cycles required in the iterative CCSD procedure.

    Note that this directive may be omitted when MXCCIT will be set to the default value of 20.

  • CCTH: This directive may be used to define a convergence threshold for CCSD iterations, and comprises a single data line read to the variables TEXT, IAMP using format (A,I). With TEXT set to the character string CCTH, IAMP is an integer parameter used in defining the threshold. At convergence, the magnitude of the CCSD T₁ and T₂ amplitudes will be converged to within an absolute error 10^-IAMP.

    Again this directive may be omitted, when the default value 10^-10 will be used.

Let us now consider the corresponding calculation with inclusion of the triples (T) component to the correlation energy. 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 - TZVP - VALENCE CCSD(T) / CCSD(T)  ENERGY = -114.2714886289
          SUPER OFF NOSYM
          NOPRINT
          ZMATRIX 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
          ACTIVE\3 TO 50 END\CORE\1 TO 2\END
          RUNTYPE CI\CCSD(T) 48 6 6
          CCTH 10
          CCIT 30
          ENTER

Now let us consider performing the CC calculation above in a sequence of jobs, where the first job carries out the SCF, the second the transformation and CCSD(T). First the closed shell case: valid data sequences for performing the calculation are shown below.

Run I: The Scf Job

          TITLE
          H2CO - TZVP SCF PRIOR TO CCSD(T) CALCULATION
          SUPER OFF NOSYM
          ZMATRIX 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
          ENTER

The only obvious point to note is the use of the SUPER directive in requesting full integral list generation required in the subsequent transformation.

Run II: The Transformation and CCSD(T) Job

          RESTART
          TITLE
          H2CO - TZVP - VALENCE CCSD(T) / CCSD(T)  ENERGY = -114.2714886289
          SUPER OFF NOSYM
          BYPASS SCF
          ZMATRIX 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
          ACTIVE\3 TO 50 END\CORE\1 TO 2\END
          RUNTYPE CI\CCSD(T) 48 6 6
          CCTH 10
          CCIT 30
          ENTER

The following points should be noted:

• The SCF computation is BYPASS'ed
• The SCF vectors from the first run will be restored from Section 1 of the Dumpfile, the default section associated with the closed-shell SCF MOs.

The calculation may be further subdivided by splitting Run II above into separate integral transformation and CCSD runs using the RUNTYPE TRANSFORM specification, with subsequent BYPASS'ing of the transformation in the CC job. Thus:

Run IIa: The Transformation Job

          RESTART
          TITLE
          H2CO - TZVP  INTEGRAL TRANSFORMATION
          SUPER OFF NOSYM
          BYPASS SCF
          ZMATRIX 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 TRANSFORM
          ACTIVE\3 TO 50 END\CORE\1 TO 2\END
          ENTER

Run IIb: The CCSD(T) Job

          RESTART
          TITLE
          H2CO - TZVP - VALENCE CCSD(T) / CCSD(T) ENERGY = -114.2714886289
          SUPER OFF NOSYM
          BYPASS TRANSFORM
          ZMATRIX 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
          ACTIVE\3 TO 50 END\CORE\1 TO 2\END
          RUNTYPE CI\CCSD(T) 48 6 6
          CCTH 10
          CCIT 30
          ENTER