12 Møller Plesset MP2 and MP3 Calculations

In this section the traditional Møller Plesset calculations are discussed. These calculations are based on a single closed shell Hartree-Fock reference determinant. Also available are multi-reference MP2 and MP3 calculations. Because the latter option is part of the Direct-CI module these calculations are described in section 23.

Møller Plesset calculations are performed under control of SCFTYPE specification, with the level of treatment, either MP2 or MP3, nominated by keyword. A second keyword may also be required, requesting the level of underlying SCF, either RHF (closed-shells) or UHF (open-shell systems). Before detailing example data files for performing such calculations, we mention some general points:

1. Møller Plesset processing involves a combination of tasks, including integral generation, SCF, integral transformation and, finally, the Møller Plesset calculation itself.
2. Several files will be generated under such processing. 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) and intermediate matrices in the Møller Plesset calculation. The number of such files is a function of the underlying SCF (RHF (closed-shells) or UHF (open-shell systems)), and the level of Møller Plesset theory requested, as follows;
     • MP2/RHF:- no additional files required;
     • MP2/UHF:- ED16, ED17, ED18 and ED19;
     • MP3/RHF:- ED16 and ED17;
     • MP3/UHF:- ED16, ED17, ED18, ED19, MT0 and MT1.
   Any restart jobs will require ED6 being saved, in addition to the Dumpfile (ED3) and Mainfile (ED2).

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

             SUPER OFF
   

   in the SCF run. Note that in contrast to CASSCF and MCSCF calculations, MP processing is driven off the skeletonised list of 2-electron integrals, so that the NOSYM parameter specification is not required on the SUPER directive.

4. In default all molecular orbitals will be deemed active in the MP calculation.

12.1 MP2 Calculations

A closed-shell MP2 calculation is to performed on the formaldehyde molecule, A valid data sequence for performing such a calculation is shown below, where we are performing all the computation in a single job.

          TITLE
          H2CO - 3-21G DEFAULT BASIS - MP2/RHF
          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
          SCFTYPE MP2 RHF
          ENTER

Note that the SCFTYPE specification above may be simplified to just

          SCFTYPE MP2

with RHF the default level of underlying SCF for closed-shell systems. Now let us consider performing the above calculation in two steps, where the first carries out the SCF, the second the transformation and MP2 calculation. Assuming we wish to avoid recalculating the 2e-integrals in the MP2 calculation, then the SUPER OFF data line should be presented in the SCF job, allowing bypassing of integral evaluation in the subsequent calculation. First the closed shell case: valid data sequences for performing the calculation are given below.

Closed shell SCF Data

          TITLE
          H2CO - 3-21G DEFAULT BASIS - CLOSED SHELL SCF
          SUPER OFF
          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
          ENTER

MP2 Data

          RESTART
          TITLE
          H2CO - X1A1 - 3-21G DEFAULT BASIS - MP2/RHF CALCULATION
          SUPER OFF
          BYPASS
          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
          SCFTYPE MP2
          ENTER

Let us now consider a MP2 calculation on the ²B₂ state of H₂CO⁺, now using the UHF formalism. A valid data sequence for performing such a calculation is shown below, where we are performing all the computation in a single job.

          TITLE
          H2CO+ - 2B2 - 3-21G DEFAULT BASIS - MP2/UHF CALCULATION
          CHARGE 1
          MULT 2
          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
          SCFTYPE MP2 UHF
          ENTER

Again the UHF flag may be omitted from the SCFTYPE data line, given that UHF is the underlying SCF for open-shell systems. Consider performing the above calculation in two steps, where the first carries out the UHF, the second the transformation and MP2 calculation. Valid data sequences for performing the calculation are shown below, where we again BYPASS integral evaluation in the MP2 job. Note again that this BYPASS'ing of integral evaluation necessitates the introduction of the SUPER OFF data line in the initial UHF job.

UHF Data

          TITLE
          H2CO+ - 2B2 - 3-21G DEFAULT BASIS - UHF CALCULATION
          SUPER OFF
          CHARGE 1
          MULT 2
          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
          SCFTYPE UHF
          ENTER

MP2 Data

          RESTART
          TITLE
          H2CO+ - 2B2 - 3-21G DEFAULT BASIS - MP2/UHF CALCULATION
          SUPER OFF
          BYPASS
          CHARGE 1
          MULT 2
          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
          SCFTYPE MP2
          ENTER

12.2 MP3 Calculations

The MP3 level of treatment is requested in equivalent fashion to the MP2 calculations detailed above, with use of the MP3 keyword on the SCFTYPE data line. Data sequences for performing a closed-shell MP3 calculation on the formaldehyde molecule, and an open-shell calculation on the ²B₂ state of H₂CO⁺ are given below.

MP3/RHF Data

          TITLE
          H2CO - 3-21G DEFAULT BASIS - MP3/RHF
          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
          SCFTYPE MP3
          ENTER

MP3/UHF Data

          TITLE
          H2CO+ - 2B2 - 3-21G DEFAULT BASIS - MP3/UHF CALCULATION
          CHARGE 1
          MULT 2
          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
          SCFTYPE MP3
          ENTER

12.3 Freezing and Discarding Orbitals

In the examples above we have assumed that all SCF-MOs are active in the subsequent Møller Plesset calculation. In many instances however this will not be the case, for the user may wish to

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

The ACTIVE directive is provided for controlling the final subset of orbitals for inclusion in the Møller Plesset calculation. The freezing of core , or inner-shell, orbitals and the discarding of virtual orbitals is achieved by nominating under control of the ACTIVE directive, the sequence nos. of the active set of SCF orbitals to appear in the calculation. Consider the MP2/RHF H₂CO calculation above. The following data sequence would be required to freeze both the O1s and C1s orbitals (with SCF sequence numbers 1 and 2 respectively) and to discard the highest virtual orbital (with SCF sequence number 22):

          TITLE
          H2CO - 3-21G BASIS - MP2/RHF (VALENCE ONLY)
          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
          SCFTYPE MP2
          ACTIVE
          3 TO 21 END
          ENTER

12.4 Direct-MP2 Calculations

We wish to perform a direct-MP2 calculation equivalent to that above. A valid data sequence for performing such a calculation is shown below:

          TITLE
          H2CO - 3-21G DEFAULT BASIS - DIRECT-MP2
          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
          SCFTYPE DIRECT MP2 
          ENTER

Note the change in syntax of the SCFTYPE directive when specifying the DIRECT option. The third parameter on the data line, MP2, points to the particular category of Møller Plesset wavefunction required i.e., MP2. At present this is the only option supported in direct-mode, and is only applicable to closed-shells. Note that the default file output in such calculations is confined to ED3 and ED7, the Dump- and Scratch-file respectively. Note also that such calculations are memory intensive, with the MEMORY pre-directive in the above example (see the machine-specific Parts) used to increase the default memory allocation in the present run.