21 Infra-red Intensity Calculations

Analytic calculations of infra-red intensities may be carried out for both closed-shell SCF and RHF open-shell wavefunctions, together with MP2 closed-shell wavefunctions. The following points should be noted;

1. Infra-red intensity calculations are performed under control of the RUNTYPE INFRARED directive.
2. RUNTYPE INFRARED is in fact a combination of tasks, requesting integral generation, SCF, gradient evaluation (with additional evaluation of derivative Fock operators), integral transformation, solution of the coupled Hartree-Fock (CHF) equations, calculation of the dipole moment derivatives, calculation of the two-electron second derivative contribution and, finally, determination of the infra-red intensities. While in most cases it is feasible to perform all steps in a single calculation, it may 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.

3. Several files will be generated under RUNTYPE INFRARED processing.
   • For SCF intensities, these include:
     • the Mainfile (ED2) and Dumpfile (ED3).
     • the Scratch file (ED7).
     • the semi-transformed (ED4) and transformed (ED6) integral files (note that ED4 is also used as a scratch file in the solution of the coupled Hartree-Fock equations).
     • the Hamiltonian file (ED12), which acts to store the derivative Fock operators.
     • temporary files for sorting both transformed integrals (the Sortfile) and intermediate matrices in the Hessian calculation.
   • The generation of MP2 intensities is significantly more complex; in addition to the files generated under SCF processing, additional temporary files will be required, including ED0, ED11, ED16, ED17, ED18, ED18, ED19, MT0 and MT1.
   Any restart jobs will require ED6 and ED12 being saved, in addition to the Dumpfile (ED3) and Mainfile (ED2).

The following examples demonstrate INFRARED usage, where in each case we show data files for performing the appropriate geometry optimisation, together with data for determining the intensities under RUNTYPE INFRARED processing;

1. Optimisation of the geometry and calculation of the SCF infra-red intensities for H₂CO;

2. Open-shell RHF geometry optimisation and intensities for the ³A^'' state of H₂CO.

3. MP2 geometry optimisation and infra-red intensities for H₂CO.

Example 1: SCF Infra-red Intensities for H₂CO

Run I: Geometry Optimisation

           TITLE
           H2CO - 3-21G DEFAULT BASIS - CLOSED SHELL SCF - OPTIMISATION
           ZMATRIX ANGSTROM
           C
           O 1 CO
           H 1 CH 2 HCO
           H 1 CH 2 HCO 3 180.0
           VARIABLES
           CO 1.203
           CH 1.099
           HCO 121.8
           END
           RUNTYPE OPTIMIZE
           XTOL 0.0001
           ENTER

Run II. Calculation of Infra-red Intensities

Note the form of the RESTART directive below; since the geometry optimisation has been conducted immediately prior to the INFRARED run, it is sufficient to use just

           RESTART

when the optimised geometry will be read from the Dumpfile, and override the ZMATRIX data in the input stream.

           RESTART
           TITLE
           H2CO - 3-21G DEFAULT BASIS - CLOSED SHELL SCF - INFRARED
           ZMATRIX ANGSTROM
           C
           O 1 CO
           H 1 CH 2 HCO
           H 1 CH 2 HCO 3 180.0
           VARIABLES
           CO 1.203
           CH 1.099
           HCO 121.8
           END
           RUNTYPE INFRARED
           ENTER

Example 2: Open-shell RHF Intensities

Run I: Initial Closed-shell SCF

           TITLE
           H2CO - 3-21G - CLOSED SHELL SCF AT 3A'' GEOMETRY
           ZMATRIX ANGSTROM
           C
           O 1 CO
           X 1 1.0 2 90.0
           H 1 CH 2 HCO 3 DI1
           H 1 CH 2 HCO 3 DI2
           VARIABLES
           CO 1.203
           CH 1.099
           HCO 121.8
           DI1 15.0
           DI2 164.0
           END
           ENTER

Run II: Geometry Optimisation

           RESTART NEW
           TITLE
           H2CO - 3-21G BASIS - 3A'' STATE OPTIMISATION
           MULT 3
           ZMATRIX ANGSTROM
           C
           O 1 CO
           X 1 1.0 2 90.0
           H 1 CH 2 HCO 3 DI1
           H 1 CH 2 HCO 3 DI2
           VARIABLES
           CO 1.203
           CH 1.099
           HCO 121.8
           DI1 15.0
           DI2 164.0
           END
           RUNTYPE OPTIMIZE
           SCFTYPE GVB
           OPEN 2 2
           LEVEL .3 1.0
           XTOL 0.0001
           ENTER

Run III: Calculation of Infra-red Intensities

           RESTART 
           TITLE
           H2CO - 3-21G BASIS - 3A'' STATE - INFRARED
           MULT 3
           ZMATRIX ANGSTROM
           C
           O 1 CO
           X 1 1.0 2 90.0
           H 1 CH 2 HCO 3 DI1
           H 1 CH 2 HCO 3 DI2
           VARIABLES
           CO 1.203
           CH 1.099
           HCO 121.8
           DI1 15.0
           DI2 164.0
           END
           RUNTYPE INFRARED
           SCFTYPE GVB
           OPEN 2 2
           LEVEL .3 1.0
           ENTER

Example 3: MP2 Infra-red Intensities

Run I: Geometry Optimisation

           TITLE
           H2CO - 3-21G DEFAULT BASIS - MP2/RHF - OPTIMISATION
           ZMATRIX ANGSTROM
           C
           O 1 CO
           H 1 CH 2 HCO
           H 1 CH 2 HCO 3 180.0
           VARIABLES
           CO 1.203
           CH 1.099
           HCO 121.8
           END
           RUNTYPE OPTIMIZE
           SCFTYPE MP2
           XTOL 0.0001
           ENTER

Run II: MP2 Intensities

           RESTART
           TITLE
           H2CO - 3-21G DEFAULT BASIS - MP2/RHF - INFRARED
           ZMATRIX ANGSTROM
           C
           O 1 CO
           H 1 CH 2 HCO
           H 1 CH 2 HCO 3 180.0
           VARIABLES
           CO 1.203
           CH 1.099
           HCO 121.8
           END
           RUNTYPE INFRARED
           SCFTYPE MP2
           ENTER