Molecular orbitals of Ethene

In this exercise, you will perform an electronic structure calculation to obtain the ethene molecular orbitals (MOs). If performed correctly, your calculations will produce a list of occupied and non occupied MOs and a series of *.cube files, that allow the visualization of the oribital with VMD.

Run a calculation with the following (commented) input file.
Note that the file contains explicit basis sets and potential for all-electron calculations. An explanation of the basis set formats is given here: Basis Sets

ethene.inp

&GLOBAL
  PROJECT ethene
  RUN_TYPE ENERGY
  PRINT_LEVEL MEDIUM
&END GLOBAL

&FORCE_EVAL
  METHOD Quickstep              ! Electronic structure method (DFT,...)
  &DFT
    &PRINT
      &MO_CUBES                 ! Controls which MOs are written to cube-files.
        NHOMO 5
        NLUMO 5
      &END MO_CUBES
      &PDOS                     ! Controls which MOs are included in the pdos-files.
         NLUMO 5
      &END
    &END PRINT
    &POISSON                    ! Solver requested for non periodic calculations
      PERIODIC NONE
      PSOLVER  WAVELET          ! Type of solver
    &END POISSON
    &QS                         ! Parameters needed to set up the Quickstep framework
      METHOD GAPW               ! Method: gaussian and augmented plane waves 
    &END QS

    &SCF                        ! Parameters controlling the convergence of the scf. This section should not be changed. 
      MAX_ITER_LUMOS 10000
      EPS_SCF 1.0E-6
      SCF_GUESS ATOMIC
      MAX_SCF 60
      EPS_LUMOS  0.000001
      &OUTER_SCF
        EPS_SCF 1.0E-6
        MAX_SCF 6
      &END
    &END SCF

    &XC                        ! Parametes needed to compute the electronic exchange potential 
      &XC_FUNCTIONAL NONE      ! No xc functional
      &END XC_FUNCTIONAL
      &HF                      ! Hartree Fock exchange. In this case is 100% (no fraction specified).   
        &SCREENING             ! Screening of the electronic repulsion up to the given threshold.               
          EPS_SCHWARZ 1.0E-10  ! Threshold specification
        &END SCREENING
      &END HF
    &END XC
  &END DFT

  &SUBSYS
    &CELL
      ABC 10 10 10
      PERIODIC NONE              ! Non periodic calculations. That's why the POISSON scetion is needed 
    &END CELL
    &TOPOLOGY                    ! Section used to center the atomic coordinates in the given box. Useful for big molecules
      &CENTER_COORDINATES
      &END
    &END
    &COORD
    C         -2.15324        3.98235        0.00126
    C         -0.83403        4.16252       -0.00140
    H         -0.25355        3.95641        0.89185
    H         -0.33362        4.51626       -0.89682
    H         -2.65364        3.62861        0.89669
    H         -2.73371        4.18846       -0.89198
    &END COORD
    &KIND H                    ! Basis set and potential for H
     &BASIS
  2
  1  0  0  3  1
         18.73113700          0.03349460
          2.82539370          0.23472695
          0.64012170          0.81375733
  1  0  0  1  1
          0.16127780          1.00000000
     &END
     POTENTIAL ALL
     &POTENTIAL
     1    0    0
     0.20000000    0
     &END
    &END KIND
    &KIND C                    ! Basis set and potential for C
     &BASIS
  4
  1  0  0  6  1
       3047.52490000          0.00183470
        457.36951000          0.01403730
        103.94869000          0.06884260
         29.21015500          0.23218440
          9.28666300          0.46794130
          3.16392700          0.36231200
  1  0  1  3  1  1
          7.86827240         -0.11933240          0.06899910
          1.88128850         -0.16085420          0.31642400
          0.54424930          1.14345640          0.74430830
  1  0  1  1  1  1
          0.16871440          1.00000000          1.00000000
  1  2  2  1  1
          0.80000000          1.00000000
     &END
     POTENTIAL ALL
     &POTENTIAL
     4    2    0
     0.34883045    0   
     &END
    &END KIND
  &END SUBSYS
&END FORCE_EVAL

If the calculation was performed correctly, a number of new files should have been written:

$ ls *.pdos *.cube
ethene-k1-1.pdos  ethene-WFN_00004_1-1_0.cube  ethene-WFN_00006_1-1_0.cube  ethene-WFN_00008_1-1_0.cube  ethene-WFN_00010_1-1_0.cube  ethene-WFN_00012_1-1_0.cube
ethene-k2-1.pdos  ethene-WFN_00005_1-1_0.cube  ethene-WFN_00007_1-1_0.cube  ethene-WFN_00009_1-1_0.cube  ethene-WFN_00011_1-1_0.cube  ethene-WFN_00013_1-1_0.cube

First have a look at the *.pdos files. PDOS stands for Projected Density of States. These files list the energies and occupation of the MOs. Furthermore, they show how the MOs are compose from basis-functions of different atoms (one pdos-file for each atomic kind) and angular momentum (s,p,d). Hence, these numbers always sum up to 1.0.

Now look at the *.cube files. Each cube-file contains the electronic density of one MO mapped onto a regular 3D-grid. Not all MOs were written to a cube-file, this is controlled by the PRINT_MO section. Their filenames tell you to which MO a cube-file belongs. For example ethene-WFN_00005_1-1_0.cube contains the 5th orbital.

Use VMD to visualize the cube-files:

1. To run vmd ethene-WFN_00008_1-1_0.cube
2. To visualize the molecule (sometimes it's not visible by default):
   Graphics > Representations > Draw style > Drawing Method=CPK
3. Add a second representation by clicking on Create Rep
4. In this second representation set Drawing Method=Isosurfaces and Draw=Wireframe
5. Finally set the Isovalue of to a reasonable value, eg. 0.1 .
6. To visualize the positive and the negative part of an orbital simultaneously, you will have to add a third representation with a negative Isovalue, e.g. -0.1 .
7. To give the two representations different colors, set their Coloring Method=ColorID and choose different ids.

What you get should look similar to this:

1. Quickly sketch the energy distribution of the MOs.
2. What's the energy of the HOMO, LUMO, and the band-gap?
3. Use VMD to identify the shape and energy of the $\pi$ and $\pi^*$ orbitals.