======= 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.
===== 1. Step: Run the calculation =====
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|Basis Sets]]
&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
===== 2. Step =====
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.
===== 3. Step =====
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:
- To run ''vmd ethene-WFN_00008_1-1_0.cube''
- To visualize the molecule (sometimes it's not visible by default):\\ **Graphics > Representations > Draw style > Drawing Method=CPK**
- Add a second representation by clicking on **Create Rep**
- In this second representation set **Drawing Method=Isosurfaces** and **Draw=Wireframe**
- Finally set the **Isovalue** of to a reasonable value, eg. 0.1 .
- 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 .
- To give the two representations different colors, set their **Coloring Method=ColorID** and choose different ids.
What you get should look similar to this:
{{ ethene_pi_orbital.png |}}
===== Questions =====
- Quickly sketch the energy distribution of the MOs.
- What's the energy of the HOMO, LUMO, and the band-gap?
- Use VMD to identify the shape and energy of the $\pi$ and $\pi^*$ orbitals.