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exercises:2014_ethz_mmm:mo_ethene

# 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 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 the printing of the MOs in the output and in the *.cube files
NHOMO 5                   ! Number of HOMOs to be printed (count starts from the highest occupied orbital. -1 = all). Here 5.
NLUMO 5                   ! Number of LUMOs to be printed (count starts from the lowest unoccupied orbital). Here 5.
&END MO_CUBES
&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 list of ALL the occupied MOs and 3 (as specified in the input) unoccupied MOs eigenvalues are printed in the output.
The ethene band gap (energy difference between HOMO and LUMO) is also printed.

  **** **** ******  **  PROGRAM STARTED AT
***** ** ***  *** **   PROGRAM STARTED ON
**    ****   ******    PROGRAM STARTED BY
***** **    ** ** **   PROGRAM PROCESS ID
**** **  *******  **  PROGRAM STARTED IN

.....
Eigenvalues of the occupied subspace spin            1
---------------------------------------------
list of eigenvalues
....

Lowest Eigenvalues of the unoccupied subspace spin            1
-----------------------------------------------------
list of eigenvalues
.....

HOMO - LUMO gap [eV] :
......

**** **** ******  **  PROGRAM ENDED AT
***** ** ***  *** **   PROGRAM RAN ON
**    ****   ******    PROGRAM RAN BY
***** **    ** ** **   PROGRAM PROCESS ID
**** **  *******  **  PROGRAM STOPPED IN

Note that the eigenvalues are given in Eh , while the Band gap is given in eV.

### 3. Step

In addition to the list of eigenvalues ( printed directly in the output file) a series of *.cube files is generated.
The number of cubes strictly depends on what you have specified in the PRINT_MO section. No extra files are generated (while in the output a default list of all the occupied MOs eigenvalues is anyway produced.)
∗.cube files report the structure of a given MO and can be visualized with VMD:

• To run vmd: vmd ethene-WFN_00008_1-1_0.cube
• To visualize the molecule (sometimes the default settings are not visible with VMD in Brutus):
Graphics > Representations > Draw style > Drawing Method: CPK
• To visualize the MO structure in VMD:
Graphics > Representations > Draw style > Drawing Method: Isosurfaces
• In Isosurfaces, set Draw to “Wireframe” (other formats may not be visible with VMD in Brutus)
• In Isosurfaces, set Isovalue to 0.1, 0.01 …
• To visualize the positive and the negative part of an orbital simultaneously, add a second isosurface representation with isovalues -0.1, -0.01, …
• To give the two representations different colors, set their “Coloring Method” to “ColorID” and choose different ids.

What you get should look similar to this:

### Questions

- Quickly sketch the energy distribution for the occupied MOs and the five unoccupied MOs.
- By using VMD, identify the shape and energy of the π and π* orbitals.