The H₄ linear cluster

In this section you will calculate the wavefunction of a H₄ clusters.

Exercise 1: Start DLVisualize, run a CRYSTAL calculation for the linear case: H4_linear.inp

Exercise 2: Run a CRYSTAL properties calculation of the energy level diagram for the H₄ linear cluster, using the Band Structure module.

A prerequisite for calculating properties is to analyse a wavefunction, otherwise the properties items are grayed out.

Calculate->CRYSTAL->Analyse Current Wavefunction

The Job List panel will open automatically and look something like this;
 
 

Select the job and the status line should report "Job has completed" - like this;
 
 

Click on Recover Files.

Select Calculate -> CRYSTAL -> Properties -> Band Structure.

The CRYSTAL Band Structure panel will open:
 
 

Select OK and the properties calculation will start as evident from the Job List panel
 
 

Select the last job in the panel. When the "Job has completed", click on Recover Files. The 1D Data Display window will open:
 
 

Once select the available 1D data set, click on the button Draw 1D data. The following energy level diagram will be plotted.
 
 

Each horizontal line corresponds to an energy level. One atomic orbital for hydrogen atom, then four atomic orbitals are combined to give four molecular orbitals. As it will be also evident at the end of Exercise 3 and 4.

Exercise 3: Run a CRYSTAL properties calculation of the density of states for the H₄ linear cluster.

Select Calculate -> CRYSTAL -> Properties -> Density of States.

The CRYSTAL Density of States panel will open:
 
 

Select OK and the properties calculation will start as evident from the Job List panel
 
 

Select the last job in the panel. When the "Job has completed", click on Recover Files. The 1D Data Display window will open:
 
 

Once select the second available 1D data set, click on the button Draw 1D data. The following Density of States will be plotted.
 
 

Which information can be obtained from a DOS plot?

1. There are 4 peaks.
2. The height of the peaks is the same. It has to be noticed that it is not the value of the height that is significant, but the following product:

   DOS(E) dE = number of levels between E and E+dE

   In fact, if the value of dE is varied, by changing the sampling point in the CRYSTAL Density of States panel (by decreasing the value from 200 to 50) the height of each peak is modified, but the product is the same and is equal to 1 in our case.
3. In fact, each peak corresponds to one of the energy level plotted in the energy diagram as it will be evident in Exercise 4.

Exercise 4: Run a CRYSTAL properties calculation of the energy level diagram + the density of states for the H₄ linear cluster.

Select Calculate -> CRYSTAL -> Properties -> Bands + DOS.

The CRYSTAL Bands + DOS panel will open:
 
 

Select OK and the properties calculation will start as evident from the Job List panel
 
 

Select the last job in the panel. When the "Job has completed", click on Recover Files. The 1D Data Display window will open:
 
 

Once select the last available 1D data set, click on the button Draw 1D data. The following energy level diagram will be plotted.
 
 

1. What are the H-H distances?
   Compare with the H-H distance in the previous systems.
2. Did you use the same hamiltonian/method adopted in the calculation of the hydrogen atom and molecule?
3. What is the energy of the H₄ cluster in Hartree?
   In the output, the energy is given in atomic unit (Hartree).
   Convert the energy in eV and in J.
   Compare this energy with the energy of two isolated hydrogen molecules. Which conclusion can be drawn?
4. What are the energies of the molecular orbitals?
   Hints: Look for the string "FINAL EIGENVALUES (A.U.)" at end of the output.
   The energies are given in atomic unit (Hartree). Convert in eV and in J.
   Do these values correspond the energy level plotted in Exercises 2-4
   Compare the energies of the molecular orbitals of H₄ with H₃.
5. Is it possible to identify a non-bonding molecular orbital?
   Compare the eigenvalues with the energy of the occupied atomic orbital of hydrogen atom.

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