Computational Lab 3
Periodic Boundary Conditions-Local Optimization of Bulk Gold and Gold surfaces with DFT
Questions:
Post all answers to a word document like Google Docs or Microsoft Word.
- Show the plot of lattice constants versus energy.
- When the lattice vectors are smaller than what they should, is your system strained or stressed? How will the energy change compared to a fully relaxed system?
- What is the optimum lattice constant found for FCC Au by hand, and what is the optimum lattice constant found with VASP ISIF=3 tag? These two results should be very close to each other!
- What assumption did we make about the lattice vectors here? Hint: what's the shape of our box?
Comparing bulk structures - What is the energy per atom for the BCC crystal structure and the FCC crystal structure?
- FCC Au is more stable than BCC Au. Does your result support this? Use the cohesive energies you calculated to answer this question.
- What is a lattice point? How many lattice points are in the FCC and BCC crystal structure?
- What is the surface energy of FCC 100 and FCC 111 gold Slabs in eV/Å2?
The equation for the surface energy is as follows:
Esurface= (Eslab - N Ebulk)/ 2A where N is the number of bulk unit cells in your slab and A is the area of exposed to vacuum. In this case you can use the N=1 and the energy from step 2. - The FCC_111 surface is more stable. Does your results support this? The surface with the lower surface energy is more stable. Use your calculated surface energies to answer this question.
- Describe in you own words what the miller indices represent.
- Why are the bottom two layers of atoms fixed in place?
Calculating binding energies - Look up the paper called Origin of the Overpotential for Oxygen Reduction at a Fuel-Cell Cathode published in the Journal of Physical Chemistry B by J K. Norskov. Look for Figures 4 and 5. Figure 4 should look familiar! How is Figure 5 different? What is the relationship between the binding energy of oxygen and the hydroxyl group?
- What is the the binding energy of the hydroxyl group on the Au (111) Surface?
- How is figure 4 and figure 5 different in the paper, Origin of the Overpotential for Oxygen Reduction at a Fuel-Cell Cathode ? What is the relationship between the binding energy of oxygen and the hydroxyl group?
- From what you know about gold, how strongly do you expect oxygen to interact with a gold surface? Explain how you came to this conclusion. Use both your calculation result as well as your everyday-knowledge.
Effect of binding sites - Report all the binding energies for you found in the calculations above. You can use the energy for O2 from lab2. Make sure this calculations was done properly! Indicate where you started the calculation (hollow, bridge, or top) and the site of the optimized configuration (where the calculation ended). You do not need to rerun these calculations if they optimize to a new location .
- Look up the paper called Catalytic activity of Au nanoparticles published in Nano Today. Which binding sites on Gold nanoparticles are found to be the most catalytically active for the CO oxidation?
- This paper mentions that 3-5 nm in diameter gold nanoparticles are catalytically active. What is the approximate diatmeter of the 38 atom nanoparticle? (Hint: The unit of length in VASP is Angstroms; you can estimate this based on the optimized Pt-38 nanoparticle from lab2.)