CAPE5710 Materials Modelling 2023-24 Assessment 3 (Scott)
Release date: Friday 22nd March
Deadline: Thursday 7 th May 2pm (Minerva)
5% per day for late submissions. The assignment must be typed.
Show all working where necessary, present the calculation results clearly and always use appropriate units.
Lecture notes, background reading and papers relating to the molecular mechanics forcefields and DFT functionals used in the calculations, are available in the Learning Resources: Atomistic modelling area of the Minerva. Data from the two lectures (11/18-March) is needed for questions 5, 6 and 7. [Total: 75 marks]
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(1) Briefly, describe the technique of molecular mechanics modelling, its application and limitations. [10 marks]
(2) Briefly, describe the ab-initio materials modelling method, density functional theory (DFT), discussing any approximations or assumptions. [10 marks]
(3) Which modelling method, with reasoning, would you use to study the adsorption and possible dissociation of hydrogen (H2) on a platinum metal surface? [5 marks]
(4) Using the Inorganic Crystal Structure Database (ICSD) or Cambridge Crystallographic Database (https://www.psds.ac.uk/) obtain the space group, unit cell parameters and a source reference for two materials associated with your CAPE5000 research project. Show images of the crystal structures (unit cell with atoms / molecules). You should provide a screen shot to show that you have used the database. [6 marks]
(5) In the modelling class, aluminium, sodium chloride, titania and graphite in their standard crystal structures were geometry optimised to obtain a theoretically predicted lattice parameter using molecular mechanics.
i) In a suitable table, present the results, showing the % deviation from the experimental lattice parameter and approximate calculations times.ii) Discuss the relative success/ accuracy of the calculations referring to the choice of force field. [10 marks]
(6) In the modelling class, aluminium, sodium chloride, titania and graphite in their standard crystal structures were geometry optimised to obtain a theoretically predicted lattice parameter using density functional theory.
i) In a suitable table, present the results, showing the % deviation from the experimental lattice parameter and approximate calculations times.ii) Discuss the relative success/ accuracy of the calculations referring to the choice of exchange correlation functional [10 marks]
(7) In the computer lab., we assessed the ability of molecular mechanics (Sutton-Chen forcefield) and ab-initio DFT (GGA-PBE exchange correlation functional) methods to predict the relative energetic stability of aluminium in face centred cubic, body centred cubic and hexagonal close packed structures.
i) In a suitable table, present the results, showing the energy per unit cell and the energy per aluminium atom.ii) Convert the energies from the units given as outputs in the calculations to kJmol-1 . State the predicted lowest energy phase of aluminium for each method and calculate the energies relative to the most stable structure in kJmol-1 . [10 marks]
(8) Most DFT codes use multiprocessor high performance computing and parallelisation to get a speed up of the calculation. Use the data supplied in the appendix. (See slides 34,35,36 in the lecture Powerpoint).
(i) Plot calculation time against number of atoms for the DFT results. Comment on the plot.(ii) Plot the DFT calculation time against the number of cores.(iii) Plot ‘scale-up’ for the DFT results, showing the line for perfect scaling with number of cores - I.e. 10 cores would be 10x faster than 1 core. Why do we not achieve perfect scale up? [14 marks]
Appendix
Single point energy, 1 core (pc), MM (Sutton-Chen), DFT (GGA-PBE)
|
Al P1 |
Atoms per unit cell |
MM time (s) |
DFT time (s) 1 core |
|
1x1x1 |
1 |
0.06
|
1.05 |
|
2x2x2 |
8 |
0.06 |
13.2 |
|
3x3x3 |
27 |
0.06 |
150 |
|
6x6x6 |
216 |
0.09 |
6452 |
|
12x12x12 |
1728 |
0.33 |
|
|
24x24x24 |
13824 |
1.86 |
|
|
48x48x48 |
110592 |
15.03 |
|
Single point energy, high performance computer (hpc) DFT (GGA-PBE)
|
Al P1 |
Atoms per unit cell |
1 core |
4 cores |
20 cores |
40 cores |
80 cores |
120 cores |
|
6x6x6 |
216 |
8000 s |
1972 s |
536 s |
398 s |
212 s |
156 s |