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Geometry Exercises

Exercise 1 - H2 dimer

Using Materials Studio, create a 'molecule in a box' as follows: · Build/Crystal/lattice 5 Å3 cell · add H atom at 0.4,0.5,0.5 · add H atom at 0.6,0.5,0.5 Hence initial bond length = 0.2*5.0 = 1.0 Å · Save As H2 Now do a CASTEP geometry optimisation using Modules/CASTEP/Calculation: · Set energy parameters = FINE, · XC functional = GGA-PBE · K-point sampling = gamma point, · TASK= geom opt And turn on Properties/Population Analysis with and bond population on Should take ~ 20 secs. If get no graphs, set castep/calculation/job control/more to 10 sec update On completion should automatically load H2.castep so can see the progress of the calculation and the final population analysis will give us the bond length at the bottom of the file 0.75855 Å Scan file for any warnings. MS creates a H2 CASTEP GeomOpt directory with files inside: 1) make sure the `animation toolbar' is visible and then click on H2 trajectory.xsd. You can then play a "movie" of the geom opt - does it look plausible? 2) click on H2.xsd and can then click on CASTEP/analysis/energy evolution -> plots graph of geometry convergence - should be nice and smooth - horizontal lines are the tolerances need to get below. Geom opt should get Energy gain of ~0.6 eV over initial configuration. What is the "correct value" for bond length? Need to do the standard electronic convergence and also check the forces. BUT note that this is a "molecule in a box" and hence only gamma-point k-point sampling. How good an approximation is this? What else do you need to vary? Expt: H2 bond length ~ 0.74 Å and vibrational frequency ~ 4395 cm-1

Exercise 2 - Si crystal

Using Materials Studio, create a 2-atom Si unit cell as follows: · new 3D atomistic document · build/crystal/symmetry group 227, lattice 5.0 Å3 cell · add atom Si at 0,0,0 (makes 8 atom conventional cell) · build/symmetry/primitive (makes 2 atom primitive cell) set CASTEP parameters as follows · energy parameters fine, · kpoints fine, · task=geom opt, more -> optimise cell, fix basis quality By default, will do FBSC will calculate and print out dEtotal/dlog(Ecut) ­ anything more than 0.1 eV is big and a sign of incomplete convergence. What is the final lattice parameter? With GGA-PBE and with LDA? Do convergence test (cut-off-energy, kpoints, grids) and for both GGA-PBE and LDA. Experimental value is 3.84 Å - can you get close?

Exercise 3 - Graphite

Using Materials Studio, load an existing graphite structure · import structures/ceramic/graphite TASK: Find the converged optimal cell parameters for GGA and LDA What is going wrong? How can you use cell constraints to fix it?

Exercise 4 ­ Extensions

Experiment with the above structures, and see how you can improve the convergence rate by tweaking the various parameters discussed in lectures. You might also want to experiment with ionic constraints and/or alternative minimisers to BFGS and/or external pressure.

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