Geometry Optimisation with CASTEP

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Figure 7:A hydrogen passivated Si(100) supercell with a 7 Åvacuum gap and 9 layers of silicon. This is a crucial feature of performing geometry optimisation on surfaces. The initial surface unit cell must be large enough to enclose any expected reconstruction. A Si(111)-1x1 supercell will not reconstruct into the Si(111)-7x7 Takayanagi reconstruction! If no suggestions have been provided as to possible reconstructed periodicities by previous theoretical or experimental work then the user might have to begin with a large supercell and perform a variable cell calculation (in case of lateral relaxations). Now we must perform the abovementioned supercell convergence checks. We will use a 9 k-point MP grid with a cutoff energy of 260eV for this (we will converge our calculation with respect to basis set parameters later). Let us start with a large vacuum gap of 15Å (I know that this is entirely sufficient from experience). We will now be able to perform several calculations with 7, 8, 9, 10 and 11 layers of silicon and not have to worry about the vacuum gap - one problem at a time. The supercell lattice matrix and the atomic coordinate list in the .cell file for 7 layers of silicon looks like %BLOCK LATTICE_CART 7.6801695932 0.0000000000 0.0000000000 0.0000000000 3.8801700000 0.0000000000
0.0000000000 0.0000000000 24.5037250000 %ENDBLOCK LATTICE_CART %BLOCK POSITIONS_FRAC H 0.2500000000 -0.0103307854 -0.0000000000 H 0.7500000000 -0.0103307854 -0.0000000000 Si 0.5000000000 0.9896692146 0.1662206460 Si 0.5000000000 0.9896692146 0.3878481741 Si 0.2500000000 0.4948346073 0.0554068820 Si 0.2500000000 0.4948346073 0.2770344101 Si 0.7500000000 0.4948346073 0.0554068820 Si 0.7500000000 0.4948346073 0.2770344101 Si 0.0000000000 0.9896692146 0.1662206460 Si 0.0000000000 0.9896692146 0.3878481741 Si -0.0000000000 0.4948346073 0.1108137640 Si -0.0000000000 0.4948346073 0.3324412921 Si 0.7500000000 0.9896692146 0.2216275281 Si 0.5000000000 0.4948346073 0.1108137640 Si 0.5000000000 0.4948346073 0.3324412921 Si 0.2500000000 0.9896692146 0.2216275281 %ENDBLOCK POSITIONS_FRAC Notice the hydrogen atoms. Now for the constraints on the bottom layer silicon atoms and the hydrogen atoms (the H atoms must also be constrained because the have a tendency to move into awkward formations). The list of constraints whose format was specified before looks like %BLOCK IONIC_CONSTRAINTS 1 H 1 1.00000000 0.00000000 0.00000000 2 H 1 0.00000000 1.00000000 0.00000000 3 H 1 0.00000000 0.00000000 1.00000000 4 H 2 1.00000000 0.00000000 0.00000000 5 H 2 0.00000000 1.00000000 0.00000000 6 H 2 0.00000000 0.00000000 1.00000000 7 Si 3 1.00000000 0.00000000 0.00000000 8 Si 3 0.00000000 1.00000000 0.00000000 9 Si 3 0.00000000 0.00000000 1.00000000 10 Si 5 1.00000000 0.00000000 0.00000000 11 Si 5 0.00000000 1.00000000 0.00000000 12 Si 5 0.00000000 0.00000000 1.00000000 %ENDBLOCK IONIC_CONSTRAINTS So now we have our supercells ready to run. The calculations were performed on 9 nodes of a Beowulf cluster. The total final energy per supercell atom as a function of the number of layers of silicon is shown
Page 1 and 2: Next: Recipe Geometry Optimisation
Page 3 and 4: Next: Inputs Up: Geometry Optimisat
Page 5 and 6: Next: The Size and Shape Up: Inputs
Page 7 and 8: In both cases if [units] are not sp
Page 9 and 10: After the atomic symbol or the atom
Page 11 and 12: KPOINTS_MP_SPACING [units] Where is
Page 13 and 14: 2005-04-04
Page 15 and 16: Next: Atomic masses Up: The .cell f
Page 17 and 18: It is possible to fix the positions
Page 19 and 20: Next: External pressure that is Up:
Page 21 and 22: Next: General Job Parameters Up: In
Page 23 and 24: When a calculation that was stopped
Page 25 and 26: Next: Electronic Minimisation Param
Page 27 and 28: Next: Example - Bulk Silicon Up: Th
Page 29 and 30: the default value is 3 but it must
Page 31 and 32: We must now choose a supercell to e
Page 33 and 34: Next: The .castep file Up: Geometry
Page 35 and 36: 4 -2.14844155E+002 -9.84322032E-003
Page 37 and 38: BFGS: Final Configuration: ========
Page 39 and 40: Next: Other output files Up: Output
Page 41 and 42: Next: A Variable Cell calculation U
Page 43 and 44: arbitrary set of basis set paramete
Page 45 and 46: 3 -2.16474423E+002 2.10512829E-007
Page 47: Figure 6:A finite vacuum gap may ca
Page 51 and 52: thickness We can see that the total
Page 53 and 54: It is interesting to look at the ev
Page 55 and 56: Next: About this document ... Up: G

Geometry Optimisation with CASTEP

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