Some Practical Considerations for Density Functional Theory Studies of Chemistry at Metal Surfaces - Metallic Systems: A Quantum Chemist's Perspective - page 188

Using. the. bulk. lattice. parameter,. the. positions. of. the. slab. atoms. in. the. trun-
cated.bulk.crystal.are.chosen..To.complete.the.deinition.of.the.slab.calculation,.the.
third. lattice. vector. of. the. super-cell,. the. slab. repeat. vector. normal. to. the. surface,.
is. needed.. As. mentioned. above,. the. slab. model. of. the. surface. requires. 10-15. Å.
of. space. between. the.atoms. of. one. slab.and. the.next. to.isolate.the.slabs.from. one.
another.(remembering.that.any.anticipated.adsorbing.species,.not.just.the.substrate.
atoms,.are.included.when.considering.the.boundaries.of.the.slab.atoms)..While,.in.
principle,.any.spacing.between.slabs.with.suficient.vacuum.is.allowed,.it.is.usually.
best.to.set.the.vacuum.spacing.to.be.in.increments.of.the.bulk.layer.spacings.normal.
to.the.surface,.so.that.the.substrate.layers.are.in.concordance.with.the.layers.of.a.bulk.
calculation.that.would.use.the.same.super-cell.
As.an.example,.we.return.to.the.Er.hcp.(0001).slab..For.a.small.slab.calculation.
of.a.1.×.1.primitive.cell.with.ive.Er.layers,.the.two.surfaces.layers.of.the.slab.are.
2 c .(four.layer.spacings).apart..Using.PBE.with. c .=.5.560.Å,.a.distance.of.at.least.2 c .
between.the.atoms.of.different.slabs.is.needed..To.allow.some.room.for.adsorbed.
species,. we. increase. the. distance. between. substrate. layers. by. an. additional. 2 c .
for.a.total.distance.of.4 c .between.the.substrate.surface.atoms.of.different.slabs..
Added.to.the.2 c .thickness.of.the.slab,.the.slab.repeat.lattice.vector.for.the.ive-
layer. slab. is. 6 c .. With. each. two. layers. added. to. the. slab,. this. slab. repeat. vector.
increases.by. c .
6.4.6 e rBium e xamPle : P roPertieS of a c lean S urface
Having.constructed.the.geometry.of.the.slab.model.of.the.surface,.the.irst.obvious.
application. is. to. determine. the. properties. of. the. clean. surface.. Creating. a. surface.
costs. energy. and. causes. atoms. near. the. surface. to. shift. from. their. bulk. positions..
DFT.calculations.of.the.clean.surface.require.assessing.many.of.the.same.consider-
ations.as.one.would.in.the.bulk.
The. k -point.sampling.now.only.needs.to.be.done.in.two.dimensions.rather.than.
the.three.dimensions.of.the.bulk,.as.the.third.dimension.is.non-periodic..The.same.
concerns. about. adequacy. of. the. 2D. surface. k -sampling. apply. as. in. the. bulk,. and.
the.convergence.of.results.versus. k -sampling.should.be.conirmed..A.crude.rule.of.
thumb.is.that.the.linear.spacing.of.the. k -grid.in.the.surface.BZ.should.be.roughly.
the.same.as.was.needed.in.the.bulk.BZ.to.converge.bulk.quantities..If.bulk.hcp.Er.
was.converged.with.a.16 2 .×.10.sampling.of.the.BZ,.a.slab.calculation.should.also.be.
converged.with.the.surface-projected.16 2 .sampling.
The.adequacy.of.the.basis.set.might.also.need.to.be.reassessed..While.a.pure.bulk.
aluminum.calculation.might.be.converged.with.a.relatively.small.plane-wave.basis,.
a. surface. calculation. may. introduce. sharper. variations. in. the. wave. functions. and.
require. a. slightly. higher. cutoff. to. achieve. similar. accuracy.. Moreover,. adsorbates.
may. require. even. higher. cutoffs,. and. total. energy. calculations. for. molecular. che-
misorption.energies. require. that. all. components—the. isolated. molecule,.the. clean.
substrate,.and.the.molecules.adsorbed.on.the.surface—are.performed.consistently,.
meaning.that.the.bulk.and.the.molecular.calculation.are.done.with.the.same. k .point.
sampling,.basis.and.energy.cutoffs.