Structure of Liquid Metal Surfaces: A First Principles Perspective - Metallic Systems: A Quantum Chemist's Perspective - page 147

TABLE 5.1
Details of Cell Geometries Used in Ab Initio MD
Simulations of Liquid Sodium Surfaces in Refs. [70-74]
Cell T (K) a (Å) b (Å) c (Å) α (°) β (°) γ (°)

(001) 400 18.06 18.06 34.03 90 90 90

500 18.24 18.24 34.03 90 90 90

(111) 400 19.16 19.16 34.93 90 90 60

500 19.34 19.34 34.93 90 90 60

Source: . Adapted.with.permission.from.Walker,.B.G.,. Ab Initio Molecular
Dynamics Studies of Liquid Metal Surfaces ,. PhD. thesis,.
University. of. Cambridge,. copyright. 2004;. Walker,. B.G.. et. al.,.
J. Phys. Condens. Matter ,. 16,. S2575,. copyright. 2004;. Walker,.
B.G..et.al.,. J. Chem. Phys .,.124,.174702,.copyright.2006;.Walker,.
B.G..et.al.,. J. Phys. Condens. Matter ,.18,.L269,.copyright.2006;.
Walker,.B.G..et.al.,. J. Chem. Phys .,.127,.134703,.copyright.2007,.
American.Institute.of.Physics.
a ,. b ,.and. c .are.the.lengths.of.the.cell.vectors.(in.Å),.and.α,.β,.and.γ.are.the.
Euler.angles.(in.degrees).

normal. to. the. surface);. the. “(111)”. cell. contained. 162. atoms,. with. 12. layers. in. the.
starting.bulk.cell..Once.mean.square.displacements.showed.that.the.bulk.simulation.
cells.had.melted.satisfactorily,.vacuum.regions.of.approximately. 11.Å.thicknesses.
were.added.along.the. z -direction.of.each.cell,.to.form.liquid.slabs..These.were.then.
equilibrated,.and.statistics.collected..For.each.simulation.cell.and.temperature,.over.
50.ps.of.molecular.dynamics.was.obtained,.with.the.last.30.ps.of.each.run.being.used.
in. calculating. time-averaged. properties.. The. Verlet. algorithm. (“leapfrog”. version.
[75]).was.used.to.integrate.the.ionic.equations.of.motion,.with.an.integration.time.
step.δ t .=.10.fs..A.Gaussian.thermostat.[76].was.used.to.maintain.ionic.temperatures.
at.the.desired.values.
The.eDFT.calculations.were.made.with.plane.wave.basis.sets.speciied.by.a.cutoff.
energy. E cut .=.100.eV;. all. integrations. were. performed. with. the. Baldereschi. k -point.
(¼,. ¼,. ¼). [77].. Norm-conserving. pseudopotentials. of. the. Troullier-Martins. type.
[78].were.used.to.describe.the.Na.atoms;.for.the.exchange-correlation.energy,.the.
gradient-corrected.functional.of.Perdew.and.Wang.(PW91).[79].was.used..A.nonlin-
ear.core-correction.[80].with.a.core.radius.of.2.0.Bohr.was.used..In.the.cold.smear-
ing,.an.electronic.temperature.equivalent.to.0.5.eV.was.used.
The. density. proiles. for. the. four. simulation. cells. are. shown. in. Figure. 5.5..
Atomic.and.valence.electron.density.proiles.for.the.two.simulation.cells,.labeled.
“(001)”.and.“(111),”.are.shown.for.the.two.temperatures.at.which.each.was.simu-
lated..They.show.deinite.oscillations.at.the.liquid.surface,.indicating.the.forma-
tion.of.atomic.layers..The.strength.of.the.layers.is.seen.to.be.reduced.at.the.higher.
temperature.for.each.simulation.cell..Average.layer.spacings.for.the.surface.and.
inner. layers. in. each. of. the. free. surface. simulations. are. given. in. Table. 5.1.. The.