Structure of Liquid Metal Surfaces: A First Principles Perspective - Metallic Systems: A Quantum Chemist's Perspective - page 141

If.Friedel.oscillations.were.present.at.the.liquid.surface,.these.might.be.expected.to.
have.an.inluence.on.the.layer.formation.there.
5.2.2.4 Surface Layering without Metallic Interactions:
Ratio of Melting to Critical Temperatures
In.contrast.to.the.layering.explanations.outlined.above,.Chacón.et.al..[46],.Tarazona.
et.al..[47],.and.Velasco.et.al..[48].proposed.that.a.metallic.system.is.not.necessary.
for.a.free.liquid.surface.to.exhibit.layering.behavior..Instead.they.suggested.that.the.
criterion. determining. whether. a. surface. would. exhibit. layers. is. that. the. substance.
has.a.low.ratio.of.melting.temperature.to.critical.temperature.(the.temperature.above.
which.the.system.cannot.be.pressurized.to.form.a.liquid)..This.conclusion.was.sup-
ported.with.molecular.dynamics.simulations.performed.using.empirical.potentials..
These.potentials.were.tuned.to.give.a.low.ratio.of.melting.temperature.( T M ).to.criti-
cal.( T C ).temperature,.and.though.not.taking.into.account.the.many-body.character-
istics,. they. produced. layer. formation. in. liquid. surface. simulations.. According. to.
this. suggestion,. for. Hg. and. Ga,. which. have. low. ratios. of. T M . to. T C . ( T M / T C .<.0.13),.
layering.should.be.quite.pronounced;.for.the.alkali.metals,.with.intermediate.ratios.
( T M / T C . ∼ 0.15),. layer. formation. would. be. weak. and. at. the. limits. of. experimental.
detection;. for. metals. with. higher. T M / T C . ratios. still. (such. as. Al. and. Mg),. layering.
should.not.be.present.
In.considering.this.conjecture.connecting.the.melting.and.critical.temperatures.
and.its.consistency.with.experimental.measurements.on.metals.and.nonmetals,.we.
note. that. measurements. on. water. (which. freezes. at. about. 0.42 T C ). showed. no. evi-
dence.of.layer.formation.[28],.while.measurements.on.tetrakis(2-ethylhexoxy)silane.
at. T / T C . ≈. 0.25. did. show. layer. formation. [29].. On. the. other. hand,. simulations. per-
formed.using.molecular.dynamics.based.on.orbital-free.DFT.techniques.of.Li,.Mg,.
and.Al.[49].showed.pronounced.layer.formation,.disagreeing.with.the.prediction.of.
Chacón.based.on.the. T M / T C .ratio.
5.3 DENSITY FUNCTIONAL THEORY-BASED
MOLECULAR DYNAMICS SIMULATIONS
Recently,.simulations.of.liquid.surfaces.of.metals.have.been.made.using.molecular.
dynamics.coupled.with.DFT,.with.the.primary.focus.on.exploring.the.explanations.
for.surface-induced.layering.outlined.above..The.use.of.quantum.mechanical.meth-
ods.is.motivated.by.the.need.to.take.account.of.the.changing.interactions.across.the.
surface,.and.the.dificulties.this.poses.for.the.use.of.classical.potentials.to.describe.
the.interactions.between.atoms..DFT.is.now.widely.used.for.performing.computer.
simulations. at. the. quantum. mechanical. level. as. it. provides,. in. practice,. a. highly.
favorable.ratio.of.cost.to.accuracy.
In. a. full. quantum. mechanical. calculation,. the. system. of. interacting. nuclei. and.
electrons.is.described.by.a.wave.function.that.contains.all.the.details.of.the.dynam-
ics. of. the. system.. As. the. nuclei. in. the. system. are. ∼2000. times. heavier. than. the.
electrons,. the. motions. of. the. electrons. and. nuclei. can. be. considered. separately. by.
making.the.Born-Oppenheimer.approximation.[50]..In.most.ab.initio.MD.simula-
tions,.the.dynamical.system.of.interacting.electrons.and.nuclei.is.considered.as.two.