Chemistry Reference
In-Depth Information
3.0
1.0
2.5
2.0
0.5
1.5
0.0
1.0
-0.5
0.5
-1.0
0.0
1.0
2.5
2.0
0.5
1.5
0.0
1.0
-0.5
0.5
0.0
-1.0
-5
0
5
10
15
20
25
-5
0
5
10
15
20
25
30
z
(Å)
z
(Å)
FIGURE 5.6 (See color insert.)
Density-density.autocorrelation.functions.(
c
ρ
).for.the.Na.
free. surface. simulations.. In. each. case,. the. red. and. green. curves. give. the. density-density.
autocorrelation. functions. referenced. respectively. to. the. left. and. right. peaks. in. the. atomic.
densities.(which.are.shown.as.the.black.curves)..The.labeling.of.the.panels.is.as.in.Figure.5.5..
(Adapted.with.permission.from.Walker,.B.G..et.al.,.
J. Chem. Phys
.,.124,.174702,.copyright.
2006,.American.Institute.of.Physics.)
Ref..[43]).for.the.oscillations.propagating.from.the.two.surfaces.were.calculated.and.
are. displayed. in. Figure. 5.6.. As. the. autocorrelation. functions. become. uncorrelated.
moving.from.the.respective.surfaces.into.the.bulk.and.each.one.shows.no.structure.
near.the.opposite.surface,.the.structures.of.the.two.surfaces.are.independent.of.one.
another.
The. importance. of. inite-size. effects. on. the. simulation. cells. used. in. the. MD.
was.examined.using.simulation.cells.with.different.thicknesses.and.cross.sections,.
which.were.described.using.the.empirical.potential.used.for.Na.by.Chacón.et.al..[46]..
Because. the. computational. requirements. of. making. simulations. are. much. smaller.
than. when. using. DFT,. slab. simulations. containing. far. greater. numbers. of. atoms.
could. be. studied.. In. the. upper. panels. of. Figure. 5.7,. the. surface. proiles. for. classi-
cal. simulations. are. compared. for. a. cell. containing. the. same. number. of. atoms. as.
the. (001). cell. used. in. the. ab. initio. MD. simulations,. and. for. one. having. a. slab. of.
atoms.twice.as.thick..The.classical.density.proiles.show.that.the.effect.on.the.sur-
face.structure.of.having.a.slab.of.a.larger.thickness.is.minimal..The.lower.panel.of.
Figure.5.7.compares.the.density.proiles.obtained.from.classical.MD.simulations.of.
slabs.having.the.same.thickness.as.the.(001).ab.initio.simulation,.but.with.various.
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