Remarks about PtH42: recalling MOs and DOS

1
Remarks about (PtH4)2- recalling MOs and DOS
?/?(z-z)
?/?(z2-z2)
There is possibility of z2-z bonding by symmetry,
but the energies are widely separated. Hence
while overlap and symmetry allow them to mix, the
bonding provided is small. When stack is
oxidized, the loss of this weak bonding is
overcome by loss of Pt-Pt antibonding when the
orbitals at top of z2-band are emptied.
2
Connection Density of States and Stability via
COOP Important for chemisorption

• We have observed that
• MO can be used to estimate bands.
• Estimated bands can be used to estimate DOS.
• MO can be used to directly estimate DOS of
  extended system.
• In addition, other quantities to help
  understanding can be derived from the
  bonding/antibonding notions.
• For example, does one orbital level interact more
  or less strongly with another level. The
  perturbation measure of interaction is

Splitting of two levels ?Eij Hij2/(Ei0 Ej0
) More or less in resonance? Overlap affects
interaction ? (f1 f2)/?2(1S12) Anti-bonding
more affect by S.
3
Density of States and Expectation for
chemisorption
Interaction relies on both resonance in energy
and overlap
Splitting of two levels ?Eij Hij2/(Ei0 Ej0
) More or less in resonance? Overlap affects
interaction ? (f1 f2)/?2(1S12) Anti-bonding
more affect by S.

• At 2 Å, H2 overlaps Ef.
• ?u more in resonance with Ni s, p
• Thus, ?u interacts more strongly.
• Why?

4
Density of States and Expectation for
chemisorption
Interaction relies on both resonance in energy
and overlap.
free H2 level
CloserBanding

• ?u more in resonance with Ni s, p
• ?Eij Hij2/(Ei0 Ej0 )
• Thus, ?u interacts more strongly.
• Note that the H2 ?g state is below Ef and little
  less that ?u is above Ef, due to overlap, of
  course. Hence it position.

5
COOP Crystal Orbital Overlap Population
In physics overlap population-weighted DOS
(OPW-DOS) but OPW or orthogonalized
plane-waves is taken.
w.f. overlap lt? ? gt lt?i cifi ?j cjfjgt
?i ci2ltfifigt ?i?j cicjltfifjgt
?i ci2 ?iltj 2cicjSij
As before, the two-center overlap integrals Sij
are assumed to be always positive. Hence,
2cicjSij called the Mülliken overlap population,
if summed over all orbitals on the two atoms,
over all the occupied MO. 2cicjSij gt 0 (lt 0
) if (anti-)bonding, which is true if ci and cj
gt 0 (lt 0). 2cicjSij reflects the
bond-order, or bonding characteristics in the
system.

• n.n overlap
• bonding to antibonding as E increases.
• n.n.n. overlap
• bonding to antibonding to bonding
• as E increases. COOP is smaller due to increased
  separation between n.n.n.
• All bands/bonds contribute, perhaps competing.
  Non-bonding is zero.

6
COOP Crystal Orbital Overlap Population
2cicjSij gt 0 (lt 0 ) if (anti-)bonding, which
is true if ci and cj gt 0 (lt 0). The integral
of the COOP curve to the Fermi level is the total
OP.

• Why does integrating up to 12 eV provide no
  overall COOP?
• Why does ds at 6 eV give COOP?

• Generic d-contributions of the Pt-Pt are mimic
  by this simple COOP.

7
What else can be garnered from the COOP curves?

• Removing electrons from the z2-type states at
  10 eV takes them from orbitals that are Pt-Pt
  anti-bonding and Pt-H non-bonding.
• What do you expect to happen to Pt-Pt bond
  distances? Increase or decrease? Why?

Remove electrons
stabilizing
Tuning electron count is solid-state means to
control properties via oxidation or
reduction. COOP curve can estimate this at a
glance, e.g. which bonds will be weaker or
stronger.
8
TiO2 Rutile Tetragonal, 4/mmm a 4.593 Å c
2.958 Å
GIFs from Dr. Heyes, Oxford
Rutile is distorted hcp O with Ti in 1/2
Octahedral holes
Mostly O 2p some t2g and eg
9
TiO2 Rutile Are the orbitals and crystal field
splitting recognizable?
Crystal Field Split t2g (lower) and eg (upper)
t2g in the O-2p band (? bonding), and eg has
small amount of DOS in the O-2s and O-2p ?
bonding.
10
Generic 3d TM DOS Generic 3d TM COOP

• Now chemisorption or surface-adsorbate
• interactions can be tracked down using COOP
  curves.
• NMR, e.g., can be used to extract p-DOS

11
COOP curves for surface-adsorbate case CO on
Ni(001)
First, recall what are the CO levels and bands
for 2D array.
Standard orbital assignments
PW Atkins, Molecular QM
Note CO forms an s-pz hybrid, hence the multiple
s-p lines. That is, there are 2 s and 6 p for a
total of 8 lines expected (bonding and
anti-bonding counted). See other examples at
http//courses.chem.psu.edu/chem38/mol-gallery/gal
lery.html
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Decomposing the DOS CO on Ni(001)

• DOS is roughly superposition of CO and Ni DOS.
• 5? peak in DOS has moved down, but remains quite
  localized (has 1.62 e-).
• But where is 2??
• It is delocalized,pushed up and mixing with the
  d-band (has 0.74 e-).
• What levels are responsible for these
  interactions?

13
COOP curve for CO on Ni(001)
Clearly, on the CO the 2? state gives negative
COOP. But, give positive COOP for
substrate-adsorbate.
carbonyl lone pair 5?
d-hybrid spdz2
dxz, dxz (the d?) CO ?-states
What does COOP say about major contributions to
bonding?
14
The CO adsorption bonding to metal
carbonyl lone pair 5?
a) Carbonyl bond with metal. b) ? bond with
back-donation
d-hybrid spdz2
dxz, dxz (the d?) CO ?-states
ab initio electron DFT calculations shows that
the ? interaction is repulsive while the ?
interaction is attractive and also weakens the
internal CO bond. Both the ? and ? interactions
increase with higher coordination, but the two
contributions partly compensate for each other.