1. Transition Metal Oxides Rock Salt and Rutile: Metal-Metal Bonding
Chemistry 754
Solid State Chemistry
Lecture #25
May 27, 2003

2. Rock Salt and Rutile: Structure & Properties
Octahedral Molecular Orbital Diagram
Rock Salt p*(t2g) and s*(eg) Bands
M-M Interactions
Properties 3d Transition Metal Monoxides
Magnetic Superexchange
Rutile p*(t2g) Bands, t and t
Properties MO2 (M=Ti, V, Cr, Mo, W, Ru)
Double Exchange in CrO2

3. Rock Salt Crystal StructureM y x

4. Generic Octahedral MO Diagram
t1u (s* + p*)
(n+1)p
a1g (s*)
Oxygen
(n+1)s
eg (s*)
nd eg (dx2-y2, dz2)
t2g (p*)
O 2p p (6) - t2g, t1u
O 2p NB (6)-t1g, t2u
(n+1)d t2g (dxy, dxz, dyz)
t1g & t2u
O 2p s (6)
a1g, t1u, eg
Transition Metal
t2g (p)
eg (s)
t1u (s + p)
a1g (s)

5. Simplified Band Structure
Bands of interest
s* [4]
(n+1)p
Oxygen
(n+1)s
M-O s* [2]
nd eg (dx2-y2, dz2)
M-O p* [3]
(n+1)d t2g (dxy, dxz, dyz)
O 2p p (12)
O 2p NB
O 2p s (6)
a1g, t1u, eg
Transition Metal
M-O p
M-O s

6. 3d Transition Metal Monoxides
AFM = Antiferromagnetic
How can we understand this behavior? Metallic conductivity for a fairly ionic Ti2+-O2- bond? Semiconducting behavior for partially filled bands?

7. Orbital Overlap in the t2g Band
G point (kx=ky=kz=0) M M
M-O p nonbonding
M-M bonding
Band Runs Uphill from G  M
M point (kx=ky=p/a, kz=0) M M
M-O p antibonding
M-M nonbonding

8. Orbital Overlap in the eg Band
G point (kx=ky=kz=0) M M
Band Runs Uphill from G  M
M-O s nonbonding
M point (kx=ky=p/a, kz=0) M M
M-O s antibonding

9. Band Structure Calculations
SrTiO3
TiO
The eg s* band is more narrow in TiO because the Ti-O distance is considerably longer and the overlap is smaller.
The t2g p* band is also slightly more narrow in TiO, except for near the G-point, where Ti-Ti bonding lowers the energy and widens the band.

10. Magnetic Structure
MnO, FeO, CoO and NiO are all antiferromagnets with the structure shown below (for MnO). eg
t2g = A F M eg
t2g = O Mn
The electrons align themselves in an antiparallel fashion due to AFM superexchange interactions arising primarily from the ½ filled eg orbitals. The magnetic ordering temperature increases from Mn  Fe  Co  Ni due to increasing covalency (see Magnetism lecture). The magnetic ordering has implications for the electronic transport properties.

11. Mott-Hubbard InsulatorsFe O
The AFM coupling of ions is shown for FeO. The ½ filled eg orbitals stabilize AFM coupling. Notice that there is no mechanism for the minority spin electrons (shown in red) to move from one Fe ion to the next without undergoing a spin flip (the t2g orbitals of the same spin are occupied).
Consequently the AFM coupling of ions forces a localization of the t2g electrons, even in the absence of a ½ filled or completely filled band. This is essentially the opposite of double-exchange. Such compounds are called Mott-Hubbard insulators.
eg 
t2g 
eg 
t2g 
M-O-M Interaction is AFM () when both TM have 1/2 filled configurations (d5-d5 or d3-d3)

12. Rutile Crystal Structurez x y

13. MO2 with the Rutile Structure

14. c/a Ratio in Rutile-Type Oxides
VO2 (T > 340K)
Metallic
V-V Even Spacing
VO2 (T < 340K)
V-V Alternating
CrO2
Metallic
Cr-Cr Even Spacing
RuO2
Metallic
Ru-Ru Even Spacing
MoO2
Metallic
Mo-Mo Alternating

15. M-M Overlap in the t2g Band
M-M s bonding M
M-M p antibonding
M-M d bonding
G point
kx=0
ky=0
kz=0
M-M s antibonding M
M-M p bonding
M-M d antibonding
Z point
kx=0
ky=0
kz=p/a

16. Combined M-O & M-M Effects
The M-O p* and M-M bonding interactions both make a contribution to the t2g band.
The M-O p* interactions are dominant, but the M-M s interactions preturb the picture. The M-M p & d interactions are of minimal importance.
As we fill up the t2g band we can roughly think of the following picture in terms of M-M bonding strength.
M-M s  d1 TM Ion EF
DOS
M-M p  d2 TM Ion
M-M d/d*
M-M p*  d5 TM Ion
M-M s*  d6 TM Ion
M-O p*
M-O p* ~ M-M s > M-M p > M-M d

17. Tetragonal Structure (TiO2,CrO2,RuO2)
M-O s* [4]
Delocalized Electrons
+ M-M s*
EF RuO2
M-O p* [2]
d eg
EF CrO2
+ M-M s
EF VO2
d t2g
EF TiO2
Transition Metal
O 2p NB
Oxygen 2p
M-O p
M-O s
Z = 2 (M2O4)

18. Band Structure Calculations
SrTiO3
TiO2

19. Calculated Band Structure (Tetragonal, Z=2)
TiO2
VO2
CrO2

20. Density of States (Tetragonal Structure)
TiO2
VO2
CrO2

21. G point Z point MoO2 Monoclinic Z=4 TiO2 Tetragonal Z=2 a a a a a a
M-M Short=Bonding
M-M Long=Bonding
M-M Short=AB
M-M Long=AB
Bonding
Z point M a M a M a
Antibonding
M-M Short=Bonding
M-M Long=AB
M-M Short=AB
M-M Long=Bonding

22. Pierls Distortion a E k E k a a a a a
The dimerization which occurs in the rutile structure and it’s effects on the band structure are similar to the Pierls distortion we discussed for a 1D chain of Hydrogen atoms, except that it occurs on top of the M-O p* interactions. a E k
p/a EF E k
p/a EF a a a a a

23. Monoclinic Structure (VO2,MoO2)
M-O s* [8]
Delocalized Electrons
M-O Antibonding
M-M s* [2]
EF MoO2
d eg
M-O p* [8]
EF VO2
M-M s [2]
d t2g
Localized Electrons
M-M Bonding
O 2p NB
Oxygen 2p
M-O p
M-O s
Z = 4 (M4O8)

24. CrO2
Tetragonal (Z=2)
MoO2
Monoclinic (Z=4)
Mo-O p*
Mo-Mo s

25. CrO2 and RuO2
Why are alternating long-short M-M contacts, indicative of Metal-Metal bonding not observed in CrO2 and RuO2. The electron count suggests that the M-M s levels should be full and the M-M s* levels empty?
There is a competition between localized M-M bonding (prefers dimers) and delocalized electronic transport in the M-O p* band (prefers equal spacing).
Favors delocalized transport in the M-O p* band
Dominant in
CrO2 (poor overlap) RuO2 (electron count)
Favors M-M bonding and localized e-
Dominant in MoO2
VO2 Intermediate

26. Double Exchange
CrO2 is ferromagnetic. A property which leads to it’s use in magnetic cassette tapes. What stabilizes the ferromagnetic state?
t||
tp*
Antiferromagnetic: Delocalized transport violates Hund’s Rule.
Localized t|| electrons
No M-M Bonding M
Delocalized t2g p* electrons
Ferromagnetic: Delocalized transport of tp* electrons allowed.
Localized t|| electrons polarize itinerant (delocalized) t2g p* electrons. Magnetism and conductivity are correlated.