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# Lecture 27 March 9, 2011 Cuprates, metals

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1. Lecture 27 March 9, 2011 Cuprates, metals Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy William A. Goddard, III, wag@wag.caltech.edu 316 Beckman Institute, x3093 Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics, California Institute of Technology Teaching Assistants: Wei-Guang Liu <wgliu@wag.caltech.edu> Caitlin Scott <cescott@caltech.edu>

2. Last time

3. Examine the bonding of XeF Consider the energy to form the charge transfer complex Xe Xe+ The energy to form Xe+ F- can be estimated from Using IP(Xe)=12.13eV, EA(F)=3.40eV, and R(IF)=1.98 A, we get E(Xe+ F-) = 1.45eV (unbound) Thus there is no covalent bond for XeF, which has a weak bond of ~ 0.1 eV and a long bond

4. Examine the bonding in XeF2 Xe+ The energy to form Xe+F- is +1.45 eV Now consider, the impact of putting a 2nd F on the back side of the Xe+ Since Xe+ has a singly occupied pz orbital pointing directly at this 2nd F, we can now form a covalent bond to it How strong would the bond be? Probably the same as for IF, which is 2.88 eV. Thus we expect F--Xe+F- to have a bond strength of ~2.88 – 1.45 = 1.43 eV! Of course for FXeF we can also form an equivalent bond for F-Xe+--F. Thus we get a resonance, which we estimate below We will denote this 3 center – 4 electron charge transfer bond as FXeF

5. Estimate stability of XeF2 (eV) Energy form F Xe+ F-at R=∞ F-Xe+ covalent bond length (from IF) Energy form F Xe+ F-at R=Re F-Xe+ covalent bond energy (from IF) Net bond strength of F--Xe+ F- Resonance due to F- Xe+--F Net bond strength of XeF2 1.3 2.7 XeF2 is stable with respect to the free atoms by 2.7 eV Bond energy F2 is 1.6 eV. Thus stability of XeF2 with respect to Xe + F2 is 1.1 eV

6. Stability of gas of XeF2 The XeF2 molecule is stable by 1.1 eV with respect to Xe + F2 But to assess whether one could make and store XeF2, say in a bottle, we have to consider other modes of decomposition. The most likely might be that light or surfaces might generate F atoms, which could then decompose XeF2 by the chain reaction XeF2 + F  {XeF + F2}  Xe + F2 + F Since the bond energy of F2 is 1.6 eV, this reaction is endothermic by 2.7-1.6 = 1.1 eV, suggesting the XeF2 is relatively stable. Indeed XeF2 is used with F2 to synthesize XeF4 and XeF6.

7. XeF4 Putting 2 additional F to overlap the Xe py pair leads to the square planar structure, which allows 3 center – 4 electron charge transfer bonds in both the x and y directions. The VB analysis indicates that the stability for XeF4 relative to XeF2 should be ~ 2.7 eV, but maybe a bit weaker due to the increased IP of the Xe due to the first hypervalent bond and because of some possible F---F steric interactions. There is a report that the bond energy is 6 eV, which seems too high, compared to our estimate of 5.4 eV.

8. XeF6 Since XeF4 still has a pz pair, we can form a third hypervalent bond in this direction to obtain an octahedral XeF6 molecule. Indeed XeF6 is stable with this structure Here we expect a stability a little less than 8.1 eV. Pauling in 1933 suggested that XeF6 would be stabile, 30 years in advance of the experiments. He also suggested that XeF8 is stable. However this prediction is wrong

9. Estimated stability of other Nobel gas fluorides (eV) 1.3 1.3 1.3 1.3 1.3 1.3 -5.3 -0.1 1.0 2.7 3.9 -2.9 Using the same method as for XeF2, we can estimate the binding energies for the other Noble metals. KrF2 is predicted to be stable by 0.7 eV, which makes it susceptible to decomposition by F radicals RnF2 is quite stable, by 3.6 eV, but I do not know if it has been observed

10. Halogen Fluorides, ClFn The IP of ClF is 12.66 eV comparable to the IP of 12.13 for Xe. This suggests that the px and py pairs of Cl could be used to form hypervalent bonds leading to ClF3 and ClF5. We estimate that ClF3 is stable by 2.8 eV. Stability of ClF3 relative to ClF + 2F Indeed the experiment energy for ClF3  ClF + 2F is 2.6 eV, quite similar to XeF2. Thus ClF3  is endothermic by 2.6 -1.6 = 1.0 eV

11. Geometry of ClF3

12. ClHF2 We estimate that Is stable to ClH + 2F by 2.7 eV This is stable with respect to ClH + F2 by 1.1 ev But D(HF) = 5.87 eV, D(HCl)=4.43 eV, D(ClF) = 2.62 eV Thus F2ClH  ClF + HF is exothermic by 1.4 eV F2ClH has not been observed

13. ClF5

14. SFn

15. PFn The VB view is that the PF3 was distorted into a planar geometry, leading the 3s lone pair to become a 3pz pair, which can then form a hypervalent bond to two additional F atoms to form PF5

16. Donor-acceptor bonds to oxygen

17. Ozone, O3 The simple VB description of ozone is, where the terminal pp electrons are not doing much This is analogous to the s system in the covalent description of XeF2. Thus we can look at the p system of ozone as hypervalent, leading to charge transfer to form

19. Application of hypervalent concepts Origin of reactivity in the hypervalent reagent o-iodoxybenzoic acid (IBX) Hypervalent O-I-O linear bond Enhancing 2-iodoxybenzoic acid reactivity by exploiting a hypervalent twist Su JT, Goddard WA; J. Am. Chem. Soc., 127 (41): 14146-14147 (2005)

20. Hypervalent iodine assumes many metallic personalities Hypervalent I alternative Oxidations CrO3/H2SO4 Radical cyclizations SnBu3Cl Electrophilic alkene activation HgCl2 CC bond formation Pd(OAc)2 this remarkable chemistry of iodine can be understood in terms of hypervalent concepts Martin, J. C. organo-nonmetallic chemistry– Science 1983 221(4610):509-514

21. New material

22. Bonding in metallic solids Most of the systems discussed so far in this course have been covalent, with the number of bonds to an atom related to the number of valence electrons. Thus we have discussed the bonding of molecules such as CH4, benzene, O2, and Ozone. The solids with covalent bonding, such as diamond, silicon, GaAs, are generally insulators or semiconductors We also considered covalent bonds to metals such as FeH+, (PH3)2Pt(CH3)2, (bpym)Pt(Cl)(CH3), The Grubbs Ru catalysts We have also discussed the bonding in ionic materials such as (NaCl)n, NaCl crystal, and BaTiO3, where the atoms are best modeled as ions with the bonding dominated by electrostatics Next we consider the bonding in bulk metals, such as iron, Pt, Li, etc. where there is little connection between the number of bonds and the number of valence electrons.

23. Elementary ideas about metals and insulators The first attempts to develop quantum theory started with the Bohr model H atom with electrons in orbits around the nucleus. With Schrodinger QM came the idea that the electrons were in distinct orbitals (s, p, d..), leading to a universal Aufbau diagram which is filled with 2 electrons in each of the lowest orbitals For example: O (1s)2(2s)2(2p)4

24. Bringing atoms together to form the solid As we bring atoms together to form the solid, the levels broaden into energy bands, which may overlap . Thus for Cu we obtain Energy Fermi energy (HOMO and LUMO Thus Cu does not have a band gap at ordinary distances Density states

25. Metals vs inulators

26. conductivity For systems with a band gap, there is no current until excite an electron from the occupied valence band to the empty conduction band The population of electrons in the conduction band and holes in the valence bond is proportional to exp(-Egap/RT). Thus conductivity incresses with T (resistivity decreases)

27. The elements leading to metallic binding There is not yet a conceptual description for metals of a quality comparable to that for non-metals. However there are some trends, as will be described

28. Face-centered cubic (fcc), A1

29. Alternative view of fcc

30. Closest packing layer

31. Stacking of 2 closest packed layers

32. Hexagonal closest packed (hcp) structure, A3

33. Cubic closest packing

34. Double hcp The hexagonal lanthanides mostly exhibit a packing of closest packed layers in the sequence ABAC ABAC ABAC This is called the double hcp structure

35. Structures of elemental metals some correlation of structure with number of valence electrons

36. Binding in metals Li has the bcc structure with 8 nearest neighbor atoms, but there is only one valence electron per atom. Similarly fcc and hcp have 12 nearest neighbor atoms, but Al with fcc has only three valence electrons per atom while Mg with hcp has only 2. Clearly the bonding is very different than covalent One model (Pauling) resonating valence bonds One problem is energetics: Li2 bond energy = 24 kcal/mol  12 kcal/mol per valence electron Cohesive energy of Li (energy to atomize the crystal is 37.7 kcal/mol per valence electron. Too much to explain with resonance New paradigm: Interstitial Electron Model (IEM). Each valence electron localizes in a tetrahedron between four Li nuclei. Bonding like in Li2+, which is 33.7 kcal/mol per valence electron

37. GVB orbitals of ring M10 molecules Get 10 valence electrons each localized in a bond midpoint note H10 is very different, get orbital localized on atom, not bond midpoint R=2 a0 Calculations treated all 11 valence electrons of Cu, Ag, Au using effective core potential. All electrons for H and Li

38. Bonding in alkalis

39. The bonding in column 11 Get trend similar to alkalis

40. Geometries of Li4 clusters For H4, the electrons are in 1s orbitals centered on each atom Thus spin pair across sides. Orthogonalization cases distortion to rectangle For Li4, the electrons are in orbitals centered on each bond midpoint Thus spin pair between bond midpoint. Orthogonalization cases distortion to rhombus

41. Geometries of Li6 cluster For H6, the electrons are in 1s orbitals centered on each atom Thus spin pair across sides. Orthogonalization cases distortion to D3h hexagone For Li6, the electrons are in orbitals centered on each bond midpoint Thus spin pair between bond midpoint. Orthogonalization cases distortion to triangular structure

42. Geometries of Li8 cluster For Li8, the electrons are in orbitals centered on each bond midpoint Thus spin pair between bond midpoint. Orthogonalization cases distortion to out-of-plane D2d structure

43. Li10 get closest packed structure

44. Li two dimensional Electrons localize into triangular interstitial regions Closest packed structure has 2 triangles per electron One occupied and one empty Spin pair adjacent triangles but leave others empty to avoid Pauli Repulsion Calculation periodic cell with 8 electrons or 4 GVB pairs with overlap = 0.52

45. Crystalline properties of B column

46. Binding of CH3 to Pt clusters

47. Binding of alkyl CH3-xMex to (111) surfaces Prefers on-top site \ Decreased binding with increasing x due to steric interactions with other atoms of Pt (111) surface

48. Binding of alkylidene CH2-xMex to (111) surfaces Prefers bridge binding site Decreased binding with increasing x due to steric interactions with other atoms of Pt (111) surface