William A. Goddard, III, wag@kaist.ac.kr

Lecture 27, December 14, 2009 Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy Course number: KAIST EEWS 80.502 Room E11-101 Hours: 0900-1030 Tuesday and Thursday William A. Goddard, III, wag@kaist.ac.kr WCU Professor at EEWS-KAIST and Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics, California Institute of Technology Senior Assistant: Dr. Hyungjun Kim: linus16@kaist.ac.kr Manager of Center for Materials Simulation and Design (CMSD) Teaching Assistant: Ms. Ga In Lee: leeandgain@kaist.ac.kr Special assistant: Tod Pascal:tpascal@wag.caltech.edu EEWS-90.502-Goddard-L15

Schedule changes Dec. 14, Monday, 2pm, L27, additional lecture, room 101 Dec. 15, Final exam 9am-noon, room 101 EEWS-90.502-Goddard-L15

Last time EEWS-90.502-Goddard-L15

Hypervalent compounds It was quite a surprize to most chemists in 1962 when Neil bartlett reported the formation of a compound involving Xe-F bonds. But this was quickly folllowed by the synthesis of XeF4 (from Xe and F2 at high temperature and XeF2 in 1962 and later XeF6.Indeed Pauling had predicted in 1933 that XeF6 would be stable, but noone tried to make it. Later compounds such as ClF3 and ClF5 were synthesized These compounds violate simple octet rules and are call hypervalent EEWS-90.502-Goddard-L15

Noble gas dimers Recall from L17 that there is no chemical bonding in He2, Ne2 etc This is explained in VB theory as due to repulsive Pauli repulsion from the overlap of doubly occupied orbitals It is explained in MO theory as due to filled bonding and antibonding orbitals (sg)2(su)2 EEWS-90.502-Goddard-L15

Noble gas dimer positive ions - On the other hand the positive ions are strongly bound (L17) This is explained in MO theory as due to one less antibonding electron than bonding, leading to a three electron bond for He2+ of 2.5 eV, the same strength as the one electron bond of H2+ (sg)2(su)1 The VB explanation is a little less straightforward. Here we consider that there are two equivalent VB structures neither of which leads to much bonding, but superimposing them leads to resonance stabilization Using (sg) = L+R and (su)=L-R Leads to (with negative sign EEWS-90.502-Goddard-L15

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 Thus there is no covalent bond for XeF, which has a weak bond of ~ 0.1 eV and a long bond EEWS-90.502-Goddard-L15

Examine the bonding in XeF2 Xe+ We saw that the energy to form Xe+F-, 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 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 We will denote this 3 center – 4 electron charge transfer bond as FXeF EEWS-90.502-Goddard-L15

Stability of XeF2 Ignoring resonance we predict that XeF2 is stable by 1.43 eV. In fact the experimental bond energy is 2.69 eV suggesting that the resonance energy is ~ 1.3 eV. The XeF2 molecule is stable by 2.7 eV with respect to Xe + F2 But to assess where someone 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 it is used with F2 to synthesize XeF4 and XeF6. EEWS-90.502-Goddard-L15

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, leading to a square planar structure The VB analysis would indicate 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. EEWS-90.502-Goddard-L15

XeF6 Since XeF4 still has a pz pair, we can form a third hypervalent bond in this direction to obtain an octahedral XeF6 molecule. 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 EEWS-90.502-Goddard-L15

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. Here we see that 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 EEWS-90.502-Goddard-L15

Halogen Fluorides, ClFn The IP of ClF is 12.66 eV which compares well 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. Indeed these estimates suggest that ClF3 and ClF5 are stable. Indeed the experiment energy for ClF3  ClF +F2 is 2.6 eV, quite similar to XeF2. EEWS-90.502-Goddard-L15

EEWS-90.502-Goddard-L15

PF5 Think of this as planar PF3+, which has a pz pair making a hypervalent bond to one F (+ z direction) with F- in the –z direction + the resonance with the other state Adding F-, leafs to PF6-, analogous to SF6, which is stabilize with appropriate cation, e.g. Li+ EEWS-90.502-Goddard-L15

Donor-acceptor bonds to O atom EEWS-90.502-Goddard-L15

Ozone We saw earlier that bonding O to O2 removes most of the resonane of the O2 ,leading to the VB configuration EEWS-90.502-Goddard-L15

Diazomethane Leading to EEWS-90.502-Goddard-L15

Origin of reactivity in the hypervalent reagent o-iodoxybenzoic acid (IBX) Hypervalent O-I-O linear bond Julius Su and William A. Goddard III Materials and Process Simulation Center, California Institute of Technology EEWS-90.502-Goddard-L15

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 Can we understand this remarkable chemistry of iodine Martin, J. C. organo-nonmetallic chemistry– Science 1983 221(4610):509-514 EEWS-90.502-Goddard-L15

New EEWS-90.502-Goddard-L15

Jamil Tahir-Kheli High Temperature Superconductors Cuprates Chiral plaquette polaron theory of cuprate superconductivity; Tahir-Kheli J, Goddard WA Phys. Rev. B 76 (1): Art. No. 014514 (2007) The Chiral Plaquette Polaron Paradigm (CPPP) for high temperature cuprate superconductors; Tahir-Kheli J, Goddard WA; Chem. Phys. Lett. (4-6) 153-165 (2009) Plaquette model of the phase diagram, thermopower, and neutron resonance peak of cuprate superconductors; Jamil Tahir-Kheli and William A. Goddard III, Phys Rev Lett, submitted

Superconducting Tc; A Story of Punctuated Evolution All Serendipity Cuprate Era A15 Metal Alloy Era Metal Era Discovery is made. Then all combinations tried. Then stagnation until next discovery. Theory has never successfully predicted a new higher temperature material. Embarrassing state for Theorists. To ensure progress we need to learn the fundamental mechanism in terms of the atomistic interactions Today Theoretical Limit (Anderson) 2020 BCS Theory (1957)

Short history of superconductivity 4.15 K 1911 Hg (Heike Kamerlingh Onnes, Leiden U, Netherlands) 3.69 K 1913 Tin (Onnes) 7.26 K 1913 Lead (Onnes) 9.2 K 1930 Niobium (Meissner, Berlin) 1.14 K 1933 Aluminum 16.1 K 1941 NbN (Ascherman, Frederick, Justi, and Kramer, Berlin) 17.1 K 1953 V3Si (Hardy and Hulm, U Chicago) 18.1 K 1954 Nb3Sn (Matthias, Gebelle, Geller, and Corenzwit, Bell Labs) 9.8 K 1962 Nb0.6Ti0.4 (First commercial wire, Westinghouse) 23.2 K 1973 Nb3Ge (Gavaler, Janocho, and Jones, Westinghouse) 30 K 1986 (LaBa)2CuO4 (Müller and Bednorz, IBM Rüschlikon, Switzerland) 92 K 1987 YBa2Cu3O7 (Wu, Ashburn, and Torng (Alabama), Hor, Meng, Gao, Huang, Wang, and Chu (Houston)) 105 K 1988 Bi2Sr2CaCu2O8 (Maeda, Tanaka, Fukutomi, Asano, Tsukuba Laboratory) 120 K 1988 Tl2Ba2Ca2Cu3O10 (Hermann and Sheng, U. Arkansas) 133 K 1993 HgBa2Ca2Cu3O8 (Schilling, Cantoni, Guo, Ott, Zurich, Switzerland) 138 K 1994 (Hg0.8Tl0.2)Ba2Ca2Cu3O8.33 (Dai, Chakoumakos, (ORNL) Sun, Wong, (U Kansas) Xin, Lu (Midwest Superconductivity Inc.),Goldfarb, NIST) Metals Era A15 Metal Alloy Era The Cuprate Era after a 15 year drought, the next generation is due soon, what will it be?

Fundamental Goals in Our Research on Cuprate Superconductivity Determine the fundamental mechanism in order to have a sound basis for designing improved systems. Criterion for any proposed mechanism of superconductivity: Does it explain the unusual properties of the normal and superconducting state for cuprates? There is no precedent for a theory of superconductivity that actually predicts new materials. Indeed we know of no case of a theorist successfully predicting a new improved superconducting material! Bernt Matthias always claimed that before trying new compositions for superconductors he would ask his Bell Labs theorists what to try and then he would always do just the opposite.

Perovskites Perovskite (CaTiO3) first described in the 1830s by the geologist Gustav Rose, who named it after the famous Russian mineralogist Count Lev Aleksevich von Perovski crystal lattice appears cubic, but it is actually orthorhombic in symmetry due to a slight distortion of the structure. Characteristic chemical formula of a perovskite ceramic: ABO3, A atom +2 charge. 12 coordinate at the corners of a cube. B atom +4 charge. Octahedron of O ions on the faces of that cube centered on a B ions at the center of the cube. Together A and B form an FCC structure

(La0.85Z0.15)2CuO4: Tc = 38K (Z=Ba), 35K (Z=Sr) 1986 first cuprate superconductor, (LaBa)2CuO4 (Müller and Bednorz) Nobel Prize Isolated CuO2 sheets with apical O on both sides of Cu to form an elongated octahedron Structure type: 0201 Crystal system: Tetragonal Lattice constants:a = 3.7873 Å c = 13.2883 Å Space group: I4/mmm Atomic positions:La,Ba at (0, 0, 0.3606) Cu at (0, 0, 0) O1 at (0, 1/2, 0) O2 at (0, 0, 0.1828) CuO6 octahedra

YBa2Cu3O7–dTc=92K (d=0.07) Per formula unit: two CuO2 sheets (five coordinate  pyramid) one CuO chain (four coordinate  square) Structure type: 1212CCrystal system: OrthorhombicLattice constants:a = 3.8227 Åb = 3.8872 Åc = 11.6802 ÅSpace group: PmmmAtomic positions:Y at (1/2,1/2,1/2)Ba at (1/2,1/2,0.1843)Cu1 at (0,0,0)Cu2 at (0, 0, 0.3556)O1 at (0, 1/2, 0)O2 at (1/2,0,0.3779)O3 at (0,1/2,0.379)O4 at (0, 0,0.159) 1987: Alabama: Wu, Ashburn, and Torng Houston: Hor, Meng, Gao, Huang, Wang, Chu

Tc depends strongly on the number of CuO2 layers: Bi2Sr2Can-1CunO4+2n double sheet CuO2 Tc= 85 K single sheet CuO2 Tc= 10 K Triple sheet CuO2 Tc= 110 K a = 3.85 Åc = 26.8 Å a = 3.85 Åc = 30.9 Å a = 3.85 Åc = 36.5 Å

Dependence of Tc on layers is not monotonic TlBa2Can-1CunO2n+3 Double sheet CuO2 Triple sheet CuO2 4 sheet CuO2 5 sheet CuO2 n= 2 Tc= 103 K n= 3 Tc= 123 K n= 4 Tc= 112 K n= 5 Tc= 107K CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 a = 3.86 Åc = 12.75 Å a = 3.84 Åc = 15.87 Å a = 3.85 Åc = 19.15 Å a = 3.85 Åc = 22.25 Å

Reining Champion since 1994: Tc=138K (Hg0.8Tl0.2)Ba2Ca2Cu3O8.33 CuO2 CuO2 CuO2 a = 3.84 Åc = 15.87 Å Triple sheet CuO2 This has the same structure as TlBa2Ca2Cu3O9 n= 3 Tc= 123 K 1994 Dai, Chakoumakos (ORNL) Sun, Wong (U Kansas) Xin, Lu (Midwest Superconductivity Inc.),Goldfarb (NIST)

Isolated layer can be greatTl2Ba2Can-1CunO2n+4 CuO2 CuO2 CuO2 n= 1 Tc= 95 K n= 4 Tc= 112 K CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 a = 3.86 Åc = 23.14 Å a = 3.85 Åc = 41.98 Å CuO2 single sheet CuO2 4 sheet CuO2

(Ba,Sr)CuO2Tc=90K single sheet CuO2 Structure type: 02"∞ -1"∞Crystal system: TetragonalLattice constants:a = 3.93 Åc = 3.47 ÅSpace group: P4/mmmAtomic positions:Cu at (0,0,0)O at (0,1/2,0)Ba,Sr at (1/2,1/2,1/2)

Some cuprates lead to electron doping not holes (Nd,Ce)2CuO4-dTc =24K For d=0 2 Nd (+3) and 1 Cu (+2) lead to 8 holes 4 O (-2) lead to 8 electrons, get insulator Dope with Ce (+4) leading to an extra electron CuO2 single sheet CuO2 Structure type: 0201T ' Crystal system: Tetragonal Lattice constants:a = 3.95 Å c = 12.07 Å Space group: I4/mmm Atomic positions:Nd,Ce at (0,0,0.3513) Cu at(0,0,0) O1 at (0, 1/2, 0) O2 at (0, 1/2,1/4) CuO2 CuO2

Our Goal Explain which systems lead to high Tc and which do not Explain how the number of layers and the location of holes and electrons affects the Tc Use this information to design new structures with higher Tc

Structural Characteristics of HighTc Superconductors: Start with Undoped Antiferromagnet Cu Cu Cu Cu Cu Cu Cu Cu O O O O O O O O Cu Cu Cu Cu O O O O Cu Cu Cu Cu O O O O O O O O O O O O 2D CuO2 square lattice (xy plane) Oxidation state of Cu: CuII or d9. (xy)2(xz)2(yz)2(z2)2(x2-y2)1 d9 hole is 3d (x2–y2). Oxidation state of O: O2– or p6. (pσ)2 (pp)2 (ppz)2. Cu – O bond = 1.90 – 1.95 Å Cu can have 5th or 6th apical O (2.4 Å) to form an octahedron or half-octahedron Undoped system antiferromagnetic with TNeel = 325 K for La2CuO4. Describe states as a Heisenberg AntiFerromagnet with Jdd = 0.13 eV for La2CuO4: Superexchange Jdd AF coupling

Superexchange coupling of two Cu d9 sitesexactly the same as the hypervalent XeF2 bond bond No direct bonding Two Cu d9 separated by 4Å leads to no bonding (ground state singlet and excited triplet separated by 0.0001 eV) With O in-between get strong bonding (the singlet is stabilized by Jdd = 0.13 eV = 1500K for LaCuO4) Explanation: a small amount of charge transfer from O to right Cu Cu(x2-y2)1-O(px)2-Cu(x2-y2)1 Cu(x2-y2)1-O(px)1-Cu(x2-y2)2 allows bonding of the O to the left Cu, but only for the singlet state The explanation is referred to as superexchange. 267-14

Characteristic of High Tc Superconductors: Doping The undoped La2CuO4 is an insulator (band gap = 2.0 eV) La2CuO4 (Undoped): La3+, Sr2+, O2–, Cu2+ Thus cation holes = 3*2 + 2 = 8 and anion electrons = 4*2 = 8 Cu2+  d9  local spin  antiferromagnetic coupling To get a metal requires doping to put holes in the valence band Doping (oxidation) La2-xSrxCuO4: Assuming 4 O2-requires 8 cation holes. But La2-xSrx  6-x holes, thus must have x Cu3+ and 1 – x Cu2+ Second possibility: assume that excitation from Cu2+ to Cu3+ is too high, then must have hole on O2– leading to O– This leads to x O– and (4 – x) O2– per formula unit. YBa2Cu3O7: Assume that all 7 O are O2– Must have 14 cation holes: since Y3+ +2 Ba2+ leads to +7, then we must have 1 Cu3+ and 2 Cu2+ The second possibility is that all Cu are Cu2+ requiring that there be1 O– and 6 O2–

Essential characteristic of all cuprate superconductors is oxidation (doping) Typical phase diagram La2-xSrxCuO4 Superconductor: 0.05 < x < 0.32 Spin Glass: 0.02 < x < 0.05 Antiferromagnetic: 0 < x < 0.02 Minimum doping to obtain superconductivity, x > 0.05. Optimum doping for highest Tc=35K at x ~ 0.15. Maximum doping above which the superconductivity disappears and the system becomes a normal metal.

Summary: Central Characteristics of cuprate superconductors, square CuO2 lattice, 16% holes Cu Cu Cu Cu Cu Cu Cu Cu O O O O O O O O Cu Cu Cu Cu O O O O Cu Cu Cu Cu O O O O O O O O O O O O CuO2 plane La2CuO4 (Undoped): La3+, Sr2+, O2–, Cu2+ d9 Cu2+  spin, with antiferromagnetic coupling Doping (oxidation) La2-xSrxCuO4: Hole  x Cu3+ and 1 – x Cu2+, Or Hole  x O– and 4 – x O2– pπ YBa2Cu3O7: Y3+, Ba2+, O2– 1 Cu3+ and 2 Cu2+, Or Y3+, Ba2+, Cu2+  1 O– and 6 O2– pσ Where are the Doped Holes? CuIII or d8: Anderson, Science 235, 1196 (1987), but CuII CuIII IP = 36.83 eV O pσ: Emery, Phys. Rev. Lett. 58, 2794 (1987). O pπ: Goddard et al., Science 239, 896, 899 (1988). O pσ: Freeman et al. (1987), Mattheiss (1987), Pickett (1989). All wrong: based on simple QM (LDA) or clusters (Cu3O8)

Which is right: ps or pp holes? undoped • Goddard et al. carried out GVB calculations on Cu3O10 + 998 point charges and found pp holes (found similar E for ps) • Electronic Structure and Valence Bond Band Structure of Cuprate Superconducting Materials; Y. Guo, J-M. Langlois, and W. A. Goddard III Science 239, 896 (1988) • The Magnon Pairing Mechanism of Superconductivity in Cuprate Ceramics G. Chen and W. A. Goddard III; Science 239, 899 (1988) doped

pp holes Goddard et al showed if the ground state has pp holes there is an attractive pair that leads to triplet P-wave Cooper pairs, and hence superconductivity. The Superconducting Properties of Copper Oxide High Temperature Superconductors; G. Chen, J-M. Langlois, Y. Guo, and W. A. Goddard III; Proc. Nat. Acad. Sci. USA 86, 3447 (1989) The Quantum Chemistry View of High Temperature Superconductors; W. A. Goddard III, Y. Guo, G. Chen, H. Ding, J-M. Langlois, and G. Lang; In High Temperature Superconductivity Proc. 39th Scottish Universities Summer School in Physics, St. Andrews, Scotland, D.P. Tunstall, W. Barford, and P. Osborne Editors, 1991 However experiment shows that the systems are singlet D-wave. Thus, pp holes does not correct provide an explanation of superconductivity in cuprates.

ps holes Emery and most physicists assumed ps holes on the oxygen. Simplifying to t–J model, calculations with on-site Coulomb repulsion suggest that if the system leads to a superconductor it should be singlet D-wave. Thus most physicists believe that ps provides the basis for a correct explanation of superconductivity. Goddard believed that if ps holes were correct, then it would lead to strong bonding to the singly occupied dx2-y2 orbitals on the adjacent Cu atoms, leading to a distortions that localize the state. This would cause a barrier to hopping to adjacent sites and hence would not be superconducting

Current canonical HighTc Hamiltonian Ops holeThe t–J Model t J J Undoped Cu d9 hole is 3d x2–y2. O 2pσ doubly occupied. Heisenberg AF with Jdd = 0.13 eV for La2CuO4. Doping creates hole in O pσ that bonds with x2–y2 to form a bonded singlet (doubly occupied hole). Singlet hole hopping through lattice prefers adjacent sites are same spin, this frustrates the normal AF coupling of d9 spins. Doped Because of Coulomb repulsion cannot have doubly occupied holes.

Summary of the t–J model Coulomb repulsion of singlet holes leads to singlet d-wave Cooper pairing. d-wave is observed in phase sensitive Josephson tunneling, in NMR spin relaxation (no Hebel-Slichter coherence peak), and in the temperature dependence of the penetration depth (λ~T2). t-J predicts an ARPES (angle-resolved photoemission) pseudogap which may have the right qualitative dependence. The t–J model has difficulty explaining most of the normal state properties (linear T resistivity, non-standard Drude relaxation, temperature dependent Hall effect, mid-IR optical absorption, and neutron ω/T scaling).

Universal Superconducting Tc Curve(What we must explain to have a credible theory) ≈ 0.16 Superconducting Phase ≈ 0.05 ≈ 0.27 Where do these three special doping values come from?

Basis for all theories of cuprate superconductors LDA Band calculations of La2CuO4 (0,p) (p,p) Un-Occupied Un-Occupied Occupied Occupied (p,0) G=(0,0) Occupied Occupied Un-Occupied Un-Occupied LDA and PBE lead to a half filled ps-dx2-y2 band; predicting that La2CuO4 is metallic! This is Fundamentally Wrong Experimental Band Gap is 2 eV LDA:Freeman 1987, Mattheiss 1987, Pickett (1989) ps-dx2-y2 band

William A. Goddard, III, wag@kaist.ac.kr