Lecture 16, February 25, 2015 Metallic bonding

Lecture 16, February 25, 2015 Metallic bonding Elements of Quantum Chemistry with Applications to Chemical Bonding and Properties of Molecules and Solids Course number: Ch125a; Room 115 BI Hours: 11-11:50am Monday, Wednesday, Friday 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 Special Instructor: Julius Su <jsu@caltech.edu> Teaching Assistants: Hai Xiao <xiao@caltech.edu> Mark Fornace <mfornace@caltech.edu> Ch125-Goddard-L16 copyright 2015 William A. Goddard III, all rights reserved Ch125a- 1 Goddard-

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 CH 4, benzene, O 2, 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 +, (PH 3 ) 2 Pt(CH 3 ) 2, (bpym)pt(cl)(ch 3 ), 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. 2

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 3

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 4

Metals vs inulators 5

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) 6

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 7

Body centered cubic (bcc), A2 A2 8

Face-centered cubic (fcc), A1 9

Alternative view of fcc 10

Closest packing layer 11

Stacking of 2 closest packed layers 12

Hexagonal closest packed (hcp) structure, A3 13

Cubic closest packing 14

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 15

Structures of elemental metals bcc hcp fcc mis some correlation of structure with number of valence electrons 16

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: Li 2 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 Li 2+, which is 33.7 kcal/mol per valence electron 17

GVB orbitals of ring M 10 molecules Get 10 valence electrons each localized in a bond midpoint R=2 a 0 note H 10 is very different, get orbital localized on atom, not bond midpoint Calculations treated all 11 valence electrons of Cu, Ag, Au using effective core potential. All electrons for H and Li 18

Stop Feb. 28, 2014 19

Bonding in alkalis 20

The bonding in column 11 Get trend similar to alkalis 22

Geometries of Li 4 clusters For H 4, the electrons are in 1s orbitals centered on each atom Thus spin pair across sides. Orthogonalization cases distortion to rectangle For Li 4, the electrons are in orbitals centered on each bond midpoint Thus spin pair between bond midpoint. Orthogonalization cases distortion to rhombus 23

Geometries of Li 6 cluster For H 6, the electrons are in 1s orbitals centered on each atom Thus spin pair across sides. Orthogonalization cases distortion to D3h hexagone For Li 6, the electrons are in orbitals centered on each bond midpoint Thus spin pair between bond midpoint. Orthogonalization cases distortion to triangular structure 24

Geometries of Li 8 cluster For Li 8, the electrons are in orbitals centered on each bond midpoint Thus spin pair between bond midpoint. Orthogonalization cases distortion to out-of-plane D 2d structure 25

Li 10 get closest packed structure 26

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 27

Crystalline properties of B column 28

CH x /Ni(111) Structures, Energetics, and Reaction Barriers for CHx Bound to the Nickel (111) Surface Mueller, JE; van Duin, ACT and Goddard, WA J. Phys. Chem. C, 113 (47): 20290-20306 (2009) wag 828 Ch120a-Goddard-L24 copyright 2011 William A. Goddard III, all rights reserved 29