IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids Experimental Aspects (a) Electrical Conductivity – (thermal or optical) band gaps; (b) Magnetic Susceptibility – localized or itinerant; para- or diamagnetic; (c) Heat Capacity – specific heat due to conduction electrons; lattice; (d) Cohesive Energy – energy required to convert M(s) to M(g); (e) Spectroscopy – XPS, UPS (for example); (f) Phase Changes – under temperature or pressure variations

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids Experimental Aspects (a) Electrical Conductivity – (thermal or optical) band gaps; (b) Magnetic Susceptibility – localized or itinerant; para- or diamagnetic; (c) Heat Capacity – specific heat due to conduction electrons; lattice; (d) Cohesive Energy – energy required to convert M(s) to M(g); (e) Spectroscopy – XPS, UPS (for example); (f) Phase Changes – under temperature or pressure variations Theoretical Aspects (a) Electronic Density of States (DOS curves) – occupied and unoccupied states; (b) Electron Density – where does electronic charge “build up” in a solid? (c) Analysis of DOS – overlap (bonding) populations, charge partitioning,… (d) Band structure – energy dispersion relations; (e) Equations of State – E(V) curves for various structures; (f) Phonon DOS – vibrational states of crystals; stability of structures (  < 0 ??) (g) “Molecular Dynamics” – phase transitions; crystallization models;

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids van Arkel-Ketelaar Triangle Average Electronegativity Electronegativity Difference L.C. Allen, J. Am. Chem. Soc. 1992, 114, 1510 Hand-Outs: 1

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids van Arkel-Ketelaar Triangle Average Electronegativity Electronegativity Difference L.C. Allen, J. Am. Chem. Soc. 1992, 114, 1510  = “Configuration Energy” L.C. Allen et al., JACS, 2000, 122, 2780, 5132 Hand-Outs: 1

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids van Arkel-Ketelaar Triangle Low valence e  /orbital ratio Low IP(I) Small  High valence e  /orbital ratio High IP(I) Small  Large  Charge transfer from cation to anion Average Electronegativity Electronegativity Difference L.C. Allen, J. Am. Chem. Soc. 1992, 114, 1510 Hand-Outs: 1

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids van Arkel-Ketelaar Triangle Electrical Conductors Paramagnetic; Itinerant magnetism Soft – malleable, ductile Electrical Insulators Diamagnetic Low boiling points Electrical Insulators; Conducting liquids Diamagnetic; Localized magnetism Brittle Average Electronegativity Electronegativity Difference L.C. Allen, J. Am. Chem. Soc. 1992, 114, 1510 Hand-Outs: 1

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids van Arkel-Ketelaar Triangle Elect. Semiconductors / Semimetals Diamagnetic “Hard” – Brittle Electrical Semiconductors Diamagnetic “Hard” – Brittle Elect. Semiconductors / Semimetals Diamagnetic “Hard” – Brittle L.C. Allen, J. Am. Chem. Soc. 1992, 114, 1510 Hand-Outs: 1

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids Schrödinger’s Equation:   {n} = E {n}  {n}  :“Hamiltonian” = Energy operator Kinetic + Potential energy expressions; external fields (electric, magnetic)  {n} :Electronic wavefunctions (complex)  (r) =   * {n}  {n} dV: Charge density (real) E {n} : Electronic energies Temperature: How electronic states are occupied – Maxwell-Boltzmann Distribution:f(E) = exp[  (E  E F )/kT] Fermi-Dirac Distribution:f(E) = [1+exp(  (E  E F )/kT)]  1

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids Schrödinger’s Equation:   {n} = E {n}  {n} “A solid is a molecule with an infinite number (ca ) of atoms.”

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids Schrödinger’s Equation:   {n} = E {n}  {n} “A solid is a molecule with an infinite number (ca ) of atoms.” Molecular Solids: on molecular entities (as in gas phase); packing effects?

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids Schrödinger’s Equation:   {n} = E {n}  {n} “A solid is a molecule with an infinite number (ca ) of atoms.” Molecular Solids: on molecular entities (as in gas phase); packing effects? Extended Solids: how to make the problem tractable? (a) Amorphous (glasses): silicates, phosphates – molecular fragments, tie off ends with simple atoms, e.g., “H”; (b) Quasiperiodic: fragments based on building units, tie off ends with simple atoms, e.g., “H”; (c) Crystalline: unit cells (translational symmetry) – elegant simplification!

IV. Electronic Structure and Chemical Bonding J.K. Burdett, Chemical Bonding in Solids Electronic Structure of Si: Fermi Level Electronic Band StructureElectronic Density of States What can we learn from this information?