11: metal bonding & band theory

1. Main structural and electronic features of metals

Form periodic structures similar to ionic crystals; all atoms are identical; electrons are delocalized (shared by all atoms in the crystal); metallic bonding is what holds the metal together

2. Main macroscopic physical properties of metals

Can be deformed (plastic); conductors of electricity and heat; luster (shiny, reflect light)

3. Basic premises of the Electron Sea Model

Metals have low electronegativity values → weak hold on their few valence electrons → share valence electrons with the whole collection of atoms; fixed cations sitting in a "sea" of free-flowing, delocalized electrons

4. How the Electron Sea Model explains metal properties

Thermal conduction: heat raises electron KE, electrons collide with other electrons and transfer/share energy → temp rises. Electrical conduction: chaotic electron motion becomes directional in an electric field or difference in potential. Plasticity: electrons act as a cushion, so cations can rearrange and electrons accommodate (unlike ionic compounds, where ions are "stuck" in position and are hard, rigid, brittle). Luster: free electrons absorb photons of visible light, get excited, and re-emit the same photons → shiny

5. Molecular orbitals and how they form (MO Theory)

Orbitals that belong to the entire molecule, formed by contribution of ALL the atomic orbitals in it; number of MOs = number of AOs combined (one MO per AO); each MO holds 0, 1, or 2 electrons; explains more properties than valence bond theory

6. Bonding vs. antibonding orbitals

Bonding orbital: lower energy than the original atomic orbitals. Antibonding orbital: higher energy than the original atomic orbitals, has at least one nodal plane (region with zero electron density) between the atoms, labeled with *

7. Constructive vs. destructive combinations

Constructive: AOs with the same phase overlap → bonding orbital. Destructive: AOs with different phases overlap → antibonding orbital

8. Two schemes for forming antibonding orbitals

(1) Add two orbitals that already have opposite phases; (2) subtract two orbitals with the same phase, where the negative sign "flips" the phases of the second orbital. Both give the same antibonding orbital

9. How p orbitals form either pi or sigma MOs

Side-by-side p orbitals form π orbitals: nodal plane containing the two bonded nuclei, electron density above and below. End-to-end p orbitals form σ orbitals: electron density roughly cylindrical between the two nuclei, no nodal plane

10. Meaning of σs, σs, σp, σp, πp, πp*

σ or π describes how the electron density is distributed (σ = cylindrical between nuclei, no nodal plane; π = density above/below a nodal plane containing the nuclei); subscript s or p = the atomic orbitals that were combined; * = antibonding

11. AO combinations that give σs, σs, σp, σp, πp, πp*

σs = s + s (constructive); σs* = s − s (destructive); σp = end-to-end p + p; σp* = end-to-end p − p; πp = side-by-side p + p; πp* = side-by-side p − p

12. Structure of an MO diagram

3 columns: the 2 outside columns are the contributing atomic orbitals, the center column is the MOs produced by combining them; energy increases upward; # MOs = # AOs combined; fill electrons bottom to top (2 per orbital, Aufbau, Hund's rule: only pair when forced to); bond order = (# bonding e− − # antibonding e−)/2, where bond order > 0 means stable and more bonds = more stable

13. Paramagnetism

Substance has unpaired electrons in its MO diagram and is weakly attracted by magnetic fields (e.g., O2 suspended between magnet poles)

14. How to tell if a substance is paramagnetic

Build its MO diagram: if there are any unpaired electrons, it is paramagnetic

15. Diamagnetism

Substance has all electrons paired in its MO diagram (most substances) and is weakly repelled by magnetic fields (e.g., bismuth levitating on a magnet)

16. How to tell if a substance is diamagnetic

Build its MO diagram: if all electrons are paired, it is diamagnetic

17. What a band is and how it forms

Combining orbitals from a huge number of atoms creates MOs whose energy separations become so small they form a continuum, called a band; bands reveal whether a material is a conductor, insulator, or semiconductor

18. Valence band

Band formed by the valence electrons; the highest occupied band (half-occupied in Na)

19. Conduction band

The first empty band; it can overlap with the valence band

20. Conditions for a material to conduct electricity

Electrons must move freely: they must be in a partially filled valence band or be able to access the conduction band

21. Why metals are good electricity conductors

In most metals the valence band is either not totally filled or overlaps with the conduction band, so electrons can move freely

22. Band gap

The energy separation between the valence band and the conduction band (units: kJ/mol or eV; 1 eV = 96.49 kJ/mol)

23. Why some materials are insulators

Band gap ≥ about 3.5 eV and the valence band is not partially filled, so electrons cannot jump to the conduction band

24. Semiconductor

Material with a band gap smaller than about 3.5 eV, small enough that electrons can jump into the conduction band; conductivity depends on temperature

25. How semiconductors become conductors

Excitation (e.g., heat) promotes electrons into the empty conduction band, where they can move, and leaves holes in the valence band that give valence electrons room to move

26. Elemental semiconductors

Semiconductors made of a single type of atom, all from group 14 (C, Si, Ge, Sn, Pb); band gap decreases down the group (C at 5.5 eV acts as an insulator, Pb at 0 acts as a conductor)

27. Compound semiconductors

Semiconductors made of two or more types of atoms (e.g., GaAs, ZnSe, AlP)

28. Doping

Adding small amounts of impurities (dopants) to a semiconductor to increase its conductivity; dopants come from the same row but a different column, so they are about the same size with a different number of valence electrons

29. Intrinsic semiconductor

A semiconductor in its natural (undoped) state

30. Extrinsic semiconductor

A doped semiconductor

31. n-type semiconductor

Doped with atoms that have MORE valence electrons than the host (e.g., Si doped with P)

32. p-type semiconductor

Doped with atoms that have FEWER valence electrons than the host (e.g., Si doped with B or Ga)

33. Why n-type conducts better than its intrinsic semiconductor

The extra electrons from the dopant (e.g., P donor level only ~4 kJ/mol below the Si conduction band) easily move into the conduction band

34. Why p-type conducts better than its intrinsic semiconductor

The dopant creates a new acceptor level just above the valence band (Ga ~7 kJ/mol above Si's); valence electrons move into it, leaving holes in the valence band that other electrons can move into, creating conduction