Inorganic and Materials Chem 2

• metallic bonding is what is seen in metals • we can obtain an estimate of the strength by looking at the energy required to vaporise the metal

• fcc, bcc, hcp • when we use the word ‘bonds’ for metals, we don’t necessarily mean the standard 2-centre 2-electron bond that we tend to deal with • it usually just means the number of nearest neighbours

• we can consider it in the same way as normal covalent bonding • normally lithium is a metal but under certain conditions it can be a diatomic • Li2 has a bond strength of 238kJ/mol, i.e. formation of 1 mole is 119kJ/mol • for metallic lithium, enthalpy of atomisation is about 159kJ/mol • this shows for some elements it is more energetically favourable to have 8 slightly weaker bonds than one stronger bond

• from left to right, Zeff increases and orbital size decreases, smaller orbitals have more effective overlap, eventually it is efficient enough for localised bonding • on the right and at the bottom, orbital sizes are greater, this means that bonding is weaker so it is better to have less-directional, delocalised bonding - metals

• they both increase but the VDW radius increases slower so their ratio gets closer to 1 • in a true metal, the ratio is 1

• the energy difference between the most B MO and most AB MO increases as the number of atoms in the chain increases • at infinity the energy difference is twice that of in Li2 • this is because in Li2 all atoms only form one B or AB interaction • whereas in at an infinite chain length all atoms form 2 B or AB interactions • the separation of the orbital energies also decreases so as you tend to infinity, we end up with a virtually continuous range of MO energies - bands

• when we have a huge metallic lattice e.g. 10^23 atoms, the spacing between individual COs (crystal orbitals) is so small that there is effectively a continuous range of energies from the lowest bonding CO to the highest antibonding CO • these continuous sections are called bands NOTE: there is not really a continuous range of energy levels within a band but it is close

• you can calculate the number of energy levels within a given energy range

band width is the difference in energy between the lowest bonding orbital and highest antibonding orbital i.e. the energy range of the band • it depends on the degree of overlap possible between the AOs, (greater overlap for smaller orbitals etc.)

• the net bonding region is the bottom half of the band • the net antibonding region is the top half of the band

• COs come in degenerate pairs • one corresponds to electrons moving one way and the other corresponds to electrons moving the other way • this means for a completely filled band, there is no net movement of electrons so no conductivity • if a band is partially empty, when an electric field is applied, some electrons near the top of the filled part of the band can move into the vacant higher energy orbitals and there is a net movement of electrons • hence, a metal conducts if it has a partially filled band

• consider Be, you expect all of the 2s orbital band to be filled leading to net AB and hence monoatomic gas • This does not occur because at the equilibrium bond length there is an overlap of the 2s and 2p bands • this means the highest energy 2s band electrons move to the lowest energy 2p band places • this leads to a net lowering of energy

• at the point where the ‘HOMO’ band e.g. 2s for Be just starts to overlap with the ‘LUMO’ band e.g. 2p for Be

• have delocalised bonding with each atom typically having eight to twelve nearest neighbours. The presence of partially filled bands or overlapping bands allow conductivity

• typically have structures with fewer nearest neighbours than metals and are usually poorer conductors of electricity than true metals. • either due to presence of V small band gap or bands which overlap to a very small degree

• metals and semimetals have lower conductivity at higher temps • semiconductors have higher conductivity at higher temps

• conduct electricity poorly but the conductivity increases with temperature and when irradiated with light of a suitable wavelength • band gap of 0.1-4eV

• electrical insulators • filled conduction band has large energy gap to vacant conduction band • energy gap usually > 4eV

• the trend follows the trend in the sizes of valence orbitals • on crossing a period, Zeff increases, valence orbital size decreases, better overlap • this gives more localised bonding, fewer nearest neighbours • on descending a group, n increases so valence orbital gets bigger so tends towards metals

• H2 molecules have B and AB MOs, when gaseous, the atoms are very far apart and do not easily interact • when the pressure is increased and they are forced together, the MOs from different molecules start to interact to form new orbitals at different energies • eventually we obtain bands • the lower energy sigma band and higher energy sigma* band are totally separated with a large energy gap so it is a conductor (unless under extreme pressure)

• our solid structure still contains molecules but all aligned regularly like in a solid • bottom of sigma band = many H2 molecules each with bonding MOs all aligned such that there are no nodes between molecules • top of sigma band = many H2 molecules with bonding MOs but with the maximum number of nodes between molecules • bottom of sigma* band = many H2 molecules with antibonding MOs but with no nodes between molecules • top of sigma* band = many H2 molecules with antibonding Mos and the max number of nodes between molecules

• in reality it all gets v complicated, v quickly for 3D structures • but we can take a simplified view and do the same thing • i.e. with all sigma in phase at bottom of sigma band etc.

• in graphite there are hexagonal layers of sp2 carbons, ABAB structure • each have one p-orbital contributing to a pi network over the whole molecule

• each atom has three sigma B AOs one pi B MO one pi* AB MO three sigma* AB MOs this forms bands of filled sigma band filled pi band empty pi* band empty sigma* band