Inorganic and Materials Chem 1

1) Constituent AOs must have suitable symmetry to interact 2) The constituent AOs must have similar energies to for significant bonding and antibonding interactions to occur 3) Even if the orbitals are close in energy, higher degrees of overlap will give a better interaction - generally smaller orbitals

• increasing atomic number • aligned vertically according to number of valence electrons, these generally have similar chemical properties - groups • arranged horizontally by highest energy level of electrons - periods

• a point charge

• s,p,d,f blocks • they roughly correspond to the subshell of the highest energy valence electrons • this is not always the case there can be exceptions so the groups often indicate similar properties e.g. Lu, Lr

• their chemical properties don’t match the s-block

• ‘Exchange Interaction Energy’ is a quantum mechanical phenomena which explains the ‘Half-shell stability’ found in Cr and Cu Cr: ….4s1, 3d5 Cu: ….4s1, 3d10

that the s and d valence orbital energies are similar that the s,d,f valence orbital energies can be similar for the f-block energies

• ‘main group’ = s,p block • ‘transition metals’ = d block • ‘rare earths’ = 4f elements

• we must also consider the repulsive electron-electron interactions • the elements can attain a lower energy by having different orbital occupancies, this is where 4s2 3dn has higher energy than 4s0 3d(n+2) 6s2, 5d0, 4fn has lower energy than 6s0, 5d0, 4f(n+2)

• the ‘Madelung rule’ • consider all n (principal quantum number) and all relevant l (angular momentum number; s = 0, p=1 etc.) • the lowest n+l orbitals fill first • if they have the same value then the lower n value ‘wins’

• calculated orbital energies using how well valence orbital energies match • determining Zeff • orbital energy is approximately equal to -1 x ionisation energy, this can be ,measured using photoelectron spectroscopy in the gas phase • standard half cell potentials • a cover all number called electronegativity can be determined • we will also look at electron attachment enthalpy

• screening • penetration • d and f block contractions • relativistic effects • exchange interaction

we can use the graph of orbital energies across the period to correctly draw the MO diagram

E = -RH (Zeff^2 / n^2) • the two variables are principal quantum number n and effective nuclear charge Zeff

• Screening: electrons don’t make perfect screens. • the energy of a given orbital decreases as the effective nuclear charge increases there are two main trends: 1) moving down a group, orbital energy increases (less -ve) because n^2 increases faster than Zeff^2, lower orbitals are good at screening higher orbitals and the radius/RDF max for higher orbitals are further from the nucleus so electrostatic force is greater 2) moving across a period, orbital energies generally decrease, e.g. period 4: from Sc to Cu, the 4s energy decreases slowly because the 3d orbital screens the 4s well from Ga to Kr the 4s decreases rapidly because electrons are now added to the 4p, not screening effectively, i.e. screening is imperfect and Zeff increases • OVERALL, Screening is always imperfect so Zeff increases

• Penetration: orbitals with the same n but different l have different rates of decrease in energy as Zeff increases • for a given n, s,p,d.. orbital energies are NOT degenerate, because s orbitals penetrate the nucleus more than p orbitals, i.e. more of their RDF is closer to the nucleus • this means for any given n, as Zeff increases, the energy of the s orbitals decreases faster than the energy of the p orbitals • this explains why no s-p mixing occurs for higher Z atoms

• d and f block contractions - a d or f section in a given period causes lowered orbital energies for elements that come after • adding a full d or f subshell means that although the same number of electrons as protons have been ‘added’ the following orbitals are lowered in energy because they do not screen perfectly so any ‘later’ subshells are lower in energy than expected

• relativistic effects: - the 6s orbital energy is lowered in period 6 elements because of the very large nuclear charge that has lowered the 1s orbital energy • 1s has its RDF max. closest to nucleus, QM says if 1s orbital’s energy and radius are decreased, all other s orbitals have lower energy and radius too • the lowering of 1s orbital’s energy technically occurs generally for any higher nuclear charge but is only noticeable in s AOs once you reach 6s • it comes from the Bohr-Sommerfeld model where electrons orbit at speed c x Z/137 so the greater z is, the faster the electron travels so the greater its mass so the greater the Rydberg constant RH so the lower the orbital energy

• secondary consequence is that lower energy s AOs are slightly better at screening so valence d and f orbitals (in particular) are raised in energy

• Exchange Interaction Energy: - QM effect that means more parallel (unpaired) electron spins gives lower energy - from Pauli exclusion principle - lowering of energy is related to nC2 where n is the number of parallel (unpaired) spins in the AOs - this is particularly noticeable in Cr and Cu where they have ‘half filled shells’

• the overall energy of the atom is lowered • this is despite the extra energy required for an electron to sit in 3d rather than 4s, this is higher energy because 3d is anyway and it is more contracted than 4s so there’s more coulombic repulsion if 3d contains more electrons • equally the 4s energy is raised slightly because the 3d screens better with more electrons • HOWEVER, the reduction in exchange interaction energy is dominant

• initially the 3d orbital is higher in energy than the 4s orbital, this explains why K and Ca have 4s1 and 4s2 • following that, the 3d orbital becomes lower in energy than 4s but we keep a 4s2 arrangement for all following atoms • this is because the 3d AOs are quite contracted so there is more electron-electron repulsion (if they contain more electrons) than the 4s orbital • hence, it is more energetically favourable to fill 4s first

• the 5 energy factors can cause complex relationships which can deviate significantly even for the isoelectronic ions

• Ionisation energies • Standard electrode potentials