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Crystal field theory (cft) explains the colors and magnetic properties of metal complexes through electrostatic interactions. This theory focuses on octahedral complexes, their d-orbitals, and the crystal field splitting energy (โ0). Cft also covers high spin vs. Low spin states and the influence of weak vs. Strong field ligands. Spectrochemical series and tanabe-sugano diagrams are used to predict absorption energies and number of peaks in uv-vis spectra.
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*** Crystal Field Theory**
-- recall what an octahedral looks like and the shapes of the d-orbitals -- we know the bond between the metal center and a ligand occurs thru the donation of a lone pair (lp) of the ligand donor atom to the central metal -- if we think of this lp approaching the d-orbitals along the corner points of the octahedral there will be more repulsion btwn the lp and the d-orbital that is pointing toward one of these corners -- the 5 d-orbitals no longer have the same energy - the d_x2-y2 and d_z orbitals are higher in energy than the d_xy, d_xz, and d_yz due to the increased repulsive energy
-- the difference in energy btwn the two sets of orbitals is the crystal field splitting energy, โ 0 = hc/ฮป where h = 6.63 x 10-34^ Js and c = 3.00 x 10^8 m/s
-- this is the relationship btwn CFT and the complex color
d-orbitals -- depending on the magnitude of โ 0 and the number of d e-'s, the metal center is refer to as low spin or high spin -- when โ 0 is large, the d_x^2 -y^2 & d_z^2 are much higher in E than the other three then the system is low spin --- e-'s pair in the lower orbitals before jumping to higher ones --- another consideration is pairing energy, PE (amount of energy needed to pair two electrons spin-up/spin down in a single atomic orbital) -> if PE < โ 0 the system is low spin -- when โ 0 is small, d_x^2 -y^2 & d_z^2 are comparable in E and so the e-'s will go to these slightly higher orbitals before pairing up - this is high spin --- in this case PE > โ 0 - it take more energy to pair than to promote -- Some metals may be both high-spin/low-spin, here are the 1st row TMs: Sc+2^ (d^1 ), Ti+2^ (d^2 ), V+2^ (d^3 ) don't have enough e-'s to make a difference btwn high-spin/low-spin Cr+2^ (d^4 ), Mn+2^ (d^5 ), Fe+2^ (d^6 ), Co+2^ (d^7 ) may be either high-spin/low-spin Ni+2^ (d^8 ), Cu+2^ (d^9 ), Zn+2^ (d^10 ) have too many e-'s to make a difference btwn high-spin/low-spin
-- Ex: Which of the following has the shortest wavelength? [Ti(H 2 O) 6 ]3+, [Ti(en) 6 ]3+, [TiCl 6 ]3+ We start by looking at the spectrochemical series and ranking them by increasing field: [TiCl 6 ]3+^ < [Ti(H 2 O) 6 ]3+^ < [Ti(en) 6 ]3+ the stronger the field the larger the โ 0 and therefore the shorter the ฮป
-- for the high spin case, CFSE โค 20, i.e. [CoF 6 ]3- the only allowable transition is 5 T 2 (^) g โ 5 Eg so we would expect to see one absorption peak in the spectrum -- for the low spin case, CFSE โฅ 20, i.e. [Co(en) 3 ]3+ we have two allowable transitions so we should see two peaks 1 1 1 1 A 1 (^) g โ T 1 (^) g A 1 (^) g โ T 2 g
-- it turns out this does in fact work pretty well at predicting spectra