Crystal Field Theory: Understanding Colors and Magnetic Properties of Metal Complexes, Study notes of Chemistry

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 (โˆ†0). 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
- the colors and magnetic properties of metal complexes are related to the d-orbitals
they possess
- crystal field theory attempts to explain these phenomena thru electrostatic
interactions
- octahedral complexes
-- 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_z2
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, โˆ†0 = hc/ฮป where h = 6.63 x 10-34 Js and
c = 3.00 x 108 m/s
- back to color - e.g. [Ti(H2O)5]3+ (500 nm)
-- โˆ†E = โˆ†0 therefore the absorption energy is the amount of energy needed to
overcome the crystal field so to speak
-- this is the relationship btwn CFT and the complex color
- high spin vs. low spin
-- recall that when we ionize a transition metal the first e-'s to go are the 4s
not the 3d
-- we call the metallic ion a dn - e.g. Fe3+ is a d5 because it has 5 e-'s in the
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*** Crystal Field Theory**

  • the colors and magnetic properties of metal complexes are related to the d-orbitals they possess
  • crystal field theory attempts to explain these phenomena thru electrostatic interactions
  • octahedral complexes

-- 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, โˆ† 0 = hc/ฮป where h = 6.63 x 10-34^ Js and c = 3.00 x 10^8 m/s

  • back to color - e.g. [Ti(H 2 O) 5 ]3+^ (500 nm) -- โˆ†E = โˆ† 0 therefore the absorption energy is the amount of energy needed to overcome the crystal field so to speak

-- this is the relationship btwn CFT and the complex color

  • high spin vs. low spin -- recall that when we ionize a transition metal the first e-'s to go are the 4s not the 3d -- we call the metallic ion a dn^ - e.g. Fe3+^ is a d^5 because it has 5 e-'s in the

d-orbitals -- depending on the magnitude of โˆ† 0 and the number of d e-'s, the metal center is refer to as low spin or high spin -- when โˆ† 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 < โˆ† 0 the system is low spin -- when โˆ† 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 > โˆ† 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

  • high field vs weak field -- depending on the identity of the ligand attached to the metal center โˆ† 0 will be large or small -- weak-field ligands: produce small electrostatic repulsion btwn the lp and the d- orbitals --- this leads to โˆ† 0 which is small --- when โˆ† 0 is small the PE is higher and therefore the system will more likely be high spin in nature --- examples of weak-field ligands: halides (I-, Br-, Cl-) -- strong-field ligands: produce large electrostatic repulsion btwn the lp and the d- orbitals --- this lead to a large โˆ† 0 --- therefore the PE < โˆ† 0 and the system will be low spin --- examples: ethylenediamine (en) and cyanide (CN-) -- spectrochemical series ranks the ligands in order of the โˆ† 0 (weak field) I-^ < Br-^ < S-^ < SCN-^ < Cl-^ < NO 3 -^ < F-^ < OH-^ < C 2 O 4 2-^ < H 2 O < NCS-^ < CH 3 CN < NH 3 < en < bipy < phen < NO2-^ < PPh3 < CN-^ < CO (strong-field)

-- 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 โˆ† 0 and therefore the shorter the ฮป

-- for the high spin case, CFSE โ‰ค 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 โ‰ฅ 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