Bonding in complexes of d-block metal ions – Crystal Field Theory. energy egeg t 2g Co 3+ ion in gas-phase (d 6 ) Δ Co(III) in complex 3d sub-shell d-shell split by presence of ligand donor-atoms

The d-orbitals: the t 2g set the e g set d yz d xy d xz dz2dz2 d x 2- y 2 xxx xx zzz zz yyy yy

Splitting of the d sub-shell in octahedral coordination d yz dz2dz2 d x 2- y 2 the three orbitals of the t 2g set lie between the ligand donor-atoms (only d yz shown) the two orbitals of the e g set lie along the Cartesian coordinates, and so are adjacent to the donor atoms of the ligands, which raises the e g set in energy z zz blue = ligand donor atom orbitals the e g set the t 2g set y y y x x x

energy egeg t 2g Co 3+ ion in gas-phase (d 6 ) Δ Co(III) in octahedral complex 3d sub-shell d-shell split by presence of ligand donor-atoms Splitting of the d sub-shell in an octahedral complex

The crystal field splitting parameter (Δ) Different ligands produce different extents of splitting between the e g and the t 2g levels. This energy difference is the crystal field splitting parameter Δ, also known as 10 Dq, and has units of cm -1. Typically, CN - produces very large values of Δ, while F - produces very small values. [Cr(CN) 6 ] 3- [CrF 6 ] 3- egeg egeg t 2g energy Δ = 26,600 cm -1 Δ = 15,000 cm -1

High and low-spin complexes: energy egeg egeg t 2g low-spin d 6 electrons fill the t 2g level first. In this case the complex is diamagnetic high-spin d 6 electrons fill the whole d sub- shell according to Hund’s rule The d-electrons in d 4 to d 8 configurations can be high-spin, where they spread out and occupy the whole d sub-shell, or low-spin, where the t 2g level is filled first. This is controlled by whether Δ is larger than the spin- pairing energy, P, which is the energy required to take pairs of electrons with the same spin orientation, and pair them up with the opposite spin. Δ > P Δ < P Paramagnetic 4 unpaired e’s diamagnetic no unpaired e’s

energy egeg egeg t 2g low-spin d 5 ([Fe(CN) 6 ] 3- ) electrons fill the t 2g level first. In this case the complex is paramagnetic high-spin d 5 ([Fe(H 2 O) 6 ] 3+ ) electrons fill the whole d sub-shell according to Hund’s rule For d 5 ions P is usually very large, so these are mostly high-spin. Thus, Fe(III) complexes are usually high-spin, although with CN - Δ is large enough that [Fe(CN) 6 ] 3- is low spin: (CN - always produces the largest Δ values) Δ > P Δ < P Paramagnetic 5 unpaired e’s paramagnetic one unpaired e High and low-spin complexes of d 5 ions: [Fe(CN) 6 ] 3- Δ = 35,000 cm -1 P = 19,000 cm -1 [Fe(H 2 O) 6 ] 3+ Δ = 13,700 cm -1 P = 22,000 cm -1

energy egeg egeg t 2g low-spin d 7 ([Ni(bipy) 3 ] 3+ ) The d-electrons fill the t 2g level first, and only then does an electron occupy the e g level. high-spin d 7 ([Co(H 2 O) 6 ] 3+ ) electrons fill the whole d sub-shell according to Hund’s rule The d 7 metal ion that one commonly encounters is the Co(II) ion. For metal ions of the same electronic configuration, Δ tends to increase M(II) < M(III) < M(IV), so that Co(II) complexes have a small Δ and are usually high spin. The (III) ion Ni(III) has higher values of Δ, and is usually low-spin. Δ > P Δ < P Paramagnetic 3 unpaired e’s paramagnetic one unpaired e High and low-spin complexes of d 7 ions: [Ni(bipy) 3 ] 3+ [Co(H 2 O) 6 ] 2+ Δ = 9,300 cm -1

energy egeg egeg t 2g low-spin d 6 ([Co(CN) 6 ] 4- ) electrons fill the t 2g level first. In this case the complex is diamagnetic high-spin d 5 ([CoF 6 ] 3- ) electrons fill the whole d sub-shell according to Hund’s rule For d 6 ions Δ is very large for an M(III) ion such as Co(III), so all Co(III) complexes are low-spin except for [CoF 6 ] 3-.high-spin. Thus, Fe(III) complexes are usually high-spin, although with CN - Δ is large enough that [Fe(CN) 6 ] 3- is low spin: (CN - always produces the largest Δ values) Δ >> P Δ < P Paramagnetic 4 unpaired e’s diamagnetic no unpaired e’s High and low-spin complexes of some d 6 ions: [Co(CN) 6 ] 3- Δ = 34,800 cm -1 P = 19,000 cm -1 [CoF 6 ] 3- Δ = 13,100 cm -1 P = 22,000 cm -1

The spectrochemical series: One notices that with different metal ions the order of increasing Δ with different ligands is always the same. Thus, all metal ions produce the highest value of Δ in their hexacyano complex, while the hexafluoro complex always produces a low value of Δ. One has seen how in this course the theme is always a search for patterns. Thus, the increase in Δ with changing ligand can be placed in an order known as the spectrochemical series, which in abbreviated form is: I - < Br - < Cl - < F - < OH - ≈ H 2 O < NH 3 < CN -

The place of a ligand in the spectrochemical series is determined largely by its donor atoms. Thus, all N-donor ligands are close to ammonia in the spectrochemical series, while all O-donor ligands are close to water. The spectrochemical series follows the positions of the donor atoms in the periodic table as: CNOF PSCl Br I The spectrochemical series: S-donors ≈ between Br and Cl very little data on P-donors – may be higher than N-donors ? spectrochemical series follows arrows around starting at I and ending at C

Thus, we can predict that O-donor ligands such as oxalate or acetylacetonate will be close to water in the spectrochemical series. It should be noted that while en and dien are close to ammonia in the spectrochemical series, 2,2’bipyridyl and 1,10-phenanthroline are considerably higher than ammonia because their sp 2 hybridized N-donors are more covalent in their bonding than the sp 3 hybridized donors of ammonia. The spectrochemical series:

For the first row of donor atoms in the periodic table, namely C, N, O, and F, it is clear that what we are seeing in the variation of Δ is covalence. Thus, C-donor ligands such as CN - and CO produce the highest values of Δ because the overlap between the orbitals of the C- atom and those of the metal are largest. For the highly electronegative F - ion the bonding is very ionic, and overlap is much smaller. For the heavier donor atoms, one might expect from their low electronegativity, more covalent bonding, and hence larger values of Δ. It appears that Δ is reduced in size because of π –overlap from the lone pairs on the donor atom, and the t 2g set orbitals, which raises the energy of the t 2g set, and so lowers Δ. The bonding interpretation of the spectrochemical series:

When splitting of the d sub-shell occurs, the occupation of the lower energy t 2g level by electrons causes a stabilization of the complex, whereas occupation of the e g level causes a rise in energy. Calculations show that the t 2g level drops by 0.4Δ, whereas the e g level is raised by 0.6Δ. This means that the overall change in energy, the CFSE, will be given by: CFSE =Δ(0.4 n ( t 2g ) -0.6 n ( e g )) where n ( t 2g ) and n ( e g ) are the numbers of electrons in the t 2g and e g levels respectively. Crystal Field Stabilization Energy (CFSE):

The CFSE for some complexes is calculated to be: [Co(NH 3 ) 6 ] 3+ : [Cr(en) 3 ] 3+ egeg egeg t 2g Δ = 22,900 cm -1 Δ = 21,900 cm -1 CFSE = 22,900(0.4 x 6 – 0.6 x 0)CFSE = 21,900(0.4 x 3 – 0.6 x 0) = 54,960 cm -1 = 26,280 cm -1 Calculation of Crystal Field Stabilization Energy (CFSE): energy

The CFSE for high-spin d 5 and for d 10 complexes is calculated to be zero: [Mn(NH 3 ) 6 ] 2+ : [Zn(en) 3 ] 3+ egeg egeg t 2g Δ = 22,900 cm -1 Δ = not known CFSE = 10,000(0.4 x 3 – 0.6 x 2)CFSE = Δ(0.4 x 6 – 0.6 x 4) = 0 cm -1 Crystal Field Stabilization Energy (CFSE) of d 5 and d 10 ions : energy

For M(II) ions with the same set of ligands, the variation of Δ is not large. One can therefore use the equation for CFSE to calculate CFSE in terms of Δ for d 0 through d 10 M(II) ions (all metal ions high-spin): Ca(II) Sc(II) Ti(II) V(II) Cr(II) Mn(II) Fe(II) Co(II) Ni(II) Cu(II) Zn(II) d 0 d 1 d 2 d 3 d 4 d 5 d 6 d 7 d 8 d 9 d 10 CFSE: 0 0.4Δ 0.8Δ 1.2Δ 0.6Δ 0 0.4Δ 0.8Δ 1.2Δ 0.6Δ 0 This pattern of variation CFSE leads to greater stabilization in the complexes of metal ions with high CFSE, such as Ni(II), and lower stabilization for the complexes of M(II) ions with no CFSE, e.g. Ca(II), Mn(II), and Zn(II). The variation in CFSE can be compared with the log K 1 values for EDTA complexes on the next slide: Crystal Field Stabilization Energy (CFSE) of d 0 to d 10 M(II) ions:

Ca 2+ Mn 2+ Zn 2+ double- humped curve Ni 2+

Log K1(EDTA) of d 0 to d 10 M(II) ions: Ca 2+ Mn 2+ Zn 2+ double- humped curve = CFSE rising baseline due to ionic contraction

Log K1(en) of d 0 to d 10 M(II) ions: double- humped curve Ca 2+ Mn 2+ Zn 2+ rising baseline due to ionic contraction = CFSE

Log K1(tpen) of d 0 to d 10 M(II) ions: Ca 2+ Mn 2+ Zn 2+ double- humped curve tpen

Irving and Williams noted that because of CFSE, the log K 1 values for virtually all complexes of first row d-block metal ions followed the order: Mn(II) Zn(II) We see that this order holds for the ligand EDTA, en, and TPEN on the previous slides. One notes that Cu(II) does not follow the order predicted by CFSE, which would have Ni(II) > Cu(II). This will be discussed under Jahn-Teller distortion of Cu(II) complexes, which leads to additional stabilization for Cu(II) complexes over what would be expected from the variation in CFSE. The Irving-Williams Stability Order: