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Encyclopedia of Physical Science and Technology EN003D-147 June 13, 2001 22:58

748 Coordination Compounds

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FIGURE 5 Distributions of electrons for ions with d –d configurations, where
E (e − t 2g ) is large.
∗
g
together under the name diamagnetism). Lone (unpaired) 1. s ↔ p, p ↔ d (etc.) atomic transitions are allowed,
electrons give large magnetic moments µ> 0 (param- but p ↔ p, d ↔ d are not; in more general terms, g ↔ u is
agnetism) interacting strongly with an applied magnetic allowed, but g ↔ g, u ↔ u are forbidden.
field, 2. The spin multiplicity does not change in an allowed
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transition. It is for this reason that all high-spin d systems
µ = [n(n + 2)] 1/2 (43)
are at best weakly colored: There is only the one possi-
wheren isthenumberofunpairedelectrons:µisinunitsof ble spin-parallel arrangement of five electrons in five d
Bohr magnetons (BM). Taking iron(III) as an example, the orbitals, so any transition must be to a state with differ-
3
high-spin (weak-field; see Fig. 4) configuration (t 2g ) (e g ) 2 ent spin multiplicity. Coordination compounds of Mn 2+
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with five unpaired electrons as in ferric alum, where the (3d ) are usually in consequence very pale. Notice that
3+
coordination sphere of the iron is [Fe(OH 2 ) 6 ] ,gives this doubly forbidden character is true for any octahedral
µ = (5 × 7) 1/2 = 35 1/2 = 5.9 BM per iron. For the low- six-coodinated high-spin ion with five d-electrons. Exam-
spin (strong-field; see Fig. 5) ferricyanide ion, where the ples include [Fe(OH 2 ) 6 ] 3+ in alums, which is a weak field
3−
0
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iron(III) has the configuration (t 2g ) (e g ) , with only one environment, but not, of course, [Fe(CN) 6 ] , which has
unpaired electron, µ = 3 1/2 = 1.73 BM. A more system- its five d-electrons paired.
atic name for this spin-paired ion is hexacyanoferrate(III).
From the first rule (sometimes called the Laporte rule),
any d–d transition in a centrosymmetric molecule is weak.
D. Colors Compared with dyestuffs (often with molar extinction co-
efficient ε ∼ 50,000), complex compounds are poor ab-
Aswithanyotherclassofmatter,ifanenergygapinacom-
sorbers of photons.
plex compound matches the energy of an incident photon,
So far, only the electronic configurations for regular
absorption occurs. In many coordination compounds, the
octahedral coordination have been given, and color has
quantum required for excitation from the ground state is
been described in terms of excitation of an electron by
of visible light, so that these compounds are of many col-
a quantum of visible light from the ground sate to an
ors, often of great beauty. Two chief selection rules decide
upper state. The size of the gap E in energy separating
which of all the possible transitions occur:
the ground and upper states controls the color (E = hν).
The larger the gap, the greater the energy of the photon
TABLE III Occupancy of Orbitals in High- and Low-Spin
Octahedral Coordination Compounds a required to promote an electron across it. The gap de-
pends on the strength of the M ← L bonds along the axes
d 1 d 2 d 3 d 4 d 5 d 6 d 7 d 8 d 9
(see Fig. 3).
In general, descending a triad of transition elements,
High spin
like cobalt, rhodium, iridium [where the M 3+ ions have
e ∗ — — — — — 1 2 3 4
g 6 6 6
t 2g 1 2 3 4 5 5 5 5 5 the configurations (3d) , (4d) , (5d) , respectively], the
3+
energy gap
E in analogous species, say M(NH 3 ) ,
Unpaired electrons (HS) 1 2 3 4 5 4 3 2 1 6
increases, as in Table IV. This means, of course, that
S 2 3 4 5 6 5 4 3 2
the compounds become less obviously colored; even
Low spin
the lowest-energy spin-allowed d–d transitions (5d → 5d)
e g — — — — — — 1 2 3
for molecules containing third-row elements go into the
t 2g 1 2 3 4 5 6 6 6 6
ultraviolet.
Unpaired electrons (LS) 1 2 3 2 1 0 1 2 1
Taking one metal ion, variation of color arises from
S 2 3 4 3 2 1 2 3 2
the same cause, the variation of the energy gap. For the
Difference (HS – LS) 0 0 0 2 4 4 2 0 0
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electronic configuration d in the coordination complexes
a HS, High spin; LS, low spin, S denotes spin multiplicity. of chromium(III), for the lowest-energy transition arising