Chapter 13. The electronic spectra of complexes The electronic spectra of atoms 13.1 Spectroscopic terms 13.2 Terms of a d2 configuration The electronic spectra of complexes 13.3 Ligand-field transitions 13.4 Charge-transfer bands 13.5 Selection rules and intensities 13.6 Luminescence 13.7 Spectra of f-block complexes 13.8 Circular dichroism 13.9 Electron paramagnetic resonance Bonding and spectra of M-M bonded compounds 13.10 The ML5 fragment 13.11 Binuclear complexes Spectroscopic terms The Russell Saunders Coupling Scheme Quantum Numbers

Electrons in an atom reside in shells characterised by a particular value of n, the Principal Quantum Number. Within each shell an electron can occupy an orbital which is further characterised by an Orbital Quantum Number, l, where l can take all values in the range:

l = 0, 1, 2, 3, ... , (n-1),

traditionally termed s, p, d, f, etc. orbitals.

Each orbital has a characteristic shape reflecting the motion of the electron in that particular orbital, this motion being characterised by an angular momentum that reflects the angular velocity of the electron moving in its orbital.

A quantum mechanics approach to determining the energy of electrons in an element or ion is based on the results obtained by solving the Schrödinger Wave Equation for the H-atom. The various solutions for the different energy states are characterised by the three quantum numbers, n, l and ml.

ml is a subset of l, where the allowable values are: ml = l, l-1, l-2, ..... 1, 0, -1, ....... , -(l-2), -(l-1), -l.

There are thus (2l +1) values of ml for each l value, i.e. one s orbital (l = 0), three p orbitals (l = 1), five d orbitals (l = 2), etc.

There is a fourth quantum number, ms, that identifies the orientation of the spin of one electron relative to those of other electrons in the system. A single electron in free space has a fundamental property associated with it called spin, arising from the spinning of an asymmetrical charge distribution about its own axis. Like an electron moving in its

orbital around a nucleus, the electron spinning about its axis has associated with its motion a well defined angular momentum. The value of ms is either + ½ or - ½.

In summary then, each electron in an orbital is characterised by four quantum numbers:

Quantum Numbers

n Principal Quantum Number - largely governs size of orbital and its energy

l Azimuthal/Orbital Quantum Number - largely determines shape of orbital

ml Magnetic Quantum Number

ms Spin Quantum Number - either + ½ or - ½ for single electron

Russell Saunders coupling

The ways in which the angular momenta associated with the orbital and spin motions in many-electron-atoms can be combined together are many and varied. In spite of this seeming complexity, the results are frequently readily determined for simple atom systems and are used to characterise the electronic states of atoms.

The interactions that can occur are of three types.

• spin-spin coupling • orbit-orbit coupling • spin-orbit coupling

There are two principal coupling schemes used:

• Russell-Saunders (or L - S) coupling • and j - j coupling.

In the Russell Saunders scheme it is assumed that spin-spin coupling > orbit-orbit coupling > spin-orbit coupling.

This is found to give a good approximation for first row transition series where J coupling is ignored, however for elements with atomic number greater than thirty, spin-orbit coupling becomes more significant and the j-j coupling scheme is used.

Spin-Spin coupling S - the resultant spin quantum number for a system of electrons. The overall spin S arises from adding the individual ms together and is as a result of coupling of spin quantum numbers for the separate electrons.

Orbit-Orbit coupling L - the total orbital angular momentum quantum number defines the energy state for a system of electrons. These states or term letters are represented as follows:

Total Orbital Momentum

L 0 1 2 3 4 5 S P D F G H

Spin-Orbit coupling Coupling occurs between the resultant spin and orbital momenta of an electron which gives rise to J the total angular momentum quantum number. Multiplicity occurs when several levels are close together and is given by the formula (2S+1).

The Russell Saunders term symbol that results from these considerations is given by:

(2S+1)L As an example, for a d1 configuration: S= + ½, hence (2S+1) = 2 L=2 and the Ground Term is written as 2D

The Russell Saunders term symbols for the other free ion configurations are given in the Table below.

Terms for 3dn free ion configurations

Configuration Ground Term Excited Terms

d1,d9 2D - d2,d8 3F 3P, 1G,1D,1S d3,d7 4F 4P, 2H, 2G, 2F, 2 x 2D, 2P

d4,d6 5D 3H, 3G, 2 x 3F, 3D, 2 x 3P, 1I, 2 x 1G, 1F, 2 x 1D, 2 x 1S

d5 6S 4G, 4F, 4D, 4P, 2I, 2H, 2 x 2G, 2 x 2F, 3 x 2D, 2P, 2S

Note that dn gives the same terms as d10-n

Hund's Rules The Ground Terms are deduced by using Hund's Rules. The two rules are: 1) The Ground Term will have the maximum multiplicity 2) If there is more than 1 Term with maximum multipicity, then the Ground Term will have the largest value of L.

A simple graphical method for determining just the ground term alone for the free-ions uses a "fill in the boxes" arrangement.

dn 2 1 0 -1 -2 L S Ground Term

d1 2 1/2 2D d2 3 1 3F d3 3 3/2 4F d4 2 2 5D d5 0 5/2 6S d6 ¯ 2 2 5D d7 ¯ ¯ 3 3/2 4F d8 ¯ ¯ ¯ 3 1 3F d9 ¯ ¯ ¯ ¯ 2 1/2 2D To calculate S, simply sum the unpaired electrons using a value of ½ for each. To calculate L, use the labels for each column to determine the value of L for that box, then add all the individual box values together. For a d7 configuration, then: in the +2 box are 2 electrons, so L for that box is 2*2= 4 in the +1 box are 2 electrons, so L for that box is 1*2= 2 in the 0 box is 1 electron, L is 0 in the -1 box is 1 electron, L is -1*1= -1 in the -2 box is 1 electron, L is -2*1= -2

Total value of L is therefore +4 +2 +0 -1 -2 or L=3.

Note that for 5 electrons with 1 electron in each box then the total value of L is 0. This is why L for a d1 configuration is the same as for a d6.

The other thing to note is the idea of the "hole" approach. A d1 configuration can be treated as similar to a d9 configuration. In the first case there is 1 electron and in the latter there is an absence of an electron ie a hole.

The overall result shown in the Table above is that: 4 configurations (d1, d4, d6, d9) give rise to D ground terms, 4 configurations (d2, d3, d7, d8) give rise to F ground terms and the d5 configuration gives an S ground term.

The Crystal Field Splitting of Russell-Saunders terms

The effect of a crystal field on the different orbitals (s, p, d, etc.) will result in splitting into subsets of different energies, depending on whether they are in an octahedral or tetrahedral environment. The magnitude of the d orbital splitting is generally represented as a fraction of Doct or 10Dq.

The ground term energies for free ions are also affected by the influence of a crystal field and an analogy is made between orbitals and ground terms that are related due to the angular parts of their electron distribution. The effect of a crystal field on different orbitals in an octahedral field environment will cause the d orbitals to split to give t2g and eg subsets and the D ground term states into T2g and Eg, (where upper case is used to denote states and lower case orbitals). f orbitals are split to give subsets known as t1g, t2g and a2g. By analogy, the F ground term when split by a crystal field will give states known as T1g, T2g, and A2g.

Note that it is important to recognise that the F ground term here refers to states arising from d orbitals and not f orbitals and depending on whether it is in an octahedral or tetrahedral environment the lowest term can be either A2g or T1g.

The Crystal Field Splitting of Russell-Saunders terms

in high spin octahedral crystal fields. Russell-Saunders

Terms Crystal Field Components

S A1g P T1g D Eg , T2g F A2g , T1g , T2g

G A1g , Eg , T1g , T2g H Eg , 2 x T1g , T2g I A1g , A2g , Eg , T1g , T2g

Note that, for simplicity, spin multiplicities are not included in the table since they remain the same for each term.

The table above shows that the Mulliken symmetry labels, developed for atomic and molecular orbitals, have been applied to these states but for this purpose they are written in CAPITAL LETTERS.

Mulliken Symbols

Mulliken Symbol for atomic and molecular

orbitals Explanation

a Non-degenerate orbital; symmetric to principal Cn

b Non-degenerate orbital; unsymmetric to principal Cn

e Doubly degenerate orbital t Triply degenerate orbital

(subscript) g Symmetric with respect to center of inversion

(subscript) u Unsymmetric with respect to center of inversion

(subscript) 1 Symmetric with respect to C2 perp. to principal Cn

(subscript) 2 Unsymmetric with respect to C2 perp. to principal Cn

(superscript) ' Symmetric with respect to sh (superscript) " Unsymmetric with respect to sh For splitting in a tetrahedral crystal field the components are similar, except that the symmetry label g (gerade) is absent. The ground term for first-row transition metal ions is either D, F or S which in high spin octahedral fields gives rise to A, E or T states. This means that the states are either non-degenerate, doubly degenerate or triply degenerate.

We are now ready to consider how spectra can be interpreted in terms of energy transitions between these various levels. *13.2 Terms of a d2 configuration The electronic spectra of complexes The spectra of the aqua ions for some first row transition metal ions are shown below.

13.3 Ligand-field transitions The observation of 2 or 3 peaks in the electronic spectra of d2, d3, d7 and d8 high spin octahedral complexes requires further treatment involving electron-electron interactions. Using the Russell-Saunders (LS) coupling scheme, these free ion configurations give rise to F ground states which in octahedral and tetrahedral fields are split into terms designated by the symbols A2(g), T2(g) and T1(g).

To derive the energies of these terms and the transition energies between them is beyond the needs of introductory level courses and is not covered in general textbooks[10,11]. A listing of some of them is given here as an Appendix. What is necessary is an understanding of how to use the diagrams, created to display the energy levels, in the interpretation of spectra.

Two types of diagram are available: Orgel and Tanabe-Sugano diagrams.

Use of Orgel diagrams

A simplified Orgel diagram (not to scale) showing the terms arising from the splitting of an F state is given below. The spin multiplicity and the g subscripts are dropped to make the diagram more general for different configurations.

The lines showing the A2 and T2 terms are linear and depend solely on D. The lines for the two T1 terms are curved to obey the non-crossing rule and as a result introduce a configuration interaction in the transition energy equations.

The left-hand side is applicable to d3 , d8 octahedral complexes and d7 tetrahedral complexes. The right-hand side is applicable to d2 , d7 octahedral complexes.

Looking at the d3 octahedral case first, 3 peaks can be predicted which would correspond to the following transitions:

1. 4T2g ¬4A2g transition energy = D 2. 4T1g(F) ¬4A2g transition energy = 9/5 *D - C.I. 3. 4T1g(P) ¬4A2g transition energy = 6/5 *D + 15B' + C.I.

Here C.I. represents the configuration interaction which is generally either taken to be small enough to be ignored or taken as a constant for each complex.

In the laboratory component of the course we measure the absorption spectra of some typical chromium(III) complexes and calculate the spectrochemical splitting factor, D. This corresponds to the energy found from the first transition above and as shown in Table 1 is generally between 15,000 cm-1 (for weak field complexes) and 27,000 cm-1 (for strong field complexes). Table 1. Peak positions for some octahedral Cr(III) complexes (in cm-1).

Complex n1 n2 n3 n2/n1 n1/n2 D/B Ref

Cr3+ in emerald 16260 23700 37740 1.46 0.686 20.4 13

K2NaCrF6 16050 23260 35460 1.45 0.690 21.4 13

[Cr(H2O)6]3+ 17000 24000 37500 1.41 0.708 24.5 This work

Chrome alum 17400 24500 37800 1.36 0.710 29.2 4

[Cr(C2O4)3]3- 17544 23866 ? 1.37 0.735 28.0 This work

[Cr(NCS)6]3- 17800 23800 ? 1.34 0.748 31.1 4

[Cr(acac)3] 17860 23800 ? 1.33 0.752 31.5 This work

[Cr(NH3)6]3+ 21550 28500 ? 1.32 0.756 32.6 4

[Cr(en)3]3+ 21600 28500 ? 1.32 0.758 33.0 4

[Cr(CN)6]3- 26700 32200 ? 1.21 0.829 52.4 4

For octahedral Ni(II) complexes the transitions would be:

1. 3T2g ¬3A2g transition energy = D 2. 3T1g(F) ¬3A2g transition energy = 9/5 *D - C.I. 3. 3T1g(P) ¬3A2g transition energy = 6/5 *D + 15B' + C.I.

where C.I. again is the configuration interaction and as before the first transition corresponds exactly to D.

For M(II) ions the size of D is much less than for M(III) ions (around 2/3) and typical values for Ni(II) are 6500 to 13000 cm-1 as shown in Table 2. Table 2. Peak positions for some octahedral Ni(II) complexes (in cm-1).

Complex n1 n2 n3 n2/n1 n1/n2 D/B Ref

NiBr2 6800 11800 20600 1.74 0.576 5 13

[Ni(H2O)6]2+ 8500 13800 25300 1.62 0.616 11.6 13

[Ni(gly)3]- 10100 16600 27600 1.64 0.608 10.6 13

[Ni(NH3)6]2+ 10750 17500 28200 1.63 0.614 11.2 13

[Ni(en)3]2+ 11200 18350 29000 1.64 0.610 10.6 3

[Ni(bipy)3]2+ 12650 19200 ? 1.52 0.659 17 3

For d2 octahedral complexes, few examples have been published. One such is V3+ doped in Al2O3 where the vanadium ion is generally regarded as octahedral, Table 3. Table 3. Peak positions for an octahedral V(III) complex (in cm-1).

Complex n1 n2 n3 n2/n1 n1/n2 D/B Ref

V3+ in Al2O3 17400 25200 34500 1.45 0.690 30.8 13

Interpretation of the spectrum highlights the difficulty of using the right-hand side of the Orgel diagram above for many d2 cases where none of the transitions correspond exactly to D and often only 2 of the 3 transitions are clearly observed.

The first transition can be unambiguously assigned as: 3T2g¬ 3T1g transition energy = 4/5 *D + C.I.

But, depending on the size of the ligand field (D) the second transition may be due to: 3A2g¬ 3T1g transition energy = 9/5 *D + C.I.

for a weak field or 3T1g(P) ¬ 3T1g transition energy = 3/5 *D + 15B' + 2 * C.I.

for a strong field.

The transition energies of these terms are clearly different and it is often necessary to calculate (or estimate) values of B,D and C.I. for both arrangements and then evaluate the answers to see which fits better. The difference between the 3A2g and the 3T2g (F) lines should give D. In this case D is equal to either: 25200 - 17400 = 7800 cm-1 or 34500 - 17400 = 17100 cm-1. Given that we expect D to be greater than 15000 cm-1 then we must interpret the second

transition as to the 3T2g(P) and the third to 3A2g. Further evaluation of the expressions then gives C.I. as 3720 cm-1 and B' as 567 cm-1.

Solving the equations like this for the three unknowns can ONLY be done if the three transitions are observed. When only two transitions are observed, a series of equations[14] have been determined that can be used to calculate both B and D. This approach still requires some evaluation of the numbers to ensure a valid fit. For this reason, Tanabe-Sugano diagrams become a better method for interpreting spectra of d2 octahedral complexes.

Using Tanabe-Sugano diagrams

The first obvious difference to the Orgel diagrams shown in general textbooks is that Tanabe-Sugano diagrams are calculated such that the ground term lies on the X-axis, which is given in units of D/B. The second is that spin-forbidden terms are shown and third that low-spin complexes can be interpreted as well, since for the d4 - d7 diagrams a vertical line is drawn separating the high and low spin terms.

The procedure used to interpret the spectra of complexes using Tanabe-Sugano diagrams is to find the ratio of the energies of the second to first absorption peak and from this locate the position along the X-axis from which D/B can be determined. Having found this value, then tracing a vertical line up the diagram will give the values (in E/B units) of all spin-allowed and spin-forbidden transitions.

N.B. Another approach has been to use the inverse of this ratio, ie of the first to second transition and so both values are recorded in the Tables.

As an example, using the observed peaks found for [Cr(NH3)6]3+ in Table 1 above then, from the JAVA applet described below, D/B' is found at 32.6. The E/B' for the first transition is given as 32.6 from which B' can be calculated as 661 cm-1. The third peak can then be predicted to occur at 69.64 * 661 = 46030 cm-1 or 217 nm (well in the UV region and probably hidden by charge transfer or solvent bands).

For the V(III) example treated previously using an Orgel diagram, the value of D/B' determined from the appropriate JAVA applet is around 30.8.

Following the vertical line upwards leads to the assignment of the first transition to 3T2g¬3T1g and the second and third to 3T1g (P) ¬3T1g (blue line) and 3A2g¬3T1g (green line) respectively.

The average value of B' calculated from the three Y-intercepts is 598 cm-1 hence D equals 18420 cm-1, significantly larger than the 17100 cm-1 calculated above and shows the sort of variation expected from these methods.

It is important to remember that the width of many of these peaks is often 1-2000 cm-1 so as long as it is possible to assign peaks unambiguously, the techniques are valuable. Charge-transfer bands Selection rules and intensities Electronic Absorption Spectroscopy

The d-d transitions in complex ions correspond to absorptions which are often, though not always, the cause for their colour. The position of absorption peaks in the spectra allow the direct measurement of ∆. This is particularly straightforward for ions with a d1 or d10 configurations.

Some complexes, usually very intensely coloured, owe their colour to charge-transfer transitions which involve the excitation of an electron from a molecular orbital largely centered on the metal to one largely centered on the ligands or vice versa. Such transitions often result in a big dipole change for the molecule which is a factor which is associated with a highly probable transition and hence an intense colour.

Selection Rules for d-d Transitions and Colour Intensity (Section 13.5) The Laporte Rule. In a molecule or ion possessing a centre of symmetry, transitions are not allowed between orbitals of the same type, for example d to d. The geometries affected by this rule include octahedral and square-planar depending on the ligands and isomers involved. The rule never applies to tetrahedral complexes. In cases where the rule applies, the colours of the complexes are usually relatively pale. The reason transitions are observed at all is because the symmetry centre is transiently destroyed by vibrations of the molecules or ions.

As examples, consider [Cu(H2O)6]2+ which is a rather pale blue colour vs [Cu(NH3)4]2+ which is an intense dark blue.

Spin Allowed - Spin Forbidden Transitions which would require an electron to change its spin are strongly forbidden. Consider the case of the high spin d5 complex [Mn(H2O)6]2+. This complex is sometimes very pale pink due to the presence of very small amounts of impurities. Finally, bear in mind that allowed and Laporte forbidden transitions can occur outside the visible region of the spectrum if the crystal field splitting is very large. This can happen with strong field ligands such as CN¯ or CO.

13.6 Luminescence 13.7 Spectra of f-block complexes 13.8 Circular dichroism 13.9 Electron paramagnetic resonance *Bonding and spectra of M-M bonded compounds 13.10 The ML5 fragment UV spectra

As we noticed before, a lot of complexes give rise to colorful solutions because of d-d transitions. Keep in mind that we see the complementary color when visible light of any wavelength is absorbed. In the Figure on the left, complementary colors are situated on the opposite sides.

UV spectra from a) [Cr(en)3]3+; b) [Cr(ox)3 ]3-; c) [CrF6]3-. υ 1 = ∆o. (roughly)

Selection rules: 1) Laporte: change of parity (g -> u or u -> g) required for an allowed transition. E.g., all d-d transitions of centrosymmetric (octahedral) complexes are Laporte forbidden thus weak. 2) Spin rule: an allowed transition must not involve a change in the total spin. Thus, no transitions are spin-allowed in a d5 high spin complex.

Range of molar absorptivities

type of transition ε [L mol-1 cm-1 ] examples

Spin and Laporte forbidden 10-3 - 1 [Mn(H2O)6]2+ Spin allowed, Laporte

forbidden 1 - 10 [Ni(H2O)6]2+

Spin allowed, Laporte forbidden 10 - 102 [PdCl4]2-

Spin allowed, Laporte forbidden 102 - 103 six-coordinated complexes of low

symmetry Spin and Laporte allowed 102 - 103 metal-ligand CT bands Spin and Laporte allowed 102 - 104 acentric complexes Spin and Laporte allowed 103 - 106 CT bands

Splitting by an octahedral field

Ground-terms arising from d1 (left) and d2 (right).

Correlation and Tanabe-Sugano diagrams

Correlation diagram for d2 in octahedral ligand field

Tanabe-Sugano diagram for d 2 in octahedral ligand field; Spin-allowed transitions

[M(H2O)6]n+

Charge transfer spectra

Charge transfer: Electron transfer from M to L or from L to M, i.e. an electron moves from a M-based orbital to a L-based orbital or vice versa [ligand-to-metal charge transfer, LMCT; metal-to-ligand charge transfer, MLCT ). Since this resembles an internal redox process, the charge transfer will depend on electron affinities and ionization energies. How to favor LMCT: take M with high ionization energy, i.e. low lying empty d orbitals, and L with low electron affinity, i.e. filled orbitals at high energies. Examples are M =

MnVII, PtIV ; L = Se2-, I-. If the d orbitals lie lower than the filled L orbitals, then a complete internal redox reaction takes place, like in [Co(H2O)6]3+ and FeI 3.

Example for LMCT: MnO4

-, permanganate ion (IUPAC nomenclature??)

MO diagram for tetrahedral ML4 showing possible LMCT transitions

All four of them are observed experimentally in the case of MnO4 -:

L(t1) -> M(e) at 17700 cm-1 (565 nm) L(t1) -> M(t2*) at 29500 cm-1 (340 nm)

L(t2) -> M(e) at 30300 cm-1 (330 nm) L(t2) -> M(t2*) at 44400 cm-1 (225 nm) Remember, visible light includes wavelengths between ca. 400 and 750 nm, i.e. frequencies between 25000 and 13000 cm-1. This explains the deep purple color of MnO4

- ( complementary to green).

Further examples: CrO42-: orange; HgI2 , red; BiI3, orange-red; PbI2: yellow.

Example for MLCT: filled M orbitals and empty low lying L orbitals needed, e.g. π antibonding orbitals like in CO and pyridine.

MO diagram for octahedral ML6 showing possible MLCT transitions