# Introduction to Inorganic Chemistry/Coordination Chemistry and Crystal Field Theory

## Chapter 5: Coordination Chemistry and Crystal Field Theory

All five d-orbitals.

Coordination complexes are compounds and molecules formed between a metal ion and a ligand. The metal ions are essentially Lewis acids while the ligands are analogous to Lewis bases. Most often, the ligand has a lone pair of electrons to which it donates to the empty d-orbitals in the metal. This forms a Lewis acid-base adduct.

Like covalent compounds, metal complexes can vary widely in size, shape, charge and stability. Metals can also form complexes with a variety of ligands and vice versa. Certain metals may have any number of the same ligand with copper(II)-ammonia complexes being an example. Copper can have from one ammonia ligand up to six in an octahedral format. (Ex: [Cu(NH3)]2+ and [Cu(NH3)6]2+. Since ammonia is a neutral complex, the charge on the complex did not change but if copper were to bind with six cyanide anions, (CN-) the complex would be [Cu(CN)6]4-. Note the negative four charge. Charge depends on both the metal and ligand as seen in the cobalt (II) and cobalt (III) hexaaqua complexes: [Co(H2O)6]2+ and [Co(H2O)6]3+, respectively.

Examples of possible metals include transition metals like iron, cobalt, copper, silver and tungsten. Metals could also be alkali or alkali earth metals like sodium and magnesium. Although these are much more rare than their transition metal complexes. P-block metals, also referred to as poor metals, like aluminum, tin and lead can also form complexes. However, each block of the periodic table and even within certain blocks, especially the transition metal series, can have varying chemistry for complexes.

Ligands can also vary widely and consist of an atom or compound which contain a lone pair or donating pair of electrons. Examples include the iodide ion, the carbon monoxide molecule and even water. Ligands are usually neutral or negatively charged. They come from elements in the p-block of the table, usually nonmetals.

Although in the first few sections of the chapter will be focused on octahedral complexes, it is possible for complexes to adapt other shapes such as tetrahedral, square planar and distorted forms of these shapes.

## 5.1 Counting electrons in transition metal complexes

In order to understand the bonds created in transition metal complexes, the energy levels of orbitals must be understood. Ligands, due to their relatively higher electronegativity than metals, thus they form orbitals of much lower energy and thusly these electrons do not participate in bonding. They can be thought of as non-bonding electrons. Transition metals have d-orbitals, orbitals of much higher energy than the ligand's orbitals. These d-orbitals are the ones involved in bonding.

Although d-orbitals are of high energy, the corresponding s-orbitals (Ex: 3d with 4s and 4d with 5s, etc.) have slightly higher energy. These s-orbitals are the first to lose electrons to form an ion. From there, the metal will continue to lose electrons until it achieves a state of low enough energy and has an oxidation number which is stable. From there, it is possible to determine the oxidation number of a metal in complex. Determining the oxidation state of the metal in a complex is relatively easy since the metal retains its oxidation number from its isolated state to its complexed state. Ligands also retain their oxidation number (the cyanide ion is always negative one and water is always neutral).

Putting this together, we see that we can use a metal's group in the periodic table and subtract from it the oxidation number to get the number of d-electrons available for complexing. For example, iron is in group 8 on the periodic table. If iron metal gets oxidized to iron (III), it will have lost three electrons. Two of these electrons come from the 4s orbital, leaving it empty and one electron comes from the d-orbital in iron. In group eight, it has six d-electrons and when it loses one, it goes to five d-electrons or d5.

The same "game" can be applied to any transition element. Copper (II), in group 11 on the periodic table has eleven electrons in its valence shell, minus two, leaving it with 9 electrons, all d-electrons. Manganese (II), in group seven, has five d-electrons. Zinc(II) in group 12 would have 10 d-electrons, a full shell and manganese (VII) has zero d-electrons.

For simplicity's sake, this equation can be used: Total d-electrons = Group #-oxidation #-2. As above, Mn2+ would be in group 7 with an oxidation state of +2. e-total = 7 - 2 - (2) = 3

These number of electrons can then fill the complex's orbitals.

## 5.2 Crystal field theory

Like p-orbitals, d-orbitals have shapes which align with a certain coordinate system. The orbitals dxy, dxz, and dyz point 45o in between the axes of the xy-, xz-, yz-planes respectively. The axes of these planes can be thought of as the bonding axes. The dz2 points in the direction of the z-bonding axis. The dx2-y2 points in the direction of the x- and y-bonding axes.

Orbitals and their relations to ligands.

An isolated metal, far from any ligand interaction will have all of these orbitals as degenerate. But as a ligand is brought closer, these orbitals start interacting with the ligand orbitals and a splitting begins to occur. The equilibrium distance of the ligands to the orbitals establish an energy noted as Δo for octahedral complexes. We will only discuss octahedral complexes for now. As discussed above with the orientation of orbitals with respect to bonding axes, the three orbitals which point in between the bonding axes (dxy, dxz, and dyz) will have less electrostatic repulsion and form orbitals of lower energy. The orbitals which point directly along the bonding axes, dz2 and dx2-y2 will form higher energy orbitals. The low energy orbitals are referred to as t2g and the high energy orbitals are called eg orbitals. The difference in energy of these two sets is Δo.

## 5.3 Spectrochemical series

The spectrochemical series refers to an ordering from soft to hard ligands. Ligands on the lower end of the series are referred to as weak field ligands and higher up on the series, the ligands are referred to as strong field. A general trend can be seen and described in this way. One rule for the series is electronegativity. Soft bases, like the iodide and bromide ions are easily polarizable due to their large size and relatively small charge. These ions are not nearly as electronegative as elements like oxygen. Oxygen holds its lone pairs much closer to the oxygen atom than the iodide does which creates poor overlap for the water molecule which results in a weaker decrease in energy for bonding. A simple electrochemical series might look like this:

Weak field I- < Br- < Cl- < NO3- < F- < OH- < H2O < Pyridine < NH3 < NO2- < CN- < CO Strong field

Low and high spin Complexes

The energy gap between the t2g and eg orbital sets depend on both the ligand and the metal. The stronger the ligand, the larger the gap and vice versa. The more acidic (the harder the metal is as an acid) the larger the gap as well. Energy can be calculated in a number of ways where E is the splitting energy, λ is the wavelength associated with the photon of light necessary to excite an electron from its ground state to an excited state, ν is the frequency of this electron, h is Planck's constant (6.626x10-34 J*s), and c is the speed of light. $\scriptstyle\tilde{\nu}$ is referred to as a "wavenumber" and is the inverse of wavelength, usually measured in cm-1. Energy gaps are usually expressed proportional to wavenumbers.

E = hν = hc/λ = hc$\scriptstyle\tilde{\nu}$

For example a red photon can have a wavelength of 620 nm and a wavenumber of 6.2x10-5 cm-1. A common carbon-carbon bond might have a wavenumber of 32000cm-1.

A list of d6 compounds and their wavenumbers are listed below:

A simple color wheel.

Co(H2O)62+ - 9300

Co(H2O)63+ - 18200

Co(CN)63- - 33500

Rh(H2O)63+ - 27000

Rh(CN)63- - 45500

As seen, the stronger the ligand, the higher the wavenumber and the larger energy gap. By nature, 4d and 5d complexes have larger CFSE. This is due to something referred to as the lanthanide contraction. In between the 5s and 4d blocks is the 4f series which has a very smooth contraction from lanthanum to ytterbium. This makes it so that the 5s and 6s orbitals of the 2nd and 3rd row transition elements are much smaller than their d-counterparts, unlike the 3d and 4s orbitals which are relatively similar in size. As a result, 4d and 5d elements have very similar chemistry.

A simple, qualitative way to see the relative crystal field splitting energy, Δo, or CSFE is to simply look at the color of a compound. The more a complex absorbs high energy photons, the larger the energy gap. However, the color a complex absorbs is opposite the color it appears/reflects on the color wheel. Thusly a compound like Co(NH3)62+ which looks blue-green would absorb in the red-orange range and Co(CN)64- looks yellow and absorbs in the violet and ultra-violet range of the spectrum. However, this method only applies to molecules which reflect and absorb in the visible range which is most metal complexes. But there are complexes which look colorless and either absorb in the ultraviolet or infrared, a large difference in energy.

## 5.4 π-bonding between metals and ligands

Strength and stability of complexes depends not only on the electronegativity of the bonding atom of the ligand but is also dependent on the other bonds inside the ligand. Carbon monoxide is higher in the electrochemical series than ammonia even though it contains oxygen, an atom known for its poor orbital overlap. This can be attributed to the extra pi bonds in the carbon monoxide compound which may participate in bonding. There are three common types of pi-bonding in metal complexes.

Carbon monoxide backbonding with a metal's d-orbitals.

The first instance is when a ligand like carbon monoxide or cyanide donates its sigma electrons to the metal, also known as "back-bonding". The metal can be referred to as a σ-accpetor and a π-donor since the metal donates π electrons to the ligands π* orbitals. This forms a dπ-pπ bond.

The second instance is when an element, like phosphorus, contains a lone pair to which it can donate. This interaction is also back-bonding and the phosphorus species is a σ-donor and a π-acceptor. This forms a dπ-dπ bond.

The third instance is when an element with two full p-orbitals donates two lone pairs and as such can be referred to as a σ-donor and a π-donor.

## 5.5 Crystal field stabilization energy, pairing, and Hund's rule

Crystal field stabilization energy is defined as the energy gained by the complex by filling the split t2g and eg orbitals. As seen in the image, the t2g orbitals are 25 the octahedral splitting energy. As electrons are added into the lower set, the crystal field stabilization energy (CFSE) increases with each electron put in. So a d3 complex would have a CFSE of (3)(250 = 65Δ0. This method of determining the CFSE as well as the electron count works well if the discussion only includes up to 3 d-electrons. However, when adding a fourth electron, there is a possible two locations for the electron to fill: either pair with an existing electron in the t2g set or fill a vacant orbital in the eg set. This depends on whether the splitting energy between the two sets is larger or smaller than the pairing energy for putting two anti-parallel electrons in the same orbital. If the pairing energy is larger than the splitting energy, that is, it is more favorable to place electrons in empty orbitals than to pair them, the complex is said to be high spin. And if the pairing energy is lower, than the complex will be low spin. High and low spin simply refer to the amount of unpaired electrons.

Metals in the 3d set with 4 to 7 electrons are the only elements affected by this. Metals with 1 to 3 d electrons will only fill the lower set and metals with 9 and 10 d-electrons will fill the orbitals regardless of the order. We will discuss 4d and 5d transition metals later. What affects this difference in energies is the spectrochemical series. That said, a strong field ligand, a ligand with a strong ability to push electrons into pairs and widen the octahedral splitting. This is the opposite for weak field ligands. As such and while using the spectrochemical series, the following complexes can be determined to either be high or low spin:

[Co(Cl)44-] contains a d7 metal with a relatively weak field ligand. This complex is known to be high spin. It's splitting pattern can be seen here: [Co(CN)44-] is also a d7 complex but contains cyanide, one of the strongest field ligands will produce a low spin complex.

As mentioned before, the issue of low and high spins for 4d and 5d complexes turns out to be rather simple. The 4s orbital for 1st row transition series is about the same size as the 3d orbital so their energies are relatively equal. But for 4d and 5d series, their d-orbitals reach out much farther than their respective s-orbitals. This correlates to a much larger Δ0 which in turn, all 2nd and 3rd row transition metal complexes are low spin.

Electrons possess four quantum numbers and one of them, intrinsic to the electron, is spin. Spin is a quantum mechanical property of the electron which is important to note when pairing electrons. Based on the Pauli exclusion principle, that is no electron may possess all four of the same quantum numbers in the same sub-orbital. If two electrons possess the same first three quantum numbers, they must not have the same spin. Further on this, electrons must fill up all available and preferred orbitals before they begin to pair. Parallel spins in adjacent orbitals, in order to maximize angular momentum, are lower in energy and thus more favored so multiple unpaired electrons are either all spin up or all spin down.

## 5.6 Non-octahedral complexes

While octahedral is the most prevalent arrangement of ligands, and the only possible arrangement for six ligand systems, other shapes are observed and predictable. By using other shapes and electronic configurations we can rationalize observed paramagnetism and explain certain effects that are impossible to glean from making an all octahedral assumption about transition metal complexes.

A common octahedral complex: Ferricyanide

Tetrahedral arrangements are the second most common shape of complex and are often observed when the ligands are much larger than the metal ion and have trouble fitting around the core. Tetrahedral differs from octahedral mostly by having four ligands instead of six and also because its crystal field splitting energy is much smaller, about 2/3rds of octahedral CFSE. Another less common class of geometry is square planar. This four ligand arrangement is based on the most stable electronic configuration for an ion with 8 d electrons. This arrangement never generates a magnetic complex by virtue of its electronic configuration which raises the energy of an unoccupied orbital to stabilize the complex.

Tetrachloronickelate(II) is an 8 d electron tetrahedral complex with large ligands relative to the metal core.
Tetracyanonickelate(II)is an 8 d electron square planar Nickel (II) complex
Crystal field splitting of square planar and tetrahedral complexes
Tetraxenonogold(II) is an unusual example of a 9 d electron system where noble gases act as ligands in a square planar complex.

## 5.7 Jahn-Teller effect

The Jahn-Teller distorted tetrahedron is another four ligand shape and is related to the square planar arrangement, but is typically observed in complexes with 9 d electrons. By virtue of their odd number of electrons, these complexes are always magnetic. The electronic configuration for these compounds is almost the same as the square planar configuration but the top orbital is only separated from the others by the theoretical CSFE of the tetrahedral shape and the second to fourth highest energy orbitals are inverted.When a complex contains a degenerate ground state orbital, it will distort itself to remove the degeneracy and lower its symmetry to become more stable. In other words, distorting the orbitals of d9(Cu2+), low spin d7 (NaNiO2), and high spin d4 (CrF2) complexes lead to lower total energies than their symmetric, octahedral counterparts. The distortion comes from elongating the z axis ligand bonds. All orbitals containing a z component are therefore lowered in energy, while the orbitals without a z component are destabilized. Although relatively uncommon, there are some notable examples of compounds with this arrangement such as Cu(II).

A Jahn-Teller distorted tetrahedron structure for high spin 4 d electron Chromium-nitrosyl

## 5.8 Tetrahedral complexes

Tetrahedral complexes are high spin complexes where the dx2-y2 and dz2 orbitals point away from ligands while the dxy, dyz, and dxz orbitals point between ligands. This increases the energy of the the dxy, dyz, and dxz orbitals and decreases the dx2-y2 and dz2 orbitals. However, the overall splitting energy between the t2 and e orbitals is about 2/3s that of an octahedral's geometry and is therefore more stable. Because of the lowered splitting energy, all tetrahedral complexes are high spin. Tetrahedral compounds are a class of complexes that are often brightly colored because they lack the center of symmetry that forbids a d-d* transition. Because that low energy transition is at least partly allowed, these complexes normally absorb in the visible range and as such have bright colors unlike many of the octahedral or otherwise Centro-symmetric compounds. Their d-d* transitions are forbidden and their other transitions require more energy. These complexes therefore absorb in the ultraviolet region and appear fairly dull.

Nickel(II)-chloride-hexahydrate, a vibrant example of a tetrahedral transition metal complex.
Cobalt(II)-chloride-hexahydrate

## 5.9 Stability of transition metal complexes

Transition metal complexes have a wide variety of stabilities depending on CFSE, hard and soft acid/base metals and ligand interactions, as well as chelate and macrocyclic effects. Hard acids are typically small, high charge density cations that are weakly polarizable such as the Lewis acids Al3+, Ti4+, and Cr6+ and some hard bases are H2O, Cl-, and NH3. Soft acids are large polarizable low charge metals such as Cu+ and Ag+ while soft ligands are anions/neutral bases such as CO and CN-). Hard acids form strong bonds and stable complexes with hard bases while soft acids do the same with soft bases. Hard bases also have the ability to stabilize higher oxidation states than soft bases. For instance CuF2 is stable while CuI2 is not. Chelating and macrocyclic ligand complexes have higher formation constants due to the large entropic effect their confirmations allow. The stability of each instance can be predicted by how alike the metal and ligand are as well as other factors like ligand dentate effects. Transition metal complexes are typically unstable when the hard soft acid base character of the ligands do not match, the oxidation state of the transition metal is unstable, or a more stable complex can be formed in the same environment.

## 5.10 Chelate and macrocyclic effects

Chelate and macrocyclic effects can dominate transition metal complex stability. The chelate effect refers to the potential of a ligand to bind multiple times to the same metal ion. The increase in entropy creates a more stable product. For example, the formation constant, Kf, of the Co(NH3)63+ complex is about 105 as weak as the Cobaltethylenediamine complex. Ethylenediamine is a bidentate ligand, meaning it has two possible binding sites, so only 3 particles must be used to form the Co3+ complex. Ammonia is only a monodentate ligand, so 6 particles must react to form the same Co complex. Other common multi-dentate ligands are acetylacetone, a bi dentate ligand, and EDTA, a hexadentate ligand that is one of the most effective complexing agents known. The macrocyclic effect follows the same principle as the chelate effect, but the effect is further enhance by their cyclic confirmation. Macrocyclic ligands are not only multi-dentate, but because they are rigidly stuck in their cyclic form, they allow less conformational freedom, almost as if the ligand is "pre-oranized" for binding. For example heme b is a quadridentate cyclic ligand which is excellent at complexing free Fe+2 ions.

Heme b
Ethylenediamine, a bi-dentate ligand that is a common chelating agent
Ammonia, a common mono-dentate ligand that can form a variety of transition metal complexes.
Acetylacetone a bi-dentate ligand.
Ethylenediaminetetraaceticacid acid a hexa-dentate ligand

## 5.12 Discussion questions

• Discuss chelating ligands and what they do, using some new examples.
• Explain (using some new examples) how we know if an octahedral complex of a metal ion will be high spin or low spin, and what measurements we can do to confirm it.

## 5.13 Problems

1. Predict the shape of the following complexes, and determine whether each will be diamagnetic or paramagnetic:

(a) [Fe(CN)6]4-

(b) [Fe(C2O4)3]4-

(c) [Zn(NH3)4]2+

(d) [Mo(CO)6]

(e) [Rh(NH3)4]+

2. Tetrahedral complexes are almost always high spin, whereas octahedral complexes can be either high or low spin. Explain.

3. For each of the Mn complexes in the table below, give electronic configurations (within the t2g and eg sets of 3d orbitals) that are consistent with the observed magnetic moments.

Compound µ (BM)
[Mn(CN)6]4- 1.8
[Mn(CN)6]3- 3.2
[Mn(NCS)6]4- 6.1
[Mn(acac)3] 5.0

4. In a solution made by combining FeCl3 with excess ethylenediaminetetraacetic acid (EDTA) at neutral pH, the concentration of Fe3+(aq) ions is on the order of 10-17 M. However, in a solution of ethylenediamine and acetic acid at comparable concentration, the Fe3+(aq) concentration is about 10-7, i.e., 1010 times higher. Explain.

5. The complex [Ti(H2O)6]3+ is violet, while the analogous complex with another monodentate neutral ligand L, [Ti(L)6]3+ is orange. How many of the following statements are true? Explain briefly.

(a) L is a stronger field ligand than H2O.

(b) [Ti(L)6]3+ is a high-spin complex.

(c) [Ti(L)6]3+ absorbs yellow and red light.

(d) Both complexes have two 3d electrons associated with the metal.

6. OH- and CN- are both Brønsted bases, and both can form complexes with metal ions. Explain how OH- can be a much stronger Brønsted base than CN-, and at the same time much lower in the spectrochemical series.

7. W. Deng and K. W. Hipps (J. Phys. Chem. B 2003, 107, 10736-10740) reported an STM study of the electronic properties of Ni(II)tetraphenyl porphyrin (NiTPP), a red-purple, neutral diamagnetic complex that is made by reacting Ni(II) perchlorate with tetraphenylporphine. When NiTPP is reacted with sodium thiocyanate it forms another complex that is paramagnetic. Draw the structures of NiTPP and the product complex, and the crystal field energy level diagram that explains each. What value of the magnetic moment (in units of μB) would you expect for the paramagnetic complex?

8. Seppelt and coworkers reported the very unusual ion [AuXe4]2+ in the salt [AuXe4]2+ (Sb2F11-)2 (Science 2000, 290, 117-118). This was the first report of a compound containing a bond between a metal and a noble gas atom. Draw a d-orbital energy diagram for this ion and predict whether it should be diamagnetic or paramagnetic. Would you expect to be able to form a similar complex using Cu in place of Au, or Kr in place of Xe? Why or why not?