Chapter 24. Chemistry of Coordination Compounds

24.1 Metal Complexes

Metal complexes (or complexes) have a metal ion (which can have a 0 oxidation state) bonded to a number of molecules or ions. If the complex has a net electrical charge it is called a complex ion. Compounds that contain complexes are known as coordination compounds. Most coordination compounds are metal compounds formed by Lewis acid-base interactions involving transition metal ions. The metal ion functions as a Lewis acid -electron-pair acceptor. The molecules or ions surrounding the metal ion in a complex are called ligands. The ligands are said to coordinate to the metal. The ligands act as Lewis bases-electron pair donors. Ligands are usually either anions or polar molecules. They have at least one unshared pair of valence electrons. The Development of Coordination Chemistry: Werner’s Theory Alfred Werner (1866 - 1919)

The most important scientific work of Werner, which led directly to the award of the Nobel Prize in 1913, was concerned with the structure and coordination theory of transition metal-amine complexes. Around the end of the last century the understanding of valence bonding and geometry in metal-amine complexes such as [Co(NH3)6]Cl3 was in a confused state. This can be readily appreciated by comparing some generally accepted formulas of that time with those postulated by Werner. The use of trivalent cobalt, pentacoordinate nitrogen and the assumption that only halogen bound to nitrogen can be easily exchanged, underpinned the acceptance of these early formulas. The suggestion from Werner that these complexes were based on an octahedral array of ligands coordinated to a central metal ion was, at that time, not well accepted. The most powerful evidence in favor of this new formulation came from stereochemical studies. Consider, for example, the three formulas 1-3 shown below, each with 6 ligands arranged

page 2

Figure 1. around a central metal ion. In the case of [MeB2A4l with the geometry of 1 or 2 there would be three possible isomers, but only two if the correct structure was 3. The available experimental evidence had never revealed the existence of more than two such isomers. Of special importance for the acceptance of an octahedral geometry was the isolation of the cis- and trans-isomers of the salts 4 and 5, [Co(NH3)6Cl2], which had been predicted to occur, but had not previously been discovered. A result of wider significance, however, was the separation of the two predicted enantiomers of [Co(en)2ClNH3]2+ (6), as well as of 7, [Co(en)3]3+. Where en = ethylenediamine. Alfred Werner proposed: Metal ions exhibit a primary and secondary valence. Primary valence is the oxidation state of the metal. Secondary valence is the number of atoms directly bonded to the metal ion. This is the coordination number. The central metal and ligands bound to it are the coordination sphere of the complex. Example: [Co(NH3)6]Cl3 • Co3+ is the metal ion. • NH3 groups are ligands. When Cl– is part of the coordination sphere, it is tightly bound and not released when the

complex is dissolved in water. • Example: [Co(NH3)5Cl]Cl2 Different arrangements of ligands are possible. Example: There are two ways to arrange the ligands in [Co(NH3)4Cl2]+. In cis-[Co(NH3)4Cl2]+: the chloride ligands occupy adjacent vertices of the octahedral arrangement. (Structure 5 above) In trans-[Co(NH3)4Cl2]+: the chlorides are opposite each other. (Structure 4) The Metal-Ligand Bond The metal-ligand bond is an interaction between: a Lewis acid (the metal ion with its empty valence orbitals) and a Lewis base (the ligand with its unshared pairs of electrons).

page 3 Ligands can alter the properties of the metal. Complexes display physical and chemical properties different from those of the metal ion or the

ligands. For example, consider the properties of Ag+ and a complex involving Ag+ and CN–: Ag+(aq) + e– → Ag(s) E˚ = +0.799 V

[Ag(CN)2]–(aq) + e– → Ag(s) + 2CN– (aq) E˚ = –0.31 V Charges, Coordination Numbers, and Geometries

The charge on a complex ion equals the sum of the charge on the metal plus the charges on the ligands. In a complex the donor atom is the atom bonded directly to the metal. The coordination number is the number of ligands attached to the metal. • The most common coordination numbers are four and six. • Some metal ions have a constant coordination number (e.g., Cr3+ and Co3+ have coordination

numbers of six). • The size of the metal ion and the size of the ligand affect the coordination number.

For example, iron(III) can coordinate to six fluorides but only to four chlorides; thus [FeF6]3– and [FeCl4] – are stable.

• The amount of charge transferred from ligand to metal affects the coordination number. • The greater the transfer of negative charge to the metal, the lower the coordination number

tends to be. • For example, [Ni(NH3)6]2+ and [Ni(CN)4]2– are both stable.

• Four-coordinate complexes have two common geometries: tetrahedral and square planar. • Square-planar complexes are commonly seen for d8 metal ions such as Pt2+ and Au3+. • Six-coordinate complexes are usually octahedral.

24.2 Ligands with More Than One Donor Atom

Monodentate ligands bind through one donor atom only. • Therefore, they can occupy only one coordination site. Polydentate ligands (or chelating agents) have two or more donor atoms that can simultaneously

coordinate to the metal ion. • They can thus occupy more than one coordination site. • Example: ethylenediamine (H2NCH2CH2NH2)

• The abbreviation for ethylenediamine is “en.” • There are two nitrogen atoms that can act as ligands. • They are far enough apart on the molecule that it can wrap around a metal ion. • The molecule can simultaneously coordinate to two sites on the metal ion. • Ethylenediamine is thus an example of a bidentate ligand. • The octahedral [Co(en)3]3+ is a typical “en” complex. Chelating agents form more stable complexes than do monodentate ligands. • Example:

[Ni(H2O)6]2+(aq) + 6NH3 → [Ni(NH3)6]2+(aq) + 6H2O(l) Kf = 1.2 x 109

[Ni(H2O)6]2+(aq) + 3en → [Ni(en)3]2+(aq) + 6H2O(l) Kf = 6.8 x 1017 The chelate effect refers to the larger formation constants, (Kf), to be discussed later, for

polydentate ligands as compared with corresponding monodentate ligands. • Chelating agents are sometimes referred to as sequestering agents. • In medicine, sequestering agents are used to selectively remove toxic metal ions

(e.g., Hg2+ and Pb2+) while leaving biologically important metals.

page 4 • One very important chelating agent is ethylenediaminetetraacetate (EDTA4–).

• EDTA occupies six coordination sites; for example, [CoEDTA]– is an octahedral Co3+ complex. • Both N atoms and O atoms coordinate to the metal.

• EDTA is used in consumer products to complex the metal ions that would otherwise

catalyze unwanted decomposition reactions. Metals and Chelates in Living Systems (We will not have time to discuss this section in detail.)

• Ten of the twenty-nine elements required for human life are transition metals (V, Cr, Mn, Fe, Co, Cu, Zn, Mo, Cd, and Ni).

• Many natural chelates coordinate to the porphine molecule.

• Porphine forms a tetradentate ligand with the loss of the two protons bound to its nitrogen atoms.

page 5 • A porphyrin is a metal complex derived from porphine. • Two important porphyrins are heme (which contains Fe2+) and chlorophyll (which

contains Mg2+).

• Two important heme-containing molecules are myoglobin and hemoglobin. • These proteins are important oxygen-binding proteins. Myoglobin is found in muscle tissue,

while hemoglobin is found in red blood cells. • In each case the heme iron is coordinated to six ligands. • Four of these are nitrogen atoms of the porphyrin ring. • One ligand is a nitrogen atom that is part of one of the amino acids of the protein. • The sixth coordination site around the iron is occupied by either O2 or water. • Other ligands, such as CO, can also serve as the sixth ligand. • A different metal complex is important in the process of photosynthesis. • Photosynthesis is the conversion of CO2 and water to glucose and oxygen in plants in the

presence of light. • The synthesis of one mole of sugar requires the absorption and utilization of 48 moles of

photons. • Chlorophylls are phorphyrins that contain Mg(II). Photons of light are absorbed by

chlorophyll-containing pigments in plant leaves. • Chlorophyll a is the most abundant chlorophyll. • The other chlorophylls differ in the structure of the side chains. • Mg2+ is in the center of the porphyrin-like ring. • The alternating or conjugated double bonds give chlorophyll its ability to absorb light

strongly in the visible part of the spectrum. • Chlorophyll absorbs red light (655 nm) and blue light (430 nm) and transmits green light. • The absorbed energy is ultimately used to drive the endothermic reaction:

6CO2 + 6H2O → C6H12O6 + 6O2

• Plant photosynthesis sustains life on Earth.

page 6 24.3 Systematic Nomenclature of Coordination Chemistry

We can name complexes in a systematic manner using some simple nomenclature rules. • For salts, the name of the cation is given before the name of the anion. • Example: In [Co(NH3)5Cl]Cl2 we name [Co(NH3)5Cl]2+ before Cl–. • Within a complex ion or molecule, the ligands are named (in alphabetical order) before the

metal. • Example: [Co(NH3)5Cl]2+ is pentaamminechlorocobalt(III). • Note that the penta portion indicates the number of NH3 groups and is therefore not

considered in alphabetizing the ligands. • The names of anionic ligands end in o, and for neutral ligands the name of the molecule is used. • Example: Cl– is chloro and CN– is cyano. • Exceptions are H2O (aqua) and NH3 (ammine). • Greek prefixes are used to indicate the number of ligands (di-, tri-, tetra-, penta-, and hexa-). • If the ligand name already has a Greek prefix or is a polydentate ligand, then enclose the name of the ligand in parentheses and use bis-, tris-, tetrakis-, pentakis-, and hexakis-. • Example: [Co(en)3]Cl3 is tris-(ethylenediamine)cobalt(III) chloride. • If the complex is an anion, the name ends in -ate. • For example, [CoCl4]2– is the tetrachlorocobaltate(II) ion. • The oxidation state of the metal is given in roman numerals in parenthesis after the name of the

metal.

24.4 Isomerism

• Two compounds with the same formula but different arrangements of atoms are called isomers. There are two kinds of isomers: • Structural isomers have different ligands bonded to the metal in the complex. • Stereoisomers have the same ligands attached but have different spatial arrangements. Structural Isomerism Four examples of structural isomerism in coordination chemistry are: • Ionization isomerism differ by the exchange of ligands with an anion or neutral molecule outside the coordination sphere. For example: [CoBr(NH3)5]SO4 and [CoSO4(NH3)5]Br are ionization isomers because the Br – ion is a ligand of the cobalt in the first compound but an accompanying anion in the second. As you may have expected there are physical and chemical differences as well. Physically: the bromo complex is violet and the sulfato complex is red. Chemically: the red isomer forms an off-white precipitate of AgBr upon addition of Ag+ ions, but no precipitate upon addition of Ba2+: [CoSO4(NH3)5]Br (aq, red) + Ag+(aq) → AgBr(s) + [CoSO4(NH3)5]+(aq) [CoSO4(NH3)5]Br (aq, red) + Ba2+(aq) → No reaction On the other hand, the violet isomer is unaffected by the addition of Ag+ ions, but it forms a white precipitate of BaSO4 upon addition of Ba2+ ions: [CoBr(NH3)5]SO4 (aq, violet) + Ag+(aq) → No reaction [CoBr(NH3)5]SO4 (aq, violet) + Ba2+(aq) → BaSO4(s) + [CoBr(NH3)5]2+(aq)

page 7 • linkage isomerism

• Linkage isomers: A ligand is capable of coordinating to a metal in two different ways. • Example: Nitrite can coordinate via a nitrogen or an oxygen atom. • If the nitrogen atom is the donor atom, ←NO2, the ligand is called nitro. • If the oxygen atom is the donor atom, ←ONO, the ligand is called nitrito. • The ligand thiocyanate (SCN–) is also capable of being involved in linkage isomerism. • hydrate (coordination-sphere) isomerism differ by an exchange between a H2O molecule and a ligand in the coordination sphere. Or to put it another way Coordination-sphere isomers differ in the ligands that are directly bound to the metal. • Example: The hexahydrate of chromium CrCl3·6H2O, may be any of the three compounds [Cr(H2O)6]Cl3 violet Can you name these compounds? [Cr(H2O)5Cl]Cl2.H2O blue-green [Cr(H2O)4Cl2]Cl.2H2O green

The addition of AgNO3 results in the precipitation of different amounts of AgCl from each of the three salts. The water molecules that are not part of the coordination sphere are easily removed in a drying oven. • Coordination isomerism occurs when one or more ligands are exchanged between a cationic complex and an anionic complex ion. An example of a pair of coordination isomers is [Cr(NH3)6][Fe(CN)6] and [Fe(NH3)6][Cr(CN)6]

Stereoisomerism

Stereoisomers have the same connectivity but different spatial or geometric arrangements of atoms. Two types of stereoisomerism are: geometrical isomerism In geometrical isomerism the arrangement of the atoms is different although the

same bonds are present. Examples are cis and trans isomers. Consider square planar [Pt(NH3)2Cl2].

The two NH3 ligands can either be 90˚ apart or 180˚ apart. • Therefore, the spatial arrangement of the atoms is different. In the cis isomer, the two NH3 groups are adjacent. The cis isomer (cisplatin) is used in chemotherapy. In the trans isomer, the two NH3 groups are across from each other.

page 8 It is possible to find cis and trans isomers in octahedral complexes as well.

• For example, cis-[Co(NH3)4Cl2]+ is violet. • The trans-[Co(NH3)4Cl2]+ isomer is green. • The two isomers also have different solubilities. optical isomerism • Optical isomers are nonsuperimposable mirror images. • These are referred to as enantiomers. • Complexes that exist as enantiomers are chiral (from the Greek cheir, meaning “hand”) Chiral species are molecules or ions that cannot be superimposed on their mirror

image. Enantiomers are very difficult to separate because most physical and chemical properties of enantiomers are identical, with one exception, they way they interact with plane polarized light. Polarization of light. Light from a source, unpolarized, consists of electric and magnetic waves vibrating in various planes in a circular manner.

A polarizer inserted in the light beam filters out all waves except those vibrating in a particular plane, say the vertical plane. If another polarizing (analyzer) filter is then inserted into the plane polarized light, but oriented perpendicular to the polarizing filter, no light will emerged through to analyzer. Now if an optically active substance is placed in the beam of plane polarized light between the polarizer and the analyzer it will rotate the plane of polarized light either to the left or to the right, and therefore light will emerge through the analyzer. An instrument called the polarimeter is used for this purpose. • Enantiomers are capable of rotating the plane of polarized light. • The mirror image of an enantiomer will rotate the plane of polarized light by the same

amount in the opposite direction. • Dextrorotatory solutions rotate the plane of polarized light to the right. • This isomer is called the dextro or d isomer. • Levorotatory solutions rotate the plane of polarized light to the left. • This isomer is called the levo or l isomer. Chiral molecules are said to be optically active because of their effect on light. A chemical reaction normally produces a mixture of equal amounts of optical isomers, called a racemic mixture. Racemic mixtures contain equal amounts of l and d isomers. Because the two isomers rotate the plane of polarized light in equal but opposite directions, a racemic mixture has no overall effect on the plane of polarized light. To show that optical isomers exist, a racemic mixture must be separated into its d and l isomers; the racemic mixture must be resolved, a tool of the organic chemist! One way to resolve a mixture containing d and l complex ions is to prepare a salt with an optically active ion of opposite charge.

page 9 For example, tartaric acid, H2C4H4O6, prepared from the white substance in wine vats, is the optically active isomer d-tartaric acid. When the racemic mixture of cis-[CoCl2(en)2]Cl is treated with d-tartaric acid, the d-tartrate salt of d- and l-cis-[CoCl2(en)2]+ may be crystallized. These salts will no longer be optical isomers of one another and will have different solubilities. [The 2001 Nobel Prize in Chemistry was awarded to W.S. Knowles and K. B. Sharples of the United

States and R. Noyori of Japan for work on the catalysis of chiral reactions.]

24.5 Color and Magnetism Color

The color of a complex depends on the metal, the ligands present, and the oxidation state of the metal. For example, pale blue [Cu(H2O)6]2+ can be converted into dark blue [Cu(NH3)6]2+ by adding NH3(aq).

A partially filled d orbital is usually required for a complex to be colored. Thus, ions with completely empty (e.g., Al3+ or Ti4+) or completely filled (e.g., Zn2+) d subshells

are usually colorless. Colored compounds absorb visible light. The color perceived is the sum of the light reflected or transmitted by the complex. An object will have a particular color if it reflects or transmits that color or if it absorbs light

of the complementary color. [See color wheel at and of Notes] • An object appears black if it absorbs all wavelengths of light. • An object appears white or colorless if it absorbs no visible light. • A plot of the amount of absorbed light versus wavelength is called the absorption spectrum.

Magnetism Many transition-metal complexes are paramagnetic (i.e., they have unpaired electrons). Consider a d6 metal ion: • Compounds of [Co(NH3)6]3+ are diamagnetic, have no unpaired electrons, but compounds of

[CoF6]3 are paramagnetic, with four unpaired electrons per metal ion. We need to develop a bonding theory to account for both color and magnetism in transition metal complexes. Valence Bond Theory of Complexes A complex is formed when electron pairs from ligands are donated to a metal ion. This does not explain how the metal ion can accept electron pairs. Nor does it explain the paramagnetism often observed in complexes. Valence bond theory provided the first detailed explanation of the electronic structure of complexes. This explanation is an extension of the view of covalent bonding described earlier in C101. According to this view, a covalent bond is formed by the overlap of two atomic orbitals, one from each bonding atom. In the usual covalent bond, hybrid orbitals, approach (A). Each orbital originally holds one electron, and after the orbitals overlap a bond is formed that holds both electrons. In the formation of a coordinate covalent bond in complexes (B), a ligand orbital contains both electrons overlaps with an unoccupied hybrid orbital on the metal atom. before bonding after bonding A B

· ·

· ·X Y X

X

Y

YX Y

· ·

· ·X Y X

X

Y

YX Y

page 10 While valence bond theory was able to explain the bonding in complex ions, and in an unsatisfactory

manner the magnetism observed in complexes, it failed to address the colors possessed by complex ions and a quantitative prediction about their energies. For example, it is easy to apply the valence-bond theory to some coordination complexes, such as the [Co(NH3)6]3+ ion, which is known to be diamagnetic. We start with the electron configuration of the transition- metal ion. Co3+: [Ar] 3d6 => [Ar] ↑↓ ↑ ↑ ↑ ↑ ___ ___ ___ ___ 3d 4s 4p We see that in the valence-shell orbitals the 4s and 4p orbitals are empty; Co3+: [Ar] 3d6 4s0 4p0 Pairing up the 3d electrons in the dxy, dxz, and dyz orbitals in this subshell gives the following electron configuration. Co3+: ↑↓ ↑↓ ↑↓ ___ ___ ___ ___ ___ ___ 3d 4s 4p The 3dx2-y2, 3dz2, 4s, 4px, 4py and 4pz orbitals are then mixed to form a set of empty d2sp3 orbitals that point toward the vertices of an octahedron. Each of these orbitals can accept a pair of nonbonding electrons from a neutral NH3 molecule to form a complex in which the cobalt atom has a filled shell of valence electrons. [Co(NH3)6]3+: ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 3d 4s 4p At first glance, complexes such as the [CoF6]3- ion, which is paramagnetic, seem hard to explain with the valence-bond theory. We start, as always, by writing the configuration of the transition-metal ion. Co3+: [Ar] 3d6 => [Ar] ↑↓ ↑ ↑ ↑ ↑ ___ ___ ___ ___ 3d 4s 4p This configuration creates a problem, because there are six electrons in the 3d orbitals but we can't find two empty 3d orbitals to use to form a set of d2sp3 hybrids. There is a way around this problem. The five 4d orbitals on cobalt are empty, so we can form a set of empty sp3d2 hybrid orbitals by mixing the 4dx2-y2, 4dz2, 4s, 4px, 4py and 4pz orbitals. These hybrid orbitals then accept pairs of nonbonding electrons from six fluoro ligands to form a complex ion. [Co(NH3)6]3+: ↑↓ ↑↓ ↑↓ ↑ ↑ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ___ ___ ___ 3d 4s 4p 4d The valence-bond theory therefore formally distinguishes between "inner-shell" complexes, which use 3d, 4s and 4p orbitals to form a set of d2sp3 hybrids, and "outer-shell" complexes, which use 4s, 4p and 4d orbitals to form sp3d2 hybrid orbitals.

page 11 24.6 Crystal-Field Theory Although valence bond theory explains the bonding and magnetic properties of coordination complexes, it is missing two important aspects. First, the theory does not explain the color of coordination complexes. Second the theory is difficult to extend quantitatively. Crystal-field theory is a model of the electronic structure of transition-metal complexes that considers how the energies of the d orbitals of a metal ion are affected by the electric field of the ligands. Crystal field theory (CFT) uses an electrostatic model to explain all metal ion-ligand interactions. (A subsequent theory—called ligand field theory—builds on the principles of CFT and allows for some covalency, as well. Further refinement of LFT leads to molecular orbital theory that we use today.) CFT, however, will suffice to explain the geometries of various transition metal-coordination complexes.) Because CFT bases all interactions on electrostatics, each ligand is represented by a negative point charge. The way these point charges interact with the d-orbitals of a metal atom explains the geometries adopted by various transition metal complexes. In the absence of ligands (meaning in the absence of a crystal field), all d-orbitals in a particular metal have the same energy and are said to be degenerate. When ligands coordinate to the metal, however, the ligands (treated as point charges) cause the d-orbitals to be either stabilized or destabilized. A stabilizing effect from a ligand lowers the energy of the interacting d-orbital, whereas a destabilizing effect raises the energy of the d-orbital. First, we will examine a very common geometry in transition metal complexes: the six-coordinate, octahedral geometry. In an octahedral complex, six ligands are placed symmetrically along the axes of a Cartesian coordinate system (the x-, y-, and z-axes in three-dimensional space), with the metal at the origin. Knowing the shapes of the five d-orbitals is essential in understanding octahedral geometry. As shown in Figure (a), there are two d-orbitals that point directly along Cartesian axes: the dz2 orbital (top drawing), which points along the z-axis, and the dx2-y2 orbital, which has lobes on both the x- and y-axes. The interaction of six ligands with the dz2 and the dx2-y2 orbitals raises the energy of these two d-orbitals through repulsive interactions. Moreover, the energy of these two orbitals is increased by the same amount, so the dz2 and the dx2-y2 orbitals are degenerate. In the nomenclature of crystal field theory, these orbitals are called the eg orbitals. The other three d-orbitals, the dxy, dxz, and dyz orbitals, which all have lobes inbetween the Cartesian axes, are repelled less by the ligands and are in effect stabilized to a lower energy. The dxy, dxz, and dyz orbitals are also degenerate; collectively, they are called the t2g orbitals. (See Figure 2 (b).)

page 12

(a) (b) Figure 2. (a) The orientation of the five d-orbitals with respect to the ligands of an octahedral complex: the degenerate eg pair, and the degenerate t2g triplet. (b) Splitting of the five d-orbitals by an octahedral field. The energy gap between these two sets of d orbitals is labeled ∆. ∆ is referred to as the crystal-field splitting energy. For example, consider the [Ti(H2O)6]3+ complex. Ti3+ is a d1 metal ion. Therefore, the one electron is in a low energy orbital. For Ti3+, the gap between energy levels, ∆ is of the order of the wavelength of visible light. As the [Ti(H2O)6]3+ complex absorbs visible light the electron is promoted to a higher energy level. This transition is called a d-d transition because it involves exciting an electron from one set of d orbitals to the other. Because there is only one d, electron there is only one possible absorption line for this molecule. The color of a complex depends on the magnitude of ∆ which, in turn, depends on the metal and

the type of ligand. [Ti(H2O)6]3+ is purple, [Fe(H2O)6]3+ is light violet, [Cr(H2O)6]3+ is violet, and Cr(NH3)6]3+ is yellow.

page 13 A spectrochemical series is a listing of ligands in order of their ability to increase ∆:

I- < Br - < Cl– < F– < OH- < H2O < NCS- < NH3 < en < NO2– (N-bonded) < CN– < CO

weak field ligand increasing ∆ → strong field ligand Weak-field ligands lie on the low end of the spectrochemical series. Strong-field ligands lie on the high end of the spectrochemical series. Example: When the ligand coordinated to Co3+ is changed from the weak-field ligand F– to the strong field ligand CN–, ∆ increases and the color of the complex changes from green (in [CoF6]3+) to yellow (in [Co(CN)6]3–). See the Figures below.

Electron Configurations in Octahedral Complexes

Recall that when transition metals form cations, ns electrons are lost first! • Thus, Ti3+ is a d1 ion, V3+ is a d2 ion, and Cr3+ is a d3 ion. If one to three electrons add to the d orbitals in an octahedral complex ion, Hund’s rule applies. • The first three electrons go into different d orbitals with their spins parallel. We, however, have a choice for the placement of the fourth electron: • If it goes into a higher-energy orbital, then there is an energy cost (∆). • If it goes into a lower-energy orbital, there is a different energy cost (called the spin-pairing

energy, P) due to pairing with the electron already present. • Weak-field ligands (which cause a small ∆tend to favor adding electrons to the higher-

energy orbitals (high-spin complexes) because ∆ is less than the spin-pairing energy, ∆ < P.

• Strong-field ligands (which cause a large ∆tend to favor adding electrons to lower-energy orbitals (low-spin complexes) because ∆ > P.

Tetrahedral and Square Planar Complexes We use similar arguments to explain the crystal field splitting of the d-orbitals in a four-coordinate, tetrahedral complex. One way to represent a tetrahedral species is to show four ligands (treated as point charges in crystal field theory) on alternating corners of a cube. In a tetrahedral complex, the ligands do not point directly at any of the five d-orbitals, but they come close to the dxy, dxz, and dyz orbitals, which are directed toward the edges of the cube, as shown in Figure (a); these orbitals are raised in energy and form a degenerate set. The dz2 and the dx2-y2 orbitals point toward the sides of the cube and are therefore directed away from the attached ligands; these two

page 14 orbitals are lowered in energy and are also degenerate. The relative energies (and crystal field

splitting) of the five d-orbitals in a tetrahedral complex are shown in Figure 3(b).

(a) (b) Figure 3. (a) The effect of a tetrahedral crystal field on a set of d-orbitals is to split them into two sets; the eg pair (which point less directly at the ligands) lie lower in energy than the t2g triplet. (b) Splitting of the five d-orbitals by a tetrahedral field. Because there are only four ligands, ∆ � � � � for a tetrahedral field is smaller than ∆oct for an octahedral field. This causes all tetrahedral complexes to be high-spin.

Square Planar Complexes Crystal field theory also explains the four-coordinate, square planar geometry. In this case, we can imagine an octahedral complex in which the ligands on the z-axis (that is, those interacting most directly with the dz2 orbital) are removed. The dz2 orbital is therefore lowered in energy. Furthermore, the other d-orbitals having z-character—specifically, the dxz and dyz orbitals—also decrease in energy. However, since the ligands are all now in the xy plane, both d-orbitals having x- and y-character—namely, the dx2-y2 and the dxy orbitals—are raised in energy. The crystal field splitting pattern of a square planar complex is shown in Figure 4.

page 15

Figure 4. (a) An octahedral complex that (b) undergoes z-axis elongation such that it becomes distorted and (c) finally reaches the square planar limit. What determines whether a four-coordinate transition metal complex is tetrahedral or square planar? The answer lies in the number of d-electrons in the central transition metal. If the metal has eight d-electrons, as is the case for Pt2+, it is energetically advantageous for the complex to adopt a square planar geometry. In this case, the eight d-electrons will achieve some stabilization in energy by occupying the dxz, dyz, dz2, and dxy orbitals. • Most d8 metal ions form square-planar complexes. • The majority of complexes are low-spin (i.e., diamagnetic). • Examples: Pd2+, Pt2+, Ir+, and Au3+.