Transition Metals The transition metals are -block metals. Sometimes the term is use to refer to all -block elements (all of which are metals), though more strictly it inclues those that are in the transition of filling their -orbitals, an exclues the Zn group which have a full 10 electron subshell. The behaviour of the zinc group is inee quite ifferent an will be treate separately. Going own a transition group, the atomic raius increases markely from the first to the secon series (perio) as an aitional electron shell is ae, however, the atoms of the secon an thir elements ten to be very similar in size. This is ue to the lanthanie contraction which occurs across the f-block: f-block elements contract as an aitional f- electron is ae as one moves right across a perio. This contraction offsets the aition of an extra electron shell between series an 3. This effect is most marke to the left of the - block, just following the lanthanie contraction after lanthanum (La of the scanium (Sc) group) an the atomic raii of zirconium (Zr) an hafnium (Hf) are almost ientical an these elements are very har to istinguish. The effect has largely isappeare by the time we reach the copper (Cu) group, an although silver (Ag) an gol (Au) have almost ientical atomic raii, their chemistries are quite ifferent. Camium (C) an mercury (Hg) have very ifferent atomic raii an quite ifferent behaviours. The first perio of transition metals behaves quite ifferently from the secon an thir perio. The secon an thir elements in each transition group ten to behave very similarly to oneanother, since their atoms are of similar size, whereas the first perio have istinct behaviour. To unerstan the chemistry of the transition metals, one nees to unerstan the effects that the -electrons have. Consier first the very ifferent shapes of the -orbitals (recall the s- orbitals are spherical, an p-orbitals umbbell shape). -block
p z orbital p an Orbitals P y an P x are the same shape but oriente along their respective axes z y x z yz xy zx x -y
As with the p-orbitals there is a technical complication for the curious to note here. The p z -orbital (hyrogen atom wave function y 10 ) is one of the elementary stationary state solutions (eigenfunctions) to Schröinger s equation for the hyrogen atom, but the p x an p y orbitals are linear combinations of two of the eigenfunctions. This is allowe since the solutions to any wave equation are waves an when we combine two or more waves (e.g. water waves) in efinite proportions we en up with another wave which is still a solution to the wave equation. The resultant px, py an pz-orbitals are of the same shape but simply oriente at 90-egrees to one-another in space. The original eigenfunctions of hyrogen for a given n (principle quantum number, or shell number) an l (orbital angular momentum quantum number) are not all spherically symmetric an yet the Coulomb potential is. Atoms in the absence of irectional forces shoul have no preferre irection, but shoul be spherically symmetric. The combine orbitals for a given shell (aing up the orbitals of ifferent values of l for the same n) are inee spherically symmetric. As the ifferent orbitals of same l an same n (e.g. all the p orbitals) have the same energy (they are egenerate) they can not be istinguishe for a free, isolate atom, instea the egenerate orbitals always combine an average out to form a spherically symmetric set (such as p x, p y an p z ). This gives us a set of linearly-inepenent basis wave-functions from which others can be constructe. For example, an electron in an atom can be in a state which is a combination of both an s an a p-orbital, however, upon measurement it must collapse into a stationary state eigenfunction (either the s or p-orbital). The combination of atomic orbitals (both pure an mixe/average eigenfunctions) must be linearly inepenent (such that any one can not be constructe from proportions of two or more others). Aitionally, it is not actually possible to truly measure the state of an electron in an isolate atom. By performing a measurement we have mae the atom interact with our measuring apparatus an the result of measurement is always the state of the atom after the measurement. Aitionally, the electron orbital is always perturbe, either by internal electromagnetic fiels (ue to the nucleus or electron spin, or to another electron in a multi-electron atom) or ue to an external fiel. If an external fiel is applie in a given irection, then the atom oes inee acquire a irection as the electrons respon to the fiel. This lifts the egeneracy of the orbitals (e.g. of the p orbitals with one irection having lower energy, another higher energy) an spherical symmetry is then remove. Atoms are very sensitive ann the electrons respon to their environment. Similarly, in the -orbitals, the z (y 30 orbital see atomic orbitals) is one of the pure wave function solutions of Schroinger s equation, but the other four - orbitals are linear combinations/averages of the pure solutions an these form geometrically-equivalent four-leaf clover shapes. This gives us a linearlyinepenent set of -orbitals which combine so as to preserve spherical symmetry in the absence of perturbing forces.
When atomic orbitals merge into molecular orbitals to form a bon, the atomic orbitals have to overlap one-another. Only wavefunction lobes of the same sign can overlap in this way (otherwise, if lobes of opposite sign overlap then an antiboning molecular orbital forms). (The wavefunction sign has no other real significance since the actual electron ensity is etermine by the square of the wavefunction). If we consier the long axis parallel to an containing the bon axis, then ifferent classes of bons become apparent. If two orbitals overlap en-to-en, e.g. two s-orbitals, such that the overlap sits irectly between the two nuclei then we have a sigma bon (s-bon). These are the strongest as the overlap is large an the electron ensity, which concentrates at the region of overlap, is irectly in line with the nuclei which are attracte to it (the nuclei o not see each-other to be repelle by oneanother). If the bon axis contains one noal plane (a plane in which the wavefunction an electron ensities are zero) as happens when two lobes overlap we have a pi-bon (p-bon) with two regions of low overlap which are not inline with the nuclei an so the force of attraction an the bon are weaker than for a sigma-bon. in a elta bon (-bon) as occurs between two -orbitals with all four lobes overlapping, there are two noal planes cutting across the bon-axis. As -orbitals are iffuse an the overlap is small, the -bon is very weak an only has a minor, but significant effect, in very few compouns. Some of these bons are illustrate below. In reality, bon formation is more complex. The scheme of sigma, pi an elta-bons is a simplification which nevertheless provies a very useful tool. For example the C=C ouble bon in ethene, CH CH, can be picture as a combination of two s-orbitals to form a sigmabon an two p-orbitals to form a secon, an weaker, pi-bon. This correlates with the fact that the ouble bon enthalpy for C=C is 61 kj/mol on average an 348 kj/mol for the C-C single bon: the ouble-bon is not quite twice as strong as the single-bon, but (61/348 =) 1.76 times as strong. Molecular orbital calculations suggest an aitional complication, however, that single bons can be of mixe character. The single sigma-bon, H-H, in the H molecule appears to be mae up of atomic orbitals consisting mostly of an s-ortbital but also partly of a p-orbital. This links to the iea that ifferent atomic orbitals combine or hybriise when they combine to form a bon. Hybriisation can often be estimate qualitatively, using another useful approximation tool (see the pf on boning in carbon for an example). Ultimately, however, only quantum mechanical calculations can preict molecular orbitals precisely. However, the calculations are too ifficult to perform exactly, but computational methos now exist that are highly accurate, even for large molecules. The figure below illustrates some of the bons forme by -orbitals.
Boning with -orbitals A -orbitals can combine en-to-en (overlap) with one other s, p or -orbital to form a sigma-bon: s s bon p s bon z s bon s bon p bon p bon p bon bon s bon
Transition Metal Complexes Metal ions have a high positive charge ensity (not only are they positively charge but they also ten to be small as positively charge ions are reuce in size ue to the lose of an outer electron shell an the increase in proton : electron ratio increasing the nuclear pull on each electron an pulling the electrons closer to the nucleus). This makes metal ions attractive to electron-rich molecules. certain molecules have both a negative charge an one or more pairs of non-boning electron (lone electron pairs) an such ensities of negative charge (lone pairs of electrons are compact) are strongly attracte to the positive charges of metal ions an the lone-pair may move towars the metal ion an became share between the onor atom an metal ion to form a covalent bon. This type of bon, in which one participant in the bon onates both electrons is calle a ative or coorinate bon. It has been shown that these bons can be highly polarise an are often more ionic than covalent. The molecules attracte to the central metal ion are calle ligans an the resulting molecule is calle a metal complex ion, or simply metal complex. the number of ligans that can fit aroun an bin to the central metal ion epens upon the size of the metal ion, larger ions being able to accommoate more ligans, the size of the ligans, an also the number of share electrons the metal ion can reaily accept. Transition metals often have high charges, giving them high chargeensities an can also accommoate aitional boning electrons in any vacant -orbitals they have, since little energy is neee to a new electrons to a shell that is alreay starting to be fille (in the neutral atom at least) an the -subshell can hol 10 electrons. thus, transition metals form a vast range of complexes an, being ions, these ominate the behaviour of transition metal ions in solution. Other metals also form complexes. For example, some s-block metals form complexes (such as the EDTA complex with Ca ) but lacking easily accessible -orbitals, the s-metals form few complexes. Complex ions can take a variety of shapes. The metal ion is central an the number of ligans boning to the central ion is the coorination number (strictly this is the number of ative bons forme, since some ligans form two ative bons each an are bientate ligans, others more than two). Of relevance to unerstaning the shapes of complex ions, are the more general concepts of the shapes of molecules with central atoms, as estimate by electron-pair repulsion theory. Basically, this theory states that pairs of electrons (whether boning electrons or lone-pairs) position themselves as far apart from one-another as possible, since they are negatively charge an repel one-another. Another important concept, illustrate below, is the ligan/crystal fiel theory. this theory starts off by consiering atomic orbitals in isolate atoms. In such atoms orbitals belonging to the same subshell are egenerate, meaning they have equal energies. For example, s-orbitals are egenerate, p-orbitals (in the same subshell) have equal energy an are egenerate, an - orbitals are egenerate. Thus, the outer-shell of a transition metal atom has egenerate s- orbitals, 3 egenerate p-orbitals (all higher in energy than the s-orbitals) an up to 5 egenerate -orbitals (all higher in energy than the p-orbitals). This applies to atoms in spherically symmetric electric fiels. However, when approaching close to another atom or molecule, those orbitals nearest the electrons on the other atom, will experience greater repulsion (like charges repel) an their energy increases, whilst those furthest away have a lower energy the egeneracy is lifte.
In an isolate atom, or an atom in spherically symmetrical (even on all sies) electromagnetic fiels there is no preferre irection. When the fiel is not symmetric, however, the atom acquires a efinite irection which we can arbitrarily assign to any coorinate axis, by convention this is usually the z-axis. Consier first a metal ion with two ligans bining to it by single ative bons (coorination number = ). Electron-pair repulsion theory tells us that the ligans will repel one-another an so position themselves at opposite ens/poles of the central atom the resulting molecule is linear. In this case the ligan fiels repel those electrons nearest to them. If we assign the long-axis of the molecule to the z-axis then by looking at the shapes of the -orbitals we can see that those with strong components along the z-axis, namely z an to a less extent xz an yz will be most strongly repelle. electrons will ten to avoi these orbitals an the energy of these orbitals is increase. The xy an x-y orbitals, however, are the least concentrate along the z-axis an so these have lower energy than the z, xz an yz orbitals. Since the total energy of the system is assume unchange, these lower-energy orbitals ecrease in energy by an equivalent amount to the increase in energy of the higher-energy orbitals, so that the total orbital energy remains unchange. Coorination (linear) z-axis L z M Energy xz, yz L xy, x -y p z p p x, p y spherically symmetric fiel (free atom) ligan fiel
Coorination 6 (octaheral) z F F F Co F F F e.g. [CoF 6 ] 3- x y Position the axes such that two ligans are at the ± ens of each axis x -y Energy xy-plane xy z xz-plane zx z yz-plane En result: yz { xy, xz, yz } all have the same energy an are stabilise { z, x -y } have the same energy an are estabilise
We now have a oubly-egenerate state (containing two orbitals of the same energy) esignate by e g, an a triply-egenerate state (containing three orbitals of the same energy) esignate t g. (Think of e for ouble-states an t for triple states). The ifference in energy between these two states is calle the crystal or ligan fiel splitting energy, symbol DE, an the gain in energy by the e g state is calle the ligan fiel stabilisation energy or the crystal fiel stabilisation energy (CFSE) since it was first observe in crystals. ote: The g subscript inicates that the orbitals have even parity (as s an orbitals o) an literally means gerae. Even parity means that inverting the orbitals in the original oes not change the sign of the escribing wavefunction. In contrast, atomic p an f-orbitals have o parity an are esignate u for ungerae. O parity means that inversion through the origin (or equivalently as the wavefunction passes through the origin) the sign changes. the sign has no effect on orbital shape, since the electron probability istribution is given by the square of the wavefunction (an a negative square is positive) but signs of wavefunctions are important in eriving boning or molecular orbitals. For the octaheral complexes the energy splitting of the -orbitals is: e g 3/5DE DE /5DE t g ote that the CFSE of /5DE follows from the fact that the total energy changes of all 5 orbitals must be zero an: ( * 3/5) (3 * /5) = 0. For example, the Ti 3 ion in water, Ti 3 (aq), forms an octaheral complex with 6 water molecules: [Ti(H O) 6 ] 3 (sometimes these complexes are written without the square brackets which simply show that the net charge is attribute to the complex as a whole). The electron configuration of Ti is: [Ar] 3 4s an of Ti 3 : [Ar] 3 1, so that the single -electron in the ion moves to the lowest available -orbital, a t g orbital an the CFSE is about 90 kj/mol (or -90 kj/mol).
Empirical Evience Colourful complexes One of the clearest pieces of experimental evience which confirms the existence of e g an t g levels is provie y spectroscopy. Electrons can jump up an own between the e g an t g levels, emitting visible or UV light as they rop own, with the frequency of the light corresponing to the energy ifference (DE). these transitions account for the vivi colours of many transition metal complexes. Colourful complexes sums up well the bulk of transition metal chemistry that we are familiar with from test-tube reactions. Above: three solutions of transition metals salts, each containing a ifferent complex. left: CuSO 4 (aq) containing blue [Cu(H O) 6 ], the copper(ii) hexahyrate complex. Centre: CoSO 4 (aq) containing rose-coloure [Co(H O) 6 ]. Right: icl(aq) containing. ote that these solutions are translucent they are true solutions an nothing to o with precipitates or collois, which also carry the colours of the complex ions (though the soli salts are also similarly coloure as they contain the same hyrate metal ion complexes). The colour given by transition complexes epens upon on the charge on the metal ion, the coorination number, an the ligan. For example, Co3 in solution gives blue [Co(H O) 6 ] 3.
As a further example, tetraheral complexes (coorination 4) of Co ten to be blue. Aing excess KCl(s) to a solution of CoSO 4 (aq) will prouce no obvious colour change at room temperature, the solution remaining translucent rosy-pink, but heating to say about 90 o C, causing more of the KCl to issolve will turn the solution purple an then navy blue as blue [CoCl 4 ] forms an then the solution turns pink again as [Co(H O) 6 ] reforms on cooling (it takes a very high concentration of Cl ions to isplace the waters from the Co ion complex). Molecular orbitals So far, our escription of the electron orbitals in complexes, using ligan or crystal fiel theory, has proven useful, but it is incomplete. When the ligans bin with the central ion, they contribute electrons to vacant -orbitals on the central ion, but the atomic orbitals on the ligan where the electrons come from has to be taken into consieration. In molecules, the electrons occupy molecular orbitals (MOs) an these are forme by combining the atomic orbitals of both boning atoms (or inee of all atoms in the molecule). Solving the quantum mechanical wave equations for these molecules is very ifficult (an requires consierable computer power)! However, an approximation can be mae using a linear combination of atomic orbitals (LCAO). In the LCAO approach, a MO is approximate by aing together the atomic orbitals that go to make-up the MO. the combination is a linear one, meaning that we a a simple numerical ratio of the orbitals. The ligan fiel theory in its entirety inclues both a covalent MO approach an an ionic electrostatic approach to boning in elements. The electrostatic theory takes into account all the charges, ionic an inuce ipoles as well as the splitting of the -orbitals that we have escribe so far. Although very useful, this approach oes not explain complexes in which the central atom has approximately zero charge, in which case the preicte boning woul be much weaker than it actually is. There can be no oubt that in at least some complexes, covalent boning becomes significant. The molecular orbital (MO) theory constructs molecular orbitals over all the atoms/ions in the complex (7 centres for an octaheral complex). For an octaheral complex we nee to combine the 6 orbitals holing the ligan lone-pairs an the 6 receptive orbitals on the central ion. These orbitals combine by overlapping en-to-en (forming sigma-bons). In a transition metal of the first series, these six orbitals are the 3 x -y, 3 z, 4s an three 4p orbitals (in the ion the 4s an 4p orbitals will generally be empty an the 3 orbitals part-fille). These orbitals are irecte towars the ligans an have the right energy (only atomic orbitals of similar energy can be combine to form MOs). The 3 x -y an 3 z orbitals are the two orbitals which were raise in energy by the presence of the ligans, because they are closest to the ligan bon-forming electrons, an hence these are the -orbitals involve in MO formation an they form the e g molecular orbitals. The t g orbitals are non-boning an o not form molecular orbitals. The s-orbital forms the a 1g MO an the three 4p orbitals form t 1u MOs. When MOs form, the total number of MOs must be the same as the number of atomic orbitals that go to make up those MOs, since one orbital, atomic or molecular, can hol a maximum of only two electrons. This conition is satisfie because for every boning MO there is an anti-boning MO. In boning MOs the electron ensity is concentrate in-between the boning nuclei an the electrostatic attraction hols the nuclei together. In anti-boning MOs the electron-ensity is reuce between the nuclei an so no bon is forme by electrons in these orbitals. onboning electrons remain in non-boning orbitals (such as the t g ). An energy-level iagram will clarify these points (see p.10).
Boning MOs in an Octaheral Complex y a1g (s, 6L ) y t1u (p z, L ) y eg ( x -y, 4L ) y t1u (p x, L ) y eg ( z, 6L ) y t1u (p y, L )
Metal ion orbitals p s Molecular orbitals t* 1u a* 1g e* g Energy t g Ligan orbitals s e g t 1u a 1g Above: the energy levels (orbitals) in an octaheral complex in which six ligans forms sigma(s)-bons to the central ion. (recall that s, p an -orbitals can sigma-bon). The high energy antiboning MOs are inicate by an asterisk (*). The boning orbitals are closest in energy to the ligan atomic orbitals an so are more ligan-like than metal-like. Each level can hol a maximum of two electrons with opposite spins. There are 1 boning electrons from the ligans to accommoate in these orbitals an in the groun state of the molecule they will occupy the lowest energy orbitals, initially spreaing apart with one electron per orbital (of the same spin Hun s rule) an then, if the boning orbitals are all singly occupie, the electrons will begin to pair, until there are electrons in each boning orbital an then any aitional non-boning outer-shell electrons will enter the next available orbitals of lowest energy. Thus, the 1 boning electrons a to the a 1g (s-s), the three t 1u (ps) an the two e g (-s) orbitals, with two electrons in each. The ion s -electrons will then populate the non-boning t g orbitals an, if neee, the e* g antiboning molecular orbitals. It is because there are molecular orbitals of lower energy than the original atomic orbitals that boning occurs. The strength of this boning is a function of the number of electrons below the original average energy (in boning orbitals) minus those above the original energy (in antiboning orbitals) an also of the energy splitting magnitue DE a larger magnitue meaning that boning results in a greater energy rop an greater stability.
Coorination 4 (Tetraheral) e.g. [MoO 4 ] O O O 109 o Mo O o -orbital points irectly at a ligan, but xy lies closer to the ligan than x -y an z. The splitting is thus not as great as for octaheral complexes, an is /3 of the octaheral case. Consiering that there are now /3 as many ligans (4 instea of 60 the total splitting is (/3 x /3 = ) 4/9 that of the octaheral case. since particles generally prefer to be in a lower energy state, this suggests that tetraheral complexes are not as stable as octaheral ones. The -orbitals are split into a lower set of two e-orbitals an a higher energy set of three t orbitals. we woul then expect the t to form boning an anti-boning molecular orbitals (an the e-orbitals to be non-boning). t g /5DE DE 3/5DE DE(tetraheral) 4/9 DE(octaheral) The octaheral an tetragonal shapes account for many transition metal complexes, but a variety of other coorination numbers an shapes are possible, as there are for other molecules with a central atom (see Shapes of Molecules). Configurations can also be istorte, for example not all ligans may be ientical an this can lower or raise the energies of certain orbitals. E.g. in a tetragonal complex (coorination 6) the two z-axis ligans are ifferent from the four ligans that bon in the square plane, an this alters the energies of those orbitals with more alignment along the z-axis an can split the e g an t g orbitals into smaller sets (lifting some of the egeneracy). e g
The three most common complex shapes are: 1) octaheral (coorination 6), the most common; ) tetraheral (coorination 4), which we have consiere, an 3) square planar (coorination 4), probably more common than tetraheral. If you are familiar with how the shapes of molecules with central p-block atoms (such as halogens or xenon) are estimate by electron-pair repulsion, you might be wanering why the non-boning lone-pairs of electrons in the -orbitals on the metal are not consiere when etermining the shape. on-boning -electrons o not affect shape in the way that nonboning s or p-electrons o. this is presumably because electrons in -orbitals are quite iffuse an sprea aroun the atom an o not form compact regions of local charge that partake in electron-pair repulsion. that is, the rules for etermining the shapes of -block compouns are similar but ifferent. The orbital splitting in square-planar compouns can be obtaine qualitatively from that for octaheral complexes by removing the two ligans along the z-axis. Square planar (coorination 4) z Br Br e.g. [Au(Br) 4 ] Au Br Br The square-planar geometry is essentially the octaheral geometry minus the two z-axis ligans. Beginning with the octaheral complex, MA 6 in which all 6 ligans, A, are ientical, if we replace the z-axis ligans with a secon ligan type boun to the central atom by longer bons, giving MA 4 B, then we have a istorte octaheron (a tetragonal complex) A B A A A A M M A A A octaheral A A B istorte octaheral What effect oes this change have on the octaheral energy levels? We woul expect those orbitals lying largely along the z-axis to relax a little the repulsion they experience from the ligans is reuce an so they shoul rop in energy. This causes the z, xz an yz orbitals to rop in energy. The remaining two orbitals, x -y an xy will then increase in energy slightly as they experience less repulsion from the z-ligans. Taking this a step further an pulling the z-ligans away to infinity, proucing a square planar complex, the z orbital rops so much as the xy increases that the two swap over, with the z having the higher energy. This is illustrate below:
x -y x -y z, x -y e g xy z xy t g xy, x z, yz xz, yz z xz, yz octaheral fiel tetragonal fiel square planar fiel Energy levels in a tetraheral, tetragonal an square-planar complex compare.
Isomerism in Complexes Isomers are compouns/molecules with the same molecular formula but ifferent structural formulae. (See pf on isomers). 1. Structural isomers Isomers in which the atoms an functional groups are joine together in ifferent arrangements. In complexes, we have so far consiere only the first co-orination sphere, the co-orination of nearby ligans to the central ion/atom. however, other ions can bin to the complex ion, such as by ionic boning to form a salt, e.g. a sulphate salt: [Co(H 3 ) 5 Br] SO 4, which is a structural isomer of the bromie: [Co(H 3 ) 5 SO 4 ] Br which contains a very ifferent complex.. Stereoisomers Molecules that have the same molecular formula an their atoms an are joine together in the same sequence, but their atoms are arrange ifferently in 3D space. a. Geometric isomerism: similar ligans may be opposite (trans) or ajacent (cis) to oneanother (coorination number 4): 3 H 3 H Cl Co H 3 H 3 3 H 3 H Cl Co Cl H 3 1. trans 1. cis Cl H 3 Cl H 3 Cl Pt Pt 3 H Cl 3 H. trans. cis Cl H 3 b. Optical isomerism. Enantiomers are pairs of stereoisomers that are non-superimposable mirror images of each other (one cannot be rotate onto the other without a mismatch, like your left an right hans!). E.g. [Co(en) 3 ] 3 Co Co CH H CH H ethyleneiamine (en)