Appendix 2. Complexes - introduction: ligands, bonding, co-ordination number and charge on complex ions

• A complex is formed by the combination of a central metal ion surrounded by, and bonded to, neutral molecules or ions acting as 'ligands' (bits stuck on or appendages).

  • If you have already read Appendix 1. you should note that it is riddled with complex ions and the central metal ion does NOT have to be a transition element. The two ligands involved were H₂O and OH^-.

• A ligand is an atom, ion or molecule which can act as an electron pair donor (Lewis base) and usually forms a dative covalent or 'co-ordinate' bond with the central metal ion.

  • The lone pair donation is usually from an O, N or halogen atom of the ligand in this covalent co-ordinate bonding.

  • The central metal ion acts as a Lewis Acid, that is, an electron pair acceptor from the ligand by way of vacant 3d, 4s, 4p  and even 4d orbitals for the 3d-block transition elements.

  • The ligand acts as a Lewis Base, that is, an electron pair donor e.g. neutral ligands like H₂O: (water, aqua in complex name) or :NH₃ (ammonia, ammine in complex name) and negatively charged ligands like :OH^- (hydroxide, hydroxo in complex name), Cl^- (chloride ion, chloro in complex name) and :CN^- (cyanide ion, cyano in complex name).

  • ...

    • A an example of the bonding in a complex ion is shown in the above diagram. The negative cyanide ion is a monodentate ligand (forms one bond per ligand) and donates an electron pair into a vacant 3d, 4s or 4p orbital in the iron(III) ion to form six dative covalent bonds.

    • The resulting ion has the formula [Fe(CN)₆]^3-, the overall charge of 3- is the aggregate of 6- (cyanide ions) plus 3+ (iron ion)

    • The co-ordination number of 6, which means there are 6 central metal ion - ligand bonds. It doesn't necessarily mean six ligands, you can get a co-ordination number of 6 from three co-ordinated bidentate ligands (2 bonds per ligand), two tridentate ligands and from EDTA just one ligand can form 6 dative covalent bonds with a central metal ion. More on this below.

    • The most common complex ion you will come across is the hexaaqua cation of many metals.

      • It has the general formula [M(H₂O)₆]ⁿ⁺

      • n, the charge on the central metal ion and hence the overall charge on the complex ion n is usually 2 or 3 e.g.

      • n = 2 for titanium(II), vanadium(II), iron(II), cobalt(II), nickel(II), copper(II) and also the Group 2 alkaline Earth metals magnesium, calcium etc.

      • and n is 3 for scandium, titanium(III), vanadium(III), chromium(III), iron(III), cobalt(III) and also aluminium from Group 3.

      • The six neutral water ligands form 6 dative covalent bonds with the central metal ion because the bonding pair of electrons comes from donation of a lone pair from the oxygen atom of the water molecule.

      • Therefore the co-ordination number is 6 and it has a symmetrical octahedral shape.

      • The O-M-O bond angles are all 90^o or 180^o.

• The ligand may attach itself by one or more bonds. The suffix '...dentate', prefixed by mono/uni/bi/ploy/multi e.g. monodentate (unidentate), bidentate, or polydentate (multidentate) is used to denote the number of bonds each ligand makes with the central metal ion.

• The total number of ligand bonds to the central metal ion is called the co-ordination number.

  • It is not the number of ligands, unless it is a monodentate ligand.

  • There is no firm rules relating shape to a particular ligand.

  • The six ligands don't have to be the same e.g. ...

    • ... which is the dichlorotetraaquachromium(III) ion. This octahedral complex with a co-ordination number of 6, and note this has an overall ion charge of (2 x - from 2Cl^-) + (3+ from Cr³⁺) = +, water is an electrically neutral ligand ...

      • ... and in equations the complex ion would be written as [Cr(H₂O)₄Cl₂]⁺

• Examples of unidentate/monodentate ligands:

  • 

  • e.g. above are shown two complexes with electrically neutral ligands: water H₂O:, ammonia :NH₃ and primary aliphatic amines like butylamine CH₃CH₂CH₂CH₂NH₂, 

  • These ligands often form octahedralshaped complexes with a co-ordination number of 6.

  • e.g. negative ligands: chloride Cl^-, cyanide CN^-,

  • The chloride ion Cl^- forms the tetrahedrale.g. the tetrachlorocuprate(II) complex ion ...

  • [CuCl₄]^2-, note the overall charge is (2+) + (4 x -) = 2- and the co-ordination number is 4.

  • The chloride ion can be too bulky to form an octahedral complex or a square planar complex, though there is no firm rules relating complex shape to ligand.

  • and CN^- square planare.g. the tetracyanonickelate(II) complex ion ...

  • [Ni(CN)₄]^2-, note the overall charge is (2+) + (4 x -) = 2- and the co-ordination number is 4.

    • Note that [Cu(H₂O)₄]²⁺, in the hydrated salt CuSO₄.5H₂O, the tetraaquacopper(II) ion, with the less bulky water molecule ligand, forms a blue square planar complex, whereas with the larger chloride ion, a tetrahedral complex is formed.

  • A linearshaped complex is formed between a silver ion the ligands ammonia or cyanide.

    • cationic [H₃N-Ag-NH₃]⁺  and anionic [NC-Ag-CN]^-

  • [Ag(NH₃)₂]⁺ is formed in 'ammoniacal' silver nitrate solution used in the test for aldehydes. The diamminesilver(I) ion has co-ordination number of 2 and an overall charge of a single + because the ammonia molecule is an electrically neutral ligand.

• Examples of bidentate ('two toothed') ligands:

  • neutral ligands: diamines like 1,2-diaminoethane (ethane-1,2-diamine) H₂NCH₂CH₂NH₂ (bonds via lone pair :N).

  • negative ligands: ethanedioate ion C₂O₄^2-, (bonds via lone pair on the :O^-). The L represents where the dative covalent bond forms.

  • shows three bidentate ligands co-ordinated to a central metal ion (co-ordination number 6, 'octahedral' in bond arrangement).

  • Examples: [Cr(H₂NCH₂CH₂NH₂)₃]³⁺, H₂NCH₂CH₂NH₂ is often represented in shorthand by en,

    • and the complex simply written as [Cr(en)₃]³⁺.

  • Bidentate ligands are the first of what are called polydentate ligands and such complexes are sometimes called chelates from the Greek for 'crab's claw' and the complex formation described as a chelation process.

• More examples of multi/polydentate ligands:

  • EDTA^4- (old name 'EthyleneDiamineTetraAcetic acid') forms six bonds with a central metal ion and tends to displace all other ligands.

    • [Ni(NH₃)₆]²⁺_(aq) + EDTA^4-_(aq) [Ni(EDTA)]^2-_(aq) + 6NH_3(aq)

  • The haemoglobin molecule acts as a multi/polydentate ligand with iron(II) ions in blood chemistry.

    • in an extremely simplified form the structure is: [protein-Fe^II-O2]

• One ligand can replace another depending on the relative bond strengths in a reaction called ligand exchange reaction.

• When a bidentate or polydentate ligand is added to a pre-existing complex of monodentate ligands, it is highly likely a more stable complex will be formed.

  • The principal reason for this, (ignoring bond strengths), is the positive entropy change accompanying the 'release' of 4 or 6 small molecules which offer a greater variation of ways of arranging the particles or energy distribution.

• If the ligands are easily exchanged, the complex is described as 'unstable' and if the ligands are more strongly bound, the complex would be described as stable.

• Complex ion stability is also related to the oxidation state of the transition metal in the presence of a particular ligand.

• See Appendix 3. for more on complex ion shape and isomerism.

• See Appendix 5. for more on electrode potentials, oxidation state and complex ion stability.

• See Appendix 8. for more on complex ion stability, entropy changes and stability equilibrium constants (K_stab).