GENERAL INTRODUCTION BY J. W. Lnwmr Inorganic Chemistry Laboratory, Oxford Received 3rd July, 1958 The general object of this meeting is to consider the properties and electronic structures of the ions of the transition elements especially when they are included in complexes; the particular aim being to bring physicists and chemists together to discuss these problems. This introduction will be divided into two parts. The first will deal with the theoretical treatments of the electronic structures and the second with the various experimental methods that are being used for studying these compounds, often in order to discover more about the electronic structures. SECTION I The three procedures for treating the electronic structures are (i) the Pauling valence bond method; (ii) the molecular orbital method; and (iii) the ligand (or crystal) field method. PAULING’S METHOD Pauling dealt only with the electronic structure of the ground state,l and was primarily interested in the shapes and magnetic moments of complexes.He designated the orbitals of a complex in terms of the orbitals of the central atom. For the first long period the important valency shell orbitals were the five 3 4 one 4s and three 4p orbitals and he supposed that a number of these, equal to the number of ligands, were involved in bond formation. He devised a most suc- cessful means of presenting his ideas ; two examples are shown in fig. 1. Pauling’s FIG. 1 .-Examples of Paulhg-type representations for (a) Fe(CN);- and (6) NiCl, . ZP(C,H,),. main achievement was his systematization of the shapes of complexes in terms of the groups of central atom orbitals involved in accepting electrons from the ligands.For instance, the group d2sp3 led to an octahedral, and sp3 to a tetrahedral arrange- ment (cf. fig. 1). The directional qualities of these groups of orbitals may be presented in terms of either hybrids 2 or configurations of maximum probability.3 The results of the two viewpoints are necessarily the same. Pauling’s approach encountered difficulties when the number of orbitals needed to accommodate all the electrons was too small, either because of the total number of electrons present, or because of the number with parallel spin 78 GENERAL INTRODUCTION as indicated by magnetic measurements. This difficulty was met by supposing either that outer orbitals (e.g.some of the five 4d, or the 5s, in the first long period) had to be considered, or that the structure of the complexes was " ionic ". Ac- cording to the latter the electronic structures of the central ion and ligand groups were, in certain cases, sufficiently separate and independent that the orbitals of the ligands had to be considered as well as the central atom orbitals. This meant that the bonding electrons which, in covalent complexes, occupied orbitals in- volving those of the central ion, occupied, in ionic complexes, orbitals separate from the central ion leaving all nine orbitals of the central ion free to accommodate the other electrons. By Hund's rule these tended to be spread with parallel spin as widely as possible among the degenerate orbitals so that the high magnetic moments of ions such as FeFg- were explained.MOLECULAR ORBITAL METHOD This employs the same orbitals of the central ion as does the Pauling method but, in addition, the N orbitals of the N ligands which are directed towards the central atom are included. For example, if there are six ligands, there are in all fifteen orbitals available for the construction of the molecular orbitals by linear combination, this being the approximation that is used. Supposing that the ligands are octahedrally disposed along the Cartesian axes, there will be three degenerate non-bonding d-orbitals (usually labelled dwy, dyz and dzx having their four lobes directed between the artesian axes),* six bonding orbitals derived from the d2sp3 grouping (cf.Paulhg) and six corresponding anti-bonding orbtials with additional nodes in the wave function between the central atom and the ligands. By analogy with Pauling's method, the molecular orbitals may be repre- sented diagrammatically as in fig. 2. The way in which the molecular orbitals are occupied is shown for some cobaltous complexes in fig. 3. This may be com- pared with a diagram for these same compounds based on the Pauling system pub- ished by Nyholm.4 With Co(H20)26' the Pauling type representation is 3d2.3d2.3d. 3d. 3d. 49.4~2.4~9.4132-4d2.4d2 the last six pairs being the bonding ones. They have been underlined to indicate this. Each of the 4d atomic orbitals has one spherical node f so that, as regards the number and general form of the nodes, they resemble the molecular orbital which may be described as " 3d anti-bonding " for this has a node between the central atom and all the ligands.The Pauling and molecular orbital representa- tions are therefore quite different in character. A Pauling type representation which would be more like the molecular orbital one is 3d2.3d2.3d. 3 d 2 . 3 d 2 . 4 ~ 2 . 4 ~ 2 . 4 ~ 2 . 4 ~ 2 . 4 d . 4d. However, it does seem that, for ions requiring this number of orbitals to accom- modate the electrons, the molecular orbital method is much sounder and more straightforward. The Pauling method has only been applied to complex ions qualitatively. The molecular orbital method is, however, capable of dealing with the system quanti- tatively, and the energy level diagram for an octahedral complex will now be * The five d orbitals will be labelled d,,, dx,, d,,, dz2 and dx2 - ,2 The first three have four lobes which are directed between the Cartesian axes given in the subscript.The last is of the same form with positive lobes in the + x and - x directions and two negative lobes in the + y and - y directions. The fourth has positive lobes in the + z and - z directions and a smaller negative " frill " in the xy plane ; its variation is in fact (3z2 - r2). t Since the number of nodes is one less than the principle quantum number, a 4d orbital has one spherical and two other nodes. For 4d,, the two other nodes are the xz and yz planes.J . W. LINNETT 9 (a) Six octahedral ligands. f l a W T1 1 1 non- bonding - T T I , T L T1 1 1 T1 1'1 + dx, dyz dxy dzz dx=-y= Px Py br (b) Four planar ligands (d)T 1 T i T T T v tl T L T1 T b10 GENERAL INTRODUCTION considered.If n-bonding is ignored, orbitals of only four symmetry classes need be taken into account. These are (a) totally symmetric A1, orbitals (e.g. 4s of the central atom) ; (b) triply degenerate 7'1, orbitals (e.g. 4p) ; (c) doubly degener- ate Eg orbitals (e.g. d,z and d,Z-,,z); (d) triply degenerate T2, orbitals (e.g. d,,, dyz and dzx). The six ligand u-orbitals can be combined to give an Al,, a pair of Eg and a trio of TlU orbitals. These can combine respectively with the 4s, dtz and dxz - p, and 4p orbitals of the central atom. The orbitals in (d) remain un- changed and are non-bonding in this approximation in the complex.Consider, for example, the two component Al, orbitals (central atom and ligand). These will combine according to the simplest molecular orbital procedure to give two new orbitals of energies E given by where El and E2 are the energies of the two component orbitals and /3 is the so- called exchange integral, which is dependent, in part, on the extent they overlap. The lowering in the energy of the orbital of lower energy (which, at this approxima- tion, is equal to the rise in the energy of the orbital of higher energy) is greater the smaller (El - E2) and the larger 18. These quantities are estimated in various more or less empirical ways. The values of El and E2 are usually obtained from a consideration of ionization potentials while those of the various 18s are fixed in a more or less arbitrary but necessarily uncertain manner to reproduce a measured quantity.Because of doubts of the above type, it is not easy to be sure what precise order the various molecular orbitals will take in a given complex. Clearly the Al,, Eg and 7'1, bonding orbitals lie below the T2, non-bonding orbitals, while the anti-bonding orbitals (Alg, Eg and 7'1,) lie above them. Owen5 gives the order of the last three as E,, A1, and 7'1, for an ion in which the ligand is " an ion like Cl- ". On the other hand a calculation for Cr(CN)z- by Gilde and Ban,6 who have used the procedure adopted by W-olfsberg and Helmholtz7 for Mn04, CrOi- and ClO,, gives the order as Al,, TI, and E, (see fig. 4). The reason for the large splitting of the Eg orbitals in this complex is that an electron in the ligand orbitals and one in the 3d orbitals of the central atom have about the same energy and the corresponding exchange integral is not small.It is possible, of course, that the order of levels may differ in different complexes. Since these are the orbitals into which electrons can be excited from the T2, orbital on light absorption they are of interest. The energy of the anti-bonding E, orbital will be higher the greater the overlap of the 3d and the ligand orbitals, and this overlap is likely to be greater the smaller the effective nuclear charge on the ligand atom adjacent to the central atom. This provides an explanation of the basic form of the spectrochemical series (see later). The ionization potentials associated with the particular orbitals will also be important.As Orgel says, molecular orbital theory, in its complete form, includes all interactions between electrons and nuclei. It is therefore the utility of the theory in a reasonably simple form " which is at stake ".* The diagrams in fig. 3 present a similar approach to the basic stereochemistry of the complexes as that due to Pauling, but some h e r points also appear. Because only one of the degenerate pair of anti-bonding d-orbitals is occupied in Co(N0,):- and it must be in either the d , ~ or d,z - ,,z orbital, it will be expected that the full octahedral symmetry will be lost and that the two polar bonds will be longer or shorter than the equatorial ones according as the d,z or dxz - y~ is the one occupied. In the former case, the Pauling treatment equivalent to this would be that, while the equatorial bonds were formed by electron pairs, a three electron and an elec- tron pair bond resonated between the two polar ligands causing a weakness of these bonds.9 They differ in detail in that the approximate wave functions constructed according to the two hypotheses would differ, allowing to a different degree for electron correlation.* 10 In Co(H20)2,+ complete octahedral symmetry wouldJ .W. LINNETT 11 also be lost since a group of three degenerate orbitals arc not symmetrically 00 cupied (i.e. filled or half-filled). However, the effect will be small because the orbitals are non-bonding. On the other hand, in Co(diAs)i' the half-filled orbital is nan-degenerate for a square arrangement so that only bond strain will destroy the full symmetry of the ion.In CoC1:- the set of three degenerate orbitals are half-filled so that the ion is a regular tetrahedron. large overlap small overlap €9 a . . . . b .. .- TI, .. : ;'. 4 p *.=' :. .. .. *. b ' a' . : : ;. 4s ; ; . . * . 3d T29 ... -.. T2g .{ Jigand 'A 8.'. TI" Alg \.* *. .. .. . :. .'. . . .. .. .. *. TIU .. * . * . * . * . 8 . E9 * . A 19 €9 . . (4 atomic and ligand orbitals. FIG. 4.-Diagrammatic representation of possible molecular orbital energy levels of AX6 in relation to the energies of the atomic and ligand orbitals for two cases : (a) Owen 5 (X is C1-) ; (b) Gilde and Ban 6 (X is CN-). (b) Pauling classed complexes as " ionic " or " covalent " according as the electron pairs on the ligands occupied solely ligand orbitals or orbitals involving contribu- tions from the central atom (e.g.FeFz-, ionic; Fe(CN)i- covalent). Molecular orbital theory would treat these two within the same framework rather than as two distinct types. The bonding and anti-bonding molecular orbitals involving the d-orbitals of the central ion are represented by a linear combination of the atom and ligand orbitals. The difference between the energy of the anti-bonding and non-bonding d-orbitals will depend on the amount of mixing with the ligand orbitals in the anti-bonding orbitals (cf. fig. 4). If the mixing is small (Pauling's " ionic ") then the energy difference will be small and the electrons will be spread, in order to reduce inter-electronic repulsion, among the non-bonding and anti- bonding orbitals (FeFz-).If there is considerable mixing Cpauling's " covalent ") * By electron correlation is meant the tendency of electrons to keep apart from one another by virtue of the fact that they are all negatively charged and because of spin effects.12 GENERAL INTRODUCTION the energy of the anti-bonding orbitals will be much greater than that of the non- bonding orbitals and all the electrons will occupy the non-bonding orbitals (Fe(CN)g-). These two treatments are not therefore very different in concept, though they are different in detail. LIGAND FIELD METHOD This has grown out of the crystal field theory11 and envisages the complex as a central ion surrounded by other ions or molecules, the orbitals of which to a first approximation are essentially separate.To that extent, it treats all complexes like Pauling’s “ ionic ” complexes. For an octahedral complex, there are six ligand orbitals fully occupied and a number of orbitals of the central ion wholly or partly occupied. In fact, for transition elements, the theory con- centrates attention on the d-orbitals and considers the effect of the field due to the ligands on their energies, the degeneracy being destroyed by the field (an effect not included by Pauling). Ligand field theory therefore considers only those d-type orbitals which, in the molecular orbital diagrams in fig. 2 are labelled non-bonding and anti-bonding, the ligand orbitals replacing the bonding ones. The sequence of energies is qualitatively the same on the two theories. They differ, however, as to the causes of this splitting.A molecular orbital calculation introduces new interactions between the electrons occupying atomic orbitals and the additional nuclei and electron cores probably allowing also in an empirical way for the other electrons, the energies of a number of new one-electron molecular orbitals being obtained. The energy of the system is then the sum of these for the occupied orbitals. The molecular orbitals may be very different in form from the individual atomic orbitals. On the other hand, the ligand field theory supposes that the ligand orbitals are not affected on complex formation. It considers the effect on the energies of the central atom orbitals by the ligands, the effect resulting mainly from the field due to the electron pairs in the ligand orbitals adjacent to the central atom.The prime cause of the splitting is therefore treated differently in the two cases and it may be that these differences are important when attempting to account for, say, the spectrochemical series and the effects of different ligands on stability constants. The success of ligand field theory lies, to some extent, in the numerical results obtained. These are surprisingly successful considering the ruthlessness involved in the approximations. It has also benefited from a shift of interest towards electronic absorption spectra and their employment in deducing electronic struc- tures. Numerically ligand field theory depends partly on parameters which are assessed empirically and partly on quantities deduced from data obtained from the atomic spectra of the central atoms.Using again an octahedral complex as the example, the field due to the ligands will split the five d-orbitals into a low-lying triplet ( d ~ ~ ~ made up of dxy, dYz and dxz) and a higher energy doublet (dE, made up of dZ2 and dxz - ,,2) (see fig. 5). It has not been possible to calculate satisfactorily the splitting that will result in a given complex, though models in which the orbitals of the central atom are perturbed by six charges or dipoles have been proposed and tested.12 As a consequence the separation of the triplet and the doublet is usually estimated from the spectrum. The data for the hydrates of the di- and tri-valent ions are the most complete.For the former, in the firFt transition series, the splitting varies between about 8,000 and 14,000 cm-1 (23 and 40 kcal/mole) changing in a somewhat irregular manner with atomic number. For the hydrates of the trivalent ions the splitting is considerably greater though not in uniform ratio to the iso-electronic divalent ions. This is peculiar and Jorgensen says : 13 “ If the ligands are not much more polarised, this result can only be explained by treatments taking intermixing of molecular orbitals into account.” The splitting of the levels is greatest with CN- as the ligand. For Cr3+ Jorgensen gives the splittings as 26,300, 21,600, 17,400 and 13,300 for CN-, NH3, H20 andJ . W. LINNETT 13 C1-. This sequence can be understood on the basis of ligand field theory (and also on molecular orbital theory).Allowance has also been made for changes in inter-electron repulsion energy for different occupations of the orbitals. This is usually carried out by a procedure devised by Condon and Shortley 14 and used also by Racah 15 (cf. also Tanabe and Sugano 16). The parameters involved in these calculations can be evaluated from atomic spectra but it appears (Orgel 17 and Owen 18) that they are smaller (half or two-thirds) in the complexes than in the isolated atoms. This decrease in the inter-electronic repulsion indicates that the wave functions are spread over a larger volume in the complexes than in the isolated atoms. This could be due to a decrease in the effective electronegativity of the central atom leading to an ex- pansion of the atomic orbital, or to a mixing of the orbitals of the central atom with those of the ligands.T A 0 S FIG. 5.-Ligand field splitting of the five d-orbitals of the free atom A, by a regular octa- hedral field 0, by a square field in the xy plane or a distorted octahedron with the bonds in the z-direction extended S, and by a tetrahedral field T. Both ligand field and molecular orbital theory predict a splitting of the 3d orbitals on complex formation so that they can clearly both explain many phe- nomena depending on this. Molecular orbital theory provides potentially the more complete description but ligand field theory, by limiting the consideration to a few orbitals, can within this limitation, be carried through more completely and with fewer subsequent assumptions.It seems that in many cases the results of the calculations are most useful (cf. earlier quotation of Orgel). The two ap- proaches should, however, be regarded as complementary, their similarities as well as their differences being borne in mind. n-BONDING So far only u-bonding has been considered. In fact, n-bonding is also possible. For octahedral complexes perhaps the most important n-bonding is that involving the dxy, drz and d,, orbitals labelled in fig. 2 as non-bonding. This n-bonding will be possible when there are appropriate orbitals on the ligands with which the d-orbitals can combine. It is probably important in some cyanides and carbonyls. In these ligands the n-bonding orbitals are filled. Therefore, in ferrocyanide, there are 15 electron pairs to be disposed between 15 molecular orbitals derived from the 3 atomic orbitals on the iron atom and the 12 bonding 7r-orbitals of the ligands.As far as complex formation is concerned, of these molecular orbitals three are bonding, three are anti-bonding, and nine are non-bonding and all are14 GENERAL INTRODUCTION occupied, it does not seem that these can provide any resultant stabilization. However, their effect must be taken into account when considering electronic transitions, because one is concerned with transitions from the highest occupied orbital and the energy of this has been affected by the n-bonding. In ions such as Cr(CN)i- where the above orbitals are not filled there may be some resultant n-bonding. However, the precise form of the low-lying n-orbitals of this type does not appear to have been examined closely.Paramagnetic resonance measure- ments show that the ones occupied by the unpaired electrons do not involve the nitrogen atoms because there is no hypedine splitting due to the nitrogen nuclei.19 On the other hand, Raman spectra and bond lengths show that the strength of the CN bonds is not greatly affected. It is not entirely clear how both these two observations are to be accommodated. A class of ligand in which 7r-bonding is almost certainly particularly important is that exemplified by PEt3 which has a vacant d-orbital which can combine with and accept electrons from a dxr orbital of the central ion. SECTION I1 The second part of the introduction will deal in general terms with some of the more common experimental methods that are being used for studying the structure of transitional metal ions and their complexes.STEREOCHEMISTRY The stereochemistry of complexes has always interested the chemist and the classical method of identifying isomers was first used in studying it. More recently X-ray crystallography has been employed and many structures have been obtained including specially interesting ones such as those of Mo(CN);-,20 and TaF;-.21 The structures of ionic crystals are also of interest. For example, CrF2 has a distorted rutile structure,22 two opposed CrF distances being longer than the other four. This can be explained on crystal field theory because there is one electron in the pair of orbitals which would be degenerate for a regular octahedron and so a Jahn-Teller distortion occurs.Also MoS2 has a layer structure, each molybdenum atom being at the centre of a trigonal prism which has the sulphur atoms at the corners.23 MoS2 is diamagnetic so it appears that bonding may be achieved by a d4sp group of orbitals.24 Nevertheless one could wish that many more crystal structures involving com- plex ions and oxide, halide, etc., lattices had been determined. For example, it is known that the six oxygen atoms are arranged irregularly round the metal atoms in Cr03, Moo3 and WO3.25 But only for Moo3 has the precise structure been determined.26 In that case the three oxygen atoms in the + x, - x and + 3 directions lie on the Cartesian axes, the molybdenum being at the origin.Those in the + y and - y directions are displaced slightly in the - z direction, while that roughly in the - z direction is displaced considerably in the 4- x direction and is much further from the molybdenum atom than the others. This is fascin- ating and it would be interesting to know the irregularities in CrO3 and WO3. Numerous examples of our ignorance of particular structures could be given and the situation is being remedied only slowly. Moreover, more detailed and accurate knowledge of precise shapes would be valuable. For instance, informa- tion about small irregularities, or a series of accurate metal-ligand bond lengths would be most acceptable. INFRA-RED AND RAMAN SPECTRA Another means of measuring the relative strengths of metal ligand bonds might be by using infra-red and Raman spectra. For various reasons this has not been carried out as extensively as might have been expected.For example,J. W. LINNETT 15 the radiation usuaUy used for exciting Raman spectra, the 4358A mercury line, is often absorbed by transition metal complexes. Probably, with the development of alternative sources, this particular difficulty may be avoided. Chatt, Duncanson and Venanzi 27 have employed infra-red spectra to assess electron drifts in platinous complexes. They measured the NH stretching fre- quencies in compounds of the general formula trans-(L, am, PtC12) where L represents a variety of uncharged ligands (P(C3H7)3, C2H4, SbEt3, SeEt2, SEt2, etc.), and “ am ” various amines (e.g. 2 : 6-dimethylaniline, piperidine, etc.).Because the NH frequencies “increase as the nitrogen atom becomes more negatively charged” drifts in the system L-Pt-N-H can be assessed. They consider their observations in connection with the relative ability of the various L groups to direct an incoming substituent into the trans position.2* They con- clude that groups capable of accepting electrons by n-bonding from the dxy orbital of the platinum exert a strong trans-directing effect because there is a withdrawal of electrons from the dx,, orbital which therefore affects particularly the position tram to L, so that nucleophilic attack is favoured in that position. THERMODYNAMIC PROPERTIES To account for the actual and relative stabilities of different complexes must be one of the main objects for the chemist.The stability is best represented by the equilibrium (stability) constant governing the formation of the complex and this may be given as the free energy change AG. In most cases these quantities refer not to some idealized reaction but to the partial or complete conversion of the transition metal ion from the hydrated form in aqueous solution to a complex involving another ligand also in aqueous solution. Ideally one would wish to know, in addition, the contributions to AG of AH, the heat content change, and TAS where AS is the entropy change. Unfortunately only in a few cases are AG, hH and AS all known so, in considering stability constants theoretically, it has usually been necessary to assume that, for the same reaction of a closely related series of ions, AS remained constant and that changes in AG reflected changes in AH.That this can be a satisfactory assumption is indicated by some data due to Care and Staveley29 who showed that AS on the production of the ethylene diamine-tetracetic acid complexes of Ni2+, Cu2f and Zn2f at 20°C were 56.7, 56.4 and 56-3 cal/mole deg. respectively. On the other hand AS for the formation of the bis(ethy1ene-diamine) complexes of the same three ions is - 14.0, - 16.5 and - 9.8.30 Chatt and Wilkins 31 have also drawn attention to the differences in the entropy changes involved in the formation of cis and trans isomers suggesting that the difference may be due to the fact that the former has a dipole while the latter has not. It must therefore be hoped that, in the future, more values of hH itself will become available.An important observation regarding stability constants was made by Irving and Williams 32 and others.33 It was noted that, for many ligands with divalent metal ions in the first transition series, the stability constants increased in the series of divalent ions of Mn, Fey Co, Ni, Cu where a maximum was reached, the constants being smaller for Zn. Irving and Williams interpreted the data in terms of the s u m of the first and second ionization potentials of the metals. However, Orgel34 has pointed out that these ionization potentials do not refer to the same electronic changes in all the above ions because the copper atom, in its ground state, has only one 4s electron whereas all the others have two. Orgel has interpreted the effect in terms of the splitting of the d-orbitals of the central atom by the field due to the ligands, though the principle of the interpretation would not be altered if the d-orbital splitting were regarded in terms of molecular orbital theory.According to Orgel electrons in the lower-lying d-orbitals (the triplet, d ~ ~ ~ , for an octahedron) favour stability, while electrons in the higher ones (the doublet, dEg, for an octahedron) favour instability. The basic covalent bond strength is supposed to be increasing from Mn to Zn. From Fe to Ni the16 GENERAL INTRODUCTION ligand field stabilization is increasing as electrons are added to the lower orbital. In Cu, the extra electron is added to the upper orbital but the anti-bonding effect of this is counteracted by the greater splitting factor for Cu and also by the de- parture from full octahedral symmetry.In Zn, ligand field stabilization is zero because the 3d-orbital is filled both in Zn2+ and in the complex. Orgel 35 has introduced this type of interpretation when he considered the heats of hydra- tion of the divalent ions from Ti2+ to Zn2+ in a paper which, by applying crystal field theory to definitely chemical data, for the first time caused this theory to have a great impact on chemists. This series shows the same behaviour from Mn2+ to Zn2+ as had been noted by Irving and Williams but the behaviour is aIso the same in the fist half of the transition series preceding Mn2+. Effects of the above type may be illustrated in greater detail by Orgel's con- sideration of the first, second and third stability constants for the ethylene-diamine complexes of Mn2+ to Zn2+.36 His analysis is summarized in table 1.The experimental values of log Kt, log K2 and log K3 and their sum are listed; in TABLE l.-LoGmms OF THE EXPERIMENTAL AND INTERPOLATED VALUES OF THE FIRST, SECOND, THIRD AND TOTAL STABILITY CONSTANTS FOR THE ETHYLENE-DIAMINE COMPLEXES, TOGETHER Wi.TH THE DIFFERENCES BETWEEN EXPEFUhENTAL AND INTERPOLATED VALUES.36 M n Fe co Ni cu Zn log K1 expt. log Kl int. A log Ki log K2 expt. log KZ int. log K3 expt. log K3 int. A log K3 log K expt. log K int. A log K A log K2 2.73 2.73 0 2.06 2.06 0 0.88 0.88 0 5.67 5.67 0 428 3-33 0.95 3-25 2-58 0.67 1.99 1-05 0-94 9-52 696 2 5 6 589 3-92 1.97 4.83 3.10 1 -73 3-10 1 -22 1.88 13-82 8.24 5.58 7.52 4-52 3.00 6.28 3.62 2.66 4 2 6 1.38 2.88 18.06 9-52 8-54 1055 5.1 1 5.44 9.05 4-14 4.9 1 - 1.0 1-55 - 2.55 18.60 10.80 7.80 571 5.71 0 4.66 4.66 0 1 -72 1 -72 0 12-09 12.09 0 addition, the values these would have if there were a linear change with atomic number from Mn2+ to Zn2+.The differences between the experimental and theoretical values are also given. For Fe, Co and Ni the increase in the values of the difference is approximately in the ratio of 1 : 2 : 3 which would be expected as 1, 2 and 3 extra electrons are added to the lower triplet of the d-orbitals. With Cu2+ there is a large increase in A log K1 and A log K2 even though, in this case, the fourth electron is being added to the upper doublet. This greater effect, it is interesting to note, is in line with the larger ligand field splitting observed for Cu2' from optical spectra.Moreover, as long as only one or two ethylene- diamine molecules are co-ordinated, the electron in the upper d-orbital will con- tinue to be in an orbital directed towards water molecules and so there is little change in its situation on forming the mono- and di-ethylene-diamine complexes. When Cueng+ is formed the situation is quite different as the geometry of the ethylene-diamine molecule imposes an approximately regular form on the complex and, because there is an odd number of electrons in the anti-bonding d-orbitals ; this is an unsatisfactory situation as shown by the abnormal value of log K3 for copper. It should also be possible to account for the relative stability of octahedral and tetrahedral complexes since for the latter the crystal field splitting is the reverse of the former being into a lower doublet and a higher triplet. Orgel36 has discussed this and pointed out, for example, that it is possible to account for the existence of COX:- complexes because with the group of seven electrons full use is made of the lower doublet whereas in the octahedral complex onlyJ .W. LINNETT 17 partial use is being made of the lower triplet. However the situation here is that more data are needed about tetrahedral complexes (spectra, stability, etc.). The variation in lattice energies for a series of transition metal halides can be understood by taking account of the crystal field splitting of the d-orbitals of the metal ion.VISIBLE AND ULTRA-VIOLET SPECTRA 0 bservations of electronic transitions provide data regarding the energy separation of the higher-occupied and the more low-lying unoccupied orbitals. Such studies will clearly be of the greatest value in giving information about the electronic structures of complex ions. The results obtained can, in principle, be handled either by molecular orbital theory or by ligand field theory. Pauling’s theory is not applicable. Almost all the detailed study and interpretation of the spectra of complexes of the transition metals has taken place in the present decade, the pioneer papers being those of Finkelstein and van Vleck37 on Cr3+, of Abragam and Pryce 38 on Co2+ and of Ilse and Hartmann 39 on Ti(H20)2’, the last involving just one optical d-electron.However, before this, Tsuchida40 had remarked that the spectra are affected only by the first co-ordination sphere and that the ligands in this first shell have the same effect in causing shifts of the position of the absorption bands whatever the central ion. Tsuchida was able to construct a spectrochemical series of ligands such that the groups affected the positions of the absorption band in the order that they were listed. A shortened series is : I-, Br-, C1-, F-, H20, CzOi-, C5H5N, NH3, en, NOz-, CN-. This can be understood either in terms of ligand field theory or of molecular orbital theory. For both it seems likely that the ligand orbital (and the electrons in it) which is directed toward the central ion will be the most important.The more this is concentrated, or is drawn, towards the central ion the greater will be its effect on both theories. The basis of the series is halogen, 0, N, C which is in the order of decreasing effective nuclear charge and electronegativity so that the electrons will be capable of being drawn towards the central atoms as one goes from left to right. As regards the ligands containing nitrogen it is understandable therefore that the negatively charged ligand should have the greatest effect, that the nitrogen which is part of an aromatic ring should have the least, and that the nitrogen atom attached to an electron- releasing aliphatic group should have a slightly greater effect than the nitrogen in ammonia. For mixed complexes a “rule of average environment” obtains, the effect of the mixture of ligands being the mean of the effects of the separate ones.Of course, in certain cases, the effect of mixed ligands is such as to produce a field at the central atom which is so much different from an octahedral field that the multiplets (the doublet and triplet) are themselves split, and as a consequence the absorption bands divide into several components. This effect can be studied quantitatively from the absorption spectra. Jorgensen 41 has discussed the spectral and other effects of changing from octahedral to tetragonal symmetry and proposes that the “ tetragonality ” for different groupings can be measured by comparing the frequencies of the principal bands of the Cu2+ complex which will be tetragonal with that of the Ni2+ complex which will only have any tendency to go tetragonal by virtue of strain effects.Optical spectra provide values of the splitting of the d-orbitals by the ligands. Our knowledge of this has increased greatly during this decade. However, though our knowledge for hexa-aquo complexes is fairly complete there are still many gaps for other octahedral complexes. For tetrahedral complexes the situation is much less satisfactory. Other features derived from electronic spectra have been mentioned in the first part of this discussion.18 GENERAL INTRODUCTION MAGNETIC SUSCEPTIBILITY Measurements of the magnetic susceptibilities of salts containing complex ions have been of the greatest interest since their importance was stressed by Pauling. Since that time this has been much developed by Nyholm and others.With transition metals, the subject divides itself into two parts : (a) the first long period for which much data are available, and (b) the second and third long periods about which very much less is known. With (a) the best representation of the magnetic moment is that based on the view that the spin moment alone contributes. This is an excellent approximation when the d-shell is less than half full, but less good when it is more than half full. The orbital contribution is completely or largely quenched. That is, the ligand field orients the orbitals that are occupied so firmly that there is no effect of the magnetic field on their orienta- tion and hence no orbital contribution. However, because the interaction be- tween the spin and orbital motion is small the spin contribution is free.Con- sequently it is possible to use the measured susceptibility to make an immediate assessment of the numbers of unpaired electrons. With Fez+, Ni2+ and CU~+, and particularly &2+, there does appear to be an orbital contribution. It is interesting that the large orbital contribution for, say, hexa-aquo cobaltous salts is associated with a considerable anisotropy (30 %). With compounds involving tetrahedrally co-ordinated cobalt (e.g. CoCl:-) the orbital contribution and aniso- tropy are much less.42 In this case, the magnetic moment can, it seems, be used as a guide to the stereochemistry, a moment just above the spin only value in- dicating a tetrahedral complex while one considerably above indicates an octahedral one.For the elements of the second and third long periods the situation is more complicated because the spin-orbit coupling is greater because of the greater nuclear charge. This causes the moment to be much less than the spin only value. Kotani43 concludes that in these cases the effective magnetic moment will be temperature dependent and this has been demonstrated for ( N H ~ ) ~ O S B T ~ . ~ ~ More work is undoubtedly needed on the magnetic moments of complexes of the heavier elements. PARAMAGNETIC RESONANCE SPECTRA If a material containing molecules or ions in which there are unpaired electrons is placed in a suitable magnetic field, the substance absorbs microwave radiation, undergoing a transition between the Zeeman sub-levels separated by the field.From this, information can be obtained about the distribution of the odd electron in a paramagnetic complex using either (a) the frequency at which the micro-wave absorption occurs, or (b) the h e structure that is sometimes shown by the ab- sorption. The separation of the levels, with the magnetic field H, is given by gHp, where p is the Bohr magneton, and g, the splitting fact being given by g = 2.0023 - (SA/A) where X is the spin-orbit coupling constant and A is the energy separation of the dTlu and dEg orbitals.45 The last can be obtained from the spectrum so that h can be calculated from g which is obtained from the frequency absorbed and the magnitude of the magnetic field. For Cu(HzO)2,+, for example, the value of h is less than for the free ion, apparently because the electron is in a molecular orbital which is made up in part only of the orbital of the central ion, but to which there is some contribution from the ligand orbitals.The ratio of h for the com- plexes to that for the free ion gives the contribution to the molecular orbital of the appropriate orbital of the central ion. For Cu(H,O)Z' the value obtained is 84 %46 which is for an electron in the d anti-bonding orbital. For the cor- responding bonding orbital the situation must be reversed, it being primarily a ligand orbital.J . W. LINNETT 19 With IrC1;- the absorption line shows a fine structure which results from the small magnetic fields produced by the moments of the chlorine nuclei. The separation of the components is smaller than would be expected for an electron in the appropriate orbital on the chlorine. The magnitude of the splitting is a measure of the contribution of the chlorine orbital to the molecular orbital occupied by the odd electron.The result indicates that the main contribution (74 %) to the molecular orbital is that of the orbital of the iridium atom.47 If the central nucleus possesses a spin magnetic moment it should be possible to make similar deductions from the fine structure caused by this. An important conclusion from this work is that it is not valid to treat the d~~~ and d~~ orbitals as pure central atom orbitals as is done by simple ligand field theory. Moreover, the method does enable definite numerical values to be given to the extent of mixing of the component atomic orbitals.This is of the greatest possible value. Unfortunately this can only be applied to paramagnetic ions. OTHER EXPERIMENTAL METHODS Other methods for obtaining information about electronic structure are nuclear magnetic resonance, particularly high-resolution work and the determination of chemical shifts, optical rotatory power, rates of substitution reactions and nature of products, but space does not permit these being dealt with here. Finally, it must be stressed that there is still need for an increase in our knowledge of the general chemistry of several of the transition elements in the second and third long periods. In conclusion I wish to record my debt to the excellent reviews of Nyholm,48 Orgel,49 Jorgensen,l3 Owen 50 and Griffiths.11 I also wish to thank my colleague Venanzi for his helpful advice.1 Pauling, Nature of the Chemical Bond (Cornell University Press, 1939), p. 93. 2 Pauling, Nature of the Chemical Bond (Cornell University Press, 1939), p. 95. 3 Linnett and Mellish, Trans. 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SOC. A, 1952, 65, 860. 20 Hoard and Nordsieck, J. Amer. Chem. SOC., 1939,61, 2853. 21 Hoard, J. Amer. Chem. SOC., 1939, 61, 1252. 22 Jack and Martland, Proc. Chem. SOC., 1957,232. 23 Wells, Structural Inorganic Chemistry (O.U.P., 1952), p. 397. 24 Linnett and Venanzi, unpublished work. 25 Braekken, 2. Krist., 1931, 78, 484. 26 Wooster, 2. Krist., 1931, 80, 504. 27 Chatt, Duncanson, and Venanzi, J. Chem. SOC., 1955,4456,4461 ; 1956, 2712. 28 Chenyaer, Ann. Inst. Platine, U.S.S.R., 1926, 4, 243 ; 1927, 5, 118. 11,381. and Fischer-Wasels, Z. physik. Chem., 1955, 4, 297.20 GENERAL INTRODUCTION 29 Care and Staveley, J. Chem. SOC., 1956, 4571. 30 Davies, Suiger and Staveley, J. Chem. SOC., 1954, 2304. 31 Chatt and Wilkins, J. Chem. SOC., 1952,4300 ; 1955, 525. 32 Irving and Williams, Nature, 1948, 162, 746; J. Chem. SOC., 1953, 3192. 33 Calvin and Melchior, J. Amer. Chem. Soc., 1948, 70, 3270. Schwarzenbach, 34 Orgel, Report of the 10th Solvay Council (Brussels, 1956), p. 292. 35 Orgel, J. Chem. SOC., 1952,4756. 36 Orgel, ref. (34), p. 302. 37 Finkelstein and van Vleck, J. Chem. Physics, 1940, 8, 790. 38 Abragam and Pryce, Proc. Roy. SOC. A, 1951,206, 173. 39 Ilse and Hartmann, 2. physik. Chem., 1951, 197,239. 40 Tsuchida, Bull. Chem. SOC. Japan, 1938, 13, 388,436,471. 41 Jorgensen, Acta Chem. Scand., 1955, 9, 1362. 42Krishnan and Mookherju, Proc. Roy. SOC. A, 1938, 237, 135. Nyholm, ref. (4), 43 Kotani, J. Physic. SOC. Japan, 1949,4, 293. 44 Lundberg and Johannsen, J. Amer. Chem. Soc., 1954,76,5349. 45 Owen, Proc. Roy. SOC. A, 1955, 227, 183. 46 Bleaney, Bowers and Pryce, Proc. Roy. SOC. A , 1955,228, 166. 47 Griffiths and Owen, Proc. Roy. SOC. A , 1954,226,96. 48 Nyholm, ref. (4), and Quart. Rev., 1953, 7, 377 ; 1957, 11, 339. 49 Orgel, ref. (8) and ref. (11). 50 Owen, ref. (5). Bowers and Owen, Reports Prog. Physics, 1955, 18, 304. Bagguley Ackermann and Prue, Nature, 1949, 63, 723. p. 258. and Owen, Reports Prog. Physics, 1957, 20, 304.