THE MAGNETIC EVIDENCE FOR CHARGE TRANSFER IN OCTAHEDRAL COMPLEXES BY J. OWEN* Clarendon Laboratory, Oxford Received 25th January, 1955 An account is given of the information about covalent bonding and electron dis- tribution in octahedral complexes containing transition group elements, which is available from paramagnetic resonance measurements. The molecular orbital treatment of u- and n-bonding in these MXg complexes is briefly described ; this suggests that the unpaired electrons responsible for the paramagnetism may be partially transferred from M to x6 in molecular orbits which are usually of antibonding type. From the observed effects in the paramagnetic resonance spectrum (e.g. hyperfine structure from X nuclei, reduction in orbital magnetic moment), the amount of electron transfer can be estimated, and some typical examples are discussed. The results indicate that in hydrated 3d group complexes there are appreciable a-bonds and usually weak or negligible T-bonds, while in the 3d group cyanides and complexes of the 4.d and 5d groups there are strong a-bonds and also appreciable r-bonds.1. 1NTRODUCTION The magnetic properties of MX6 complexes, where M is a transition group element, have long been used as a guide to the nature of the bonding between M and X. Pauling 1 first suggested that the anomalously low magnetic moment and total electronic spin of complexes like [Fe(CN)6]3- was evidence for covalent bonding, and on the basis of this '' spin-criterion ", bonds in many M& complexes have been rather sharply classified as being either ionic or covalent.However, van Vleck2 pointed out that this spin criterion does not directly distinguish between ionic and covalent bonds at all, but only shows whether the bond energy is greater or less than the energy of Russell-Saunders coupling between the d-electrons belonging to M. The only satisfactory way of distinguishing between the bonds requires an estimate of the electron distribution over the complex, and this can only be found by the measurement of properties which give detailed information about the orbits of the electrons, and not by measurement of the total spin. The paramagnetic resonance method is well suited for this purpose, since it gives very precise information both about the orbital magnetic moment of the unpaired d-electrons, and about hyperfine interactions between these electrons and any nuclei with non-zero spin which are included in the orbit.For example, the resonance spectrum of [l[rC16]2- shows 3 that there is a small anomalous reduction in the orbital magnetic moment of the single unpaired d-electron, and that there is hyperfine interaction with Cl as well as with Ir nuclei; these effects can be ascribed to r-bonds in the complex, which involve a partial transfer of the electron from Ir to c16. Subsequent work has given information about (3: and/or r-bonds in many other MX6 complexes, and it is the purpose of this report to collect together some of these results, and to explain how they are obtained from the paramagnetic resonance data. Accordingly, a general discussion of the orbits, energy levels and bonds in MXtj complexes will be given first, and this will be followed by a more specific treatment of the effects of covalent bonding on the magnetic properties of particular complexes.* at present at Department of Physics, University of California, BerkeIey, 127128 OCTAHEDRAL COMPLEXES 2. ORBITS AND ENERGY LEVELS OF MX6 In discussing the orbits and energy levels it is convenient to assume first that the bonds between M and X are ionic, then to consider the effect of introducing covalent cr-bonds, and finally to consider the effect of a-bonds. For the most part, the discussion will follow that of van Vleck,2 Stevens4 and 0wen.S It is assumed throughout that the MX6 complex is a regular octahedron, i.e., that there is cubic symmetry.2.1. IONIC BONDS In this case M is a positive ion with an unfilled 3d, 4dor 5d shell, e.g., Cr3f = 36, Ru3+ = 4d5, Ir4+ == 5d5. The magnetic electrons occupy &orbitals on M, i.e. orbitals of the form d , ~ - ~ 2 , d3z2-r~, dxy, dYz, dzx. The first two orbitals (usually called dy type), if filled with electrons would correspond to negative chargeclouds with lobes pointing towards the attached negative X ions, and consequently are of higher electrostatic energy than the other three orbitals (de type) which have lobes pointing between the attached ions (see fig. 1). This is the origin of the crystal (0) ( b) FIG. 1.-Rough illustration of some atomic orbitals of M and x6. (a) Central dx2-y2 orbital, and 4 of the 6 attached pa orbitals. These are used to construct the molecular orbitals u:2-y2, 0x2-v2 (eqn.(1) and (2)). The admixtures are such that the signs of the central and attached orbitals are all the same (u) or opposite (o*) in the region of overlap. (b) Central dxy orbital, and 4 of the 12 attached pn orbitals. These are used to construct rzy, nxy molecular orbitals (eqn. (3) and (4)). Note that for the corresponding orbitals in the yz plane [p& denotes p&), etc. field splitting between the dy doublet and de triplet energy levels (fig. 2). On the ionic model X can often be treated as a diamagnetic negative ion with a filled p shell; for example, if X = C1- = 3p6 this is literally true, while if X = H20, then as far as M is concerned, X looks something like an 02- ion ' ( 2 ~ 9 . The highest occupied orbital energy levels of x6 can then be approximately represented as in fig.2. The levels are slightly different if X = CN- (see below). On this ionic model the magnetic properties of MX6 depend on the paramagnetic ion M and the crystal field splitting between dy and de levels. 2.2. COVALENT cr-BONDS Using the molecular orbital method one now considers the mixing which can occw when central ndy, (n + 1)s and (n + I)p orbitals, (n = 3, 4 or 5 ) appreciably overlap pa orbitals belonging to &j (cf. fig. 1). In general, s orbitals on X are also involved, and it can be assumed that such s admixtures are included by the symbol pa. The molecular orbitals which can be constructed from linear com- binations of these central and attached atomic orbitals are given by van Vleck.2J .OWEN 129 The*-c arc six bonding and six antibonding Gombinations, of which those involving the magnetic dy orbitals are (neglecting terms containing overlap), * - o3+ y2 = ad3z2-y~ - (1 - a2)'(1/J2)'[2P6 - 2P3 + PI + PZ - P4 - PSI~ 0:2- y2 = ( 4 2 y2 - (1 - a2>* +[P2 + P4 - Pl - PSla, (1) 03~2--r2 ( 1 - a2>"3z2-r2 + a ( 1 / w w 6 - 2p3 + p1 + p2 - p4 - PSI6 032 - y z = (1 - a2)3dx2.-y2 + a4-[p2 + p4 - p1 - psla. (2) In these expressions the suffixes 1, 2, 3, 4, 5 and 6 denote the X at'oms on the x, y , z, - x, - y and - z axes respectively; ~ , Z - ~ Z , etc., denote bonding orbitals and o* antibonding orbitals. (1 - a2)& is the admixture coefficient, which is zero if the bonding is purely ionic. On the other hand, if the bonding is what might be Orbital O r b i t a l O r b i t a l levels of leve I s of levels 01 M tM X61 ' 6 FIG.2.-Diagram showing probable energy order of some of the orbits in an MX6 com- plex, where X is an ion like C1- (see text). The diagram is not drawn to scale. The number of electrons which can be accommodated in each level is shown in brackets, and the available electrons fill these levels in the appropriate energy order ; for examples, see 0 3. called purely covalent, a2 = 1 - a2 = 0.5, corresponding to an equal sharing of electrons between M and X6. If the molecular orbitals involving central s and p orbitals also correspond to equal sharing, one then has, in effect, the d2sp3 bonds of the directed valence-bond method (see van Vleck 2). In practice, one might expect a2 to have some value between these extremes, 1 Z a2 > 03, although, as will be seen below, there is no direct evidence that a2 is never less than 0.5, The probable energy changes resulting from o-bonding are indicated in fig.2 . It will be noted that twelve pa electrons are partially transferred from x6 to M and have their energy lowered, while a small number of dy electrons (not more than three if MX6 is paramagnetic) are partially transferred from M to x6 and have their energy raised. It can be pictured that the net gain in stability results because there is a net transfer of electrons from x6 to M which helps to even out the charge distribution over the complex. The magnetic properties are affected by the a-bonding because (i) the splitting between dy and de levels is increased, and (ii) any unpaired dy electrons are partially transferred from M to x6.E130 OCTAHEDRAL COMPLEXES 2.3. COVALENT n-BONDS In this case one considers the mixing between de orbitals on M and pn orbitals on X. The admixtures would be expected to be smaller than for the o-bonds discussed above, because of the smaller overlap (cf. fig. 1); the experimental evidence, as far as it goes, appears to confirm this. The molecular orbitals which can be constructed are given by Stevens;4 here we will make some slight modifications (see Owen 5) in that terms containing overlap will be neglected, and also the orbitals of the magnetic de electrons are assumed to be antibonding for most cases, rather than bonding. There are then three bonding and three antibonding combinations of the form (cf.fig. 1) (3) (4) and the other combinations, rYz, rrzx, etc., are obtained by cyclic permutation of the suffixes. As in eqn. (1) and (2) the admixture coefficient (1 - P2)* = 0 if there is no n-bonding. The energy changes which result from the v-bonding are indicated in fig. 2, where it is assumed that the orbitals on X which are used for n-bonding are filled with electrons, e.g. X = C1-, H20. Then six pn electrons are partially transferred from Xg to M and their energy is lowered, and the remaining eighteen pn electrons on x6 are non-bonding ; * the magnetic dc electrons on M are partially transferred from M to xfj and their energy is raised. It will be noted that the dc-dy splitting is decreased by the bonding. If X = CN-, on the other hand, the energy levels and eqn.(3) and (4) have to be changed slightly. In this case it seems likely that the orbitals on X available for n-bonding with M look something like Zp, orbitals on C atoms, which are unoccupied and of higher energy than the central de-orbitals, cf. Orgel.6 (The 7r-orbitals on N are assumed not to contribute appreciably because paramagnetic resonance measurements 15 on complexes such as [Cr(CN)#- show that there is at most only an extremely small hyperfine splitting due to the N nuclei, cf. 6 3.2 below.) If this is so the magnetic dc electrons are bonding rather than anti- bonding, their energy is lowered by the transfer from M to Xg, and in eqn. (3) the sign of the admixture coefficient must be changed so that it represents a bonding orbital.There is no electron transfer from xg to M. Thus, with X .-= CN-, it seems likely that n-bonding results in a net transfer of electrons from M to Xg (Pauling 7), and also in an increase of the splitting A between the dc and dy energy levels. For example, in [Fe(CN)g]3-, r-bonds help to increase A, while in [FeF& they tend to decrease A according to the arguments above. We will now consider the magnetic properties of the orbitals discussed above, and show for some cases how these orbitals are related to the observed para- magnetic resonance spectra. 3. THE MAGNETIC PROPERTIES OF MX6 * - n;,v = Pdxy - (1 - B2)wPl + P2 - P4 - PSI, (1 - P2>*dxy 4- P#& 4- P2 - P4 - PSI, r x y The main effects of covalent bonding on the magnetic properties and para- (i) Such bonds may help to cause a reduction in the electronic spin of the (ii) There may be hyperfine interaction between the magnetic electrons and (iii) There may be a reduced orbital magnetic moment.(iv) There may be a reduced hyperfine interaction with the M nucleus. These four effects will be discussed in turn. * Strictly speaking, six of these eighteen electrons may also be weakly bonding through small admixtures of central p to attached pn orbitals. These admixtures are neglected throughout. magnetic resonance spectrum of Mx6 are its follows : ground state. the X nuclei.J . OWEN 131 3.1. THE ELECTRONIC SPIN OF THE GROUND STATE The electronic spin of the ground state depcnds on the number of d-electrons on M, the Russell-Saunders coupling between thcm, and the de-dy splitting A.Covalent bonding affects thc value of the spin mainly because it affects the value of A (fig. 2), but sincc thcre is no obvious way of sorting out the various contribu- tions to A, a knowledgc of the spin-value gives no direct information about covalent bonding, as has already been mentioned abovc.2 When A is small compared with the Russell-Saundcrs coupling cncrgy, the d electrons fill both de and dy orbitals in such a way that there is a maximum number of unpaired electrons, i.e. maximum spin (Hund‘s rule), and, when this condition is fulfilled, a minimum number of electrons occupy the high encrgy dy orbitals. (There are slight cxceptions for the configuration d2 and d7.) Most hydratcd iron s o u p complexes arc in this category. For examplc, the ground state spin and configuration of d-electrons for hydrated complexes of Cr3+ are S = 3/2, (3&)3, for Fe3+, S = 5/2, (3d~)3(3dy)2, and for Ni2+, S == 1, (3&)6(3dy)2.Becausc of the configurations, to a good approximation the transfer of unpaired electrons to (H2O)6 arises in Cr3+ only from n-bonds, in Fe3+ from both (T- and n-bonds, and in Ni2+ onIy from o-bonds. When A is large compared with the Russell-Saunders coupling energy, thc lowcst state of the systcm * is obtained by putting the first six d-electrons into the lower energy de triplet, and the maximum spin is formed consistent with filling this triplet, i.c. as the number of electrons incrcases from d l to d6, the ground state spin has values 1/2, 1, 3/2, 1, 1/2, 0.Thus the spin is anomalously low for d4, d5, and d6. The 3d group cyanides, and all known octahedral complexes of the 4d and 5d groups are in this catcgory. A reduced spin might be expected to occur more frequciitly in the higher transition groups, (i) because the Russcll- Saunders coupling is smaller, and (ii) because the d-wave functions extend farther from the ccntral nucleus thus giving greater overlap and stronger bonding. Since the unpaired electrons are in de orbitals, they are transferred to x6 only because of n-bonding, and magnetic measurements can give no dircct information on (T- bonding in these complexes. 3.2 HYPERFINE STRUCTURE FROM X NUCLEI If an unpaired d-electron from M is partially transferred to an orbit on X, therc may be hyperfine intcraction with the magnetic inomcnt of the X nucleus, whose order of magnitude is the product of the hypcrfinc structure of the free X atom and thc probability of finding the unpaired electron on X.This efiect was fist found in ammonium cliloroiridate.3 Here the [IrC16]2-- complcx is a perfectly regular octahedron, the configuration is Ir4-’- := (5&)5, and there is a single unpaired clcctron, which occupies antibonding n* orbitals (eqn. (3)). This unpaired elcctron is thus approximately 8 2 on Tr and i(1 -- 62) on each C1 atom. Each C1 nucleus, (I :== 3/2 for 35. Wl), then causcs a splitting of each Iinc in the paramagnetic resonance spectrum into 21 4- 1 == 4 components, with separa- tion between adjacent components,4 ( 5 ) In this expression y is the Cl nuclear gyromagnetic ratio, p’ the Bohr magneton, PN thc nuclear magneton, Y the radius of a pn orbit on C1, and 0 is thc angle between thc applied magnetic field and the Ir-Ci direction.(The quantity -$f y p ’ p ~ (m)z3a. where a is the hyperfine structure constant for the 2P312 ground state of a free C1 atom.) The measured splitting, A := 26.5 x 10-4 cm-1, leads to the value 82 = 0.74. The experimentally observed spectrum is complicated by the fact - A cos e := Q (1 - p)[-5s yp’pN(i/r3)1 cos e. * Detailed energy level diagrams showing how a large value of A can bring down a state of low spin below the normal ground level are given by Tanabe and Sugano.8132 OCTAHEDRAL COMPLEXES that two or more C1 nuclei, and also the Ir nucleus, contribute to the structure at the same time.A typical spectrum and reconstruction is shown in fig. 3 ; for details of how to make the reconstruction? and of similar structures in [li-Br6]2-, see Griffiths and Owen.9 Structures from the X nuclei have been found in a few other MX6 complexes, but these have not yet been analyzed in detail. For the majority of complexes which have been measured there are no such structures because X has zero nuclear moment, e.g. X = 02-. However, if a salt containing [cU(&O)6]2' complexes, for example, could be prepared using the isotope 170, a structure at least as large as that in [hC16]3- would be expected due to the magnetic electron transfer arising from a-bonds. 3.3. REDUCTION IN ORBITAL MAGNETIC MOMENT The orbital magnetic moment of an unpaired d-electron on M is in general reduced if this electron is spread out in a molecular orbit over MX6; the spectro- scopic splitting factor (g-value), may then depend on the charge transfer.The theory of this effect was first given by StevensP with particular reference to the anomalously low g-value found in ammonium chloroiridate, where there was direct evidence for electron transfer (see above). We will illustrate the effect with the following three examples, where it is assumed, unless otherwise stated, that the octahedron is regular, i.e., cubic symmetry. (i) [ITCJ6]2-, (5d45, S = 112. As discussed above, there is a single unpaired electron in T* orbitals, which is approximately 82 on the Ir atom and +(l - /32) on each C1 atom. The g-value is 4 (6) Experimentally, g = 1.775 giving 82 = 0.66.9 The difference of this value of /32 from that found from the X hyperfine structure (p2 = 0.74), can probably be attributed to certain simplifying approximations made in the derivation of eqn.(5) and (0, and to the value assumed for (llt-3) when using eqn. (5). For a number of other examples of reduced g-values in this type of complex, see, for example, Griffiths, Owen and Ward.10 (ii) [Ni(H20)6]2+, 3d*, S = 1. The configuration of d-electrons can be written (3d46(3dy)2, and the two unpaired electrons are in a*-antibonding orbitals (eqn. (l)), so that each electron is approximately cc2 on the Ni2+ ion and +(l - cc2) on each H20. Neglecting .rr-bonds, i.e. assuming ,@ = 1, the g-value is 5 where A is the spin-orbit coupling constant, and A is the dc-dy splitting (fig.2) which can be found from optical absorption data. The experimental values of g, X and A lead to a2 = 0.83. (iii) [Cu(H2o)6l2+, 3d9, S = 1/2. If the complex is elongated along the z-axis (in practice, the distortion is usually more complicated), the unpaired electron is in the antibonding orbital a~2-,,2, and is approximately a2 on the Cu2+ ion and +(l - cc2) on each H20 in the xy plane. The g-value measured along the z-axis is then given by eqn. (7), if n-bonds are neglected. The experimental data give a2 = 0.84 (see Bleaney, Bowers and Pryce,ll Owen.5) g = 2 - *(l - 82). - g = 2.0023 - C C ~ ~ X ~ A , (7) 3.4. REDUCED HYPERFINE STRUCTURE FROM M NUCLEUS If the unpaired d-electrons on M are partially transferred to x6, there is a corresponding reduction in the hyperfine interaction with M nucleus. So far, this effect has only been studied quantitatively in [CU(H20)6]2+, 3d9, by Bleaney, Bowers and Pryce.11 The experimentally observed reduction in hyperfine structure gives a2 in fairly good agreement with the value 0.84 deduced from the g-values.J .OWEN 133 For many other complexes there is considerable evidence of variations in the hyperfine structure from a particular M ion, with variations of x6, especially for M = Mn2+. This can certainly be attributed in part to variations in the amount of electron transfer, but no quantitative analysis has yet been published. 4. DISCUSSION OF RESULTS The molecular orbital treatment of covalent bonding in MX6 complexes described above, can be summarized by the following approximate electron transfer scheme, where 1 - a2 and 1 - p2 can be considered to be measures of the amounts of a-bonding and .rr-bonding respectively.(i) Ionic bonds, (a = /3= 1). M has closed shells, plus 1 to 9 d-electrons with configuration ( d ~ ) ~ ( d c ) ~ , where 0 < n < 4, 0 < rn < 6 ; x6 has closed shells plus (usually) 12 cr-el&trons, and (ii) o-bonds, (a < 1). 4(1 - a2) o-electrons 8x o-electrons n(1 - a2) dy-electrons 24 .rrelectrons. x6 -+ M(d2) (bonding), x6 -+ M(sp3) (bonding), M+X6 (antibonding). Magnetic measurements give information about unpaired dy-electrons, and hence, under favourable conditions, the value of a2. They give no information about x, which probably lies in the approximate range 0 < x < - 0.5.either (iii) .n-bonds (p < 1) : .g., x = c1-, .n-electrons x6 -+ M (bonding) m(1 - ,822) deelectrons M -+ X6 (antibonding) or e.g., X = CN-. (b) ?(I 0 p2) deelectrons M -+ & (bonding) n-electrons X6+M Magnetic measurements give information about unpaired deelectrons, and hence, under favourable conditions, the value of 182. They do not distinguish between cases (a) and (b), which requires a measure of the sign of ,8. All of the charge transfers given above are approximate mainly because terms containing the overlap integral have been neglected throughout. This becomes a poor approximation as a2 or /32 become appreciably less than 1. A selection of values of a2 and /32 which can be found from paramagnetic resonance measurements are collected in the table below.These are mostly obtained from g-values only, as described in 3 3, and some of them may be modified slightly by new experimental results and further refinements of the theory (cf. the discrepancies in the results on [IrC16]2-). The values of a2 for (&)5 complexes cannot be found because there are no dy electrons. In these complexes the o-bonding is likely to be stronger, i.e., a2 smaller, than for any hydrated complex, but a2 is not likely to be much less than 0.5, the " pure covalent bond " value (see 5 2) ; thus, very approximately, one might expect - 0.5 .< a2 < -0.7. It should be pointed out that all of the complexes in the table generally occur in crystals as distorted, rather than regular, octahedra, and then the transferred d-electrons are not equally distributed over x6.For some such complexes, details of the exact distribution can be found from paramagnetic resonance measurements, e.g. [IrC16]2-, [IrBr6I2-. The foregoing discussion indicates the type of information about charge- transfer and covalent bonding in MX6 complexes which can be found from para- magnetic resonance measurements. The results show clearly that the same kinds134 OCTAHEDRAL COMPLEXES of bonding occur to a greater or lesser extent in all of these complexes, and that there is no sudden transition from an ionic to a covalent type of complex, as is suggested by the Pauling spin criterion. The results are also of interest because they arc, likely to lead to a better understanding of several other properties of [IrC16]2- [lrBr6]*- configuration (3dc)I ( 3 4 3 (3d€)6(3d# (3 de)6(3 dy) 3 (3d~)5 (4dc)5 (4d+ (5de) 5 (5d45 TABLE 1 reference spin.a2 8 2 112 ? < 0.9 1 2 a2t92 0.63 ((a2 - 0.7, /32 - 0*9)} 1 0.83 1.0 2 1 /2 0.84 1.0 2, 3 1 /2 ? 0.75 4 1 /2 ? 0.90 5 112 ? -0.9 6 7 1 /2 ? 1 /2 ? 3/2 0.66 from g-value 0.74 from h.f.s. 0.66 from g-value 0.74 from h.f.s. 7 References : (1) Bleaney, Bogle, Cooke, Duffus, O’Brien and Stevens, 12 (2) Owen ; 5 (3) Bleaney, Bowers and Pryce; 11 (4) Baker, Bleaney and Bowers; 13 ( 5 ) Griffiths, Owen and Ward ; 10 (6) Owen and Ward (unpublished) ; (7) GriEths and Owen.9 these complexes. For example, anomalies in the optical absorption spectrum of hydrated iron group salts (see Owen 5) can probably be attributed to covalent bonding. Also the mechanism of exchange coupling between neighbouring paramagnetic ions in crystals undoubtedly involves the magnetic electron transfer to the intervening diamagnetic ions (cf. Andersonl4), and an exact knowledge of the transfer is very relevant to this problem. This report has been written during the tenure of a U.S. Foreign Operations Administration Fellowship and a grant from the U.S. Office of Naval Research and the US. Signal Corp, and this support is gratefully acknowledged. 1 Pauling, J. Amer. Chem. SOC., 1931,§3, 1367. 2 van Vieck, J, Chem. Physics, 1935, 3, 807. 3 Owen and Stevens, Nature, 1953,171, 836, 4 Stevens, Proc. Roy. SOC. A, 1953,219, 542. 5 Owen, Proc. Roy. SOC. A, 1955 227, 183. 6 Orgel, 1955 (submitted for publication, J. Chem. Physics). 7 Pauling, Nature of the Chemical Bond (Cornell University Press). 8 Tanabe and Sugano, J. Physic. SOC., Japan, 1954,9, 766. 9 Griffiths and Owen, Proc. Roy. SOC. A, 1954, 226,96. 10 Criffiths, Owen and Ward, Puoc. Roy. SOC. A, 1953, 219, 526. 11 Bleaney, Bowers and Pryce, 1955 (submitted for publication). 12 Bleaney, Bogle, Cooke, Duffus, O’Brien and Stevens, Proc. Physic. Soc. A, 1955, 13 Baker, Bleaney and Bowers, 1955 (submitted for publication). 14 Anderson, Physic. Rev., 1950,79, 350. 15 Bowers, Proc. Physic. SOC. A , 1952, 65, 860. 68, 57.