摘要:

MAGNETIC RESONANCE OF DWFERENT FERRIC COMPLEXES BY J. F. GIBSON, D. J. E. INGRAM AND D. SCHONLAND * Dept. of Electronics, University of Southampton Receiued 1st July, 1958 This paper summarizes the results of electron resonance measurements on different derivatives, in which a transition metal atom is held at the centre of a square of four nitrogens. All the complexes that have been studied contain a porphyrin or porphyrin- like plane, and most of the measurements have been on different ferrihaemoglobin deriv- atives. The g-value variations with respect to the porphyrin plane are summarized for the different types of bonding with the iron atom, and then some earlier measurements on similar copper and cobalt complexes are quoted for comparison. The first-order molecular-orbital treatment of these square-bond derivatives is then given and it is shown that the order of the predicted energy-level splittings is the same as for those of the octahedral complexes.A systematic survey of different derivatives in which metal atoms of the first transition group are held in the centre of a large molecular plane is being under- taken at Southampton. The first series of complexes to be studied have been those containing a porphyrin or porphyrin-like plane, in which the metal atom is surrounded by a square of four nitrogens. All the results summarized in this paper are therefore for iron group atoms held in such a bond and sometimes also with a fifth and sixth ligand to complete an octahedral co-ordination. The main experimental results with which this paper is concerned are recent measurements on different ferric complexes, but previous determinations on copper and cobalt derivatives 1 are also summarized as a comparison.A theor- etical treatment of the simple square-bond configuration of the phthalocyaniiie structure is then given and it is shown that this is consistent with the theory pre- viously developed for the octahedral case.2 This theory follows the normal molecular orbital approach and considers the overlap between the 3d, 4p and 4s orbitals of the transition metal atom with those of the pn and po orbitals of the surrounding nitrogens. From this the splittings of the resultant levels of the central metal atom in the complex are deduced. It will be seen that good agree- ment is obtained between the theoretical predictions and experimental results for the square-bond complexes.The parameters determined experimentally and calculated theoretically are the g values and hyperfine splittings as expressed by the normal spin Hamiltonian. The experiments have therefore been carried out on single crystals of the different complexes so that maximum information should be available. In such large organic derivatives this requirement has not always been easy to fulfil, but it has now proved possible to perform accurate measurements on separate single crystals of copper and cobalt phthalocyanine, and of quite a number of different derivatives of ferrihaemoglobin. Since these crystals are often of small dimensions most of the experiments have been performed at 1.25 cm or 8 mm wavelengths, and at temperatures down to 20°K.The results obtained are summarized after a very brief description of the experimental technique. * Dept. of Mathematics, University of Southampton. 72J . F. GIBSON, D. J . E . INGRAM A N D D. SCHONLAND 73 EXPERIMENTAL TECHNIQUE The electron resonance spectrometers used in this work have employed a transmission waveguide system and have been either of the simple " crystal video " or the " high-fre- quency magnetic-field modulation " type: In taking a large number of results for a given crystallographic plane, direct presentation of the signal on an oscilloscope has great advantages, and whenever sensitivity considerations permitted, this method of display has been employed. In work with the small Q-band and K-band cavities it has been found far more satisfactory to rotate the magnet around the cavity containing the crystal than to rotate the crystal within the cavity.All the measurements have therefore been made with HI11 cylindrical cavities with the crystals fked to the bottom in the required crystallographic plane. For all important directions, such as maxima and minima or cross-over points in the g value or hyperfine splitting variations, the magnetic field values of the resonance have been determined directly by simultaneous measurement with proton-resonance. The orientation of the crystal within any crystallographic plane can be determined directly from the resonance measurements since the crystal symmetries ensure that the curves due to different ions in the unit cell cross over along the axial directions.In certain cases 3 this fact affords a more accurate determination of crystal orientation than attempts at visual alignment before measurement. Most of the measurements were taken at 20"K, but this was for sensitivity, and not spin-lattice broadening, considerations. RESULTS FERRIC COMPLEXES All the measurements on this type of ferric derivative have been made on ferrihaemo- globin complexes. In these the iron atom is held at the centre of the porphyrin plane, surrounded by the square of nitrogens, as shown in fig. 1. An octahedral co-ordination R FIG. 1.-Structure of centre of haemo- globin molecule showing location of GLOBIN is then completed by the bonding to the protein molecule (most probably via a nitrogen of a histidine group), below the plane, and to another atom or group above the plane.The different derivatives are prepared by changing the nature of the group at this sixth co-ordination point from HzO to F-, OH-, Ng, or CN-. Since the normal isotope of iron has no nuclear moment, no hyperfine structure from the iron atom is expected, and none has yet been observed from any of the surrounding nitrogen atoms. The parameters that have to be determined for the spin Hamiltonian are therefore only the g values in this case. The porphyrin plane itself forms the main element of symmetry in these molecules and the axis normal to it will therefore be one of the directions of principal g value. It will be seen that in some cases this acts as an axis of symmetry and the g value perpendicular to it is isotropic, whereas in other cases the two other principal axes of the g tensor lie at right-angles to each other in the porphyrin plane.The experimental measurements can be divided into two distinct steps, the first being to determine the orientation of the porphyrin plane within the particular crystal being studied. These data were not available from X-ray work and have had to be obtained from an analysis of the resonance results themselves. The second step, once the orientation of the porphyrin plane has been established, is to measure the g value variation with respect to this for as many different derivatives as possible. The determination of the orientations will not be discussed in detail here, but the results are summarized in fig.2 for type A crystals, which Is the type on which most work has been performed.374 MAGNETIC RESONANCB OF FERRIC COMPLEXES H2O AND F- DERIVATIVES Magnetic susceptibility measurements 4 show that the derivatives with H20 or F- at the sixth co-ordination point have a moment corresponding to five unpaired spins. It would therefore appear that the splitting between the eg and tzg orbital levels is not very great and each orbital contains one unpaired electron corresponding to “ ionic binding ”. cQ ,c FIG. with J a The electron resonance measurements on both of these derivatives are identical and show that there is only one electronic tran- sition with a g tensor which has a minimum of 2.0 along the axis normal to the porphyrin plane, and an isotropic value of 6.0 in all directions in the porphyrin plane. A typical plot of the observed g values is shown in fig.3 for a type A crystal. The crystal was so orientated that one of the molecules in the unit cell had its porphyrin plane hori- zontal, and the constant g value of 6.0, as the magnet is rotated, is shown by the curve labelled P. This behaviour of Fe in an octahedral “ ionic bond ” is in striking contrast to the results obtained on simpler hydrated salts,s where five electronic transitions centred on a g value of 2.0 are observed. The difference can be explained if it is assumed that the spin orientation has been effectively 2.arientation of the porphMn planes quenched in this case, and that the splitting respect to the crystallographic axes for between the sz = f 4 and the Sz = f 312 and f 512 levels is considerably larger than the micro-wave quanta.This is illustrated schematically in fig. 4. The exact cause of this large splitting of the levels in ferrihaemo- globin has yet to be established, but it may be accounted for by higher orbital admixtive in the particular symmetry group considered.6 type A crystals. L I I I I I I I 270 0 90 FIG. 3.-Variation of g value in type A crystal mounted with one porphyrin plane horiz- ontal. The curve labelled P is for the acid-met derivative in the porphyrin plane, that labelled Q is for the azide derivative in the molecular plane. N3- AND OH- DERIVATIVES Magnetic susceptibility measurements4 show that the derivatives with NF or OH- at the sixth co-ordination point have a moment corresponding to one unpaired spin.It would therefore appear that the splitting between the eg and tzg levels is now largerJ . F. GIBSON, D. J. E. INGRAM AND D. SCHONLAND 75 than the energy required for pairing, and the five magnetic electrons have entered the three lower tzg orbitals. The electron resonance results co&m this since only one electronic transition per atom is observed, with g values spread across the free-spin value. The actual magnitudes of these g values with respect to the porphyrin plane, for the azide derivative, are shown in fig. 5. It is evident that there is no longer axial symmetry about the normal to the \ - H FIG. 4.-Splitting of the (3@ 6s levels in ferrihaemoglobin H20 and F- derivatives. FIG. 5.-Variation of g value in ferrihaemoglobin azide, with respect to the porphyrh plane.plane, and it would appear that the asymmetry produced by the protein groups below are now affecting the g values within the porphyrin plane itself. Griffith 2 has shown that these g values are consistent with a splitting between each of the three levels in the tzg group of about 1000 cm-1, with dxY lying lowest and dzx next. This may also suggest that the direction of minimum g value is that of the projection of the histidine plane on the porphyrin plane. The hydroxide derivatives were prepared by passing acid-met ferrihaemoglobin crystals into solutions with successively higher pH values. The results obtained with these crystals were of particular interest in that two quite distinct resonance spectra were obtained, and the ratio of their intensities varied with the pH of the last solution in which the crystal was76 MAGNETIC RESONANCE OF FERRIC COMPLEXES placed.The first type of resonance was similar to that obtained from the azide derivatives consisting of a single electronic transition with extrema and variation of its g tensor very similar to that of the azide. The actual values obtained are summarized in fig. 6a. It would appear that the anisotropy in the porphyrin plane is again mainly determined by the orientation of the histidine plane below. This might suggest that the OH and azide radicals are rotating faster than the microwave frequency. At higher pH values, a second spectrum is observed with a g value tensor quite different in magnitude from that of the first, but with approximately the same angular orientation.FIG. A -3.4 FIG. 6.-Variation of g value in ferrihaemoglobin hydroxide : (a) transition appearing at pH 7-83 ; (b) transition appearing at pH > 8-5. 2 !4 ~ 1 OH I I Co1oI fiOo3 I I I I I I 270 0 90 7.-Variation of g values in (001) plane of type A crystal for ferrimyoglobin OH1 and OH11 spectra. This is seen quite clearly in fig. 7 which is a plot for all the transitions observed in the (001) plane of a type A crystal at a pH of 9.5. The results for this new transition are summarized in fig. 6b, in which a direct comparison between the two types of OH derivative is possible. Initial measurements have also been made on cyanide derivatives. These are difficult, however, since the spectra are now very broad at 20"K, and appear to have a considerable spin-lattice contribution to their width. This is in contrast to all the other derivatives in which no change of width with temperature has been observed.The preliminary results indicate, however, that the g value variation of the cyanide derivative is very similar to that of the azide. CUPRIC AND COBALT COMPLEXES Measurements have also been made on derivatives of copper and cobalt held in a square of four nitrogens at the centre of a porphyrin-like plane. The actual crystals usedJ . F . GIBSON, D. J . E. INGRAM AND D. SCHONLAND 77 were phthalocyanine derivatives with the structure as shown in fig. 8. In the crystal structure, neighbouring molecules are so arranged that each metal has two other nitrogen atoms above and below it, so that the symmetry of its surroundings is thus pseudo-octa- hedral.Both copper and cobalt nuclei have magnetic moments so that the hyperfine splitting is now an additional parameter in the spin Hamiltonian. No extra structure from the surrounding nitrogens has yet been observed on the main hyperfine components. Most of the work on the phthalocyanines was performed by J. E. Bennett and has already been published in a condensed form.1 The results are therefore summarized only briefly here, but the parameters are quoted so that they can be used to test the theoretical cal- culations. With copper phthalocyanine it was found that there was axial symmetry FIG. 8.-Structural formula of the copper phthalocyanine molecule. about the normal through the metal atom perpendicular to the molecular plane, and the parameters can therefore be expressed in terms of 811 and gA, and A and B, the latter representing the hyperfine splitting along, and perpendicular to the axis, respectively.In the cobalt derivative there is a slight anisotropy of the g value in the molecular plane. The values obtained are summarized in table 1. TABLE 1 .-PARAMETERS FOR COPPER AND COBALT PHTHALOCYANINE A cm-1 B cm-1 gll 81 cuz+ 2.165 & 0.003 2.045 f 0.003 0.022 f 0.001 0.003 -J= 0.001 co2+ 1.92 f 0.01 2-88 to 0.017 f 0.001 0.027 f 0.001 2.92 f 001 DISCUSSION THE PHTHALOCYANINE RESULTS THE ENERGY LEVEL SCHEME As a first approximation one can imagine a phthalocyanine derivative to contain a divalent metal ion at the centre of the square of four nitrogen atoms, each of which holds two electrons in a a-orbital pointing towards the metal.The electrons on the central ion are held in d-orbitals which, because of the tetra- gonal symmetry, are non-degenerate with the exception of the pair dxz, d,,=. (We take the x and y axes along the diagonals of the square and the z axes perpendicular to the molecular plane.) Since the Co2+ ( 3 4 7 and Cu2+(3d)9 derivatives are both78 MAGNETIC RESONANCE OF FERRIC COMPLEXES found to have one unpaired spin while Ni2+(3d)8 phthalocyanine appears to be diamagnetic one can conclude that the unpaired electrons in cobalt and copper phthalocyanine are held in non-degenerate orbitals ; the anisotropy in the g values and hyperfine structure suggests that these are respectively d2z and dx2+.This association of d22 with cobalt phthalocyanine accords with the observation that the g values of this molecule in solution are sensitive to the nature of the solvent while those of copper phthalocyanine are not. There is no direct qualitative evidence to indicate the ordering of the remaining levels, but the results on copper phthalocyanine discussed below indicate that dxy is more stable than dxz and dyz as indicated in fig. 9. FIG. 9.4uggested level scheme for copper phthalocyanine. The left-hand column shows the nine Cu2+ electrons placed in 3d " ionic " orbitals : the central column illustrates the effect of bonding on the dx2 - y2 orbital. The scheme for cobalt phthalocyanine is obtained by removal of two electrons leaving one unpaired electron in dz2.One can now take account of covalent bonding by allowing the formation of bonds between the nitrogen ligands and the central ion. These bonds will utilize 4s, 4px, 4py and 3d,~-~z orbitals with the result that the " ionic " d'2+ orbital is effectively replaced by an anti-bonding d*xz-y~ orbital whose energy has been raised relative to the other d-orbitals. Since dZ2 has the same transformation properties, under tetragonal symmetry, as 4s it is possible that the orbital labelled dZz in fig. 9 may contain some admixture of 4s and of nitrogen o-orbitals. This possibility is indicated in the figure and discussed below in connection with the results on cobalt phthalocyanine. The dxr and dyr orbitals are capable of forming n-bonds with the surrounding molecule.If this type of bond formation occurred one would need to postulate an anti-bonding doubly degenerate level lying below d*x2-y~ in which the unpairedJ. P. GIBSON, D. J . B. INGRAM AND D. SCHONLAND 79 electron in the copper derivatives would have to be placed. It does not appear possible to reconcile this with the detailed measurements on copper phthalocyanine or with the diamagnetism of zinc phthalocyanine so that we conclude that this .zr-bond formation does not in fact take place. COPPER PHTHALOCYANINE On the basis of this orbital picture, copper phthalocyanine contains one un- paired electron in the anti-bonding d*+p orbital, and the situation is formally very similar to that of Cu2+ in a Tutton salt.' If a is the coefficient of d,2+ in the anti-bonding orbital and 5 is the spin-orbit coupling constant for a 3d electron, a first-order perturbation treatment gives where El is the energy difference between dxy and d*,2-,.2, and E2 that between the degenerate pair d,,, dY2 and d*x2--y2.Comparison with the measured g values then gives El = 48.5 ta2; E2 = 44.4 1.2. An estimate of the value of u2 ean be obtained from a consideration of the hypedine structure. One finds for the hyperfine structure constants A = --P[+ct2 - (81, - 2) - +(gL - 2) + K], where K is the parameter describing the s-electron effect and P = 27@&--3> in the usual notation. From an analysis7 of the optical hyperfine structure of the free copper atom, Abragam and Pryce estimate P = 0.036 cm-1, K = 0-36. If one takes this value for P, the measured values of A and B are fitted by: (i) u2 = 0.984, K = 0.23 if A is negative and B is positive ; (ii) a2 = 0790, K = 0.34 if both A and B are negative.One cannot distinguish the signs of A and B experimentally but since bonding is expected to be important we shall assume that B is negative and take a2 = 0.79. Then, assuming El = 31,700 cm-1, E2 = 29,000 cm-1 = 828 cm-1, one finds for the energy separations so that the dxy level lies about 3,000 cm-1 below the d,,, dyr pair. Against this smaller value for a2 may be put the failure to abserve any hyper- fine structure from the nitrogens. Although this might have been due to poor resolution and the small magnetic moment of nitrogen, it may indicate that there is a negligible overlap of the d*,~,a orbital on the nitrogens which is consistent with the larger value of a2 = 1 above.COBALT PHTHALOCYANINE For this molecule the postulated level scheme contains one electron unpaired in 4 2 . This is directly connected by the spin-orbit interaction to dX2 and a',, and in a first approximation the problem can be treated as that of one hole in this set of orbitals. If the energy separation between the 4 2 and the d,,, dY2 states of the hole is denoted by A and if c is the spin-orbit coupling constant one obtains, to first order in E = [/A, gL = 2 + 6 ~ , gll = 2. The value of 2.90 for gL then gives E = 0.15. Since gll = 1.92, however, it is evident that second-order terms are not negligible. The second-order contribution from the states considered gives rise to a reduction in 811 and the experimental results80 MAGNETIC RESONANCE OF FERRIC COMPLEXES can be fitted well with a single value of E when this is taken into account.This agreement must, however, be regarded as to some extent fortuitous since other excited configurations will also contribute in second order. The situation is discussed in detail by Griffith in another paper in this Discussion. With the above value for E, the first-order calculation for the hyperfine-structure constants gives Taking A = 0.017 cm-1, B = 0.027 cm-1 then gives a fit with P = 0.04 cm-1 and K % 0. This value of P differs substantially from the value of 0-022 cm-1 obtained from optical measurements on cobalt.* The value of P deduced from the above expression is, however, rather sensitive to the values assumed for A and B.If one puts P = 0.022 cm-1 and chooses K to give the mean of A and B correctly, one finds K = -0.44 which gives A = 0.019 cm-1, B = 0.025 cm-1 in tolerable agreement with the measurements. The value of K required for this fit demands some explanation since it is markedly different from the value of 0.2 appropriate to cobalt. A possible explanation of the discrepancy is that the d,z orbital contains a small amount of 4s which would contribute directly to the hyperfine structure via the contact term in the Hamiltonian. A rough calculation using hydrogen-like radial wave functions indicates that a 4 % admixture will suffice to explain the discrepancy. A = P (0.44 - K), B = P (0.68 - K). GENERAL It has been shown that the level scheme of fig.9 can be used to explain the g values and hyperfine structure of copper and cobalt phthalocyanine. In this scheme one has to place dxv below d,, and dvz, and these in turn below d,~, which may seem puzzling in view of the concentration of electron density in the xy plane. The fact that dXy lies below d,, and dvz has been explained by Griffith,2 who found the same result in his examination of ferrihaemoglobin azide, as due to the effect on these latter orbitals of n-electrons on the surrounding nitrogen atoms. For d,Z one may remark that in the crystals it is subject to the electrostatic field arising from nitrogen atoms on the z-axis above and below the molecular plane belonging to other molecules, which will tend to raise its energy. Further, if our interpretation of the cobalt results is correct, the small 4s admixture may also tend to raise the energy of this orbital. The authors would like to express their thanks to Dr. J. S. Grfith for a valuable discussion of some of the theoretical points presented above. His paper in the Discussion covers some of the same topics and readers are referred to it for a more accurate and extensive treatment of cobalt phthalocyanine. One of us, J. F. G., would also like to thank the D.S.I.R. for a maintenance grant for the period during which this work was performed. 1 Bennett and Ingram, Nature, 1955,175,130 ; Faraday SOC. Discussions, 1955,19,140. 2 Griffith, Nature, 1957, 180, 30. 3 Bennett, Gibson and Ingram, Proc. Roy. SOC. A, 1957,240,67 ; Ingram and Kendrew, 4 Hartree, Ann. Reports, 1948, 63, 287. 5 Bleaney and Trenam, Proc. Roy. SOC. A , 1954, 223, 1. 6 Griffith, Proc. Roy. SOC. A , 1956, 235, 23. 7 Abragam and Pryce, Proc. Roy. Soc. A, 1951, 206, 164. 8 Abragam and Pryce, Proc. Roy. SOC. A , 1951,206, 173. Nature, 1956, 178, 905.

ISSN:0366-9033    

DOI:10.1039/DF9582600072

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

THE ELECTRONIC STRUCTURES OF SOME FIRST TRANSITION SERIES METAL PORPHYRINS AND PHTHALOCYANINES BY J. S. GRIFFITH Dept. of Theoretical Chemistry, University of Cambridge Received 30th June, 1958 A theoretical discussion is given of electron resonance and magnetic susceptibility measurements on copper, nickel, cobalt and iron porphyrins and phthalocyanines. The experimental data are consistent with the order for the 3d orbitals 3d&< 3dzx, 3dyz < 3dx2-y~ and a variable position for 3d+, when the OX and OY axes are chosen so that they each pass through the metal nucleus and two of its adjacent nitrogen nuclei. 1. INTRODUCTION Both phthalocyanines and porphyrins consist of large planar conjugated ring systems containing nitrogen, carbon and hydrogen atoms. In the centre of the ring system there is a hole which is just large enough to accommodate a metallic cation.This is shown for copper in fig. l a where only the central part of the ring system is shown. The phthalocyanine or porphyrin ring lies in the plane of the paper and has approximate fourfold symmetry about an axis through the \ I N \ / N- Cu'-N / \. N / \ (14 FIG. 1.-Some classical chemical structures for the bonding of copper in copper phthalocyanine or porphyrin. cation and at right-angles to the paper. We will call this axis the Z-axis and use the words parallel and perpendicular to refer to measurements relative to OZ (for example 811 will be a g value along OZ), Other chemical structures could be written instead of la, and lb and l c show parts of typical ones.One might say that the true structure is a resonance hybrid between la, lb, l c and other canonical structures or alternatively that the copper electrons are spread to some extent over the adjacent atoms. 8182 PORPHYRINS AND PHTHALOCYANIMES We adopt a crystal field approach and ask what information we can obtain about the electronic ground states in first -transition-series metal porphyrins and phthalocyanines. Take OX and OY passing through the nitrogen nuclei in fig. 1 and write I m+ >, I m- ) for 3d orbitals having r n l = m and rn, =+ 3 and - + respectively. Define Then the 3d orbitals span a reducible representation under D4h (or C4,) which breaks up into four irreducible components spanned respectively by I 0 ), I >, 1 p >, ( I 1 >, I - 1 )).These five orbitals are the most convenient for discussing magnetic properties of planar compounds. The ultimate problem is to determine the order and approximate orbital energies. Theoretically it is clear that I E < (which is often written dX2 - u2) must lie highest and we see in the next section that electron resonance in copper phthalocyanine coniirms this. Theory is of little help with the others, except to suggest that I p ), I 1 > and I - 1 ) should have approximately the same energy (they are the f 2 g orbitals of the octahedral group). In this paper, I discuss the interpretation of the magnetic properties and con- sider the extent to which it can give information about the electronic structure of the metal ion which resides in the middle of the porphyrin or phthalocyanine ring.2. COPPER PHTHALOCYANINE Here the data show that the unpaired electron of the cupric ion is in the I E > orbital.1-3 They are inconsistent with the assumption that it is in I 0 > or that it is in a 4pz orbital. The pair I 1 >, I - 1 ) probably lie about 5c (1 is always taken to be the spin-orbit constant for a single 3d electron and is positive) above 1 p >. This latter conclusion should be accepted with some reservation because it is possible that delocalization may have a different effect on 811 than it does on 81. 3. NICKEL PHTHALOCYANINE AND PORPHYRINS Nickel phthalocyanine and porphyrins appear from susceptibility measure- ments always to have spin zero, although some contrary evidence exists.4-6 Electron resonance is not observed, but again there is a little doubt.7~8 It may be that a paramagnetic state lies very low and appears after certain methods of preparation.Assuming that the diamagnetic state is lower we deduce 9s 10 that 1 0 > has an energy at least 15,000 cm-1 below I E ). 4. COBALTOUS PHTHALOCYANINE Solid pure cobaltous phthalocyanine has a susceptibility which shows that it is low-spin.6 It is possible that there is a small percentage of the high-spin variety present but there is no reason for believing this. Electron resonance yields 1 = 1-92 f 0.01, g, = 2.92 & 0.01, gu = 2.88 f 0.01, A = 0.017 + 0.01, B = 0.027 f 0.01. We neglect the small difference between g, and gy here and take gl = 2-90. Assuming cobalt phthalocyanine is low spin, it has one hole in the dia- magnetic d8 configuration found in the nickel compounds.The hole may be in I p), I 0 ) or (I l), I - 1>) and we must decide which. If the hole is in I p>, the ground state is the Kramers doublet 46 = I 12 - 12p+o2), $6 = 1 12 - 12p-o2>, (1)J . S. GRIFFITH 83 in the first approximation, where the notation implies antisymmetrization. If it is in I 0), we have (2) If the hole were in 1 l), I -1) we would have two Kramers doublets with an energy separation f: and the doublet (3) lying lower. In this order of approximation the g values of the three ground states are, respectively, 811 = g l = 2 ; 811 = g l = 2 ; gll = 4, gl = 0. This makes it very unlikely that the hole is in I l), I - 1). In the next approximation we consider those states which are mixed into the ground state by spin-orbit coupling.For $6 and $6 they are, respectively, $6 = 1 12 - 12p20+), +G = I 12 - 12p20-). Xd = I 12 - l+p202), xi = I 1- - 12pW> +1 = 1 12 - 12€+02), $1 = I 12 - 1-p202), $2 = 11- - 12p+c02), 952 = I 12 - l+pq+€+), 43 = I 1- - 12pW), $3 = 1 12 - 12p-O+€+), $4 = I 12 - l+/L+€+02), $4 = I 1- - 12p20+€-), $5 = I 12 - 12p+O+€-). The ground states now become (4) where xi(E(4i) - E($o)) = yj(E($i) - E($o)) = f:. p and y are determined by normalization. We now calculate g, A and B to first order in the Xi yi, and have /3 = y = 1. This is straightforward and leads to the formulae, g 1 = 2 + 2 x 3 , B = P ( - K + - ; + + 3 ) Y for $. The g values may be fitted with x1 = 0.01, x3 = 0.45 in the function 4. Using these values of x1 and x3 and the calculated electrostatic energies of the +i we deduce that x2 M 0.01.x4 is probably about 0.02 but could be much larger. With x4 = 0.02, P = 0.035, K = 0-23 we find A = -0-017, B = 0-027. Using the function $y g l is fitted by y1 = 0.15 and we shall see shortly 811 can be less than 2 when we use a more accurate theory. With this value of y1, A = 0.017, and B = 0.026 by taking P = 0-039, K = 0. The value assumed for y1 is perfectly reasonable and x1 = 001 is nicely consistent with the data for copper phthalocyanine when we take into account the difference in the spin-orbit coupling constants.84 PORPHYRINS A N D PHTHALOCYANIMES We now have two alternative interpretations of the experimental data, ap- parently equally satisfactory, and must see if there is any way of deciding which is more likely to be correct.First consider the energy separation 5 q = W3) - E(40) = E(I p)) - HI 0, I - 1)) - 7 4 where B is a Racah parameter for d electrons.11 Then if 4 is the ground state the orbital I p) lies at least 16000 cm-1 above the pair I l), I - 1). This seems a little improbable and would be very different from the situation which appears to be true in copper phthalocyanine. The second consideration is the value of K. For 4 this is quite close to the value found by Abragam and Pryce12 for high-spin cobaltous salts, but for $ it is anomalously low. This is just as we should expect in both cases as we now see. The crystal field will mix the orbital I 0), i.e. 3&, with the 4s orbital to give a linear combination 3dZz cos a + 4s sin a.This will then give a negative contribution of a sin2 cc to PK for # where a w 0.2 cm-1 is the interval parameter for a 4s electron. The 4s orbital gives no contribution via the crystal field to $ because the unpaired electron is not in the 1 0 ) orbital (see eqn. (4)). If z,h is the ground state, then sin a = 0.2. Thirdly, we should consider the electrostatic energies of $0, #O and XO. They are E(4o) = 21A - 16B + 18C, E($o) = 21A - 36B + lSC, E(X0) = 31A - 23B + lSC, and so if 4 is the ground state we have the relation between the orbital energies E(p) - E(0)) 20B w 20,000 cm-1. The appcoximate orbital energies relative to E(E) as zero, are E(p) =- l00~,E(1, - 1) =- 1025 - 15B, E(O)(- 1005 - 2 0 B ~ - 60,000cm-1 for 4 as ground state.For z,h as ground state we require E(1, - 1) - E(0) = 13B - 6-75 rn 20,000 cm-1, so E(0) -50,000 cm-1. These numerical values are deduced assuming the spin-orbit constant 5 is 400 cm-1 compared with 533 cm-1 for the free ion. They seem slightly to favour the ground state being #, both because of the position of I 0) and because if it is 9 then the relative position of I p) and 1 l), 1 -1) has changed by about 20,000 cm-1 from the situation in copper phthalocyanine. We conclu'de, then, that the ground states of the cobaltous ion in cobalt phthalo- cyanine are probably I 12 - 12 p20*) but that the alternative states I 12 - 12pf02) are consistent with the electron resonance measurements. The two possibilities could be distinguished through a measurement of the sign of the ratio of the nuclear hyperfine constants A and B.It is illuminating to calculate the g values to second order in xi and yi and the results are 811 = 2 - 8x1 - 3Xz2 - 3X32 + 3X42 + 4X1X4 f 4X2X3 , gl = 2 + 2x3 - 4X12 - (x2 - x4)2 + 2x1~2 + 2~2x3, 811 = 2 - 3n2 + 3 ~ 2 ~ - 3 ~ 4 ~ + 43939 - 4 ~ 4 ~ 5 g1 = 2 + 6Yl - 6Y12 - b72 - Y4)2 , (9) for 4 and (10) for #. We see how 811 can be less than 2 for z,h. We also see that it is possible for gll to become greater than 2 and this OCCUTS for solutions of cobalt phthalocyanine in pyridine or quinoline. 811 = 2-05 and gl = 2.2. The reduction of gl is inter-J . S . GRIFFITH 85 preted as a small lowering of the position of I l), I - 1) for # and, more probably, as a raising of the position of I 0) for $ due to co-ordination in the fifth and sixth positions by the nitrogen atoms of the heterocyclic rings of the solvent.Alter- natively, it is possible that rotation has led to a partial averaging of the g values. Finally, I remark that the second-order calculation of g should be regarded as illustrative rather than quantitative because other states as well as +i, #i are mixed into the ground state by spin-orbit coupling in second order. Other approxima- tions in the present treatment may also have comparable effects on the g values. 5. FERRIC PORPHYRIN CHLORIDE Here 811 = 2, gl = 3.8 1 and the most natural interpretation is to suppose S = - Sz = i - whereupon one deduces 811 = 2, gl = 4. S = - or - are not consistent with the g values. Representatives of the three possible ground states, with their electrostatic and orbital energies, are 3 1 1 5 2’ 2 2 2 41 = 1 12 - l+p+O+), $2 = 1 1+ - 1+p20+), E = 10A - 19B + 6C + E(1, - l), E = 10A - 25B + 6C + E(p), $3 = I I+ - 1+p+O2), E = 10A - 17B + 6C + E(0).(1 1) The first type of ground state is split in first order by spin-orbit coupling and the lowest Kramers doublet has 811 = 8, gl = 0 so we eliminate this possibility. Because of the chlorine anionwe expect the 1 0) level to lie considerably higher than in cobaltous phthalocyanine and therefore that the ground doublet should be 1 $+ = - (1 1+ - 1+pw-> + I 1+ - 1-p20+> + I 1- - l+p20+)), d3 1 4- = -(I 1- - 1-p20+) + I 1- - l+p20-) + I I + - l-pW-)). (12) d3 The lowest states of the system are those which would be classified as 6A1, 4T1 and 2T2 under the octahedral g1-0~p.13 In an octahedral field, 4T1 could not lie lowest,l4 but in a planar compound it splits into an orbital singlet and a doublet.The orbital singlet gives two Kramers doublets of which one is given in eqn. (12). It is interesting to use the copper phthalocyanine g values to determine E(e)-E(p), take estimates of Racah’s B and C by interpolation of free ion data, and deduce the energies of the three spin types. We take E(E) - E(p) = 40,000 cm-1, B = 1100 cm-1, C = 4200 cm-1 (all parameters should be reduced somewhat in the compound). Then the relative energies are A1 = 3800 for the sextet and A2 = 22000 + x for the doublet, both relative to the orbital singlet of the quartet. x = E(l, - 1) - E(0) m 30,000 for cobalt phthalocyanine but would be much smaller algebraically here.A simple calculation then shows that the relative energies of the Sz = f 4 and Sz = 3/2 states are - 2<2/5& and - 52/A2 respectively. Both energies are around 10-20 cm-1 and the electron resonance result shows that A2 > 5A1. It is interesting to remark here that the gll = 2, gl = 6 in high-spin haemo- globin compounds which was interpreted as arising from the S, =& 3 doublet 15 requires that this doublet should be depressed relative to the Sz =f 3/2, 5/2 states. In the d5 configuration of the free ion, only the 4P512 level mixes with the ground term to first order in spin-orbit coupling. The 4P term passes over into the lowest 4T1 term in the compound. A tetragonal field then splits this 4T1 term and calculation shows the final effect of this field to be a lowering of the Sz =i 3 doublet as required, although it is a little difficult to obtain a sufficient We have shown that it is reasonable for the quartet to be lowest.86 PORPHYRINS A N D PHTHALOCYANLMES energy separation in this manner 16 (there are other effects which may have an equal influence).The most important matrix element in the haemoglobin cal- culation is then just the one which lowers the Sz = f t doublet in ferric porphyrin chloride. An approximate calculation for ferrous phthalocyanine using the same orbital parameters gives the relative energies of singlet, triplet and quintuplet as 1 l,OOO+x, 0 or lo00 - x, and 15,000 respectively. There are no electron resonance data here, but the susceptibilities 5 ~ 6 of ferrous phthalocyanine and porphyrin suggest that the ground state of the ion is a triplet in both cases, although it is possible that there might be a thermal equilibrium between Merent spin states. 1 Gibson, Ingram and Schonland, preceding paper. 2 Abragam and Pryce, Proc. Roy. SOC. A, 1951,206, 164. 3 Bleaney, Bowers and Pryce, Proc. Roy. SOC. A, 1955,228, 166. 4 Pauling and Coryell, Proc. Nat. Acad. Sci., 1936, 22, 159. 5 Klemm, 2. Elektrochem., 1939,45, 590. 6 Senff and Klemm, J. prakt. Chem., 1939,154,73. 7 Ingram and Bennett, J. Chem. Physics, 1954,22, 1136. 8 Ingram, private communication. 9 Orgel, J. Chem. Physics, 1955, 23, 1819. 10 Maki, J. Chem. Physics, 1958,245, 651. 11 Racah, Physic. Rev., 1942, 62,438. 12 Abragam and Pryce, Proc. Roy. SOC. A, 1951,206, 173. 13 Tanabe and Sugano, J. Physic. SOC. Japan, 1954, 9, 766. 14 Griffith, J. Inorg. Nucl. Chem., 1956, 2, 1. 15 Griffith, Proc. Roy. SOC. A, 1956,235, 23. 16 Griffith and Orgel, unpublished calculations.

ISSN:0366-9033    

DOI:10.1039/DF9582600081

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. J. S . Griffith (Cambridge University) said: Prof. van Vleck has raised the question of nomenclature for the irreducible representations of the finite groups and I would like to make a few proposals about these. I favour using A , E, T, U, V, W for representations having the respective degrees 1, 2, 3, 4, 5, 6. This is Mulliken’s notation 1 (B is used for some of the representations of degree one 1). T, U, V, Ware better than F, G, H, I used by some authors, because the latter (but not the former) can be confused in practice with the total orbital angular momentum classifications of atomic states. I am writing a book on ligand-field theory and use Mulliken’s notation. I had, therefore, to decide what notation to use for the two-valued (or spin) repre- sentations and, not liking mixed notations, decided upon Mulliken-type symbols for the spin representations also.To distinguish them from the proper, i.e. one-valued, representations I use dashes. Thus r,, I‘,, I’8 (in Bethe’s notation) of the octahedral group become E’, E”, U‘. I always use E’ to denote the repre- sentation (irreducible in all cases of interest) spanned by the pair of basic spin functions. As fwther examples, the two-valued representations of the dihedral group 0 4 are E‘, E” and of the icosahedral group are E’, E”, U’, W’. I would like, therefore, to confine dashes to the two-valued representations. In favour of Mulliken’s notation I would say that the symbols tell us something about the nature of the representation. Further, it gives, in a sense, a name rather than a number to a representation and just as I prefer to call the iron atom Fe rather than 26 so I prefer E to r3.Dr. Jerrgensen has been kind enough to show me his comments on this topic.2 The use of T, U, V meets his point about confusion with atomic states. Apart from my personal inclination towards the use of Mulliken’s notation I am in general agreement with him. I, too, commend the use of I’, rj as a name for representation symbols in any general theoretical treatment. Dr. C. K. J#rgensen (Tech. University of Denmark) said : Long before quantum mechanics rationalized the data of atomic spectroscopy, the concepts of orbital energies and energy separations within a given configuration, caused by different sorts of coupling, were used in the empirical description of spectra of gaseous ions and atoms.Perhaps, the whole concept of “ electronic configurations ” is a useful classification, giving the observed number of energy levels and their qualitative distribution, rather than a valid approximation to any large extent for the w ave-funct ion. I think that it will be equally useful to introduce molecular orbital energies from absorption spectra, if possible, rather than to try to calculate them, e.g. by the Helmholz-Wolfsberg method. In this method, it is assumed that the non- diagonal elements are proportional (by a somewhat dubious factor) to the overlap integrals between two orbitals with the same y,, (in most published calculations, the radial functions are assumed to be hydrogenic, which they certainly cannot be).The fundamental problem, however, is the diagonal elements of energy, which must be subject to large first-order perturbations. Thus, in octahedral com- plexes, the lone-pairs of the ligands must be highly separated in energy according to their 7 ~ - or o-symmetry along the line between the nuclei of the central ion and the ligand considered. I shall try to estimate such energy differences from electron transfer spectra, especially of hexahalide complexes. These spectra seem for the moment to have about the same lack of general classification as had the ligand 1 see, e.g. Eying, Walter and Kimball, Quantum Chemistry (Wiley, 1948). 2 Jsrgensen, this Discussion. 8788 GENERAL DISCUSSION field spectra before the calculations of Tanabe and Sugano.To some extent it can be concluded that the two sets of orbitals y3 and 75, representing d-electrons in the electrostatic and “central field” covalency model, are rather isolated in energy, compared to the other orbitals. When compared with the absorption spectra, results like those of Gilde and Ban (fig. 4 of Linnett’s paper) seem un- realistic. Prof. van Vleck asked for a discussion about the nomenclature of ligand field theory, which perhaps is somewhat confusing to chemists (even though I person- ally do not think the existence of several independent nomenclatures as the most serious difficulty for understanding recent papers about the subject. A certain spiritual inertia in chemists, having not the time or the necessary curiosity and desire for new ideas, may well be expressed in such a belief in confusing nomen- clature.) The Tenth Solvay Council of Chemistry, Brussels, May, 1956, tried to clear up many of the differences evolved between different authors, and it was recommended to use A rather than 10 Dq or (El - Ez), to use minor letters for orbitals and capital letters for the states of systems, etc.One of the residual problems, which did not achieve a solution, was the choice between Bethe and Mulliken nomenclatures. Even though I know I am in a minority, I may indicate arguments for Bethe’s system. The main disadvantages of Mulliken’s nomen- clature are, in my opinion : (i) That the symbols Al, A2, E, T I , T2, U, V(or F1, F2, G, H by some authors) are so dissimilar and resemble the symbols of other quantities (energy, states of atomic spectroscopy, etc.).Chemists may be confused by e without subscript and t 2 expressing the two sets of d-orbitals. On the other hand, r, is known to be somewhat relevant to group theory (even though it is not perfectly specific), Something completely new, like the Irish letters, might have been used, if this meeting had been held earlier. At least, I would heartily recommend the use of r as a common name to the Mulliken symbols when used in a general, theoretical treatment. (ii) That the symbols are only of interest in degeneracy numbers and some few other group-theoretical properties and not in the actual symmetry of the complex. Thus, by reading a paper on copper (II) complexes, you must be extremely careful on seeing the word “ e-orbital ” to know whether it is referring to cubic or to tetragonal symmetry, meaning completely different orbitals. This was originally also a criticism against Bethe’s nomenclature, but the addition of the subscript t to the tetragonal number subscript yr5 rather than y3 has removed this difficulty.As pointed out by my colleague, Dr. Claus Schaffer, there are other problems in low symmetries, common to both nomenclatures. Thus, in the rhombic sym- metry D2, the names of the three symmetries A2, B1, B2 (but not Al) are freely interchangeable by changing the names of three axes. (iii) The double groups, e.g. the representations r6, r, and rg in Oh, do not easily find names in Mulliken’s nomenclature. Dr. Griffith proposes E’, E” and U‘. It is a general problem whether the names give much information about the intrinsic properties.Of course, the Mulliken nomenclature gives some such meaning. On the other hand, one gets easily acquainted with the Bethe nomen- clature, regarding I‘, as pure names, just as with the names of chemical elements or persons. There may finally be raised a fundamental problem common to all democratic communities : is it better to have one not so good nomenclature, or to have a bad (a personal opinion) and a good one at the same time? I am not certain about this point, but I would still like to have both systems indicated in a table in any larger contribution published. I am not convinced that it is so terrible that both nomenclatures are in use. Dr. R. Englman (Bristol University) said: Theoretical work on the intensities of the optical absorption of some paramagnetic ions has recently been carried out in Bristol.The calculations were initiated by Prof. Pryce, mainly for two reasons. One was to confirm quantitatively that we are here dealing with electricGENERAL DISCUSSION 89 dipole transitions, the second to find out which of the possible mechanisms is, or are, responsible for the transitions. There is also the very real possibility that information may be gleaned from observed intensities which would indicate the electronic distribution and covalency effects existing in the ion and its immediate surroundings. In this way, and provided one proceeds warily, intensity measure- ments supplement the knowledge got from energy-level determinations.Concerned with these calculations were Dr. Koide, who considered hydrated manganous (h4n2f) and cobaltous (Co2+) ions and myself, who dealt with nickel (Ni2+). It should be mentioned that essentially similar calculations were per- formed by Liehr and Ballhausen for Cu2+ and Ti3+. Both the initial and final states in the transitions correspond to electron dis- tributions which are of even parity with respect to the nucleus of the paramagnetic ion, provided the surroundings of the ion are also centro-symmetrical. In such conditions the transitions are forbidden. In reality, thermal motion and local fluctuation in the crystal will distort the octahedra forming the environment of the ion. This distortion will in turn deform the electron-cloud of the ion into a shape which is not quite centro-symmetrical (and so susceptible to electron dipole transitions).The distortion of the octahedron can be analyzed into independent vibrational modes of which the odd modes are of three types. The effect of these modes on the electron distribution can only be found as a result of detailed calculation; it is nevertheless worth discussing these modes and quoting the result of the calcula- tions. (Clearly, even vibrational modes do not yield any electronic dipole moment.) The three types are TI*+, TI,- and T&, in standard group-theoretical notation with plus and minus signs added for distinction. The vibrational frequencies have been estimated, and are roughly 300 cm-1 for TI,, half and quarter of this for T I , and T2u. The description of these types is the following.In equilibrium there are four ligands and the ion in a horizontal plane; two ligands occupy polar positions and we consider the vertical motion of the complex. Then in the TI*+ mode the planar and polar ligands will move (relative to the central ion) in phase, the former with one-third of the velocity of the latter. In the TI,- mode the polar ligands will be virtually stationary relative to the ion, so that only the planar ligands will move. This is (rigorously) so in the T2* mode, with the difference that now neighbouring planar ligands move in anti-phase. It is found that it is the T I , and T2* modes which are in general effective in bringing about the transitions. The calculated results agree reasonably well with experimental oscillator strengths.Dr. R. Englman (Bristol University) (communicated): The details of the red band of Hartman and Miiller are very interesting. They suggest that the four peaks found in the region of 14,000 cm-1 (or 690mp) arise from spin-orbit FIG. 1.90 GENERAL DISCUSSION interaction. In fact, the detailed examination of the energy levels of the nickel ion in octahedral surroundings with the spin-orbit interaction taken into account agrees fairly well with experiment. The relevant portion of the energy levels, plotted against the crystal field parameter A, is shown in the figure. In the weak field end, the left-hand side of the diagram, the 3T1 cubic states of Ni2+ arising from the 3F term split under the spin-orbit interaction into the three levels shown.The distance separating the two lowest levels is 3/45 , where 5 is 670 cm-1 in the free nickel ion and is about 15 % less in the crystal. The approach of the E state arising from the 1D term results in the separation of the E and T2 levels, as shown. It is evident from the separation of the first two peaks shown by Hartmann and Miiller that we are in the region where the E state is about half-way between the TI and A1 states, and the first peak is due to Eand A1 combined. A calculation, which takes into account the crystal field mixing of the 3 F with the 3P states and of the ID with the 1G states gives the following results. (E + A11 14,070 + Tl 180 180 180 T2 1,400 1,040 1,215 E 1,860 1,280 1,620 The first column shows the experimentally observed energy levels in cm-1.The calculated results are shown in the second and third columns, taking for 5 the values 570 cm-1 and 670 cm-1 respectively. I have seen Dr. Jerrgensen’s calculations, with which mine are in substantial agreement. It seems to me, nevertheless, that there may be a gain in clarity by presenting the argument in the way done here. Dr. C. K. Jpargensen (Tech. University of Denmark) said: The absorption spectra of the nickel (11) hexaquo ion has attracted the interest of many ligand field theoretists 1 and the distribution of the three excited triplet levels are well established. The splitting of the band in the red might either be caused by a first-order L,S-coupling effect, splitting 3 r 4 in its components, or due to second- order intermixing with singlet levels.The latter possibility was supported by the fact that a large series of nickel (11) complexes all show a narrow band in the range 12,500-14,000 cm-1, but this band is only comparatively intense when it is near to one of the triplet levels.2 The double band in the red is one of these cases, re- presenting as excited level. Recently, Dr. Griffith of Cambridge calculated the matrices of intermediate coupling for dg in the symmetry Oh, and I found also the diagonal elements by use of the baricenter and diagonal sum considerations.3 Dr. Griffith has proved the general theorem that all r 4 and rs levels are split as P-terms with the same total spin S, viz. that for S = 1 the r, components occur at 3 r 4 : at - 5, r, at - 46, and r, and r5 at + 35, 3 r 5 : r, at - 5, Ps at - 35, and r3 and I‘, at + 3C, where is a simple multiple of & for d-electrons.The total width 3/25 (reckoned negative, if the level is inverted with 3 r 5 always - 3/4&; or r 2 highest energy) is for d* : lowest 3 r 4 for A -+ o(3~) + 914 5nd and for A -+ a(y,’y$) - 3/45nd ; highest 3 r 4 for A + O(3F) - 3/2 [nd and for A + co(&$) + 3 / 2 c d . 1 Becquerel and Opechowski, Physica, 1939,6,1039. GrEiths and Owen, Pruc. Roy. SOC. A, 1952, 213, 459. Ballhausen, Kgl. Videns. Selsk. Mat. fys. Medd., 1955, 29, no. 8. Jmgensen, Acta Chem. Scand., 1954, 8, 1502. Owen, Proc. Roy. SOC. A, 1955, 227, 183. Orgel, J. Chem. Physics, 1955, 23, 1004. Lacroix, Arch. Sci., 1955, 8, 317, etc. 2 Acta Chem. Scand., 1955,9, 1362; 1956,10, 887. 3 Acta Chem.Scand., 1955, 9, 116.GENERAL DISCUSSION 91 Thus, the first band of Ni(H20):+ should be split some 4OOcm-1 apart, which can hardly be observed. The second band of all octahedral nickel (11) complexes shows a splitting between the limiting values + 9/4 and - 3/4c3d. The hexaquo ion has a value of A, corresponding to a mixture (in the squares) of 90 % (3F) and 10 % (3P), and therefore, the total width should be + 1.88 531, while the third spin-allowed band should have - 1-13 53d. These values, about 1,000 and 600 cm-1, respectively, should be observable. However, since Ni(NH3):+ should exhibit a similar splitting + 1,54531 of the second spin-allowed band, it can reasonably be concluded that the first-order L,S-coupling effects are not sufficient to explain the peculiar behaviour of Ni(H20);+.Actually, Dr, Griffith has calculated the non-diagonal element between l r 3 (con- sidered as the pure sub-shell configuration y : ~ : ) and each of 3rs and "4 of &: to be 2/3/2 c3, - 800 cm-1 (agreeing with the previously published, empirical values). If we consider this as the only second-order perturbation, acting on the first 3r4 of Ni(H20);+, the order of the Trcomponents will be, in units of 53,: assuming coincidence between the energies of 3I'4 and IT3 without L,S-coupling. This is in reasonable agreement with Hartmann and Miiller's experimental value, as also the splitting in components - 0.38, + 0.38, and + 0.75 fl3d of the highest 3 r 4 . I am not convinced that a genuine tetragonal splitting has been observed in their " 3 4 , 7&0.Generally, it is extremely diffcult to observe any effects of tetragonal substitutions in paramagnetic nickel (11) comp1exes.l The L,S- coupling produces a sufficient number of sub-levels to account for the fine-structure, but a closer study of the distortion from gaussian shape of the bands as function of temperature might be valuable. One puzzling problem remains in the treatment of Ni(II), the origin of the weak band at 18,400 cm-1. Once, I proposed that it was 'TI, anomalously de- pressed, but it is much less firmly established than in the range 22-24,000 cm-1 of several complexes and IT4 at higher energy. Dr. R. J. P. Williams (Oxford University) said: There is no doubt that a change of symmetry from octahedral to tetrahedral is not the only factor of importance in controlling intensities of forbidden absorption bands in complexes.For ex- ample, although the bonds in CoCli- are much more intense than those in the cobaltous hydrate, the change in intensity on going from the ferrous or nickel hydrates to the MClq- ions is much less.a This indicates that the intensity changes are specific properties of cations. To show the effect of different ligands we note that although there is little change in intensity in the series of cobaltic complexes Co(NH&X2+ where X is chloride, ammonia, water, thiocyanate or thiosulphate there is a considerable change in the octahedral cobaltous complexes Co(H20)sX where the intensities are extinction coefficient 6.0 9.0 12-7 44.4 375 position of charge transfer band mp < 250 <250 250 275 295 We see that the intensity increases with the increase in wavelength of the nearest charge transfer band although there is no overlap of bands for the d-d transition in the region 510-530 mp.This suggests that charge transfer is responsible for the changes of intensity in keeping with a number of other correlations.s Mr. R. P. Bell (Oxford University) said: I should like to ask Dr. Owen if it is possible to deduce from his measurements on mixed crystals whether the number of pairs or triplets of iridium atoms is in accord with statistical expectations, rl - 1-25, r3 - 0.97, r4 - 0.63, rs + 0.63, r, + 1.60, X 3320 N H 3 c1- SCN- s20;- 1 Bostrup and Jnrrgensen, Actu Chem. Scund., 1957,11, 1223. 2 Nyholm, this Discussion. Williams, J.Chem. SOC., 1956, 8.92 GENERAL DISCUSSION or whether there is evidence of a tendency for the iridium atoms to cluster to- gether or to avoid one another. Measurements of this kind might give valuable information about the statistical distribution in mixed crystals. Dr. J. Owen (Oxford University) said : In reply to Mr. Bell, our measurements of intensity of the microwave absorption from singles, pairs and triplets, indicate that there is a random distribution of Ir ions in the mixed crystal. The experi- mental accuracy is not better than f 20 %. I agree that in principle this provides a method for measuring distributions, but it is not a very convenient method to apply in practice because of the difficulty of finding and identifying the absorption lines. Dr.C. K. J#rgensen (Tech. University of Denmark) said: It is interesting that Dr. Hayes has established that the electron configurations of Crf, Fe+ and Nif in NaF are 3dn rather than 3dn-14s as for the gaseous ions. This demonstrates the highly anti-bonding character of the 4s-orbitals in the complex, or rather of the empty 71-orbital. Is there any evidence that the hyperfine-structure of the paramagnetic resonance curve is particularly influenced by low 4s-levels ? Can any optical absorption bands be assigned to ligand field 3dn-transitions or to Laporte-forbidden 3dn -+ 3dn-14~ transitions ? Dr. W. Hayes (Argonne Nat. Lab.) said: The spectrum of Mn2+ shows an anomalously large hyperfine-structure. For a discussion of this effect I refer to the work of Abragam, Horowitz and Pryce 1 and Heine.2 We have not attempted so far to look for optical transitions of the impurity ions but we intend to do so.Dr. R. Englman (Bristol University) said: I would like to know from Dr. Hayes to what extent the jumps of the vacancies round the impurity ion affect the observations. The significant energy differences involved in the observations amount to oscillation frequencies of the order of 108 sec-1; on the other hand the frequency with which the vacancies change positions may be (at room temper- atures and on the basis of rather uncertain data) as high as 1010 sec-1. Ac- cordingly, this effect can be expected to be observable. Put in another way, one would like to question the justification for treating the situation as a static one, with vacancies in well-defined positions.Dr. W. Hayes (Argonne Nat. Lab., Ill.) (communicated): In reply to Dr. Englman, the effect of vacancy diffusion in the case of Mn2+ may be observed initially as a broadening of the lines. As the vacancy-jump frequency increases with increasing temperature the outside fine-structure components will eventually be averaged out, and a single narrow central component will be observed. These effects are expected to occur when the jump frequency is in the range lOg-lO11 sec-1 and have not been observed in NaF at the temperature of measurement (90°K). The onset of broadening has been observed for associated Mn2+ in NaCl at about 200°C (Watkins, private communication) and it is estimated that a temperature of 750°C would be required to observe motional narrowing.Dr. L. E. Orgel (Cambridge University) said: I should like to describe a mechanism by means of which a paramagnetic ion can induce a spin density on a neighbouring ligand which has the opposite sign to the spin on the ion itself. To be specific I shall consider the Cr3+ ion, but the argument applies with minor changes to any other paramagnetic metal ion. The Cr3f ion has the configuration (t2$ in an octahedral environment. Let us consider the electron affinity of this ion for a 4s electron. If the s electron has spin parallel to the d electron spin we get a quintet state (the SA2 component of 5F), while if the electron has spin antiparallel the state is mainly a triplet state (the 3A2 component of a 3F state). In the latter case there is a small contribution (1/4) from the quintet state with the appropriate m, value.Since the quintet state is 0.9 eV more stable than the triplet the electron affinity is greater if the spin of the added electron is parallel to the spins originally on the ion. This is 1 Abragam, Horowitz and Pryce, Proc. Roy. Soc. A, 1955,230, 169. 2 Heine, Physic. Rev., 1957, 107, 1002.GENERAL DISCUSSION 93 a quite general result and follows from the sign of two-electron exchange integrals. It would apply equally to the acquisition of s or p electrons by any metal ion, or to the acquisition of d electrons by empty metal d orbitals, for example eg electrons by Cr3+ In view of this difference of electronegativity, electrons will be transferred to empty orbitals of the metal ion from the ligand slightly more with spin parallel than with spin antiparallel to the spins on the metal. This should leave a net antiparallel spin on the ligand.Thus this mechanism has the opposite result to that of the electron delocalization usually considered in which electrons are trans- ferred to half-filled orbitals necessarily with spin antiparallel to those on the metal ion. The effect of the new mechanism should be smaller for any given class of orbitals than that produced by the conventional one, since we are dealing with the difference between parallel and antiparallel spin transfer rather than with a purely antiparallel transfer. Transfer to d orbitals of the metal should give an anisotropic contribution and to s orbitals an isotropic contribution to the metal nuclear hyperfine-structure. Similarly transfer from s or p orbitals should give a characteristic contribution to the ligand hyperfine-structure.I should like to ask if there is any experimental evidencz for this. Dr. D. J. E. Ingram (Southampton University) said: We made a careful study of the ferrihaemoglobin hydroxide derivatives because Pauling’s earlier suscepti- bility measurements had indicated that this might be a rare case in which S = 3/2 for the ferric ion. A theoretical treatment by Griffith has indicated, however, that for this particular molecular symmetry, it will not be possible for the S = 3/2 state to exist if the S = 5/2 and S = 1/2 have already been shown to occur- as in the acid-met and azide ferrihaemoglobin derivatives respectively.It was therefore suggested that the hydroxide derivative consisted of a thermal admixture of the S = 5/2 and S = 1/2 state, the equilibrium of the mixture depending on the pH value of the particular solution, and the temperature. Our experimental observations on the hydroxide derivatives confirm these predictions since only transitions corresponding to S = 5/2 (with Sz =i. 1/2), or to S = 1/2 are observed, and there is no sign of an S = 3/2 state throughout the pH range of 6.5 to 10.0. It should be pointed out, however, that the S = 5/2 component of the thermal admixture associated with the hydroxide derivative will occur at identical resonance conditions as those of the normal acid-met de- rivative. It is therefore difficult at low pH values to determine how much of this particular component is due to the OH derivative and how much is due to unchanged acid-met derivative.It is noticeable, however, that for the second OH spectra, as summarized in fig. 7 of our paper, there appears to be no cor- responding increase in the S = 5/2 component, and this may therefore correspond to a genuine S = 1/2 complex. In this connection it may be mentioned that the only case in which electron resonance appears to have given conclusive evidence for an S = 3/2 state in the ferric ion is in chloro-ferric phthalocyanine, which has an additional chlorine attached to the iron atom. In this case we observe a g, of about 4.0 and it would appear that this can only be explained by assuming S = 3/2 and that Sz = & 1/2 lies lowest, some 5 cm-1 below Sz = & 3/2.The situation is then very similar to that in the acid-met ferrihaemoglobin and a gl = 4 with a gI1 = 2.0 is pre- dicted. Dr. R. J. P. Williams (Oxford University) said: In the ferric and cobaltous complexes of porphyrin-like structure, it is possible that the fifth and sixth co- ordination positions are bound by water molecules. What methods were used by Ingram et al. to analyze their compounds? It is stated that in some ferric complexes there may be an equilibrium between two spin forms of the same complex. This is indicated also by the absorption spectra of many complexes of the haemoglobin type. What percentage of one94 GENERAL DISCUSSION spin form in the presence of another could the authors detect by their methods? This is an important question as the percentage of the two spin forms varies con- siderably from the solid to solution, and in solution the reactivity of a complex depends upon the spin state it is in.From the discussion of ferrihaemoglobin hydroxide it would appear that the hydroxide ion produces a greater field effect than a water molecule. Again from a comparison of magnetic data of iron (ferric) porphyrin complexes it would appear that. chloride exerts a greater field than water. These field effects are in the opposite order from the spectroscopic “ fields ” produced by these ligands once again suggesting that the spectroscopic data should not be used in considering the field in the ground states of complexes. Dr. D. J. E. Ingram (Southampton University) said : In answer to Dr.Williams, the only other “ ionic ” ferrihaemoglobin compound we have studied in detail as yet is the ferrihaemoglobin fluoride. This also has a large splitting between its quantized spin orientations so that gl remains isotropic at 6-0 down to the lowest wavelengths at which we have measured (6 mm). It would therefore appear that the binding between the acid-met and the fluoride derivatives are very similar and the detection of any small quantitative differences will require higher-frequency radiation sources. It should be added that the nature of the haemoglobin and phthalocyanine crystals that we study are very different. The former are typical organic crystals containing a large amount of free water and the condition of the iron atom is thus probably very similar to that in solution.The phthalocyanine crystals are grown by sublimation at high temperature, however, and will contain no, or very little, occluded water. It may be of interest that we have been hoping to resolve the hyperfine- structure from the surrounding nitrogen atoms in some of the phthalocyanine crystah, but have, as yet, had no success. This may be due in part to the limited diamagnetic dilution which we have so far been able to employ. The crystals themselves are very small and a limit tn the maximum dilution with zinc phthalo- cyanine is set by sensitivity and signal-to-noise ratio considerations. There appears to be some evidence that a concentration-independent half-width of 30 gauss is reached, however, and it is hoped that future work may demonstrate whether this is due to unresolved nitrogen hyperfine-structure. No hyperfine-structure has been observed on the haemoglobin resonance either, but in these cases there is a marked variation in the width of the lines with orienta- tion for which no satisfactory explanation has yet been found. Dr.D. Schonland (Southampton University) (communicated) : It has been pointed out to us that the argument given in justification of the neglect of n-bonding is fallacious and that no conclusions about this can be drawn on the evidence avail- able. Inclusion of n-bonding affects the expressions given for the g-values by reducing the effective spin-orbit coupling constant 5 ; the amount of the reduction depends on the amount of r-bonding and will be different for the parallel and perpendicular directions. The numerical values we suggest for the energy level spacings must therefore be treated with reserve. Any appreciable amount of n-bonding will reduce the spacings required to explain the g-values. The fist- order calculations for the hyperfine structure and the conclusions drawn from these are not essentially affected by the presence of n-bonding. Dr. J. S. GrifEth (Cambridge University) (communicated) : With reference to Dr. Williams’ communication,l there is only evidence for an equilibrium with the hydroxide.2 As for the absorption spectra, Prof. P. George of the University of Pennsylvania has made an interesting analysis 3 of the spectra of ferrihaemo- 1 Williams, this Discussion. 2 Ingram, this Discussion. 3 George and G a t h , to be published.GENERAL DISCUSSION 95 globin and ferrimyoglobin hydroxides and shown them to be consistent with the view that the hydroxides are thermal mixtures of S = 5/2 and S = 1/2 in the proportions suggested by the observed susceptibilities. As we ascribe the intense visible and near-visible absorption in both the S = 5/2 and S = 1/2 compounds practically entirely to transitions in the porphyrin ring and, probably, partly to charge transfer to and from the metal ion, it is difficult to regard the analysis as an independent proof of the existence of a thermal equilibrium. Its possibility and plausibility is, however, satisfactory. I should say that ow interpretation of the S = 5/2 spectrum differs somewhat from that of Dr. Williams for he assigns the intense absorption band (E,,, = 8500) at 605 mp in ferrihaemoglobin fluoride to the spin-forbidden d-d transition 6S to 4G of the ferric ion. Such a transition would be expected to have an intensity not much greater than emax = 1. Williams, Faraday SOC. Discussions, 1955,20, 291.

ISSN:0366-9033    

DOI:10.1039/DF9582600087

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

II. ENERGETICS OF COMPLEXES THE MAGNETIC BEHAVIOUR OF REGULAR AND INVERTED CRYSTALLDVE ENERGY LEVELS BY J. H. VAN VLECK Lyman Laboratory of Physics, Harvard University, Cambridge 38, Massachusetts, U.S.A. Received 13th June, 1958 A crystalline potential of dominantly cubic symmetry accounts largely for paramagnetic anisotropy in salts of the iron group. The great variations in the degree of anisotropy from ion to ion are caused by a peculiar inversion effect in the Stark pattern. A con- sistent cubic potential can be used throughout the iron group, but evidence is presented that in alums, though not in ferrites, the non-cubic portion of the field depends greatly on the nature of the cation itself because of the latter's " back action " on its surroundings. One such polarization mechanism is the Jahn-Teller effect.An explanation is given why this effect plays a fundamental rule in the Abragam-Pryce theory of the susceptibility of copper fluosilicate, and still is inconsequential in Low's microwave experiments on FeO and other oxides. 1. REGULAR AND INVERTED CUBIC LEVELS-MAGNETIC ANISOTROPY The amount of magnetic anisotropy in salts of the iron group varies in a striking way with the nature of the cation. Typical experimental results 1 are shown in table 1. TABLE 1 .-MAGNETIC ANISOTROPY ion state Cr3+ . . . d34F Mn2+ . . . d56S Fe3+ . . . d56S Fe2+ . . . d65D Co2+ . . . d74F Ni2+ . . . d83F cu2+ . . . d92D anisotropy, "lo 0.25 0.10 0.20 16 30 1 -50 20 It is generally recognized that the explanation of the apparently irregular variations is found in the assumption of crystalline fields of nearly but not per- fectly cubic symmetry, as the writer suggested 2 in 1932.In the iron group, the cubic crystalline potential is large compared to the spin-orbit interaction, so that as a first approximation one considers the purely orbital Stark problem. The very small anisotropy of the S states is obviously no problem, for S wave functions are centro-symmetric, and the small existing anisotropy is caused by high-order perturbing effects of spin-orbit interaction, which we shall not discuss. The splitting pattern for D and F levels is shown in fig. 1. When a degenerate level such as r4 or rs (Bethe's notation) is deepest, a high amount of magnetic anisotropy can be expected, for the triplet is decomposed by the non-cubic portions of the field, and the full cubic symmetry is achieved only if all the components are equally inhabited, true only at T = co.On the other hand, if a r, level is deepest, the 96J . H. V A N VLECK 97 anisotropy should be very small, as T2 orbital wave functions, being non-de- generate, carry no orbital moment. The same is also the case if the r3 state is deepest, for cubic r3 states, though degenerate, are by exception devoid of orbital moment. The comportment of magnetic anisotropy shown in table 1 is understandable if, and only if, fig. 1 is upright for Fe2+(d6), C02+(d7) and inverted for Cr3+(d3), Ni2+(d8), Cuz+(d9). This behaviour need not be taken as an ad hoc assumption. Instead, it is one of the striking consequences of quantum mechanics that pre- cisely this inversion phenomenon is predicted if one assumes a consistent cubic potential throughout the transition series.Theory also predicts that fig. 1 be upright for Ti3+(d), V3+(d2) and inverted for Crzf(d4). No adequate anisotropy data are available for these ions in salts comparable in structure with those of table 1. The proof2 of this inversion phenomenon, which we omit, is exceedingly simple, being based only on the invariance of the diagonal sum in individual and collective space quantization, and the dictums of group theory on the general structure of matrix elements of Tesseral harmonics. It is very similar to Goudsmit’s proof of the inversion of spin-orbit multiplets in the second half of an incomplete shell. In our case, however, the centres of inversion are at the quarter rather than half periods of the group.From the foregoing it might seem that Ni2+ and Cu2+ should have comparable anisotropies, as both have non-magnetic orbital states except for spin-orbit per- turbations. The reason that the cupric ions are more anisotropic is a somewhat special one, viz., they, unlike nickel ions have corrections to the “ spin-only ” first-order Zeeman effect of the order @A Vnc/ Vc2. Here /3, A , Vc, Vnc are respec- tively the Bohr magneton, the spin-orbit constant, the cubic and non-cubic parts of the crystalline potential. The foregoing discussion is all on the assumption that the cation is six- co-ordinated with the six nearly cubically spaced neighbouring ions or molecules (usually water) negatively charged or polarized so that the negative end of the dipole is nearest the cation.A simple expansion3 of the potential from point charges or dipoles with this model shows that then for a one-electron system, the left side of fig. 1 is upright for the case of Ti3+, as we have tacitly assumed as the starting point of our discussion concerning which levels are upright and which are inverted. If, however, the cation is tetra-co-ordinated, as with four surrounding negative charges at the corners of a tetrahedron, this calculation shows that fig. 1 should be inverted for Ti3+, and the statement of which ions have inverted and upright cubic levels is just the inverse of that given in the caption of fig. 1. Hence tetra- co-ordinated divalent cobalt should be like six-co-ordinated nickel and show very little magnetic anisotropy.Krishnan and Mookherji 4 have found that the magnetic anisotropies of the tetra-co-ordinated compounds Cs3CoCls and Cs2CoC14 are respectively 6+ % and 5 %, much lower than the 30 % for the six- co-ordinated case (cf. table 1). The deviations of the susceptibility from the spin-only value are also much less, as one would expect. The anisotropy is, however, much larger than for nickel. In an unpublished dissertation (Oxford, 1953), Owen shows that this difference is caused by the fact that the cubic splitting are smaller in 4- than in 4-coordinated compounds ; in consequence the im- portance of deviations from cubic symmetry is accentuated in the former. The magnetic behaviour (anisotropy, etc.) also the colour, of CuSO4.5H20 is very similar to that of CuK2(SO4)2. 6H20, indicating that there is a co-ordina- tion number of six in the pentahydrate.5 At one time this prediction was at vari- ance with the view then generally accepted that the co-ordination number was 4 since only five water molecules are available per cation. Fortunately Beevers and Lipson 6 subsequently made a detailed X-ray analysis of CuSO4 . 5H20, and found that in reality there is a group of six oxygens around Cu2+, of which four are furnished by the water molecules and the remaining two by the SO4 radicals. D98 CRYSTALLINE ENERGY LEVELS This is a case where magnetic analysis made predictions on crystalline environment even before X-ray analysis. In the preceding discussion it has been predicated that the crystalline field is not powerful enough to break down If coupling and invalidate the Eund rule, In the cyanides, the crystalline field, or alternatively, covalency effects are so strong that a state of lower multiplicity is deepest.Even in the conventional cases (Tutton salts, alums, etc.) whers the ground state is that of maximum multiplicity, there is Some error in the assumption L = Lax. when the ground state is of the type r 4 , since the true wave function is a linear combination of Fr4 and Pr4. It has sometimes been assumed that consequently the orbital moment and spin- orbit energy are materially lowered. Actually the reduction can be calculated,7 and is small (8 % in the cobalt case). There are no corresponding corrections for the other ions, as there is only one state of the type r3 or T's if the multi- plicity is the maximum possible.In all cases, there may be material reduction in the orbital moment and spin-orbit energy by the Stevens wandering effect.* But this is another matter. 2. INVERSION PHENOMENA IN SPLITTINGS CAUSED BY DEVIATIONS FROM CUBIC SYMMETRY So far we have discussed the inversion of levels in a cubic field. This subject was fairly well understood some 25 years ago, when consequently the broad lines of the quantum-mechanical theory of ferromagnetic anisotropy became estab- lished. Analogous inversion phenomena of more problematical character and hence more current interest are encountered in the additional decompositions caused by deviations from cubic symmetry.If a field of trigonal symmetry along one of the body diagonals is added to the cubic field, or one of tetragonal symmetry along one of the principal cubic axes, then the triply degenerate I'4 or I's ground states are split into a two-fold level E and a non-degenerate state A, as shown in fig. 1. (Since the theory for Cu*+ ions is quite well established, we omit discussing the case that the r3 level is the ground state; it is split by a tetragonal but not a trigonal field.) The inversion problem is whether the state E is higher or lower than A. If one and the same potential is operative throughout the sequence, then calculation 9 shows that the splitting should be (2.1) (2.2) AS = E(DrsE) - E(Dr5A) = 42(r3d2)av + a4(r3d4>av & = EW4E) - E W d ) =- 3%a2(r3d2)av - $a4(r3d4)av for d, d6(Ti3+, F&+), and for d2, d7(V3+, Co2+). The a2 and a4 terms result respectively from second- and fourth-order harmonics in the development of the crystalline potential.Still higher order members a6 . . . do not exist as long as one is dealing with d electrons. The signs and numerical values of the a factors cannot be obtained without an explicit model of the clusters about the cation. The point, however, to keep in mind is that with a given model of the crystalline field, in other words with given crystalline spacings and with no variation in polarization effects created by the cation on its sur- roundings, the coefficients a2, a4 remain the same for d, d4, d6, d7. In writing (2.2) we have supposed that the deviations from cubic symmetry are of the trigonal type, substantially the case in alums and ferrites; if instead they are tetragonal, one should replace - &, - 3 in (2.2) by - i$, - 3 respectively.One immediately sees from (2.1) and (2.2) that & and A, will have mutually opposite signs for most choices of the constants a2, a4. This inversion phenomenon explains why the energy of ferrimagnetic anisotropy is about a hundred times larger for CoFe203 than Fe304. Under normal circumstances (e.g. if the a2J . H. VAN VLECK 99 terms are more important than the a4 ones), the E level will be deepest in Co2+ if the A level is in Fez+. The contributions of the orbital moment of the E state to the magnetic energy are highly anisotropic, whereas there is very little aniso- tropy arising from the A state.In an interesting paper, Slonczewskilo shows that the order of magnitude of and also the temperature dependence of the mag- netic anisotropy of ferrites with small amaunts of cobalt are explicable under the limiting approximation A = CO, in which interaction with the excited A state is not considered. The fact that the calculated anisotropy is about twice the observed is no doubt attributable to A4 being finite rather than infinite. One also looks for the inversion phenomenon in the pair Ti3+, V3+, which are analogous to Fe2+, Co2+ in the spectroscopic classification of their crystalline energy levels. Here the experimental data are on the alums, and they are difficult to explain. Siegert’s theory 11 of the paramagnetism of vanadium alum requires that the A level be deepest and that the trigonal splitting be quite large (700 cm-l upright in Ti3+ (d 2D), Fe3+ (d6 5 0 ) ; inverted in Cr2+ (d4 5D), Cu2+ (d9 20) ; upright in V3+ (d2 3F) Co2+ (d7 4F) ; inverted in Cr3+ (d3 4F) Ni2+ (d8 3F). FIG.1.-Schematic energy level diagram in a nearly cubic field. The additional decom- position of a r4 or r, ground level by a perturbation of trigonal or tetragonal symmetry is also shown. See 0 2 concerning whether the A or E state is lowest. Coincident levels (e.g. the three components of Fs) are shown slightly separated to reveal the degree of degeneracy. or more). If the same field were used as in the ferrites, the E level would be deepest but there is no a priori reason that the crystalline potential be the same in the ferrites and alums as regards the small deviations from cubic symmetry.The susceptibility of titanium alum is, however, completely inexplicable if the E level is deepest. Hence there cannot be an inversion of the E, A levels in the V, Ti alums, unlike the Co, Fe ferrites. Under certain rather exceptional conditions, eqn. (2.1), (2.2), to be sure, do not give an inversion. According to (2.1) and (2.2), the ratio of the splittings for the two alums is (2.3) & - - h + % k &- 1 - k where k = - a4(r3d4>av/a2<r3d2>av. Examination of the expansion of the crystal- line potential shows that the dimensionless ratio k should be positive, and of the order of magnitude of the square r2/R2 of the ratio of the radius of the 3d shell to the distance of an H20 molecule from the paramagnetic cation.If the fourth- order terms are sufficiently large, the ratio (2.3) can be positive and there is no inversion. Then the A level can be deepest in both V3+ and Ti3+. In a paper 9 written in 1939, I endeavoured to show that there were reasonable atomic models100 CRYSTALLINE ENERGY LEVELS that would make this ratio positive. A difficulty has, however, developed sub- sequently. Oxford microwave measurements 12 on titanium caesium alum give 811 = 1.25, g, = 1.14 and so show that its susceptibility deviates far more from the spin-only value than was realized in 1939. The quenching of the orbital angular momentum consequently is incomplete, and so the separation A5 must be small, as is also indicated by the abnormally short spin-lattice relaxation time of titanium alum.Bleaney and collaborators 12 find that the magnetic data on titanium alum can best be fitted with a separation A, only about 50 cm-1. It is, however, very diffcult to find an atomic model that will give values of the ratio A4/A5 as large as 10 or more. If the field is attributed to the neighbouring water dipoles, r/R would have to be practically unity in order to make k large enough, The upshot of the preceding discussion is that it is very difficult, though perhaps not absolutely impossible, to find a physically reasonable set of values of the con- stants a2, a 4 in (2.1), (2.2) that will work satisfactorily and consistently for both V and Ti alum. We are therefore led to the suggestion that whereas the main cubic part of the potential is quite stable, the deviations from cubic symmetry are influenced by the cation, so that in a sequence of analogous salts, a2 and a4 in (2.l), (2.2) vary from ion to ion. Such a behaviour is not a priuri unreasonable for the angular shapes of the electronic charge cloud for I'4 and I'5 differ from each other, as well as from the more nearly symmetrical configuration r 2 . In support of this idea, a number of facts may be mentioned. One is that W. M. Walsh, Jr.13 finds that the splittings of the 3 r 2 and 4 r 2 multiplets in NiSiF6. 6Hz0 and NH4Cr(SO4)2 , 12H20 respectively (small higher-order effects we do not treat) vary with pressure, as well as temperature, in a highly involved fashion that cannot be explained on the basis of " scaling ", i.e.stretch or shrinkage of the crystal with preservation of relative distances. The interplay of the cation with its surroundings thus appears to be very complicated. In copper fluosilicate, the Oxford microwave data 14 show that locally the deviations from cubic sym- metry even change from a trigonal to a tetragonal character as the temperature is lowered. A second piece of evidence is the fact, according to Segleken and Torrey,ls the ratio of the nuclear quadrupole splittings in the ammonium and potassium aluminium alums is the same as that of the electronic 4 r 2 splitting in the ammonium and potassium chrome alums. Since only the second-order har- monics contribute to the nuclear quadrupole splittings, this presumably means that a4 is negligible in (2.1) or (2.2), for it is highly unlikely that substitution of potassium for ammonia changes the fourth- and second-order terms in the same ratio.The I'2 state of Cr3+ or Ni2+ has a practically centrosymmetric charge cloud, and so probably resembles Al3+(SI'1) in not distorting the surrounding clusters. It is strange that fourth-order terms are not more important, for dipoles or charges at the distance of the H20 molecules from the cation give 9 ~ 1 3 appreci- able values of a4/a2. Purely second-order terms are incompatible with the Bleaney and Siegert interpretations of the Ti and V alums, as aq = 0 gives A4/A5 = - 1/10 rather than &/A, = + lo! Finally may be mentioned the fact that micro- wave data show that in substances as similar as Cu(NH&(S04)2. 6H2O and Ni(NH&(S04)2.6H2O the direction of the local tetragonal axis at the cation difTers by 90O.16 It thus appears that the non-cubic part of the field is not consistent from ion to ion, at least in materials with loosely bound, and presumably easily squashed waters of hydration. This difficulty, however, may not arise in an- hydrous oxides and ferrites, which are tougher in structure. 3. THE JAHN-TELLER EFFECT We thus seem to be left with the rather unpleasant prospect that in hydrated salts the non-cubic part of the potential is influenced by the nature of the cation, so that the constants a2, a 4 in (2.1), (2.2) vary materially from ion to ion even in the same type of compound. This extra degree of freedom complicates and dif-J . H . VAN VLECK 101 fuses the theory of magnetic energy levels, for it is hard to evaluate the amount of “ back action” of the cation on its surroundings.There are good theoretical reasons for believing that such polarization effects may be of importance. One of them is the so-called Jahn-Teller effect, which is essentially the fact that in a degenerate level (other than a Kramers doublet) the linear terms in the expansion of the crystalline potential in the normal vibrational co-ordinates cannot be simultaneously eliminated from all the components. As a result the equilibrium positions of the surrounding atoms are shifted. The system resonates through a variety of such positions, so that there is no extra decomposition of the energy levels. With a sufficiently high J-T effect, the orbital angular momentum is largely quenched, and the susceptibility has substantially the “ spin-only ” value.The theory of the susceptibilities of the titanium and vanadium alums should, in our opinion, be re-examined in the light of recent work by Moffitt,17 Pryce,lg and their collaborators on the J-T effect, but the problem may be too complicated for tangible results. In this connection the trigonal field should presumably be assumed smaller than in the early work of Siegert and of the writer. The possibility that in titanium the A-E separation be large with E deepest, and that the J-T effect be operative only within the E pair is not tenable, as it gives g, = 0 contrary to experiment. It is somewhat dubious whether the susceptibility of vanadium alum can be ex- plained by using mainly the J-T effect, and having the trigonal field play a rather minor role.In general, it is not too clear just how important is the role of the J-T effect but there is one case in which it is clearly a major factor, and one in which it appears to be negligible. The work of Abragam and Pryce 19 shows unambiguously that the magnetic behaviour of copper fluosilicate at room temperatures is explicable only on the basis of a large J-T effect. On the other hand, the elegant spectroscopic measurements of Low 20 on magnetically dilute oxides (MgO with a little of the Mg replaced by a paramagnetic ion) shows that in structures of the form Me-0 the pattern can be nicely explained by assuming a perfectly cubic field with no J-T modulations. At first sight there thus appears to be a paradox for it does not make sense to have the J-T effect only operative part of the time under similar circumstances.However, the situation is not the same in copper fluosilicate and in the oxides studied by Low. In the first place, the oxygen atoms in the transition group oxides are doubtless more firmly bound to their normal equilibrium posi- tions than are the water molecules and their constituent atoms in the Auosilicates or Tutton salts. Nevertheless, mere difference in firmness of binding is not the main reason for absence of J-T effects in the Low experiments. With Mn2f or NG+, the absence of a J-T effect poses no problem, for a or I‘2 ground-orbital state has no degeneracy. The lowest level of the Co2+ ion in a cubic field inclusive of spin-orbit interaction is a Kramers doublet, and the J-T effect is incapable of removing its degeneracy or under certain conditions of changing its g value. As Opik and Pryce 18 point out and study in detail, the stability in Zeeman pattern results when the s-o interaction is so large that it is legitimate to drop J-T matrix elements non-diagonal in the s-o energy.By J-T matrix elements we mean those of the crystalline potential which are linear in the normal co-ordinates or vibra- tional displacements. FeO requires more examination. (Incidentally, Low apparently finds some evidence of the J-T effect if Fez+ is substituted in ZnS rather than MgO.) If s-o interaction is included, the lowest level of the complex 5DT5 is a triplet. As we will show elsewhere, the J-T matrix elements internal to this triplet are non-vanishing, but are one-tenth as large as the corresponding matrix elements for the I‘5 orbital triplet without spin. (A similar result has also been obtained by Pryce in unpublished work.) This reduction by a factor 10 because of s-o interaction can be sufficient to make the J-T effect virtually inoperative, as in the rare earths, for initially the J-T corrections to the Zeeman splittings are quadratic in the J-T matrix elements. There is thus no conflict between the Abragam-Pryce theory for copper fluosilicate and Low’s results.102 CRYSTALLINE ENERGY LEVELS 1 Rabi, Physic. Rex, 1927, 29, 174.Krishnan, Mookherji and Bose, Phil. Trans., 2 Van Vleck, Physic. Rev., 1932, 41, 208. 3 Gorter, Physic. Rev., 1932, 42,437. 4 Krishnan and Mookherji, Physic. Rev., 1937, 51, 528 and 774. 5 Jordahl, Physic. Rev., 1934, 46, 79. 6 Beevers and Lipson, Proc. Roy. SOC. A , 1934, 146, 570. 7 Finkelstein and Van Vleck, J. Chern. Physics, 1940, 8, 797, footnote 21. 8 Stevens, Proc. Roy. SOC. A , 1953,219, 542. 9 Van Vleck, J. Chem. Physics, 1939,7, 79. 10 Slonczewski, J. Appl. Physics, 1958, 29, 448; Physic. Rev., 1958,110, 1341. 11 Siegert, Physica, 1937, 4, 138. van den Handel and Siegert, Physicu, 1937, 4, 871. 12Bleaney, Bogle, Cooke, Duffus, O’Brien and Stevens, Proc. Physic. SOC. A, 1955, 13 Walsh, Thesis (unpublished), Harvard University, 1958. 14Bleaney and Powers, Proc. Physic. SOC. A, 1952, 65, 667. Bleaney, Bowers and 15 Segleken and Torrey, Physic. Rev., 1955, 98, 1537. 16Griffiths and Owen, Proc. Physic. SOC. A , 1951, 64, 583. 17Moffitt and Liehr, Physic. Rev., 1957, 106, 1195. Moffitt and Thorson, Physic. 18 Opik and Pryce, Proc. Roy. SOC. A , 1957, 238,425. Longuet-Higgins, Opik, Pryce 19 Abragam and Pryce, Proc. Physic. SOC. A , 1949,63,409. 20 Low, Physic. Rev., 1956,101, 1827 ; 1957,105,801 ; 1958,109,247 and 256; (Ann. 1939, 238, 155. 68, 57. Trenam, Proc. Roy. SOC. A , 1955,228, 158. Rev., 1957, 108, 1251. and Sack, Proc. Roy. SOC. A , 1958, 244, 1. N. Y. Acud. Sci., 1958,72, 104.

ISSN:0366-9033    

DOI:10.1039/DF9582600096

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

THE MAGNETIC PROPERTIES OF SOME d:, dz AND dz CONFIGURATIONS BY B. N. FIGGIS, J. LEWIS, R. S. NYHOLM AND R. D. PEACOCK Chemistry Dept., University College, London Received 30th July, 1958 The variation in the magnetic susceptibility over a temperature range for some com- plexes of osmium, ruthenium, rhenium and iridium, in d,3, d$ and dl configuration, have been measured. This variation in susceptibility has been discussed in terms of the Kotani theory and the relative importance of the various assumptions made in this theory are examined in the light of the magnetic data. During the past few years, greatly increased interest in the magnetic properties of the second- and third-row transition-metal compounds has been evident. Earlier the Van Vleck and the Pauling approaches to octahedral six-covalent complexes satisfactorily accounted for the moments of spin-free (e.g.K3FeF6) and spin-paired (e.g. K$e(CN)6) compounds of the first row but for many com- pounds of the heavier transition metals the behaviour was not understood. Thus, the moment of K20SC16(d4)(peff = 1.4 p ) is less even than the spin-only value of 2-83 p. In 1949, the Kotani theory 1 provided a reasonably satisfactory explanation for these low moments in terms of the increased spin-orbit coupling. However, closer investigation shows that moments which differ markedly from the Kotani theory are often observed; thus, although this theory predicts a temperature independent moment of 3-88 /3 for all octahedral d: complexes the hexahalorhenates (IV), e.g. K2ReF6 have moments as low as 3.2 @.A general investigation of these anomalies has been proceeding in these laboratories and this paper summarizes the results of our studies of the variation of peff over a range of temperature for several octahedral d,3, d$ and dz complexes. The complexes of the heavier transition elements differ from those of the fist row mainly because of four effects: (i) greater crystal field effects manifest as larger energy separations A between d, and 4 orbital levels, leading always to spin-paired complexes for octa- hedral d$ and d,5 configurations ; and (ii) the much larger spin-orbit coupling con- stants of these elements; (iii) a relative decrease in interelectronic repulsions as compared with I--s coupling energies, which tends to enhance the importance of intermediate forms of coupling over Russell-Saunders coupling; (iv) the in- fluence of anti-ferromagnetic interactions, which are also important in the first row, can be appreciable.It has been with the aim of investigating the relative importance of these factors under various conditions that the measurements reported in this paper were performed. When a transition metal ion is surrounded by six equivalent ligand atoms at the vertices of an octahedron the d orbitals of the ion are split up into two sub- sets, the energetically higher lying & pair, E, symmetry, directed towards the ligand atoms and the lower d, triplet, of T2g symmetry, directed in between the ligand atoms. Many of the magnetic properties of spin-paired octahedral com- plexes may be explained if it is assumed that the electrons of the transition d shell of the ion are allowed to occupy only the d, set of orbitals until this has been filled.The magnetic behaviour to be expected for the various d t configurations has been calculated by Kotanil and is found to depend, in most cases, on the relative magnitude of the spin-orbit coupling constant for the ion and the value of RT. 103104 d3, d4 AND d: CONFIGURATIONS In of fig. the 1 to 4 the splitting of the ground state involved and the mode of variation magnetic moment peff for the ion is given as a function of the parameter 3 l l 0 I RTIA FIG. 1. 2 Peff I 2 0 0 . 0 2 0.04 0.06 0.08 O*I k/TA Fh3. 2. ATIA. A is the shgle-electron spin-orbit coupling constant for the ion, often referred to as y,,&a being the principle quantum number of the d shell involved; A = rt 2rh.For-the first, transition: series kT/A is, for cases of interest, seldomB. N. FIGGINS, J . LEWIS, R . s. NYHOLM AND E. D . PEACOCK 105 much greater than 1 at room temperature, and it may be seen that the moment then does not depart radically from the spin-only value for the number of un- paired electrons involved. If, however, A becomes of the order of 1OOOcm-1 or more, as indicated from the spectroscopic evidence available for certain heavy metal ions, for the 2nd and 3rd transition series ions, moments may be very considerably lowered with respect to the spin-only value. It is important to I I I I / / I I \ \ \ 4 \ \ 4 -92 - 0 - - spin-orbit magnetic coup1 inq field FIG.3.-Splitting of d,' by spin-orbit coupling and magnetic field. (Invert for d:.) 1 0 --,-, A I I I / 3 - 0 - ,-*-<-- -- I / coupling magnetic field FIG. 4.-Splitting of d;, 37'1 ground state by spin-orbit coupling and magnetic field. (Invert for d:.) emphasize the assumptions upon which the theory of Kotani is based : it assumes (i) the effect of the ligand field is greater than the mutual repulsions between the electrons of the d shell, (ii) that these electronic repulsions are larger than the spin-orbit coupling for the ion, and (iii) that the ligand field is of perfect cubic symmetry. It is presumed that we are dealing with magnetically dilute systems. The likely effects of the failure of one or more of these assumptions will be dis- cussed in connection with some of our experimental results.We have confined our attention to the configurations, d,3, d,4 and d5. It may appear, at first sight, that comparatively little interest is to be associated with the d3, configuration as it is expected to be simple in magnetic behaviour, having a moment independent of spin-orbit coupling, temperature and, incidentally, of departures of the, ligand field from cubic symmetry of any reasonable magnitude. This last fact follows as only one quartet level can arise from the orbitals of the d, set? However, we considered it essential to study the d,3 codguration in some106 d:, d: AND d: CONFIGURATIONS detail in order to estimate the magnitude of the effects of antiferromagnetism in the absence of as many complicating phenomena as possible and also to utilizea second-order effect to estimate spin-orbit couplings for comparison with the values obtained for the other configurations by other methods.THE d? CONFIGURATION Table 1 summarizes the results which we have obtained by the measurement of the magnetic susceptibility of a number of octahedral complexes over the range of temperatures 80" to 300°K. The equipment and experimental procedure used in connection with these measurements will be published elsewhere in detail. TABLE 1 .-MAGNETIC BEHAWOUR OF d,3 CONFIGURATIONS ? "eff ion complex solution peff 300°K e B 3-32 40" 3.50 3-25 - I 3-25 86 3-70 3.5 3-19 105 3.70 3.6 - I 3.32 -100" 3.70 3.25 - 3 3.30 0 - I - From the results set out in table 1 it is evident that interaction of an antiferro- magnetic nature is probably present in all of the rhenium complexes studied.In no case did we observe a maximum in the plot of XRe against T; however, for rheniiodide definite signs of an incipient maximum were discernible and it is probable that this occurs not much below the lowest temperature at which we were able to make measurements, 80°K. It is this effect which leads to the ap- proximate nature of the value of e quoted for K2ReI6. It is our intention to carry out measurements at lower temperatures in order to confirm the hypothesis of antiferromagnetism in these compounds. On the other hand, the low values of 0 observed for the osmifluorides indicate that antiferromagnetism plays a negligible part in determining the magnetic moment for these complexes.The fact that the magnitude of the antiferromagnetic interaction apparently increases with the atomic number of the halogen acting as ligand is a puzzling feature of the results, as from other systems it had seemed that fluorine is one of the most effective spin-coupling transmitters in super-exchange mechanisms. The proposal that part of the responsibility for the lower-than-spin-only moments reported for rhenihalides in table 1 is due to antiferromagnetic inter- actions is supported by the measurements made on solutions of the complexes; the exception to this is the fluoride where a small decrease in moment was found. The last column of table 1 lists the moments which are calculated for the com- plexes on the assumption that the value of 8 observed is due to antiferromagnetic effects.The expression Even after such allowance had been made for the presence of antiferromag- netism in the complexes of table 1 it is seen that the moments observed are quite appreciably below the spin-only value of 3.88 which is predicted by the theory of Kotani. A theory which accounts for moments of less than the spin-only value in d3, systems has long been available from the description of the magnetic properties of Cr3+ given by Penney and Schlapp.z They describe the 4Fstate of the Cr3+ ion as being split into a lowest lying singlet level and two higher lying triplet levels. The composition of the singlet level is entirely d3. The magnetic moment of the Cr3+ ion is then given by the expression = 2.841/Xae(T + 0) is employed. PCP' = CLSpin-ody (1 - &-J = 3-88 (1 -&).B .N. FIGGINS, J . LEWIS, R . s. NYHOLM AND R . D . PEACOCK 107 For Cr3+, A is small and the effect results in moments only a few percent below the spin-only value. However, if A becomes large it is possible to account for moments appreciably lower than the spin-only value. The above formula (1) also holds for the effects of spin-orbit coupling mixing in dzd, configurations into the d: level. Consequently, from the moments of d,3 configurations it is possible to obtain estimates of the spin-orbit coupling constants associated with the ions concerned. For rhenium it is difficult to decide upon which value of the moment to choose even for each halide. As a representative value for the whole set of rhenihalides one may take 3.6 /3 but it must be kept in mind that a factor of more than 2 in the quantity (3-88 - peff) is observed.It has been suggested that lODq for the ReClz- ion is 27,000 cm-1.3 If the value of 25,000 cm-1 is taken as representative for the rhenihalides then the expression leads to a value of 135Ocm-1 for A for Re4+. Any such value obtained for A pertains only to the ion in its environment of ligand atoms and must be expected to be some 20 to 40 % less than the free ion value.4 For the osmifluorides the ambiguity in choice of moment is removed and if, somewhat arbitrarily, lODq is taken to be 25,000 cm-1 also, A is found to be 2000cm-1. These estimates of A for Re4+ and O S ~ + are of the expected order of magnitude when compared with values of from 2000 cm-1 to 7OOOcm-1 estimated from spectroscopic data for ions of configurations 5d6 to 5d96s.3 The relative order of A between the two ions is also in keeping with the fact that A is expected to rise with atomic number and with ionic charge.THE d4 CONFIGURATION Table 2 contains the results of our measurements on compounds containing the d,4 configuration. In this table the value of A has been derived by extrapolating the susceptibility to zero temperature when, according to Kotani, XM = 24NP2/A. The measurements enclosed in parenthesis in the table are those in which the extrapolation to zero temperature was somewhat unreliable, as the susceptibility was still varying appreciably at the lowest temperatures of our measurement. For d$ the theory of Kotani requires that the suceptibility be independent of temperature for A > kT.In agreement with this, for Os4+ and Ir4+ compounds, a plot of d? against peff was linear. The lines passed through or near the origin, except for those in parenthesis in table 2. It is seen that for ruthenium the observed moments and susceptibilities lead to the estimation of values for A of between 1600 and 1850 cm--1, while for osmium a range of values between 5000 and 10,000 cm-1 is necessary. For iridium about 87OOcm-1 is required. The value of A from Ru4+ results is rather larger than the value obtained from the data in Ru3+; unfortunately no estimate of A for Ru5+ is available from data on the d,3 configuration but it seems certain that A must be expected to be somewhat smaller than the values found for Re4+ and OsS+ from this configuration.The values of A for Os4+ and W+ are a good deal greater than expected, perhaps by a factor of three or four-a value of 2000 cm-1, as for Os5+ in the d? configuration, might be anticipated. Except for the measure- ments enclosed in parenthesis the form of behaviour of the magnetic suscepti- bility with temperature for all these compounds is such as to suggest there is little, if any, interaction of an antiferromagnetic nature present. Calculations have been performed to investigate the effect of departures from cubic symmetry of the ligand distribution about the central ion on the magnetic susceptibility of the df configurations. For d:, owing to the fact that the lowest level-the only one occupied in complexes with spin-orbit coupling constants as large as the ones being considered-is single, the introduction of a tetragonal distortion of con- siderable magnitude-equivalent to several thousand cm-14s necessary to have any major effect on the susceptibility.A possible explanation of the abnormally large spin-orbit coupling constants derived from the theory of Kotani for Os4+ and Ir5+ can be understood if we re- consider the basis of this theory. The sph-orbit coupling constants for these108 d’, dl AND di CONFIGURATIONS TABLE 2.-MEASUREMENTS ON COMPOUNDS HAVING THE di CONFIGURATION ion compound 4?B 10‘ XM 300°K extrapolated to B zero temperature A (cm-1) Ru4 + K ~ R u F ~ 2.9 3910 1600 K ~ R u C ~ ~ 2.9 3900 1610 K2RuBr6 2.8 3560 1760 RbzRuCls 2.75 (4550) (1380) R~~RuBI-6 2.8 3410 1840 O S ~ + K2OsF6 1.30 715 8800 K2OSCls 1.50 94 1 6700 K~OSBI-6 1 -20 609 10,300 K ~ O S I ~ 1.38 (870) (7200) 1r5 + KIrF6 1.26 725 8700 CSIrF6 1.26 725 8700 I I /- - ..L - - <-,2A I I I I / 2 / 8 I 4 /-><:=-:- A 2 - 5 ~ (2% ’ .) da 15 40 8 \ \ \ -A 6 spin-orbit magnetic coupiing field -- 0 - 0- ‘ 6 FIG.5.-Splitting of d,2 by spin-orbit coupling and magnetic field. (Invert for d:.) atoms, even as evaluated from the d,3 configuration, suggest that the approximation that spin-orbit interaction is much smaller than the interelectronic repulsions is no longer valid. If the converse approximation is made, namely, that the spin- orbit coupling is larger than the electronic repulsion terms, then an equivalent of the j-j coupling scheme can be constructed within the d, orbital set.j-j coupling is known to be a better approximation for the spectroscopic terms of a number of ions of atomic number comparable to osmium and iridium. In fig. 5 the splittings which occur for the d,4 configuration under the influence of spin- orbit coupling alone are given to the first approximation. It is seen that the lowest level is still single and consequently it is to be expected that the para- magnetism associated with this set of conditions will still be of the temperature- independent type. The matrix element of the magnetic field connecting the higher levels of the configuration with the lowest level is reduced relative to that for the treatment of Kotani and the susceptibility at zero temperature is required to be X~=(16/3)N,2/A, Accordingly, if the data of table 2 is used in this approximation the values of A derived are smaller by a factor of 912 compared to those given in the table.A is then about 1700 cm-1 for Os4+ and 1900 cm-1 for Ir5+. Of course, it is likely that some intermediate form of coupling is more applicable and weB . N. FIGGINS, J . LEWIS, R . S. NYHOLM AND R. D. PEACOCK 109 intend to perform the calculation of the susceptibility of intermediate forms to see what degree of transition to j-j type coupling is necessary to explain the ob- served susceptibilities and their dependence on temperature and to account for the smaller exhaltation of the value of A for Ru4f derived from Kotani's theory. A difficulty which arises in connection with this explanation is that coupling of thej-j type might also, then, be expected to apply to the d,3 configuration.Under this type of coupling scheme the lowest level of the d,3 configuration remains four-fold degenerate, and there is no first-order Zeeman effect. Con- sequently, it is difficult to account for the approximation to the spin-only moment and the applicability of (1). It is true that the electron repulsion terms are larger for d? than for d$ (9F24A2 t += 2T2 + 2E2 against 6F2 3 T 1 t -+ IT2 + 1E in Condon-Shortley parameters, neglecting terms in F'), and this may be sufficient to explain the absence of the effect in d i . More detailed calculations are in hand to investigate the effect of intermediate coupling schemes in this configuration. The range of values of susceptibility found for the complexes of osmium re- ported in table 2, of over a factor of 2, presents a problem to which no single simple explanation is obvious.It has been mentioned that the presence of appreciable antiferromagnetic interactions is unlikely, and that departures from cubic sym- metry of the ligand distribution around the central ion would not be expected to produce effects of this magnitude. Some variation in the susceptibility ob- served for different osmihalides might be expected on account of the different degrees of delocalization of electrons on the central ion, with consequent change in the effective value of A.4 However, this effect should change regularly with increasing atomic number of the halogen involved, whereas the distribution of susceptibilities in table 2 is apparently random with regard to both the halogen ligand and the alkali metal cation. THE d? CONFIGURATION Table 3 contains the results of our measurements on complexes of Ru3+. The values of A in table 3 were derived by fitting the room-temperature moment to the curve of Kotani for d5. Of course the method is very insensitive as the TABLE 3.-MEASUREMENTS ON COMPLEXES OF THE d2 CONFIGURATION ion compound peff 300'K B A cm-1 1000 1100 870 610 rate of change of peff with kT/A is small. Consequently, the values of A are only of order-of-magnitude significance. There is also the difFiculty that only two of the complexes are strictly cubic with all six ligands identical and some effect is to be expected from the ligand fields of symmetry less than cubic. The values of A obtained for the symmetrical complexes support the evaluation made from the d 4 configuration of about 1600 cm-1. 1 Kotani, J. Phys. SOC. Japan, 1949, 4, 293. 2 Penney and Schlapp, Phys. Rev., 1932, 666. 3 Jmgensen, Quelques Probl2mes de Chimie Minirale, Institut International de Chimie 4 Owen, Proc. Roy. SOC., 1955, 227, 183. Solvay, May, 1956, p. 355.

ISSN:0366-9033    

DOI:10.1039/DF9582600103

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

THE INTERELECTRONIC REPULSION AND PARTLY COMPLEXES COVALENT BONDING IN TRANSITION-GROUP BY CHR. I(LD(BULL J0RGENSEN Chemistry Dept. A, Technical University of Denmark, Copenhagen Received 5th June, 1958 The ligand field theory expresses the energy levels of a partly filled d-shell in com- plexes in terms of two types of parameters : the orbital energy differences (in octahedral complexes A) and the integrals of interelectronic repulsion. The variation of A as a function of the ligands for a given central ion is Tsuchida’s spectrochemical series. Schaffer and Jarrgensen established the nephelauxetic series, i.e. the decrease of inter- electronic repulsion parameters relative to the gaseous ion, in many octahedral com- plexes by application of Tanabe and Sugano’s determinants. The distance 6S-4G in ds-systems will be discussed here, because it is independent of A to a very high approxim- ation.The decrease of this distance can be ascribed to two effects : that the d-shell has the radial function expanded due to the presence in the core of electrons donated from the ligands (central fieEd covalency) and that the d-shell participates directly in covalent bonding by forming linear combinations with the orbitals of the ligands (symmetry- restricted covalency). The apparent absence of effects of configuration intermixing will be discussed. An atom or an ion in gaseous state can be described to a good approximation 1 as having an electron configuration, i.e. an integral number (between 0 and 41 + 2) of electrons in each n, I-shell. This is not sufficient to indicate the energy, since each configuration, containing a partly filled shell with I > 1, is representeq by several energy levels.In the Russell-Saunders’ coupling case, the energy levels can be assembled in multiplet terms, characterized by the quantum numbers L and S. Ligand field theory describes how these energy leveIs behave, when the sym- metry of the environment is lowered from the spherical symmetry of the empty space. In the approximation discussed above, the n, I-shells will be substituted by molecular 7,-orbitals, and the L, S-terms will be separated in levels, charac- terized by I“, and S. For transition group comp€exes, the central ion contains a partly filled d-shell, and several approximations can be made : (1) Electrostatic model as (2), and assuming either well-defined L (“ weak field ” diagonal elements) or well-defined sub-shell configurations y,ay,6 .. ., where y,, ym, . . ., are the orbitals formed from the d-shell (“ strong field ” diagonal elements). (2) Electrostatic model, taking the intermixing of L and of y”r,b . . . for if given set of levels with the same combination of r, and S into account. It is assumed that the 7,-orbitals can be written as the product of the radial d-function, known (e.g. Hartree’s calculations) for the gaseous ion (which is certainly not hydrogenic) and a linear combination of hydrogenic angular functions, corresponding to I = 2. (3) Expanded radial function model, assuming 2 with another radial function than of the gaseous ions. The energy levels in regularly octahedral com- plexes in this model are given, e.g.by Tanabe and Sugano.2 110C. K . JPIRGENSEN 111 (4) General molecular orbital theory, assuming diagonal elements, cor- responding to pure subshell configurations, but where ‘yn is not assumed to be separable in the product of a radial function and a hydrogenic angular function, i.e. the partly filled shell is not necessarily a pure d-shell. The agreement with experiment, assuming the most suitable choice of energy parameters, increases considerably by going from (2) to (3), demonstrating partly covalent bonding of the complexes. Some evidence can be presented that (4) gives a better description of other properties, e.g. the temperature-independent paramagnetism, than (3). However, the three models (2), (3) and (4) all give nearly the same overall distribution of the energy levels, and it was therefore very difficult to conclude inversely from the absorption spectra, which is the most correct model.The energy of a given level is dependent on four different types of quantities : A. Diagonal elements of one-electron operators, expressing the kinetic energy and the negative, potential energy due to the nuclear attraction of an elec- tron in a given orbital. B. Diagonal elements of two-electron operators, expressing the repulsion between each pair of electrons. Since this interaction mainly has spherical symmetry in atomic spectroscopy it is convenient to regard most of it as an effectively oneelectron quantity, the central field, together with the nuclear attraction.Only the part of the interelectronic repulsion which cannot be expressed in this way, is responsible for the energy difference between multiplet terms of a given configuration. The diagonal elements of the latter type can be expressed by two parameters: the Coulomb integral .I(&) which is the electrostatic interaction between the extended charge distributions a2 and b2, and the exchange integral K(ub) which is the electrostatic interaction between a6 and itself. a and b denote the (real) wave-functions of two orbitals. C. Non-diagonal elements of one-electron operators, which intermix two different orbitals, having the same yn. D. Non-diagonal elements of two-electron operators, affecting at most four different orbitals. This is the cause of the intermixing of configurations, which makes the approximation mentioned above partly invalid.The ligand field can be separated into a (large) Component Yo of spherical sym- metry and other, relatively small, components of lower symmetry. In the follow- ing, the special case of an octahedral field, consisting of Yo + Vwt, acting on the terms of a @-ion, will be considered. The diagonal elements A from V, will be large, but perturb the two equivalent y3 (e in Mulliken’s notation) and three equivalent yS(tz)-orbitals from a given d-shell to the same extent. The diagonal element of Voct will separate these two sets of orbitals, thus producing the “ electrostatic ” part of the energy difference A (also sometimes denoted by (El - E2) or 10 09) between y3 and 73.The “ covalent ” part of A is produced by the non-diagonal elements C, changing the orbitals from the shape in the gaseous ion. Even though electrostatic ligand field contributions E w thus formally are first-order perturbation energies and covalent contributions E,, are second-order perturbation energies, it cannot be assumed that the ratio &v/&,lectr is below 1, or that it decreases strongly in the cases, where both Em, and Eelectr are very small. Actually, in the lanthanides, the ratio seems rather increased, relative to the three ardinary transition groups. This can be explained by the very small value of Eeleccr, produced by Vmt, com- pared to the effects of V,. The diagonal elements of interelectronic repulsion B are also affected by ligand fields.It can approximately be described as the action of Vo added to the central field, producing expanded radial functions of the d-shell, as assumed in112 TRANSITION-GROUP COMPLEXES model (3) above. If the more general model (4) is considered, the two-electron operator quantities B actually give a contribution to the observed values of A, making this quantity a rather ill-defined mixture of one and two-electron operator energies (as is actually any empirical value of an orbital energy; only the energy levels of the total system and not of the electrons are measurable). This is one reason why interelectronic repulsion parameters are liable to be much more accessible to semi-empirical prediction than orbital energy parameters such as A. The present paper tries to distinguish between two reasons for the decrease of the interelectronic repulsion, relative to the gaseous ion.They might be called " central field " covalency and " symmetry-restricted " covalency. Central field covalency is explained by the expansion of the radial function, caused by the presence in the core of the central ion of electrons, donated by the ligands. It must be emphasized that these electrons may occupy orbitals of any symmetry, e.g. the even 71- and odd y4-electrons, formed by linear combination of s- and p-electrons, respectively, from the central ion with the appropriate a-bonding orbitals, formed from lone-pairs of the ligands. On the other hand, the symmetry- restricted covalency of the partly-filled shell occurs by formation of the anti- bonding component of the symmetries y3 (by a-bonding) and y5 (by n-bonding) from the d-shell and the appropriate orbitals of the ligands.It is easily seen that if central field covalency is the most important contribution to the change of the partly-filled shell, then model (3) will be plausible. If symmetry-restricted covalency is important, it will probably be necessary to consider model (4). Schaffer and the present author 3 have discussed the " nephelauxetic " series, i.e. the variation with ligands and with central ion of 6 in the Jahn-Teller-stable, octahedral complexes, assuming Tanabe-Sugano's model 3 with best fitting values of A and of /?, the ratio between interelectronic repulsion parameters in the complex and in the gaseous ion. This function of ligands and of the central ion can be separated with 2-4 % average deviation into the product of two functions of one variable, just as the " spectrochemical " series of A : A = f (ligand) X g (central ion), (1 - 6) = h (ligand) X k (central ion), with the approximate values : f 6 H20 1.00 6 NH3 1-25 3 en 1 *28 3 0x2- 0.98 6 C1- 0.80 6 CN- 1.7 6 Br- 0.76 h 1.0 1.4 1.5 1.5 2.0 2.0 2 3 g k Mn (11) 8,000 cm-1 0.07 Ni (11) 8,900 0.12 Cr (111) 17,400 0.2 1 Fe (111) 14,000 0.24 c o (111) 19,OOO 0.30 Rh (111) 27,000 0.30 Ir (111) 32,000 0.3 It is interesting to note that the function f and h are very different, and that h corresponds more to general ideas about the tendency towards covalent bonding. Most of the evidence, concentrated in the tables given above, is the result of much computational work, since the wave-numbers of most transitions depend both on A and /3.However, two transitions (degenerate for E = 2) occur between 6I'l(S) (6A1 in Mulliken's notation) and the two levels 4rl(G)(4kf1) and 4I'j(G)(4E) of the ds-systems within the same sub-shell configuration 7 9 3 ~ 3 2 , which is well- defined for any value of A. Thus, this energy difference consists only of inter- electronic repulsion parameters and is independent of A. It is therefore possible to compare directly with the transition 6S-4G in the gaseous ions. The wave- numbers of the centre of gravity of the bands are given in table 1. The experi-C. K . J0RGENSEN 113 mental details about iron (111) complexes without literature references will later be published by C.Schaffer and the present author. The bands, indicated in table 1, are much narrower than the transitions from 6 r l to the two first quartet levels 4 r 4 and 4 r 5 . As explained by Orgel 26 from the Frank-Condon principle, the two first quartet levels correspond mainly to the sub-shell configuration 75473 with decreased internuclear equilibrium distances of the excited state. The residual half-width of the bands in table 1 (which often are double with a separation about 300 cm-1) may be caused by the Frank-Condon effect of increasing Q-4G distance for increasing distances to the ligands during the vibrations. TABLE 1 .-THE WAVENUMBER IN CM-1 CORRESPONDING TO THE ENERGY DIFFERENCE 6S-4G IN d5 OF SEVERAL GASEOUS IONS AND OF MANGANESE (11) AND IRON (111) COMPLEXES N 20,5 164 25,279 4 26,846 4 24,650 7 24,000 8 23,800 8 23,800 9 22,300 8 20,000 27 25,000 5, 6 Fe3+ 3d5 N Fe(H20)63+ Fe urea$+ Fe mal33- Fe formiate& Fe 0x33- FeC14- FeF63- 32,000 4 25,350 24,450 5 23,250 22,800 22,750 22,200 18,800 1% 11 en = ethylenediamine ; enta4- = ethylenediaminetetraacetate ; 0x2' = oxalate ; mal2- = malonate ; py = pyridine.Unfortunately, the distance 6S-4G in d5 of Fe3f is not known from atomic spectroscopy, but is extrapolated by EdlCn.4 When we consider the nearly linear dependence of term distances in an isoelectronic series on the ionic charge,l2 a value - 32,800 cm-1 seems more probable. Table 1 gives the impression of an " effective ionic charge " Zeff varying from 1.8 to 1.0 in manganese (11) complexes and from 1.8 to 0.7 in iron (111) complexes, when compared to the gaseous ions Cr+, Mn2+ and Fe3f.This cannot be inter- preted as only 0-2 to 2.3 electrons being transferred from the ligands to the central ion, since it is the effect on the average radius of the d-shell, which can be estimated. Thus, Zeff of 3d54s2 of gaseous Mn is 1-75 on this scale, showing rather small screening effects by the widely extended 4s-electrons. When Orgel 13 compared this behaviour with that of Mn(H20)62+, he actually gave the first indication of central field covalency, while previous treatments, such as that of van Vleck,l4 correspond to symmetry-restricted covalency. The Pauling d2sp3-hybridization is a very special case of symmetry-restricted covalency, assuming identical energies of 3d, 4s, and 4p.It is difficult to improve the latter theory without separating the behaviour of the three sets of orbitals, as done in the molecular orbital theory. The electroneutrality principle seems to work in a certain sense to produce the same Zeff for the same ligand, e.g. the hexa-aquo ions of Mn (11) and Fe (111). However, the decrease of Zeff for Fe (111) complexes seems so large that a pro- portion of symmetry-restricted covalency is plausible. It cannot be argued that MnBr42- and FeC4- are especially covalent, because they are tetrahedral, this is only caused by the high values of the function h for C1- and Br- in the nephel- auxetic series, as can also be seen 13 from CoC142- and CoBr$-. The most inter- esting result of table 1 is that the term distances are not changed more from the gaseous atom.If the model (4) is assumed, the distance 6I'1-4rI will be expressed15 as 5/2(K(l, 4) + K(3,4)) just as the transition 4r2--2I'3 of 753 of chromium (111) complexes is expressed 15 as 3K(4, 5), where the numbers refer to a tetragonal classification of the orbitals. In this case, the K-integrals represent the spin- pairing energy needed to reverse the spin of one electron in a given set of singly114 TRANSITION-GROUP COMPLEXES occupied orbitals, since the parent terms of both 6 r 1 and 4 r 1 are 3 r 2 x 4 r 2 . On the other hand, the energy of 4r3, which is degenerate with 4F1 for 1 = 2 (model (3)) is a complicated squareroot expression in K-integrals, because two sets of parent terms are possible. It is well known that the helium atom is calculated to have slightly too high energy of the ground-state IS, if a pure configuration 1.9 is assumed.This cor- relation effect, corresponding to the neglect of the quantities D, p. 113, is nearly constant, 9200-9900 cm-1, in the isoelectronic series 16 He, Li+, . . ., C4f. The similar correlation effect 17 is 47,000 cm-1 in F- and AP+. Thus, it might be hoped that it is nearly constant, also in chemical compounds, for a given number of electrons. However, it is rather surprising for a chemist to know that the neon atom is stabilized 250 kcal/mole by having intermixed configurations, differ- ing from ls22s22p6. It may be asked, what are the effects of configuration inter- mixing on gaseous ions and complexes of the transition groups.Recently, several physicists 1% 19 have pointed out that a calculation 1 of interelectronic repulsion parameters Fk from Hartree-Fock’s self-consistent 3d-radial wave-functions of Fe and Ni give 10-30 % larger results than the empirical values, and similar results are obtained by Dr. Klaus Appel, Kvantkemiska Gruppen, Uppsala, for 3d5 6s of gaseous Mn2+ (where the distance 6S-4G would be predicted to 33,200 cm-1, if the Slater theory applies with identical 3d-radial functions in the two levels). This systematical decrease of term distances can hardly be explained by a constant square sum of non-diagonal elements, divided by the distance of the considered term from the lower limit of the continuum or another representative place of the iqteracting terms. Rather, some mechanism must destroy the ap- proximation of electron configurations slightly more for the excited states than for the lowest state of a given configuration.Especially, low values of L and S seem more depressed than high oves, corresponding to the correlation effects compensating pqrtly the high first-order energy B, produced by the unfavourable small average distaqce between the electrans in the partly filled shell. Thus, we cannot directly conclude that the energy Werences given in table 1 are exactly inversely proportional to the average radii of the partly filled shel1,20 since they must partly be dependent on effects of configuration intermixing. However, the present author believes that these effects are to a great extent comparable in complexes and in gaseous ions, and that especially the evidence from man- ganese (II) complexes in table 1 suggests a continuous development of the wave- function, known from Mn2f.This expansion is probably mainly beginning as an effect of central field covalency, since the latter phenomenon would occur even with a very shielded d-shell (analogous to the behaviour 21 of the fishell in Pr (111) and other lanthanides). It is remarkable that the ligand field theory is able to describe the energy levels of transition group complexes with some 1-2 % accuracy by use of semi-empirical orbital energy differences and interelectronic repulsion parameters, while very little is known about the wavefunctions.* The description of molecules, which deviate much more from spherical symetry than the transition group complexes, is much less successful, partly because of the great effects of canfiguration inter- mixing.Actually, the correlation effects will make most a priori calculations of molecular energy levels practically impossible, until a proof has been given for * It cannot be argued that the relative importance of hypefine-structure 23, 24 in the paramagnetic resonancecurves from the nuclei of the ligands and of the central ion gives a quantitative measure of the distribution of the partly filled shell on the linear combin- ations assumed in molecular orbital theory of symmetry-restricted covalency. Actually, neither d-electrons nor the x-bonding lone-pairs of the ligands are able to come near to the nuclei (only s-electrons are so) and effects of configuration intermixing are necessary to explain most of the hypefine-structure.*s (Cf.the discussion of Mn (11) compounds by van Wieringen 28.) The resulting weak effects might be rather out of proportion to the relative presence of the partly filled shell in the considered atoms.C. K . JPIRGENSEN 115 the validity of, e.g., Moffitt’s22 approach of “ atoms in molecules”. It was reasonable to initiate the last six years of investigation of transition group energy levels only because very little was realized about the theoretical difficulties, and the reasons for the regular behaviour of the levels of octahedral complexes are still to be discovered. 1 Condon and Shortley, Theory of Atomic Spectra (Cambridge, 1953). 2 Tanabe and Sugano, J. Physic. Soc.Japan, 1954,9, 753 and 766. 3 Schaffer and Jerrgensen, Proc. Symp. Co-ordination Compounds (Rome, September, 1957) and Acta Chem. Scand. ; J. Jnorg. Nuclear Chem., 1958, 8, 143. 4 Moore, Atomic Energy Levels (Nat. Bur. Stand. Circ. no. 467, vol. 11). 5 Jerrgensen, Acta Chem. Scand., 1954,8, 1502. 6 Pappalardo, Phil. Mag., 1957, 2, 1397. 7 Schlafer, Z. physik. Chem., 1956, 6, 201. 8 Jsrgensen, Acta Chem. Scand., 1957,11, 53. 9 Asmussen and Soling, Acta Chem. Scand., 1957, 11, 1331. 10 Metzler and Myers, J. Amer. Chem. Soc., 1950, 72, 3776. 11 Friedman, J. Amer. Chem. Soc., 1952, 74, 5. 12 Jsrgensen, J. Inorg. Nuclear Chem., 1957, 4, 369. 13 Orgel, J. Chem. Physics, 1955, 23, 1004. 14 Van Vleck, J. Chem. Physics, 1935,3, 803. 15 Jsrgensen, Acta Chem. Scand., 1958, 12, 903. 14 Lowdin and Yoshizumi, Correlation Problem in hfany-Electron Quantzrm Mechanics 17 Framan, Calculation of Correlation Energies and Relativistic Corrections of some 18 Stern, Physic Rev., 1956, 104, 684. 19 Watson, Solid-state and Moiecular Theory Group (Massachusetts Institute of Tech- 20 Jlargensen, Energy Levels of Complexes and Gaseous Ions (Gjeilerups Forlag, Copen- 21 Jsrgensen, Kgl. Danske Vid. Selsk. Mat. fys, Medd., 1956, 30, no. 22. 22 Moffitt, Proc. Roy. Soc. A, 1951,210,224 and 245. 23Stevens, Pmc. Roy. Soc. A, 1953, 219, 542. 24 Tinkham, Proc. Roy. Soc. A, 1956,236,535 and 549. 25 Abragam, Physica, 1951, 17, 209. 26 Orgel, J. Chem. Physics, 1955,23, 1824, 1958. 27 Kroger, Physica, 1939,7, 369. 28 Wieringen, Faraday SOC. Discussions, 1955, 19, 118. Kvantkemiska Gruppen (Uppsala, 1957). He- and Ne-like Systems. Kvantkemiska Gruppen (Uppsala, 1958). nology, Quart. Progress Report, 15, January 1958). hagen, 1957).

ISSN:0366-9033    

DOI:10.1039/DF9582600110

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

ORBITAL MODIFICATION IN METAL COMPLEXES BY D. P. CRAIG AND E. A. MAGNUSSON Sir William Ramsay and Ralph Forster Laboratories, University College, Gower Street, W.C.l Received 2nd Jiily, 1958 The conditions under which atomic orbitals are contracted or expanded by ligands are discussed. Under the influence of the negative charges of a ligand field 3d orbitals in the first transition series are expanded, allowing the reduction in term spacings and Slater-Condon parameters in complexes to be partially, even if not wholly, explained without electron transfer into the 3d orbitals. The effect of ligands on outer d orbitals is less than in molecules such as SF6, but may lead to significant 4d covalent character in the metal-ligand bonds. Some consequences of outer d covalent character are discussed.1. INTRODUCTION Polarization of one atom by another in a molecule can often be simply treated by changing the effective nuclear charge of the orbital wave function of the polarized atom; that is, the atomic orbitals used in molecule formation are not taken to be exactly those of the free atoms but are modified by changing the mag- nitude of the charge that determines their radial distribution, as, for example, in a Slater orbital, according to some criterion such as that of minimizing the energy. Experience with simple molecules such as H2 and HeH+ has shown 1.2 that this is perhaps the most important single type of flexibility in 1.c.a.o. approximations, and one can expect it to have an application in complex molecules. Modification of this type will be most important where the atoms are manifestly easily polar- izable such as sulphur in its sp3d2 valence configuration, and should be a useful way of treating certain analogous cases in complex compounds of the transition metal ions.If one takes an electron in a weakly bound atomic orbital of atom A and another in a ligand orbital at By forms a molecular orbital and minimizes the energy with respect to the 1.c.a.o. coefficients and the exponent of the weakly bound orbital one finds, as was shown by Coulson and Duncanson 2 in the simplest such case of HeH+, that the electron drifts somewhat towards B and that the orbital at A is greatly contracted. In more complex systems, in which only rather simple calculations have been made, the effect of bonding on orbital size can be simulated to a certain approximation in an electrostatic model in which the ligand atoms are supposed to act (towards weakly bound orbitals) as point positive charges, the potential of which stands for not only the true classical potential but also a virtual potential to represent the effect of quantum-mechanical exchange.3 Then, in higher approximations, dipole and even higher order poles canbe introduced into the perturbing field.The results of such calculations on weakly bound orbitals may be illustrated graphically. Fig. 1 and 2 refer to the change in effective nuclear charge a for a 3d electron, such as in the 3s3p33d valence configuration of phosphorus, per- turbed by sets of charges (fig. l), and by point dipoles or distributed dipoles (fig.2) in an octahedral arrangement, obtained by methods previously explained.3 The results in fig. 1 and 2 are, over the entire range of parameters shown, obtained using only the spherically symmetrical component of the octahedral field, that is to say, the effect on highly Muse orbitals of the six charges or dipoles 116D . P . CRAIG A N D E. A . MAGNUSSON 117 spread evenly on the surface of a sphere of radius equal to the bond distance. It is easy to show that, so far as calculations of effective nuclear charge are con- cerned, this is a close approximation3 It becomes progressively less satisfactory I I I I m I 4 - - 3 - - a-Za 1 2 - I - 4 3 2 a -Za I 2 1 I I I 2 3 P FIG. 2.-Effective nuclear charge increment (a - 2,) as a function of the dipole moment of perturbing positive-inward dipoles in an octahedral array.In order downwards the curves refer to (a) 2, = 1, u = 3 ; (b) 2, = 1, u = 4 ; (c) 2, = 1.5, u = 4 ; for 3d orbitals in each case. The dipole moment is expressed in atomic units, the dipole length being fked at 1 atomic unit.118 ORBITAL MODIFICATION in at least two ways as conditions change. If the orbitals are already comparable in size to the bond radius the angular dependence of the field becomes more prominent, and if the field is of lower symmetry the spherical field approximation is less useful in that its breakdown with diminishing orbital size sets in earlier than for high symmetry. The relative significance of spherical and angular terms for octahedral sym- metry is illustrated in fig.3. One sees that as the initial size of the orbital defined by the nuclear charge 2, diminishes, the orbital contraction (related to the difference (a - 2,) between contracted and initial nuclear charges) steadily decreases while the relative importance of the angular terms goes up. In fact the contribution by the spherical term approaches zero, whereas the angular term passes through zero to negative values, corresponding to the fact that as the orbital becomes small -1 I 8 2 I a -2, 0 -I 0 I 2 3 4 5 2, FIG. 3.-Effective charge increment (a - 2,) for 3d orbitals for an octahedral array of positive charges, each 2/3 units of charge, at 4 atomic units radius. The full curve refers to calculations on dy orbitals including spherical and angular terms, leading to expansion of orbitals initially small as well as contraction of those initially large.The dashed curve refers to d orbitals under the effect of a spherical potential only, and shows only the contraction effect. compared with the bond length it tends to be expanded by positive charges. How- ever, before this stage is reached the model ceases to be realistic since the ligands are less well represented by positive charges when the perturbed orbital ceases to envelop them substantially. The effects of a change in the symmetry, as for example, between cis and trans X4Y2 octahedral fields, are rather small for loosely bound orbitals, provided that no change is made in bond distance or total charge on the perturbing centres. For more tightly bound electrons the difference between the effects of fields of different symmetries may be quite important, but this stage is not reached before contraction becomes relatively a small effect compared with the familiar ligand field repulsions, the effects of which are, of course, sensitive to symmetry.Some conditions under which orbital size will be altered may be summarized. (i) Loosely bound orbitals (a < 2) will be contracted by the positive field associated with the more electronegative ligands to an extent dependent on the strength of binding of the orbital in the valence state of the atom determined by the nuclear charge (ZJ, the magnitude of the positive field sources (&), and the distance a between the perturbed atom and the ligand.D . P. CRAIG AND E. A. MAGNUSSON 119 (ii) Strongly bound orbitals directed towards the field sources will be expanded by positive charges, the cross-over point between expansion and contraction being a - n2/0, where n is the principal quantum number.(iii) The effects of the less electronegative ligands, while dependent on the strength of binding of the orbital concerned and the bond distance, will depend also on the distribution of the bonding and non-bonding electrons of the ligand. A consequence of the contraction of a loosely bound orbital is the increase of promotion energy into it from a more tightly bound orbital.3 In the spherical approximation to the field of 6 octahedral charges 2, at a distance a an electron wholly within the sphere has its ionization potential increased by 6ZJu. The increase for an electron projecting outside the sphere is less than this because, roughly speaking, only a part of the electronic charge has to be withdrawn through the spherical surface.Consequently one can say that the spread of energies of the electronic levels will be increased : the inner orbitals become deeper by 6Zs/q and the outer ones are progressively less affected according to their increasing size in relation to the radius of the perturbing charges. If the perturbing field is pro- duced by positive-inward dipoles of finite length there is a qualitatively similar spreading of energies and increased promotion energies, but now the effect takes place from a different energy zero, since the ionization potential of an inner orbital is unchanged, and of a projecting orbital actually diminished relative to the free atom.Contrariwise a field produced by negative charges, or by negative inward dipoles of finite length, leads to a closing-up of energy intervals and a decreased promotion energy from a less to a more projecting orbital. In positive fields this effect imposes a limitation on the possibilities of promotion into outer d orbitals, and in negative fields it has some importance in connection with observed changes of term value spacings of inner d electrons in complexes.4~ 5.6 2. EFFECTS ON INNER 3d ELECTRONS The field imposed by electronegative ligand atoms on loosely bound outer d electrons is attractive and simulated in the electrostatic approximation by posi- tive charges. The field imposed on inner d electrons by the same ligands is re- pulsive, being produced mainly by electron repulsions between the d electrons and those of the ligands.In the electrostatic model the field sources are accord- ingly negative charges or negative-inward dipoles.6- 7 Their effects on orbital size are the opposite of positive charges, namely, an expansion traceable to the spherically symmetrical term in the potential, combined with either a contraction (for very tightly bound orbitals) or a further expansion by the angle-dependent term. The latter is, of course, responsible, together with covalent binding, for the characteristic splitting in ligand fields, and is generally speaking the dominating influence on 3dorbitals. In negative fields there are two other potentially important features. One is the change due to outer screening on term spacings, and the other the orbital expansion.Suppose one has two electrons in the configuration 3d2 in the field of a nucleus of charge 6, a value chosen to be near to those found in the transition metals. Then, the energies of 1G and 3F terms being set up in terms of Slater parameters and minimized with respect to the effective nuclear charge a, one finds values of a for the two terms differing by 0.15 charge units, namely, a(1G) = 5-55; 43F) = 5.70. For the two triplet terms 3P and 3F the difference is 0.05. Thus the usual assumption that the Slater effective nuclear charge is the same for terms of the same configuration probably only holds to a few tenths of a charge unit. We now take an octahedral field, with unit negative charges, either isolated or forming one end of dipoles of finite length.Then, since states in the crystal field arising from different terms have different a values there will be a differential outer screening caused by the field sources. The orbitals in the higher terms project more and the term values are less reduced, leading to a reduction in level spacings. The free ion levels will therefore crowd120 ORBITAL MODIFICATION into a smaller range, with bigger changes occurring in the higher terms. This is broadly the mechanism suggested by Schlafer,8 but calculation shows it to be a small effect; fields which produce Dq values of about the right size diminish term splittings by only 100 cm-1 or so. The second feature is the orbital expansion, which can be estimated making the same approximations as for contraction.3 Under conditions such as those found for inner d orbitals there is more expansion in a field of negative charges than there would be contraction if the charges were positive.The reason for this is that for positive charges a steadily increasing perturbation causes increasing contraction, but the increments diminish as the orbitals shrink. With negative charges an increasing perturbation causes expansion in increasing increments until the 3 d electron becomes unstable and is lost by ionization. Thus there is no symmetry in the change of orbital size with respect to sign of the perturbing charge. To get an idea of magnitudes one has to make an assumption about the sources of the negative field.In many cases with either ionic or neutral ligands the field must be largely that of the dipoles induced in the ligand by the charge on the central ion, which causes an inward charge drift. We have assumed a field of octahedrally arranged negative-inward dipoles of length 1 atomic unit and a charge of one electron, i.e. with a dipole moment of 1 atomic unit, or - 2.5 D. The distance between the dipole and the central ion can be treated as a parameter to be chosen to give the right order of Dq value. The table lists some representative results from these calculations, referring to one d electron in a central field of nuclear charge 2, plus the dipolar field with a mean radius (to the centres of the dipoles) of (T atomic units. EXPONENT CHANGES IN 3d ORBITALS 3.5 5.55 5-0 5-65 3-5 5.7 5.15 5.70 4.5 5.55 5.4 5-55 4 5 5.7 5.6 5.7 The Dq values calculated from the energy minima are 2500-3OOOcm-1 for cr = 3.5 and about 500 cm-1 for (T = 4.5.Experimental values are given by Orgel 9 for hydrates as about 1000 cm-1 for bivalent and 2000 cm-1 for trivalent ions, and higher values are found for some other ligands. Thus one can expect reductions of up to 10 % in a values of de orbitals on account of orbital expansion under conditions which are realized in actual examples. Moreover, if calculations of the outer screening effect on term value differences are now repeated using the expanded orbitals in relation to the inner shell of negative charges corresponding to dipoles at 3.5 a.u. a significant decrease is found, amounting to some 2000 cm-1 in a free ion interval of 20,000 cm-1.If this decrease is also expressed as a change in a value the total drop in apparent effective nuclear charge from electrostatic considerations alone can be as much as 20 %, which is already of the right order to fit observation, though larger decreases than this are sometimes found in practice. It appears that it is not necessary to rely on inner screening as the sole mechan- ism for reduction of term differences and lowered a values, caused by electron transfer from the ligands into the 3d shell. On the other hand, it is implied in the electrostatic model that transfer out of the 3d orbitals (to form r-bonds if suitable ligand orbitals are available) is facilitated on account of the expansion and the tendency of the electrons to move outside the charged shell; and this tendency increases with the strength of the perturbing field.Thus the model associates large Dq values with a strong tendency to w-bonding, as is often found.D. P. CRAIG AND E. A . MAGNUSSON 121 It should perhaps be emphasized that we are not suggesting a return to a purely electrostatic view of the bonds in complexes, Polarization of the ligands gives rise to an electron drift which can equally well be described as partial occupancy of the metal orbitals 4s, 4p, etc., leading to partial covalent character in the bonds. The extent to which 3d orbitals are populated from the ligands, however, cannot, on this view, be answered from a study of term value differences and altered Slater-Condon parameters, when they display such a strong dependence on the effects of outer screening.3. EFFECTS ON 4d ORBITALS With respect to outer d orbitals, ligands may display electron-attracting be- haviour, leading to contraction. Contraction is therefore of potential interest in connection with the use of 4d orbitals in bonds of partial covalent character involving metals of the first transition series. One can consider the situation when the metal ion regains enough charge from its ligands to become roughly neutral, according to the Pauling electro-neutrality principle. This charge can be supposed to populate fractionally the 4s, 4p, and perhaps the 4d orbitals, and the effective nuclear charges of these orbitals worked out from Slater’s rules for the neutral atoms.The values for Ni in the configuration (3d)8(4~)113(4p)1(4d)213 are Z(4s, 4p) = 4.3 ; Z(4d) = 0.7 ; this configuration is derived from Ni2+ by with- drawing 2 electrons from the octahedral ligands. For Ni4f we similarly obtain (3d)6(4~)213(49)2(44413 with Z(4s, 4p) = 5.5 ; Z(4d) = 1.2. Comparison of these values with those for octahedral sulphur: Z(3s, 3p) = 6-15; Z(3d) = 1-65 and trigonal bipyramidal phosphorus Z(3s, 3p) = 5.15; Z(3d) = 1 show a somewhat less favourable situation for the use of the d orbitals in bonds, especially when the wave function exponents Z/n are compared instead of the effective charges. However, if 4d covalency is important in any actual examples, then it will con- tribute an energy which at best is one of several terms determining the stereochem- istry and other properties.Normally it will be small, much smaller than the 3d ligand field term, but in special cases it might predominate. It is realistic to expect marked 4d covalency, and with it an octahedral configuration, only in the higher valency states of the metals to the right of the table and with the smaller and more electronegative ligands-the former because of the need for the highest initial 4d exponent and the latter because contraction effects are largest for closest approach of the perturbing centres. Octahedral structures might be expected to occur more frequently with neutral ligands, especially the more electronegative ones (e.g. H20) than with negative ions (e.g. C1-). &p hybridization is less likely to occur in configurations containing a few 3d electrons since this, by reducing the screening leads to a greater disparity between 4s, 4p and 4d exponents.These conditions can be related to the properties of the transition metal ions in their halide complexes. Spin-free behaviour is almost the rule with fluoride complexes of the trivalent ions of the first transition series metals and has often been associated with 4d covalency. It occurs with other ligands as well in higher valence states but less regularly in lower valence states. Even exceptions to this rule, such as the diamagnetic K2NiF6, and the spin-paired behaviour of the analogous complexes of the second and third transition series metals, do not necessarily mean that outer d orbitals are not used at all in these complexes. On the contrary, in many of the complexes we find conditions which should lead to substantial outer d participation in the metal-ligand bond.Some borderline cases occur among complexes of divalent ions where the octahedral configuration gives way to tetrahedral in the recently described 10 series of chloride complexes ; FeCl$-, CoClp, NiCl$-, CuC42- and ZnCl$, for all cases except possibly copper (II). Partial covalent 4s4p3 bonding is here retained in spite of 3 d ~ repulsions. In the fluoride complexes of the same ions the particular ability of the halogen to polarize 4d orbitals is even more important.1 22 ORBITAL MODIFICATION Although the metals will not form the anionic [MF6]4- complexes, a configuration in which the metal is surrounded octahedrally by fluoride ions occurs in the perovskite structure for the compounds, KMF3 (where M = Mn, Fe, Co, Ni and Zn), these compounds, with the exception of the diamagnetic KZnF3, ex- hibiting an antiferromagnetic reduction of the moment from the expected high- spin value.11 Such a disposition of negative ions, of course, increases their con- tracting ability because the greater amount of charge transfer from each ion increases its electronegativity. This situation probably occurs in many com- plexes in the solid state. The authors are glad to acknowledge many useful discussions on this subject with Dr. T. M. Dunn. 1 Rosen, Physic. Rm., 1931,38,2099. 2 Coulson and Duncanson, Proc. Roy. Soc. A , 1938, 165,90. 3 Craig and Magnusson, J. Chem. Soc., 1956,4895. 4 Owen, Proc. Roy. SOC. A, 1954,227, 183. 5 Brown, J. Chem. Physics, 1958, 28, 67. sJmgensen, Acta Chem. Scand., 1957, 11,53. 7 Ilse and Hartmann, Z. physik. Chem., 1951, 197, 239. 8 Schlger, 2. physik. Chem., 1955, 6, 201. 9 Orgel, J. Chem. Physics, 1955, 23, 1819. 10 Gill, Nyholm and Pauling, Nature, 1958, 182, 168. 11 Martin, Nyholm and Stephenson, Chem. and Ind., 1956, 83.

ISSN:0366-9033    

DOI:10.1039/DF9582600116

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

THE INFLUENCE OF n-BONDING IN SOME TRANSITION METAL COMPLEXES BY R. J. P. WILLIAMS Wadham College, Oxford Received 9th June, 1958 Current theories of the stability of complex ions of transition metal cations are de- scribed. It is shown that attempts to correlate stabilities and the ligand (crystal) field splitting factor, A (10 Dq), determined from spectra, cannot hold generally. The vari- ation in A from complex to complex is discussed noting both the dependence on ligand and on cation. The A values can be explained if a dependence on the acceptor and donor character of the d orbitals in both ground and excited states is assumed. We conclude that the stabilities of complex ions should be referred only to the properties of the ground states and not to A. The purpose of this paper is to enquire into the degree to which covalent bonding has an influence upon the stability of complex ions of transition metals.There have been three distinct phases in the history of this topic. The first, as put forward in the work of Van Arkel for example, described the stability of com- plex ions in terms of the polarization of the ligand by the cation (an electrostatic model); in the second place the stability was discussed in terms of the polariz- ation of the ligand and the electron affinity of the cation which implies a covalent model ; 1,2 in the third phase the crystal (ligand) field theory has been used to introduce the concept of the polarization of the cation d electrons by the ligands.3~ 4 Although all the authors who now discuss the stability of complex ions agree about the qualitative aspects of the description of the binding, i.e.that it contains polarization terms referring to ligand and cation and that there is a degree of covalent binding, within the realm of this qualitative agreement there is a wide variety of opinion about the relative importance of covalency. Grfith and Orge1,s for example, maintain that the variations of stability constants of com- plexes with atomic number, at least for the divalent cations, do not show a de- pendence on the electron affinity of the d states of the cations. They refer to the ions from Can to Znn in the first transition series. The way in which they reached this conclusion will be described later. Other authors maintain 6.7 that there is from 10-30 % overall transfer of an electron from the co-ordinating ligands to the d states in the divalent state and that this transfer affects stabilities.7 In lower valence states the transfer of electrons to d states is thought to be smaller whereas in high valence states it is larger.In the lower valency states, however, it has always been postulated that there is considerable d electron transfer from cations to ligands. At the present time there is still very little quantitative data about these electron transfers and so we considered it useful to describe our own empirical approach, which requires data on both the stabilities of complex ions and their absorption spectra. The problem is quite general to all compounds of the transition metal ions, i.e. to both complex ions and solid compounds, but we will only discuss complexes here.THE EXPERIMENTAL DATA The stability constants of a wide variety of ligand + cation complexes are known especially in the series of divalent cations from Mnn to Znn. The reactions take the form Mn(H20), + XL + MnLx(H20), + (n - m)H2O. 123124 INFLUENCE OF n-BONDING From the stability data only a free energy difference - AG can be found for this reaction. However, it is a reasonably plausible assumption that the entropy change in the reaction will be approximately constant for a series of very similarly sized ions such as those under consideration and that the values of - AG will therefore reflect the values of - AH. We will assume that in a series of such cations - AG values can be analyzed as if they depended upon - AH alone.Now - AG does not fall in an order of the cations which is independent of the number x of ligands taking part in the above reaction even for a given ligand, say ammonia. If x is from 1 to 4 for monodentate ligands, such as ammonia, or from 1 to 2 for bidentate ligands, such as ethylene diamine, NH2 . CH2 . CH2 . NH2, Mn Fe co Ni cu Zn FIG. 1.-Stabilities of ethylene-diamine complexes, 0 N = 2, and 0 N = 3. then the order is Cun > Nin > CoI1 > Fen > Mnn and Cun > Znn with re- markably few exceptions. If the equilibrium is taken for six monodentate ligands or three bidentate ligands the order is more uncertain but if we refer only to weak field complexes is usually Cun $ Nin > Con > FeII > Mnn, and Cun > Znn (fig.1). For the complexes ML4 the increments in stability between successive ions tends to increase along the series jumping rather sharply between nickel and cupric. For the complexes ML6 (amines) there is a steady rise to nickel but no further increment at cupric and but a small change from ML4 to ML6 for zinc. The stability rises below manganous, i.e. at chromous and is thought to fall to calcium possibly with exceptional values at vanadium (11). These stability orders have been given one of two extreme interpretations, which will now be described. (a) THE CRYSTAL (LIGAND) FIELD APPROACH The ligand field stabilization factor in an octahedral field13.4 is TABLE 1 no. of d electrons stabilization fact0.p .in umts of orbital splittmg 4 (10 Dq). 0, 5 or 10 0 1, 6 0.4 2, 7 0.8 3, 8 1.2 499 0 6R. J .P . WILLIAMS 125 It will be observed that this theory predlcts that the half empty d shell of manganous and the full d shell of zinc ions have no effect on the stability of manganous and zinc complexes. The effect of the d states for the other ions is given by the orbital splitting A times the stabilization factors S, see table 1. Now A can be found from spectroscopic measurements: it is an averaged term taken from the energy splitting between d,, and ri, electrons. The crystal field theory suggests that we might correlate the product A . S and the stabilization energy due to d electrons. The latter term has been calculated 3 . 4 by assuming that if the d electrons played no part in the series of complexes from Can to Znn there would be a continuous relationship between the heat of hydration (stability constant or lattice energy) and the atomic number which would run through the experimental value for manganous. The differences between the smooth values and the observed ones give the crystal field stabilizations.In many cases there is good agreement, with one or two notable exceptions (see below), between the thermodynamic and the spectroscopic data. Now if the values of A found from spectroscopic data had been independent of the cation the ligand field theory would have had very much to recommend it. Values of A are given in table 2. ligand v= Cr" Mn" Fe" Con Nil1 CU" TABLE CR CRYSTAL FIELD SPLIITING FACTORS (K units) 9 HZO oxide NH3 en enta 12,600 13,900 7,800 9,100? 6,800 10,400 10,400 9,700 9,700 9,700 10,500 11,000 10,200 8,500 8,500 10,800 11,600 10,100 12,600 12,600 15,100 16,400 13,600 In the table "en" is ethylene diamine and " enta" is the ethylene diamine tetra- acetate anion.Note the way in which the order of the A values changes as the ligand is changed from the oxygen to the nitrogen type. We note (i) the magnitude of A does not always follow the same order of cations. (ii) A is not necessarily in the order of diminishing size of the cations (it is largest for the largest cations amongst divalent hydrates) yet this is the order of the expected polarization of a given ligand. The assumed ligand field A is not related simply to the polarization of the ligands by point charges nor to the order of the electron affinity of s andp states of the cations.(iii) A can be calculated for the complexes of Mnn (Fern) and has very low values. However, the calculation of A is not identical with that used for other transition cations as we will explain below. (iv) A is very large indeed for Cun and Crn: so large on occasions that the total stabilization A . S is as great for Cun as for Nin despite the fact that there is but one hole in the cupric d states and two in the nickel states. These observations suggest that A is related to characteristics of the individual cation states. Even if we attempt to take into account under (iv) the influence of Jahn-Teller distortion for cupric and chromous complexes it is difficult to appreciate why the d stabilization has such a large influence, apparently doubling the effective field in extreme cases.A final peculiarity of the theory is its inability to describe the stabilities of oxalate and hydroxide complexes. The value of A for these complexes is equal to or slightly less than that found for the hydrates whence the ligand field stabil- ization calculated on an electrostatic model should have preferentially stabilized the hydrates or have had no effect, i.e. the effect of the ligand field should have126 INFLUENCE OF 7?'-BONDING been in the unusual order of stabilities NP < Con < FelI < Mnn. In fact the order of stabilities in the oxalates and hydroxides is the reverse of this, and there is little difference between the stability increments in these series and those found in other ligand series if we take series in which the bonding is through oxygen only (table 3).The value of A from spectra changes considerably amongst these ligands as some are saturated and some unsaturated (see later). We deduce that in the series of oxygen-type complexes there are stability increments moving in a similar manner to those found in series of transition metal complexes with other ligands which are not explicable on the simplest crystal field model. We will attempt to show how a consideration of covalency removes this anomaly. At the same time it leads to an explanation of the divergent values of A in different cation complexes with the same ligand. TABLE 3.-sTABm CONSTANTS log K1 OF SOME COMPLEXES IN WHICH CO-ORDINATION IS THROUGH OXYGEN ATOMS M n Fe c o Ni c u zn oxalate 3.89 - 4-70 5.30 6.16 489 salicyaldehyde 3-73 4.22 4.67 5.22 7.40 4-50 malonate 3.29 - 3.72 4.01 5.75 3.68 acetylacetonate 4.2 5-1 5.3 6.0 8.2 5-0 Data are from ref.(1) or from the recently published tables of stability constants hydroxide (3-5) 4.5 4.0-5.0 (5.0) 6-1 4.5 (Chemical Society, London). THE ELECI'RON AFFINITY OF CATIONS AND ITS EFFECT ON THE STABILITY OF COMPLEXES The salient points in the discussion of the stability of complexes (or lattice energies) from the covalent point of view are (i) that there is considerable electron transfer from the ligands to the cation and (ii) that this transfer is dependent upon the electron affinity of the cation, estimating this affinity from observed ionization potentials.* Few chemists would not agree that the higher stability of complexes of such ions as zinc, cadmium and mercuric as compared with cal- cium are due to the enhanced electron affinity of the cations of the B-subgroups.Disagreement is not found in the extension of this idea to the s and p states of the cations from calcium to zinc. Somewhat paradoxically it is only when we deal with d states that the idea, that the electron affinity of states plays a part in stabilizing complexes, is disputed. In what follows we will assume that the effect of differences in s and p states has been taken into account and we will interest ourselves only in the d states. The d states change in energy in the first transition series in a systematic manner no matter which valence state is considered (fig. 2). The graph has two features of interest.First, it gives maxima at the ions with 4 and 9 electrons, e.g. chromous and cupric. Secondly, it has a minimum at the d5 configuration, e.g. manganous. The stability of complex ions show similar features (fig. 1). The enhanced stability of the chromous complexes was predicted on this basis. If we consider the ground state of the complex as arising from the splitting of d states into d,, and de orbitals in which the latter are prefer- entially occupied we can consider the possible covalency arising from the d states. As the 4 states are not fully occupied they act as electron acceptors throughout the series of cations Mnn to CUE. It is not unreasonable to suppose that the strength of the acceptor properties of these d states will be proportional to the electron affinity of the d states of the cations concerned and that this strength will be the order in which the CT electrons of the ligands are stabilized by d states of the cation.The first excited state of the cations involves a transfer of an electron from the de to the d,, states. It is this transfer which is used to estimate A in the ligand field treatment of cations such as Fen, COn, Nin and Gun. Now * It would be better to take a mixture of states but nothing is known of the percentages which should be mixed.R. J . P. WILLIAMS 127 in the excited state the acceptor properties of the d,, orbitals will be reduced relative to the ground state, they are more occupied, but the d8 orbitals will now be able to act as electron acceptors.The effect of this difference in the acceptor orbital between the ground and excited states is readily appreciated. Consider the exchange of ligands from a molecule such as water to an anion such as hydroxide or oxalate. It is probable that both the a and n- donor strengths of the latter ligands are greater than those of water. Now in these circumstances the ground state of the oxalate complex relative to the hydrate will be stabilized in the order Znn < Cuu > Nin > Co" > Fen > MnlI < Crn through the d,, acceptor pro- perties. This should be reflected in the stability of the complex although its effect will be offset to some extent by the greater repulsion between ligand rr electrons and d8 electrons. On the other hand the excited states will be stabilized 3 0 1.P. volts electron 2 0 IC CO SC T i V Cr Mn Fe Co Ni Cu 2" FIG. 2.-Ionization e iergies of d electrons for valence state changes indicated. in the order of the &acceptor properties of the excited states of the cations and this will also be in the given sequence. Thus the splitting between d, and d,, states might not be the same in ground and excited states for in the ground state the dy electrons are moved in part into anti-bonding states in order to stabilize (T electrons of the ligand whereas in the excited state the d8 electrons are moved, in part, into anti-bonding orbitals in order to stabilize the v electrons of the ligand. On exchanging the ligands co-ordinated to a cation from water to oxalate or hydroxide there could well be an appreciable stabilization of the ground state and the excited state by different factors so that A is changed very little although the ground state stabilization is considerable.If this is the case it is dangerous to calculate the stability of complex ions from A. We have quoted the oxalate and the hydroxide ion but the argument is generally valid and we shall now use it in other cases. The calculation of the stability of complex ions from spectro- scopic data has been very successful for the ammines using a value of A almost independent of cation. (It must be understood that the calculation is not suc- cessful for oxalates.) The ground state in the ammines is stabilized relative to the hydrate by an increase in the u donor properties and a reduction in the 7~ donor properties of ammonia relative to water.The excited state, on the contrary, is perhaps less stabilized by the ammonia molecule than by the water molecule be- cause of the weakness of ammonia as a n-donor. Thus A is large in ammines128 INFLUENCE OF n-BONDING and correlated well with the high stability of ammines, whereas it was small in oxalates and correlated badly with their considerable stability. In cyanides we can expect that A will be very large so we predict that the spectroscopically cal- culated stability will over-estimate the ground state stabilization of cyanides. The prediction is made on the basis of the strong interaction between the d, donor properties of the ground states of cations which we will discuss below and the n-acceptor properties of cyanide.Accepting the idea that the electron acceptor and donor properties of cations play some part in the formation of complexes we have also an explanation for the very large Jahn-Teller stabilization assumed in cupric complexes in order to fit in with the general crystal field theory. It arises through the large (relative to the neighbouring cations) acceptor properties of the cupric and chromous ions in their ground states. The sharp maxima in fig. 1 and in table 2 at cupric are due to the contribution of dsp2 orbitals as well as to crystal field splitting. We must also explain the very low field strength observed in the complexes of the manganous salts. The field strength for the half-filled shell cations must be ascertained from transitions of electrons involving the pairing of spins.These transitions are not the same as those involving only a change of an electron from a ds to a 4 state for in manganous a completely unoccupied d orbital is created in the excited state. The excited state will be strongly stabilized therefore by its acceptor properties and the usual crystal field calculation using factors taken from table 2 will give rise to a low apparent field strength. It is not too exaggerated to say that the excited state is a strong field whereas the ground state is a weak field complex.* It should be noted that if, as we suggest here, covalency ought to be considered in the manganous ground state also then the stabilization by d-state interaction with the ligands will not be zero as given in table 1. There is a danger that the application of the data in table 1 will lead to the use of manganous and ferric ions as reference ground states with zero stabil- ization from d-orbitals.This in turn will lead to an underestimate of the d stabil- ization in complexes generally. We have introduced n-bonding terms in the excited state and have suggested that the n-acceptor properties of cations follows the order of the electron affinity of d states. The logical extension of the argument is to the consideration of the n-bonding in the ground states. We should find first that the ground states are more stabilized by ligand n-donor properties where there are cation n-acceptor properties, i.e. where there are holes in the d, electrons. We are led then to think of the increasing field, A, in table 2 in the order Nin < Con < Fen < Mnn < Vn in the hydrates on the basis of the assumption of an increasing importance of acceptor properties in the ground states of these cations as the number of d8 electrons is reduced.O i s argument can be extended to the solid state and then explains the greater stabilization of the first five elements relative to the cor- responding later five elements in the transition series in such compounds as oxides and halides.) The discussion leads to the general supposition that ions early in the transition series should be stabilized by n-donors, e.g. F-, OH-, oxalate, whereas ions later in the transition series should be more stabilized by ligands of weaker n-donor character as well as great a-donor character, e.g.NH3. This is an observation which is readily versed in any inorganic chemistry text. It appears to be in agreement with the order of values of A in ammines and phenanthrolines which is Nin > Con rather than the reverse. n-ACCEPTOR LIGANDS The general reasons for assuming that there is donation of dB electrons from a cation to a ligand are well established. No attempt has been made to state how this binding will vary from cation to cation. If we refer to fig. 2 we observe that *The values of A are likely to over-estimate the ground-state stabilization in the strong-field complexes relative to weak-field cases for similar reasons.R. J . P. WILLIAMS 129 the ionization energy from + 2 to + 3 states lies in the sequence Fe C Co < Ni < Cu < Zn < Mn.We expected the n--donor character of the divalent cations to follow the reverse of this sequence and we have sought confirmation of these trends by comparative studies of the stabilities of complex ions. We are referring to the weak-field case only as only in these cases have we the correct ionization potentials (but see footnote, p. 128). In a recent paper we have shown (see fig. 2 of that paper) that the Fen complexes are stabilized relative to zinc= complexes by strengthening the n-electron acceptor properties of ligands by substitution. The same type of figure (fig. 3) is given log KMn here for a comparison between manganous and ferrous complexes and it illus- trates the same point. The unsaturated ligands stabilize the ferrous ion pre- ferentially relative to the manganous ion.We bring this out in a different way in fig. 4 where we have plotted the stability of phenanthroline (I) and 8-hydroxy- quinoline 5-sulphonate (II) complexes against ethylene diamine (TII) and glycinate (IV) complexes respectively for all the cations with which we are concerned. The FIG. 3.-Aromatic ligands 0; aliphatic ligands 0. so5 I OH R CH2 NH2 (111) I NH2 E130 INFLUENCE OF %-BONDING Iigands are chosen so as to give the basic skeletons N-C-C-N and N-C-C-0' in the aliphatic (weak 7.r-effects) and aromatic (strong n-effects) systems. The resulting figure shows that the complexes of nickel, cobalt and ferrous ions are stabilized to a greater extent than zinc, manganous and magnesium ions by the aromatic ligands. The stabilization of ferrous cobaltous and nickel ions is ap- parently about equal in this figure.1% KeLl or log Kglyc. FIG. 4.-Phenaathroline and ethylenediamine 0, 8-hydroxyquinoline 5-sulphonic acid and glycine 0. However, from a plot of ferrous stabilities against nickel stabilities we find a general movement to relatively higher ferrous stabilities in aromatic as opposed to aliphatic complexes. We are making other comparative measurements in an attempt to establish the different 7~ contributions. So far we have been unable to find a divalent cation which is more affected by n-bonding than Fen. We note that Low 8 states that the importance of T effects increases in the series Feu > Con > Nin in the oxides although we have not been able to study his results. Elsewhere 10 we have commented upon the u- and T-bonding in the different valence states of cations. We have shown that in substituting ligands with T- electron donors we find 8 general stabilization of ferric complexes as against ferrous complexes, whereas substituents which are n-electron acceptors appear to stabilize ferrous complexes preferentially. We hope to be able to make some comments on cuprous/cupric couples at the meeting. 1 Irving and Williams, J. Chem. SOC., 1953, 3192. 2 Calvin and Melchior, J. Amer. Chem. SOC., 1948, 70, 3270. 3 Orgel, J. Chem. Soc., 1952, 4756. 4Bjerrum and co-workers, see, for example, Rec. trav. chim., 1956, 75, 658. Penney, Trans. Faraday SOC., 1940, 36, 627.) 5 Griffith and Orgel, Quart. Rev., 1957, 11, 381. 6 Owen, Furaday Sac. Discussions, 1955, 19, 127. 7 Williams, J. Chem. SOC., 1956, 8. 8 Low, Physic. Rev., 1958, 109,247 and 256. 9 Jsrgensen, Energy Levels of Complexes and Gaseous Ions (Gjellerups, Copenhagen, (Cf. 1957). 10 Tomkins and Williams, J. Chern. Soc., 1958, 2010.

ISSN:0366-9033    

DOI:10.1039/DF9582600123

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

THE TRANSMISSION OF ELECTRONIC EFFECTS THROUGH A HEAVY METAL ATOM BY J. CHATT,* L. A. DUNCANSON,* B. L. SHAW * AND L. M. VENANZI t Received 30th June, 1958 The transmission of electronic effects through a metal atom is being investigated by examining the effect of different ligands on certain hydrogenic vibrations in the infra-red spectra of some platinum, palladium and rhodium complexes. It is concluded that the effects transmitted by uncharged ligands are mainly inductive in origin. There are anom- alies which can be interpreted as due to mesomeric effects, and in some cases to the inter- action of the N-hydrogen atoms with the d-orbitals of the metal in primary and secondary amino-complexes and the amines. The effects transmitted from anionic ligands such as the halide ions are not fully understood and appear to be anomalous.The results are presented for discussion. During the previous five years there have been many investigations of the effects of the cornmoner ligands on the splitting of the energy levels in the d-shell of transition metal ions, but so far there have been very few of the transmission of electronic effects across a metal atom from one ligand atom to another. That important effects are transmitted is shown by the directing effects which operate during certain substitution reactions. Thus when ammonia replaces chloride ion from [PtCl@- to give a diammine only the cis-isomer is formed, but when chloride ion replaces ammonia the trans-isomer is the sole product : [ptCI#- + 2NH3 -+ ci~-[(NH3)2PtC12] + 2C1-, m(NH3)4]2+ + 2C1- 4 trans-[(NH3)2PtCl2] + 2m3.These directing effects, collectively named “ the trans-effect ” because of Chernyaev’s ideas on their mode of operation, are most marked in platinous complexes.1 Platinum (II), therefore, seemed a suitable atom for a study of the transmission of electronic effects from one ligand to another. It also has the great advantage that it forms stable complexes with more types of ligand atoms than any other metal. We are therefore making an extensive study of its com- plexes from this point of view. The investigation is not yet complete and this paper presents a summary of the data obtained to the present. The detailed results together with the pre- parations of the complexes are being published in a series of papers in J. Chern.Soc., as each phase of the work is completed.2p39 4 So far only planar 4-co-ordinated complexes have been investigated. These were all non-ionic and soluble in carbon tetrachloride or other organic solvents. They contained one molecule of either a primary or a secondary amine when N-H stretching frequencies were measured, or in some platinum complexes a Pt-H bond whose stretching frequency was measured. The investigation falls into two parts, first, the influence of ligands on the frequency of the above hydrogenic vibrations and, secondly, their influence on the relation between frequency and intensity. * Imperial Chemical Industries Limited, Akers Research Laboratories, The Frythe, t Inorganic Chemistry Laboratory, South Parks Road, Oxford. Welwyn, Herts. 131132 ELECTRONIC EFFECTS I N METAL COMPLEXES THE INFLUENCE OF AN UNCHARGED LIGAND ON AN AMINE IN hYZRiY-POSITION TO IT, IN ANALOGOUS PLATINOUS AND PALLADOUS CHLORIDE comLEms.-The infra-red spectra of a series of compounds of the type I were investigated in carbon tetrachloride solution to see how the N-hydrogenic stretching frequencies changed as the ligands L were changed.The most commonly used amines were ptoluidine, n-octylamine and piperidine although others were examined in L c1 preliminary experiments. Various ligands L were chosen but the most significant from the point of view of this investigation were the 12-alkyl derivatives of the phosphorus and sulphur triads. The length of the n-alkyl chain has no significant effect on the NHRR' N-hydrogenic stretching frequency and the quartenary nitrogen atom is not sensitive to mesomeric effects.For example, when L = PPr:, R = H and R' = p-substituted phenyl, there is only 1 cm-1 difference between VN-H in the complexes of p-nitro aniline and anisidine. The spectra show that the complexes of primary amines are appreciably associated \ / Pt / \ Q c1 ligands clrctro- I negativity+ 2.8 AsR, R,Te PR, SbRl 2.2 2.0-- 1.6 - - *a\ ::*::::- 1 I I I I I I I I 3210 20 3 0 40 SO 6 0 70 80 9 0 3300 10 20 3330 FIG. 1 .-Relation between the electronegativity of the ligand atom in L and W-H (cm-1) t of the complexes trans-[L, am MC121 in CC4 at 20". (M = Pt or Pd.) 0 and 0 = Piperidine complexes trans-[L, pip MClp]. and El = p-Toluidine complexes trans-[L, p-to1 MC121 x = n-Octylamine complexes trans-[L, 0ct.n NH2 PdC121.* Pritchard and Skinner's " best values " (Chem. Rew., 1955, 55, 767). t In the case of p-toluidine complexes the mean of N-H stretching frequencies is plotted. by intermolecular hydrogen bonding of the N-hydrogen atom to a chlorine atom, but for the purpose of this investigation only the bands due to monomer are impor- tant. The hydrogen bonding is discussed in ref. (34. Fig. 1 shows the results of the investigation. It will be seen that there is a linear relation between the electronegativities of the ligand atoms and VN-H. Only phosphorus is anomalous, and the anomaly is greater in the platinous than in the palladous complexes. It could be that the electronegativity of phosphorus has been wrongly assessed and should lie between that of arsenic and antimony as has been suggested by Allred and Basolo,S but this tively strong dative ?r-bonding from the metal to phos- would eliminate the anomaly only for palladium. We attribute the anomaly, at least with platinum, to rela- phorus 6 and shall return to this aspect of the problem when we consider the relation between the frequencies and intensities of the N-H stretching bands.R 2 y e Pt N--H / . L-l ';+ CI The interpretation of these results appears to be I1 Effect of increasingelectro- very simple. In the compounds trans-[l, amine PtC121, increasing the electronegativity of L causes it to with- hold its lone pair of electrons from the platinum atom in the L-Pt bond and so increase the attraction of the platinum atom for the electrons in the Pt-N bond as indicated in 11.Thus the nitrogen atom will become less negative and the proton less strongly bound, i.e. YN-H should decrease as is 0bservd.7 negativity of L on YN-H.J . CHATT, L. A . DUNCANSON, B. L. SHAW AND L. M. VENANZI 133 THE INFLUENCE OF UNCHARGED LIGANDS ON A Pt-H BOND IN cis-POSITION TO THEM IN COMPLEX PLATMOUS mRmm.-This investigation is in its initial stages. Here we are observing the effect of similar uncharged ligands on the Pt-H stretch- ing frequency in compounds of the type III, where L is the uncharged ligand and X a univalent anionic ligand. The configuration of 111 is not completely estab- lished but a preliminary X-ray investigation of (PEt&PtHBr indicates that it almost certainly has a trans-planar configuration as shown in IZI.8 Its dipole moment of 4.2 D is consistent with this.L X-Pt-H L 3. t L c k l ‘ I x-Pt - 4 ” L IV Effect of in- creasing electronega- tivIty of L on v p t - - ~ (111) It is not easy to predict how the movement of electrons in the Pt-H bond will affect its stretching frequency. If the hydrogen tends to be positively charged we should expect a movement towards the platinum atom to weaken the bond ; if it tends to be negatively charged such a movement should strengthen the bond. Since the hydrogen atom has taken the place of an anionic ligand and has a chemical shift of + 22 p.p.m. ( H 2 0 standard) it seems most probable that it is negatively charged. Thus we would expect the increasing electronegativity of the ligands L to cause increasing ~ p t - ~ according to scheme IV.The data in table 1 accord with this. Again a change of alkyl groups in the ligands L scarcely effects the pertinent hydrogenic stretching frequency, but their replacement by phenyl groups has a marked effect, as has the replacement of arsenic by phosphorus. Through- out, the introduction of more electronegative groups either on the platinum or the phosphorus atoms causes V ~ H to increase. TABLE STRETCHING FREQUENCIES (Cm-1) OF THE R-H BOND IN A SERIES OF COMPOUNDS ~~U~ZS-[L~F’~HX] IN HEXANE AT 20” x = c1 L AsEt3 PMe3* PEt3 PPr+ PPhEt2 PPhzEtt PPh3fS vPt-H 2174 2182 2183 2183 2199 2210 2224 X = I L AsEt3 PEt3 PPhEt2 PPh3t VPt-H 2139 21 56 2179 2190 * in carbon tetrachloride. t in benzene. 2 In our preliminary announcement 1 we reported an initial failure to obtain (PPh3)2PtHCI.By very slight modification of the method of preparation we are now able to obtain it. THE INFLUENCE OF AN ANIONIC LIGAND ON A R-H BOND IN fTGnS-POSITION TO IT IN COMPLEX PLATJNOUS HYDRIDES.-T~~S was observed by examining the compounds IJI in which L is triethylphosphine and X various univalent anionic ligands. The results are given in table 2 where the anionic ligands are listed in order of increasing tram-effect according to recent publications from Russian workers9 except that iodine has been retained between bromine and the nitro- group in accordance with Chernyaev’s original order.10I34 ELECTRONIC EFFECTS IN METAL COMPLEXES TABLE 2.-~"RETCHING FREQUENCIES (Cm-1) OF THE Pt-H BOND IN THE COMPOUNDS truns-[LzPtHX] IN HEXANE AT 20" X NO3 CI Br I NO2 SCN CN L = PEt3 2242 2183 2178 2156 2150 2112 2041 L = AsEt3 - 2174 2167 2139 - 2108 - It will be seen that this order is also the order of decreasing Pt-H frequency and therefore of decreasing Pt-H bond strength.It bears little relation to the order of increasing ligand field strengths, vjz., I < Br < C1< NO3 < NO;! < CN.11 FIG. 2.-Relation between the electronegativities of the halogens and vpt--~ (cm-1) of the complex hydrides truns-[L2PtHX] in hexane at 20". = trans-[(PEt3)pPtHX]. * Pritchard and Skinner's best values (Chern. Rev., 1955, 55, 767). 0 = trans- [(AsEt3)zPtHX] Jh this case the observations are consistent with the widely held view that the trans-effect of a ligand is associated with a weakening of the bond in tram-position to it.This must not be taken to imply that the weakening of the trans-bond is the sole cause of trans- directed substitution, although that was Chernyaev's originally proposed mechanism from which the effect was named. When we come to plot the electronegativities of the halo- gens against the Pt-H frequency (fig. 2) a linear plot is not Of in- obtained but the relative positions of the halogens are those expected from their relative electronegativities according to creasing electro- negativity of X on scheme V. The absence of linearity is evidence of mesomeric effects but the data are too few to allow one to disentangle vpE--H them from inductive effects, especially when they are considered together with the conflicting data of the next section.L e I _Q X- Pt - H I v? - L Effect THE INFLUENCE OF ANIONIC LIGANDS ON AN AMINE IN Cis-POSITION TO THEM IN SIMILAR COMPLEXES OF PLATINUM, PALLADIUM AND RHODIUM.--The COmPOUndS under this heading are of types (VI) and (VII) (X = halogen) and were examined in carbon tetrachloride solution.J. CHATT, L. A. DUNCANSON, B. L. SHAW AND L. M. VENANZI 135 The results are recorded in fig, 3. Again a very good linear relation between the electronegativities of the ligands X andvN-H is found, but this time the plot has a slope of the wrong sign for the effects of the halogens to be explained on the basis of electronegativity according to scheme Vm. It should also be noted ligands clectro'- negativity* ' I I I I I I I 1 - 3200 10 2 0 30 4 0 3250.. 3290 3300 10 2 0 3300 cm-' FIG.3.-Relation between the electronegatitives of the halogens and VN-H (cm-1) t of certain amino-complexes in CC4 at 20". + = [I : 5-cyclo-octadiene, piperidine RhX] 0 = trans-[(PPrg) piperidine PtX21 = trans-[(PPr;) piperidine PdX2] * Pritchard and Skinner's best values (Chem. Rev., 1955, 55, 767). t In the case of p-toluidine complexes the mean of N-H stretching frequencies is = trans-[(PPrg)p = toluidine PtX21 = trans-[(PPr;)p-toluidine PdXz] plotted. that the effect produced by the one halogen in VII is almost exactly half of that due to the two halogens in VJ. It is difficult to believe that these relations are purely coincidental but it appears to be so. The fact that VN-H varies against its prediction on the basis of electronega- tivity might be explained qualitatively by supposing that dative r-bonding from metal to halogen increases so rapidly along the series C1 < Br < I that the total electron drift from metal to halogen also increases in that order, i.e.against the normal trends of electronegativity. However, if this were the true explanation we would have expected to observe a similar effect in the relation of Vpt-H to electronegativity discussed above. It may be that the N-hydrogen atom interacts directly with the adjacent halogen atoms, but with the present data the effects of the halogen atoms on VN-H presents an enigma which can only be solved by collecting more data. However, any suggestions, or discussion of this point, will be welcome. IN COMPLEXES OF THE TYPE trans-b, piperidine PtCl2].-The simple interpretation (scheme 11) of the effects of the uncharged ligands upon YN-H in the compounds THE RELATION OF INTENSITY TO FREQUENCY OF THE N-H STRETCHING BANDS136 ELECTRONIC EFFECTS IN METAL COMPLEXES rranr-[L, piperidine PtC121 allows only one path for the electronic influence of the ligand L to reach the N-H bond.This is through the Pt-N a-bond, since the nitrogen atom is saturated and not influenced directly by mesomeric effects. Under these circumstances the frequency and intensity of the N-H bands cannot vary independently and we should find a smooth relation between them. In fact, we find a linear relation between the frequency and square root of the intensity * except when L is a tertiary phosphine and ethylene (fig. 4).These two ligands, especially the latter, are often anomalous and we have usually attributed the anomalies to their greater capacities to form dative T-bonds involving the d- electrons of the metal. There are two obvious interdependent ways in which the mesomeric effect resulting from the formation of the n-bond might affect the N-H vibration. 3215 I I 3.5 4.0 4.5 FIG. 4.-Plot of W-H (cm-1) against the square root of the band intensity of the complexes, trans-[L, pip PtC121. ledintensity (&I+ %) cm2 molecules sec-1. ampy = 4 : n-amylpyridine pip = piperidine. (a) The electron drift from the d-orbitals of the metal to the ligand L would in- crease the electron affnity of the metal and so by electron withdrawal in the Pt-N o-bond decrease VN-H. (b) The receipt of electrons into the m-type orbitals of L by decreasing the electron affinity of L would allow greater release of electrons to the metal in the L-Pt a-bond and this in turn a release of electrons in the Pt-N o-bond so raising VN-H.Doubtless both of these effects occur, and if they were the only effects of double bonding (b) must outweigh (a), since the net effect is to raise VN-H above the value expected on the basis of electronegativity alone (fig. 1). However, the above effects cannot explain anomalies in the VN-H against intensity relation, because the net result of these effects can be transmitted only through the Pt-N o-bond. In this way it would be quite impossible to produce N-H bands of the same frequency and Werent intensities, but this is what we find in the spectra of truns-[Et2Te, piperidine PtCI2I and ~~wzs-[C~H~, piperidine PtC121.We need at least two modes of transmission from the platinum to the N-H bond to account for this observation. * Over the small range of frequencies and intensities covered by our measurements there is an equally good linear relationship between frequency and intensity, but the square root of the intensity was chosen as being the more fundamental property of the bond, being proportioned to the rate of change of dipole moment during vibration.J . CHATT, L. A . DUNCANSON, B . L. SHAW AND L. M. VENANZI 137 We think it very probable that the second mode of transmission is a direct interaction of the N-hydragen atom with the filled d- (or dp-hybrid) orbital of the metal. In this way the mesomeric effect could be transmitted directly from L to the hydrogen atom.This interaction which is a type of intramolecular hydrogen bond might also be looked upon as orbital following of the N U stretching vibration or screening of the proton by electrons in a d- (or dp-hybrid) orbital of the metal. This explanation fits the facts since double bonding by L would involve mesomeric withdrawal of electrons from the d-orbitals so reducing the screening of the proton and raising the intensity of the N-H band, i.e. double bonding by L should shift the points corresponding to L in the frequency against (intensity)) plot (fig. 4) to the side of higher intensity as is observed. The possibility that the second mode of transmission from the metal atom to the hydrogen atom is through the adjacent halogen atoms cannot be ruled out.Then the anomalies in the frequency against (intensity)’ curve should depend upon the halogen atoms in the complex, and we have not yet investigated this possibility. This is a report of work in progress. It shows that inductive and mesomeric electronic effects are strongly transmitted by metal atoms, even when they are co-ordinatively saturated, but many more data are needed before the mechanism of transmission is completely understood. The halogens attached to the metal appear to behave anomalously, especially in their effect on the N-H vibration of an amine in cis-position to them, but as yet the data are too few to allow of anything but speculation as to the cause of the anomaly. It must be recalled that in benzene substitution reactions the halogens appeared to be anomalous because of their capacity to withdraw electrons inductively in the o-bond and release them mesomerically to the benzene nucleus in the wbond. In complex compounds the effect of the halogens may be even more complicated. In addition to the above- mentioned possibilities of inductive withdrawal and mesomeric release of electrons into d-orbitals of the metal, chlorine, bromine and iodine have also the possibility of effecting a mesomeric withdrawal of electrons from the d-orbitals of the metal into their own d-orbitals depending upon the electron affinity and electron occupancy of the d- (and p-) orbitals of the metal.This means that an extensive series of measurements involving similar com- plexes of different metals and of the same metal in different valeiicy states is necessary before interpretation can be put on a sound basis. This will take a considerable time, and it seems worth while therefore to present the data we have now collected, since it may be of use to others who are making a different type of approach to this problem, e.g. by studying the kinetics of inorganic substitution reactions. 1 For recent review of the trans effects, see Basolo and Pearson, Mechanisms of In- 2 Chatt and Venanzi, (a) J. Chem. SOC., 1955, 3858 ; (b) 1957, 2445 ; (c) 1957, 4735. 3 Chatt, Duncanson and Venanzi, (a) J. Chem. SOC., 1955, 4456; (b) 1955, 4461 ; (c) 1956, 2712. 4 Chatt, Duncanson and Shaw, (a) Proc. Chem. Soc., 1957, 343 ; (b) Chem. and Ind., in press. 5 Allred and Basolo, private communication ; see also Allred and Rochow, J. Inorg. Nucl. Chem., 1958, 5, 264, 269. 6 Chatt, Nature, 1950, 165, 637. Craig, et al., J. Chem. SOC., 1954, 332. Jaffk, J. Physic. Chem., 1954, 58, 185. 7 cf. Richards, Trans. Faraday Soc., 1948, 44, 40. Flett, Trans. Faraday SOC., 1948, 44, 767. Fuson, et al., J. Chem. Physics, 1952, 20, 145. Linnett, Trans. Faraday Soc., 1945, 41, 223. Longuet-Higgins, Trans. Faraday Soc., 1945, 41, 233. organic Reactions (John Wiley & Sons, Inc., New York, 1958), p. 172. 8 Owston and Partridge, private communication. 9 Hel’man, Akad. Nauk, U.S.S.R., Bull. Plat. Sect., 1954, 28, 88. 10 Chernyaev, Ann. Znst. Platine, U.S.S.R., 1927, 5, 118. 11 see Griffith and Orgel, Quart. Rev., 1957, 11, 381.

ISSN:0366-9033    

DOI:10.1039/DF9582600131

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

FERROELECTRICITY AND THE STRUCTURE OF TRANSITION-METAL OXIDES BY L. E. ORGEL Dept of Theoretical Chemistry, University Chemical Laboratory, Pembroke Street, Cambridge Received 24th June, 1958 A study of the structural chemistry of the higher oxides of the A sub-group elements suggests that there is no sharp transition from octahedral to tetrahedral stereochemistry but rather a slowly developing instability of the octahedral structures as the metal ion becomes " smaller ". This leads successively to loosening of the metal ion at the centre of the octahedron, off-centre displacement characteristic of ferroelectrics and many other oxides, extensive displacement of oxide ions giving fivefold co-ordination, and finally to tetrahedral co-ordination. " Size " in this context is not to be identified with ionic radius, although it is closely related to it. It decreases roughly in the order Hf4+, W+, Ti4+, Nb5+, Ta5+, W6+, Mo6+, V5+, Cr6+, Mn7+ for ions exhibiting their group valency.~~~ 1. INTRODUCTION It is generally recognized that octahedral co-ordination of a metal ion by anions is only possible if the ratio of the radius of the metal ion to that of the anion is sufficiently large. If the metal ion is too small tetrahedrally co-ordinated structures are usually formed. The radius ratio rules which have been used extensively in discussions of oxide stereochemistry are an attempt, based on a very crude model, to make this generalization quantitative.1 In this paper we examine more carefully the stereochemistry of the oxides of metals, the ionic radii of which lie in the critical range corresponding to the change from octahedral to tetrahedral co-ordination.We shall try to show that the occurrence of ferroelectric distortions, particularly in oxides with a perovskite structure, is not an isolated phenomenon but fits naturally into a general scheme of stereochemistry which rationalizes much of the X-ray data on the oxides of the A sub-group metals. 2. THE STABILITY OF REGULAR OCTAHEDRALLY CO-ORDINATED STRUCTURES Let us consider a stable structure involving regular octahedrally co-ordinated metal ions and inquire into the consequences of reducing continuously the radius of the metal ion. The instability which must arise sooner or later can be of two rather different kinds. There may be a second, completely unrelated, structure involving tetrahedral (or other) co-ordination which becomes stable relative to the original structure before the latter becomes unstable to small distortions.On the other hand, instability to small distortions may develop first so that for certain values of the ionic size the stable structure involves neither regular octahedral nor tetrahedral co-ordination, but rather distorted octahedral co-ordination. There is then the further possibility that such a structure can go over through more and more extensive distortion into a tetrahedrally co-ordinated structure. These possibilities are illustrated diagrammatically in fig. 1. The structures of the oxides of divalent transition-metal ions are consistent with the first simple picture.In the absence of Jahn-Teller distortions 2 an environ- ment cjf the metal ion which is either regular octahedral or tetrahedral occurs. The structures of the higher oxides of the A sub-group metals, however, are more consistent with the second picture. The Ti4+, Z1.4+, Hf4+, Nb5+, Ta5+ ions are 138L. E. ORGEL 139 usually six-co-ordinated, while the V5+, Cr6+, Mn7+ and Re7+ ions usually OCCUT in tetrahedral environments. The smallest ions of the first class, the Ti4+ and Nb5+ ions, and the largest of the second, the V5+ ion, commonly OCCUT in dis- torted or intermediate environments. The Mo6+, W6f and perhaps AP+ ions, which form both octahedrally and tetrahedrally co-ordinated oxides, are also among the ions which occur in distorted structures. Many of the oxides in which we are interested cannot reasonably be treated as ionic solids, so we must make our criterion of critical size more precise without introducing any assumptions about the nature of the bonding.We shall then be in a position to rationalize the structural data on the basis of purely stereo- chemical arguments. E R Q R b R C FIG. 1 .-Potential energy diagrams showing possible types of transition from octahedral to tetrahedral co-ordination - = stable; - - - - - = unstable. (a) Transformation from stable octahedral to stable tetrahedral co-ordination ; (6) development of unstable octahedral co-ordination before transition to stable tetrahedral configuration ; (c) un- stable octahedral co-ordination changing continuously to tetrahedral co-ordination.If we suppose the Born-Oppenheimer separation to be valid the potential energy determining the motion of a central ion M within a fixed regular octahedron of negative oxide ions may be expressed as a power series in the Cartesian co- ordinates of the displacement from the centre of the octahedron in the form V = A r 2 f B r 4 + C x 4 + y 4 + 2 4 - - r 4 + . . . . ( 5 3 , If 2L, the distance between the opposed oxide ions, is sufficiently large then only the Coulomb forces between the different ions need be considered and the sym- metrical configuration is one of maximum potential energy, that is A > 0. On the other hand, if 2L is very small any reasonable potential makes the symmetrical configuration stable and A < 0. Somewhere between these two extremes there must be a value LO of L for which A = 0.We call LO the maximum contact distance between M and 0. It does not correspond to the sum of the ionic radii of M and 0 but may be used to define the point at which " rattling " of the positive ion within the octahedron of negative ions begins.* Jn discussions of stability to distortion we are concerned with the extent to which the distance 2L in the crystal differs from the critical distance 2Lo rather than with the ratio of the radii of the M and 0 ions. The atahedral environment of oxide ions postulated in our model should not be thought of as a set of six isolated oxide ions, but rather as a part of an * We have discussed elsewhere the importance in stereochemistry of low lying excited states of such symmetry (Tlu in octahedral oxide structures) that they can be mixed with the ground state by vibrations.LO in the present case must be sensitive to the position of the 7'1~ charge-transfer states obtained by transferring an electron from the T orbitals on the oxide ions to the d orbitals of the metal. The details of this dependence are closely related to the problem of charge-distributions and bonding, particularly double-bonding, in oxides and the changes of bond properties occurring at ferroelectric transitions.140 FERROELECTRICITY OF METAL OXIDES extended structure containing a vacancy of regular octahedral symmetry. It is part of the argument that in a series of closely related structures LO must be almost constant, while when the further environment of the oxide octahedron is changed radically, for example on going from titanates such as BaTi03 to the oxide Ti02, LO may change rather more, but still not very extensively.3. STRUCTURAL EVIDENCE In ferroelectric and antiferroelectric oxides the characteristic type of distortion is one in which the octahedron of 0 2 - ions around an A sub-group ion remains almost regular but the metal ion moves away from its centre, sometimes by as much as 15 A.3 The three most common types of distortion from regular octa- hedral co-ordination involve motion of the central ion towards a vertex, an edge, and a face of the octahedron respectively. This is illustrated in fig. 2. (In this discussion we do not consider compounds containing the Pb2+ ion, since these often have atypical structures.3) b C a FIG.2.-Distortions from octahedral co-ordination which preserve (a) a fourfold axis; (b) a twofold axis; (c) a threefold axis. We now present structural evidence suggesting that distortions of individual octahedra similar to, and sometimes more extensive than, those occurring in ferro- electrics occur also in many A sub-group oxides. Titanium dioxide crystallizes in a number of different structures, of which the rutile structure has been studied most carefully. The six T i 4 bonds are almost identical in length and there is no phase transition above 50"K.l The structure of V02 is closely related to that of Ti02, and can be described as a distorted rutile structure in which the vanadium ion has moved away from the centre of the oxide octahedron surrounding it along a three-fold axis.4 The resulting configuration corresponds to that said to occur in the low-temperature forms of BaTi03 and KNbO3.3 The lengths of the long and short bonds in V02 are 2.03,201,2.05 ; and 1.86, 1.87, 1.76 A, respectively.At 68"C, V02 undergoes a transition from one antiferromagnetic phase to another, but nothing is known about the crystal structure above the phase transition.5 MoO2, W02, Tc02 and Re026 have structures closely related to that of V02, but the dioxide of the larger Ta4+ ion has the undistorted rutile structure.7 It is perhaps worth mentioning that a distortion something like that in tetragonal BaTi03 occurs in hydrated vanadium dioxide, V2O4, 2H20,g in which there is one V-0 bond much shorter than any other. These facts suggest that Ti4+ in the rutile structure has L w LO, but that V4+ has L > LO and so gives rise to structures containing V4+ ions displaced from the centre of their octahedral environments.It seems quite reasonable that V4+ should give distorted structures more readily than Ti4+ since almost any theory of electronic structure leads to the conclusion that V4+ is " smaller " than Ti4+. It would be interesting to know whether the phase transition at 68°C in V02 is accompanied by a structural change similar to one of those found in BaTi03. There is one complicating factor which must be considered in connection with the structure of V02, MoOz, W02, TcOz and Re02, namely, that they carry respectively, one, two and three, presumably unpaired, d electrons. Now theL. E.ORGEL 141 principal active vibration producing the distortions is of TI, symmetry, and so the distortions cannot be of the Jahn-Teller type. Furthermore, the degeneracy of the d electron configurations does not seem to be involved since the distortions are similar in Tc02 and Re02 which have non-degenerate 4A2, ground states, in Moo2 and WO2 with 3T1, ground states, and in V02 with a 2T2, ground state. Nonetheless, some sort of bonding interaction between metal ions, involving the use of the d electrons, cannot be excluded? In order to contrast the crystal chemistry of Ti4+ with that of somewhat smaller metal ions without introducing the complication of an incomplete d electron shell one is obliged to go to V5+ and Cr6+. This has the disadvantage that the change is rather great, but the compensating advantage that comparison with Nb5+, Ta5+, Mo6+ and W6+ becomes possible.The structure of V2O5 as determined by Bystrom et al.,lo is illustrated in fig. 3. The co- ordination about the V5+ is so strongly distorted from regular octahedral that the compound is usually regarded as fivefold co-ordinated. None- theless the sixth oxide group can be recognized at the very great distance of 2-83 A from the V5+ ion. In CrO3 the distortion has proceeded even further.11 The structure is that of a chain of tetrahedra linked together by pairs of corners. The arrangement of chains is such that the nearest oxide neighbours of a Cr6+ ion in neighbouring chains are two in number and complete a very distorted octahedron. CrO3 can be regarded as having a very strongly distorted Re03 structure.Moo3 on the other hand has 0 0 FIG. 3.-The environment of the V5+ ion in V2O5. an octahedral structure which, although much distorted towards a square pyramid, is more nearly regular than Cr03.12 The relation of the structure of KVO3 13 to KNb03 and KTa03 3 is very similar to that of CrO3 to WO3. While the compounds of the heavier elements are ferroelectrics based on the perovskite structure the vanadate is a tetrahedrally co-ordinated structure containing infinite chains like those in CrO3. A group of compounds of quite a different kind which may be relevant in the present context are the tungstates ca3wo6, sr3wo6, Ba3W06 and a number of related molybdates.14 These compounds are often cubic at high temperatures but undergo phase transitions to tetragonal or other distorted forms above room temperature. No detailed structure analysis has been carried out, but analogy with Na3AIF6 which has a very similar X-ray diagram and in which the Al-F bond lengths are unequal15 suggests that the W-0 bonds do not have equal lengths.The possibility that the AlF63- ion is itself distorted through " rattling " is suggested by the fact that Na3FeF6, which contains the somewhat larger Fe3+ ion, has a regular cubic structure. A further large group of compounds with off- centre displacements of Mo6+ and W6+ ions has been described by Magneli,l6 and the observed variations of co-ordination with metal valency agree well with our theory. We believe that these selected examples and many others which we cannot discuss here indicate that the ferroelectric and antiferroelectric distortions in perovskites containing Ti4+, Nb5+, Ta5+ and W6+ are of the same kind as those which occur in other oxides where the metal ion is close to the critical size for transition from octahedral to tetrahedral co-ordination.A comparison of the crystal structures of a large number of oxides suggests that instability to distortion increases, that is " size " decreases along the series of ions Hf4+, Zr4+, Ti4+, Ta5+, Mb5+, W6+, No6+, V5+, Cr6+, Mn7f.142 FERROELECTRICITY OF METAL OXIDES 4. APPLICATION TO FERROELECTRICS We have seen that the environment of the metal ion in a variety of oxides may be derived from regular octahedral co-ordination by an off-centre displacement of the central ion, often with only minor changes in the positions of the other ions.This is just the class of distortion to be anticipated if the type of instability which we have discussed is important. We must now consider the special charac- teristics of ferroelectrics and see, among other things, if we can account for their distribution among the oxides of the A subgroup metals. Two features distinguish ferroelectrics from the other substances which we have considered. First, their structures are such as to allow the correlation of the distortions of neighbouring octahedra to give a resultant dipole to the crystal. More important from our point of view is the requirement that the barrier opposing reversal of the directions of the distortions must be sufficiently small to allow the direction of polarization of the crystal to be changed by an applied electric field. The second of these conditions shows that only ions which have size close to that at which instability sets in can give rise to ferroelectric structures. Larger ions are too stable in regular octahedral environments; smaller ions form struc- tures which are so strongly distorted that no phase transition occurs below the melting point and, if the structure is polar, the field required to reverse the polar- ization cannot be attained.For this reason oxide ferroelectrics are largely re- stricted to compounds containing the group of ions of intermediate size, Ti4+, Nb5+, Tasf, W6+. Investigations of the oxides of ions with unpaired d electrons should reveal further ferroelectric and antiferroelectric structures, for example, among the oxides of V4+, M05+, etc., and perhaps AP+.We must emphasize that the idea of a critical ionic radius at which “ rattling ” of positive ions within their oxide environments begins is the basis of Mason’s and Matthias’ theory of ferroelectricity.17 Here we have tried to place this hy- pothesis in its proper context of structural chemistry rather than to justify it on theoretical grounds. We turn next to the nature of the co-operative interaction which leads to the correlation of distortions in neighbouring octahedra. The single outstanding fact about distortions in perovskites, WO3, and the other compounds of related structure is that if in the undistorted structure an oxide ion is attached collinearly to two metal ions then if in the distorted structure one metal-oxygen bond shortens the other lengthens.3 On the other hand if one metal ion moves at right angles to the M-0 bond direction the other may move in a parallel or antiparallel direction depending on the finer details of the structure.This suggests that the direct interaction between pairs of M-0 bonds which have an oxide ion in common leads to a strong one-dimensional ordering, but that the ferroelectric and antiferroelectiic phase transitions are made possible by much weaker and more variable interactions perpendicular to the direction of strong interaction. It is therefore quite reasonable to postulate a strong, perhaps partly covalent interaction in one direction, and a weaker, less specific interaction in the two perpendicular directions. If we do suppose that the major interaction within chains is between nearest neighbour M-0 bonds it is natural to write the potential energy for such a chain in the form V = 1A.f +.. . + K Z I Z l z j f . . ., i I where zi is the z displacement of the i’th atom in the chain and the double s u m is taken only over nearest neighbours. The condition for a ferroelectric distortion of the type which occurs in BaTi03 is then that A + K > 0. This shows that theories which postulate octahedra with six-fold potential minima, etc., are notL. E. ORGEL 143 necessarily sharply to be distinguished from those which attribute the distortions entirely to co-operative effects. A strong co-operative interaction could overcome a slight intrinsic stability against distortion of individual octahedra and so lead to a ferroelectric or other transition. While this may be the case in some ferro- electrics it is unlikely to apply in the more strongly distorted structures.Finally, we must emphasize that although we have dealt with the interactions between distortions of neighbouring octahedra the long-range interactions which are included in the Lorentz field may have sisnificance in certain structures.18 These have been discussed extensively in the literature but, as we shall see, calculations based on purely ionic models are not to be taken very seriously. The M-0 bonds in perovskites are similar to those in discrete molecular ons; thus octahedrally co-ordinated W03 is to be compared with tetrahedral MnO4-.Ions such as these have been discussed at length in the chemical liter- ature.19 The one conclusion that is generally accepted is that an ionic picture becomes less and less adequate and double bonding more and more important as the cation charge increases. Even for trivalent transition-metal oxides the deviation from simple ionic behaviour is quite large, so that for most of the ferro- electric perovskites the bonding must be extensively homopolar in character. This throws some doubt on theories of ferroelectricity which postulate the presence of large formal charges on metal atoms in substances like WO3. The two topics which have been controvefsial in the theories of bonding in the perovskites are the nature of the changes at the phase transitions and the origin of the ca-operative interaction.In order for a perovskite to be ferroelectric the MO6 octahedra must either be unstable in the symmetrical configuration or have only a very shallow potential minimum. Thus it is an ordering of long and short bonds, in the restricted sense already defined, or a fixing of bonds which previously had very large vibrational amplitudes which occurs at the phase transition rather than a change in the type of bonding. In more strongly distorted compounds the short bonds acquire an extra double-bond character, and it is probably this that distinguishes the oxides of the higher valency ions of the A subgroup elements from those of the lower valency transition-metal ions, and allows the former more readily to form structures with co-ordination intermediate between regular tetrahedral and octahedral co-ordina- tion.The solution chemistry of V4+ and V5+ in particular is largely determined by this tendency to double-bond formation and provides a close analogy with the crystal chemistry. The interaction between neighbouring octahedra in perovskites is not wider- stood fully. It must be partly electrostatic in nature, although the close metal- metal contacts in distorted rutile structures throws some doubt on the adequacy of the electrostatic theory as a general theory of ferroelectric and related dis- toitions. One feature of structural chemistry which is directly relevant is the fact that M-0 bonds are shorter if there is no second attachment to the oxide ion, thus in CrOl 0 00 00 00 0 \/ \/ v v Cr Cr Cr Cr /\ /\ /\ A 0 0 0 0 0 the Cr-0 bonds in the chain are longer than the isolated ones.The simplest hypothesis is that the ability of an oxide ion to form covalent bonds, particularly double bonds, is limited in the sense that if one M-0 bond has a strong covalent character the remaining bonds formed by that oxide ion tend to be weaker. This conclusion is a consequence of almost any electronic theory of covalent bonding, for example, of the molecular orbital theory, and is supported by much experi- mental evidence.144 FERROELECTRICITY OF METAL OXIDES 5. APPLICATIONS TO CHEMISTRY (i) SOLUTION CHEMISTRY The stability of the vanadyl ion V02f is not easily explained by the usual electronic theories of transition-metal chemistry.There is much evidence sug- gesting that in vanadyl compounds there is one short V-0 bond. Four other ligands are attached by moderately strong bonds and together with the 0 2 - com- plete a square pyramid about the V5+ ion. Often there is a sixth weak bond to a further ligand which completes a strongly distorted octahedron.20 In the light of our discussion of solid oxide structures, it is natural to suggest that the formation of the vanadyl ion in solution marks the transition from octahedrally to tetra- hedrally co-ordinated cations. The solution chemistry of the oxides of V5+ 21 and Ta5+ 22 is unusually com- plex, but little is known about the structures of the polymeric ions which are in- volved. We anticipate that much of the complexity will be found to be due to the existence of irregular co-ordination about the metal ions.(ii) CATALYSIS The importance of oxidation-reduction potentials in determining the efficiency of different solid oxides as oxidation catalysts has tended to obscure other im- portant factors. Here we emphasize the relevance of variable co-ordination number. If oxygen atoms are to be removed from the surface of an oxide catalyst in a process requiring only a low activation energy the metal ion must be stable in two environments of Merent co-ordination number. We believe that the importance of V205 as an oxidation catalyst besides being dependent on the variable valency of vanadium, is connected with the size of V5+ ion which allows it to adopt both tetrahedral and five-fold (distorted octahedral) co-ordination. It is hoped to develop the more chemical consequences of this hypothesis in greater detail elsewhere. The author is grateful to Prof. J. D. Dunitz for interesting discussion and to Dr. H. Megaw for a most helpful correspondence. 1 Wells, Structural Inorganic Chemistry, 2nd ed. (Oxford University Press, 1950). 2 Dunitz and Orgel, J. Physics. Chem. Solids, 1957, 3, 20, 3a Megaw, Ferroelectricity in Crystals (London, 1957). 3b Orgel, to be submitted for publication. 4 Anderson, Acta Chem. Scand., 1956,10, 623. 5 Klemm and Hoschek, 2. anorg. Chem., 1936,226, 359. 6 Magneli and Anderson, Acta Chem. Scand., 1955,9, 1328. 7 Sconberg, Acta Chem. Scand., 1954, 8,240. 8 Evans and Moore, Acta Crystal., 1958, 11, 56. 9 Morinder and Magneli, Acta Chem. Scand., 1957, 11,2635. 10 Bystrom, Wilhelmi and Bratzen, Actu Chem. Scand., 1950, 4, 11 19. 11 Bystrom and Wilhelmi, Acta Chem. Scand., 1950, 4, 1131. 12 Anderson and Magneli, Acta Chem. Scand., 1950, 4, 793. 13 Sorum, Kgl. Norske Vid. Selsk. Fork., 1943, 15, 39. 14 Steward and Rooksby, Acta Cryst., 1951, 4, 503. 15 Naray-Szabo and Sasvari, 2. Krist., 1938, 99, 27. 16 Magneli, J. Inorg. Nucl. Chem., 1956, 2, 330. 17 See particularly, Phase Transformations in Solids, ed. Smoluchowski, Mayer and 18 Kanzig, Solid State Physics, vol. 4 (New York, 1957). 19 Pauling, The Nature of the Chemical Bond, 2nd ed. (Oxford University Press, 1940). 20 Sidgwick, The Chemical Elements and their Compounds (Oxford University Press, 21 Rossotti and Rossotti, J. Inorg. Nucl. Chem., 1956, 2, 201. 22 Jorder and Ertel, J. Inorg. Nucl. Chem., 1956, 3, 139. Weyl (Wiley, 1951), pp. 335-366. 1950).

ISSN:0366-9033    

DOI:10.1039/DF9582600138

出版商:RSC    

年代:1958

数据来源: RSC