R. Krishnamurthy and Ward B. Schaap'
Indiana Universitv Bloomington, 47401
I 1
I
Computing Ligand Field Potentiah and Relative Energies of d Orbitals A simple,
I n recent years, the concepts and uses of the crystal field or ligand field theories have been recognized as an essential part of the training of chemists. The use of simple crystal field arguments in the description of bonding, molecular geometry, magnetism, spectra, and reactivity of transition metal complexes is becoming commonplace in teaching materials being written for lower division college students. Effective use is made of pictorial representations of the boundary contours of the five real d orbitals, as illustrated in Figure 1, which may have different energies and symmetry properties with respect to the arrangement of ions or ligands in crystals or complexes. I n
approach
complicated to be presented to beginning students. In this article we attempt to bridge this gap by presenting a simple, general approach which permits the derivation of the expressions for ligand field potentials and the quantitative evaluation of the energies of d orbitals (for the d' configuration) in a large variety of geometriEal situations. These quantities are obtained from the potential expressions and from energies of the d orbitals derived for a minimum number of small primary ligand configurations. The primary groups are combined in building-block fashion to produce more complex structures. Similarly, the effects of the potential fields of the primary groups on the energies of the individual d orbitals are added algebraically to produce the effectof the overall structure. The geometric aspects of such combinations of primary groups are easily visualized; yet the results for both the ligand field potentials and the energies of the d orbitals are rigorously correct. Background
Figvre 1. Illustration of h e boundary mntourr and tho angular dependence of the ''real" d orbit01 wove functions in tetragono1 orientation.
the usual treatment, the splitting of the five d orbitals in an octahedral arrangement of negative charges into a triply degenerate set, &,(d,,, d,,, d,,), and a doubly degenerate set, e,(d,..,~, d,3, as shown in Figure 2, is discussed first, followed by an introduction of the concept of crystal field stabilization energy and a discussion of the inversion of the splitting pattern in fields of tetrahedral geometry. A qualitative treatment of the orbital splitting in fields of other symmetries, e.g., square planar, is also usually included. Although the qualitative presentation of the crystal field theory is effective and satisfying from the pedagogic point of view, a quantitative discussion of the relative d-orbital energies in fields of various symmetries would be of even greater value, but unfortunately is too This work was supported in part by the U S . Atomic Energy Commission under Contract AT(l1-1)-256 (Document No. COO-256-78). Presented in part before the Division of Inorganic Chemistry at the 155th National Meeing of the American Chemical Society, San Francisco, Calif., April, 1968, and before the XI International Conference on Coordination Chemistry, Haifa, Israel, September, 1968. ' Author to whom correspondenoe may be addressed.
The basic principles of crystal field theory were originally developed by Bethe (1) in 1929. His classic paper considered. the effects of the electrostatic potential on a "free ion" which result when that ion is incorporated in an electrical field of prescribed symmetry. He showed by means of group theoretical arguments how the degenerate orbitals and atomic terms of an ion of a given electronic configuration split when placed in a lattice of a particular symmetry. Because the effects of the nearest-neighbor ions far outweigh the effects of more distant charges, subsequent workers applied the basic idea to coordination clusters in solution (B-6), that is, to central metal ions whose innermost coordination spheres contain specific arrangements of ligands. These ideas have now developed into one of
Figure 2. Energy level diogroms showing ligand fleld splitling potterns ford orbilalr in some common soordinotion environmenb.
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/ 799
the principal theories of coordinat,iou complexes and are described in a numher of boolcs which treat the theory and its applications from either a qualitative (7, 8) or a quantitat,ive (9-12) ~t~andpoint. Although the qualitat,ive effects of cryst,al or ligand fields on the relative splittings of the d orbitals are easily and widely understood, the quantitative calculation of ligand field effects is a matter of considerable mathematical complexity. The calculation involves first setting up an expwssiou for the total crystal field potential, V,.,., of suit,able symmetry stimulated a t the central metal ion by a given geometrical disposition of the ligends. The effect of this potential on the rl orbitals is then investigated and the problem takes the form known as the perturbation theory for degenerate systems. Using the expression for V,., as an operator, the matrix elements involving the d orbitals are evaluated. The resuking secular determinant for tthe pert,urbation energy is then solved in t,erms of the radial parameters. The integrals involving the radial part of the wave function, ( p , ( r ) ) , are not usually solved, but instead are left as empirical paramet,ers. Their presence in the results does not detract from the usefulness of the calculations of the relative splittings of the (1 orbitals due to various types of ligand arrangements, but requires that. the results he expressed in terms of a n empirically evaluated parameter such as Dq, where Dq = (I/,) ( p , ( r ) ) , and where certain values for the ratio ( p , ( ~ . ) ) / ( p , ( r ) ) , expressed in terms of a parameter p, are assumed. The expression for the potential field a t the central metal ion due to a part,icular ligand geometry is obtained by summing the potentials due t,o the individual ligands making up the complex. This procedure implies that, just as certain geometrical arrangements can be considered t,o be const,ructcd from several smaller Table 1.
Coordination number and configuration of primary group
I . C.N.
1 One ligand or charge located on the Z axis =
11. C.N. = 2 T~~ ]igands at right
constituent arrangemenls, the potential of the larger geometrical arrangement is the sum of t,he fields of its constituents. Thus, if the potential fields of a relatively small number of primary constituent groups of specific geometry are known, the crystal fields of many larger, more complex arrangements can be easily obtained. For example, the potential field due to a regular octahedral arrangement of six ligands is precisely equal to the sum of t,he fields arising from a square planar arrangement of four ligands in the X-Y plane and a linear arrangement of two ligands along the Z axis, all equidistant from the central atom. Similarly, the potential due to eight ligands a t the corners of a regular cube is equal to t,wice the field generat,ed by two tetrahedral arrangements of four ligands each, in which each ligand lies a t the same distance from the central atom. Although the relationships between the crystal field potentials of simpler component sets of ligands and those of larger, more complex geometrical arrangements that can be obtained from them are obvious from an inspection of the expressions for potential fields arising from various arr~ngement~s of the ligands (9), the implications of these relationships have not been adequately realizcd. I n particular, to our knowledge it has not been pointed out previously that, subject to a few limitations arising from symmetry considerations, it is possible to obtain the Dq values of all the d orbitals in many complex configurations of ligands by a mere summation of the Dq values of the corresponding d orbital in each of several component sets of ligands. The result is of import,ance to the practicing chemist; for if the Dq values of rl orhitals are known for a few basic, primary component groups of ligands, the Dq values due to a new configuratiou derived from these components can be obtained a t once wit,hout having to solve the fundamental quantum mechanical problem.
Potential Field Expressions and Relative d-Orbital Energies far Three Primary Geometric Configurations
Relative energy of d orbital in units of Dp for p = 2.0 (Values for p = 1.0 in parentheses) d,, d,n., d=v d., a,=
Potential field expressian"J 1 + x1~ z ( ~ ) +~ 23P4(r)z40] 0
= *?*PW
v1
V9 =
angles in the A'-Y plane (on the X and Y axes)
5.14 (3.43)
-2.14 (-0.43)
GET
-3.14 (-1.43)
6.14 (4.43)
-3.14 (-1.43)
0.57 (-0.285)
0.57 (-0.285)
1.14 (-0.57)
-2.57 (-1.71.5)
-2.57 (-1.715)
+
4% z40 Tzr+O]
1 zPd(r)(:
P
111. C . N . = 4 Four ligands in a
(Dp values as a foncbion of 8 )
staggered, tetrahedml-like arraneement, two shove &d two below the X-Y plane; each a t avariable angle 6 with resnect to the =tZaxes
I
p 1 . 1 1i d x
I
I
I
I
i . . . r I I
i
.,
I I
A
h
I .
I
The V . I ~ ~ U I I1- ~ ~ 1 1 1 %P, s ell.. R I V ~ ~ c r q lwil iri ~ ll~ .t i f I '1 . I~W~ 1111,I W I> VP C ionvtiwa: i i 1 1 1 ~1.131 11 1 h 1 9 1 \ w r n l ~ r. x I .I . ~t.t.atl\. ~l .r C \ OIIIV 11 .~I e ~ ~ : ~ r i +e miW . ~ C W I I(I( " ia~.~lil.~ . C.I f. < r f u ~ ~ h it xv~ l 3 n n :
ort.rsit,lr i n h!trrt~
+
+
MXsY is related to its octahedral parent MXs. That is, if a ligand X of higher field strength is substituted on cis-MX3Yato give cis-MXIY,, the spectral relations and splitting patterns are the same as the case in which a ligand of higher field stength (Y) substitutes on MX6 to give MXaY. In both cases, one of the transitions in the visible region remains a t the energy of the single d-d transition of the parent "cubic" complex while the other is displaced toward higher energy and is separated in energy from the 10 D q transition by 4.86 ( D ~ YD q x ) . In case DqY > D y x , the complex cis-MX2Y4 behaves as a singly-substituted derivative of the pseudocubic complex MX,Y,. This is the case illustrated in Figure 6. The fact that the splitting of d-d spectral bands in cis-disubstituted complexes is one-half that expected for trans-disubstituted complexes is well known and has been used as one of the criteria for distinguishing between cis- and trans-isomers on the basis of their spectra (17,lS). Cis-MX2Y4, Trans-MXzY4, MXY5. The energy levels for the more highly substituted complexes can be derived in an' analogous manner and show splitting patterns similar to those in the examples cited above. Energy level diagrams for the series of substituted
DUX. A~~
&orbital energies for M X , (90') in X-Y plane for two X ligands on Z axis for M Y . (90")in X-Y plane
dd - 0 . 4 3 Dqx 6 . 8 6 Dyx - 0 . 4 3 Dqu
d&v2 4.43Dpx - 2 . 8 6 Dpx 4.43Dpy
-057Dpx -2.86 Dqx -0.57Dpu
d,, -1.715Dqx -0.57 Dpx - 1 7 1 5 Dyy
-1.715Dpx -0.57 Dqx -171.5 Dqy
Sum (for cis-MXdYa)
6 . 4 3 Dpx - 0 . 4 3 Dqy
1.57Dpx + 4 4 3 Dqu
-343Dqx -0.57 Dqu
-2.285Dyx -1.715Dqy
-2.285Dqx -1.715Dpy
Examination of the energy levels shows that the splitting of both the lower and the upper sets of energy levels is the same as it is in the case of the monosubstituted complex, MXsY. I n fact, if D q x > D q u , cis-MX4Yzis related to the pseudo-cubic trisuhstituted complex 1,2,3-MX3Y3 in exactly the same way as
dzv
duz
octahedral complexes between MX6and MY6 are shown in Figure 6. The levels are drawn to illustrate the specific case in which D ~ Y= 1.25 D q x . The vertical scale is given in units of D y x . The only substituted complex missing from the series is trans-MX~YI,to which this approach cannot be applied because this Volume 46, Number 12, December 1969
/
807
isomer cannot be constructed from the primary ligand groups.
The prediction of the energy level diagrams for d orbitals by the procedures described in this paper is useful in understanding and interpreting the d-d spectral transitions of d1 and dycomplexes in the visible and ultraviolet spectral regions, as well as those of d4 and CP complexes in their high spm (weak field) configurations. As examples, quantitative comparisons will be made of calculated and observed frequencies of d9 copper chloride complexes with two different structures. The crystal structure, spectrum and magnetic properties of CszCuC14have been investigated by Ferguson (19) and others (13, 14, 20). The CuClp2- portion of the complex has a distorted (flattened) tetrahedral structure (D2J in which the average value of tho polar angle 6 is about 62'. Spectral transitions are observed at 9050 cm-', 7900 cm-I and -5200 (4800,5550) em-'. For these complexes, the value p = 1 appears to be the better choice for this parameter. From Table 1, the relative energies of the d orbitals in Dq units in the field of the four-coordinate third primary group at B = 54'44' (tetrahedron) and at 13 = 62"28' (compressed tetrahedron) are as shown in Figure 7, assuming p = 1. The distortion present in the
Figure 7. Energy level diogrom of the d orbitals in Dq vnih in the Reld of fie four-coordinate third primary group in o tetrahedroi ond o compreaed tetmhedral field.
CuClrz- structure causes appreciable splitting of both the 1, and e levels predicted for the regular tetrahedral structure. Because all the orbitals except the uppermost are occupied in a dy complex, the transition of lowest energy that can occur is one in which an electron from either the d,, or d,, orbitals jumps up to the d,, level, causing the vacancy or "electron hole" to move down in the opposite direction. I n the transition of higher energy, the hole would jump from its ground (d,,) level to the &2-u2 orbital, while in the highest energy transition, the hole would move from its ground state to the d,. level. The energies of these transitions are seen from the diagram to be 4.11, 6.40, and 7.08 Dq units, respectively, and are designated by arrows. (The order of the energy states of the dy complex are just the reverse of those of the d1 system. If the diagrams above were drawn in terms of the energies of the atomic states instead of the orbitals, the diagrams for the 808
/
lournol o f Chemicol Educofion
d1 system would be the same as those shown, but the diagrams for the d9system would be inverted.) The value of the Dq parameter is usually not precisely known, though tables giving approximate values have been published (12). Dq values vary with the metal ion, the ligand, the valence state, the coordination number, the type of structure, and the metal-ligand distance. I t is usually preferable to evaluate Dq by fitting one or more observed transitions to a calculated expression and then to use this value to calculate the remaining transitions. For the case being considered, Dq can be calculated by equating the expressions for the highest energy transition, i.e.,
Using this value for Dq the other transitions are calculated
The agreement of the calculated and experimental values is good in this example. As a second example, the spectral transitions predicted for the five-coordinate C u C I P ion will he calculatcd using the value of Dq evaluated above. I n the crystal [Co(NH,),] [CuCl,] the chloride ions are known to lie in a slightly distorted trigonal bipyramidal arrangement around the cupric ion and the d-d spectral transitions are observed at 8200 and 10,400 cm-' (IS, 1 4 ) According to Table 3, the relative energies of the d orbitals in Dq units in increasing order are -3.14 (d,, and d,,), 0.035 (d,s-,n and d,,) and 6.21 (d,.) for a regular trigonal bipyramid and for p = 1 (19). Placing the nine d electrons in these orbitals leaves one unpaired electron and the "electron hole" in the d,%orbital (ground state). I n the states of higher energy, the electron hole first jumps to the degenerate d,*-,. and d,, orbitals and then to the degenerate d,, and d,, set. The energies of these transitions are seen to be 6.175 Dq (YI) and 9.35 Dq (vr). Using the value 1280 cm-' for Dq, we calculated vl = 6.175 X 1280 = 7900 cm-' and vz = 9.35 X 1280 = 12,000 cm-l. Although one of the calculated values is too high and the other too low, they agree reasonably well with the observed values, especially in view of the distortion of the structure and the change in coordination number between the two examples, which may change the metal-ligand bond distances. The fit between the calculated and observed energies of the transitions can be improved if the changes in metal-ligand bond distances and the distortion from a regular trigonal bipyramidal configuration are both taken into account. A recent study of the crystal structure of [ C O ( N H ~ ) ~ ] [ C U(21) C ~ ~has ] verified the presence of appreciable axial compression in this complex in that the three equatori$l chloride ions have a Cu-Cl bond distance of 2.39 A, while the two axis1 chloride ions have a shorter bond distance of 2.30 A. If it is assumed in accord with the ionic crystal field model that, for small changes in bond distances, Dq values vary in proportion to I/+, where T is the metalto-ligand distance, then the effectiveDq values for both the equatorial and axial chloride ligands in CUCI,~-can be calculated from the value of 1280 cm-' established in the previous example for chloride ligands in Cs2CuC14.
I n this latter complex, the average Cu-C1 bond distance is 2.22 A (22), so that the corrected Dq values are Equatorid: Dq,, Axid: Dq.,
=
=
1280 X (2.22/2.39)5 = 885 cm-' 1280 X (2.22/2.30)' = 1070 cm-'
The effects of the distortion due to the presence of two different metal-to-ligand bond distances can be calculated by the approach discussed previously for substituted complexes. One can obtain the Dq values of the d orbitals in the desired axially substituted complex IMX3X2' by simply adding the Dq values given in Table 3 for a plane triangular group (MX3) with those given for the linear (axial) MX,'group, keeping in mind that the Dq values for the two types of ligands X and X' are different, i.e., Dqx = Dq., and Dq,, = Dq,,. Using the tabulated values for p = 1, it is seen that the relative energies of the d orbitals in the distorted trigonal bipyramid structure are as shown in Figure 8.
Figure 8. Energy level diogrorn of the d orbitals in tho distorted trigond bipyrmmid structure.
Inserting the values of Dq,, and Dqa, calculated above gives the relative energies of the orbitals shown a t the right of Figure 8. From these values we obtain
These values are in better relative agreement with the experimental frequencies than are the values calculated above for the regular structure with no axial compression. The correction for the distortion has made the difference in the frequencies of the two transitions approximately the same as that of the observed transitions (-2400 versus 2200 em-'). The fact that both calculated frequencies are somewhat low indicates that the calculation of Dq values from the value obtained for CszCuC14is not precise. Apparently, the Dq values for both the axial and equatorial ligands should be slightly larger, though the ratio of their values, (2.39/2.30)5 = 1.21, must be approximately correct. As an alternative, it is also possible to apply the relation Dqa, = 1.21 Dq,,, which corrects for the distortion from a regular structure, and then to solve for the value of Dq,, by equating the calculated expression for the energy of one transition to the observed frequency, as was done in the first example. I n the example being considered F, =
7.65 Dq,,
The frequency of the other transition is then predicted to be
+ 0.58 Dp,
=
8.23 Dq, = 8200 om-'
and Dp, = 995 cm-I
+
Dq., 3.26 Dq., = 10.91 X 995 = 10.900 cm-'
This value, obtained by evaluating the Dq parameter from data for the same complex, is in much better agreement with the experimental frequency than the others. The above examples demonstrate that the calculation of the frequencies of spectral transitions of complexes in terms of experimentally evaluated parameters is not only easy to perform, but is also surprisingly successful. The errors and approximations inherent in the simple point-charge crystal field model are largely washed out if Dq and p are treated as empirical parameters to he evaluated by fitting to experimental data. Calculations of crystal field effects in an absolute sense, on the other hand, have not been very successful with the simple crystal field model (23). Other Applications. The Dq values and relative energies of the d orbitals of many other complexes containing more than one type of ligand can be derived in a manner analogous to that illustrated above for suhstituted six-coordinate complexes. The method is applicable to other geometrical configurations and coordination numbers and is subject to the limitation mentioned previously that each type of ligand be added only in units of primary groups. For six-coordinate complexes, the most highly substituted species that can be treated by the simple approach presented here is the complex with four different types of ligands MX2Y2AB, where the two A' ligands and the two I' ligands occupy cis positions in the X-Y plane and the ligands A and B lie at trans positions on the Z axis. In the case of substituted four-coordinate complexes, only the cisdisubstituted square planar complex, MX2Y2,can he constructed from the primary groups. The possibility of calculating the Dq values of d orbitals in various real or hypothetical configurations of ligands has applications also in the area of kinetics (8). Because crystal field stabilization energies can he easily computed for many postulated configurations, it is possible to compare the stabilization energy of a given complex in its ground state with the energies of possible reaction intermediates of either lower or higher coordination number, thus affording a comparison of the contributions of the ligand fields of the possible intermediate structures to the activation energy (24).
Limitations
The method described here for obtaining the Dq values of d orbitals in fields generated by various numbers and configurations of ligands is based on the simple crystal field theory as applied to a dl electronic configuration. Complicating factors such as the Jahn-Teller effect (25) and spin-orbit coupling (9-12) have not been considered. For the d1 configuration there are no interelectronic repulsions such as arise in the presence of two or~moreelectrons, so that the splitting of the energy levels is determined only by the geometry and strength of the ligand or crystal field. The d' electronic configuration is thus the simplest system for assessing Volume 46, Number 12, December 1969
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809
the effects of ligand fields. Unfortunately, relatively few complexes with the d l electronic configuration have been prepared and studied, and relatively few spectra have been recorded. More exam~lesare known of comvlexes with a d gconfiguration, together with their spedra. The approach described for the d l system is directly applicable to ds complexes, but the order of the energies of the states will he inverted. In this case, however, the approximations should not he as good as in the d' case because the neglected spin-orbit coupling constants may become significant factors. The d' energy levels should also he applicable to d4 and d6 complexes in their weak field (high spin) configurations. The tetragonally oriented basis set of d orbitals used (Fig. 1) is compatible with ligand fields in which the Z axis is the principal axis of symmet,ry and is (in effect) at least a four-fold rotation axis. I n such fields the real d orbitals do not mix, hut retain a direct one-to-one correspondence with the roots of the perturbation energy equation obtained from only the diagonal matrix elements. In a few ligand fields, such as those of C2. (f go0), C X a (SOo), f Dz,, and Dad symmetry, a different linear combination of d orbitals should be used since the presence of off-diagonal elements in the potential fields of these point groups serves to mix the d orhitals. I n these groups for which the additivity of Dq values does not apply, the ligand positions of the original group plus all positions generated by the allowed inversion through the origin do not give rise to a rotation axis of at least fourth order. In some other small groups to which the additivity relations do apply, such as C,,, C2,(9Oo),C8,(900),D2&and D3,, the ligand points of the original group, together with thc points generated by inversion through tbc origin, always result in a structure in which the Z axis is the principal n-fold rotation axis and n 4. I n these cases all the terms in the potential field expressions which can give rise to off-diagonal matrix elements vanish, and the d orbitals of the defined set do not mix hut remain discrete so that the effects of the ligands on their energies are additive.
>
Summary
A simple approach has been presented for calculating the relative energies of d orbitals in crystal fields of a large variety of geometrical configurations. The method is based on the use of three small, primary groups of ligands which serve as building blocks in the construction of larger, more complex structures. As the building blocks are combined to form the more complex structures, the resultant energies of the d orbitals are obtained by adding algebraically the Dq values associated with the ligand fields of the primary groups. Changes in orbital degeneracies and energies arising from symmetry differences in structures of equivalent coordination number are easily taken into account. The results obtained by use of this principle of addi-
810
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Journal of Chemical Education
tivity of Dq values of d orbitals are identical to those derived from complete perturbation treatments applied t o the over-all structures. Relative d-orbital energies are calculated for d' complexes with almost all known structures and with coordination numbers rauging from one to twelve. The approach is also applicable to d9 complexes, to weak-field d4 and dB complexes, to many distorted structures, and to most substituted complexes, providing that the substituting ligands are added in units corresponding to the primary groups or in units derivable from them. Literature Cited
(1) BETHE, H., Ann. Physik, 3, 133 (1929). (An English translation of this paper is available from Consultants Bureau, Inc., New York, N. Y.) (2) VANVLECK,J., "The Theory of Electric and Paramagnetic Susceptibilities," Oxford Univ. Press, 1952. R., and PENNY, W., Phw. Re"., 42,666 (1932). (3) SCHLAPP, (4) ILSE,F., A N D HIRTMAN, H., Z. physlk Chem., 197, 239 (19.51). (5) ORGEL,L. E., J. Chem. Soe., 4756 (1952). R. S., Qzm-1. Rev., 7, 377 (1953). (6) NYHOLM, (7) ORGEL,L. E., "An Introduction to Transition Metal Chemistrv: Lieand Field Thoorv." .. Methuen and Ca.. Ltd., ~ o i d o n fi60. , R., "Mechanisms of Inorganio BASOLO,F., A N D PEARSON, Reactionn," John Wiley & Sons, Inc., New York, 1958, Chapt. 2. (2nd Ed., 1967). GRIFFITH,J. S., "The Theory of Transition Metal Ions," Cambridge Univ. Press, Cambridge, 1961. BALLHAUSI:N, C. J., "Introduction to Ligand Field Theory," McGraw-Hill Book Co., New York, 1962. J#RGENSEN, C. K., "Absorption Spectra and Chemical Banding in Complexes," Pergamon Press, Lid., London, 1962. FIGGIS, B. N., "Introduction bo Ligand Fields," John Wiley & Sam, Inc., New York, 1966. HATFIELD, W., A N D PIPRR,T. S.,Inorg. Chem., 3,841 (1964). DAY,P., Proc. Chem. Sac., 18 (1964). COTTON,F. A,, "Chemical Applications of Group Theory," Interscienee (division of John Wilev & Sons Inc.), New York, 1963. (16) JAFFE, H., A N D ORCHIN,M., "Symmetry in Chemistry," John Wiley & Sons, Inc., New York, 1965. R., SCHAAP, W. B., AND PERUMAREDDI, (17) KRISANAMURTHY, J., Inorg. Chem., 6, 1338 (1967). (18) L ~ w r s J., , A N D WILKINS,R., (Editom),"Modern Coordination Chemisiry," Interscienee (division of John Wiley & Sans, Inc.), New York, 1960. (See especially chapters 4 and 6). (19) FsncusoN, J., J . Chcm. Phgs., 40, 3406 (1960). &I., L&\!-Is, J., I N D SLIDE, R., 1. (20) FIGGIS,B., GERLOCH, Chem. Sac., 2028 (1968). I., ELLIOTT,N., LAL.\NCETTG, R., A N D BRENNIN, (21) BERNAL, T., "Progress in Coordination Chcmistry," (Editor: M. CIIS) Elsevier, Amsterdam, 1968, p. 518. (22) . . HELMHOLE, . L... A N D I
