JOURNAL O F T H E AMERICAN CHEMICAL SOCIETY Registered in U.S. Patent Ofice.
@ Copyright, 1963, by thc American Chemical Society
VOLUME85, NUMBER 3
FEBRUARY 19, 1963
PHYSICAL AND INORGANIC CHEMISTRY [CONTRIBUTIOS FROM
THE
DEPARTMEST OF CHEMISTRY, UNIVERSITY OF SOUTHERX CALIFORNIA,Los ASCELES7, CALIF.,THE BELL AND THE MELLONINSTITUTE, PITTSBURGH 13, PEXXA ]
TELEPHOSE LABORATORIES, Ixc., MURRAY HILL,N. J.,
Ligand Field Theory of Transition Metal Cyanide Complexes. Part I. The Zero, One and Two Electron or Hole Configurations1 BY J. R. P E R U M A R E DANDREW DI,~~!~ D.
L I E H R ? ~ , AND ~
ARTHUR111. .ID.OISON~~
RECEIVEDJUNE 2, 1962 The magnetic and spectroscopic demeanor of cyano-transition metal compounds is discussed from the standpoint of the modern theory of ligand fields. It is emphasized that for such compounds the naive electrostatic crystal field theory is inapplicable, and that the more general molecular orbital based crystal field theory (the socalled ligand field theory) is required t o rationalize the existent experimental data. Equations which determine the spectral characteristics of zero, one, and two electron or hole cyanide compounds are derived, and their theoretical and experimental consequences are investigated. The prospects for future progress in this area are commented upon, and the avenues of greatest promise are mapped. Hope is expressed that such progress will soon circumscribe the domain of applicability of simple ligand field techniques.
crystalline field treatment which uses a molecular orbital basis (the so-called ligand field method3‘) can yield a satisfactory explanation of the magnetic and spectroscopic properties of the transition metal cyanides.6-8 Experimental
Introduction Of the various aspects of the chemistry and physics of Werner complexes which have been studied latterly, those which have been scrutinized most intensely, both qualitatively and quantitatively, have been their magnetochemical and spectrochemical behaviors. And although great success has been met of late in understanding the magnetic and spectroscopic deportment of a large number of such complexes, the cyanides have as yet eluded all efforts to codify their optical transitions. For the most part this failure has arisen because of the inapplicability of the electrostatic crystal field theory to such ~ y s t e m s . ~But the failure has not been entirely complete. In 1935, Howard4 explained the magnetic demeanor of the ferricyanide ion,5and others have since noted that the chromicyanide ion is also explicable on the basis of the simple theory of crystalline fields. Extensions of this simple technique to other cyanide complex ions have met with discouraging results. We shall show, however, that a slightly more sophisticated
Preparations.-Preparations scribed in references 10-15.
(1) This paper is based, in part, on a thesis submitted in June, 1902, b y one of us iJ. R . P.) t o t h e Department of Chemistry, University of Southern California, in partial fulfillment of the requirements for t h e Ph.D. degree. A portion of this material was presented a t t h e Symposia on Molecular Structure and Spectroscopy, Ohio State University, Columbus, Ohio, June 1961 and 1962. ( 2 ) (a) University of Southern California. (b) T h e Mellon Institute. (c) Bell Telephone Laboratories, I n c . , and t h e hIeilon Institute. (3) (a) D . S.McClure, “Solid State Physics,” Eds. F. Seitz and D. Turnhull, Academic Press, Inc., New York, N. Y., 1’01. 9, 1959; (b) J. s. Griffith, ” T h e Theory of Transition Metal Ions,” Cambridge University Press, Cambridge, 1961; (c) L. E. Orgel, “An Introduction t o Transition-Element Chemistry. Ligand Field Theory,” Methuen, London, 1960; (d) C. K. J@rgensen, “Absorption Spectra and Chemical Bonding in Complexes,” Pergamon, New York, N. Y., 19G1; (e) C. J. Ballhausen, “Introduction t o Ligand Field Theory,” McGraw-Hill Book Co., Inc., New York, N . Y., 1962; (f) A. D. Liehr, J . Chem. Edirc., 39, 135 (1962); (g) C. K . J@rgensen, “Solid State Physics,” Eds. F. Seitz and D. Turnbull, Academic Press, Vol. 13, 1962. (4) J. B. Howard, J . Chem. Phys., 3, 813 (1935). Howard realized full well t h a t he was actually using a simplified molecular orbital theory a I n Van Vleck, rather than the elementary electrostatic crystal field theory. ( 5 ) C. S. Naiman libid., 36, 323, 1503 (1961)1 has recently examined t h e optical spectra of t h e ferricyanide and nitrosylchromocyanide anions from t h e theoretical standpoint: and H. B. G r a y and C. J. Ballhausen [ibid., 36, 1151 (1962) I have done the same for t h e nitrosylchromo-, manganoand ferrocyanide anions.
249
were generally carried out as pre-
(6) M. B. Robin has independently utilized a similar treatment lately in his theoretical and experimental studies of the mixed valence transition metal dye materials such a s Prussian blue. See M. B. Robin, “Symposium on Molecular Structure and Spectroscopy,” Ohio State University, Columbus, Ohio, June, 1901; “Symposium on Ligand Field Theory,” 140th Meeting of t h e American Chemical Society, Chicago, Ill., September, 1961; Imrg. Chem., 1, 337 (1962). (7) F. J. Gilde and M. I. Ban have also used the molecular orbital method t o treat (a) t h e hexacyanochromium(lI1) anion [F. J. Gilde and M . I. Ban, Acta Uniu. Szegediensis Acto Phys. et Chein. [ S . S . ] , 3, 42 (1967), (b) the I. Ban, Acta Chim. Acnd. Sci. Hung., 19, 459 tetracyanonickel(I1) anion [M. (195911, and (c) t h e hexacyano-manganese(III), -iron(III) and -cobalt(III) anions [F. J. Gilde, Acla Unio. Szegedieizsis Acla Phys. el Chem. L\’,S,],6, 3 (1960) 1. ill1 these treatments follow t h e Wolfsberg-Helmholz scheme.8 [UnFortunately, these treatments are marred by the neglect of a portion of the available bonding 7-electron pool (6. Fig. 2a, c, 4 , 5 and 10a of the present paper).] A highly naive model of chemical ligature and spectra based upon simple overlap considerations has also been applied t o the hexacyano-iron(I1) and -cobalt(III) anions (amongst others) by (d) A. Bertoluzza and A. Marinangeli, A n n . Chint. (Rome), 49, 808 (10.591, e l sep. (8) S. Kida, J. Fujita, K. Nakamoto and R . Tsuchida [Bull. Chem. SOL. ( J a g u n ) , 31, 79 (1958)l have utilized t h e modified molecular orbital technique of M . Wolfsberg and L. Helmholz [ J . Chem. Phys., 20, 837 (19.52) 1 t o compute t h e energy levels of copper(1) and nickel(I1) tetracyanide and chromium(II1) and cobalt(I1J) hexacyanide, amongst others, and have compared their results favorably with experiment. Where overlap exists, our ligand field results differ in several important respects from those of t h e Japanese authors. T h e interested reader is urged personally to compare t h e two alternative methods. I t has been demonstrated elsewhere t h a t spurious results are sometimes obtained from t h e Wolfsberg-Helmhoh method.’ (9) Witness, for example, (a) C . J. Ballhausen and A. D. Liehr, J . M o l . Spectry., 2, 342 (1958) [Ewata, i b i d . , 4, 190 (19GO)I; (b) A. Carrington and C. K . Jorgensen, Mol. Phys., 4 , 395 (1961); IC) hl. C. R . Srmons, “Advances in t h e Chemistry of the Coordination Compounds,” E d . S . Kirschner, T h e Macmillan Co., New York, N. Y . , 1961. (10) KIW(CN)B and K&W(CN)s: E. L. Goodenow and C. S. Garner, J . A m . Chem. SOC.,77, 5268 (1955). (11) KsMo(CN)s: W. R. Bucknall and W. Wardlaw, J . Chem. Soc., 2986 (1927). (12) KAlo(CN)e: N. H . Furman and C . 0. Miller, “Inorganic Synthesis,” Ed. L . F. Audrieth, McGraw-Hill Rook Co., Inc., New York, N. Y., Vol. 3, 1950.
Vol. 85
J. R.PERUXAREDDI, A. D. LIEHRAND A. W. ADAMSON
250 4.5
\ I
[d”)
CU(CN);’
4.0
SIMPSON, E. A. A N D WAIND, G. N
3.5
ci 0 0 -I
3 .O
2.5
2.0 220
240
260
280
300
320
XMAX
h(mp)).
VMAX
(mp)
(ern:')
EMAX
225 234 2606) 274
44,440 42,735 38,460 36,496 Figure IC
9J60 10,590 1,637 650
4(1
1
Zn(cN1:
Cd (cN); (3) Hg (CN)T
(2)
(d”) 11 11
--[
A_---
100
I
-4
I b
\
J. BRIGANDO, BULL. CHIM. SOC. FRANCE 5 , 503 (1957)
~
,oh’ 50,000
h (rnp1.
1 4a.000
I
46,000 ~lcm-’i
I
I
44.C30
42.000
1 1
Figure Id Figure l b Fig. la, b, c, d.-The absorption spectra of the d10 transition metal cyanide complex anions. Figures l a , c show the spectra of the copper(1) complexes, and Figures l b , d the spectra of the zinc(II), cadmium(II), mercury(II), silver(1) and gold(1) complexes. (13) KrRe(CNh and [Co(NHi)ola [Re(CN)s]t: R. Colton, R. D . Peacock and G. Wilkinson, J . Chem. SOC.,1374 (1960). (14) NarV(CNh: A. G. MacDiarmid and N . F. Hall, J. Am. Chem. SOC.,
(15) (a) K,Ni(CN),: W. C. Fernelius and J. J. Burbage, “Inorganic Synthesis,” Ed. W. C. Fernelius, McGraw-Hill Book Co., Inc., New York, N. Y.,Vol. 2 (1946); (b) KAu(CN)d: A. Wogrinz, Prokl. Ckem., 3, 5
P6, 4222 (1954).
(1952).
Feb. 5 , 1963
CONFIGURATIONS O F
TRANSITION METALC Y A N I D E
251
COMPLEXES
TABLE I SPECTRAL DATAFOR X,
mp
vms~.cm. -1
THE
d'o TRANSITION METALCYANIDE COMPLEX ANIONS f X 10-
b.sx
Assignment
234 42,740 11,OOO4~* Charge transfer 'A1 -C 'Tz 250 40,000 3,500" Charge transfer 'Ai --c lTz( ?) 265(s) 37,740 600" Charge transfer 'Al + ITl, 'E, or 'AI(?) 29 5 33,900 190°Bb Charge transfer Zn( CN;4= 600-200 16,667-50,000 v1 > v2 and > v4 > v6 in the notation of Fig. 8 and eq. 2. In the present context the one-electron molecular orbital assignments of Fig. 8 should now be interpreted as “one-hole” molecular orbital assignment^.^^ The spectra of the Ni(CN)4-2 and Au(CN)d-l anions are shown in Fig. l l a , b. The data derived therefrom are epitomized in Table V, together with the data of J@rgensen40for the Pd(CN)*-2 and Pt(CN)4-* anions.41 C4”, D4 and Did (Civ and Di are subgroups of the complete D4h group) are isomorphous ( i . e . , have the same symmetry labelsag), and since the Cw, D4 and Dzd geometries under consideration have mutually inverse one-electron molecular orbital level schemes, according t o our previous stipulation (compare Fig. 5 and 6b with Fig. 2 of ref. 3f), the ds-complexes of Ddh geometry and the dz-complexes of Did geometry which meet our physical specifications will have identical energy level parades. (39) The subscripts 1 and 2 of the square planar b-type molecular orbitals are somewhat arbitrary, and thus differ from author t o author, or within a series of publications by the same a ~ t h o r , ~ ‘ d e y e n d e upon nt the coordinate system utilized. If the x and y-coordinates are chosen t o bisect the ligandmetal-ligand bond angle, as in Fig. 2b, 5 and Fb and in Fig. 2 of ref. 3f, the orbital dxy obtains the label bz,, and becomes the strongly u-antibonding bzs* level, while the dX* - y 2 obtains the label big and becomes the strongly r-antibonding big* level. On the other hand, if the x and y coordinates are chosen t o lie along the metal-ligand bond, as in Fig. loa, b, then i t is the big* yz) level which becomes the strongly u-antibonding level and the big* (x* (xy) level which becomes the strongly a-antibonding level. Thus, no physical import should be attached t o the subscripts 1 and 2 if the coordinate system utilized is not given. [Another example of the use of an alternative coordinate system may be discovered on comparison of L. E. Orgel’s (J. I t m u g . Nucl. Ckem., 14, 138 (1960)) discussion of the ground electronic state of the octacyanides with t h a t given in this article.] (40) C. K. Jcrrgensen, “Absorption Spectra of Complexes of Heavy Metals,” Report t o t h e European Research Office, U.S. Department of the Army, Frankfurt am Main, under Contract No. DA9l-508EUC-247, October, 1958. (41) These data are in substantial agreement with those of other workers. Scan, e.g., ref. 8 and (a) L. Szegii and P. Ostenelli, Cass. chim. ita!., 60, 946 (1930); (b) A. Kiss, J. Csaszar and L. Lehotai, Acfa Chim. Acad. Sci. Hung., 14, 225 (1958); a n d (c) A. Kiss, J. Csaszar and E. Horvath, i b i d . , 15, 151 (1958). T h e infrared absorption bands for t h e transition metal cyanides reported by these latter workers are spurious. No cyanide, t o our knowledge, absorbs, either vibrationally or electronically, in the spectral range 4000 t o 11,000 cm.-I. An interpretation of the square planar d*-cyanide spectra different from ours has lately been proposed by C. J. Ballhausen and H. B. Gray (to be published). Their interpretation bases itself upon an analysis of the square planar charge transfer spectra. I n their view ai&*)
-
CONFIGURATIONS OF TRANSITION METALCYANIDE COXPLEXES
Feb. 5, 1963
As in the case of the R ~ ( C N ) S anion,33 -~ we have procured the semi-empirical parameters of the Ni(CN)4-2 anion, Ak (k = 1,2,3), from a theoretical fit of the spinallowed bands (taking the ratio of F2:F4to be eleven), and used these parameters to compute the positions of the spin-forbidden bands (as a check).42 The agreement seems quite e n ~ o u r a g i n g . ~ ~ Conclusion I t is evident from the foregoing that ligand field theory (that is, molecular orbital based crystal field theory3') is quite successful in rationalizing the observed spectroscopic and magnetic properties of the dn (n = 0,1,2,8,9,10) transition metal cyanide complexes. * This situation is quite in contrast to the general T.riewpoint prevalent heretofore (with the exception of a few isolated o u t ~ r i e s ~ - ~ .It~ ~is~to ) . be hoped that the initial success obtained in this paper for an entire family of cyano compounds will be extensible in the future to other families of this same sort [e.g., the dn cyanides ( n level is variable in the homologous series MX4-2, where hl equals S i , Pd and Pt. T h e energetic position of t h e al,(zz) level is imagined t o vary from a location between t h e bPg(xy) and eg(xz;yz) [for h-i(II)] levels t o one below t h e eg(xz,yz) levels [for P t ( I I ) ] . Although inte!lectually stimulating, their interpretation cannot be regarded a s final, a s it is founded upon uncertain charge transfer assignations. [They have n o t been able t o differentia t e between the equally probable (and likely) bonded-antibonded, nonbonded-antibonded, and antibonded-antibonded charge transfer processes in these complexes (see Fig. 1 0 4 . As a n instance of t h e importance of t h e bonded-antibonded processes read J. S. Grifith ( M o l . Phys., 3, 477 (1960))l. ( 4 2 ) T h e one-electron Ak (k = 1, 2 , 3) molecular orbital energies for t h e Ni(CN)r-2 anion thus derived have the values Ai[(x2 - y') 2'1 = 32,140 xy; = 32,760 cm.-l and Aa[(xZ y') - (xz,yz)]= cm.-1, A?[(.- - y?) xy] these tetraco36,010 cm.-l. With t h e exception of A?[(x? - y 2 ) ordinated one-electron molecular oi bital parameters are similar t o those uncovered previously for t h e octacoordinated cyanides (Fig. Gb). [Please keep in mind t h a t here a s throughout t h e text, t h e symbols s, x, y, z, xy, xz, yz, x* y2 and 2 2 (and, a t times, s, px, py, pz, d,,, d,,, d,,, dx2 - ,z and d.z-see Fig. 2b and 6a, b) d o nnl imply t h a t t h e molecular orbitals used are primarily ns, n p or nd, ( n = 3, 4 , 5 ) , in character. These symbols imply only t h a t t h e molecular orbitals thereby specified have spatial charge amplitude distributions which angularly mimic those of the simple ns, np or nd distributions, b u t d o nnt, in any sense, equal them. Of course in the simple linear combination of atomic orbital approximation these orbitals are pictured as composites of t h e metallic ns, n p or nd functions and t h e ligand atomic functions; see Fig. 2a,c, 4, 5 and loa, b]. T h e spectra of the Au(cS)4-1, Pd(C?i)a-2 and Pt(CS)r-2 anion5 were too diffuse t o analyze and compare similarly. ( 1 3 ) I t is t o be marked that our assignment negl?cts t h e possibility of a large Jahn-Teller separation fur t h e 'E, or 'E, electronic state. Hence, some alteration in t h e theoretical parameterization would be required if this neglect were invalid. A discussion of t h e consequences of t h e Jahn-Teller theorem for systems with a single fourfold rotation or rotation-reflection axis [e.g., Clv, Dah, Dad, Lhd,etc., systems] may be found in ;a) A . U . Liehr, "Progress in Inorganic Chemistry," E d . F. A. Cotton, Interscience Publishers, Inc., K e n I'ork .T. Y . , 1-01, 4 , 1962; (b) Annual Reviews of Physical Chemistry, Ed. H. Eyring. Annual Reviews, Inc., Palo Alto, Calif., Vol. 13, 1962, pp. 41-76 and in ref. 3f. [These discussions are based on t h e mathematical treatment given by (c) A. D. Liehr, J . Phys. Chem., February, 19631. Please keep in mind t h a t t h e low symmetry of the octacyanide geometry ((2.1 is no1 due t o t h e Jahn-Teller theorem, b u t t o ordinary coulombic and inelastic forces. Fur a discussion of the stereochemistry of such forces see ref. 43a,b and (d) A. D. Liehr, J . Phys. Chem., February, 1963. SOTE ADDEDIN PROOF.Since this article went t o press two further closely related works have appeared: (a) R. hL Golding a n d A. Carrington, Mol. Phys. 5 , 377 (1962) (on t h e octacyanides) and (b) B . R. McGarvey, J . Chein. Phys., 37, 2001 (19G2) (on t h e perchromates). Golding a n d Carrington's octacyanide work is marred by a lack of spectral resolution and by a consequent theoretical misassignment. E. Konig (to be published) has corrected their treatment (Dr. Kanig is presently a visiting Fellow a t t h e Mellon Institute), Two additional related works which have appeared too late for inclusion in this paper are: H. L. Schlafer, E. Kdnig a n d H. von Hirschhausen, A n n . chim. (Rome), 62, 663 (1962); and A. Bertoluzza and A. M. Marinangeu, ibid., 62, 6137 (1962).
-
-
-
-
-
SPECTRAL
DATA FOR
Amax,
Yrnax,
mil
cm. -1
266.0 284.0 309.5 330.0 357.0 386.0 426.0 486.0
37,590 35,220 32,300 30,310 28,010 25,900 23,470 20,580
212.0 220.5 210.2
47,800 45,400 41,600
242 255.2 258 4 279.9 217 264 323
259
TABLE V ds-TRANSITIOX METAL CYANIDE COMPLEX ANIONS THE
emax
f X 10-4
Assignment
Calcd. frequency cm-1
Ni( CN)r' (F2= 11F4= 770 cm.-l) 16,150 965 Charge transfer 310 Charge transfer 4,820 770 71.5 lAlg 'E, Fitted 44 5 l - j l g -+ lA*g Fitted 409 8 . 14 l.11~-t 'Big Fitted 79 0 6-2 'Aig + 3.1zg 25,410 7.8 .21 lA41g-+ 3Eg 24,880 -2.0 -0.75 .10 'Ale: 3 B ~ g 19,750
-
-
-
Pd(CS)4': C. K. J@rgensenN 9,000 ... Charge transfer 7,200 (700) Charge transfer 1,200 54.0 Charge transfer
Pt( C. K. J@rgensen4O (41,320) 1,880 200 Charge transfer 39,180 29,500 (38,680) 26,000 35,720 1,590
3500
Charge transfer
(?I
35.0
Au( C S ) 4 - : A. Kiss, J. Csaszar and L. Lehotai41* 46,083 2,400 ... Charge transfer 37,879 33 1 ... (?) 30,960 51 ... (?)
= 3,4,5,6,7), the nitrosyls, the carbonyls, the mixed cyanides, nitrosyls and carbonyls, etc. 3. In later publications we hope to report on whether this hope is justified or not. Our present progress within the dn ( n = 3,4,5,6,7), cyanide families is not sufficiently advanced a t this time to give any indication of the true goodness of our theory. However, this circumstance should be rectified shortly, and we shall soon know how far elementary ligand field concepts can be pushed and still give valid results. When this latter question is answered, we shall have established once and for all the limits and boundaries of ligand field applications, and have set the frontiers for future experimental and theoretical advancement. Acknowledgments.--We should like to express our thanks to Professor C. S. Garner for his gift of samples of K3m'(CN)Band K,W(CN)s and to Drs. S. T. Spees, Jr., and RI. A. Bennett, individually, for the preparation of the samples of K2Ni(CN)4 and K3Re(CS)4, each. lye are also grateful to Professors C. J. Ballhausen, D. S. Martin and K. Ruedenberg, and Drs. R. F. Fenske, E. Konig, h i . B. Robin, S. Naiman and J. D. Swalen for freely discussing their related researches with one of us (ADL). This article has greatly benefited from their astute remarks. We are especially grateful to Dr. Konig for providing us with preprints of his and Dr. Gliemann's separate and complementary papers, and to Dr. Swalen for supplying us with a preprint of his recent article. This work was partially supported by an A.E.C. grant (Contract No. A T 11-1113) for which we are very grateful.
c.
