E.P.R.SPECTRA OF TRIS-COMPLEXES OF C U + ~
March 20, 196.1
[COSTRIBCTIOSFROM
25, I>. c.,A S D
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NATIOSALBUREAUOF STANDARDS, WASHIXGTOS UNIVERSITY O F HAWAII,HONOLULU 14, HAIX'AII]
THE
THE
The Electron Paramagnetic Resonance Spectrum of Some Tris-Complexes of Copper(II)la
c.X L L E X , J R . , ] ~G E R . 4 L D
B Y HARRY
F. KOKOSZK.4,lb
.4ND
RICHARD G.
INSKEEP"
RECEIVEDSEPTEMBER 12, 1963 T h e e . p . r spectrurn of t h e tris-coordination compound of Cu + * with l,lO-phenanthroline a n d 2,2'-dipyridine has been examined a s a function of temperature. .It high temperatures a single absorption is observed in each compoutid indicating a n isotropic g-value. At liquid nitrogen temperature, each compound exhibits a n absorption pattern corresponding t o an anisotropic g-tensor with two unique principal values T h e measured g-values a r e : phenanthroline complex, g = 2.134 a t high temperature, g,l = 2.273, gL = 2.062 a t liquid nitrogen temperature; dipyridine complex, g = 2,111 a t high temperature, gl = 2.268, gl = 2.046 a t liquid nitrogen temperature. These spectra have been interpreted as arising from a Jahn-Teller tetragonal distortion, frozen in a t the lower temperatures a s described in t h e theoretical treatment of Liehr and Ballhausen.
Introduction There has been considerable recent interest in the e.p.r. spectra of bis-Cu+?chelates?; however, up to the present, no work has been reported on tris-Cu+? chelates. These complexes should be of considerable interest since they are expected to be octahedrally coordinated and exhibit a Jahn-Teller distortion. The theory of the Jahn-Teller effect, recently worked out by Liehr and Ballhausen3 for octahedral coordination, seems to account for the e.p.r. spectrum of copper fluorosilicate hexahydrate and Cui' in some inorganic salts,l but as pet no example has been found in a chelate. Recent work on the infrared spectra of the tris-Cu+' complex with %,%'-dipyridinegives some reason to believe that there is a Jahn-Teller distortion in this complex. This evidence is lacking in the infrared spectrum of the tris- 1,lO-phananthroline complex. IVe have investigated the e.p.r. spectra of the triscomplexes of Cu+' with these ligands as a function of temperature in the range from liquid helium temperature to 130'. The result seems to be accounted for by the Liehr-Ballhausen theory. Experimental The tris-%,2'-dipyritiine and l,l0-phenanthroline complexes were prepared as n i t r a t e salts by t h e method described by Inskeep." In order t o obtain niagnetical1~-dilute samples, t h e diamagnetic tris-%n-z complexes 'iuere prepared containing small amounts of Cu'?. Percentages of Cu-? ranged from 0.1 t o 3. Co~npositionsof t h e complexes were checked for C , H , S,and metdl by chemical analysis. d l 1 samples corresponded t o t h e tris-complex. Owing t o difficulties encountered in the interpretation of the complexes containing naturally occurring copper with its two isotopes 63 and 7 5 , samples were also prepared by the same procedure containing only the "Cu isotope. T h e e . p . r . spectra were recorded on a I-arian Model 4500 e . p . r . spectrometer using 100 kc. tnodulation except a t liquid H e temperature, At t h e latter temperature a modulation of 400 C . P . S . was used. T h e spectra were recorded on polycrystalline samples a n d the g-values determined b y t h e method of Sands6" and I i ~ i e u b u h l . ~ " .Itypical spectrum of these two cotnplexes containing naturally occurring copper a t 130' is sho\rn iii Fig. 1. Although this is for the pherianthroline colnplex, t h e spectrum of t h e bipyridine complex is quite similar. There is a single absorption indicative o f an isotropic g = 2.134. Figure 2 s h o w a typical spectrum a t liquid nitrogen temperature. T h e high-field strong absorption (1) (a) Presented a t the 114th Sational Jleeting of American Chemical Society. Rlarch 3 1 - A ~ r i l 6, 1H6,'3, Los Angeles, Calif ; ( b ) National Bureau of Standards, [ c ) University of Hawaii (21 A H RIaki and B R XlcGarvey, J . Chem P h ? s , 29, X I , 3.5 (1938), 1) Kivelson and I< Zieman, i b i d . , 36, 149, 1.56, 162 (1961), H R Gersmann and J I ) Swaien, i b i d , 36, 3221 (1962) ( 3 ) A 11 Liehr and C J Ballhausen, A n n P h y s , 3, 30.1 (1958). (4) €3 Bleaney, K . D . Bowers, and K . S. Trenham, Pvoc. Ror SOC.(Lond o n ) , A228, l 5 i (1955); J H hl Thornley, B W. LIangum, J H . E. Griffiths. and J. Owen, PYOCP h y s . SOC.( I n n d o n ) , 78, 1263 (1961). (,j)I < . G Inskeep, J . I n o r p . .Yucl Chem., 24, 763 (1962) (6) (a) I 0 , the crystal-field approximation expressions for the g-values are, when the distortion is frozen in g! = 3
,
Fig 4 -The variation of t h e e p r spectrum of t h e C u c 2 trisl,l0-phenanthroline complex with temperature
this value, calculate the expected g-value for the lowtemperature spectrum. The results are summarized in Table 11. The agreement between the observed and calculated values is about 2 parts in 1000, which is remarkable agreement for this crude approximation. TABLE I1 C O M P A R I S O S O F O B S E R V E D A S D CALCULATED g - v A L U E S
Ohsd
Phenanthroline
gl,
Dipyridine
gl g g-
. ? ,\
in which X is the spin-orbit coupling constant and 2, is the crystal-field splitting of the d-orbitals of the copper in an octahedral field For the high temperature case
IX
2600
3200
Complex
+ 8lX' 1
1
For the phenanthroline spectruin, one can evaluate 1 from the high temperature g-value and, using
2 273 2.062 2.268
2.046
Calcd
2.268 2 067 2 238 2 057
I n the dipyridine complex, the agreement is not nearly as good as in the phenanthroline complex, although the results still agree to about 2yc. This is the complex for which the infrared evidence suggests a Jahn-Teller distortion. For the effect t o be apparent in t h e infrared it must be quite large. This is reasonable because the dipyridine ligand is much less rigid
hlarch 20. 1964
ASSOCIATION CONSTANTS
than the phenanthroline ligand and so is more easily distorted. If the distortion is large enough, it is no longer sufficient to use an averaged crystal field splitting in the formulas for the low temperature g-values. Assuming that X remains constant, this reasoning leads to a splitting of about 2000 cm.-l of the degenerate electronic state in the distorted configuration. This figure is reasonable when compared to other studies in which the ligands around the Cu t rare tetragonally distorted. The spectrum does not show a sharp transition point with temperature but rather goes over slowly from one limiting spectrum to the other. Figure 4 shows a series of spectra run at various temperatures. I t is not possible to account for these spectra quantitatively a t the intermediate temperatures, but they seem to be superpositions of the two limiting spectra. Conclusion The line width of the high temperature spectrum is equal to the line width of the two components observed a t low temperature. This observation would seem to lend weight to the interpretation given here. One
[ COXTRIBUTIOS FROM
THE
FROM SPECTROPHOTOMETRIC
DATA
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would expect that the hyperfine structure would be washed out a t the high temperature owing to the breadth of the energy levels involved in the transitions. This work on polycrystalline samples poses some questions to be answered. Single crystals of the diluted compounds are being grown to help answer these questions. The optical spectrum will be investigated a t low temperature to see if the Jahn-Teller splitting of the electronic state can be observed. Similarly, since the Liehr-Ballhausen treatment assumes that the distortion arises from a vibronic coupling to the E-modes of vibration, the infrared spectrum should be investigated as the vibrational states should also be perturbed. Observation of these effects would eliminate any doubts that may exist concerning the origin of the observed effects. X-Ray diffraction investigations should be done on the crystals a t various temperatures to see if any information can be deduced as to the extent of the distortion. Acknowledgment.-The authors wish to thank Professor Gilbert Gordon for many stimulating and useful discussions during the course of this work.
DEPARTMEXT OF CHEMISTRY, KANSASSTATE UNIVERSITY, MANHATTAX, KANSAS!
Machine Computation of Association Constants from Spectrophotometric Data: An Analysis of Errors BY KENNETHCONROW, G . DAXAJOHNSOK,
AND
RONALD E. BOWEN'
RECEIVED SEPTEMBER 5 , 1963 Fortran language programs have been written which successfully calculate equilibrium constants, K , and molar absorptivities, c , from experimental d a t a for self-association and heteroassociation. The calculated parameters are, however, inordinately sensitive to variations in t h e input d a t a . Experiments using t h e programs with synthetic d a t a reveal t h e results to be most sensitive t o concentration errors. T h e errors are discussed in terms of t h e KoseeDrago treatment of this kind of d a t a . Suggested approaches for the improvement of this situation are given.
The simplicity and accuracy of spectrophotometric measurements have led to their use in the determination of a great variety of association constants, especially where the association occurs between two different species. A wide variety of methods has been devised for the treatment of the experimental data, but owing to the complexity of the problem i t has usually been necessary to limit the approach to special cases (such as special concentration relationships) or to make simplifying approximations. The best known methods are graphical and are comparatively tedious and often imprecise. One digital method has been proposed for the determination of self-association constants3 b u t i t has been shown t o fail.4 X digital method has been presented by Liptay for the calculation of association constants of electron donoracceptor complexes which avoids many of the restrictions implicit in the earlier methods but which, too, necessarily makes simplifying assumptions in order to keep the labor of the calculation within bounds.5 In the current work we sought to write a program for a digital computer which would accept spectrophotometric data and fit to it, without simplifying approximations, equilibrium constants and molar absorptivi(1) S a t i o n a l Science Foundation Research Participation f o r College Teachers Fellow ( 2 ) F J C. Rossotti and H . Russotti. "The Iletermination of Stability Constants,'' McGraw-Hill Book Co., Inc , New I'urk, K T., 1961 (3) P . A I ) . de Maine and .4. G Gohle, 7 r a n s F a r ~ d n yS o c , 63, 427 ( 1 9 5 7 ) ; P. A . 1) d e Maine, M 11.de 1Iaine. A . A . Briggs, and G E . L l c ~ Alonie, J Mol. S p e c f r y , 4 , 398 (1960) (4) B M u s u l i n , \V.1,ee. and R 1,. Foley, $bid , 9 , 251 (1962). ( 5 ) W . 1-iptay, Z E l e k l r o r h r m , 6 6 , 37: i l H f i 1 ) .
ties according to the least-squares criterion. Activity coefficient effects were assumed to be negligible; Beer's law was assumed to hold for every species involved. The kind of approach used in developing the computer program is akin to that used by Coburn and Grunwald6 and more recently by S i l l h 7 The problem may be stated as follows: The three independent variables which have an effect on the value of the optical density (at a given temperature in a given solvent) are the initial concentration of substrate(s), the values of the equilibrium constants for the equilibria involved, and the values of the molar absorptivities for the species involved. Of these three independent variables, only the concentration is experimentally controlled. The task which confronts one is to deduce values of the equilibrium constants and molar absorptivities which predict the experimentally determined values of the optical density ( D m )a t various wave lengths and experimental values of the concentration of substrate (s). The variety of possible ways this might be done is summarized with the following diagram. T o illustrate the interpretation of this diagram consider the upper left leg. If one knows the values of K and the initial concentrations (C,)one can calculate the equilibrium concentrations (C,)of the species. Conversely, if one knows the equilibrium concentrations and the initial concentrations one can derive the equilibrium constant. (6) \V C . Cohurn and E Grunwald, J A m . Chem. S O L . ,80, 1318, 1322 (19.58) ( 7 ) I ) I l y r s s e n , N Ingre. and I. G. SillCn, A c l a Chem Scand., 1 6 , 694 ( l e f i l ) , I,, G Sillen. ibid., 1 6 , 159, 191 (1962).
