- Email: [email protected]
Study of the quinquevalent chromium compounds by ESR and optical spectra
J. lnorg. Nucl. Chem., 1963, Vol. 25, pp. 933 to 944. Pergamon Press Ltd. Printed in Northern Ireland
STUDY OF THE QUINQUEVALENT CHROMIUM COMPOUNDS BY ESR AND OPTICAL SPECTRA H. KON NAIG Nuclear Research Laboratory, Kawasaki, Japan (Received 6 November 1962; in revised form 6 February 1963)
Abstract--Quinquevalent chromium complexes of the type CrOCla ÷ 1(or 2) RC1, where R = pyridinium, quinolinium, tetramethylammonium (or potassium) ion, were prepared and their electron spin resonance absorptions were observed in solution at room temperature and at 77°K, as well as in polycrystalline form. The results, together with those of the optical absorption spectra, indicate that these complexes have a common paramagnetic structural unit CrOCl~-. The observed values of fill and g.L of this species were explained on the basis of the molecular orbital theory. The transient, narrow ESR lines with similar feature were also observed during the reduction of K2Cr20~ (or CrOs) with a variety of acids. They were interpreted as due to some Cr tv~oxyion complexes. IN the previous communication tl) the author postulated the existence of the quinquevalent chromium compounds in CrO3-(or K2Cr2Ov-)conc.H2SO 4 system to explain the narrow ESR (electron spin resonance) absorption lines which can easily be observed at room temperature and which consist of four narrow lines with uneven intensities, their line widths being from about 1 to 5 G. To the best of the authors knowledge, there are not many ESR observations reported of quinquevalent chromium compounds. CARRINGTON et al. first observed ESR signal of Cr(V)O~ 3-. In remarkable contrast to the case of CrOa-conc.H2SO 4 system, however, the ESR line width of CrO43- is temperature dependent, broader at higher temperature, and could not be observed above T = 20°K t2J. This is the behaviour to be expected not only for CrO43- but also for other transition metal ions in general with single unpaired d-electron, provided they are placed in the crystalline field with the cubic symmetry or with the nearly cubic symmetry, which, furthermore, is not so strong as to lift the degeneracy of the d-orbitals sufficientlyt3k More recently, SWALEN and IBERS reported the ESR study of peroxychromate ion, Cr(V)O83-, in polycrystalline form at 20°C. This ion has D2d symmetry, and the ESR line width AH1/2 was determined by the numerical analysis to be 23.5 G. t4) It would be of interest to see whether there are any other compounds of the Cr ion with single unpaired d-electron, which show the narrow ESR lines such as those observed in CrO3-conc.H2SO 4 system (ca. 1-5 G). For this purpose, the following complexes of Cr(V) were prepared, and their ESR and optical absorption spectra were observed. K2Cr(V)OCI 5 and
Cr(V)OCIs-RC1,
,1~ H. KON, Bull. Chem. Soc. Japan, 35, 2054 (1962). t2~A. CARRINGTON, D. J. E. INGRAM,D. SCHONLANDand M. C. R. SYMONS, J. Chem. Soc. 4710 (1956). is) B. BLEANEYand K. W. H. STEVENS,Rep. Prog. Phys. 16, 141 (1953). t4~ (a) J. D SWALENand J. A. IBERS, J. Chem. Phys. 37, 17 (1962); (b) J. A. IBERSand J. D. SWALEN, Phys. Rev. 127, 1914 (1962). 933
934
H. KoN
where R is pyridinium, quinolinium or tetramethylammonium ion. These compounds were first synthesized by WEINLAND et al./5,6~ who ascertained that Cr is in the quinquevalent state. There has been little information available concerning the structure of these molecules, but these complexes may be considered as the analogues of the many, fairly well studied vanadyl complexes, where the crystalline field symmetry surrounding the V ion is shown to have an axial component which is strong enough to make the lowest excited orbital sufficiently high above the ground orbital, thus making the ESR lines easily observable at room temperature, tT) One of the purposes of this paper is to present the detailed results of the ESR, visible and infra-red absorption measurements of the complexes in solution as well as in polycrystalline form. Deductions will be made in relation to the nature of the bonds from the standpoint of the ligand field and molecular orbital theory. It was suggested by JABLCZYNSKIand several other workers that during the course of the reduction of CrO 3 or K2Cr207 by the acids such as formic, oxalic and so on, Cr passes through an intermediate valence state between Cr(VI) and Cr(III), and the results of a series of kinetic studies of these reactions are best understood by assuming the quinquevalent state for Cr. ts,9) In the present report, the above assumption will also be proved by the direct observation of ESR signals, which show the feature similar to the K2Cr(V)OC1s and Cr(V)OC13RC1. EXPERIMENTAL Chemical procedures
CrOC13RC1 type compounds were prepared following the method by WErNLANDet al. t5"e~ About 100 ml of a dilute acetic acid solution (ca. 10-8 M) of CrO3 was reduced by passing dry HC1 gas through the solution. The calculated amount of the base, such as pyridine, quinoline or tetramethylammonium chloride was dissolved in the least possible amount of acetic acid saturated with dry HCI gas. By adding the latter solution to the reduced CrO3 solution, the fine lustrous crystalline precipitate was obtained. The colour varied from reddish to dark brown according to the base used. It was found that in order to obtain the homogeneous crystalline material, the reduction by HC1 gas must be complete before adding the solution of the base; otherwise the precipitate was the mixture of more than one complex of various colours. The reduction was best monitored by observing the ESR signals at different stages of the reaction. The pattern near the end of the reaction is free from the complication due to by-products. Samples were dried and kept over K O H or conc. H2SO, in vacuum. The complexes are all very sensitive to the humidity and, therefore, every precaution was taken to prevent the decomposition during the handling. The yield was very good for CrOC13RC1, whereas only a very small amount of cyrstalline material was obtained for K~CrOCIs. To observe the transient ESR signals of Cr(V) caused by the reduction with organic acids other than acetic acid, a portion of the dilute stock solution of KzCrzO7 in glacial acetic acid was mixed with the acid with constant stirring until the colour of the solution became dark brown. CrO3 gave rise to the ESR signal simply by dissolving it in the acetic acid. ESR measurement
All the measurements were carried out with Varian Associates model V-4500 spectrometer with 100 kc/s field modulation. The field strength was calibrated by measuring the proton resonance frequency with the Hewlett-Packard model 524C electronic counter combined with the 525A frequency converter. To determine g-values, the measurement of the resonance field for DPPH (g = 2'0036) 16) R. F. WEINLANDand W. FRIDRICH, Ber. Dtsch. Chem. Ges. 38, 3784 (1905). tt~ R. F. WEINLANDand M. FRIEDEP,.ER,Bet. Dtsch Chem Ges. 39, 4042 (1906); 40, 2090 (1907). tT~ B. R. McGARVE*, J. Phys. Chem. 61, 1232 (1957). ts) K. JABLCZYNSKI,Z. Anorg. Chem. 60, 38 (1908). ~9~C. WAGNER,Z. Anorg. Chem. 168, 279 (1928).
Study of the quinquevalent chromium compounds by ESR and optical spectra
935
preceded each spectrum, the kylstron frequency being kept constant throughout a series of measurements. The observations of the polycrystalline ESR were carried out either at room temperature for the solid material or at the liquid nitrogen temperature for the solution. The concentration of most of the solution was ca. 10-~ ~ 10-3 M. When acetic acid was used as solvent for CrOC13"RC1 the signal looked like some superposition of more than one spectrum and there was usually remarkable decrease in signal intensity. Normal line shape and intensity were recovered by passing the dry HC1 into the solution.
Optical spectra The visible absorption in solution and the infra-red absorption in KBr press were measured by Hitachi Co. model EPS II spectrophotometer and Japan Spectroscopic Manufacturing Co. model DS-401G grating infra-red spectrophotometer, respectively. Dried acetic acid saturated with HC1 gas, or nitrobenzene was used as solvent. RESULTS CrOC13RCI, K 2 C r O C I 5 The E S R spectra o f these complexes (R = pyridinium, q u i n o l i n i u m o r t e t r a m e t h y l a m m o n i u m ion) in s o l u t i o n at r o o m t e m p e r a t u r e are virtually all identical in their g-values, line widths a n d the average hyperfine splittings due to 53Cr (the n a t u r a l a b u n d a n c e = 9.55 p e r cent, the n u c l e a r spin n u m b e r I = ~), as s u m m a r i z e d in T a b l e 1. I n Fig. 1 is shown a r e p r o d u c t i o n o f a typical s o l u t i o n spectrum,, for p y r i d i n i u m complex. The following features are w o r t h y to note. TABLE 1 .--g-VALUES, LINE WIDTHS AND AVERAGE HYPERFINE-SPLITTINGS OF C r O C I a R C 1 AND K z C r O C l s IN SOLUTION AT ROOM TEMPERATURE
g (Solution)t
Line width (G)** AH. . . . s~ope
Av. hfs (G)**
K=CrOC1/ CrORC14: R = pyridinium
1.9877
2.8"
19.7
1.9877
19.9
R = quinolinium
1"9880
R = tetramethylammonium
1.9875
2.8* 2.1:~ 2-6* 2.0++ 2.7* 1'9~
Sample
19'9 19.8
* in glacial acetic acid; :~ In nitrobenzene. 1"Accurate to ca. -4-0.0003; ** Accurate to ca. q-0-1 G. First, the observed E S R lines are all very narrow, even n a r r o w e r t h a n in the v a n a d y l ion solutions o f a b o u t the same c o n c e n t r a t i o n as in the present study. (1°) I n general, the E S R line width is k n o w n to be affected b y m a n y c o m p l i c a t e d factors, b u t it m a y be d e d u c e d f r o m the a b o v e results that the electrostatic field s u r r o u n d i n g the Cr(V) ion is strongly p e r t u r b e d f r o m the cubic s y m m e t r y , since, otherwise, a low lying excited level m a y cause a short spin-lattice relaxation time a n d m a y result in a v e r y b r o a d line as, for example, in the Ti 3÷ alum. (3) The r e s o l u t i o n o f the two inner c o m p o n e n t s o f the 5ZCr hyperfine structure is p a r t l y d i s t u r b e d b y the s u p e r p o s i t i o n on the m a i n line d u e to the a b u n d a n t 52Cr (lo) R. N. ROGERSand G. E.
PAKE,
J. Chem. Phys. 33, 1107 (1960).
936
H. KON
I
5.7 I
Gouss
FIG. 1.---A representative ESR absorption curve of CrOC13'RC1 in solution
at room temperature (R = pyridinium ion). The solvent is the acetic acid saturated with HC1 gas. complex. (The situation is better in the nitro-benzene solution where the lines are narrower). Nevertheless, it can be seen that there is little variation of the line width of the individual hyperfine component with the nuclear quantum number Iz. Such variation of the line width has been observed in several complexes so far studied (as well as in the cases to be discussed in the next section), and the origin was first explained by MCCONNELL(11). Recently, ROGERS and PAKE(1°) formulated the line width as a polynomial in Iz, based on the general theory of KWELSON~I~): 1/T~ ----*rx/(3 ) (al + a2Iz + a3I~2), where
aI
~---
1-c {(7/45)(A~H0) 2 + 63 b2/16} + K,
as ---- --%{(7/15) b AVHo), a 3 = % {be/lO), and A v = (fl/h)(g, -- g . ), b = (2/3)(A, -- A.).
H o is the external magnetic field strength, % the correlation time and K is a constant to take into account all relaxation mechanisms not sensitive to the nuclear orientation. The above formula was shown to explain the line width variation in VO 2+ aq. solution successfully. Thus under ordinary conditions the variation of the hyperfine line width with Iz is governed by the two parameters AV and b, the anisotropies of g- and the hyperfine interaction tensors, respectively. Since the anisotropy in g-tensor of the complexes under discussion estimated from the spectrum of the frozen solution of CrOC1U (gll = 2"00 8, g , = 1"974, vide infra), Ag = 0.034, is not particularly smaller than other cases where the variation of the hyperfine line width is remarkable (for ex., in vanadyl porphyrins, ~aS) Ag ----- gH - - g - = 0.042), the apparent absence of the tm H. M. McCorct,mLL,d. Chem. Phys. 25, 709 (1956). tx2~O. KIVELSONJ. Chem. Phys. 33, 1094 (1960). ~x3~E. M. ROBERTS,W. S. KOSK1and W. S. CAUGH~Y,3". Chem. Phys. 34, 591 (1961).
Study of the quinquevalent chromium compounds by ESR and optical spectra
937
variation in hyperfine line width in the present case may be explained by an approximately isotropic hyperfine interaction tensor. The average hyperfine splitting is larger than in Cr + cyanide complex ~14~(13.8 G) in which the unpaired spin is considered to be in 3d~ orbital as in the present complexes. The fact that all these compounds show the ESR patterns which are identical within the experimental accuracy, indicates the existence in solution of the same paramagnetic species c o m m o n to the systems. The frozen solutions (*)(77°K) also exhibit identical ESR patterns such as the one shown in Fig. 2, from which one may
I
Flo. 2.---A representative ESR absorption curve of CrOC13.RC1 in frozen solution at 77°K (R = pyridinium ion). The solvent is the acetic acid saturated with HC1 gas. Field strengths are shown in gauss. conclude that the paramagnetic species has an axial (or nearly axial) symmetry in solution. Thus one reasonable structure of the common paramagnetic species may be assumed as, Cl
0
La
1 \c,J. Cl
-
The estimated values of gll and g . are ~z~ glt=2"00 8
and
from which go = (½)(gll + 2 g . ) = 1"98 5 in
g i ---- 1"974 approximate
agreement
with
the
g-values observed in solution (1.9875-1.9880, Table 1). The estimated values are subject to a small correction for the unresolved UCr hyperfine structure which is only barely discernible under the conditions of the present study; also the estimation is based upon the assumption of the 6-function * Acetic acid saturated with HC1 was used as solvent. When nitrobenzene was used as solvent, the observation was disturbed by the remarkable saturation broadening. ~14~I. BERr~ALand S. E. HARRISON,J. Chem. Phys. 34, 102 (1961). ~15~R. H. SANOS,Phys. Rev. 99, 1222 (1955). For the more recent and rigorous analysis of the powder ESR spectra, see for ex., Reference (4b), and H. R. G~RSMANNand J. D. SWALEN,J. Chem. Phys. 36, 3221 (1962). 3
938
H. KON
for the crystalline line shape, and the Gaussian broadening must be taken into account, implying little exchange interactions between the molecules, since the solution is sufficiently dilute (10-3-10 -3 M). The same applies to the estimation of g-values from the frozen solution spectra in the next section. On the other hand, the ESR patterns of the crystalline powder diluted with dry KC1 powder are different depending on the organic base used, as shown in Fig. 3.
3345 3332_//~/Tetramethyl-ammonium //
f
\
\Py~diniurn
s %Je \3382 3.--Polycrystalline ESR patterns of pyridinium, quinolinium and tetramethylammonium complex at room temperature. Field strengths are shown in gauss. The relative positions of the three curves are arbitrary. FIG.
This can be explained as the result of the considerably strong interactions between the molecules, and the apparent g-values estimated and listed in Table 2 should be taken as only approximate. TABLE 2.--APPARENT/f-VALUES OF POLYCRYSTALLINEPOWDER* Sample
Pyridinium complex Quinolinium complex Tetramethylammonium complex
gll
/f.I.
go = (gll 4- 2g.t)/3
2.000 1"991
1"978 1.991
1"985 1.991
1"989
1"989
1'989
* Uncertainty in measurement ca. 4-0.001. In harmony with the above observations, the visible absorption spectra of nitrobenzene solution at room temperature are also almost identical in the four systems. There are at least three absorption bands with the peaks at 18,000, 22,400 (sh) and 23,500 cm -1 as shown in Fig. 4. The results of the infra-red absorption measurements were summarized schematically in Fig. 5. Each absorption pattern of pyridinium-, quinolinium- and tetramethyl ammonium chloride is contrasted with that of the respective Cr complex. One can easily see there, that the absorption of the complex (except for K~CrOC15) is composed of the slightly shifted lines from the base itself plus a few new absorptions which appear in the range 870--1020 cm -1. This would mean that in the crystals the bases exist in the form of pyridinium, quinolinium and tetramethylammonium
Study of the quinquevalent chromium compounds by ESR and optical spectra
939
2O
4-
I.C
I
400
I 500
I
I 600
i
I 700
I
I 800
Wove Lengi'h(ml~) FIG. 4.--A visible absorption spectrum of CrOCI3RCI in
nitrobenzene solution (R = quinolinium ion). ,
K2CrOCI5
I[,
I I[
II
Ill
I.i
I II
, I
Ill
II,II
I i I Ill J l I ill
I I OHc' Pyridinium l I complex
. I
I I, ,i ,,,, ,, I h ,~ ,,, I I , II
,II,, Quinolinium OQ l Il[
complex N(CH3)*CI "EM.A , complex i
1600 1500 1400
1500 1200
I1'00
I000
900
8C)0
700
coo0(cm-I )
FIG. 5.--Infra-red absorption spectra of K~CrOCI~, and CrOC13'RC1 (R = pyridinium, quinolinium and tetramethylammonium ion). The lengths of the lines are approximately proportional to the observed absorption intensity.
ion, respectively, without being perturbed seriously. The 950 cm -1 band observed in K2CrOC15 may be assigned to the Cr-O stretching vibration. This is comparable to the V-O stretching frequencies in VOCla (1035 cm -1) and in VO-etioporphyrin-I
(995 cm-1) (16).
Miscellaneous quinquevalent Cr systems As was mentioned in the previous section, a variety of narrow ESR signals are obtained as the result of the reaction of K2Cr207 with various acids such as trifluoro acetic, oxalic-, lactic- or citric acid and of the reaction of CrO 3 with acetic acid. The signal shows that the paramagnetic species are unstable and the life time varies (a6) j. G. ERDMAN, V. G. RAMSAY,]'q. W. KALENDAand W. M. E. HANSON, J. Amer. Chem. Soc.
5844 (1956).
78,
940
H. KoN
considerably with the system from several minutes to a week. Unfortunately, the attempts to isolate the paramagnetic compounds have been unsuccessful so far and the composition remains unknown. However, it seems valid to say that the paramagnetic species are some unstable reduction products of K2Cr20 7 (or CrOa) by the acids and are stabilized by the complex formation with the acids or some oxidation products of the adds.
Ha
FIG.
6.--ESR absorption curve of KsCrzOT--CF3COOHsystem at room temperature.
,5,7, Gauss
FIG. 7.--ESR absorption curve of K2Cr~OT--CFsCOOH system frozen at 77°K. The field strengths are indicated in gauss.
8.--ESR absorption curve of KzCrsO7 --oxalic acid system at room temperature. (Solvent = acetic acid).
FIG.
The results of ESR observation, especially the fact that all observed lines are very narrow, are best interpreted by assuming the complexes of some quinquevalent Cr oxyions, such as CrO z+ or CrO2 +. Considering that the possible complexing agents are likely to be mononegative, bi- (or mono-) dentate ions, CrO2 + seems more plausible. (l) KzCrzO 7 in CF3COOH; Oxalic acid plus K2Cr207 in glacial acetic acid; CrO 3 in glacial acetic acid. The ESR patterns of the solutions at room temperature and at 77°K are shown in Figs. 6-11. The general aspects common to these systems can be summarized as follows. The line width of the hyperfine component increases monotonically from low to high field. This indicates, according to the theory by McCoNNELL(u) and ROGERS etal., ta°) that the hyperfine interaction tensor is fairly anisotropic. The pattern of the
Study of the quinquevalent chromium compounds by ESR and optical spectra
J
941
FIG. 9.--ESR absorption curve of KzCr2OT-oxalic acid system frozen at 77°K. (Solvent = acetic acid). The field strengths are in gauss.
:5303
5529~
Fie. 10.--ESR absorption curve of CrO3-acetic acid system at room tempearture. ~5.7° Gouss
absorption curve of CrO3-acetic acid system frozen at 77°K. Field strengths are in gauss. FIG. 1 1 . - - E S R
I
5319
frozen solution shows the characteristic feature of the crystalline field of the axial symmetry, from which one can estimate the values ofgj~l and g± as tabulated in Table 3. In relation to K2Cr207-CFaCOOH system, the following observation may be worthy to note: by passing HC1 gas into the solution, the ESR signal disappears at an early stage and a doublet with very much reduced intensity appears at a lower field. On passing HC1 further, one component of the doublet grows up, until eventually the whole spectrum becomes identical with the one due to CrOC14- discussed in the preceding section. I f one passes dry N 2 gas to drive out the HC1 from the solution, the original spectrum characteristic of KzCr~O7-CFaCOOH system can be recovered. Thus a reversible conversion between two types of complexes seems to be taking place. (2) Lactic, citric or tartaric acidplus K2fr~O 7 in glacial acetic acid. These systems show more or less similar absorptions, of which the ones for citric acid are reproduced
942
H. KON TABLE
3.--g-VALUESOF THE FROZEN SOLUTION (77°K)*
System CrOa in Acct. acid K2CrzO7 in CFsCOOH K2Cr207 + (COOH)~ in Acetic acid
gll
g'.I.
1'959 1"961 1'962
1"970 1.977 1"978
• Uncertainty in measurement ca. 4- 0.001. in Figs. 12 and 13. There are two features immediately noticeable in these results; the line width of the hyperfine component shows a minimum at the second component from the low field end, and the line shapes of the frozen solutions are different from those observed above and appears to be best interpreted as resulting from the crystalline field with rhombic symmetry. The g-values along the axes can be estimated by the extension (17) of the method used in the axial field, and are given in Table 4. In Table 5 are summarized the g-values, line widths and the average hyperfine splittings of the solutions at room temperature. DISCUSSION Examining the g-values obtained here (Table 3) and the ones for the analogous VO-porphyrin complexes(In, is) (gtl = 1.947, g . = 1.987), one will notice that g . is in general greater than gll, but the complexes of the type CROCI4- appear to be
15-7j No
Gauss
FIG. 12.--ESR absorption curve of K2CraOT-citric acid system at room temperature. (Solvent = acetic acid.)
FIG. 13.--ESR absorption curve of KzCr2OT--citric acid system frozen at 77°K. (Solvent = acetic acid). Field strengths are shown in gauss.
TABLE 4.--g-VALUES OF THE FROZEN SOLUTIONS (77°K)*
System K~Cr207 + Lactic acid in Acetic acid K2Cr~O7 + Citric acid in Acetic acid
gl
g2
g8
1.975
1"979
1-968
1-973
1"978
1.985
* Uncertainty in measurement ca. -4-0.001
~1~ F. K. K~rEtraOnL, 3". Chem. Phys. 33, 1074 (1960). c18)D. E. O'R~ILLV,J. Chem. Phys. 29, 1188 (1958).
Study of the quinquevalent chromium compounds by ESR and optical spectra TABLE
943
5.--g-VALUES,LINE WIDTHS AND AVERAGE HYPERFINE SPLITTINGS AT ROOM TEMPERATURE*
System
Line width (G) Av. hf splitting AHmax.slope (G)
g
CrO3 + Acetic acid K~Cr207 ÷ CF3COOH K2Cr207 + (COOH)2 K2Cr207 + Lactic acid K2Cr207 + Citric acid
1"9652 1-9710 1.9779 1"9780 1'9781
2-2 1"6 1-5 1-5 1"0
21.0 22'0 18'4 18"6 18"4
* Accuracy is the same as in Table 1 ; Solvent = Acetic acid. exceptions. In general, if the electric field surrounding the Cr ion is assumed to have a tetragonal symmetry along the z-axis (see Fig. 14) the g-values can be calculated by the perturbation theory, taking the spin orbit interaction (2L. S) into account: g~l = 2.0023 (1 -- 42/AE~)
and
g . = 2.0023 (1 -- ;t/AE~),
where AE~ (AE=) is the energy separation between the lowest orbital (3dxv) and the excited orbital whose wave function has its maximum in (out of) the xy-plane. Given
©
GI, CIr.#/" FI~.
C
14.--The structural unit CrOC14 to show the numbering of C1 ions.
the g-values and the excitation energies, the spin orbit interaction constant would be calculated by the equations. Take, for example, the case of CrOC14-, where g± = 1.974. If the first absorption band at 18,000 cm -1 corresponds to the vertical excitation, then 2 is calculated to be 230 cm -1. * However, if this value is used in the equation for gll, taking into account the fact that the observed gll is practically equal to the free spin value, then AE~ is found to be much higher than seems likely. Thus, the ionic model without taking into account the covalency between the Cr ion and the ligands seems to fail to interpret the result in this case. If the molecular orbitals are formed within the hypothetical structural unit CrO 3+, using the three 2p-orbitals of the oxygen atom (in a more rigorous treatment, s-p hybridization should be taken into account) and the 3d-orbitals of Cr, the situation would not be improved, because it can be shown by the group theory that both d~_~2 and d~ can not form a molecular orbital with the oxygen 2p orbitals and, therefore, the expression for gll remains unchanged. However, the observed g-values * This is considerably lower than the value by MOORE(383 c m - t ) quoted in Reference (4a).
944
H. KON
can be better accounted for, if the molecular orbital treatment is extended to the CI- ions, and if certain conditions are fulfilled by the bonding parameters. Thus twenty molecular orbitals are constructed from five 3d orbitals of Cr, as the bases for the irreducible representations of the symmetry group C4~. They are 4A 1 + A 2 + 3B1 + 2B2 + 5E Of the thirty-one electrons in all, thirty p electrons from the ligands are allotted in the following bonding orbitals: 3A1 + A2 + 2B1 + B z + 4E Thus the discussion concerns only the remaining//2 antibonding orbital which is occupied by the unpaired d-electron, and the excited//1 and E-orbitals with which the B~ orbital is coupled through the angular momentum operators. 4(BO =/sd~_~, + (y/2)(Xl -- y~ -- x~ + Y3, 41(E) =
~d~o - - ~ ' p ~
- - 6" (z~ - - z , ) ,
42(e) = --(~d,x "q- (~'JOx "q- ~" (gl -- g3), q~(B=) = yd~ -- (y'/2)(y~ + Xz --Ya -- x4), where d and p designate the 3d-orbitals of Cr ion and 2p-orbitals of O atom, respectively, and xi, Yi and z i stand for 3p,, 3pu and 3p, orbitals on the i-th CI atom, the numbering being shown in Fig. 14. Using these molecular orbitals, the g-values can be calculated as, g,, = 2.0023 [1 -- (42/AE~){fly + (/5y' -- 2/5'y) S --/5'y'/2}21, g~ = 2.0023 [1 -- (2/AE.){y~ + y'~"}~], where S is the overlap integral between the central d~2_vs and 3p, (or 3p~) on CI 1 (or 2), and where the hydrogen-like atomic orbitals are adopted. /5' and y' are given by/5' = / 5 S + %/(1 --/53) and y' = %/(1 -- y2), respectively. The overlap integrals between d,v and ligand orbitals are neglected. Setting, for instance,/5 = 0.8, y = 0.9 and S = 0.2, g, is calculated as, g, = 2.0023 (1 -- 0.34
2/AE,).
The quantitative aspect of the result should not be taken too literally because of the simplifications adopted in the treatment. In particular, in order to get a more quantitative result, one must use, instead of the simple p- and d-orbitals, the xp hybridized ligand orbitals and the tetragonally hybridized (for ex., dapz or d2sp2) orbitals of the Cr ion. The present result shows that the molecular orbital formation brings the predicted AE~ value to the reasonable range of magnitude, and is indicative of the nature of the bonding in this complex. Thus one can understand the observed g-values of CrOC14- complex by assuming considerable amount of covalency between Cr and C1. A similar explanation would be applicable to VO-bisacetylacetonate where gtt and g± are 2.02 and 1.95, respectively. ~x°)
Acknowledgment--Theauthor is indebted to T. Oucm for his help in the infra-red absorption measurements. t~ R. D. FELTnAM. Thesis (University of California, 1957).
STUDY OF THE QUINQUEVALENT CHROMIUM COMPOUNDS BY ESR AND OPTICAL SPECTRA H. KON NAIG Nuclear Research Laboratory, Kawasaki, Japan (Received 6 November 1962; in revised form 6 February 1963)
Abstract--Quinquevalent chromium complexes of the type CrOCla ÷ 1(or 2) RC1, where R = pyridinium, quinolinium, tetramethylammonium (or potassium) ion, were prepared and their electron spin resonance absorptions were observed in solution at room temperature and at 77°K, as well as in polycrystalline form. The results, together with those of the optical absorption spectra, indicate that these complexes have a common paramagnetic structural unit CrOCl~-. The observed values of fill and g.L of this species were explained on the basis of the molecular orbital theory. The transient, narrow ESR lines with similar feature were also observed during the reduction of K2Cr20~ (or CrOs) with a variety of acids. They were interpreted as due to some Cr tv~oxyion complexes. IN the previous communication tl) the author postulated the existence of the quinquevalent chromium compounds in CrO3-(or K2Cr2Ov-)conc.H2SO 4 system to explain the narrow ESR (electron spin resonance) absorption lines which can easily be observed at room temperature and which consist of four narrow lines with uneven intensities, their line widths being from about 1 to 5 G. To the best of the authors knowledge, there are not many ESR observations reported of quinquevalent chromium compounds. CARRINGTON et al. first observed ESR signal of Cr(V)O~ 3-. In remarkable contrast to the case of CrOa-conc.H2SO 4 system, however, the ESR line width of CrO43- is temperature dependent, broader at higher temperature, and could not be observed above T = 20°K t2J. This is the behaviour to be expected not only for CrO43- but also for other transition metal ions in general with single unpaired d-electron, provided they are placed in the crystalline field with the cubic symmetry or with the nearly cubic symmetry, which, furthermore, is not so strong as to lift the degeneracy of the d-orbitals sufficientlyt3k More recently, SWALEN and IBERS reported the ESR study of peroxychromate ion, Cr(V)O83-, in polycrystalline form at 20°C. This ion has D2d symmetry, and the ESR line width AH1/2 was determined by the numerical analysis to be 23.5 G. t4) It would be of interest to see whether there are any other compounds of the Cr ion with single unpaired d-electron, which show the narrow ESR lines such as those observed in CrO3-conc.H2SO 4 system (ca. 1-5 G). For this purpose, the following complexes of Cr(V) were prepared, and their ESR and optical absorption spectra were observed. K2Cr(V)OCI 5 and
Cr(V)OCIs-RC1,
,1~ H. KON, Bull. Chem. Soc. Japan, 35, 2054 (1962). t2~A. CARRINGTON, D. J. E. INGRAM,D. SCHONLANDand M. C. R. SYMONS, J. Chem. Soc. 4710 (1956). is) B. BLEANEYand K. W. H. STEVENS,Rep. Prog. Phys. 16, 141 (1953). t4~ (a) J. D SWALENand J. A. IBERS, J. Chem. Phys. 37, 17 (1962); (b) J. A. IBERSand J. D. SWALEN, Phys. Rev. 127, 1914 (1962). 933
934
H. KoN
where R is pyridinium, quinolinium or tetramethylammonium ion. These compounds were first synthesized by WEINLAND et al./5,6~ who ascertained that Cr is in the quinquevalent state. There has been little information available concerning the structure of these molecules, but these complexes may be considered as the analogues of the many, fairly well studied vanadyl complexes, where the crystalline field symmetry surrounding the V ion is shown to have an axial component which is strong enough to make the lowest excited orbital sufficiently high above the ground orbital, thus making the ESR lines easily observable at room temperature, tT) One of the purposes of this paper is to present the detailed results of the ESR, visible and infra-red absorption measurements of the complexes in solution as well as in polycrystalline form. Deductions will be made in relation to the nature of the bonds from the standpoint of the ligand field and molecular orbital theory. It was suggested by JABLCZYNSKIand several other workers that during the course of the reduction of CrO 3 or K2Cr207 by the acids such as formic, oxalic and so on, Cr passes through an intermediate valence state between Cr(VI) and Cr(III), and the results of a series of kinetic studies of these reactions are best understood by assuming the quinquevalent state for Cr. ts,9) In the present report, the above assumption will also be proved by the direct observation of ESR signals, which show the feature similar to the K2Cr(V)OC1s and Cr(V)OC13RC1. EXPERIMENTAL Chemical procedures
CrOC13RC1 type compounds were prepared following the method by WErNLANDet al. t5"e~ About 100 ml of a dilute acetic acid solution (ca. 10-8 M) of CrO3 was reduced by passing dry HC1 gas through the solution. The calculated amount of the base, such as pyridine, quinoline or tetramethylammonium chloride was dissolved in the least possible amount of acetic acid saturated with dry HCI gas. By adding the latter solution to the reduced CrO3 solution, the fine lustrous crystalline precipitate was obtained. The colour varied from reddish to dark brown according to the base used. It was found that in order to obtain the homogeneous crystalline material, the reduction by HC1 gas must be complete before adding the solution of the base; otherwise the precipitate was the mixture of more than one complex of various colours. The reduction was best monitored by observing the ESR signals at different stages of the reaction. The pattern near the end of the reaction is free from the complication due to by-products. Samples were dried and kept over K O H or conc. H2SO, in vacuum. The complexes are all very sensitive to the humidity and, therefore, every precaution was taken to prevent the decomposition during the handling. The yield was very good for CrOC13RC1, whereas only a very small amount of cyrstalline material was obtained for K~CrOCIs. To observe the transient ESR signals of Cr(V) caused by the reduction with organic acids other than acetic acid, a portion of the dilute stock solution of KzCrzO7 in glacial acetic acid was mixed with the acid with constant stirring until the colour of the solution became dark brown. CrO3 gave rise to the ESR signal simply by dissolving it in the acetic acid. ESR measurement
All the measurements were carried out with Varian Associates model V-4500 spectrometer with 100 kc/s field modulation. The field strength was calibrated by measuring the proton resonance frequency with the Hewlett-Packard model 524C electronic counter combined with the 525A frequency converter. To determine g-values, the measurement of the resonance field for DPPH (g = 2'0036) 16) R. F. WEINLANDand W. FRIDRICH, Ber. Dtsch. Chem. Ges. 38, 3784 (1905). tt~ R. F. WEINLANDand M. FRIEDEP,.ER,Bet. Dtsch Chem Ges. 39, 4042 (1906); 40, 2090 (1907). tT~ B. R. McGARVE*, J. Phys. Chem. 61, 1232 (1957). ts) K. JABLCZYNSKI,Z. Anorg. Chem. 60, 38 (1908). ~9~C. WAGNER,Z. Anorg. Chem. 168, 279 (1928).
Study of the quinquevalent chromium compounds by ESR and optical spectra
935
preceded each spectrum, the kylstron frequency being kept constant throughout a series of measurements. The observations of the polycrystalline ESR were carried out either at room temperature for the solid material or at the liquid nitrogen temperature for the solution. The concentration of most of the solution was ca. 10-~ ~ 10-3 M. When acetic acid was used as solvent for CrOC13"RC1 the signal looked like some superposition of more than one spectrum and there was usually remarkable decrease in signal intensity. Normal line shape and intensity were recovered by passing the dry HC1 into the solution.
Optical spectra The visible absorption in solution and the infra-red absorption in KBr press were measured by Hitachi Co. model EPS II spectrophotometer and Japan Spectroscopic Manufacturing Co. model DS-401G grating infra-red spectrophotometer, respectively. Dried acetic acid saturated with HC1 gas, or nitrobenzene was used as solvent. RESULTS CrOC13RCI, K 2 C r O C I 5 The E S R spectra o f these complexes (R = pyridinium, q u i n o l i n i u m o r t e t r a m e t h y l a m m o n i u m ion) in s o l u t i o n at r o o m t e m p e r a t u r e are virtually all identical in their g-values, line widths a n d the average hyperfine splittings due to 53Cr (the n a t u r a l a b u n d a n c e = 9.55 p e r cent, the n u c l e a r spin n u m b e r I = ~), as s u m m a r i z e d in T a b l e 1. I n Fig. 1 is shown a r e p r o d u c t i o n o f a typical s o l u t i o n spectrum,, for p y r i d i n i u m complex. The following features are w o r t h y to note. TABLE 1 .--g-VALUES, LINE WIDTHS AND AVERAGE HYPERFINE-SPLITTINGS OF C r O C I a R C 1 AND K z C r O C l s IN SOLUTION AT ROOM TEMPERATURE
g (Solution)t
Line width (G)** AH. . . . s~ope
Av. hfs (G)**
K=CrOC1/ CrORC14: R = pyridinium
1.9877
2.8"
19.7
1.9877
19.9
R = quinolinium
1"9880
R = tetramethylammonium
1.9875
2.8* 2.1:~ 2-6* 2.0++ 2.7* 1'9~
Sample
19'9 19.8
* in glacial acetic acid; :~ In nitrobenzene. 1"Accurate to ca. -4-0.0003; ** Accurate to ca. q-0-1 G. First, the observed E S R lines are all very narrow, even n a r r o w e r t h a n in the v a n a d y l ion solutions o f a b o u t the same c o n c e n t r a t i o n as in the present study. (1°) I n general, the E S R line width is k n o w n to be affected b y m a n y c o m p l i c a t e d factors, b u t it m a y be d e d u c e d f r o m the a b o v e results that the electrostatic field s u r r o u n d i n g the Cr(V) ion is strongly p e r t u r b e d f r o m the cubic s y m m e t r y , since, otherwise, a low lying excited level m a y cause a short spin-lattice relaxation time a n d m a y result in a v e r y b r o a d line as, for example, in the Ti 3÷ alum. (3) The r e s o l u t i o n o f the two inner c o m p o n e n t s o f the 5ZCr hyperfine structure is p a r t l y d i s t u r b e d b y the s u p e r p o s i t i o n on the m a i n line d u e to the a b u n d a n t 52Cr (lo) R. N. ROGERSand G. E.
PAKE,
J. Chem. Phys. 33, 1107 (1960).
936
H. KON
I
5.7 I
Gouss
FIG. 1.---A representative ESR absorption curve of CrOC13'RC1 in solution
at room temperature (R = pyridinium ion). The solvent is the acetic acid saturated with HC1 gas. complex. (The situation is better in the nitro-benzene solution where the lines are narrower). Nevertheless, it can be seen that there is little variation of the line width of the individual hyperfine component with the nuclear quantum number Iz. Such variation of the line width has been observed in several complexes so far studied (as well as in the cases to be discussed in the next section), and the origin was first explained by MCCONNELL(11). Recently, ROGERS and PAKE(1°) formulated the line width as a polynomial in Iz, based on the general theory of KWELSON~I~): 1/T~ ----*rx/(3 ) (al + a2Iz + a3I~2), where
aI
~---
1-c {(7/45)(A~H0) 2 + 63 b2/16} + K,
as ---- --%{(7/15) b AVHo), a 3 = % {be/lO), and A v = (fl/h)(g, -- g . ), b = (2/3)(A, -- A.).
H o is the external magnetic field strength, % the correlation time and K is a constant to take into account all relaxation mechanisms not sensitive to the nuclear orientation. The above formula was shown to explain the line width variation in VO 2+ aq. solution successfully. Thus under ordinary conditions the variation of the hyperfine line width with Iz is governed by the two parameters AV and b, the anisotropies of g- and the hyperfine interaction tensors, respectively. Since the anisotropy in g-tensor of the complexes under discussion estimated from the spectrum of the frozen solution of CrOC1U (gll = 2"00 8, g , = 1"974, vide infra), Ag = 0.034, is not particularly smaller than other cases where the variation of the hyperfine line width is remarkable (for ex., in vanadyl porphyrins, ~aS) Ag ----- gH - - g - = 0.042), the apparent absence of the tm H. M. McCorct,mLL,d. Chem. Phys. 25, 709 (1956). tx2~O. KIVELSONJ. Chem. Phys. 33, 1094 (1960). ~x3~E. M. ROBERTS,W. S. KOSK1and W. S. CAUGH~Y,3". Chem. Phys. 34, 591 (1961).
Study of the quinquevalent chromium compounds by ESR and optical spectra
937
variation in hyperfine line width in the present case may be explained by an approximately isotropic hyperfine interaction tensor. The average hyperfine splitting is larger than in Cr + cyanide complex ~14~(13.8 G) in which the unpaired spin is considered to be in 3d~ orbital as in the present complexes. The fact that all these compounds show the ESR patterns which are identical within the experimental accuracy, indicates the existence in solution of the same paramagnetic species c o m m o n to the systems. The frozen solutions (*)(77°K) also exhibit identical ESR patterns such as the one shown in Fig. 2, from which one may
I
Flo. 2.---A representative ESR absorption curve of CrOC13.RC1 in frozen solution at 77°K (R = pyridinium ion). The solvent is the acetic acid saturated with HC1 gas. Field strengths are shown in gauss. conclude that the paramagnetic species has an axial (or nearly axial) symmetry in solution. Thus one reasonable structure of the common paramagnetic species may be assumed as, Cl
0
La
1 \c,J. Cl
-
The estimated values of gll and g . are ~z~ glt=2"00 8
and
from which go = (½)(gll + 2 g . ) = 1"98 5 in
g i ---- 1"974 approximate
agreement
with
the
g-values observed in solution (1.9875-1.9880, Table 1). The estimated values are subject to a small correction for the unresolved UCr hyperfine structure which is only barely discernible under the conditions of the present study; also the estimation is based upon the assumption of the 6-function * Acetic acid saturated with HC1 was used as solvent. When nitrobenzene was used as solvent, the observation was disturbed by the remarkable saturation broadening. ~14~I. BERr~ALand S. E. HARRISON,J. Chem. Phys. 34, 102 (1961). ~15~R. H. SANOS,Phys. Rev. 99, 1222 (1955). For the more recent and rigorous analysis of the powder ESR spectra, see for ex., Reference (4b), and H. R. G~RSMANNand J. D. SWALEN,J. Chem. Phys. 36, 3221 (1962). 3
938
H. KON
for the crystalline line shape, and the Gaussian broadening must be taken into account, implying little exchange interactions between the molecules, since the solution is sufficiently dilute (10-3-10 -3 M). The same applies to the estimation of g-values from the frozen solution spectra in the next section. On the other hand, the ESR patterns of the crystalline powder diluted with dry KC1 powder are different depending on the organic base used, as shown in Fig. 3.
3345 3332_//~/Tetramethyl-ammonium //
f
\
\Py~diniurn
s %Je \3382 3.--Polycrystalline ESR patterns of pyridinium, quinolinium and tetramethylammonium complex at room temperature. Field strengths are shown in gauss. The relative positions of the three curves are arbitrary. FIG.
This can be explained as the result of the considerably strong interactions between the molecules, and the apparent g-values estimated and listed in Table 2 should be taken as only approximate. TABLE 2.--APPARENT/f-VALUES OF POLYCRYSTALLINEPOWDER* Sample
Pyridinium complex Quinolinium complex Tetramethylammonium complex
gll
/f.I.
go = (gll 4- 2g.t)/3
2.000 1"991
1"978 1.991
1"985 1.991
1"989
1"989
1'989
* Uncertainty in measurement ca. 4-0.001. In harmony with the above observations, the visible absorption spectra of nitrobenzene solution at room temperature are also almost identical in the four systems. There are at least three absorption bands with the peaks at 18,000, 22,400 (sh) and 23,500 cm -1 as shown in Fig. 4. The results of the infra-red absorption measurements were summarized schematically in Fig. 5. Each absorption pattern of pyridinium-, quinolinium- and tetramethyl ammonium chloride is contrasted with that of the respective Cr complex. One can easily see there, that the absorption of the complex (except for K~CrOC15) is composed of the slightly shifted lines from the base itself plus a few new absorptions which appear in the range 870--1020 cm -1. This would mean that in the crystals the bases exist in the form of pyridinium, quinolinium and tetramethylammonium
Study of the quinquevalent chromium compounds by ESR and optical spectra
939
2O
4-
I.C
I
400
I 500
I
I 600
i
I 700
I
I 800
Wove Lengi'h(ml~) FIG. 4.--A visible absorption spectrum of CrOCI3RCI in
nitrobenzene solution (R = quinolinium ion). ,
K2CrOCI5
I[,
I I[
II
Ill
I.i
I II
, I
Ill
II,II
I i I Ill J l I ill
I I OHc' Pyridinium l I complex
. I
I I, ,i ,,,, ,, I h ,~ ,,, I I , II
,II,, Quinolinium OQ l Il[
complex N(CH3)*CI "EM.A , complex i
1600 1500 1400
1500 1200
I1'00
I000
900
8C)0
700
coo0(cm-I )
FIG. 5.--Infra-red absorption spectra of K~CrOCI~, and CrOC13'RC1 (R = pyridinium, quinolinium and tetramethylammonium ion). The lengths of the lines are approximately proportional to the observed absorption intensity.
ion, respectively, without being perturbed seriously. The 950 cm -1 band observed in K2CrOC15 may be assigned to the Cr-O stretching vibration. This is comparable to the V-O stretching frequencies in VOCla (1035 cm -1) and in VO-etioporphyrin-I
(995 cm-1) (16).
Miscellaneous quinquevalent Cr systems As was mentioned in the previous section, a variety of narrow ESR signals are obtained as the result of the reaction of K2Cr207 with various acids such as trifluoro acetic, oxalic-, lactic- or citric acid and of the reaction of CrO 3 with acetic acid. The signal shows that the paramagnetic species are unstable and the life time varies (a6) j. G. ERDMAN, V. G. RAMSAY,]'q. W. KALENDAand W. M. E. HANSON, J. Amer. Chem. Soc.
5844 (1956).
78,
940
H. KoN
considerably with the system from several minutes to a week. Unfortunately, the attempts to isolate the paramagnetic compounds have been unsuccessful so far and the composition remains unknown. However, it seems valid to say that the paramagnetic species are some unstable reduction products of K2Cr20 7 (or CrOa) by the acids and are stabilized by the complex formation with the acids or some oxidation products of the adds.
Ha
FIG.
6.--ESR absorption curve of KsCrzOT--CF3COOHsystem at room temperature.
,5,7, Gauss
FIG. 7.--ESR absorption curve of K2Cr~OT--CFsCOOH system frozen at 77°K. The field strengths are indicated in gauss.
8.--ESR absorption curve of KzCrsO7 --oxalic acid system at room temperature. (Solvent = acetic acid).
FIG.
The results of ESR observation, especially the fact that all observed lines are very narrow, are best interpreted by assuming the complexes of some quinquevalent Cr oxyions, such as CrO z+ or CrO2 +. Considering that the possible complexing agents are likely to be mononegative, bi- (or mono-) dentate ions, CrO2 + seems more plausible. (l) KzCrzO 7 in CF3COOH; Oxalic acid plus K2Cr207 in glacial acetic acid; CrO 3 in glacial acetic acid. The ESR patterns of the solutions at room temperature and at 77°K are shown in Figs. 6-11. The general aspects common to these systems can be summarized as follows. The line width of the hyperfine component increases monotonically from low to high field. This indicates, according to the theory by McCoNNELL(u) and ROGERS etal., ta°) that the hyperfine interaction tensor is fairly anisotropic. The pattern of the
Study of the quinquevalent chromium compounds by ESR and optical spectra
J
941
FIG. 9.--ESR absorption curve of KzCr2OT-oxalic acid system frozen at 77°K. (Solvent = acetic acid). The field strengths are in gauss.
:5303
5529~
Fie. 10.--ESR absorption curve of CrO3-acetic acid system at room tempearture. ~5.7° Gouss
absorption curve of CrO3-acetic acid system frozen at 77°K. Field strengths are in gauss. FIG. 1 1 . - - E S R
I
5319
frozen solution shows the characteristic feature of the crystalline field of the axial symmetry, from which one can estimate the values ofgj~l and g± as tabulated in Table 3. In relation to K2Cr207-CFaCOOH system, the following observation may be worthy to note: by passing HC1 gas into the solution, the ESR signal disappears at an early stage and a doublet with very much reduced intensity appears at a lower field. On passing HC1 further, one component of the doublet grows up, until eventually the whole spectrum becomes identical with the one due to CrOC14- discussed in the preceding section. I f one passes dry N 2 gas to drive out the HC1 from the solution, the original spectrum characteristic of KzCr~O7-CFaCOOH system can be recovered. Thus a reversible conversion between two types of complexes seems to be taking place. (2) Lactic, citric or tartaric acidplus K2fr~O 7 in glacial acetic acid. These systems show more or less similar absorptions, of which the ones for citric acid are reproduced
942
H. KON TABLE
3.--g-VALUESOF THE FROZEN SOLUTION (77°K)*
System CrOa in Acct. acid K2CrzO7 in CFsCOOH K2Cr207 + (COOH)~ in Acetic acid
gll
g'.I.
1'959 1"961 1'962
1"970 1.977 1"978
• Uncertainty in measurement ca. 4- 0.001. in Figs. 12 and 13. There are two features immediately noticeable in these results; the line width of the hyperfine component shows a minimum at the second component from the low field end, and the line shapes of the frozen solutions are different from those observed above and appears to be best interpreted as resulting from the crystalline field with rhombic symmetry. The g-values along the axes can be estimated by the extension (17) of the method used in the axial field, and are given in Table 4. In Table 5 are summarized the g-values, line widths and the average hyperfine splittings of the solutions at room temperature. DISCUSSION Examining the g-values obtained here (Table 3) and the ones for the analogous VO-porphyrin complexes(In, is) (gtl = 1.947, g . = 1.987), one will notice that g . is in general greater than gll, but the complexes of the type CROCI4- appear to be
15-7j No
Gauss
FIG. 12.--ESR absorption curve of K2CraOT-citric acid system at room temperature. (Solvent = acetic acid.)
FIG. 13.--ESR absorption curve of KzCr2OT--citric acid system frozen at 77°K. (Solvent = acetic acid). Field strengths are shown in gauss.
TABLE 4.--g-VALUES OF THE FROZEN SOLUTIONS (77°K)*
System K~Cr207 + Lactic acid in Acetic acid K2Cr~O7 + Citric acid in Acetic acid
gl
g2
g8
1.975
1"979
1-968
1-973
1"978
1.985
* Uncertainty in measurement ca. -4-0.001
~1~ F. K. K~rEtraOnL, 3". Chem. Phys. 33, 1074 (1960). c18)D. E. O'R~ILLV,J. Chem. Phys. 29, 1188 (1958).
Study of the quinquevalent chromium compounds by ESR and optical spectra TABLE
943
5.--g-VALUES,LINE WIDTHS AND AVERAGE HYPERFINE SPLITTINGS AT ROOM TEMPERATURE*
System
Line width (G) Av. hf splitting AHmax.slope (G)
g
CrO3 + Acetic acid K~Cr207 ÷ CF3COOH K2Cr207 + (COOH)2 K2Cr207 + Lactic acid K2Cr207 + Citric acid
1"9652 1-9710 1.9779 1"9780 1'9781
2-2 1"6 1-5 1-5 1"0
21.0 22'0 18'4 18"6 18"4
* Accuracy is the same as in Table 1 ; Solvent = Acetic acid. exceptions. In general, if the electric field surrounding the Cr ion is assumed to have a tetragonal symmetry along the z-axis (see Fig. 14) the g-values can be calculated by the perturbation theory, taking the spin orbit interaction (2L. S) into account: g~l = 2.0023 (1 -- 42/AE~)
and
g . = 2.0023 (1 -- ;t/AE~),
where AE~ (AE=) is the energy separation between the lowest orbital (3dxv) and the excited orbital whose wave function has its maximum in (out of) the xy-plane. Given
©
GI, CIr.#/" FI~.
C
14.--The structural unit CrOC14 to show the numbering of C1 ions.
the g-values and the excitation energies, the spin orbit interaction constant would be calculated by the equations. Take, for example, the case of CrOC14-, where g± = 1.974. If the first absorption band at 18,000 cm -1 corresponds to the vertical excitation, then 2 is calculated to be 230 cm -1. * However, if this value is used in the equation for gll, taking into account the fact that the observed gll is practically equal to the free spin value, then AE~ is found to be much higher than seems likely. Thus, the ionic model without taking into account the covalency between the Cr ion and the ligands seems to fail to interpret the result in this case. If the molecular orbitals are formed within the hypothetical structural unit CrO 3+, using the three 2p-orbitals of the oxygen atom (in a more rigorous treatment, s-p hybridization should be taken into account) and the 3d-orbitals of Cr, the situation would not be improved, because it can be shown by the group theory that both d~_~2 and d~ can not form a molecular orbital with the oxygen 2p orbitals and, therefore, the expression for gll remains unchanged. However, the observed g-values * This is considerably lower than the value by MOORE(383 c m - t ) quoted in Reference (4a).
944
H. KON
can be better accounted for, if the molecular orbital treatment is extended to the CI- ions, and if certain conditions are fulfilled by the bonding parameters. Thus twenty molecular orbitals are constructed from five 3d orbitals of Cr, as the bases for the irreducible representations of the symmetry group C4~. They are 4A 1 + A 2 + 3B1 + 2B2 + 5E Of the thirty-one electrons in all, thirty p electrons from the ligands are allotted in the following bonding orbitals: 3A1 + A2 + 2B1 + B z + 4E Thus the discussion concerns only the remaining//2 antibonding orbital which is occupied by the unpaired d-electron, and the excited//1 and E-orbitals with which the B~ orbital is coupled through the angular momentum operators. 4(BO =/sd~_~, + (y/2)(Xl -- y~ -- x~ + Y3, 41(E) =
~d~o - - ~ ' p ~
- - 6" (z~ - - z , ) ,
42(e) = --(~d,x "q- (~'JOx "q- ~" (gl -- g3), q~(B=) = yd~ -- (y'/2)(y~ + Xz --Ya -- x4), where d and p designate the 3d-orbitals of Cr ion and 2p-orbitals of O atom, respectively, and xi, Yi and z i stand for 3p,, 3pu and 3p, orbitals on the i-th CI atom, the numbering being shown in Fig. 14. Using these molecular orbitals, the g-values can be calculated as, g,, = 2.0023 [1 -- (42/AE~){fly + (/5y' -- 2/5'y) S --/5'y'/2}21, g~ = 2.0023 [1 -- (2/AE.){y~ + y'~"}~], where S is the overlap integral between the central d~2_vs and 3p, (or 3p~) on CI 1 (or 2), and where the hydrogen-like atomic orbitals are adopted. /5' and y' are given by/5' = / 5 S + %/(1 --/53) and y' = %/(1 -- y2), respectively. The overlap integrals between d,v and ligand orbitals are neglected. Setting, for instance,/5 = 0.8, y = 0.9 and S = 0.2, g, is calculated as, g, = 2.0023 (1 -- 0.34
2/AE,).
The quantitative aspect of the result should not be taken too literally because of the simplifications adopted in the treatment. In particular, in order to get a more quantitative result, one must use, instead of the simple p- and d-orbitals, the xp hybridized ligand orbitals and the tetragonally hybridized (for ex., dapz or d2sp2) orbitals of the Cr ion. The present result shows that the molecular orbital formation brings the predicted AE~ value to the reasonable range of magnitude, and is indicative of the nature of the bonding in this complex. Thus one can understand the observed g-values of CrOC14- complex by assuming considerable amount of covalency between Cr and C1. A similar explanation would be applicable to VO-bisacetylacetonate where gtt and g± are 2.02 and 1.95, respectively. ~x°)
Acknowledgment--Theauthor is indebted to T. Oucm for his help in the infra-red absorption measurements. t~ R. D. FELTnAM. Thesis (University of California, 1957).