On Copper Complexes as Catalysts of the Oxidative Coupling

as pointed out above, when pyridine, dimethyl sulfoxide. (DMSO), dimethylformamide ..... The MO calculation was carried out for cop- per complexes whi...
0 downloads 0 Views 740KB Size
Download PDF
Oxidative Coupling Reaction of Phenol Derivatives

On Copper Complexes as Catalysts of the Oxidative Coupling Reaction of Phenol Derivatives Shigeru Tsuruya,*' Teijiro Yonezawa, Department of Hydrocarbon Chemistry, Faculty of Engineering, Kyoto University, Kyoto, Japan

and Hiroshi Kato Department of General Education, Nagoya University, Nagoya, Japan (Received August 27, 1973)

Copper complexes as catalysts of the oxidative coupling reactions of phenol derivatives were studied by esr and electronic absorption spectroscopy. The differences between catalytically active copper complexes, prepared by the oxidation of CuCl in the presence of ligands (CUI-02 system), and the inactive copper complexes, which were prepared by mixing CuC12 with ligands under oxygen (Cu" system), were investigated by esr and electronic absorption spectroscopy and discussed in connection with the catalytic activities. The similarities in character between the CUI-02 and the CuII-OH- systems were also observed by esr and electronic absorption spectra. The CuII-OH- system was prepared by adding KOH to CulI systems and had the same catalytic activity as the CUI-02 system. From the intensities of the esr spectra of these copper complexes, it was found that concentrations of esr-detectable copper(I1) ions in the CUI-02 and CuII-OH- systems were smaller than those in Cu" systems with all solvents used. The bonding parameters of these copper complexes were estimated from the esr and electronic absorption spectra data using Maki and McGarvy's theory and indicate that the metal-ligand bonds in CUI-02 systems have less covalent character than those in Cull systems. The bonding parameters estimated by molecular orbital calculations run parallel to those derived from the experimental data, The orbital energies of half-occupied and unoccupied orbitals, atomic bond populations, and atomic populations of copper complexes calculated by these methods for model compounds are discussed in terms of catalytic activity.

I. Introduction The oxidative coupling reaction of phenol derivatives catalyzed by copper complexes is interesting because it might help to reveal a mechanism oPa biochemical synthesis of a natural product and mechanisms of reaction of important enzymes of the oxidase type. The oxidative coupling reaction of 2,6-disubstituted phenols catalyzed by a copper(II)-pyridine complex has been reported by Hay, et'ul.** The copper complex with pyridine ligands which has catalytic activity for this oxidative coupling reaction has been derived either from a cuprous salt by autoxidation or from a cupric salt which has been suitably modified to produce an active species such as the copper(I1)-KOH system (basic copper(I1) complex). Substitution of the copper(II) chloride system under oxygen gives a catalytically inactive system for the phenolic coupling reaction.2b In the previous paper,3 it was reported that copper(1) chloride complexes with dimethyl sulfoxide (DMSO), dimethylformamide (DMF), and hexamethylphosphoramide (HMPA) in the presence of oxygen have catalytic activities for the oxidative coupling reaction of 2,6-dimethylphenol although their catalytic activities seem to be less than that of the pyridine system. However, again in these cases, the copper(I1) chloride complexes with DMSO, DMF, and HMPA are not effective for the oxidative coupling reaction of 2,6dimethylphenol. There has been no reported study in which the differences between the copper(1)-oxygen systems and copper(11) systems were compared systematically in conjunction with their catalytic functions. In the study described above, it may be expected that some information will be

obtained which makes clear the relationship between the bonding character of these copper complexes and their catalytic activities. In the systems of copper(1) chloride with oxygen, it is obvious that copper(1) species are oxidized to the divalent state as a result of oxygen ~ p t a k e The . ~ oxidative polymerization of 2,6-dimethylphenol will be performed with divalent copper species rather than with copper(1) species, as pointed out above, when pyridine, dimethyl sulfoxide (DMSO), dimethylformamide (DMF), and hexamethylphosphoramide (HMPA) are used as ligands. However, the copper(I1) chloride system is not effective for the oxidative coupling reaction of 2,6-dimethylphenol. The purpose of the present work is to seek the differences between the C U I - 0 2 systems, which have catalytic activities, and the CuI1 systems, which do not; and also the similarities of the Cu"-OH- to the CUI-02 systems, using electronic and esr spectroscopy; and to estimate the bonding parameters from the experimental data, from which the role of the copper complexes as catalyst in the oxidation of the phenol derivatives may be revealed. Furthermore, an attempt was made to obtain the electronic structures of the copper(I1) complexes uiu an extended Huckel LCAO-MO calculation. The trend of bonding parameters calculated was consistent with that estimated from the experimental data using Maki and MacGarvy's formula. In both methods, it was found that the bonding parameters of the copper complexes which were catalytically active were larger than those of the copper complexes which were inactive. Finally, some electronic states of these complexes, calculated by the MO method, are discussed in connection with the catalytic activities. The Journalof Physical Chemistry, Voi. 78, No. 8, 1974

S.Tsuruya, T. Yonezawa, and H. Kat0

812

11. Experimental Section

Materials. Copper(1) chloride was prepared by the method of Stathis.5 Anhydrous copper(I1) chloride was prepared by heating copper(I1) chloride at 110-120" for 12 hr under vacuum; it was used without further purification. Solvents used were purified by standard techniques. Preparation of Copper Complexes. ( a ) Copper(Z)-Oxygen System. A portion of copper(1) chloride was added to the corresponding solvent and stirred magnetically for 2 hr under an oxygen atmosphere. ( b ) Copper(ll) Chloride System. A portion of copper(I1) chloride was added to the corresponding solvent and magnetically stirred under an oxygen atmosphere. ( c ) Copper(Il) Chloride-Potassium Hydroxide System. A solution of potassium hydroxide in methanol was added to a solution of copper(II) chloride in the corresponding solvent and stirred magnetically. Electronic Spectra. The electronic spectra of copper complexes were observed a t room temperature using a Hitachi recording spectrophotometer Model ESP-3T with 1-cm cell. The concentration of the copper(I1) chloride of each complex measured was usually 0.01 M . Esr Spectra. The esr spectra of the copper complexes were measured with a JEOL Co. JES-3BS-X instrument equipped with a 100-Hz modulation unit. The magnetic field was measured with Mn2+ salt and peroxylamine disulfonate. The measurements at 77°K were made by cooling with liquid nitrogen. The integration of the esr spectra of copper complexes was performed by the integrator accompanying the esr instrument. 111. Results and Discussion

Electronic Spectra of Copper Complexes. The electronic spectra of CUI-02 systems and CuI1 systems with DMSO, DMF, and HMPA as ligands, respectively, are shown in Figure 1, where the concentration of copper chloride in these systems is 0.01 M . The bands shown in Figure 1 are assigned as d-d transition bands. The electronic spectrum of the copper complex consists of a broad peak in the visible or far-infrared region although theoretically, for example, the three transitions alg-blg, bzg-blg, and e,-blg are possible in the case of a copper complex of D4h symmetry. The schematic orbital representation (hole configuration) of the copper(I1) ion (Ddh) is shown below.

--

d,,, dyde,) dz2(alg) dxy(b*g) dX2--2(blg)

The differences between the bands of CUI-02 systems and CulI systems are summarized as follows. (1)The A,, of CUI-02 systems shifts to shorter wavelengths than that of CulI systems irrespective of the ligands used. (2) The intensities of absorption of CUI-02 systems are smaller than those of CuI1 systems. A similar trend in the electronic spectra has been observed for the CuII-OH--pyridine and the CUI'-pyridine system, where the CuIIOH--pyridine system also has catalytic activity similar to the CUI-02-pyridine complex,6 but the CUI1-pyridine system is inactive. As described later, in order to estimate the bonding parameters, the values of AE,, ( = E,, - E x . x y z ) ,and AEx+ The Journalof PhysicalChemistry, Vol. 78, No. 8, 1974

I/,''/' 600 Figure 1.

,

800

I

I

1000 1200 Wave iength(mp)

I

I

1400

1600

Electronic spectra of copper complexes.

( = E,, - E,z-,z) must be determined, but it is not easy to determine accurately the values of A E , and AE,,, the components of the d-d transition energy, from the broad peak which was shown in Figure 1. The value of AE,, is usually assigned to a broad band in the 12,000-16,OOOcm-l region and the value of AE,, is sometimes assigned to the 22,000-28,000-~m-~r e g i ~ n In . ~ this work the components of the d-d transition energy were estimated by the following two methods. (I) A,, of the observed band shown in Figure 1 was used as the value of the AExy only and the value of AE,, was not estimated; accordingly, (3, which is the measure of the out-of-plane T bonding of d,, and dyz copper orbitals, was not calculated. (11) The values of AE,, and AE,, were approximately determined by the method of Yokoi and Isobe,8 in which the observed values of AExy and AExz which were obtained from the circular dichroism measurement of the copper(I1)-diaminopropane complex by Gillard,g were used to estimate the values of AE,, and AE,, of the observed single broad absorption peak of the copper(II) complex in methanolwater mixed solvent. Yokoi and Isobe applied their procedure to copper(II) complexes with ligands that were analogous to 1,2-diaminopropane, such as ethylenediamine. In the present study of copper(I1) complexes, the ligands are much different from 1,2-diaminopropane, so that the absolute magnitudes of AE,, and AExz obtained by procedure I1 may not have a quantitative meaning; however, the trend of the bonding parameters may be discussed qualitatively. Esr Spectra of the Copper(l0 Complexes. The observed esr spectra of the copper complexes a t 77°K were anisotropic, in which the peak at the highest magnetic field corresponds to g l and the four peaks with equal spacing correspond to the resonance at g , , , except in the case of the DMSO ligand. On the other hand, esr spectra of both CUI-02 and CuII systems with DMSO ligand showed only one broad peak and no anisotropic spectra. The fact that only the one broad is apparent in the case of DMSO lig-

81 3

Oxidative Coupling Reaction of Phenol Derivatives TABLE 111: Relative Intensity of Esr Spectra of CUI' Ionsa

TABLE I: Magnetic Parameters of Copper Complexes at 77 OK Solvent

Pyridine DMF HMPA

Copper complex

gi I

81

All, G

ALL, G

Solvent

copper complex system

Relative intensity) %

CUI-02 CU" CuI-02 CUI' C~'-02 CU"

2.271 2.264 2.401 2.281 2.397 2.352

2.066 2.067 2.085 2.072 2.088 2.088

153.8 161.9 121.4 154.3 122.1 122.5

15.3 13.7

Pyridine

CUI-02 CU'I-OHCUI-02

40 5 35 5c 20 f 5

DMSO

**

Concentration of copper salt, 0.01 M. Based on Cu" system. Reference 6.

TABLE IV: Bonding Parameters of Copper Complexes TABLE 11: Magnetic Parameters of CuII-OHPyridine Complexes at 77 OKa KOH, M

0 0.001 0 .0025 0.01 a

KOH/CuCl

A 1 1, G

181 180 177 177

0 0.1 0.25

1.o

gl I

2.262 2.261 2.263 2.268

g1

2.048 2.048 2.047 2.057

CuClz: 0 . 0 1 M, pyridine: 5 ml, MeOH: 5 ml.

Solvent

Pyridine DMF

HMPA

Copper complex system

CuI-02 CUI1 CuI-02 CU'I C~1-0~ CU"

U2

812 a

0.74 0.75 0.79 0.76 0.79 0.71

0.76 0.69 1.OO 0.58 0.95 0.85

PIS

0.63 0.58 0.83 0.48 0.79 0.66

82

0.77 0.75 0.89 0.62 0.89 0.74

Method I (see text). Method I1 (see text).

align pairwise with each other. It is well known that the binuclear complex involves the copper-copper interaction due to pairs of copper ions coupled together by exchange forces, with the formation of a lower singlet state and an upper triplet state which is detectable by esr.I1 The decrease of the esr intensities of CUI-02 and CuII-OH- systems in comparison with CuI1 systems may be interpreted as described above, although no triplet state could be obH = g,,PH, + glP(H, + H,) + A,,S,I, + A.L(SJ, + served in the esr spectra of the former systems in the SJJ A L ~ ~ S+J LA~L I ( S J L ~+ S J L ~ ) present study. Also, in DMF and HMPA solvents similar phenomena were observed qualitatively. Ochiai and where LL is the nuclear spin of ligand. It can be found Hirai12 recently pointed out the possibility of the formafrom Table I1 that A , values of CUI-02 systems are smalltion of a binuclear structure in CUI-02-pyridine systems. er than those of CuI1 systems, and on the contrary, the g We also previously6 suggested bi- or poly(even-number) values of the former systems are larger than those of the nuclear structure of copper complexes in the CuII-OH-latter. As has been previously reported,6 if KOH is added pyridine system from observations of the absorption into the copper(I1) system, the resulting system exhibits tensities of the esr spectra. The apparent decreases of the catalytic activity for the oxidation reaction of the phenol esr intensities for the CUI-02 and CuII-OH- systems may derivatives. In order to study the effect of KOH, copperbe explained in this manner, (11) chloride-pyridine complexes containing various conBonding Parameters of Copper Complexes. The theory centrations of KOH were investigated by esr spectroscopy of Maki and McGarvey13 has been used to obtain the coat liquid nitrogen temperature. The esr results $re sumvalent bonding parameters for different orbitals in the marized in Table 11. The decreases in the g values (gll and copper(II) ion from the experimental data. These covalent g L ) as the concentration of KOH added increases is obbonding parameters were calculated for the C U I - 0 2 and vious from Table 11. This trend is compatible with the reCuI1 systems with pyridine, DMF, and HMPA ligands, sults shown in Table I. respectively. Maki and McGarvey have developed a theory The esr spectra of both the CuI-02-pyridine and the to describe the esr spectrum of a square-planar copper(I1) Cu1-02-DMS0 systems were integrated and these intecomplex. The theory relates experimentally measured g grated spectra were compared with those for the Cu"factors (gll and g l ) , hyperfine constants ( A l l and A L ) , and pyridine and Cu"-DMSO systems, respectively, for the d-d transition energies to parameters which are measures same concentration of copper salts. The results are preof the covalent bonding between the copper d orbitals and sented in Table 111, together with the results for the Cu"the surrounding ligands. The notation of Maki and OH--pyridine system, reported previously,6 for the sake McGarvey for a square-planar complex will be used here. of comparison. The intensities of the esr absorption peaks The following antibonding orbitals are those of highest enof the CUI-OH- and Cdl-02 systems are smaller than ergy, being given in the order of increasing energy for a those of the Cu" systems, as seen in Table 111. This fact is 3dl hole configuration worthwhile to note in connection with the fact that oxidases containing copper ions show a similar phenomenon in the esr measurements; for example, in cytochrome oxidase the esr signal that is attributable to CuII ions accounts for only a fraction (40%) of the copper found in the enzyme by chemical determinations.1° As discussed briefly for the Cu"-OH--pyridine system,6 the copper complex in this sytsystem, as well as in the CuI-02-pyridine system, is likely to form a binuclear complex, in which copper ions and may indicate that the copper complexes of both CUI0 2 and CuI1 systems with DMSO have tetrahedral structure rather than square planar. The magnetic parameters obtained from the esr spectra of the copper complexes are listed in Table I. The quantities in the table appear in an approximate spin Hamiltonian as

+

The Journal of Physical Chemistry, Voi. 78, No. 8, 1974

a i4

S.Tsuruya, T. Yonezawa, and H. Kat0

where the *a], and * b ~ , orbitals are both u type MO's, and the *bag and *e, orbitals represent the in-plane T bonding oribitals. The value of the a2 parameter in @bl, is a measure of the u bonding strength between the dxz-yz copper orbital and the u orbitals of the four ligands in the xy plane, and the P i 2 parameter value is a measure of the in-plane T bonding of the dxy copper orbital. The p 2 parameter becomes a measure of the out-of-plane T bonding of the d,, and dyz copper orbitals. The second-order perturbation calculation results in the following approximate expressions which relate the experimental magnetic data to the covalency parameters.8

a + (g,l - 2) +

A , ~= P ( - ~ Y ~+/ ~ A.L

-

- 2) + gIl = 2.002 - 8A/AE,, C U ~ P ,-~ (f ~ l) g, = 2.002 - 2x/AE,, ff2/32(1- f 2 )

=

P(ff2~z17 - k,)

+

3 1 , ( ~ ~

11/14(gL

2)

+ f3)

f4)

where P = 2yPoPN(dxz-yzir-31dxz-y~), ko is the fermi contact term, AExy = Exy - E,z-,z, AExz = Ex, E Z Z - ~and Z f l , f z , f 3 , and f 4 are 0.04, 0.04, 0.33, and 0.005, respectively, as shown in Yokoi and Isobe's report.8 As described above, the components of the transition energies, AExy and AExZ,were estimated by methods I and 11. The values of the bonding parameters were calculated using the above equations, where P = 0.036 cm-I, ko = 0.42, which are listed in Table IV. The bonding parameters estimated indicate generally that the bonding is appreciably covalent in the Bl,, Bz,, and E, orbitals. a2, the u bonding parameter, is 0.7-0.8 for both the Cu"-02 and the CuI1 system in each of the solvents and the differences in the values for both systems are not large although CU" systems tend to have smaller values of a2, or to put it in other terms, the CuI1 systems tend to have larger covalent u bonding characters than do the CUI-02 systems. The covalent T bonding parameters 01 and P vividly show the difference between CUI-02 and CulI systems, regardless of the solvents used. These facts imply that the CUI-02 systems have weaker covalent in-plane x bonding than the Cu11 systems, and this observation may be used to evaluate the role of the CUI-02 systems in the oxidation reaction of phenol derivatives. The strength of the coordination of ligands in the CUI-02 systems is not so strong as those in Cull systems. Also, comparing the values of P2, the parameter of covalent out-of-plane x bonding, there is a remarkable difference between the CUI-02 and CUI' systems. Although the difference is less than that for pl2, the same tendency, the CUI-02 systems having larger values of p 2 than those of CulI systems, was found as shown in Table IV. Some remarks will be presented regarding the application of Maki and McGarvey's theory to the present systems: the estimation of the components of d-d transition energy, and the use of the value of 0.43 as ko, the Fermi contact term, for all the present systems. Although the absolute magnitudes of the bonding parameters estimated by the present method may involve some ambiguity due to the reasons described above, the comparison of the values of these bonding parameters estimated for the CUI0 2 and Cu" systems will be useful and offers several points of interest regarding the difference in bonding character between the CUI-02 and CuI1 systems. In the CUI-02 systems which have catalytic activities for the oxidative coupling reaction of phenol derivatives, the covalent bonding is less than that of Cu" systems. It The Journal of Physical Chemistry, Vol. 78, No. 8, 1974

is possible that part of the catalytic activity may be due to the difference in bonding parameters, though other factors can be thought of. While we have not quantitatively estimated the bonding parameters of Cull-OH- systems, the behavior of the esr parameter (Table 11) was consistent with the trend for CUI-02 systems. Kivelson and Neimanim4have reported that as the bonding parameters a and p decrease, the bonds become more covalent in nature, g,, and g l decrease, and A , , and A L increase. Hence it is concluded that the higher the concentration of KOH, the less is the covalency of the copper-ligand bond; for the complex which has catalytic activity for oxidative coupling of phenol derivatives, the bond strength between copper atom and ligands is weaker than that in the complex which has no catalytic activity, which is compatible with the observations in Table IV. The bonding parameters estimated according to the present method are discussed in light of the results of MO calculations in the next section. MO Calculations for the Model Compounds of Copper Complexes. The M O calculation was carried out for copper complexes which were assumed to be model compounds for the present catalysts. At first, the copper(I1) complex which has the composition Cu(Cl)z(NH3)2 was assumed as a compound which has no catalytic activity for the oxidative coupling reaction of phenol derivatives. As model compounds which have catalytic activity, we assumed both CuCl(OH)(NH& and CuC1(02-)(NH3)2. It seems reasonable that chlorine atom is replaced by a hydroxy group when KOH is added in a solution of copper(11) chloride in methanol. Although the pertinent evidence of the replacement of C1 by 0 2 - is lacking, CuC1(02-)(NH3)2 is assumed as a model compound representing the CUI-02 system because of the possibility of the presence of 02- species, correlating with observed oxygen uptake of the ~ y s t e m Since .~ copper(I1) complexes generally have a coplanar configuration, we supposed that these copper(II) complexes have the orientation shown in Figure 2 . The atomic orbitals were 1s of hydrogen, 2s and 2p of nitrogen, 2s and 2p of oxygen, 3s and 3p of chlorine, and 3d 4s, and 4p of copper. The values of diagonal elements, H,,, for the atoms used were taken as follows. H: 15.10 eV for the 1s orbital, N, 23.60 eV for the 2s orbital, and 11.40 eV for the 2p orbital; 0: 29.30 eV for the 2s orbital and 13.60 eV for the 2p orbital; C1: 21.90 eV for the 3s orbital and 10.90 eV for the 3p orbital; Cu: 10.60 eV for the 3d orbital, 7.75 eV for the 4s orbital and 3.95 eV for the 4p orbital. The nondiagonal elements, H,,) were obtained by the method of Wolfsberg and Helmholz,l5 using the approximation

H,,

=

%K(H,L + H,,)S,,

where K was kept constant, 1.75.16 The overlap integrals, S,, were estimated using exponent values obtained by the Slater rule,l7 but for copper atom Clementi's values18 were used. The calculated orbital energies of half-occupied orbitals of these three copper(I1) complexes are given in Table V. Generally, as the energies of the half-occupied and/or lowest unoccupied orbitals become lower, the strength of the electron affinity becomes greater and the oxidizing power increases. The energies of half-occupied orbitals and lowest unoccupied orbitals of the model compounds calculated by the extended Huckel method explain the experimental trend in the catalytic activities quite well. Name-

815

Oxidative Coupling Reaction of Phenol Derivatives TABLE VI: Calculated Bonding Parameters

T

Copper(I1) complex

I

H

c1 C U C l z (NH3)

0.796 0.796 0.716

PI2

P2

0.977 0.977 0.918

0.980 0.980

0.960

(CU( I I ) - C l - ) 0

TABLE VII: Atomic Bond Populations of the Copper (11) Complexes

C u - N : 2 . 0 5 A. C u - C l : 2.28.A CU-0: 2.34 4 0-H: 0.936 A

H\

a2

Cu'I-OHCUII-02CU"-Cl -

N-Cu-N

Copper(I1) complex

Cu"-OH CUI 1-0 2 Cu"-Cl-

\

H

Atomic bond population

-0.01

0.052 0.228

0

H' C U C l ( 0 H ) (NH3)z

TABLE VIII: Atomic Populations of Copper Atoms of the Copper (11) Complexes

( C u ( I 1 ) -OH-)

Copper(I1) complex

Cl

I

t(i

N-CU-

Cu"-OH CU"-02CU"-Cl-

\H

0

C u C l ( O - - ) (NH3)2

(Cu(II)-O--)

Flgure 2. Configurations and atomic distances for model cop-

per(ll) complexes.

TABLE V: Orbital Energies of Half-Occupied and Lowest Unoccupied Orbitals of the Copper (11) Complexes Copper(I1) complex

CUII-OH CU"-O2 CUI'-c1-

Orbital energy of half-occupied orbital, eV

-10.44 -10.44 - 10.37

Orbital energy of lowest unoccupied orbital, eV

-3.14 -3.14 -3 .OO

ly, the orbital energies of half-occupied and lowest unoccupied orbitals of the copper(I1) complexes CuCl(OH)(NHs) and CuC1(02-)(NH& are smaller than those of the copper(I1) complex CuC12(NH& although the energy differences between the former and the latter are not so large as expected. Table VI contains calculated bonding parameters obtained for the model compound of the copper(I1) complexes, where a2, P l 2 , and P 2 represent the square of the coefficients of the atomic orbitals of the copper atom in the molecular orbitals which have half-occupied orbital character. The parameters a2, P l 2 , and P2 indicate the bonding parameters of the atomic orbitals dXz-yz, dxy, and dzz, respectively. Accordingly, the bonding parameters calculated here correspond to those (Table IV) estimated from the experimental data using Maki and McGarvey's theory. The results obtained from the MO calculations lead us to a conclusion that the bonding parameters of the copper(I1) complex which is a potent catalyst are considerably larger than those of the copper(I1) complex without catalytic activity. However, certain discrepancies become apparent if the two sets of bonding parameters obtained by the two methods are compared quantitatively: P bonding parameters, PI, p, estimated on the basis of the experimental data, particularly in the CuI1 systems, become smaller than the u bonding parameters in the corresponding system, and the quantitative

Atomic population of Cu atom

9.299 9.353 9.521

difference between the experimental result and calculated one is larger than what might be inferred. The common drawbacks in the application of theory to the estimation of bonding parameters using experimental data are due to lack of knowledge of the exact magnitudes of the magnetic parameters and the d-d transition energy of the samples measured in polycrystalline form and also to uncertainties concerning the magnitude of ko, which is a measure of the Fermi contact term in the hyperfine interaction, the spin-orbit coupling constant, A, and the parameter P as pointed out by Heuvelen and Goldstein.' Normally one expects stronger u bonding. Based on this expectation, the result gained from the calculation seems to reflect the trend in comparison with that estimated from the experimental data using Maki and McGarvey's theory. Accordingly, it seems that quantitative interpretation of bonding parameters obtained by both methods does not have much meaning, but once again a composite of the present studies would support the following ordering of copper-ligand bond strength for the above systems: CuII-Cl > CuII-OH-, CuII-02-. It is of interest to note that the magnitude of every bonding parameter of C U ~ ~ - Ois~identical with the corresponding one of CulI-OH- as shown in Table VI. This result may give support for the possibility of the existence of the C ~ 1 1 - 0 ~and/or its analog in the CUI-02 systems. The atomic bond populations between copper atom and OH-, 0 2 - , and C1 are presented in Table VII. These populations reproduce a fair correlation with the trend of the bonding parameters calculated as shown in Table VI. Thus the atomic bond populations also indicate that the copper-ligand bond strength in question in the Cul*-OHand Cu11-02- systems is weaker than that in the CuII-Cl system. The net charge of copper atom seems to be a measure of oxidizing ability of the copper complex. The calculated atomic populations of copper atoms are reported in Table VIII, in good agreement with the results of experimental evidence shown above. The atomic population of copper atom in the CuII-Cl system is larger than that in the CuII-OH- and C U ~ ~ - Osystems, ~suggesting that the latter systems have more oxidizing power than the former one. Again it may be noted that the atomic bond populaThe Journalof Physical Chemistry, Vol. 78, No. 8, 1974

816

Karoly Vadasdi

tions and atomic populations for CuII-OH- and C U ~ ~ - O ~ -(2) (a) A. S. Hay, H. S. Blanchard, G. F. Endres, and J. M. Eustance, J. Amer. Chem. SOC., 81, 6335 (1959); (b) H. S. Blanchard, H. L. are similar to each other. Finkbeiner, and G. A. Russell, J. Polym. Sci., 58, 469 (1962). In conclusion, we can relate the experimental and cal(3) T. Yonezawa, S. Tsuruya, and T. Kawamura, J. Polym. Sci., B6, 447 (1968); T. Yonezawa, S. Tsuruya, S. Tsuchiya, and T. Kawamculated results on the catalytic activities of the oxidation ura, Kogyo Kagaku Zasshi, 71,1007 (1968). reaction of phenol derivatives as follows: the weaker the (4) H. Finkbeiner, A. S. Hay, G. F. Blanchard, and G. F. Endres, J. copper-ligand bond, the more facile is the substitution of Org. Chem., 31, 549 (1966). (5) E. C. Stathis, Chem. lnd. (London), 633 (1958). phenolate anion as ligand, though more factors inherent in (6) A. S. Hay, Japanese Patent S 39-29373 (1963); S.Tsuruya, T. Shithe catalytic function of the present copper complexes, rai, T. Kawamura, and T. Yonezawa, Makromol. Chem., 132, 57 (1970). must, of course, be present.

Acknowledgment. S . T. wishes to give special thanks to Dr. K. Kawamura for his helpful discussion and also to Dr. H. Konishi for the computer program used for the MO calculations. The calculations were carried out on a FACOM 230-60 computer at the computation center of Kyoto University. References and Notes (1) Department of Chemical Engineering, Faculty of Engineering, Kobe University, Nada, Kobe, Japan.

(7) A. V. Heuvelen and L. Goldstein, J. Phys. Chem., 72, 481 (1968). (8) H. Yokoi andT. Isobe, Bull. Chem. SOC.Jap., 41, 2835 (1968). (9) R. D. Gillard, J. lnorg. Nucl. Chem., 26, 1455 (1964). (IO) H. Beinert, “The Biochemistry of Copper,” Academic Press, New York, N. Y., 1966, p 213. (11) B. Bleaney and K. D. Bower, Proc. Roy. Soc., Ser. A, 214, 451 (1952). (12) E. Ochiai and H. Hirai, Kogyo Kagaku Zasshi, 72, 1785 (1969). (13) A. H. Maki and B. R . McGarvey, J. Chem. Phys, 29, 31 (1958). (14) D. Kivelson and R. Neiman, J. Chem. Phys., 35, 149 (1961). (15) D. Wolfsberg and L. helmholz, J. Chem. Phys., 23, 853 (1955). (16) R. Hoffman, J. Chem. Phys., 39, 1397 (1963). (17) J. C. Slater, Phys. Rev., 36, 57 (1930). (18) E. Clementi and D. L. Raimondi, J. Chem. Phys., 38, 2686 (1963).

On Determining the Composition of Species Present in a System from Potentiometric Data Karoly Vadasdi Research Institute for Technical Physics of the Hungarian Academy of Sciences, Budapest, Ujpest 1, Pf. 76, Hungary (Received August 17, 1973)

The mass balances of chemical systems and derivatives or integrals of them have been written as matrix equations in the case of suitably chosen mixtures. The appropriate combination of these equations may be put into Jordan’s normal form giving the stoichiometric coefficients as matrix eigenvalues. On the basis of the derived equations a computation method has been developed for determination of the number and composition of species in two-component chemical systems using emf data. The application of the method requires the knowledge of the free concentration of each component. Selecting matrix elements by interpolation the computation basically consists of a “pseudo-inverse” computation and finally an eigenvalue determination.

Introduction A number of different methods have been proposed for the determination of the compositions of species formed in equilibrium mixtures.1-3 A common feature of all these methods, which have found wide practical application, is that they can be applied only under restricted conditions. The usual conditions are, e.g., only a single species present in the system, or in the chosen experimental range; the system follows some special mechanism, etc.4-7 Those systems which do not satisfy the necessary conditions are treated by “least-square” computations, testing various “guessed” mechanisms, and the best “least-square fit” corresponds to the “most probable” mechanism.8.9 During the past 10 years several authors1°-13 have published methods for the determination of the number of species present in a system from optical data, applying matrix rank analysis. The use of these methods facilitates The Journal of Physical Chemistry, Vol. 78, No. 8, 1974

the application of different “least-square” programs to the systems, giving an upper limit for the number of possible combinations. No similar method is known in the literature for the treatment of data from other types of measurements, e.g., potentiometric or extraction. In this paper a general computation method is given that in principle allows the determination of the number and composition of the species present in an equilibrium system, using potentiometric data. It goes without saying that in a very complicated system, consisting of several components and several species, experimental errors may frustrate the aim. Discussion of the circumstances leading to such a shortcoming, however, does not constitute the subject of this paper. Potentiometric D a t a For the sake of simplicity, let us consider a system con-