Spectrochlmica Acta, 1967 Vol. 2SA, pp. 2057 to 2042. Pergamon P r e u Ltd. Pr inted In Northern Ireland

Temperature dependence of association constant, extinction coefficient and total absorption intensity of an organic

charge-transfer complex

R. FOSTER and I. B. C. MATHESON

Chemistry Department, Queen's College, University of St. Andrews, Dundee, Scotland

(Received 1 November 1966)

Abstract--Determinations of association constant, extinction coefficient and total absorption intensity for the system hexamethylbenzene- tetracyanoethylene in 1,2-dichloroethane have been made over a temperature range of 45 °. The extinction coefficient of the complex decreases slightly with increasing temperature whilst the total absorption intensity remains constant. The observations are consistent with the postulate that, under the conditions used, a single 1 : 1 complex species is formed with no significant contributions from isomeric complexes, or from contact charge transfer.

INTRODUCTION

ELECTRON donors (D) and electron acceptors (A) m a y in te rac t in solut ion to form a charge- t ransfer complex [1]. The complex is usual ly character ised b y an absorpt ion band, or bands, no t present in e i ther component . This absorp t ion has been assigned to an in termolecular charge t ransfer transit ion(s) [1]. The in tens i ty of the band(s) has been t aken as a measure of the concent ra t ion of the complex. I f i t is assumed t h a t only a 1:1 complex D A is fo rmed t hen an association cons tant K~ m a y be defined as

K~ = [DA] / [D][A] (1)

Many algebraic methods have been used to eva lua te Ko and e (the molar ex t inc t ion coefficient(s) of D A ) f rom values of the to ta l concentra t ions (free and eomplexed) [A]0 and [D]o of A and D respect ively and measurements of optical dens i ty (d) due to the absorp t ion by the complex [2].

Some of the results which have been ob ta ined are anomalous [2]. Various explanat ions have been suggested, for example the presence of te rmolecula r complexes [3], specific solvat ion [4] and the appa ren t disobedience of Beer 's law b y the complex species [2]. W h a t e v e r the cause of these anomalies, the most consistent results f rom optical da t a are ob ta ined when [A]0 ~ [D]o, and when the degree of association is fair ly high [2, 4].

However , even unde r the condit ion [A]0 ~ [D]0 the possibility, envisaged b y

[1] R. S. M ~ I ~ , J . Am. Chem. Soe. ~ , 600 (1950); J . Phys. Chem. 56, 801 (1952); J. Am. Chem. Soe. 74, 811 (1952).

[2] See for example: P. H. EMSLIV., R. FOSTER, C. A. F~'~. and I. H o R n , Tetrahedron 21, 2843 (1965).

[3] S. D. Ross and M. M. L~ES, J. Am. Chem. Soe. 79, 76 (1957); G. D. JOH~rSO~ and R. E. BowE~¢, ibid. 87, 1655 (1965).

[4] S. CA~TER, J. N. MUgRET.T. and E. J. Rosc~, J. Chem. Soc. 2048 (1965). 2037

2038 R. FOSTER and I. B. C. MATHESON

ORGEL and MULLIKEN [5], of isomeric 1:1 charge transfer complexes and 1:1 contact pairs still exists. The following work was carried out in order to test for the presence of either of these perturbing influences on the observed optical absorption in a given system.

Hexamethylbcnzene-tetracyanoethylene in 1,2-dichloroethane was chosen for the following reasons: (a) the charge-transfer absorption maximum at 540 m/~ is a single band well separated from the absorptions of the component molecules; (b) the association constant is known to be reasonably large ; (c) the solvent will dissolve a sufficient quanti ty of tetracyanoethylene to permit solutions with [A]0 ~ [D]o to be used.

EXPERIMENTAL Mater ia l s

1,2-Dichloroethane was washed with dilute aqueous potassium hydroxide, then with water; dried over, and distilled from, phosphoric oxide. I t was finally frac- tionated, b.p. 83.5°/760 mm. Tetracyanoethylene was recrystallized from benzene as the benzene complex. The benzene was then pumped off and the tetracyanoethylene twice sublimed, m.p. 198-200 °. Hexamethylbenzene was prepared by the method of CULLI~AN]~ et al. [6]. I t was recrystallized five times from ethanol and twice sublimed, m.p. 165-165.5 °.

A n a l y t i c a l

Optical density measurements were made using a manually-operated Optica CF4 Spectrophotometer. The optical density calibration was checked using standard potassium chromate-potassium hydroxide solutions. The technique for measuring the solutions has been described [7]. The temperature of the solutions was controlled to within +0.05 ° by circulating water or aqueous ethylene glycol through a specially constructed cuvette jacket. Appropriate corrections were made for the effect of solvent expansion on the concentrations of the various species present.

For solutions where [D]0 ~ [A]0 let:

[D]0 = n[A] 0 (2)

I f the measured absorption is corrected for the small absorption due to the free D, A and the solvent then:

d = [ D A ] . l (3)

where l is the path length in cm of the optical cuvette. From equations 1, 2 and 3 it may be shown that [8]:

l[A]o ( n + l ) ] ] 1 - - - - - - + . (4)

d n e n K c e [A]o

The plot of [A]o/d against [A]0 -1 should be linear. From the gradient and the intercept with the ordinate, Kc and e may be evaluated.

[5] L. E. ORGEL and R. S. MtmLIKE~r, J. Am. Chem. Soc. 79, 4839 (1957). [6] N. ~. CIYLLIZ~ANE, S. J. CTrAXD and C. W. C. DAw~u~s, Org. Syn. 35, 73 (1955). [7] R. FOSTER, J. Chem. Soc. 1075 (1960). [8] cf. Ref. [3], also R. FOSTER, d. Chem. Soc. 5098 (1957).

Temperature dependence of association constant of an organic charge-transfer complex 2039

A min imum of t h i r t y points was used in an y single de terminat ion . The best s t ra igh t line was ob ta ined b y the least squares method. E v e r y de te rmina t ion was repea ted at least once.

F o r band measurements , the ex t inc t ion coefficients p lo t ted against f requency and the ba nd wi th (A~) a t ha l f the m a x i m u m band height was measured. The band area was es t imated b y assuming a Gaussian shape so t h a t the to ta l in tens i ty (A) = 1-0645 ~. A~. F r o m this value, the oscillator s t rength (f) was calculated using the relat ionship [9]:

f : 4.319 × 10 - g l ' e . d ~ (5)

where i t is assumed t h a t A = S e dr . In equa t ion 5, e is measured in 1.mole -1 cm -1 and ~ is measured in cm -1.

RESULTS

Values of /£c and ~ ob ta ined f rom plots of [A]o/d against [A]o -1 using equa t ion 4 are summar ized in Table 1. Plots of logx0K~, log10 (Kc~) and loglo e against T -1 (where T is the t empe ra tu r e in °K) are given in Fig. 1. The gradient of the

Table 1. Calculated values for K c, Kce and e for the complex between hexamethyl- benzene and tetracyanoethylene in 1,2-dichloroethane at various temperatures

Temp. Kv Kce e (°G) (1. mole -1) (1.~ molo -2 cm -1 × 10 -4) (I. molo --1 cm -1 × 10 -a)

--3.90 46-53 17.660 3.79~ 3.40 35.54 13.287 3.739

11.45 26.75 9"795 3.675 19-45 20-4 s 7.463 3.645 27.45 15.9~ 6.893 3.69 o 33-70 13.11 4-773 3.641 41.00 10.98 3.915 3.57 o

first plot gives AH = --5.4 e kca l . mole -1. F r o m the plot of lOglo (/£~e) AH = - -5 .64 kc a l . mole - i , AS = 12.6 e.u., AG298o = --1.69 k ca l . mole -I, TAS29so ~- - - 3 . 7 7 kca l . mole -1 (for s t anda rd s ta te of 1 mo le . 1-1).

The spec t rum of the charge t r a n s f e r band for a given solutions corrected for absorp t ion by the components and b y the solvent is shown in Fig. 2. The absorp t ion band intensit ies are summar ized in Table 2. A n y shift in 2max----540 m/~ wi th t e m p e r a t u r e is too small to be measured over the range --3.9 ° to -}-41.0 ° .

DISCUSSION

ORGEL and MULTX~EN [5] have discussed the possibil i ty of the optical absorpt ion of an organic donor - accep to r sys tem being affected b y complex isomerism and con tac t charge t ransfer . T h e y define t rue complex format ion as being the s i tuat ion where the numbe r of 1 : 1 D A pairs exceeds the n u m b er which m a y be expec ted on

[9] C. SAI~DORFY, Electronic Spectra and Quantum Chemistry, p. 105. Prentice-Hall (1959).

2040

1"8 F

I "

1.6

1.4

1.2

I-C

o . s ~ 5-5 5 5

T~l (OK' lx i0 3)

Fig. 1. Plots of (A) logzoKc; (B) logx0(Kc~); (C) logz0¢ against the reciprocal of the absolute temperature for the complex hexamethylben- zene-tetracyanoethylene in 1,2-diehloroethane.

R. FosT~,~ and I. B. C. MATS~,SON

- - 5"4 4¢"-

-- 5 2 A

g

- - 5"0

7 x

- 4 . 8

3 '59

5,58 w

5.57 o

- - 3 . 5 6 _~

- - 3.55

- - 3.54 _L____ 5.7 12 14 16 18 20 22 24 26

v, cm -~ x 10 -5

Fig. 2. The charge-transfer absorption spectrum of the complex hexamethylben- zene-tctracyanoethylcne in 1,2-diehloro- ethane, corrected for the absorption by the components and the solvent, at --3.9°C.

Table 2. Variation of extinction coefficient (e), band width at half maximum intensity (Av) and oscillator strength (t) of the charge-transfer band with temperature

Temp. • Av (°C) (1.mole -1 cm -1) × 10 -a (cm -1) × 10 -a i

-3 .90 3.79~ 5.15 0.0844 3.40 3.739 5.25 0.0848

11.45 3.675 5-26 0-0835 19.45 3.645 5.35 0.0842 27.45 3.690 5.34 0.0851 33.70 3.641 5.36 0.0843 41.00 3.57 o 5-50 0.0848

the basis of r a n d o m encounters . The excess is the n u m b e r of t rue complexed pairs present . T h e y suggest t h a t i t is possible t h a t in the case of r a n d o m contac ts the over lap in tegra l of the a p p r o p r i a t e donor and accep t e r orbi ta ls is appreciable . This gives rise to opt ical a b s 0 r p t i o n - - a process which t h e y t e r m contac t charge t ransfer . Complex i somer ism refers to the s i tua t ion where more t h a n one t rue charge t rans fe r complexes of different geometr ic configurat ions are present .

Tempera ture dependence of association constant of an organic charge-transfer complex 2041

ORGEL and MUH,TKEN [5] also showed tha t for the case of the presence of several isomeric complexes, the normal type of B~.~.SI--I-hLDEBRAND [10] evaluation of Kc, where [D]0 >> [A]o, will give:

'K c (measured) = ~ K~ (6)

(measured) = ~ K~/ZK~ (7)

where K~ and s~ are the values of Kc and ~ respectively for the i-th 1 : 1 complex between A and D.

For contact charge transfer in a given system, ORGEL and MVLLrKE~" [5] derived the relationship

e measured = e(1 + K ~ ) (8)

where C = constant. More recently I~UE [11] has pointed out tha t random collisions will themselves lead to a finite association constant.

Determinations of K~ (and e) will consequently not demonstrate the presence or absence of isomeric complexes or contact charge-transfer, although if they are present the values of K~ and e obtained will be incorrect. However, unless AH for the formation of the different 1 : 1 complexes is identical, plots of log10 K vs. T -1 should be non-linear, i.e. AH (measured) should be temperature dependent, likewise if isomeric 1 : 1 complexes and/or contact charge transfer are present, the intensity of the charge transfer band should be temperature dependent [5].

For the system studied there is no evidence for a deviation from linearity of the plot of lOglo Ko vs. T -1 over a 45 ° temperature range (Fig. 1). This suggests tha t only one 1:1 complex is present under the experimental conditions employed. Because of the only slight variation of e with temperatures, a plot of log10 (Kce) yields a straight line with effectively the same slope (Fig. 1). This is of importance in experimental determinations of AH. There is much doubt concerning the validity of many results obtained f o r / ~ from optical data using the condition [D]0 >> [A]0. However, several groups of workers [2-4] are agreed that from such determinations the product K~e may be estimated with reasonable certainty, (though for very different reasons). The present results suggest that the temperature variation of this product K~e may yield good estimates of AH.

The value of E shows in fact a slight decrease with increasing temperature (Fig. 1). This is entirely accounted for by the temperature band-broadening and is reflected in the temperatures independence of the oscillator strength f. This latter observation confirms the conclusion that no isomeric 1:1 complexes are present and it suggests that contact charge transfer is also insignificant. The only published value of f for this complex [12]; namely f = 0.18 is at variance with the present value (f = 0.084). Although former value is based on an extinction coefficient obtained from a Benesi-Hildebrand type of analysis which, as stated above, yields

[10] H. A. BENESI and J. H. HILDEBRAI~D, J. Am. Chem. Soc. 71, 2703 (1949). [11] J. E. PRUE, J. Chem. Soc. 7534 (1965). [12] G. BRIEGL~.B, Electr°nen'D°nat°r-Accept°r'K°mplexe' p. 62. Springer (1961).

2042 R. FOSTER and I. B. C. MATHESON

doubtfully separa ted values of e and Ko, nevertheless the difference between the two values of f appears to be too large to be completely explained in this way.

Although in the present work for the system studied under the conditions used, no evidence for isomeric 1:1 complexing or for contact charge-transfer has been obtained, this cannot in itself be taken to show that such behaviour cannot occur in other electron donor-electron acceptor systems.

Acknowledgement--The Authors are grateful to the Science Research Council for a grant (to I. B. C.M.).