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Analysis of the association constants for charge-transfer complex formation
Journal of Molecular Structure 1033 (2013) 131–136
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Analysis of the association constants for charge-transfer complex formation William D. McKim, Jayanta Ray, Bradley R. Arnold ⇑ Department of Chemistry and Biochemistry, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, United States
h i g h l i g h t s " Absorption spectra and association constants for charge transfer complexes were measured. " A model was used to predict the absorption maxima for the charge transfer bands. " The model assumes charge transfer interactions are important to complex formation. " Several classes of complexes do not conform to the model predictions. " Charge transfer interactions are not important to complex stability in many cases.
a r t i c l e
i n f o
Article history: Received 23 March 2012 Received in revised form 9 August 2012 Accepted 9 August 2012 Available online 23 August 2012 Keywords: Association constant Equilibrium constant Acceptor donor complex Absorption spectra
a b s t r a c t The phenomenon of charge transfer (CT) complex formation has been of interest for more than 50 years and has led to the development of numerous applications. Even with the prolonged interest in these complexes the interactions responsible for complex formation have yet to be fully characterized and remain an area of sustained relevance. This report outlines the measurement of the association constants for CT complex formation of a series of methylated benzene donors with tetracyanoethylene, pyromellitic dianhydride, 2,3-dichloro-5,6-dicyano-p-benzoquinone, and 1,2,4,5-tetracyanobenzene acceptors in 1,2-dichloroethane solvent. The evaluation of the position of the CT absorption maximum and the magnitudes of the association constants within a theoretical model is described. The influence of solvent polarity on the magnitudes of the association constants was also discussed. These studies show that non-bonding interactions are important in most complexes while ion-pair interactions play a significant role in a select few of the complexes studied. Published by Elsevier B.V.
1. Introduction The spectroscopy of charge-transfer (CT) complexes continues to be of significant interest after more than half a century of sustained research [1–5]. CT complex formation has been used to characterize derivatives, to estimate ionization potentials and electron affinities, to induce crystallization for X-ray analyses, or to aid in the chromatographic separation of components [2,5–8]. These complexes play an important role in many organic and inorganic reaction mechanisms as well as in biological processes, imaging applications, and the design of photoelectric devices [9–12]. Understanding the nature and thermodynamics of complex formation can be important to understanding protein folding and to the control of macromolecular assembly [13–15]. After considering the significance these complexes play in such a broad array of applications it is clear that a detailed understand of the thermodynamics of complex formation is of paramount importance.
⇑ Corresponding author. E-mail address: [email protected] (B.R. Arnold). 0022-2860/$ - see front matter Published by Elsevier B.V. http://dx.doi.org/10.1016/j.molstruc.2012.08.015
It has been suggested that a correlation between the magnitude of the association constant (KCT) and the wavelength of the CT absorption maximum (kmax) could be expected based on a perturbation treatment (Eq. (1)) [16].
logðK CT =K CT0 Þ ¼ Cðkmax k0 Þ
ð1Þ
Here KCT0 and k0 are the association constant and absorption maximum, respectively, for an arbitrarily-chosen standard complex. Linear correlations between log(KCT/KCT0) and (kmax k0) have been described previously for several classes of acceptors and donors. As described by Dewer in his initial report [16], the appearance of linear correlations according to Eq. (1) would be a necessary condition, but not sufficient, to prove coulomb–coulomb interactions were important to the stability of the complex. For weak acceptors and donors, where the ion-pair could play a minimal role in the stability of the ground state, such correlations may be due to non-bonded interactions that also happen to correlate with changes in kmax values. In our previous report [17], we presented the results of our studies on the complexes formed between 1,2,4,5-tetracyanoben-
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zene (TCNB) or tetracyanoethylene (TCNE) as acceptors with a series of methyl substituted benzene donors. Linear correlations between the measured association constant and the CT kmax within each series of complexes were observed, in agreement with Eq. (1). However, we suggested that ion-pair contributions were not important to the ground state stability of these complexes based on the relative magnitudes of the slopes observed when considering the plots according to Eq. (1). Also described in our earlier report, the HMB/TCNE complex was unique among the complexes studied because it did not correlate well with the other complexes included in the initial study [17]. At that time we suggested that the anomalous behavior of this specific complex could be due to a change in the bonding contributions and that ion-pair interactions might be contributing significantly to the ground state stability of this complex. Alternative explanations for the anomalous behavior were possible and have yet to be explored fully. For example, the anomalous behavior could also be due to slight changes in the ground state geometry for the sterically demanding HMB complex. Given that the potential energy surface for complex formation is relatively shallow, such changes in geometry may not influence the magnitude of the association constant in a measureable way. However, significant changes in the vertical excitation energy and therefore to the position of the absorption maxima, could result. What was needed was a different approach to examine these data that would allow absorption maxima and association constants to be evaluated independently. CT complexes are usually described using a two-state model in which a combination of non-bonded (WN) and ion-pair (WI) states are assumed [1–5]. The ground state (WG) and first excited state (WE) wave functions are generally represented by a linear combination of these many electron wave functions given by the following equations.
WG ¼ c0 WN þ cI WI
ð2aÞ
WE ¼ c0 WI cI WN
ð2bÞ
Additional contributions due to localized excited states of either the acceptor or donor are usually ignored. Using a variational approach the energy of the ground state (EG) and excited states (EE) can be described as given in the following equation.
EE=G ¼
ðW I:I þ W N:N 2W I:N SI:N Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðW I:I W N:N Þ þ 4ðW I:N W I:I SI:N ÞðW I:N W N:N SI:N Þ 2 I s2I:N
ð3Þ The derivation of Eq. (3) has been presented by several authors [18] and the details will not be included here. The symbols W1:1 and WN:N represent the solutions to the appropriate coulomb integrals while W1:N and SI:N are the solutions for the exchange and overlap integrals based on the wave functions depicted in Eq. (2). The term ðW I:I W N:N Þ corresponds to the energy difference between the pure ion-pair state and the pure non-bonded state, which can be approximated by:
ðW I:I W N:N Þ ID EA þ C
ð4Þ
where ID is the vertical ionization potential of the donor, EA is the electron affinity of the acceptor and C is the coulomb energy release due to solvating the ions at the equilibrium configuration (i.e. solvating the ion pair within the complex geometry). This model predicts the excitation energy for the CT complex, DECT, as the energy difference between the ground and excited state, EE EG. Thus, letting B0 ¼ ðW I:N W N:N SI:N Þ and substitution of Eq. (4) into the model function depicted in Eq. (3) results in Eq. (5):
DECT ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðID EA þ CÞ2 þ 4ðB0 ÞðB0 ðID EA þ CÞSI:N Þ ð1 S2I:N Þ
ð5Þ
Eq. (5) can be used to predict the CT excitation energy based on three adjustable parameters; C, B0, and SI:N, when EA of the acceptor and ID of the donor are known. The application of Eq. (5), or variations of it, to the observed absorption spectra of multiple families of CT complexes has been described [2,3,5,19]. Indeed, the relationship between DECT and EA has been used to predict the electron affinities for many classes of acceptors with moderate success [20,21]. The analysis of the energies can be extended to determine the stabilization of the ground state CT complex by assuming the predicted ground state energy, EG, is related to the enthalpy of complex formation. Thus, Eq. (3), again with the appropriate substitutions, gives the association constant, KCT according to:
ln K CT ¼
DECT ð1 S2I:N Þ ðID EA Þ W 2RTð1 S2I:N Þ
ð6Þ
It should be noted that Eq. (6) has a single adjustable parameter, W, because DECT can be estimated from the spectra and SI:N can be fixed based on the application of Eq. (5). The term W includes the entropic contribution to complex formation, DSCT, as well as WI:I, WI:N, and other factors. Specifically, W is given by:
W ¼ 2 W 1:1 W 1:N S1:N 1 S21:N T DSCT þ C
ð7Þ
Based on Eq. (6), a relationship should exist between the stability of the ground state complex and (ID EA) for families of CT complexes in which the ion pair interactions contribute to complex stability. Comparisons among different groups of acceptors and donors should give insight into the nature of the interactions that bind these complexes together. Thus, using Eqs. (5) and (6) to fit excitation energies and association constants simultaneously should yield valuable information concerning the nature of these interactions. This report outlines our continued effort to understand the thermodynamics of charge transfer complex formation. Explanations for the previously observed anomalous behavior [17] of the HMB/TCNB complex are explored. Additional families of complexes are included in the current study, specifically complexes between methylated benzene donors and pyromellitic dianhydride (PMDA) or 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ) as acceptors in addition to the TCNE and TCNB complexes. The acceptors and donors used in this study are collected in Chart 1. The influence of solvent on the stability of these complexes is also described. 2. Experimental 2.1. Materials The acceptors and donors used in this study are shown in Chart 1 along with their ionization potentials or electron affinities [22]. Tetracyanoethylene (TCNE) and 2,3-dichloro-5,6-dicyano-pbenzoquinone (DDQ) were purchased from Aldrich and were purified by vacuum sublimation followed by repeated recrystallization from chloroform. 1,2,4,5-Tetracyanobenzene (TCNB) was purchased from Aldrich and was purified by passing it twice through silica gel with dichloromethane as the elution solvent, followed by recrystallization twice from chloroform. Pyromellitic dianhydride (PMDA) was recrystalized multiple times from ethyl acetate. The methylated benzene donors were purchased from Aldrich with the exception of toluene, which was purchased from Fisher Scientific. Toluene (TOL) was purified by passing it through activated alumina. Purification of p-xylene (PXY) was completed by recrys-
W.D. McKim et al. / Journal of Molecular Structure 1033 (2013) 131–136
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Chart 1.
talization in chloroform at low temperature. Mesitylene (MES; 1,3,5-trimethylbenzene) was fractionally distillation at atmospheric pressure. Durene (DUR; 1,2,4,5-tetramethylbenzene) and pentamethylbenzene (PMB) were purified by passing them through silica gel with 1,2-dichloroethane as the elution solvent followed by repeated recrystallization from ethanol. Hexamethylbenzene (HMB) was purified by sublimation twice and repeated recrystalized from ethanol. For all the acceptors and donors used the UV absorbance was monitored and purification was continued until no further improvements in baseline absorbance were observed. The solvents dichloromethane (DCLM), and 1,2-dichloroethane (DCLE) and acetonitrile (ACN) were of HPLC grade from EM Science and used without further purification. Butyronitrile (BCN) was purchased from Aldrich and fractionally distilled under nitrogen before use.
Fig. 1. Absorption spectra of PMDA solution in DCLE in which successive aliquots of HMB solution have been added showing the formation of the PMDA/HMB CT complex.
3. Results 2.2. Methods The absorption spectra were recorded as a function of acceptor and donor concentrations at 25 °C using a Beckman Model DU-640 spectrophotometer. The temperature of the cell compartment of the spectrophotometer was kept constant using a temperaturecontrolled water circulator purchased from VWR Scientific. Solutions containing the individual acceptors and donors were prepared immediately prior to use. The method used to determine the association constants has been described in detail previously [17,23]. Briefly, two series of absorption data were recorded for each complex. The first type of absorption data required placing an aliquot of dilute acceptor into a 10 cm quartz cell and adding successive volumes of donor from a concentrated stock solution. The absorption spectrum of the sample was recorded after each addition of donor. We have called data collected under these conditions the ideal solution set. The acceptor concentrations were typically 104 M while the donor concentrations were varied between 103 and 102 M. The second series of absorption data was recorded with the acceptor and donor both starting at 102 M and diluting the sample with successive volumes of solvent. The absorption spectrum of the samples was again recorded after each addition of solvent. We have called data collected under these conditions the quadratic data set. Five repetitions of both data sets, using freshly prepared stock solutions, were recorded for each complex to establish the precision of the association constant determination. The reported error limits are based on 95% confidence intervals obtained by multiple replicated measurements.
A typical ideal data set for the HMB/PMDA CT complex in DCLE is shown in Fig. 1. The absorption measurements were used to produce the plot shown in Fig. 2a where the observed absorbance at 450 nm is plotted as a function of the product of the initial acceptor and donor concentrations, [A]0[D]0. Data obtained using quadratic conditions for the HMB/PMDA CT complex in DCLE were also collected and the observed absorbances at 450 nm are included in Fig. 2b. There has been significant dialog detailing the difficulties encountered with the application of Benesi–Hildebrand [24] or related methods [25–27] to the determination of the association constants for weakly bound CT complexes [17,23,28–31]. Much of the discussion has focused on the need for significant curvature in these plots if KCT is to be extracted from them [32]. It is equally important to maintain concentrations sufficiently low to avoid higher order complex formation. Indeed, the method of constant variations, or Job’s analysis [33], shows that for these acceptors and donors, at concentrations below 102 M, as used in this study, dimerization, and higher order complexes, are not important [17,23]. Examination of Fig. 2 shows that neither of the plots displays significant curvature. Thus, taken individually, neither data set allows KCT to be determined with accuracy. When analyzed together, however, these two plots sample significantly different sections of the complexation surface so that KCT can be determined with sufficient accuracy by comparing both data sets simultaneously. The initial slope of the ideal plot obtained in Fig. 2a is extrapolated onto the quadratic plot in Fig. 2b for comparison. Given that the ideal slope is measurably different from the slope observed from the quadratic data set is solid evidence that
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W.D. McKim et al. / Journal of Molecular Structure 1033 (2013) 131–136 Table 1 Association constants for CT complex formation with methylated benzene donors.
0.02
Absorbance
0.01
0.00
Acceptor
Donor
kCTa (nm)
KCTb (M1)
eCTc (M1 cm1)
TCNE
TOL PXY MES DUR PMB HMB
410 445 465 490 510 540
1.8 ± 0.2 2.1 ± 0.3 2.7 ± 0.4 4.8 ± 0.4 10.5 ± 0.8 21.7 ± 1.0
430 ± 20 500 ± 25 1120 ± 20 1300 ± 30 2130 ± 40 3110 ± 50
PMDA
TOL PXY MES DUR PMB HMB
360d 375d 380 400 409 433
1.4 ± 0.3 2.0 ± 0.3 2.5 ± 0.4 3.7 ± 0.4 8.5 ± 0.5 18.3 ± 0.6
160 ± 10 160 ± 10 190 ± 12 200 ± 20 200 ± 17 210 ± 20
TCNB
TOL PXY MES DUR PMB HMB
320d 354 359 400 406 430
1.8 ± 0.2 2.9 ± 0.3 3.4 ± 0.3 5.9 ± 0.5 6.8 ± 0.6 9.1 ± 0.9
130 ± 13 90 ± 9 140 ± 20 100 ± 10 150 ± 15 200 ± 20
DDQ
TOL PXY MES DUR PMB HMB
530d 540d 545d 583 586 618
3.5 ± 0.4 10.4 ± 0.4 17.0 ± 0.7 65.3 ± 1.0 107 ± 1.2 184 ± 1.5
205 ± 10 397 ± 10 447 ± 15 524 ± 15 901 ± 20 1620 ± 25
2.0x10-6
1.0x10-6
0.30 0.20 0.10 0.00 0.0
0.4x10-4
0.8x10-4
1.2x10-4
2
[PMDA]0[HMB]0 (M ) Fig. 2. (a) Plot of the absorbance of the PMDA/HMB CT complex observed at 450 nm as a function of the product of the initial acceptor and donor concentrations, [PMDA]0[HMB]0, under ideal conditions (see text). (b) Plot of the absorbance of the HMB/PMDA CT complex observed at 450 nm as a function of the initial acceptor and donor concentrations, [PMDA]0[HMB]0, collected under quadratic conditions. The slope of the line obtained from the ideal conditions is extrapolated onto this plot (dashed line).
the association constant can be extracted with accuracy. The absorption maxima and association constants obtained using non-linear least squares fitting of both the ideal and quadratic data sets for each complex, as described in our earlier reports [17,23], for several families of complexes in DCLE solvent are collected in Table 1. 4. Discussion The acceptors and donors used in this study are shown in Chart 1. The electron affinities for the acceptors, when available, and the ionization potentials for the donors are also included in the chart [21,22]. A plot of the observed absorption maxima for the CT complexes in DCLE solvent (Table 1) versus the ionization potentials of the donors and the electron affinities of the acceptors according to Eq. (5) is shown in Fig. 3. The EA values for TCNB and TCNE have been determined experimentally and are available in the literature [21,22]. Complexes in which TCNB and TCNE are used as acceptor are shown in the plot as filled circles and filled diamonds, respectively. The values of the electron affinities for PMDA and DDQ have yet to be reported. Complexes with these acceptors are included in the plot as open triangles and open squares, respectively, where the individual EA values for these two acceptors have been estimated to give the best fit according to Eq. (5) for all complexes included in the plot. The best fit using the available data from all four acceptors results when B0 = 0.90 eV, SN:I = 0.38, and C = 4.5 eV. These values are similar to reported values of these parameters [34]. It should be noted that a positive value of B0 leading to equally good fits to these data can also be obtained. The negative value of B0 has been reported here to be consistent with previous reports. A detailed discussion of these values is premature until a significant test of the validity of these values can be devised. The fitting procedure also predicts values of the electron affinity for the acceptors DDQ EA = 3.5 eV and PMDA EA = 2.3 eV. The predicted electron affinities correlate well with the reported single electron reduction potentials for this series of acceptors [22]. Similar plots for families of donors with many different types of accep-
(2.1) (2.3) (3.4) (3.7) (4.1) (20.0)
a
kCT of the wavelength of maximum absorbance for the lowest energy CT band. KCT is the association constant for complex formation in DCLE solvent at 25 ± 1 °C. Values in parentheses are for DCLM solvent at 25 ± 1 °C taken from Ref. [12]. c eCT is the extinction coefficient of the lowest energy CT band at the wavelength indicated. d Wavelength at which data was collected; a distinct maximum is not observed in this case. b
tors have been reported with equally good correlations being observed [2–5]. Based on correlations similar to these, the theoretical description of the observed spectral transition as being a charge transfer transition has been uniformly accepted. More germane to the present discussion, all of the complexes used to construct the plot shown in Fig. 3 conform to the relationship as described by Eq. (5) with no significant outliers. It can be concluded that the absorption spectra are not the source of the deviation observed in the case of the HMB/TCNE complex observed earlier [17]. Therefore, the anomalous behavior observed for this specific complex must be tied to a unique characteristic of the association constant. Turning to the evaluation of the association constants, plots of lnKCT versus (ID EA) for TCNB and DDQ complexes with several methylbenzene donors are shown in Fig. 4. The plots in Fig. 4 show that the association constants fall cleanly into two distinct family groupings according to the acceptor used. Previous examples of this type of analysis have resulted in poor correlations between lnKCT and (ID EA) being observed [2–5,17]. There are two possible explanations for the improvement in the observed correlation. The families of complexes included in the current study were chosen specifically to minimize possible differences in complex formation; they are all p-type acceptors and donors and were recorded in the same solvent. The second explanation concerns the method used in determining the association constants. There are reports of the association constants for TCNE complexes with HMB that vary more than 50% while the reported association constants for TCNE:TOL complexes differ by more than an order of magnitude [17]. With such a wide range of reported association constants to choose from, there is little wonder that correlations between the association constants and models functions have previously failed to produce reasonable results. On the bright side, there is reason to be more confident in the values of the association constants reported
W.D. McKim et al. / Journal of Molecular Structure 1033 (2013) 131–136
Fig. 3. Plot of the transition energies of the CT complexes as a function of the difference between the ionization potentials of the donors and the electron affinities of the acceptors. The solid line indicates the best fit of the data according to Eq. (5) for the methylated benzene donors with DDQ (squares), TCNE (diamonds), PMDA (triangles), and TCNB (circles) as acceptors in DCLE.
herein. Close examination of the plots in Fig. 4 shows that even the relatively small scatter observed within each family of complexes is likely do to real differences in the binding interactions between the acceptors and the individual donors because the systematic nature of the observed patterns. Included in Fig. 4 are the predicted curves (dashed lines) according to Eq. (6) for each of the families of complexes. The predictions are based on Eq. (6) where the value of SIN obtained from the analysis of the absorption data is included as fixed values and only W is allowed to vary. Thus, the slope of the model function is fixed but the off-set can be adjusted to fit the association constants within each family. The predicted association constants, based on the established correlation with the absorption spectra, do not allow a reasonable fit to the measured association constants to be obtained. The model predicts a far steeper dependence of the association constant on ID EA than is observed experimentally. It can be concluded that the theoretical interpretation of the association constants as being due to CT interactions is not supported by the observed correlations in Fig. 4. Plots of the association constants for the methylbenzene donors with PMDA and TCNE as acceptors are shown in Fig. 5. Both data sets again fall into distinct family groups according to the acceptor used. Attempts to fit either of the full data sets according to Eq. (6) and the absorption data again fail. Comparing the plots shown in Fig. 5, with those shown in Fig. 4 suggests that the plots using for the PMDA and TCNE acceptors have far greater curvature than observed for the plots with the DDQ and TCNB complexes. This observation suggests that PMDA and TCNE families are remarkably different the TCNB and DDQ complexes described above. When the
Fig. 4. Plot of the natural logarithm of the association constant for CT complex formation verses the difference between the ionization potentials of the donors and the electron affinities of the acceptors. Dashed lines are the best fit of the data according to Eq. (6) for the DDQ (squares) and TCNB (circles) families of complexes with methylated benzene donors.
135
association constants for the HMB, PMB, and DUR complexes are considered separately from the constants for the weaker donors within the PMDA or TCNE families, excellent agreement with these specific association constants can be achieved. The dashed lines included in Fig. 5 show the best fit to the selected association constant data using the parameters obtained from the fit of the absorption spectra as fixed values with W as the only adjustable parameter. The remaining weak donors in these families, specifically the MES, PXY, and TOL donors, do not correlate well with the behavior predicted. Instead, these weaker complexes appear to have shallow slopes similar to those observed for the TCNB and DDQ complexes as shown in Fig. 4. This observation suggests that there is a change in the type of interactions responsible for complex formation. For the TCNE and PMDA complexes, with the better donors included in these studies, specifically for HMB, PMB, and DUR complexes, it appears that ion-pair interaction may play a significant role in complex formation. For the weaker donors, specifically MES, PXY, and TOL, and all of the TCNB and DDQ complexes studied, ion-pair interactions do not contribute significantly to complex stabilization. We previously reported anomalous behavior for the TCNE/HMB in methylene chloride solvent [17]. It appears that this behavior is repeated for some of the current complexes in DCLE solvent. This observation suggests a simple test. If ‘‘non-bonded’’ interactions are important to complex stability, the association constants should decrease in more polar solvent because the solvent–solute interactions compete with complex formation. However, ion-pair interactions should be favored in a more polar solvent because charge separation should be better supported in the more polar solvent. Thus, it can be expected that with decreasing solvent polarity the association constants for complexes decrease if ionpair interactions contribute significantly to the complex stability but they should increase if ion-pair interactions are negligible. Fig. 6 includes the plots of lnKCT versus (ID EA) for TCNE complexes with methylated benzene donors in DCLE (e = 10.4) and in DCLM [17] (e = 8.9). Slight, albeit consistent, decreases in the association constants for the weaker donors indicate that for these complexes the ion-pair interactions do not contribute significantly to the ground state stability. Small increases for the association constants for the better donors in the more polar solvent support the view that ion-pair interactions contribute to the ground state stability in these special cases. Can the ion-pair contribution be ‘‘turned on’’ simply by using more polar solvents? To examine this possibility, the TCNB complexes have been examined in several solvents. The data plotted in Fig. 4 for TCNB complexes indicates that the ion-pair
Fig. 5. Plot of the natural logarithm of the association constant for CT complex formation verses the difference between the ionization potentials of the donors and the electron affinities of the acceptors. Dashed lines are according to Eq. (6) for the TCNE (diamonds) and PMDA (triangles) families of complexes with methylated benzene donors in which only the HMB, PMB, and DUR complexes are considered (see text).
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root cause of the lack of significant correlation being observed in previous examples of plots like those shown in Figs. 4–6 [2,3,5]. However, the correlations between CT absorption spectra and the association constants for closely related complexes can be used as a significant test of the influence of ion-pair contributions to the stability of these complexes. 5. Conclusion
Fig. 6. Plot of the natural logarithm of the association constant for CT complex formation verses the difference between the ionization potentials of the donors and the electron affinity of TCNE. Data are for DCLE (filled diamonds) and DCLM (open diamonds). Arrows indicate the increase in association constant for weaker donors but a decrease in association constant for the stronger donors as the solvent polarity decreases from DCLE to DCLM (see text).
contribution to the ground state stability is not important in DCLE solvent. The association constants for the TCNB:HMB complexes were measured in butyronitrile (BCN, e = 24.8) and acetonitrile (ACN, e = 36.6) and were found to be KCT(BCN) = 8.4 ± 0.8 M1 and KCT(ACN) = 7.5 ± 0.7 M1, respectively. The association constants for the TCNB:PXY complexes were also measured and found to be KCT(1 and KCT(ACN) = 2.2 ± 0.4 M1 in BCN and ACN, BCN) = 2.6 ± 0.3 M respectively. If ion pair contributions were to become important the association constants for the HMB complexes would increase with increasing solvent polarity. Clearly, they do not. Instead, for both the PXY and HMB complexes, the decreases in association constant with increasing solvent polarity supports the idea that ion-pair interactions do not contribute significantly to the complex stabilization in these complexes. It is of interest that the apparent change in stabilization occurs in both the PMDA and TCNE families but not in DDQ or TCNB families. A priori DDQ would be expected to be the best acceptor used in this study based on its electron affinity (or reduction potential). It would seem reasonable to assume that complexes between DDQ and the donors used here would be the most likely to have significant ionpair interactions in the ground state. There is no evidence to support this assumption. Why are ion-pair interactions seemingly important to PMDA complexes but not to the DDQ complexes where ion-pair interactions would be more probable? Part of answer to this question may be buried in the magnitudes of the off-set terms, W. These offsets play a significant role in determining when the ion-pair interactions reach stabilization energies that are competitive with the strengths of non-bonded interactions within a specific complex family, as shown by the plots in Figs. 4 and 5. Examination of Eq. (7) reveals that the absolute value of W is poorly defined because the individual values of WI:I and WI:N cannot be determined experimentally. Assuming the variation in W between families of donors is due solely to differences in DSCT for the different acceptors does allow D(DSCT) for complex formation to be estimated. Evaluation of the fitted lines in Fig. 5 for TCNE and PMDA complexes gives a measure of the D(DSCT) = 40 50 JK1 mol1. The magnitude of this difference is consistent with the TCNE complexes being more highly ordered than the related PMDA complexes as is expected for stronger complex formation in the case of TCNE. A more detailed discussion of the offset values is not warranted until additional examples of complexes in which ion-pair contributions are important can be found. The sensitivity of the observed association constants to relatively minor changes in DSCT, through the off-set term W, does suggest that small variations in complex structure will lead to significant variation in the association constant and could be the
Accurate measurements of the association constants for CT complex were reported and compared with theoretical model predictions. The results show that these complexes fall into two categories; those complexes in which ion-pair contributions are negligible and those where ion-pair interactions contribute significantly to the ground state stability of the complex. References [1] (a) R.S. Mulliken, J. Am. Chem. Soc. 72 (1950) 600; (b) R.S. Mulliken, J. Am. Chem. Soc. 72 (1950) 4493; (c) R.S. Mulliken, J. Chem. Phys. 19 (1951) 514; (d) R.S. Mulliken, J. Am. Chem. Soc. 74 (1952) 811; (e) R.S. Mulliken, J. Chem. Phys. 23 (1955) 397. [2] R. Foster, Organic Charge-transfer Complexes, Academic Press, New York, 1969. [3] R.S. Mulliken, W.B. Person, Molecular Complexes, Wiley, New York, 1969. [4] S.P. McGlynn, Chem. Rev. 58 (1958) 1113–1156. [5] M.W. Hanna, J.L. Lippert, in: R. Foster (Ed.), Molecular Complexes, Elek Science, London, 1973. Chapter 1. [6] S. Ahuja, Chiral Separations by Chromatography, Oxford University Press, Washington, D.C., 2000. [7] B.M. Rosen, C.J. Wilson, D.A. Wilson, M. Peterca, M.R. Imam, V. Percec, Chem. Rev. 109 (2009) 6275–6540. [8] K. Matsumura, T. Mori, Y. Inoue, J. Org. Chem. 75 (2010) 5461–5469. [9] M. Chanon, M.D. Hawley, M.A. Fox, in: M.A. Fox, M. Chanon (Eds.), Photoinduced Electron Transfer, Elsevier, New York, 1988. Chapter 1. [10] X.-D. Zhuang, Y. Chen, B.-X. Li, D.-G. Ma, B. Zhang, Y. Li, Chem. Mater. 22 (2010) 4455–4461. [11] E. Faulques, D.L. Perry, A.V. Yeremenko, Spectroscopy of Emerging Materials, Kluwer Academic Publishers, Boston, 2004. [12] C. Wang, H. Dong, W. Hu, Y. Liu, D. Zhu, Chem. Rev. 112 (2012) 2208–2267. [13] a) P.L. Anelli, P.R. Ashton, R. Ballarini, V. Balzani, M. Delgado, M.T. Gandolfi, T.T. Goodnow, A.E. Kaifer, D. Philp, M. Pietraszkiewicz, L. Prodi, M.V. Reddington, A.M.Z. Slawin, N. Spencer, J.F. Stoddart, C. Vincent, D.J. Williams, J. Am. Chem. Soc. 114 (1992) 193–218; b) R.A. Bissell, E. Cordova, A.E. Kaifer, J.F. Stoddart, Nature (London) 369 (1994) 133–137; c) M. Asakawa, P.R. Ashton, S.E. Boyd, C.L. Brown, R.E. Gillard, O. Kocian, F.M. Raymo, J.F. Stoddart, M.S. Tolley, A.J.P. White, D.J. Williams, J. Org. Chem. 62 (1997) 26–37. [14] C.-H. Sue, S. Basu, A.C. Fahrenbach, A.K. Shveyd, S.K. Dey, Y.Y. Botrosac, J.F. Stoddart, Chem. Sci. 1 (2010) 119–125. [15] S.K. Lee, S.Y. Shin, S. Lee, C. Lee, J.W. Park, J. Chem. Soc. Perkin Trans. 2 (2001) 1983–1988. [16] M.J.S. Dewar, C.C. Thompson, Tetrahedron Suppl. 7 (1966) 97–114. [17] B.R. Arnold, A. Euler, K. Fields, R.Y. Zaini, J. Phys. Org. Chem. 13 (2000) 729– 734. [18] See, for example, equation 2.22 in Ref. 2, equation 2.15 in Ref. 3, and equation 19 in Ref. 5, as well as Ref. 13. [19] R.S. Mulliken, W.B. Person, Ann. Rev. Phys. Chem. 13 (1962) 419. [20] W.B. Person, J. Chem. Phys. 38 (1964) 109–117. [21] G. Briegleb, Angew. Chem. (Int. Ed.) 3 (1964) 617. [22] P.J. Linstrom, W.G. Mallard (Eds.), NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology, Gaithersburg MD.. [23] R. Zaini, A.C. Orcutt, B.R. Arnold, Photochem. Photobiol. 69 (1999) 443–447. [24] H.A. Benesi, J.J. Hildebrand, J. Am. Chem. Soc. 71 (1949) 2703–2707. [25] R.L. Scott, Recl. Trav. Chim. Pays-Bas. 75 (1956) 787. [26] R. Foster, D.L. Hammick, A.A. Wardley, J. Chem. Soc. (1953) 3817–3820. [27] N.J. Rose, R.S. Drago, J. Am. Chem. Soc. 81 (1959) 6138–6141. [28] R. Wang, Z.-W. Yu, Acta Phys. -Chim. Sin. 23 (2007) 1353–1359. [29] C. Yang, L. Liu, T.-W. Mu, Q.-X. Guo, Anal. Sci. 16 (2000) 537–539. [30] S.M. Hoenigman, C.E. Evans, Anal. Chem. 68 (1996) 3274. [31] K.A. Connors, J. Pharm. Sci. 84 (1995) 843. [32] G. Weber, in: B. Pullman, M. Weissbluth (Eds.), Molecular Biophysics, Academic Press, New York, 1965. [33] P. Job, Comp. Rend. 180 (1925) 928–930. [34] For comparison purposes only, the reported values for I2 complexes with aromatic donors are: B0 = 0.6 eV, SIN = 0.1 and C = 3.5 eV when the ionization potential of I2 is taken as 1.7 eV (Ref 14).
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Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Analysis of the association constants for charge-transfer complex formation William D. McKim, Jayanta Ray, Bradley R. Arnold ⇑ Department of Chemistry and Biochemistry, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, United States
h i g h l i g h t s " Absorption spectra and association constants for charge transfer complexes were measured. " A model was used to predict the absorption maxima for the charge transfer bands. " The model assumes charge transfer interactions are important to complex formation. " Several classes of complexes do not conform to the model predictions. " Charge transfer interactions are not important to complex stability in many cases.
a r t i c l e
i n f o
Article history: Received 23 March 2012 Received in revised form 9 August 2012 Accepted 9 August 2012 Available online 23 August 2012 Keywords: Association constant Equilibrium constant Acceptor donor complex Absorption spectra
a b s t r a c t The phenomenon of charge transfer (CT) complex formation has been of interest for more than 50 years and has led to the development of numerous applications. Even with the prolonged interest in these complexes the interactions responsible for complex formation have yet to be fully characterized and remain an area of sustained relevance. This report outlines the measurement of the association constants for CT complex formation of a series of methylated benzene donors with tetracyanoethylene, pyromellitic dianhydride, 2,3-dichloro-5,6-dicyano-p-benzoquinone, and 1,2,4,5-tetracyanobenzene acceptors in 1,2-dichloroethane solvent. The evaluation of the position of the CT absorption maximum and the magnitudes of the association constants within a theoretical model is described. The influence of solvent polarity on the magnitudes of the association constants was also discussed. These studies show that non-bonding interactions are important in most complexes while ion-pair interactions play a significant role in a select few of the complexes studied. Published by Elsevier B.V.
1. Introduction The spectroscopy of charge-transfer (CT) complexes continues to be of significant interest after more than half a century of sustained research [1–5]. CT complex formation has been used to characterize derivatives, to estimate ionization potentials and electron affinities, to induce crystallization for X-ray analyses, or to aid in the chromatographic separation of components [2,5–8]. These complexes play an important role in many organic and inorganic reaction mechanisms as well as in biological processes, imaging applications, and the design of photoelectric devices [9–12]. Understanding the nature and thermodynamics of complex formation can be important to understanding protein folding and to the control of macromolecular assembly [13–15]. After considering the significance these complexes play in such a broad array of applications it is clear that a detailed understand of the thermodynamics of complex formation is of paramount importance.
⇑ Corresponding author. E-mail address: [email protected] (B.R. Arnold). 0022-2860/$ - see front matter Published by Elsevier B.V. http://dx.doi.org/10.1016/j.molstruc.2012.08.015
It has been suggested that a correlation between the magnitude of the association constant (KCT) and the wavelength of the CT absorption maximum (kmax) could be expected based on a perturbation treatment (Eq. (1)) [16].
logðK CT =K CT0 Þ ¼ Cðkmax k0 Þ
ð1Þ
Here KCT0 and k0 are the association constant and absorption maximum, respectively, for an arbitrarily-chosen standard complex. Linear correlations between log(KCT/KCT0) and (kmax k0) have been described previously for several classes of acceptors and donors. As described by Dewer in his initial report [16], the appearance of linear correlations according to Eq. (1) would be a necessary condition, but not sufficient, to prove coulomb–coulomb interactions were important to the stability of the complex. For weak acceptors and donors, where the ion-pair could play a minimal role in the stability of the ground state, such correlations may be due to non-bonded interactions that also happen to correlate with changes in kmax values. In our previous report [17], we presented the results of our studies on the complexes formed between 1,2,4,5-tetracyanoben-
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zene (TCNB) or tetracyanoethylene (TCNE) as acceptors with a series of methyl substituted benzene donors. Linear correlations between the measured association constant and the CT kmax within each series of complexes were observed, in agreement with Eq. (1). However, we suggested that ion-pair contributions were not important to the ground state stability of these complexes based on the relative magnitudes of the slopes observed when considering the plots according to Eq. (1). Also described in our earlier report, the HMB/TCNE complex was unique among the complexes studied because it did not correlate well with the other complexes included in the initial study [17]. At that time we suggested that the anomalous behavior of this specific complex could be due to a change in the bonding contributions and that ion-pair interactions might be contributing significantly to the ground state stability of this complex. Alternative explanations for the anomalous behavior were possible and have yet to be explored fully. For example, the anomalous behavior could also be due to slight changes in the ground state geometry for the sterically demanding HMB complex. Given that the potential energy surface for complex formation is relatively shallow, such changes in geometry may not influence the magnitude of the association constant in a measureable way. However, significant changes in the vertical excitation energy and therefore to the position of the absorption maxima, could result. What was needed was a different approach to examine these data that would allow absorption maxima and association constants to be evaluated independently. CT complexes are usually described using a two-state model in which a combination of non-bonded (WN) and ion-pair (WI) states are assumed [1–5]. The ground state (WG) and first excited state (WE) wave functions are generally represented by a linear combination of these many electron wave functions given by the following equations.
WG ¼ c0 WN þ cI WI
ð2aÞ
WE ¼ c0 WI cI WN
ð2bÞ
Additional contributions due to localized excited states of either the acceptor or donor are usually ignored. Using a variational approach the energy of the ground state (EG) and excited states (EE) can be described as given in the following equation.
EE=G ¼
ðW I:I þ W N:N 2W I:N SI:N Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðW I:I W N:N Þ þ 4ðW I:N W I:I SI:N ÞðW I:N W N:N SI:N Þ 2 I s2I:N
ð3Þ The derivation of Eq. (3) has been presented by several authors [18] and the details will not be included here. The symbols W1:1 and WN:N represent the solutions to the appropriate coulomb integrals while W1:N and SI:N are the solutions for the exchange and overlap integrals based on the wave functions depicted in Eq. (2). The term ðW I:I W N:N Þ corresponds to the energy difference between the pure ion-pair state and the pure non-bonded state, which can be approximated by:
ðW I:I W N:N Þ ID EA þ C
ð4Þ
where ID is the vertical ionization potential of the donor, EA is the electron affinity of the acceptor and C is the coulomb energy release due to solvating the ions at the equilibrium configuration (i.e. solvating the ion pair within the complex geometry). This model predicts the excitation energy for the CT complex, DECT, as the energy difference between the ground and excited state, EE EG. Thus, letting B0 ¼ ðW I:N W N:N SI:N Þ and substitution of Eq. (4) into the model function depicted in Eq. (3) results in Eq. (5):
DECT ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðID EA þ CÞ2 þ 4ðB0 ÞðB0 ðID EA þ CÞSI:N Þ ð1 S2I:N Þ
ð5Þ
Eq. (5) can be used to predict the CT excitation energy based on three adjustable parameters; C, B0, and SI:N, when EA of the acceptor and ID of the donor are known. The application of Eq. (5), or variations of it, to the observed absorption spectra of multiple families of CT complexes has been described [2,3,5,19]. Indeed, the relationship between DECT and EA has been used to predict the electron affinities for many classes of acceptors with moderate success [20,21]. The analysis of the energies can be extended to determine the stabilization of the ground state CT complex by assuming the predicted ground state energy, EG, is related to the enthalpy of complex formation. Thus, Eq. (3), again with the appropriate substitutions, gives the association constant, KCT according to:
ln K CT ¼
DECT ð1 S2I:N Þ ðID EA Þ W 2RTð1 S2I:N Þ
ð6Þ
It should be noted that Eq. (6) has a single adjustable parameter, W, because DECT can be estimated from the spectra and SI:N can be fixed based on the application of Eq. (5). The term W includes the entropic contribution to complex formation, DSCT, as well as WI:I, WI:N, and other factors. Specifically, W is given by:
W ¼ 2 W 1:1 W 1:N S1:N 1 S21:N T DSCT þ C
ð7Þ
Based on Eq. (6), a relationship should exist between the stability of the ground state complex and (ID EA) for families of CT complexes in which the ion pair interactions contribute to complex stability. Comparisons among different groups of acceptors and donors should give insight into the nature of the interactions that bind these complexes together. Thus, using Eqs. (5) and (6) to fit excitation energies and association constants simultaneously should yield valuable information concerning the nature of these interactions. This report outlines our continued effort to understand the thermodynamics of charge transfer complex formation. Explanations for the previously observed anomalous behavior [17] of the HMB/TCNB complex are explored. Additional families of complexes are included in the current study, specifically complexes between methylated benzene donors and pyromellitic dianhydride (PMDA) or 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ) as acceptors in addition to the TCNE and TCNB complexes. The acceptors and donors used in this study are collected in Chart 1. The influence of solvent on the stability of these complexes is also described. 2. Experimental 2.1. Materials The acceptors and donors used in this study are shown in Chart 1 along with their ionization potentials or electron affinities [22]. Tetracyanoethylene (TCNE) and 2,3-dichloro-5,6-dicyano-pbenzoquinone (DDQ) were purchased from Aldrich and were purified by vacuum sublimation followed by repeated recrystallization from chloroform. 1,2,4,5-Tetracyanobenzene (TCNB) was purchased from Aldrich and was purified by passing it twice through silica gel with dichloromethane as the elution solvent, followed by recrystallization twice from chloroform. Pyromellitic dianhydride (PMDA) was recrystalized multiple times from ethyl acetate. The methylated benzene donors were purchased from Aldrich with the exception of toluene, which was purchased from Fisher Scientific. Toluene (TOL) was purified by passing it through activated alumina. Purification of p-xylene (PXY) was completed by recrys-
W.D. McKim et al. / Journal of Molecular Structure 1033 (2013) 131–136
133
Chart 1.
talization in chloroform at low temperature. Mesitylene (MES; 1,3,5-trimethylbenzene) was fractionally distillation at atmospheric pressure. Durene (DUR; 1,2,4,5-tetramethylbenzene) and pentamethylbenzene (PMB) were purified by passing them through silica gel with 1,2-dichloroethane as the elution solvent followed by repeated recrystallization from ethanol. Hexamethylbenzene (HMB) was purified by sublimation twice and repeated recrystalized from ethanol. For all the acceptors and donors used the UV absorbance was monitored and purification was continued until no further improvements in baseline absorbance were observed. The solvents dichloromethane (DCLM), and 1,2-dichloroethane (DCLE) and acetonitrile (ACN) were of HPLC grade from EM Science and used without further purification. Butyronitrile (BCN) was purchased from Aldrich and fractionally distilled under nitrogen before use.
Fig. 1. Absorption spectra of PMDA solution in DCLE in which successive aliquots of HMB solution have been added showing the formation of the PMDA/HMB CT complex.
3. Results 2.2. Methods The absorption spectra were recorded as a function of acceptor and donor concentrations at 25 °C using a Beckman Model DU-640 spectrophotometer. The temperature of the cell compartment of the spectrophotometer was kept constant using a temperaturecontrolled water circulator purchased from VWR Scientific. Solutions containing the individual acceptors and donors were prepared immediately prior to use. The method used to determine the association constants has been described in detail previously [17,23]. Briefly, two series of absorption data were recorded for each complex. The first type of absorption data required placing an aliquot of dilute acceptor into a 10 cm quartz cell and adding successive volumes of donor from a concentrated stock solution. The absorption spectrum of the sample was recorded after each addition of donor. We have called data collected under these conditions the ideal solution set. The acceptor concentrations were typically 104 M while the donor concentrations were varied between 103 and 102 M. The second series of absorption data was recorded with the acceptor and donor both starting at 102 M and diluting the sample with successive volumes of solvent. The absorption spectrum of the samples was again recorded after each addition of solvent. We have called data collected under these conditions the quadratic data set. Five repetitions of both data sets, using freshly prepared stock solutions, were recorded for each complex to establish the precision of the association constant determination. The reported error limits are based on 95% confidence intervals obtained by multiple replicated measurements.
A typical ideal data set for the HMB/PMDA CT complex in DCLE is shown in Fig. 1. The absorption measurements were used to produce the plot shown in Fig. 2a where the observed absorbance at 450 nm is plotted as a function of the product of the initial acceptor and donor concentrations, [A]0[D]0. Data obtained using quadratic conditions for the HMB/PMDA CT complex in DCLE were also collected and the observed absorbances at 450 nm are included in Fig. 2b. There has been significant dialog detailing the difficulties encountered with the application of Benesi–Hildebrand [24] or related methods [25–27] to the determination of the association constants for weakly bound CT complexes [17,23,28–31]. Much of the discussion has focused on the need for significant curvature in these plots if KCT is to be extracted from them [32]. It is equally important to maintain concentrations sufficiently low to avoid higher order complex formation. Indeed, the method of constant variations, or Job’s analysis [33], shows that for these acceptors and donors, at concentrations below 102 M, as used in this study, dimerization, and higher order complexes, are not important [17,23]. Examination of Fig. 2 shows that neither of the plots displays significant curvature. Thus, taken individually, neither data set allows KCT to be determined with accuracy. When analyzed together, however, these two plots sample significantly different sections of the complexation surface so that KCT can be determined with sufficient accuracy by comparing both data sets simultaneously. The initial slope of the ideal plot obtained in Fig. 2a is extrapolated onto the quadratic plot in Fig. 2b for comparison. Given that the ideal slope is measurably different from the slope observed from the quadratic data set is solid evidence that
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W.D. McKim et al. / Journal of Molecular Structure 1033 (2013) 131–136 Table 1 Association constants for CT complex formation with methylated benzene donors.
0.02
Absorbance
0.01
0.00
Acceptor
Donor
kCTa (nm)
KCTb (M1)
eCTc (M1 cm1)
TCNE
TOL PXY MES DUR PMB HMB
410 445 465 490 510 540
1.8 ± 0.2 2.1 ± 0.3 2.7 ± 0.4 4.8 ± 0.4 10.5 ± 0.8 21.7 ± 1.0
430 ± 20 500 ± 25 1120 ± 20 1300 ± 30 2130 ± 40 3110 ± 50
PMDA
TOL PXY MES DUR PMB HMB
360d 375d 380 400 409 433
1.4 ± 0.3 2.0 ± 0.3 2.5 ± 0.4 3.7 ± 0.4 8.5 ± 0.5 18.3 ± 0.6
160 ± 10 160 ± 10 190 ± 12 200 ± 20 200 ± 17 210 ± 20
TCNB
TOL PXY MES DUR PMB HMB
320d 354 359 400 406 430
1.8 ± 0.2 2.9 ± 0.3 3.4 ± 0.3 5.9 ± 0.5 6.8 ± 0.6 9.1 ± 0.9
130 ± 13 90 ± 9 140 ± 20 100 ± 10 150 ± 15 200 ± 20
DDQ
TOL PXY MES DUR PMB HMB
530d 540d 545d 583 586 618
3.5 ± 0.4 10.4 ± 0.4 17.0 ± 0.7 65.3 ± 1.0 107 ± 1.2 184 ± 1.5
205 ± 10 397 ± 10 447 ± 15 524 ± 15 901 ± 20 1620 ± 25
2.0x10-6
1.0x10-6
0.30 0.20 0.10 0.00 0.0
0.4x10-4
0.8x10-4
1.2x10-4
2
[PMDA]0[HMB]0 (M ) Fig. 2. (a) Plot of the absorbance of the PMDA/HMB CT complex observed at 450 nm as a function of the product of the initial acceptor and donor concentrations, [PMDA]0[HMB]0, under ideal conditions (see text). (b) Plot of the absorbance of the HMB/PMDA CT complex observed at 450 nm as a function of the initial acceptor and donor concentrations, [PMDA]0[HMB]0, collected under quadratic conditions. The slope of the line obtained from the ideal conditions is extrapolated onto this plot (dashed line).
the association constant can be extracted with accuracy. The absorption maxima and association constants obtained using non-linear least squares fitting of both the ideal and quadratic data sets for each complex, as described in our earlier reports [17,23], for several families of complexes in DCLE solvent are collected in Table 1. 4. Discussion The acceptors and donors used in this study are shown in Chart 1. The electron affinities for the acceptors, when available, and the ionization potentials for the donors are also included in the chart [21,22]. A plot of the observed absorption maxima for the CT complexes in DCLE solvent (Table 1) versus the ionization potentials of the donors and the electron affinities of the acceptors according to Eq. (5) is shown in Fig. 3. The EA values for TCNB and TCNE have been determined experimentally and are available in the literature [21,22]. Complexes in which TCNB and TCNE are used as acceptor are shown in the plot as filled circles and filled diamonds, respectively. The values of the electron affinities for PMDA and DDQ have yet to be reported. Complexes with these acceptors are included in the plot as open triangles and open squares, respectively, where the individual EA values for these two acceptors have been estimated to give the best fit according to Eq. (5) for all complexes included in the plot. The best fit using the available data from all four acceptors results when B0 = 0.90 eV, SN:I = 0.38, and C = 4.5 eV. These values are similar to reported values of these parameters [34]. It should be noted that a positive value of B0 leading to equally good fits to these data can also be obtained. The negative value of B0 has been reported here to be consistent with previous reports. A detailed discussion of these values is premature until a significant test of the validity of these values can be devised. The fitting procedure also predicts values of the electron affinity for the acceptors DDQ EA = 3.5 eV and PMDA EA = 2.3 eV. The predicted electron affinities correlate well with the reported single electron reduction potentials for this series of acceptors [22]. Similar plots for families of donors with many different types of accep-
(2.1) (2.3) (3.4) (3.7) (4.1) (20.0)
a
kCT of the wavelength of maximum absorbance for the lowest energy CT band. KCT is the association constant for complex formation in DCLE solvent at 25 ± 1 °C. Values in parentheses are for DCLM solvent at 25 ± 1 °C taken from Ref. [12]. c eCT is the extinction coefficient of the lowest energy CT band at the wavelength indicated. d Wavelength at which data was collected; a distinct maximum is not observed in this case. b
tors have been reported with equally good correlations being observed [2–5]. Based on correlations similar to these, the theoretical description of the observed spectral transition as being a charge transfer transition has been uniformly accepted. More germane to the present discussion, all of the complexes used to construct the plot shown in Fig. 3 conform to the relationship as described by Eq. (5) with no significant outliers. It can be concluded that the absorption spectra are not the source of the deviation observed in the case of the HMB/TCNE complex observed earlier [17]. Therefore, the anomalous behavior observed for this specific complex must be tied to a unique characteristic of the association constant. Turning to the evaluation of the association constants, plots of lnKCT versus (ID EA) for TCNB and DDQ complexes with several methylbenzene donors are shown in Fig. 4. The plots in Fig. 4 show that the association constants fall cleanly into two distinct family groupings according to the acceptor used. Previous examples of this type of analysis have resulted in poor correlations between lnKCT and (ID EA) being observed [2–5,17]. There are two possible explanations for the improvement in the observed correlation. The families of complexes included in the current study were chosen specifically to minimize possible differences in complex formation; they are all p-type acceptors and donors and were recorded in the same solvent. The second explanation concerns the method used in determining the association constants. There are reports of the association constants for TCNE complexes with HMB that vary more than 50% while the reported association constants for TCNE:TOL complexes differ by more than an order of magnitude [17]. With such a wide range of reported association constants to choose from, there is little wonder that correlations between the association constants and models functions have previously failed to produce reasonable results. On the bright side, there is reason to be more confident in the values of the association constants reported
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Fig. 3. Plot of the transition energies of the CT complexes as a function of the difference between the ionization potentials of the donors and the electron affinities of the acceptors. The solid line indicates the best fit of the data according to Eq. (5) for the methylated benzene donors with DDQ (squares), TCNE (diamonds), PMDA (triangles), and TCNB (circles) as acceptors in DCLE.
herein. Close examination of the plots in Fig. 4 shows that even the relatively small scatter observed within each family of complexes is likely do to real differences in the binding interactions between the acceptors and the individual donors because the systematic nature of the observed patterns. Included in Fig. 4 are the predicted curves (dashed lines) according to Eq. (6) for each of the families of complexes. The predictions are based on Eq. (6) where the value of SIN obtained from the analysis of the absorption data is included as fixed values and only W is allowed to vary. Thus, the slope of the model function is fixed but the off-set can be adjusted to fit the association constants within each family. The predicted association constants, based on the established correlation with the absorption spectra, do not allow a reasonable fit to the measured association constants to be obtained. The model predicts a far steeper dependence of the association constant on ID EA than is observed experimentally. It can be concluded that the theoretical interpretation of the association constants as being due to CT interactions is not supported by the observed correlations in Fig. 4. Plots of the association constants for the methylbenzene donors with PMDA and TCNE as acceptors are shown in Fig. 5. Both data sets again fall into distinct family groups according to the acceptor used. Attempts to fit either of the full data sets according to Eq. (6) and the absorption data again fail. Comparing the plots shown in Fig. 5, with those shown in Fig. 4 suggests that the plots using for the PMDA and TCNE acceptors have far greater curvature than observed for the plots with the DDQ and TCNB complexes. This observation suggests that PMDA and TCNE families are remarkably different the TCNB and DDQ complexes described above. When the
Fig. 4. Plot of the natural logarithm of the association constant for CT complex formation verses the difference between the ionization potentials of the donors and the electron affinities of the acceptors. Dashed lines are the best fit of the data according to Eq. (6) for the DDQ (squares) and TCNB (circles) families of complexes with methylated benzene donors.
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association constants for the HMB, PMB, and DUR complexes are considered separately from the constants for the weaker donors within the PMDA or TCNE families, excellent agreement with these specific association constants can be achieved. The dashed lines included in Fig. 5 show the best fit to the selected association constant data using the parameters obtained from the fit of the absorption spectra as fixed values with W as the only adjustable parameter. The remaining weak donors in these families, specifically the MES, PXY, and TOL donors, do not correlate well with the behavior predicted. Instead, these weaker complexes appear to have shallow slopes similar to those observed for the TCNB and DDQ complexes as shown in Fig. 4. This observation suggests that there is a change in the type of interactions responsible for complex formation. For the TCNE and PMDA complexes, with the better donors included in these studies, specifically for HMB, PMB, and DUR complexes, it appears that ion-pair interaction may play a significant role in complex formation. For the weaker donors, specifically MES, PXY, and TOL, and all of the TCNB and DDQ complexes studied, ion-pair interactions do not contribute significantly to complex stabilization. We previously reported anomalous behavior for the TCNE/HMB in methylene chloride solvent [17]. It appears that this behavior is repeated for some of the current complexes in DCLE solvent. This observation suggests a simple test. If ‘‘non-bonded’’ interactions are important to complex stability, the association constants should decrease in more polar solvent because the solvent–solute interactions compete with complex formation. However, ion-pair interactions should be favored in a more polar solvent because charge separation should be better supported in the more polar solvent. Thus, it can be expected that with decreasing solvent polarity the association constants for complexes decrease if ionpair interactions contribute significantly to the complex stability but they should increase if ion-pair interactions are negligible. Fig. 6 includes the plots of lnKCT versus (ID EA) for TCNE complexes with methylated benzene donors in DCLE (e = 10.4) and in DCLM [17] (e = 8.9). Slight, albeit consistent, decreases in the association constants for the weaker donors indicate that for these complexes the ion-pair interactions do not contribute significantly to the ground state stability. Small increases for the association constants for the better donors in the more polar solvent support the view that ion-pair interactions contribute to the ground state stability in these special cases. Can the ion-pair contribution be ‘‘turned on’’ simply by using more polar solvents? To examine this possibility, the TCNB complexes have been examined in several solvents. The data plotted in Fig. 4 for TCNB complexes indicates that the ion-pair
Fig. 5. Plot of the natural logarithm of the association constant for CT complex formation verses the difference between the ionization potentials of the donors and the electron affinities of the acceptors. Dashed lines are according to Eq. (6) for the TCNE (diamonds) and PMDA (triangles) families of complexes with methylated benzene donors in which only the HMB, PMB, and DUR complexes are considered (see text).
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root cause of the lack of significant correlation being observed in previous examples of plots like those shown in Figs. 4–6 [2,3,5]. However, the correlations between CT absorption spectra and the association constants for closely related complexes can be used as a significant test of the influence of ion-pair contributions to the stability of these complexes. 5. Conclusion
Fig. 6. Plot of the natural logarithm of the association constant for CT complex formation verses the difference between the ionization potentials of the donors and the electron affinity of TCNE. Data are for DCLE (filled diamonds) and DCLM (open diamonds). Arrows indicate the increase in association constant for weaker donors but a decrease in association constant for the stronger donors as the solvent polarity decreases from DCLE to DCLM (see text).
contribution to the ground state stability is not important in DCLE solvent. The association constants for the TCNB:HMB complexes were measured in butyronitrile (BCN, e = 24.8) and acetonitrile (ACN, e = 36.6) and were found to be KCT(BCN) = 8.4 ± 0.8 M1 and KCT(ACN) = 7.5 ± 0.7 M1, respectively. The association constants for the TCNB:PXY complexes were also measured and found to be KCT(1 and KCT(ACN) = 2.2 ± 0.4 M1 in BCN and ACN, BCN) = 2.6 ± 0.3 M respectively. If ion pair contributions were to become important the association constants for the HMB complexes would increase with increasing solvent polarity. Clearly, they do not. Instead, for both the PXY and HMB complexes, the decreases in association constant with increasing solvent polarity supports the idea that ion-pair interactions do not contribute significantly to the complex stabilization in these complexes. It is of interest that the apparent change in stabilization occurs in both the PMDA and TCNE families but not in DDQ or TCNB families. A priori DDQ would be expected to be the best acceptor used in this study based on its electron affinity (or reduction potential). It would seem reasonable to assume that complexes between DDQ and the donors used here would be the most likely to have significant ionpair interactions in the ground state. There is no evidence to support this assumption. Why are ion-pair interactions seemingly important to PMDA complexes but not to the DDQ complexes where ion-pair interactions would be more probable? Part of answer to this question may be buried in the magnitudes of the off-set terms, W. These offsets play a significant role in determining when the ion-pair interactions reach stabilization energies that are competitive with the strengths of non-bonded interactions within a specific complex family, as shown by the plots in Figs. 4 and 5. Examination of Eq. (7) reveals that the absolute value of W is poorly defined because the individual values of WI:I and WI:N cannot be determined experimentally. Assuming the variation in W between families of donors is due solely to differences in DSCT for the different acceptors does allow D(DSCT) for complex formation to be estimated. Evaluation of the fitted lines in Fig. 5 for TCNE and PMDA complexes gives a measure of the D(DSCT) = 40 50 JK1 mol1. The magnitude of this difference is consistent with the TCNE complexes being more highly ordered than the related PMDA complexes as is expected for stronger complex formation in the case of TCNE. A more detailed discussion of the offset values is not warranted until additional examples of complexes in which ion-pair contributions are important can be found. The sensitivity of the observed association constants to relatively minor changes in DSCT, through the off-set term W, does suggest that small variations in complex structure will lead to significant variation in the association constant and could be the
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