J. Phys. Chem. 1984,88, 1347-1350
+
~t .CH3 .H reactive pathway (MAPS/CH4-I). In constructing this model potential we used the available spectroscopic data in conjunction with a b initio calculations to define the asymptotic limits of methane and methyl radical. These limits were then joined by using a set of switching functions based on a b initio calculations performed along the dissociation path. This switching-function formalism confers a great deal of flexibility on the analytic model of the potential energy surface. One may, for example, use either ab initio or spectroscopic force constants in the two asymptotic limits. Further, as more detailed and sophisticated a b initio information describing the reaction pathway becomes available, it can be incorporated into this model by refitting the parameters of the switching functions. In effect, the construction and modification of a model potential energy surface has been divided into two more tractable steps: (1) determination of each asymptotic limit; (2) connection of these limits by physically realistic analytic functions. The general symmetric potential proposed in this paper only addresses the CHp .CH3 -H channel. There is another allowed reaction channel, namely, CH4 e H2 CH2('A1). However, the available thermochemical data49-51indicates that
+
+
(49) D. R. Stoll and H. Prophet, eds., "JANAF Thermochemical Tables", 2nd Ed., National Bureau of Standards, Washington, DC, 1971, Natl. Stand. Ref. Data Ser. ( U S . , Natl. Bur. Stand.) No. 37. (50) S.P. Heneghan, P. A. Kndat, and S. W. Benson, Int. J . Chem. Kinet., 13, 677 (1981). (51) C. C. Hayden, D. M. Neumark, K. Shobatake, R. K. Sparks, and Y. T. Lee, J . Chem. Phys., 76, 3607 (1982).
1347
its threshold is approximately 15 kcal/mol higher than that for the former channel. Even the symmetry-forbidden reaction CH, 2 H2 + CH2(3B1)has an endothermicity which is approximately 7 kcal/mol higher than that for the CH4 ~t .CH3 + .H reaction pathway. Triplet methylene undergoes an abstraction reaction with H, to form hydrogen atoms and methyl radicals.52 The model potential proposed here can be used, following Miller,53to find the .CH3 -H C H reaction path. Variational criteria can then be applied to locate the critical configuration as a function of energy and the activated complex as a function of temperature. Finally, this model potential can be used in quasiclassical trajectory calculations of the CHI 2 C H 3 .H unimolecular and bimolecular rate constants at energies where these are the only open reaction channels on the potential energy surface.
+
-
+
Acknowledgment. We express our gratitude to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and to the National Science Foundation for their support of this research. We also thank the Wayne State University Computing Center for providing the facilities which were used to carry out our calculations. Special thanks to Dr. K. N. Swamy for his helpful conversations. Registry No. CH4, 74-82-8; CH,, 15194-58-8; H, 12385-13-6. ~~
(52) C. W. Bauschlicher, Jr., Charles F. Bender, and H. F. Schaefer 111, J . Am. Chem. Soc., 98, 3072 (1976). (53) W. H. Miller, N. C. Handy, and J. E. Adams, J. Chem. Phys., 72, 99 (1980).
Kinetic Parameters for Hydrogen Bonding to an Anion Radical Gerald R. Stevenson,* James B. Sedgwick, and Richard C. Reiter Department of Chemistry, Illinois State University, Normal, Illinois 61 761 (Received: February 18, 1983; In Final Form: August 1 1 , 1983)
Electron spin resonance and relaxation theory have been utilized to measure the rate constant and its temperature dependence of hydrogen-bond formation to the p-cyanonitrobenzene anion radical (PCNB-a). The rate constant (k,)for hydrogen-bond exchange from the solvent to the unassociated anion radical (PCNB-. + HMPA-H-OEt PCNB-. --H-OEt + HMPA) is (7.0 & 1.0) X lo7 M-' s-l at 25 OC where the solvent is hexamethylphosphoramide(HMPA) and the hydrogen-bond donor is ethanol. The negative entropy of activation and entropy of reaction are interpreted in terms of an activated complex that consists of an ethanol molecule having a partial hydrogen bond to a solvent and anion radical molecule. This is the first report of activation parameters controlling the rate of hydrogen-bond formation to an anionic species.
-
In protic solvents, the most important phenomenon incorporated into the free energy of solvation of anions is hydrogen bonding. However, there are very few reports of thermodynamic parameters controlling hydrogen-bond formation to solvated anions due to experimental difficulties and complexities that arise from competing interactions such as ion association and solvent-solvent hydrogen-bonding interactions. These problems have been discussed by Benoit and co-workers.' For a few systems these difficulties have been overcome, and free energies of hydrogenbond formation to ion associated halide ions have been determined by using IR spectroscopy.2 For several systems, the presence of hydrogen-bonded anions in solution has been noted by their effect upon I R and N M R s p e ~ t r a . ~The - ~ difficulties of studying the (1) Lam, S. Y.; Louis, C.; Benoit, R. L. J . Am. Chem. SOC.1976,98,1156. (2) Symons,M. C. R.; Thomas, V. K. J. Chem. Sor., Faraday Trans. 1 1981, 77, 1891. ( 3 ) Srauss, I. M.; Symons, M. C. R.; Thompson, V. K. J . Chem. Soc., Faraday Trans. 1 1977, 73, 1253.
0022-3654/84/2088-1347$01 SO10
formation of hydrogen bonds to anions are greatly enhanced when one tries to study the kinetics of these processes. Thus, other than a single report from our laboratory,6 the literature is devoid of reports of the kinetics of hydrogen bonding to anions. Further, there are no reports of activation parameters for hydrogen-bond formation to anions in solution. Here we wish to report the first enthalpy and entropy of activation for hydrogen-bond formation to a solvated anion. This kinetic study is carried out with an anion system that is paramagnetic so that relaxation theory can be applied. The anion radical must be generated free from association with the cation and must be polarizable enough so that the formation of anion radical-proton donor hydrogen bonds will perturb the spin density in the anion radical. Also, the interpretation of the data, in this (4) Ritzhaupt, G.; Devlin, J. P. J. Phys. Chem. 1977, 81, 67. (5) Ryall, R. R.; Strobel, H. A,; Symons, M. C. R. J. Phys. Chem. 1977, 81, 253. (6) Stevenson, G. R.; Castillo, C. A. J. Am. Chem. SOC.1976, 98, 7950.
0 1984 American Chemical Society
1348 The Journal of Physical Chemistry, Vol. 88, No. 7, 1984
initial study, would be simplest if the enthalpy of transfer of the hydrogen bond from the solvent is near zero, so that the process would resemble a symmetrical double-well model. The system of choice is the p-cyanonitrobenzene anion radical in hexamethylphosphoramide (HMPA) with added ethanol (EtOH) serving as the proton donor. It is well established that anion radicals can be generated free of ion association in HMPA' and that the addition of a proton donor to the solution results in the formation of both hydrogen-bonded HMPA and hydrogen-bonded anion radical.8 The problem of dimerization of the proton donor is circumvented by the formation of the strong hydrogen bond between the HMPA and the proton donor, and the exchange of this hydrogen bond to the anion radical (PCNB--) from the solvent can be monitored via electron spin resonance (ESR) (reaction 1). PCNB-.
+ HMPAa-H-OEt
a PCNB-* *-H-OEt
Stevenson et al. + t o vacuum
+ HMPA
(1) Since the equilibrium to be studied (reaction 1) is fast on the ESR time scale, the equilibrium constant can be studied by the use of time-averaged ESR coupling constants (eq 2).839 A simple
-
1/(AN ANo) = 1 /(&(AN' - AN') [HMPA..*H-OEt]}
+ 1/(AN' - AN') (2)
plot of l / ( A N - ANo) VS. l/[HMPA-H-OEt] should yield a straight line (where AN is the nitrogen hyperfine splitting constant in the presence of added proton donor, ANois the coupling constant for the anion radical free of hydrogen bonding, and A,' is the nitrogen coupling constant for the hydrogen-bonded anion radical. Since the concentration of HMPA (the solvent) is much much greater than that for the anion radical (PCNB--), the concentration of HMPA-.H-OEt is simply that of the added ethanol. Once the enthalpy and entropy of the hydrogen-bond exchange reaction (reaction 1) have been determined, the kinetic study can be carried out by making use of the relaxation theory as applied to the two-site model, which has been derived by Fraenkel.Io His expressions have been programmed into our computer system so that a simulated spectrum can be generated given an estimated rate constant for the hydrogen-bond exchange in the forward direction (kf),the equilibrium constant for the exchange, the concentration of added proton donor (ethanol), and the coupling constants for both the free and the hydrogen-bonded anion radicals (see Experimental Section). A high energy barrier (more than about 5 kcal/mol) to hydrogen-bond exchange would indicate considerable solvent rearrangement during the formation of the activated complex. However, one might expect to observe a very low barrier, as is the case for the electron exchange between an anion radical and a neutral molecule. If the barrier is found to be very low (less than about 2 kcal/mol), it would indicate that the process is essentially diffusion controlled. That is, each geometrically viable encounter between the anion radical and a hydrogen-bonded solvent molecule would result in an exchange of the hydrogen bond. Preliminary experiments indicate that the rates of hydrogen-bond exchange are very fast: which is consistent with the low-barrier model, but actual activation parameters are yet to be reported. The entropy of activation should be near zero if the process is encounter controlled but quite negative if there is much solvent organization involved in the formation of the activated complex. Answering the questions alluded to above represented part of our motivation for initiating this study.
Experimental Section The neutral p-cyanonitrobenzene (PCNB) was reduced in HMPA with sodium metal in the apparatus shown in Figure 1. Absolute ethanol was distilled into the frozen (in a liquid-nitrogen (7) (a) Levin, G.; Jagur-Grodzinski, J.; Szwarc, M. J . Am. Chem. SOC. 1970, 92, 2268. (b) Stevenson, G. R.; Alegria, A. E.; McB. Block, A. Ibid. 1975, 97, 4859. (8) Stevenson, G. R.; Pourian, M. J. Phys. Chem. 1982, 86, 1871. (9) Kokosinski, J. D.; Forch, B. E.; Stevenson, G. R.;Echegoyen, L.; Castillo, C. A. J . Phys. Chem. 1980, 84, 793. (10) Fraenkel, G. K. J . Phys. Chem. 1967, 71, 139.
Figure 1. Apparatus used for the generation of hydrogen-bonded anion radicals. HMPA was distilled from potassium metal directly into the apparatus, which was charged with a small piece of sodium metal and some PCNB. After complete dissolution of the sodium metal, an ESR sample was sealed from the apparatus. The apparatus was then reconnected to the vacuum line, and absolute ethanol was distilled into the frozen HMPA solution from a break seal. After dissolution of the ethanol, the second ESR sample was taken. The difference between AN and ANo was obtained by comparison of the two spectra.
bath) anion radical solution from a break seal. The ethanol was not added until after the reaction between the sodium metal and the PCNB was complete. ESR samples were sealed from the apparatus before the addition of ethanol and after each addition. The solvent (HMPA) was distilled under vacuum from calcium hydride prior to use. It was then distilled directly into the apparatus (Figure 1) from potassium metal under high vacuum. The ESR spectra were recorded on a Varian E-4 ESR spectrometer coupled with a Varian temperature controller that was calibrated with an iron-constantan thermocouple. Computer simulations were generated to the same scale as the experimental recordings using a MINC I1 64K system. The simulated spectra were generated by using Lorentzian line shapes as adapted to Fraenkel's two-site model.1° The entire expression used to generate the lines of the simulated spectra is shown in eq 3. Equation 3 relates the rate constant for reaction 1 to the relative line widths and line position of the m = 0 (center) line and the m = -1 line of the NOz group. A similar expression can be written for any two lines in the spectrum.
+
k f = (21~,1/3'/~6~)[1 - (60/6-1)]-'([EtOH] K,,-')-'[(6o/G-,)([EtOH](H'_, - H-1)' - KeL1(HO-l - H-1)') ([EtOHI(Hb - Hdz - KeQ1(@0 - HO)zlI (3) where kfis the rate constant (forward direction) for reaction 1, l ~ , l is the gyromagnetic ratio for an electron, 6O is the line widths of the ESR lines of PCNB-. in the absence of EtOH, 6o is the line is the line width width of the m = 0 line of the NOz nitrogen, of the m = -1 line of the NOz nitrogen, H b is the line position in gauss of the center line of PCNB-.--HOEt, Po is the line position in gauss of the center line of PCNB-. (free), H'C1 is the line position of the m = -1 line of PCNB---HOEt, H"-l is the line position of the m = -1 line of PCNB-- (free), Ho is the observed line position of the center line, and H-l is the observed line position of the m = -1 line. The values for the ESR line positions were determined by sealing the anion radical solutions into ESR tubes that also contained a small capillary tube that contained a sample of the anion radical of cyclooctatetraene (COT) in HMPA. In this manner, the ESR spectra of PCNB-- and C O T - could be obtained simultaneously. Relative line positions could be determined from
The Journal of Physical Chemistry, Vol. 88, No. 7, 1984 1349
Hydrogen Bonding to an Anion Radical TABLE I: ESR Coupling Constants for PCNB'. (A") and for PCNB-. ..*HOEt (A') atom
A,G
A',G (25 "C)
atom
N(N0,)
4.90 (AN') 0.87
7.0 1.0 (AN')' 0.70
*
H (ortho)
2.38
3.1
H (meta)
0.48
1.0
N(CN)
A',G
4
A , G (25°C) 0
a The error in AN' was propagated from the error in the intercept of Figure 2.
Y
c
2
0
15
17
:9
1 OOO/RT Figure 3. Van't Hoff plot for reaction 1 showing that the enthalpy is within experimental error of zero.
Y
\ ri
0
4
8
1/
12
16
2ci
[EtOHI
Figure 2. Plot of l / ( A N- A N o )vs. l/[EtOH], at 25 OC.
the distance between the central line of PCNB-. and that for COT.. This procedure has been previously d e ~ c r i b e d .For ~ the experiments described here the central line position (g value) did not change with hydrogen bonding to PCNB-- within experimental error. The ethanol was not added to the solution in the apparatus (Figure 1) until all of the sodium metal had dissolved and reacted with the PCNB. Dissolution of the sodium metal necessarily means that it had all reacted, since ESR analysis (before ethanol addition) showed that the solutions were devoid of solvated electron. We attempted to generate each anion radical solution from an equal number of millimoles of PCNB and metallic sodium, in order to eliminate perturbations in the line widths due to electron transfer between any unreacted PCNB and the anion radical. This electron transfer was not always absent for a given solution, but it could easily be detected from the ESR spectrum of the first sample taken (containing no ethanol). Ethanol was not added to a solution until it was demonstrated that both the effects of electron transfer and other sources of line-width perturbations such as spinspin exchange were absent. The absence of these effects was clear from the ESR spectra and computer simulations (Figure 4) generated for the samples taken from the solutions before ethanol was added. For all of the experiments, the concentration of the PCNB anion radical was between and lop5M. The neutral PCNB concentration was unknown, but it was too small to result in appreciable broadening due to electron transfer.
Results and Discussion Thermodynamic Study. Before eq 3 can be utilized to evaluate the rate constant for hydrogen-bond exchange, it is necessary to evaluate the free energy for this reaction (reaction 1). As mentioned above, some effort was spent upon finding a system with an enthalpy of reaction close to zero prior to initiating the kinetic study. Successive addition of ethanol to the free anion radical of PCNB in HMPA (ANo = 4.90 G) results in an increase in the observed nitrogen coupling constant due to the rapid formation and dissociation of the hydrogen-bonded anion radical. The coupling constants for the cyano nitrogen and the protons also vary but much less drastically (Table I). As predicted by eq 2, a plot of AN - ANo) VS. l/[HMPA-.EtOH] is linear (Figure 2) and yields an equilibrium constant of 0.25 f 0.1 1. The relatively large error in Kq is due to the small intercept of Figure 2 (large AN' value). This results in small saturation factors, which should
Figure 4. ESR spectrum (upper) and computer simulation (lower) of the free anion radical of PCNB in HMPA at 25 OC.
extend as much as possible into the region where s is between 0.2 and 0.8." For the ESR experiment described here s = [PCNB-e] / [PCNB-. -.HOEt] = (AN
- ANo)/(AN'
- ANo) (4)
Calculated from eq 4 our saturation factor (s) varied from 0,013 to 0.28. The equilibrium constant was found not to vary with temperature from 0 to +60 OC. The HMPA solutions freeze below 0 O C . Over this temperature range A@ = -0.4 f 0.6 kcal/mol (Figure 3). This leads to an entropy for reaction 1 of -5.1 1.9 cal/(mol deg). Kinetic Study. The addition of ethanol to the PCNB anion radical in HMPA results not only in the spectral changes shown in Table I but also in considerable line-width changes (Figures 4 and 5). At 25 OC, computer simulations show that the rate constant for reaction 1 is kf = (7.0 f 1.0) X lo7 M-I s-l. In order to determine the effect of temperature upon this rate of transfer of the hydrogen bond from the HMPA to the anion radical, it is necessary to know how the coupling constants vary with the temperature. From Figure 6 it is clear that both ANoand AN vary in a nearly linear fashion with the temperature. Further, the two lines are -~ (1 1) Deranleau, D. A. J . Am. Chem. SOC.1969, 91 4044. ~
Stevenson et al.
1350 The Journal of Physical Chemistry, Vol. 88, No. 7, 1984 2c
,
I
16
----I :7
:5
19
:i l ? Z I / R T Figure 7. Arrhenius plot for reaction 1. E , taken from this plot is 4.61 & 0.26 kcal/mol. PCNB
-. “H.. ..O=P[N(CH3)2]3 I *
OEt
Figure 5. ESR spectrum (upper) and computer simulation (lower) of the PCNR anion radical in MMPA with added ethanol (0.310 M). The simulation was generated by using a rate constant of 5.0 X lo7 M-’ s-’. The temperature is 12 O C .
Figure 8. Energy diagram for reaction 1
kcal/mol for the enthalpy of activation. On the basis of Eyring’s equation kf = ( k T / h ) exp(AS*/R - AH*/RT), the entropy of activation for the forward reaction (reaction 1) is AS: = -8.0 f 1.4 cal/(mol deg).
48 -10
50
14 T (ti
Figure 6. Plot of AN and ANO (lower line) vs. the temperature. The sample used to obtain the upper line contained 0.714 M ethanol. The lines are nearly parallel.
parallel. The fact that the two lines are parallel is further indication that the enthalpy of reaction 1 is close to zero (the value for l / ( A N- A N o )does not vary with temperature; thus, Keq does not vary with temperature either). Utilizing the temperaturedependent coupling constants, computer simulations were generated using estimated values for k p An Arrhenius plot of the data is shown in Figure I and yields a value of 4.02 f 0.26
Conclusions An energy diagram for the hydrogen-bond exchange reaction is shown in Figure 8. The relatively large enthalpy of activation and negative entropy of activation indicate that there is some net solvent organization in going from the hydrogen-bonded solvent and free anion to the activated complex. A linear activated complex is shown in Figure 8. The fact that the entropy of the reaction is also negative further indicates that the activated complex is more like the products (PCNB-- --H-OEt + HMPA) than the reactants (PCNB-. HMPA-.H-OEt). We can think of this in terms of a longer partially formed hydrogen bond between the HMPA and the donor than between the anion radical and the donor in the activated complex. To our knowledge this represents the first report of kinetic parameters for hydrogen bonding to an anion radical.
+
Acknowledgment. We thank the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this work. We are grateful to the National Science Foundation for the purchase of the computer system. Registry No. PCNB--, 12402-47-0; ethanol, 64-17-5.
