J . Phys. Chem. 1990, 94, 1372-1376
1372
adenine. It is clear that the E tautomer is still significantly higher in energy at all levels of calculation presented here. As with guanine (see above), the 6-31G results agree very well with the 3-21G results at the Hartree-Fock level. Here also, the effects of including polarization and correlation are not additive with respect to the predicted tautomeric preference. In light of recent disagreements based on interpretations of the infrared spectra of adenine41v42 as to whether tautomer B is present in an inert argon matrix, we have also evaluated the RMP2/631G*(5D)//RHF/3-21G energy (with an estimate of the zeropoint energy) of tautomer B (Table 111). We find that B is 8.3 kcal/mol higher in energy than A at this level of calculation and is therefore predicted not to be present in significant quantities. Conclusions At the semiempirical AMI and Hartree-Fock (using STO-3G and 3-21G basis sets) levels performed here, extensive tautomerism
studies suggest that both adenine and guanine moieties substituted at the 9-position will exist predominantly as their usually depicted tautomeric forms in the gas phase. However, more extensive studies on selected low-energy tautomers, with extended basis sets at the MP2 level and including zero-point energy corrections, predict that the guanine moiety substituted at the 9-position may also exist, in significant amounts, as the enol tautomer. Thus, predictions of the tautomeric preferences of these systems at the ab initio level are sensitive to the basis set used and degree of correlation included. The present results suggest that these (correlation and polarization) effects should not be evaluated separately as they do not appear to be additive in these systems. Acknowledgment. We are very grateful to Guy Talbot for very valuable technical assistance. Registry No. Adenine, 73-24-5; guanine, 73-40-5
ESR Measurement of the pK, of Carboxyl Radical and ab Initio Calculation of the Carbon-I3 Hyperfine Constant A. S. Jeevarajan, Ian Carmichael, and Richard W. Fessenden* Radiation Laboratory and Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556 (Received: June 26, 1989) The pKa value for the equilibrium C02H t H++ C02- has been determined by ESR methods to be -0.2 f 0.1. Formate that had been enriched in I3C was reacted with SO4'- in steady-state photolysis experiments to produce the radical. The positions of the hyperfine lines did not vary over the pH range 1.6-10 but were found to change continuously as the acid concentration was increased over the range pH 1.2 to about pH 0, where the intensity became too small for study. The change in average hyperfine constant followed the behavior expected for a simple equilibrium under the assumption that exchange of the acid proton is rapid. The I3C hyperfine constants in aqueous solution were found to be 146.4 f 0.1 G for COT and 166 f 5 G for C02H. Ab initio molecular orbital calculations generally agree with the measured hyperfine constants and predict a higher value for the neutral form of the radical. ESR lines from a reduced oxalate radical containing 13C were also detected.
Introduction Several different values have been reported for the pKa of the equilibrium C 0 2 H z H+
+ C02-
(1)
The most widely based on different types of accepted value of 1.4 is based on the change in absorption at 250 nm in pulse-irradiated solutions of formate or formic acid.4 A discussion of the earlier measurements is given in that paper. This radical appears in a number of chemical processes and is commonly used as a reducing agent in studies of the redox reactions of a wide variety of compounds at various pH values. A recent papers has reported a detailed study on the reduction potential of the couple C 0 2 / C 0 2 -(and also for the alcohol radicals) and makes use of the pKa value to determine that the radical is completely in the dissociated form under the experimental conditions used. The pK, is not used directly in calculating the potential of this couple but does affect the value calculated for C02/C02H. A study of the couple CO,/HCO, has also been made? and here, the value of the pK, of C02H directly affects the standard potential
and free energy change. Other discussions of the thermodynamics involving C02- also depend on the pK,.' From these and other examples, it is clear that knowledge of this pK, value is important. Where ESR methods can be applied, they are often superior to optical methods of determining pKa values in that identification of the spectra of the two forms of the radical is more definitive and no assumptions are needed regarding how the chemical yields vary as the pH is changed. The most favorable situation for ESR occurs when the acidic proton is rapidly exchanged with water or H+ and the ESR parameters of the two forms of the radical are significantly different. In such a case, the observed ESR parameter, hyperfine coupling (hfc) or g factor, represents the concentration-weighted average for the two forms. The fact that the ESR spectrum can be followed continuously as pH is changed gives great confidence that the identification of the corresponding radical is correct. Previous work has shown that COz- can be prepared photolytically by the reactions
s2082-E ! +. SO4'- + HC02-
( I ) Buxton, G. V.; Wilmarth, W. K. J . Phys. Chem. 1963, 67, 2835. (2) Gutlbauer, F.; Getoff, N. Z . Phys. Chem. 1966, 51, 255. (3) Fojtik, A.; Czapski, G.; Henglein, A. J . Phys. Chem. 1970, 74, 3204. (4) Buxton, G. V.: Sellers, R. M . J . Chem. Soc., Faraday Trans. I 1973, 69, 555. ( 5 ) Schwarz, H. A.; Dodson, R. W. J . Phys. Chem. 1989, 93, 409. (6) Surdhar, P. S.: Mezyk, S. P.:Armstrong, D. A. J . Phys. Chem. 1989, 93, 3360.
0022-3654/90/2094- 1372$02.50/0
SO4'-
+ HC02H
-
2~0;-
+ H+ + S042C02'- + 2H' + Sod2C02'-
(2) (3a)
(3b)
and that the g factor of C 0 2 - does not vary over the pH range 4.6-0.8.8 More recent work on the radical HP03-9has shown ( 7 ) Koppenol, W.
H.; Rush, J. D. J . Phys. Chem. 1987, 91, 4429.
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1373
pK, and Hyperfine Constant of Carboxyl Radical TABLE I: Experimental I3C Isotropic Coupling Constants for CO, medium counterion aim,"G ref 3-MP glass molecular sieve zeolite molecular sieve H20:COJ2-glass CD3OD:CO3" glass CH,CO,Li CHJC02Na NaHCO, NaHC204 MgO/C02 A12OJCO Si02/C02
TMPD' N a+
K+ Ca2+ H' D+ Lit Na' Na', H' Na', H' Mg2+ AI'+ Si4+
122 133 133 167 147 150 157 165 167 171 196 218 217
a
b b b C C
d e
f
g
h i j
"Johnson, P. M.; Albrecht, A. C. J . Chem. Phys. 1966, 44, 1845. bSogabe, K.; Hasegawa, A.; Yamada, Y.; Miura, M . Bull. Chem. SOC. Jpn 1972, 45, 3369. CSymons,M. C. R.; Zimmerman, D. N . Int. J . Radiar. Phys. Chem. 1976, 8, 595. dNunome, K.; Toriyama, K.; Iwasaki, M. J . Chem. Phys. 1975, 62, 2927. eFujimoto, M.; Janecka, J . J . Chem. Phys. 1971, 55, 5. /Ovenall, D. W.; Whiffen, D. H. Mol. Phys. 1961, 4, 135. gwesterling, J.; Lund, A. Chem. Phys. Lett. 1988, 147, 11 I . Meriaudeau, P.;Vedrine, J. C.; Ben Taarit, Y.; Naccache, C. J . Chem. SOC.,Faraday Trans. 2 1975, 71, 736. 'Shimokoshi, K.; Sugihara, H.; Yasumori, 1. J . Phys. Chem. 1974, 78, 1770. jHochstrasser, G.; Antonini, J. F. Surf. Sci. 1972, 32, 644.
*
that its g factor does not change even when the radical protonates as indicated by a change in the 31Phfc. Thus, the constancy of the g factor of C02- does not necessarily prove that the form of the radical is the same over the pH range investigated. If I3Cenriched COT is studied, the situation is better because the I3C hfc is large (roughly 150 G, see below) and would be expected to show a significant change upon formation of C 0 2 H . Indeed, the value of the hfc depends more strongly on the environment than is characteristic of most radicals (see Table I), and values from I22 to 2 18 G have been reported depending on factors such as the charge on the counterion. Formation of COzH may well be like association of COz- with a cation so that the hfc should increase upon protonation. Thus, it is reasonable to expect that a measurement on 13C-enriched radicals in solution would find a change in I3C hfc as the form of the radical changed from COT to COZH. (The change in hfc would have to be substantial because of the 2.343 line width8 for COT.) This report presents the results of such an experimental study along with results of high-quality ab initio molecular orbital calculations of the hfc of the two forms of the radical.
Experimental Section Radicals were produced by photolysis of suitable solutions with a I-kW Hg-Xe lamp in a housing with an elliptical mirror. A CoS04-NiSO, filter solution removed visible and IR wavelengths to reduce heating effects. The ESR spectrometer was a modified Varian V-4502 with V-7000 9411. magnet and V-7200 power supply with Fieldial Mk I1 Hall probe. The microwave frequency was measured with a Hewlett-Packard 5245L frequency counter with 5255A converter and corrections made to line positions to compensate for changes in microwave frequency. The microwave cavity was kept at a constant temperature by circulating coolant from a constant-temperature bath at 21 OC. The solution temperature was 23 OC. Measurements of relative g factors were made by comparison with the position of the ESR line of S03*-.10 Solutions were prepared by diluting sulfuric acid with water, cooling, and then adding an appropriate amount of peroxodisulfate. Care was taken to avoid introducing any Cu or Fe which catalyze the decomposition of the peroxodisulfate. The sodium formate (8) Chawla, 0. P.;Fessenden, R. W. J . Phys. Chem. 1975, 79, 2693. (9) Davis, H. F.; McManus, H. J.; Fessenden, R. W. J . Phys. Chem. 1986, 90, 6400. (IO) Jeevarajan, A. S.;Fessenden, R. W. J . Phys. Chem. 1989,93, 351 1. This determination of the g factor of SO,'- is regarded as superior to earlier
ones by us because the frequency for 'HNMR was measured with the probe directly in the ESR cavity.
TABLE 11: Experimental Results on PH
g
amplitudeb
pH
g
amplitudeb
12.93 4.91 3.65 2.74
2.00060 2.00061 2.00061 2.00057
3.0 3.60 2.94 2.80
1.42 0.76 0.39
2.00066 2.00063 2.00063
2.30 1.13 0.88
"Solution contained 10 mM NaHCO, and 50 mM Na2S208. The temperature was 23 OC. bArbitrary units.
--pH 5.0
-1OG-
pH 0.4
t
t
t
"c
'3c
'3c
Figure 1. A representation of the ESR spectra of COT at two pH values. The upper portion gives the lines seen at pH 5.0 with that for the unenriched radical in the center and on either side (in an enriched sample) the two lines for 'JCOc. The modulation amplitude was chosen to give good signal amplitude for C O T but not too much broadening. The somewhat weaker line to the left (lower field) of the center is that attributed to reduced oxalate. The uppermost trace shows that line at a lower field modulation. The bottom row gives the lines at pH 0.4. The relative position of the lines for the "C species at the two pH values is given correctly based on the field scan rate given by the 10-G spacing.
was added only a few minutes before the solution was to be used to reduce thermal reaction." All solutions were deoxygenated by bubbling with argon. The pH measurements were made using an Orion Research 8 1 1 pH meter and Orion 8 166 Ross combination electrode with calibrations at pH 1.68 and 4.01. The unenriched samples flowed through the 0.4-mm spacing flat cell under gravity at about 10 cm3/min. The enriched samples (and some unenriched ones for comparison) were forced through the cell by means of a motor-driven syringe at 2.6 cm3/min. The water was purified by a Millipore Milli-Q system. Sodium peroxodisulfate was obtained from the Alfa Division of Ventron. Ordinary sodium formate was from Aldrich Chemical Co., and the I3Cenriched sample (92.4% 13C) was from MSD Isotopes. Sulfuric acid (Reagent A.C.S.) was obtained from Fisher Scientific.
Results and Discussion eoz-.The ESR line of COT was studied in previous workE over the pH range 4.6-0.8, and no change in width or g factor was found although the intensity decreased at higher acidity. A repetition of those experiments on normal (unenriched) COT gave results that agree with the earlier work except that the g factor was found to be slightly higher (2.00065) than the value reported earlierEpartly as a result of an increase of 0.000 10 in the value for the reference SO3-.Io Measured g factors and signal heights for different acidities are shown in Table 11, and a typical spectrum of the 'zCOz- species is shown at the top center of Figure 1. The smaller line to the left (lower field) is at the position for reduced oxalate (g = 2.0041) which is expected to be formed as a secondary product by the reactions 2H' + 2C02'H2CZO4 (4) 4
C0Z'-
+ HzC2O4
-+
COZ
+ [HzC201]'-
(5)
This radical will be discussed further below. Part of the decrease in intensity of the ESR line of COz- at higher acidity is the result of increased dielectric loss of the sample at higher acidity, but there may also be some change in either the formation or dis(11) Kimura, M . Znorg. Chem. 1974, 23, 841.
1374 The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 TABLE 111: Experimental Results on 13C02*-' PH ( a ) , bG PH (a),bG 10.00 146.4 0.53 149.4 5.00 146.4 0.43 149.7 I .20 146.4 0.40 150.3 0.61 148.9 0.35 150.4
PH 0.31 0.23 0.14
Jeevarajan et al.
( a ) , bG 151.0
t
151.5 152.2 I
O
Measured under similar conditions to those in Table 11. bSee ref 12.
n 0 W
appearance mechanisms which would lower the concentration of the radical. The change in dielectric loss by the sample accounts for about a factor of 2 decrease in signal amplitude at pH 0.4 relative to higher pH. Experiments with the I3C-enriched formate at higher pH gave clear signals for the I3CO2-radical as shown in the top row of Figure 1. The I3C hyperfine constant is 146.4 G, and the g factor is the same as that for the IZCspecies. The same spectrum was found at all pH values between pH 10 and pH 1.6. The g factor previously identified the radical as C02-,*and the large I3C hyperfine constant gives strong confirmation. It should be noted that the 13C hfc found for aqueous solution is close to the value in a solid glass involving water (see Table I). It is quite certain that the ESR line under study is that of COz-. The width of the lines of I3COy is the same as that of the I2Cspecies, and so the heights of the lines of 13CO; can be compared with that of 1 2 C O ~ . In all cases, the lines from I 3 C O are ~ close to one-half the height of those from '2COF under the same conditions. It may be concluded that the radical under study is the main reaction product. At higher concentrations of acid (below pH 1.2), the positions of the lines from W02-move in a sense corresponding to an increase in hfc. This change is attributed to the shift of equilibrium (1) toward the acidic form, COzH. Table I11 shows the measured hyperfine constants for a number of acid concentrations. Because it was clear that the g factor did not change with pH, only one line was measured for the I3C radicals, and the hyperfine constant was determined on that basis.I2 (This approach was used to conserve the enriched formate.) Measurements on both lines were made at a few points to verify this procedure, and no problem was found. It is highly probable that the rate of exchange of the proton with the solution at these pH values is rapid enough as to cause the line observed to be at the concentration-weighted average position. Further discussion of this point will be given below, after the behavior has been analyzed under this assumption. The beginning of the shift in position at about pH 0.8 implies that the pK, of the radical is at least 1 unit below this value (depending upon the difference in hyperfine constants between the two forms). As a consequence of this fact together with the decrease in ESR intensity with acid, it did not seem practical to carry out measurements over the whole of the transition. The data can be analyzed with the equation [ ( a )-a_]-'
=
[a0 - a-]-'(l
+ K,/[H+])
(6)
where a. and a- are hyperfine constants for the neutral (C02H) and basic (COT) forms, ( a ) is the average (observed) value, and K, is the equilibrium constant for the dissociation, reaction 1. In Figure 2 is shown a corresponding plot of the data from Table I l l . The [H+] values were activities calculated from the pH readings. A good straight line is obtained. The intercept corresponds to a hyperfine constant for I3CO2Hof 166 f 4.6 G, and the ratio of slope to intercept gives an equilibrium constant of reaction 1 as 1.6 or a pK, value of -0.2 f 0.1. The errors are from an analysis of the scatter of the data points from the straight line. It is now possible to go back and determine whether exchange of the proton should be rapid enough to give an ESR line at the average position. A reasonable value of the rate constant for the protonation in equilibrium (1) is 4 X 1O1O M-' s-l. Based on the ( 1 2) The calculations involved full diagonalizationof the isotropic magnetic Hamiltonian. Fessenden, R. W. J . Magn. Reson. 1969, I , 277.
0.0' 0.0
2.0
4.0
I 6.0
I / [H+] M-' Figure 2. A plot of the [ ( a ) - ao]-I vs [H+]-l (actually the reciprocal of the Ht activity as given by the pH reading). The line was determined by the method of least squares.
equilibrium constant of 1.6, the forward rate constant becomes 6.3 X 1O'O s-l. The line width for rapid exchange is given by
r = r0 + Ye7PflB((bH0)2) (7) where r and roare the widths (in gauss) of the exchanging and static systems, y e is the magnetogyric ratio, T is the chemical relaxation time, pA and pB are the fractional concentrations of the two forms, and 6Hois the distance the line shifts between the two forms. If the excess line width is calculated for pH 0.8 (the highest used in the analysis of Figure I), it is only 2 mG. At lower pH the excess line width is even smaller and there is considerable room for smaller rate constants for the two reactions before there will be significant broadening of the line. Thus, the analysis made under the assumption of fast exchange is quite appropriate. (The value at pH 1.2 should have been shifted some from 146.4 G. It is not clear whether the assumption of rapid exchange is valid at this pH.) The pK, found here is considerably lower than the previous values, and it is appropriate to discuss its validity. The large "C hfc leaves little doubt that the ESR spectrum is properly attributed to CO;/CO2H. The direct correlation of the spectra at different pH values clearly shows the changes in the spectra to be the result of changes in the form of the radical. The present results could be consistent with one of the earlier values only if the equilibrium measured here represented a second protonation and there was no difference in the 13Chfc of COT and C02H. This explanation seems very improbable. It is necessary to comment more specifically on the disagreement between the present value of pK, = -0.2 and that of 1.4 from optical pulse radiolysis experiments by Buxton and Sellers4 which is the most widely quoted. Those pulse radiolysis experiments were well conceived and seem to have been well carried out. Thus, it is not clear why the different higher pK, value should have been obtained. Further experiments by Buxton,'j however, have failed to duplicate certain aspects of the earlier work, possibly because of problems with scattered light corrections in the earlier work. In particular, experiments with 1.18 M formic acid and either 1 M NaC104 or 1 M HC104 showed only about a 15% decrease in absorption at 250-270 nm from higher pH (1 M NaC104) to the lower pH (1 M HCIO,). This result contrasts with nearly a 50% decrease in more acid solutions reported earlier.4 Also, measurements of the rate constant for reduction of methyl viologen by CO,H/CO, at a constant ionic strength of 1.8 M did not vary significantly from 0.1 to 1.8 M HCIO,. However, the rate constant was significantly decreased at 0.1 M HC104 (from 6.5 X IO9 to 2.9 X lo9 M-' S-I) as the ionic strength was raised (with NaC104) from 0.1 to 1.8 M. The small changes in either optical absorption or rate constant with pH for reduction of methyl viologen at constant ionic strength mean either that both forms of the radical have very similar properties or that the form of the radical does not change in the pH range covered. The ionic strength effect (1 3) Buxton,
G.V. Private communication.
pK, and Hyperfine Constant of Carboxyl Radical at 0.1 M HC104 is clearly in qualitative accord with the radical having a negative charge at that pH. In conclusion, the newer pulse radiolysis results do not seem to support the earlier optical work but are consistent with a lower pK, value such as that found here. It appears that neither of the properties mentioned above is a sensitive indicator of the state of ionization of the radical. Reduced Oxalic Acid. The small line at g = 2.004 10 in Figure 1 is clearly that of reduced oxalic acid as a line in exactly the same position is seen when a solution of oxalic acid, acetone, and isopropyl alcohol is phot01yzed.l~ The central region of the spectrum was also scanned in some of the experiments with the enriched formate. If the oxalic acid comes from the coupling of two COzradicals, then about 80% of it should contain two 13Cnuclei. Only a pair of narrow lines separated by 5.78 G at g = 2.004 10 could be seen between pH 3.5 and 0.2. In addition, an experiment with an equimolar mixture of normal and enriched formate (which should produce a preponderance of oxalate with one 13C) gave three lines in the region around g = 2.0041. The central line was clearly from the unenriched species, and the other two somewhat broader lines were split by 2.83 G around the same center. (We note that Zeldes and Li~ingston’~ searched for the I3C splitting at natural abundance and found lines corresponding to a 2.6-G splitting.) The nearly 2:1 ratio between the splittings in the spectra of the doubly and singly enriched indicates that 2.8 G is the average hfc. Also, the lack of a 1:2:l spectrum for the species with two I3C nuclei shows that the radical is not symmetrical and that the other half of the intensity is in lines that are broadened by exchange of protons. The lines that are seen should be those for the I3C spin states aa and &3. If it is accepted that oneelectron-reduced species generally have higher pK, values than the parent compound, then the radical would be (H0)2CC02H. It is somewhat surprising that lines at the position of the average splitting are seen for the singly labeled species but no line is seen in the center for the doubly labeled species. The difference in the two I3C splittings and the rate of proton exchange are unknown factors. If the rate of the exchange were determined by dissociation of ( H 0 ) 2 C C 0 2 Hrather than by addition of a proton to the free oxygen, then the rate would not depend strongly on pH over the range studied and the lines would remain broad over a range of pH. Because of the weakness of the spectra and the limited amount of material, more extensive studies were not made. The most accurate measure of the average I3C hfc is one-half the separation for the doubly labeled species or 2.89 G. The smallness of the I3C hfc is not surprising as the carbonyl carbon hfc in biacetyl anion are 0.58 G for the trans form and 1.14 G for the cis.I5
Theoretical Section Some years ago, a number of calculations were performed on the carboxyl radical anion with the principal goal of providing an interpretation of a body of spectroscopic data then available for complexes of alkali metals, M, with carbon dioxide in diverse environments.16 The calculations were carried out within the unrestricted HartreeFock (UHF) approximation using relatively small basis sets, slightly better than double-!: quality, including a single shell of polarization (d) functions on each atom. Hyperfine coupling constants obtained a t this level of theory are known to be suspect, in that the spin-polarization contribution to the contact spin density is often greatly overestimated. This phenomenon is associated with spin contamination in the U H F wave function. Some effort to alleviate this problem was expended at the time by invoking complete spin projection of these contaminating states to give the expected pure doublet multiplicity (PUHF) together with a concomitant reduction in the computed coupling constants. This procedure is not without its own drawbacks, however, and here a much more satisfactory approach to the improvement of the U H F prediction is implemented. (14) Zeldes, H.; Livingston, R. J . Phys. Chem. 1970, 74, 3336. ( I 5) Russell, G. A.; Lawson, D. F.;Malkus, H. L.; Whittle, P. R. J . Chem. Phys. 1971, 54, 2164. (16) Carmichael, I.; Bentley, J . J . Phys. Chem. 1985,89, 2951. Bentley, J.; Carmichael. 1. Ibid. 1985, 89, 4040.
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1375 TABLE IV: Calculated 13C Hvwrfine Solittine in C0,aim,G method/basis method/basis UHF/DZP PUHF/DZP UCISD/DZP
149 143 127
UHFITZPb UCISD(Q)/TZP UCCD(ST)/TZP
ah, G
147 124 120
“Calculations with the D Z P basis set performed at U H F / D Z P geometry. *Calculations with the T Z P basis set performed at the UMP2(fu11)/6-3 1 1G(d) geometry.
Following a treatment applied successfully in atoms,” we evaluate the correlation correction induced by considering the effect of all single and double replacements in the U H F determinant. The variational wave function obtained is used to compute the spin density as an expectation value over the appropriate operator. We denote this the UCISD method. Alternatively, the spin density may be computed as the response to a Fermi-contact perturbation introduced directly into the molecular Hamiltonian.l* This finite-field prescription allows calculation of the spin density with an arbitrary wave function, and here the effect of excitations higher than double from the UHF reference are considered by two independent techniques. Firstly, the UCISD estimate may be improved by the addition of an approximate size-consistency correction,19which largely accounts for the effect of quadruple replacements, denoted UCISD(Q). Alternatively, a coupled-cluster expansion of the wave function may be adopted, leading to an energy, UCCD, correct through all orders of perturbation for the effect of double (and simultaneous double) replacements in the U H F determinant. Approximate correctionZofor the effect of single and triple replacements may be made leading to a technique, denoted UCCD(ST), which has proved remarkably accurate in giving a satisfactory account of the spin density distribution in a number of “difficult” cases.21,22 Results for the 13C isotropic splitting in the carboxyl radical anion determined from each of these approaches are collected in Table IV. The calculations with the polarized double-!: basis set,23 denoted DZP, were performed at the UHF/DZP optimized geometry, r(C-0) = 1.228 A and O(0-C-0) = 135.15’. With the larger triplet-[ basis TZP, some further measure of electron correlation was introduced during optimization of the structure of the radical anion. Results reported here were evaluated by Mdler-Plesset perturbation theory carried through second order (for which analytic gradients are available) employing a polarized triple-split-valence basis set,z5 giving geometries at the UMP2(fu11)/6-311G(d) level of theory, viz., r(C-0) = 1.245 & , and s(o-c-0) = 134.670. The UCCD(ST)/TZP//UMP2(full)/6-3 11G(d) result for the carboxyl radical anion coupling constant may be assumed to give a reasonable account of the splitting to be expected in the isolated radical ion and is in agreement with the value reportedz6 following photolysis of TMPD in a 3-methylpentane glass formed in the presence of I3C-enriched carbon dioxide. Clearly, in aqueous solution it is considerably perturbed, presumably by hydrogen bonding and the presence of nearby counterions. Such effects are known both empirically, from studies in crystalline environments, and theoretically to increase the coupling constant at carbon. Thus, the observed value at 146.4 G in not at all unexpected. For example, in the complex formed between Li and C02, UHF/TZP calculations predict an increase in ai,(I3C) of about 50 G from the free COP value. Only about 5 G of this is directly attributable to the closing of the 0 - C - 0 angle in this complex. A value of Carmichael, I. Chem. Phys. 1987, 116, 351. Sekino, H.; Bartlett, R. J. J . Chem. Phys. 1985, 82, 4225. Langhoff, S. R.; Davidson, E. R. Int. J . Quantum Chem. 1974,8, 61. Raghavachari, K. J . Chem. Phys. 1985, 82, 4607. Carmichael, I. J . Phys. Chem. 1987, 91, 6443; 1989, 93, 190. Carmichael, I. J . Chem. Phys. 1989, 91, 1072. Dunning, T. H. J . Chem. Phys. 1970, 53, 2823. van Duijneveldt, F. B. IBM Res. J . 1971,945. d exponents are from: Lie, G.C.; Clementi, E. J . Chem. Phvs. 1974. 60. 1275. (25) Krishnan, R.; Binkley, J. S.; Seeger, R:; Pople, J. A. J . Chem. Phys. (17) (18) (19) (20) (21) (22) (23) (24)
1980, 72, 650. (26) Johnson, P. M.; Albrecht, A. C. J . Chem. Phys. 1966, 44, 1845.
1376 The Journal of Physical Chemistry, Vol. 94, No. 4. 1990 Formyloxyl CzV ['E,]
i
1.095
A
Jeevarajan et al. TABLE V: Calculated Hyperfine Splittiw in anti-HOCO method/basis aiW,G method/basis aim,G UHF/DZP' 21s UCISD(Q)/TZP 190 UCISD/DZP 184 UCCD(ST)/TZP 186 UHF/TZPb 220 'Calculations with the DZP basis set performed at UHF/DZP geometry. bCalculations with the T Z P basis set performed at the UMP2(fuI1)/6-311G(d,p) geometry.
1.4 kcalimol
9.8
ant1
ryn
H
Hydroxyformyl Cs ['A']
Figure 3. Calculated energies and equilibrium geometries for the various structures of C 0 2 H .
y(CbC-0) = 127.60' is obtained at the UMP2/6-311G(d) level of theory. The remainder may be accounted for by the formal charge density shift from COz- to Li+ which occurs on complexation and which results in the contraction of the spin density in the vicinity of the carbon nucleus. Following the same computational procedures, investigations were pursued concerning the structure of possible protonated forms. C-protonation leads to the computationally hazardous formyloxyl radical, while 0-protonation results in the two, synand anti-periplanar, isomers of the hydroxyformyl radical, HOCO. Bond lengths and angles for these species were determined from the corresponding stationary points on the UMP2(fu11)/6-3 1 1G(d,p) energy hypersurface, with the formyloxyl radical artificially constrained to be of C , symmetry. The equilibrium geometries are collected in Figure 3, together with that of the transition state separating the syn and anti forms. The optimized parameters for the local minima closely resemble those for the formate anion and cis- and tranr-formic acid, and computed vibrational frequencies correspond well with those assigned to the isomeric hydroxyformyl radicals from an infrared spectrum taken in low-temperature CO following vacuum-ultraviolet photolysis of water.z' These isomers are essentially isoenergetic at the UHF level, and with the UMP2 optimized structures further extensively correlated calculations were carried out using the larger polarized triple-!: basis set, leading to a convincing preferential stabilization of the anti-periplanar form by about 2 kcal mol-l, a t the UCCD(ST)/TZP level, in agreement with the results of previous calculations.B The energy separations displayed in the figure reflect the results of these much (27) Milligan, D. E.; Jacox, M. E. J . Chem. Phys. 1971,54, 927. (28) McLean, A. D.; Ellinger, Y. Chem. Phys. Lett. 1983, 98, 450.
more extensive computations. The barrier height for anti-syn interconversion has been similarly estimated at about 10 kcal mol-]. We thus concentrate calculations of the spin density on the anti-periplanar 0-protonated species and present results derived from computational procedures similar to those applied above for the carboxyl radical in Table V. A comparison between Tables IV and V indicates that the predicted shift in 13Csplitting accompanying protonation is of the order of 60 G and is already accounted for at the U H F level of theory. This shift agrees only in direction but not in magnitude with the 20-G change observed in aqueous solutions. However, at least 25 G of the difference is directly attributable to medium effects on the carbon coupling in the carboxyl radical anion. As mentioned above, the presence of both hydrogen bonding and nearby positive ions can be shown to lead to increase in the 13C splitting. On the other hand, similar causes produce much smaller, but similarly directed, effects on the calculated carbon coupling constant in HOCO. However, if the hydrogen of the hydroxyformyl radical itself is involved (as a donor), then, provided some relaxation toward equivalent C-O bond length occurs, the carbon splitting is indeed seen to decrease. The calculations reported above have been performed with a modified version of the GAUSSIAN 86 series of programs29running on either a VAX 11/780 or a CONVEX C120 computer.
Conclusions The ESR spectrum of the radical C0,/C02H has been studied over the pH range from 10 down to 0. The I3C hyperfine splitting remains constant from pH 10 to about pH 1.6 and increases below that. Analysis of the increase shows it to be consistent with the protonation equilibrium (1) with a pK, value of -0.2 and a I3C hfc for the C 0 2 H form of 166 G. Calculations show the anti form of C 0 2 H to be most stable and support an increase of the "C hfc from COz- to COZH,although the predicted increase is considerably larger than observed. Acknowledgment. The research described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is Document No. NDRL-3210 from the Notre Dame Radiation Laboratory. The authors thank Dr. G. V. Buxton for permitting us to quote his recent pulse radiolysis results. Registry No. COz-, 14485-07-5; COZH,2564-86-5; ( H 0 ) 2 C C 0 2 H , 28600-39-7; "C, 14762-74-4; HCOO, 16499-21-1. (29) Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Meliu, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rolfing, C. M.; Kahn, L. R.; DeFrees, D. J.; Seeger, R.; Whiteside, R. A.; Fox, D. J.; Fleuder, E. M.; Pople, J. A. GAUSSIAN 86; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1984.
