3778
J . Phys. Chem. 1988, 92, 3778-3781
200 levels of aniline below 3300 cm-l by stimulated emission spectroscopy using the two-color ionization dip method. The result proves the utility of the method for the study of the detailed ground-state vibrational level structure of a polyatomic molecule over a wide energy region. The method particularly has a great
advantage in the detection of combination and overtone levels which are hardly observed by IR, Raman, and fluorescence spectroscopies. Registry No. m-Fluorotoluene, 352-70-5; aniline, 62-53-3.
13C Hyperfine Constants of Allyl Radical Hugh J. McManus, Richard W. Fessenden,* and Daniel M. Chipman Radiation Laboratory and Department of Chemistry, University of Notre Dame, Notre Dame, Indiana 46556 (Received: October 29, 1987)
The 13Cisotropic hyperfine constants of the allyl radical have been measured by in situ radiolysis ESR experiments carried out on aqueous solutions of propene that was labeled at either the 1- or 2-position. The values are 21.93 and 17.21 G for the end and center carbons, respectively. Ab initio calculations have been used to calculate the equilibrium geometry and IH and 13Cisotropic and anisotropic hyperfine constants. The calculated isotropic hfc are in reasonable agreement with the experimental values. Values calculated from the Karplus-Fraenkel equation with standard values of the Q parameters are also in accord with the experimental values.
The allyl radical has long been used as a prototype in discussions of electronic structure and spin density in conjugated radicals.'-2 It is the simplest example of an odd alternant radical and as such shows sign alternation of the a spin density on the carbons, with negative spin density at the central p ~ s i t i o n . ~It has played an important conceptual role in formulating the linear relationship which is found to hold between proton hyperfine constant (hfc) and a spin density on the adjacent carbon The I3C hfc for the central carbon is unusual in this radical because it receives negative contributions from both the negative a spin density on that carbon and by means of spin polarization of the u bonds from both positive spin densities on the end carbons. Because of the small number of atoms, it is often used to test theoretical calculations. Even though accurate 'H hfc have been known for a long time,5 no values of the 13C hfc have been measured for the unsubstituted radical. It is desirable to have these parameters to evaluate the accuracy of calculations. Values have been determined for several allyl radicals which are substituted with bulky groups such as tert-butyl to make the radicals much longer lived.6 However, it is always unclear in such cases whether the substitutions significantly affect the values of the hfc by, for example, preventing the two ends of the radical from being coplanar. This paper presents the results of experiments designed to measure the I3C hfc of allyl radicals formed from enriched precursors and of calculations designed to give the geometry and iso- and anisotropic hfc of this radical.
Experimental Section Several routes to the allyl radical are possible. The one chosen here involves abstraction of an H atom from propene by radiolytically produced 0- in basic aqueous solution. A main advantage of this method is the commercial availability of propene labeled a t either the 1- or 2-position. Design of an apparatus that allowed dissolution of 100 cm3 of propene in a fixed volume of solution so that little gas remained (1) McConnell, H . M.; Chesnut, D. B. J . Chem. Phys. 1958, 28, 107. (2) McConnell, H. M. J . Chem. Phys. 1958.28, 1188; Ibid. 1959, 29,244 (3) The term spin density is conventionally used in this context. What is meant is the spin population of the pI atomic orbital on the specific carbon. A negative density arises if the spin orientation is opposite to that on the radical as a whole. (4) McConnell, H. M. J . Chem. Phys. 1956, 24, 764. Weissman, S. I. J . Chem. Phys. 1956, 25, 890. Bersohn, R. J . Chem. Phys. 1956, 24, 1066. (5) Fessenden, R. W.; Schuler, R. H . J . Chem. Phys. 1963, 39, 2147. (6) Ahrens, W.; Schreiner, K.; Regenstein, H.; Berndt, A. Tetrahedron Lett. 1975, 50, 45 1 1 .
0022-3654/88/2092-3778$01 .50/0
in any dead space was a major challenge. The idea was to provide an adjustable volume by use of a syringe and to circulate the solution through a tower filled with glass beads to provide extra surface for more rapid dissolution of the propene. A diagram of the apparatus finally used is shown in Figure 1. There were two distinct sections to the equipment. The first section was a loop which allowed recirculation of the solution through the cavity. During the experiment, the solution was extracted from the bottom of the tower, pumped through the ESR cell, and reinjected through the top of the tower. The second section involved the gas-handling apparatus. It consisted of a gas bulb of 100-cm3 volume, a Teledyne Hastings-Raydist 0-1000-Torr vacuum gauge, and a peristaltic pump. When a gas sample was to be injected into the recirculation loop, the output of the peristaltic pump was connected to the top of the tower. In a typical experiment, N,O was flushed through the recirculation system for about 1 h. Two liters of > 18 Mohm cm water were purged with N20, and 25 g of KOH was added. The basic solution was then pumped into the system which had a capacity of 1 L. The second section of the apparatus was then pumped down to -6 Torr with the peristaltic pump and filled with N2 by reversing the pump. This process was repeated twice more. After the third evacuation, the lecture bottle was opened and the 100-cm3volume filled with propene at 1 atm. The propene gas was then admitted into the cylinder by simultaneously opening the taps on the pump side of the bulb and on the cylinder. The syringe slowly filled with solution. When it had reached 100 cm3, the tap on top of the cylinder was closed. The solution was recirculated with pressure periodically applied to the plunger of the syringe to coax the gas into solution. Dissolution of the gas typically took around 1 h. In experiments with the I3C-enriched samples, their containers took the place of the 100-cm' bulb. ESR spectra at X band were taken with the in situ radiolysis apparatus described previously.' The magnetic field was computer controlled by means of a field-tracking N M R unit and frequency counter which also read the microwave frequency. In this way, a field/frequency lock was maintained and compensation for any drifts in microwave frequency could be provided; very accurate and slow field scans could be made. The system time constant was 18 s, and repetitive scans of the same field region were used in some cases for signal averaging for additional signal-to-noise ratio improvement. The g factors were determined by reference to the line of SO3'- at g = 2.003 06.* Radiolysis was with a 2.5-1A
-
~~~~
~~
~~~~~
~~
~
(7) Jinot, C.; Madden, K. P.; Schuler, R. H . J . Phys. Chem. 1986, 90,
4979.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 13. 1988 3119
I3C Hyperfine Constants of Allyl Radical PERISTALTIC PUMP
VACUUM GUAGE
t PROPENE
IOOcc GLASS BLUE
1
LECTURE BOTTLE
u
FRITTED GLASS
+500 cc
RESERVOIR
Figure 1. Diagram of the experimental setup used to handle the sample solution. The tower on the left consisted of a 500-cm' measuring cylinder modified by adding the various inlets with fritted glass plugs and high-vacuum Teflon stopcocks. This cylinder was filled with glass beads to provide a larger surface area to help the gas dissolve. The 100-cm' syringe provided an adjustable volume to allow the gas sample to be introduced into the tower before it was dissolved. The compliant volume with a small amount of gas at the top reduced the effect of pressure pulsations on the flat cell in the ESR cavity.
TABLE I: Measured Hyperfine Constants" radical a('3CI [CH;CHCH2] ' [CH213CHCH2]' 17.21 ["CH2CHCH2]' 21.93
~(€3,) 4.20 4.22 4.20
n(H,)
dHd
B
14.83 14.87 14.83
13.92 13.97 13.92
2.002 52 2.002 53 2.002 52
factor
lines fitb
rmsc
12 13 17
0.04 0.05 0.05
'Values in gauss as determined by a least-squares procedure.' bNumber of lines used in the least-squares procedure to determine the hfc. error between observed line position and those calculated from the best parameters.
beam of 2.8-MeV electrons from a van de Graaff accelerator. The unenriched propene was from Matheson, and the enriched samples were obtained from MSD Isotopes. The samples of both [ l-I3C]propene and [2-I3C]propene were 100-cm3volume (STP) and were stated to be 90 atom % I3C. The temperature of the solution was measured at the exit of the ESR cell to be 17 "C.
Experimental Results The first experiments were performed with 100 cm3 of unenriched propene to make sure the method would work. It was found that a given sample of solution could be irradiated and recirculated for up to 4 h before the ESR signal amplitudes dropped below an acceptable level. Part of the reason for the reduction in intensity involved partial blockage of the cell by radiation-produced polymer. ESR, lines were observed from both allyl and the radical CH3CHCH20Hwhich resulted from O H addition to the propene. In all, 12 of the 18 lines of the unsubstituted allyl radical were observed and analyzed by a least-squares routine9 to yield the hyperfine constants and g factor, which are given in Table I. These values are in good agreement with previous values taken in liquid cyclopropane at -120 Experiments were carried out with both [1-l3C]propene and [2-I3C]propene. The positions of 17 and 13 lines, respectively, were measured and the parameters again determined with the least-squares procedure. Samples of recordings of selected lines (8) Behar, D.; Fessenden, R. W. J . Phys. Chem. 1972, 76, 1706. (9) Fessenden, R.W. J . Magn. Reson. 1969, 1, 217.
/
I
\
\
Figure 2. Representation of the spectrum of l3CH2CHCH2and recordings of selected lines within that spectrum. The two sets of lines for the two orientations of the "C nuclear spin are indicated at the top. All lines were measured at the same gain setting; the different intensities arose because the various lines were recorded at different stages in the deterioration of the signal intensity.
for [l-'3C]allyl are shown in Figure 2. The values of all parameters for the two species are given in Table I. It is seen that there is no measurable change in any of the proton hfc upon substitution by 13C. The hyperfine constants for I3C at t h e two
3780 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988
McManus et al. TABLE III: Comparison of Theoretical and Experimental Isotopic Hyperfine Coupling Constants of Allvl Radical in Gauss
l
zH o ~
Hjb
~
13.9 (.19.7)
4H*) a('Hb) 4H2) a(l3CI) a(13C2)
Y
-L
Figure 3. Labeling used for the atoms in allyl radical. The experimental and calculated (in parentheses) hyperfine constants are given beside the
atoms. TABLE 11: Comparison of Theoretical and Experimental Geometrical Parameters of Allyl Radical, with Bond Lengths Given in Angstroms and Bond Angles in Degrees MCSCF/ 142121 electron diffraction"
R(ClC2) R(CIH,) R(CIHb) R(C2H)
1.402 1.073 1.075 1.076
L(cic2c3)
124.7 121.3
(C2C,Ha) 4CKiHJ f
121.3
ROHF+SP-SECI/ [42121 -18.2 -17.3
MCSCF+SECI/
5.5
(-) 13.92'
18.3
21.8 -23.7
(-) 17.2 1
The experimental assignment of the two larger IH hfc to the endo and exo positions was made from the spectra of the methyl-substituted allyl radicals derived from cis- and trans-butene-2 [Kochi, J. K.; Krusic, P. J. J . Am. Chem. SOC.1968, 90, 71571. TABLE IV: Comparison of Theoretical and Experimental Anisotropic Hvwrfine CouDline Constants of Allvl Radical in Gauss"
-5.3
0.2 5.6 1.8
0.4
Reference 15. bExperimentally,the three independent CH bond lengths were taken from a single refined mean CH distance. Experimentally, the two independent C2ClH bond angles were assumed to be equal.
(10) Huzinaga, S. J . Chem. Phys. 1965, 42, 1293. (1 1) Dunning, T. H. J . Chem. Phys. 1970, 53, 2823. (12) Paldus, J.; Cizek, J. Chem. Phys. Letr. 1969, 3, 1. McKelvey, J. M.; Berthier, G. Chem. Phys. Left. 1976, 41, 476. Feller, D.; Davidson, E. R.; Borden, W . T. J . Am. Chem. Sot. 1984, 106, 2513. (13) Kikuchi, 0. Chem. Phys. Lett. 1980, 72, 487. (14) Takada, T.; Dupuis, M. J . A m . Chem. SOC.1983, 105, 1713. (15) Vajda, E.; Tremmel, J.; Rozsondai, B.; Hargittai, I.; Maltsev, A. K.; Kagramanov, N. D.; Nefedov, 0. M. J . Am. Chem. Sot. 1986, 108, 4352.
(-)14.83'
-21.2
(I
Ab Initio Calculations Theoretical characterization of the allyl radical was carried out with the Huzinaga (9514) primitive Gaussian basisf0as contracted to double { [4212] size by Dunning." The labeling of the atoms is given in Figure 3. Due to the well-known symmetry instability encountered for this system in R O H F methods with small basis sets,'* a more general 4-configuration MCSCF model was used for geometry optimization, although C2, symmetry of the nuclei and the wave function was assumed throughout. This corresponds to all ways of distributing the three a electrons among three a molecular orbitals, keeping all o molecular orbitals doubly occupied and enforcing overall *A2symmetry on the wave f ~ n c t i o n . ' ~ The allyl radical geometry calculated here, which is very close to the MCSCF/3-21G calculation by Takada and Dupuis,I4 is compared to a recent electron diffraction determinationI5 in Table 11. They generally agree quite well. The only notable difference is that the CC bond length is calculated to be 0.026 A shorter than is observed experimentally, this deviation being twice the estimated experimental error. The dipole moment is calculated to 0.05 D, which should be interpreted as essentially zero. We have previously emphasized the necessity of including single excitations with at least a full double { basis set (including flexibility in the outer 1s core and inner 2s valence regions) for
exptl
-20.5 -19.7
4.20 21.93
2.9
1.428 i 0.013 1.069 0.016' 1.069 f 0.016' 1.071 i 0.016b 124.6 f 3.4 120.9 f 3.4' 120.9 i 3.4'
positions are 21.93 and 17.21 G, respectively. The sign of the hfc for the center carbon is not given by the experiment, but by reference to calculations it is certainly negative. These values for I3C can be compared with those found for the substituted radicals studied by Ahrens et aL6 For example, the values for the 1,2,3tri-tert-butylallyl radical are 23.9 and 16.8 G, and after making an empirical correction for the effect of substitution, they estimate that the values for the unsubstituted radical should be 22.3 and 16.9 G. These values are very close to the observations.
[42121
"Refer to Figure 3 for the coordinate system. The component for the direction perpendicular to the molecular plane can be determined from the zero-trace condition. bReference 19, measured on the substituted radical 'CH(CHCOOH)2. satisfactory spin density calculations in a radicals.16 In this work spin density properties have been evaluated in two distinct ways, both at the MCSCF/[4212] equilibrium geometry. First, the R O H F wave function was augmented with all spin-polarization single excitations (Le., those involving triplet spin coupling of a virtual orbital to the previously doubly occupied MO) to produce 128 space- and spin-adapted configurations (CSF's) in a ROHF+SP-SECI/ [4212] model. Second, all possible single excitations with respect to any of the four MCSCF configurations were allowed, leading to 1132 CSF's in a MCSCF+SECI/[42)2] model. This latter model then contains many double excitations with respect to the dominant configuration, and it is of interest to see if that has a significant effect on the spin density. Comparison of the theoretical and experimental isotropic hfc determined in this work are given in Table I11 and Figure 3. Calculations were for the geometry given in Table 11, and no attempt was made to take account of the effect of nuclear vibrations on either the IH or I3Chfc. The ROHF+SP-SECI and MCSCF+SECI calculations agree well with one another and reasonably well with the experimental values. It can be concluded that even the simple ROHF+SP-SECI model provides a satisfactory description of the spin density distribution in the allyl radical. Earlier relative assignments of hfc to the nearly equivalent methylene hydrogens are confirmed here, as is the negative sign of a(I3C2). The theoretical results obtained here describe well the large-small-large pattern of a(H), which is a major failing of UHF- and PUHF-based wave function m0de1s.I~ The present calculation also fares better than the large-scale C I results of Ha et al.,'* who report, for example, the very high value of 35.4 G for a(13C,)and the rather low value of 1.1 G for a('H,). The origin of these large discrepancies is not clear in that latter work, ~
~
(16) Chipman, D M J Chem Phys 1983, 78, 3112 (17) Chipman, D M J Chem Phys 1979,71,761 Chipman, D M Ibid 1983, 78, 4785 (18) Ha, T -K , Baumann, H , Oth, J F M J Chem Phys 1986, 85, 1438
J . Phys. Chem. 1988, 92, 3781-3784 which seemingly utilizes a satisfactory wave function model and basis set for spin density determination. The encouraging agreement of calculated and experimental isotropic hfc leads us to report calculated anisotropic hfc in Table IV. There are no direct experimental measurements on allyl itself available for comparison, so we settle for comparison to Hb and H, in the substituted radical CH(CHCOOH),,I9 under the implicit assumption that the unpaired electron does not delocalize onto the carboxyl groups. The ROHF+SP-SECI and MCSCF+SECI results are generally within 1 G or so of agreeing with one another and differ from experiment by up to several gauss where comparison is possible. Since the effect of carboxyl substitution on the experimental results is unknown, it is not possible to determine whether these differences are significant or not. In any case, the agreement with experiment is fairly good and the calculations should provide reasonable estimates of those anisotropic hfc not yet measured. It is of interest to compare the orientation of the tensors with that of the bonds. The principal tensor values (in gauss) from the R O H F calculation for HI, and Hlbare (9.1, -8.4, -0.7) and (8.4, -7.3, -l.O), respectively, with the first two values corresponding to directions in the plane of the molecule. The positive value in each case corresponds to a direction very close to the C H bond as is expected. For HI, that principal axis is 0.7' clockwise from the bond direction (see Figure 3), and for H,, it is 0.3' clockwise. The positive value corresponds to 0.67 and 0.62 of that calculated analytically for a C H fragment,,O in approximate agreement with the spin density. Interestingly, the proton with the smaller isotropic hfc also has the smaller anisotropic hfc. The I3C anisotropic tensor for C I ( R O H F calculation) is nearly of cylindrical symmetry with principal values (3 1.4, -16.0, -1 5.4). The positive value is 0.48 of that ascribed to a p electron on carbon.,'
Semiempirical Treatment It is also useful to compare the measured I3C hfc with those predicted by the Karplus-Fraenkel equation.,*
The Q& parameters together represent the effect of A spin density on the ith carbon atom in spin polarizing the 2s orbital of that carbon. Three parameters are used to describe the bond properties (19) Heller, C.; Cole, T. J . Chem. Phys. 1962, 37, 243. (20) McConnell, H. M.; Strathdee, J. Mol. Phys. 1959, 2, 129. (21) Morton, J. R. Chem. Rev. 1964, 64, 453. (22) Karplus, M.; Fraenkel, G. K. J . Chem. Phys. 1961, 35, 1312.
3781
when the carbon is bonded to different atoms X, (C or H in this case). The term $ represents polarization of the carbon 1s orbital. The QCxc parameters represent the spin polarization of the ith carbon 2s orbital by spin density located on the adjacent atom X. The standard values in gauss are Sc = -12.7, Q& = 19.5, Q& = 14.4, and QEcC= -13.9. The equation aH = QHpCcan be used in several ways to determine pc, the ?r spin density on the carbon to which the hydrogen is attached. The most straightforward is to use a common QH for both carbons in allyl radical and to use the average hfc of the two protons on the end carbons. The A spin densities so determined are 0.582 and -0.164 for the end and center carbons, respectively. If these values are used with the standard Karplus-Fraenkel parameters, then the two I3C hfc are predicted to be 25.8 and -19.2 G. These hfc are in reasonable agreement with the experimental values. This calculation draws attention to the effect produced by ?r spin density on the end carbons on the hfc of the center carbon. The A spin density on the center carbon contributes only 5.8 G to the hfc while the rest comes from spin polarization by the end carbons. An alternative way of proceeding is to use the measured hfc values to determine empirically better values of Q& and Q&. The values so determined are Q& = 11.4 G and Q& = -10.8 G. These values are close to those obtained from fitting other I3C data.23
Conclusion The present study has shown how to dissolve a limited volume of gas to produce the desired I3C-labeled allyl radicals in aqueous solution. The hfc found do, in fact, agree rather closely with those found previously for some highly substituted derivatives, thus showing that the latter radicals cannot be seriously distorted by the bulky substituents. A good description of the 'H and the I3C hfc can be obtained from the simple ROHF+SP-SECI/ [4212] ab initio wave function. The calculations confirm previous beliefs about the sign of a(I3C2)and the relative assignment of hfc to the two methylene hydrogens. The Karplus-Fraenkel relation appears to be useful in discussing the magnitude of the I3C hfc for this radical in the sense that the values so determined are in g o d agreement with experiment. This treatment emphasizes the effect of A spin density on adjacent atoms in producing a negative contribution to the hfc at the central carbon. Acknowledgment. The research described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is Document No. NDRL-3045 from the Notre Dame Radiation Laboratory. (23). McManus, H. J.; Madden, K. P.;Fessenden, R. W.; Schuler, R. H., unpublished data.
13C Hyperfine Constants of H,CN', H(HO)CN', and 'CONH, Hugh J. McManus, Richard W. Fessenden,* and Daniel M. Chipman Radiation Laboratory and Department of Chemistry, University of Notre Dame, Notre Dame, Indiana 46556 (Received: October 29, 1987)
The "C hyperfine constants of the radicals H2CN', H(HO)CN', and 'CONH2 derived from I3C-enriched CN- have been measured in aqueous solution by ESR experiments using in situ radiolysis. The values found are 28.9, 20.5, and 158.4 G, respectively. Detailed ab initio calculations were also performed on these species, showing each of the radicals to be planar and yielding calculated hyperfine constants that are in reasonable agreement with the observed ones. The calculations show a large decrease in the CH proton hyperfine constant from H2CN' to H(H0)CN' paralleling that found experimentally. No significant geometry change is required to explain this effect. The large I3C hyperfine constant of 158 G found for 'CONHI demonstrates the u nature of this radical.
An unexplained feature of the ESR hyperfine constants (hfc) of the methylene protons of cyclohexadienyl radicals is the rela0022-3654/88/2092-3781$01.50/0
tively large decrease in the value when one proton is replaced by OH. This reduction is from 48 G for C6H7to 34 G for C6H60H.132 0 1988 American Chemical Society
