ENDOR studies at 4.2 K of the radicals in malonic acid single crystals

2B8

J. Phys. Chem. 1993,97, 2888-2903

ENDOR Studies at 4.2 K of the Radicals in Malonic Acid Single Crystals R. C. McCaUey Research and Development Division, Lockheed Missiles and Space Company, 3251 Hanover Street, Palo Alto, California 94304

Alvin L. Kwiram' Department of Chemistry and Office of Research AH-20, University of Washington, Seattle, Washington 98195 Received: November 24, 1992

Proton hyperfine tensors based on ENDOR measurements at 4.2 K are reported for five distinct radical types in X-irradiated crystals of partially deuterated malonic acid. A total of 30 tensors are reported reflecting slightly different orientations of the damage products in the crystal: four tensors for RCHR; four for (RCH&; ten for ( R C H Z ) ~four ; for the u radical, (RCH2C-O)u; six relatively isotropic proton tensors; and two d i k e tensors. R = -COOH throughout. The classic RCHR radical is found in two conformations at 4.2 K, separated by a f 1 2 O rotation of the >C-H direction with respect to the C-C-C plane of the room temperature neutron diffraction structure. It is hypothesized that the RCHR radical observed at room temperature is undergoing rapid librational motion between these potential energy minima (separated by 24O) thereby explaining the observed asymmetry of the dipolar hyperfine tensor. The proton hyperfine tensors for the RCH2 radicals whose plane is nearly parallel to the malonic acid C-C-C plane were measured to a precision of f50 kHz, allowing an accurate determination of the anisotropy difference between the two protons. From this difference, the spin density delocalization onto the carboxyl oxygens has been deduced and compared with the results of ab initio calculations. The set of radicals with relatively isotropic proton tensors are tentatively assigned to stabilized forms of a malonic acid reduction product, in which an extra electron is trapped on one of the carboxyl groups.

I. Introduction The experimental and theoretical foundations for the understanding of proton hyperfine interaction (hfi) in oriented organic free radicals was established by McConnell and co-workers in their classic studies of the radicals in X-irradiated malonic' and succinic2 acids. Using the framework established in that pioneering work, the field of free-radical structural studies has expanded for over three decades, leading to a remarkably detailed understanding of the electronic structure of a wide variety of free radica1s.l-5 Today the generalizations regardingnuclear hyperfine interactions and spin distribution are used routinely by thousands of investigators in dozens of fields. Given the position of malonic acid as a prototype system, it may seem a bit presumptuous to suggest that further basic information on radical structure can be obtained from the study of radical species trapped in malonic acid. Nevertheless, the purpose of this work, which is based on the enhanced precision and spectral resolution possible with the electron-nuclear double resonance (ENDOR)G8 technique, is to characterize the known malonic acid radicals more fully and to describe new radical species in this important system. The RCHR radical (R = -COOH) in malonic acid represents the prototypical >CH fragment where the unpaired electron in a 2pr orbital on carbon interacts with a directly bonded -a'' proton. The measured value of the isotropic hfi, 141, is about 60 MHz and provides the most direct way of determining spin densities in organic free radical^.^ McConnell's study of the anisotropic hfi in malonic acidlo demonstrated that the sign of a is negative. The anisotropic component of the interaction between an unpaired electron in the >CH fragment and the a proton provides important geometric information.Il The RCHRanisotropy, both measured and calculated, is roughly (0, -30, 30) MHz for the directions (x, y , z ) along the 2pa orbital (designated throughout as Bi, for intermediate), perpendicular to both the 2 p r orbital and the CH bond direction (designated B, for most negative), and along the CH bond direction (Epor BV), respectively.12 The

overall ESR splittings along the three principal axes of the hfi tensor are thus about (60, 90, 30) MHz respectively. In other words, the smallest ESR splitting is observed when the external field is along the C-H bond, and the largest splitting occurs when the field lies perpendicular to both the C-H bond and the 2pa orbital. A persistent question is: what is the experimental anisotropy for a ">CH fragment" with unit spin density. Several assumptions made in the early work on malonic acid about the nature of the radical and its spin distribution have not been entirely appropriate, as we will show. For example,the hfi tensor measured at room temperature, and assumed to be a reasonably accurate reflection of the properties of the >CH fragment, actually is a motionally averaged composite resulting from rapid interconversion between two potential energy minima separated by about 24O in the single crystal. A closely related problem involves the characterization of the 13C hfi in RCHR'3J4 which has served as the experimental benchmark for the carbon hfi tensor in general.sy15-'7The earlier attemptssJ5to reconcile the theoretically calculated values for the I3C hf interaction with the RCHR experimental values have resulted in uncertainty both in estimating the spin density on carbon and in establishing the "best" value of the fundamental anisotropic coupling constant for unit a-unpaired spin on '3C. As we show below, this problem can be largely resolved by recognizing the effect of motional averaging on the room temperature I3C tensors. Other uncertainties have also persisted in the literature on the structure of radicals in malonic acid. For example, it was claimed in the original reportt8of the structure of an RCH2 free radical (a second prevalent species in malonic acid) that there was a dihedral angle of 90° between the CH2 plane and the carboxyl plane of this radical. Further work perpetuated this error.I9 We confirm more recent studies20 that all RCH2 radicals in malonic acid are fully planar. We will also demonstrate that the precise difference in anisotropy measured between the two protons in

0022-3654/93/2091-2888~04.00/0 0 1993 American Chemical Society

Radicals in Malonic Acid Single Crystals RCHz allows the spin delocalization within the -COOH group to be determined experimentally. Irradiated malonic acid also exhibits a complex collection of radical species which have heretofore not been described, in part because the ESR spectrum of malonic acid irradiated at room temperature is very congested. For example,three radical species with isotropic hfi tensors are identified and characterized. Two versions of these radicals each possess two relatively isotropic &protons, indicating that there is a >CHZ group adjoining the radical center. The third and most prominent of these radicals possesses a single&tensor, as well as a highly anisotropiccarboxyl proton tensor. All three species appear to be stabilized versions of the reduction products formed by the addition of an extra electron to one or the other type of carboxylic dimer ("parallel" or "perpendicular") in the malonic acid crystal. In all three cases the spin density on the carboxyl carbon is about 0.5-0.6 with the remainder distributed over the oxygensof the associated carboxyl group and with perhaps some delocalization onto the other carboxyl group as well. There is an extensive literature on the radiation damage mechanisms in organic crystals as studied by ENDOR and ESR. The specific mechanisms for radical formation in malonic acid crystalshave been studied in detail by Kikuchi et al.20 The primary formation of the positive and negative ions is followed by decarboxylation of the positive ion yielding the RCH2 radical. The negative ion loses HzO (perhaps after a proton is transferred toform-C(OH)z) togeneratean R C H z C 4 radical. The shortlived R C H 2 C 4 radicals were originally discovered in freshly irradiated deuteriomalonic acid'3 and have since been observed in other systemsSz2(The ENDOR data for the proton hfi tensors of these (RCHzC--O)ll radicals are also reported in this work.) The RCHz and R C H z C 4 radicals may, in turn, abstract a hydrogen atom from a neighboring molecule to form the RCHR radical. This radical cascade in malonic acid is generally consistent with what has been described in the extensiveliterature on radiation damage mechanisms in organic crystals.22 All together, a total of 30 proton hfi tensors are presented for the 17 distinct radicals and orientations that have been identified in irradiated malonic acid crystals. (The raw tensor elements in the crystal axis system are listed in Table VII.) This detailed analysis has been made possibleby using electron-nuclear double resonance (ENDOR) to characterize the hfi at 4.2 K where librational motion is minimized. Equally important, crystals of malonic acid were used that were enriched to the 70-80% level in deuterium in order to improve the proton ENDOR resolution in two ways. First, this strategy narrows the line widths significantly without seriously reducing the signal-to-noise ratio of the proton ENDOR spectrum. Second, the solid-state radical reactions occur more slowly in the deuterated crystal so that short-lived acyl radicals responsible for fast nuclear relaxation persist for hours rather than minutes at room t e m p e r a t ~ r eThis .~~ shortens the repolarization time of the ENDOR signals and increases the saturated ESR amplitude, allowing for faster rf scans with much better signal-to-noise ratio. The work presented here, however, does not exhaust the rich storehouse of information that malonic acid has to offer. Several additional proton ENDOR transitions, from unknown radicals, could not be followed through three data planes because they were quite weak and were often obscured by the many other lines in the spectrum. This does not mean that they cannot be determined, but rather that more specificallydesignedexperiments will have to be carried out in order to extract accurate tensors. Another important class of data which is not reported here is the myriad of weakly coupled ( < l o MHz) proton interactions.Z4Js These hfi represent interactions of the unpaired electron with carboxyl protons on the same radical center and with protons on neighboring molecules. These weakly coupled protons give rise to multiple hfi tensorsfor each radical species. Since these lines all fall within roughly f5 MHz of the free proton line (at 13.8 MHz in an X-band ENDOR experiment), even the ENDOR

The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2889 C

1

a

a*

Figure 1. Malonic acid crystal morphology in the usual growth habit, showing the five major faces and the crystallographic axes, a, b, c. The (100) and (010) planes are good cleavage planes, intersecting along e, which is the intermolecular hydrogen-bonding axis.

spectrum becomes extremely congested,making the analysisboth difficult and time consuming. We had hoped to achieve a more complete treatment of this fertile system, and indeed the publication of this material has been delayed for many years in the hope that we could accomplish that larger task. Some of the original work to explore the unexpected complexity of the malonic acid ENDOR spectrum was undertaken in the course of the doctoral dissertation of one of the authors.23 Final ENDOR measurements in three data planes were carried out at the University of Washington;complete analysis of the spectra took place at Dartmouth College and at the present institutionsof theauthors. Theoccasion of thisspecial commemorative issue has given us the opportunity to dedicate this ongoing work-our present understanding of the malonic acid radicals-to Harden McConnell, the pioneer in this area and our personal inspiration in magnetic resonance.

II. Experimental Methods Clear single crystals of partially protonated (25%) perdeuteriomalonic acid, weighing about 0.1 g, were grown by slowly desiccatingan aqueoussolution at room temperature. The crystals grew with the same morphology described by Derbyshire et a1.26 and illustrated in Figure 1. The Miller indices on the figure refer to the a, b, c crystallographic axes defined in the crystal structure determined by X-ray diffra~tion.2~ Two major cleavage planes, (100) and (OIO), exist because the malonic acid molecules are hydrogen-bonded together in infinite chains extending along the c axis.28 The space group for malonic acid at room temperature is P i , with the unit cell comprised of two hydrogen-bonded molecules related by a center of symmetry as shown in Figure 2. (We assign primed numbers to the "upper" molecule in the figure. Thus CI in the "lower" molecule is related to C,' in the upper molecule through the center of inversion.) Because the crystals are triclinic, there is no natural choice for a Cartesian axis system; several different choices have previously been made for magnetic resonance studies in malonic acid.z9 For this work, we have chosen a Cartesian axis system closely related to the local molecular symmetry. It is based on the (100) cleavage plane (usually the largest crystal face, and easily used for crystal mounting) and its intersection axis c with the other cleauageplune (010). If a* is defined to be normal to (loo), then b* = c X I*. This axis system, which we will use throughout, is operationally convenient for preparing crystal rotations in the three Cartesian planes and has the aesthetic bonus that the principal axis directions for most of the magnetic resonance tensors lie nearly in the Cartesian data planes. The original X-ray diffraction studyz7indicated that the C-C-C "molecular plane" was roughly 14.5' from the (100) plane. However,deuteron magnetic resonance studies in our laboratory23

McCalley and Kwiram

2890 The Journal of Physical Chemistry, Vol. 97, No. 12, 1993

c, '. - . 011

4

1

H 4

Figure 2 Projection of the two malonic acid molecules in the unit cell onto the b*c plane. The room temperature structure shows an inversion center between the two molecules. The inversion related atoms in the upper molecule have the same numbering system but are labeled with a prime.

and by Haeberlen and c o - ~ o r k e r ssuggested ~~ that this angle should only be about 9'. Recent neutron diffraction data3' confirm these earlier magnetic resonance results and indicate that thecoordinates for the central carbon atom (Q)in the X-ray study are in error. Detailed information from the neutron diffraction study30is summarized in Table VI11 which lists vectors and interatomic distances frequently required in analyzingthe magnetic resonance data. The C-C-C "molecular planen is tilted only 9O away from the b*c plane (loo), and the malonic acid >CH2 plane lies only 4O from the a*b* coordinate plane. Figure 2 shows that one of the carboxyl groups is roughly parallel to the C-C-C plane (rotated cw by about So if looking from C1 to Q); it will be referred to as (COO)[ . The plane of the (COO)! group lies within 4 O of the b*c plane. The other carboxyl group in the molecule lies roughly perpendicularto the C-C-C plane and will be referred to as (COO)1. The 0-0 direction in (C0OH)I lies nearly along a*. The Q H2 vector lies essentially in the a*b* plane. The H-C-H bisector lies at loo from -b* (80° from a*). This can be compared to the 9O angle between b* and the C-C-C bisector. Fr&-radical concentrations of up to about 1:500032 were produced by X-irradiation for 1 2 4 0 h at room temperature, with the crystal 5 cm from a copper target in a Phillips X-ray source operating at 40 kV and 18 mA. Each irradiated crystal was mounted and cooled promptly to minimize radical conversions. We have found that maintaining the presence of the short-lived acyl radicals2'in X-irradiated malonic acid significantly shortens the electron and nuclear relaxation times, improving the intensity and response time of the ENDOR signals at 4.2 The ENDOR spectrometer (with T&11 microwavecavity)has been described by K ~ i r a m .The ~ ~ENDOR coil mount especially designed for this study is a stationary Rexolite frame keyed inside a brass collar (to prevent fracture and slippage in cycling to low temperature). It supports two turns of no. 32 wire wound in a vertical plane and fits snugly within the 0.8 cm diameter quartz inner Dewar tail. The inner crystal rotators, also of Rexolite polystyrene, allow the (100) crystal face, the b*c plane, to be mounted precisely horizontally or vertically. The rotator is

-

K.23933

orientableto fO.2O from the other end of an 80-cm stainless-steel shaft. Analysis of the crystal rotation data revealed that the rotation axis remained perpendicular to the static magnetic field to within 0.3O. ENDOR spectra were recorded by observing the saturated ESR signal while sweeping the radiofrequency, usually from 16 to 62 MHz. The crystal orientation was changed in increments of So or loo within planes near the three Cartesian coordinate planes. For each proton there are two ENDOR transitions at frequencies given approximately by (vpf A/2), where vp is the proton Larmor frequency and A is the magnitude of the hf splitting for that orientation. We will designatethe high (low) frequency ENDOR lines by v> (v lines with strongly anisotropic behavior characteristic of a protons are observed. Figure 3 displays two sections of a typical spectrum, for which

The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2891

Radicals in Malonic Acid Single Crystals

twist, for most radicals in deuterated malonic acid that possess the C-C-C framework of the undamaged molecule. The sitedoubling has nor been detected in ENDOR spectra of undeuterated malonic acid at 4.2 K, suggesting a dependence of the lowtemperature phase transition on the isotopic content of the hydrogen-bonded carboxyl dimers. A similar site doubling at 4.2 K was observed in deuterated but not undeuterated crystals of inosit01.~’ An unexpected additionaldoubling of the ENDOR lines from the RCHR species is illustrated in Figure 5 , a spectrum for H oriented at +89O in the Figure 4 data plot. The small splitting of the A2 lines at 27 MHz and the A, lines at 30 MHz is the site-doubling discussed above, while the major splitting between the AI and A2 pairs indicates there is a 24O difference between two possible orientations of the C-H bond of the RCHR radical. The same two orientations are observed in the spectrum of aged crystals of undeuterated malonic acid at 4.2 K. Since only one conformation of RCHR is found by ESR at temperatures above 46 48 50 52 54 100 K,IS8 we hypothesize that this radical freezes out at 4.2 K into two shallow potential wells separated by 24O in the a*b* plane. The implications of such a large-amplitude motional effect on the room-temperaturehyperfine tensors of RCHR are discussed in section IV. The central line (labeled E/E’) of Figure 5 has an angular variation in b*c that is identical to the variation of an equally intense line (D) but is shifted by 120° (Figure 4). Since the middle principal hyperfine tensor direction, Bi (parallel to the radical *-orbital axis for a protons) coincides within 1So for D i0 22 24 26 is and E, these matched protons together constituteoneconformation Figure 3. ENDOR spectra of the B/C complex. (a) u> lines and (b) U < lines. In plane 3 (b*c) at 4 O from c. Frequency is in MHz. of the RCH2 radical in malonic acid. The -CHI plane of this radical lies within 5’ of the b*c plane; and its bisector (at +33O in Figure 4) is directed within 3 O of the C&I axis of malonic the magnetic field, H,is nearly parallel to c. At least five RCH2 acid. The radical plane is the same, within 6 O , as that of the conformations contribute to the observed resonances. The lower spectrum of Figure 3 shows the weak Y< ENDOR transitions -(COO)11 carboxyl plane (Figure 2); we refer to this species as from 19 to 26 MHz that match the Y > lines in the upper spectrum (RCH2)ll. During its formation by proton loss and decarboxylation from the same set of protons. When observed, the Y< lines are of the other (perpendicular) carboxyl group, the -CH2 group rotates into the plane of the parallel carboxyl dimer, with one separated from the stronger Y> lines by (2vp- k), where 0 < k C-H bond (E) oriented approximately along the original H-C-H < 1.5 MHz, depending on the hyperfine a n i ~ o t r o p y .Since ~ ~ the bisector and the other C-H bond (D) oriented nearly along the Y< lines contribute no additional spectroscopic information, they former CO-C~axis of the -(COO)I. This radical is present in will not be considered further; all hyperfine tensors were two conformations of equal intensity, differing primarily in a determined from the Y> transitions, using up 13.77 MHz. small site-doubling separation of 2.3O between the E and E’ In addition to the anisotropic a-proton ENDOR lines, many protons. The well-resolved ENDOR lines from (RCH& are easy weaker and relatively isotropictransitionscan be observed between to follow, yielding hyperfinetensorsof high precision,which reveal 30 and 50 MHz at favorable magnetic field orientations. Figure novel information about the spin-density distribution in the 4 presents the angular behavior, for H oriented in the b*c plane, carboxyl group (see section IV). of all the Y> ENDOR lines which were traceable through three The strongest ENDOR lines of freshly-irradiated malonic acid data planes to yield satisfactory hyperfine tensors. Angular are produced by pairs of a protons located in -CH2groupsroughly patterns in the b*c plane are especially revealing because it lies bisected by the C r C 2 axis of the -(COO)I carboxyl group. In only 9O from the C 4 - C “molecular plane”, so that proton contrast to (RCH2)11, these (RCH2)Lradicalsarepresent in many anisotropies can be readily related to the CO-C~ or C&2 directions. The angular patterns show greater curvature at the conformations (Figure 3), generating B/C spectral patterns (dashed lines in Figure 4) that were much moredifficult to resolve. minima than at the maxima because the square of the ENDOR The multiplicity of sites is reproducible in detail, even between frequency follows a sin2 fl function. crystals of deuterated and undeuterated malonic acid, although Many of the ENDOR lines in Figure 4 appear in closelyrelative intensities may vary. Of the dozen or so B and C lines matched pairs, for example the U and V pairs in the weaklyfollowed well enough in three planes to yield high precision coupled region and the pairs of isotropic K and L lines between hyperfine tensors, five pairs could be matched together by 40 and 50 MHz. This doubling is a consequence of the absence, requiringcoincident *-orbital directions (within 1 O for these five). in malonic acid at 4.2 K,of the crystallographic inversion center At -35O in the Figure 4 data plot, the B and C lines separately present at room temperature. Originally detected as a doubling coalesce near 52 and 55 MHz, where H approaches within a few of the quadrupole splitting patterns in the deuteron magnetic degrees of the C&2 axis (thus roughly bisecting the-CH2 group resonance of malonic acid at 4.2 K,23this loss of symmetry has been confirmed by variable temperature magnetic r e s ~ n a n c e , ~ ~ of the radicals). Orienting H 90° away, roughly normal to the (COO) I carboxyl plane of malonic acid, causes all 10 B/C lines infrared,36 and neutron diffraction studies.31bHence, there are to coalesce. essentially two pairs of molecules per unit cell which are almost Figures 6 and 7 display portions of the malonic acid ENDOR but not quite related by a center of From the spectrum containing transitions nor associated with the a-proton principal directions of the 4.2 K deuteron quadrupole splitting radicals. Numerous ENDOR lines below 17 MHz are transitions tensors, one can deduce that the two molecules in the unit cell differ mainly by a 3 O relative rotation of their >CDz groups due to carboxyl protons on each of the many conformations of about the normal to the D-C-D plane (approximately the c RCH2 and RCHR; these lines are usually not resolved; tensors from these protons are not reported in this study. Figure 6 covers axis*).23 This site-doubling is observed, as roughly a 3 O >CH2 I

2392

The Journal of Physical Chemistry, Vol. 97, No. 12, 1993

McCalley and Kwiram

Angle lrom c (deg)

IO

15

20

25

30

35

45

40

50

55

60

65

70

ENDOR Frequency (MHz)

Figure 4. Variation of proton ENDOR frequencies with magnetic-fielddirection in the b*c plane of malonic acid, for 28 distinct Y> ENDOR transitions. Solid and dashed lines plot the behavior calculated from the hyperfine tensor elements of Table VI1 (including second-order perturbation corrections). (+) Five conformations of ( R C H Z ) ~the , B/C lines; (e) D and E lines from (RCH2)ll; (0) four conformations of RCHR, the AI and A2 lines; (A) two conformations of (RCHzC==O)[, the U/V lines; (m) so-called isotropic protons (see text), the N, M, L, K lines; (0 and 0) F and G lines (from an anion-like radical; see text). Omitted from the this plot for clarity are (1) the D’ and E’ lines (nearly coincident with D and E in this plane), (2) the many weakly-coupled proton lines below 20 MHz, (3) several low-intensityisotropic lines near 30 and 55 MHz, and (4) the low-intensityY< ENDOR lines in the region below 30 MHz. 0

e/e’

V V’

x

18

20

22

24

18

20

22

24

is

20

22

i4

Y

UU’

1

Frcqucney (MHn)

u

X

i6

-

is

3b,

Figure 5. ENDOR spcctra of RCHR and (RCH2)ll in plane 3 (b*c) at l o from -b* c.

the region just above 17 MHz, with the magnetic field in a plane perpendicular to b*c, intersecting it at the - 6 5 O angle in Figure 4. The line pairs labeled (U,V)and (U’,V’) are from a single radical (and its site-doubled partner in the unit cell) which bears one proton well above the radical plane (b*c) and one proton well below it. The hyperfine tensors for these lines are the same as those measured by room-temperature ESR for the (RCH2C==O)11 acyl radical of malonic acid, where the spin density is primarily in a u-orbital on C1.21J3Figure 7 shows two more line pails, labeled (K,L) and K’,L’) from ‘isotropic” protons and their sitedoubled partners. As in the case of U and V, spectra in planes perpendicular to b*c indicate the two protons are symmetrically disposed about a radical plane nearly coincident with b*c. In Section IV,we show that these lines arise from interaction of the central >CH2 group with spin density of 0.5-0.6 at the C I carbon of (COO)11. Other isotropic ENDOR lines besides K and L are plotted in Figure 4, which shows that these lines (F, M,and N)

is

U’ v V’

W/W’

20

22

20

22

24

\ 6 Y 1

18

24

is io 22 24 Figure 6. ENDOR spectra (primarily from the u RCH*C=O radical) in plane 1’ (n*b*) near the b*c plane (Cp = 80° is 3’ from b*c, and Cp = 85O is 2O from b*c).

maximize in the opposite direction from c. Consequently, these lines arise from the hyperfine interaction of protons at COwith spin density at the C2 carbon of -(COO)L. While M and N also behave in a mirror-image way (like K, L and U,V) in data planes perpendicular to b*c, the F line is unique, with axial anisotropy within the b*c plane. Its ENDOR amplitude is much greater than that of the other isotropic lines (Figure 7), and it seems to be paired in amplitude with the single

The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2893

Radicals in Malonic Acid Single Crystals

TABLE II: Malonic Acid a-Proton Tensors (RCHZ)~, eigenvalues radical

Aii

Bii

direction cosines

b*

a*

A( iso)

C

D I

M

N

38

K/K'

4b

42

41

i = y -93.57 i = x -59.56 i= z -28.73 D' -93.44 -59.64 -28.75

-32.95 0.0124 1.06 0.9973 31.89 0.0717 -32.83 -0,0075 0.97 0.9977 31.86 -0.0675

E

-33.36 -0.0832 1.03 0.9954 32.34 -0,0489 -33.36 0.0812 1.18 0.9967 32.19 0.0068

-94.05 -59.66 -28.35 -94.13 -59.59 -28.58

46

E'

-0.8984 -0.4390 -60.62 -0.0205 0.0698 0.4388 -0,8957 0.8995 0.4368 -60.61 -0.0228 0.0639 -0.4362 0.8973 -60.61 (av) 0.0586 0.9948 -60.69 -0.0436 0.0858 -0.9974 0.0547 -0.0613 -0,9948 -60.77 -0.0019 0.0815 0.9981 -0.0610 -60.73 (av)

TABLE 111: Malonic Acid a-Proton Tensors (RCHd , eigenvalues radical

A,,

direction cosines

B,,

a*

b*

C

-33.21 0.92 32.28 -32.43 0.56 31.86 -32.90 0.55 32.34 -32.36 0.11 32.25

-0.5684 0.0871 -0.8182 -0.4519 0.0876 0.8847 0.5620 0.1009 0.8210 0.4643 0.1160 -0.8781

0.6175 0.7022 -0.3542 -0.5968 0.7072 -0.3790 -0,6513 0.6659 0.3640 0.6180 0.6677 0.4150

-0.5437 0.7066 0.4529 0.6588 0.7016 0.2716 0.5100 0.7392 -0.4399 -0.6344 0.7353 -0.2384

A(iso)

BI

FREQUENCY ( M H r )

& .

42

44

46

Figure 7. ENDOR spectra (primarily isotropic lines) (a) in plane 1' (r*b*) at 2O from b*c; compare Figure 6. (b) in plane 3 (b*c) at 16' from c -b*. The break in the curve for (a) arises from a delay in

-

resuming the frequency sweep.

TABLE I: Malonic Acid a-Proton Tensors (RCHR) eigenvalues radical

direction cosines

Ai;

Bii

a*

b*

c

A(iso)

-92.17 -59.57 -26.70 -91.89 -59.16 -26.70 -9 1.24 -57.98 -25.46 -92.50 -58.87 -26.32

-32.69 -0.09 32.78 -32.64 0.09 32.55 -33.02 0.24 32.76 -33.27 0.36 32.91

0.0037 0.9400 0.3410 0.0114 0.9319 -0.3625 0.0697 0.9940 -0.0843 -0.0498 0.9982 0.0346

0.0638 0.3401 -0.9382 -0.0567 0.3626 0.9302 0.0382 -0,0871 -0.9955 -0.0379 -0,0365 0.9986

0.9980 -0.0252 0.0587 -0.9983 -0.0100 -0,0569 0.9968 -0.0661 0.0440 -0.9980 -0.0484 -0.0396

-59.48

i = y -93.65 i = x -59.52 i = z -28.16 CI -92.19 -59.80 -28.50 BI' -92.94 -59.49 -27.70 CI' -92.26 -59.79 -27.65

-60.44 -60.36 -60.04 -59.90 -60.18 (av)

~

AI i=y i=x i= I

AI' A2 A2'

-59.25

TABLE IV: Malonic Acid a-Proton Tensors (RCH2)* eigenvalues radical

direction cosines

A,,

B,,

a*

b8

c

A(iso)

-93.60 -59.66 -28.30 -92.38 -59.90 -27.51 -93.37 -59.35 -28.88 -92.51 -59.38 -28.83 -93.25 -59.28 -29.16 -92.20 -59.51 -28.46

-33.08 0.86 32.22 -32.45 0.03 32.42 -32.84 1.18 31.65 -32.27 0.86 31.41 -32.69 1.28 31.40 -32.14 0.55 31.60

-0.6183 -0.0964 -0.7800 -0.4035 -0.0866 0.9108 0.5698 -0.3505 0.7433 0.3878 -0,3527 -0,8517 -0.5692 0.1729 -0.8038 -0.4410 0.1620 0.8827

0.5422 0.6661 -0.5122 -0,7100 0.6576 -0.2521 -0.3140 0.7430 0.5911 0.6692 0.7430 -0.0029 0.5497 0.8071 -0,2156 -0.4585 0.8049 -0.3767

-0.5690 0.7395 0.3596 0.5771 0.7484 0.3268 0.7594 0.5702 -0.3133 -0.6338 0.5688 -0,5241 -0.6115 0.5646 0.5544 0.7716 0.5709 0.2807

-60.52

B2

i= y i =x i =z

-58.22

C2 -59.23

G line, the most intense of the outer weakly-coupled transitions (Figure 6). These prominent F and G lines are denoted by circles in the Figure 4 data plot; possible identifications of this unusual species are discussed in Section IV. Diagonalized hyperfine tensors for the ENDOR lines of Figure 4 (plus Dl and El) are collected in six tables: (1) four RCHR in Table I, (2) two (RCH2)ll in Table 11, (3) the BI/CI pairs of the (RCH2)L species in Table 111, (4)the other Bi/Ci pairs of the (RCH2)1 species in Table IV,(5) the isotropic proton lines and the G tensor in Table V,and (6) the (RCH~C=O)II tensors in Table VI. Each table includes the principal elements Aii,the direction cosines for each element relative to the a*b*c crystal axis system, the tensor trace u = Ai,, and the traceless anisotropy tensor elements Bii. The direction of the B , element gives the vector from the proton to the effective center of the local spin density interacting with that proton, while the Bncgdirection gives the normal to the local spin-density plane, unless the proton is influenced by both positive and negative spin densities.

IV. Discussion A. The R a - R Radical System. 1 . The Proron Tensors. The radical characterized most fully in the original pioneering studies of the >&H fragment by McConnell and co-workers is

93

c3 B4

c4

-59.93 -60.53 -60.24 -60.56 -60.06

formed by the simple yremoval*of one of the methylene hydrogen atoms. However, in contrast to the ESR spectra observed at room temperature, low-temperatureENDOR results are far richer in detail and more complex as well. Table I lists the hyperfine tensors for the four distinct RCHR radicals observed. There are four magnetically inequivalent RCHR radicals because the two slightly different molecules in the unit cell each give rise to two distinct conformers. This is readily seen by examining the direction cosines for the C-H bond direction in the radical (correspondingto the smallest negative eigenvaluein Table I), and by consulting Figure 8. One notes that the projection of the C-H direction, B,, on the a*b* plane lies at 1 9 . 9 O from -b* for A, and at 2 1 . 3 O for A,', its almost equivalentinversionpartner. The average is 20.6O,and the relative twist between these two nearly inversion-relatedradicals is 1 . 4 O . Likewise,the projection

2894

The Journal of Physical Chemistry, Vol. 97, No. 12, 1993

McCalley and Kwiram

TABLE V: Malonic Acid @-ProtonTensors (RCHzR') radical

K K' L L' M

N

F F' "G"

eigenvalues B,,

A,,

72.00 63.07 62.09 73.01 63.85 62.52 62.86 54.40 53.17 63.88 55.25 54.02 54.92 45.33 37.03 52.60 43.59 34.23 59.52 49.89 49.59 59.99 50.16 49.95 8.41 -15.79 -19.53

6.28 -2.65 -3.63 6.55 -2.61 -3.94 6.05 -2.41 -3.64 6.16 -2.47 -3.70 9.16 -0.43 -8.73 9.13 0.12 -9.24 6.52 -3.1 1 -3.41 6.62 -3.21 -3.42 17.38 -6.82 -10.56

a*

direction cosines b* c

0.2299 -0,4424 0.8668 0.2976 -0.3984 0.8675 0.4104 -0.0267 0.91 14 0.3518 - 0 . 1 104 0.9295 0.5478 -0.5646 0.61 74 0.6358 -0.5566 0.5347 0.0215 -0.8716 0.4891 0.0141 -0.6876 0.7237 0.5021 -0.3345 0.7974

0.8046 -0.4147 -0.4251 0.7824 -0.4 190 -0.4608 -0.8273 0.4097 0.3852 -0.8509 -0.4516 0.2685 0.7304 -0.037 1 -0.6821 -0.7238 -0.1892 0.6636 0.7177 -0.3276 -0,6147 0.7189 0.5116 0.4723 -0.5234 -0,8516 -0,0277

0.5476 0.7950 0.2607 0.5470 0.8 159 0.1872 -0.3836 -0,9117 0.1444 -0.3901 0.8853 0.2527 -0.4080 -0.8246 -0,3920 0.2683 0.8089 0.5232 -0.6960 -0.3647 -0,6188 -0.6949 0.5153 0.5032 0.6884 -0.4035 -0,6027

A(iso) 65.72

-

-1

56.81 57.72

-I

0

3

2

I

4

45.76

Figure 8. Projections onto the a*b* plane of the B , directions for the AI and A2 radicals, showing the two orientations of the RCHR radicals at +12O from the original molecular plane.

43.47

TABLE VI: Malonic Acid o-Proton Tensors (RCH~C==O)II eigenvalues

53.00

radical

Ai)

Bii

direction cosines a*

b*

c

Aliso) ~~

U 53.37

U' -8.97

of the C-H direction on the a*b* plane for A2 is at 4 . 8 ' from -b* and for A2' lies at -2.0° from -b*. The average lies at -3.4', and the relative twist between the A2 and A2' partners is 2.9O. The average direction of the C-H bond direction for the A1 and the A2 groups lies at 20.6 - (1/2)(20.6 3.4) = 8.6O from -b*. The normal to the C-C-C plane lies at 9.2O from a* (and 91.4O from c). Thus the average of the C-H bond directions for these four radicals lies within 0.6O of the C-C-C plane for the parent molecule as defined by the room temperature neutron diffraction data. Taking into account the low-temperature phase transition, and estimated experimental error of about O S o , we conclude that the average of the C-H directions for the AI and A2 radicals is coincident with the original molecular (C-C-C) plane. In other words, instead of a single radical with the C-H bond oriented roughly along the direction of the bisector of the former H-C-H group (or, alternatively, the C-C-C group), we find two unique orientations of the radical at *12O from the 'expected" position. In particular, when the radical is formed, the molecule has to relieve the strain caused by the changed CI-CO-C2 angle (from the tetrahedral 109.5O to the sp2 120O) and by the slight changes in bond length (value unknown), and has to do so within the constraints of the van der Waals contacts on neighboring molecules. The resulting adjustment can be thought of as a movement of the >&H fragment toward either the (symmetrically nearly equivalent) +a* or -a* direction. If one views this movement as a rotation about the C I C2 axis then one finds that the A, radical is "rotated" ccw by 12O from the position of the original bisector of the H-C-H plane and the A2 radical is "rotated" cw by 12'. In short, there are symmetrically located potential minima at f12O from the original orientation of the C-C-C plane. Thus the 'single RCHR radicar observed at room temperature is the motionally averaged tensor due to rapid interconversion between the two potential minima at * I 2O. We will return to this point later. The principal values for the A2 tensor are consistently lower than for A'2 (by about 1 MHz in each case). The trace is lower by about 1 MHz even though A'2 is very similar to AI and A']. This could simply mean that the A2 data are less reliable. This seems unlikely. On the other hand, the low values may be due to small differences in the delocalization of the spin density onto the carboxyl group. If we ignore the slight differences in the trace for the RCH2

+

0

66.46

V

V'

4.36 -13.29 -17.85 4.30 -13.27 -17.60 6.89 -11.01 -15.84 7.01 -11.21 -15.73

13.29 -4.36 -8.92 13.16 -4.41 -8.74 13.54 -4.36 -9.19 13.65 -4.57 -9.09

0.5324 -0.5198 0.668 1 0.5986 -0.5308 0.5999 0.4764 -0.4445 0.7586 0.5672 -0.4253 0.7052

-0,7066 0.1619 0.6889 -0.6592 0.0990 0.7454 0.7691 -0.2074 -0.6045 0.7245 -0.1495 -0.6729

-0.4662 -0,8388 -0,281 1 -0.4551 -0.8417 -0.2907 0.4261 0.8714 0.2431 0.3916 0.8926 0.2234

~~

-8.93 -8.86 -6.65 -6.64

radicals we can take the average for all four radicals and obtain a value of -59.05 MHz. Using the McConnell equation, a = Qp, and setting Q = 27 G as suggested by Wertz and Bolton: we find that p PT 0.78. Estimates of the spin density based on different choices of Q have ranged from about 0.66-0.93. An independent method for estimating the spin density on the central carbon atom is provided by examining the anisotropic hfi interactions of the 13C nucleus. 2. The "C Hyperfine Interactions in RCHR. The I3C hyperfine interaction in RCHR was first measured at room temperature in malonic acid by McConnell and Fessendenl3 and later refined by Cole and Heller.14 The experimental tensor was (for A = a B), krp = (42.2,22.8,212.7)MHz. The isotropic value ac a (1 /3) Tr A = 92.6 MHz. The anisotropic tensor Bcxp = (-50.4,-69.8,120.1) MHz. Since there isonlyone independent parameter provided by the anisotropic hfi for I3C,one should be able to estimate the spin density from this experimental information. Unfortunately, the measured anisotropic tensor B is not axially symmetric, contrary to what one would expect for a 2pa orbital on carbon. This makes any estimate of the spin density based on these data suspect. Moreover, a reliable theoretical value for the isotropic coupling constant for I3C is also not available. This quandary led to a number of attempts to reconcile the observed anisotropic values with reasonable estimates for the spin density, but the results were not very satisfactory. Thus, for example, BoltonI5demonstrated the difficulty by showing that the principal anisotropiceigenvalue( 120 MHz) led to an estimated p = 0.66 whereas using the theoretical value for the isotropic hfcc led to a value of p = 0.93. Clearly, these results were inconsistent. Gordys likewise outlined the difficulty of trying to use the isotropic value to estimate spin density. He noted that motional averaging might be at least partially responsible for the lack of agreement. This state of affairs has been quite unsatisfactory. More recently, an extensive temperature-dependent study of the I3C hfi tensors in malonic acid was carried out by Bonauola et al.,3* and an effort was made to take into account motional averaging in the RCH2 radical. We will return to this system later. However, the authors wereunable tofinda satisfactoryresolutionoftheproblem

+

The Journal

Radicals in Malonic Acid Single Crystals

of Physical Chemistry, Vol. 97, No. 12, 1993 2895

TABLE MI: hoton Hyperfine Tensor Elements in Crystal Axis System’ 1 Ea*

2 P be, 3 e c

AII

A12

AI3

A22

A23

A33

fitting error

data Doints

55.75 54.90 57.91 58.92 59.41 59.49 59.83 59.82 49.56 42.22 48.63 42.01 53.56 38.32 53.57 42.20 50.83 41.67 54.31 52.75 38.51 40.50 62.80 63.65 54.8 1 55.27 45.05 44.55 44.80 49.79 49.88 -12.07 -10.32 -8.53 -9.72 -7.60

10.53 10.93 -2.64 -1.06 -1.3s -1.14 -1.68 -0.38 -21.07 19.51 -21.75 21.03 -23.91 16.74 -19.47 8.52 -15.85 16.93 -2 1.29 -22.97 16.66 12.98 2.00 2.66 -3.26 -2.88 7.33 -7.47 -7.33 0.26 0.04 -6.27 -8.74 -8.87 +8.77 +9.63

-0.54 -1.04 2.43 1.72 1.80 1.76 -2.76 -2.77 22.16 -17.48 21.07 -16.29 20.74 -17.20 21.81 -21.78 25.24 -18.82 21.94 21.80 -17.14 -16.77 0.9 1 1.28 -1.57 -1.48 -0.14 -1.08 -0.50 -0.04 -0.17 10.16 -3.52 4.03 2.74 3.33

30.77 31.17 25.80 26.46 8 1.07 81.11 28.63 28.82 68.60 67.05 69.47 66.65 61.41 74.21 52.07 74.22 68.15 61.97 55.42 58.14 72.84 75.62 68.67 69.18 60.05 61.42 46.59 44.19 43.04 54.75 55.28 -9.16 -6.64 -8.04 -2.19 -3.70

3.89 3.57 2.69 2.56 25.53 25.37 3.71 4.00 -6.43 -9.75 -6.02 -9.55 4.69 -10.64 -2.48 -14.10 -7.82 -8.27 -3.93 4.35 -1 1.56 -1 1.87 4.04 4.02 2.58 2.77 -5.08 -5.00 -5.69 -4.90 -4.88 -8.78 +6.69 +6.21 +6.58 +5.85

91.92 91.68 90.97 92.32 41.38 41.22 93.60 93.66 63.18 71.81 62.03 71.03 66.59 67.25 75.98 64.29 62.73 76.52 73.2Sb 69.44b 67.17c 68.68c 65.68 66.55 55.59 56.48 45.66 41.68 43.19d 54.46 54.946 -5.68 -9.81 -10.00 -8.05 -8.64

0.05 0.05 0.05 0.05 0.05 0.07 0.05 0.04 0.07 0.06 0.06 0.08 0.06 0.05 0.06 0.06 0.05 0.05 0.04 0.07 0.1 1 0.09 0.04 0.08 0.04 0.03 0.06 0.13 0.28 0.09 0.16 0.02 0.03 0.04 0.04 0.03

62 60 62 60 64 63 69 68 61 57 68 61 61 55 59 43 31 47 31 28 33 28 25 28 24 26 48 34 35 50 50 41 43 38 34 26

~~

A1

A‘I

A2 A‘2 D D’ E E’ BI CI B’ I C’I B2 c 2

B3 c 3

B4 c 4

Bib B’2b C2b C’2b K K‘ L L’

M N (”1 F

F‘ G V V‘ U U’

All ENDOR data are reported in megahertz. All of these elements for RCHR and RCH2 radicals (A-E) should be multiplied by -1 to yield negative-trace tensors. One plane represented by only one set of data rather than the normal two sets. Data were not well fitted, and tensors were somewhat anomalous. The fit was not excellent. for the R C H R radical. T h e values they reported for the latter are B = (-55.7, -63.3,118.7) M H z . In the following discussion we will use the values reported earlier by Cole and Heller. W e consider the theoretical anisotropic hyperfine tensor elements for a n unpaired electron in a 2p, orbital centered on a I3C nucleus which a r e given as3

Btheo= (-90.8, -90.8, 18 1.6) MHz In view of the two forms of the radical a t low temperature as discussed above, we begin by assuming that the room temperature 13C hfi tensors represent averaged values as a result of rapid motion between the two low temperaturesites. In order to estimate thevalueof thespindensityon thecentral carbon atom we assume that the Byyelement is unchanged by the motion about the y axis of the radical, and assume further that the spin density, p, on the carbon atom issimply the ratioof the theoretical and experimental values of Byy. This yields a value of (69.8/90.8) = 0.77, which is nearly identical to the value of 0.78 deduced above from the proton hyperfine tensor results for RCHR (using the estimated value of Q = 27 G). This excellent agreement reinforces the assumptions that the observed hfi interaction isdue almost entirely to the spin density on the central carbon and that the Byyelement is largely unaffected by the motional averaging (in part because the >CH fragment is so well tethered by the hydrogen-bonded carboxyl groups). Using p = 0.77, we find a-1, = 120.5 for unit spin density, which is comparable to the 115 i 8 M H z reported for the methyl radical.39 Adjusting the tensor elements for the estimated spin

density p = 0.77, we predict for the anisotropic hfi tensor in the R C H R case

Bcalc(0,77) = (-69.8, -69.8, 139.6) M H z The simplest way to demonstrate the origin of the non-axiality d u e to librational averaging, is to assume that the radical is jumping rapidly between the two putative potential energy minima a t +8 and -19. The average value for B,, in this case is given by

(BZz= ) 139.6 cos219- 69.8 sin2 0

(1)

If we use 8 = 12O based on the location of the potential minima for R C H R as described above we obtain

( B)calc= (-60.7, -69.8, 130.5) MHz

(B),.xp= (-50.4, -69.8, 120.1) MHz Obviously, ( B y y )remains unchanged a t -69.8 M H z since we assumed that the averaging motion occurs about t h e y axis. The calculated asymmetry (9.1 MHz) is still smaller than the experimental value (19.4 M H z ) , but that is expected, since the 12O value we used is a lower limit on the librational angle, given the fact that zero point vibration within the potential well will add to 8. An increase of 6 by as little as So would bring the calculated and observed values into rough coincidence. However, the calculation outlined above ignores any asymmetry in the spin polarization in the sp2 orbitals (estimated to be a few megahertz) and ignores any contributions to the hfi tensor due to spin density on neighboring atoms in the radical.sS@ In the latter case, the combination of a small (negative) spin density on the adjacent

McCalley and Kwiram

2896 The Journal of Physical Chemistry, Vol. 97, No. 12, 1993

TABLE VIII: Useful Data A. Atomic Coordinates fractional coordinates" atom

-

co Clh 1.5034' co c2

a

b

C

0.598 675 0.572 945 0.551 824 0.553 952 0.573 341 0.803 230 0.229 929 0.5 0.397 355 0.858 8 19 0.538 425 0.208 501

0.129 549 0.301 810 0.285 817 0.543 315 0.173 717 0.413 744 0.275 833 0.5 -0,039 640 0.054 702 0.282 799 0.390 318

0.246 360 0.362 7 18 0.135 010 0.372 486 0.449 038 0.184 184 -0.013 505 0.5 0.169 062 0.326 606 0.519 424 -0.077 910

-0.064 148 93.68' 4 . 1 16 788 96.7 1 4 . 6 9 5 698 134.08 0.898 761 26.00 -0.057 964 93.32

-

1 .SO36

C o d HI 1.0846 Cod H2 1.0849 CI 011 1 .22iJ1

-

orthogonal coordinates 0,

b, Y 0.424 339 1.301 075 1.228 618 2.523 741 0.656 260 1.776 846 1.300 775 2.326 261 -0.350 599 -0.051 273 1.218 524 1.885 102

x

2.243 901 2.147 462 2.068 298 2.076 274 2.148 946 3.010 596 0.861 800 1.874 056 1.489 33 1 3.218 950 2.018 077 0.781 485

B. Interatomic Distances (in A) and Unit Vectors (Direction Cosines) C I 01, 0.001 149 -0.499 163 0.583 175 0.809 810 ._ 4

35.92' -0.836 804 146.80 0.074 349 85.74 0.005 909 89.66 4 . 0 7 4 368 94.26

54.33. 0.534 902 57.66 -0.714 477 135.60 -0.438 400 1 16.00 0.995 545 5.41

1.291s 012-H3 0.9900

-

c2 0 2 1 1.2172 c2 0 2 2 1.2890

022

H4

0.9751

89.93 -0,132 195 97.60 0.774 120 39.28 -0,935 985 159.39 -0.082 362 94.72

119.94 0.567 959 55.39 0.450 382 63.23 0.055 978 86.74 0.599 219 53.19

c, z

0.370 004 1.587 460 -0,888 215 1.496 126 2.706 807 -1.429711 -1.336 224 3.190 890 0.450 645 0.376 415 3.51 1 032 -2.112 771

0.866 507 29.94 0.812 371 35.67 0.444 852 116.41 -0.347 560 110.34 -0.769 338 142.78

C. Coordinates of Mirror Image (Primed) Moleculed ~~

~

a', b', c'

Y

X

(COOH)', Group Coordinates (u'= 1 - u, b'= 1 - b, c'= 1 - c) 1.600 650 3.351 447 (0.427 055,0.698 190,0.637 282) 2.128 782 (0.446 048,0.456 685,0.627 514) 1.671 838 1.599 166 3.996 263 (0.426 659,0.826 283,0.550 962) 3.433 999 (0.461 575,0.717 201,0.480 576) 1.730 035 (COOH)'I Group Coordinates ( a ' = 1 - u, b'= 1 - b, c ' = 1 - c) (0.448 176, 0.714 183,-0.135 010) 1.679 8 I4 3.423 905 (0.196 770,0.586 256, -0.184 184) 0.737 516 2.875 676 (0.770071,0.724 167,0.013 505) 2.886 312 3.351 748 2.966 627 2.767 421 (0.791 499,0.609 682.0.077 910)

C'I 0'1I 0'12

H'3 C'2 0'2 I 0 2 2

H'4

z

4.794 320 4.885 654 3.674 974 2.870 749 -4.033 -3.491 -0.385 -2.808

105 609 096 548

D. Interatomic Distances (A) and Unit Vectors (Direction Cosines)

-c*-CI 01I

C'I 0'12

012~0'11

012 021

022 022

C'2 H3

+

0'22 H4 0'21

0.533 203 (57.78') 0.550 949 (56.57') 0.550 949 (56.57') -0.569 474 (1 24.7 1 ') 0.567 959 (55.39') -0.589 332 (126.11') 0.599 219 (53.19') -0.589 332 (1 26.1 1')

-0,142 200 (98.18') 4 . 1 7 8 512 (100.28') -0.178 512 (100.28') 0.100 776 (84.22') 4.132 195 (97.60') 0.046 507 (87.33') -0,082 362 (94.72') 0.046 507 (87.33')

0.833 950 (33.49') 0.815 223 (35.39') 0.815 223 (35.39') 0.818 808 (35.33') 0.812 371 (35.67') 0.806 551 (36.24') -0.796 338 (142.78') 0.806 551 (36.24')

3.8454 2.6727 2.6727 3.8549 0.989 972 2.6723 0.975 148 2.6723

E. Interatomic Angles CI-CO-C? 111.0' CO-CI-O~~ 114.2'

L, M, Nc

H I - C ~ H ~ 108.2' 011-C1-012 124.1'

Ccj-Cl-Ol~ C,-012-H3

121.6' 114.9'

012-H3-011'

Co-C2-021

175.5' 121.5'

C I - O I I - H ' ~ 119.3' 021-C2-022 123.0'

F. Information about Maior Planes' Direction Cosines (Angles) The C-C-C Plane The (COO-)I Plane 0.031 939 (88.17') 0.029 289 (88.32') 0.999 061 (2.84') LI 0.972 947 (13.36') 0.224 387 (77.03') -0.159 704 (99.19') 0.986 877 (9.29') 4.023 826 (91.36') MI -0.169 632 (99.77') 0.530 659 (57.95') 0.986 648 (9.37') 0.158 793 (80.86') -0.036 197 (92.07') NA -0.156 966 (99.03') 0.817 344 (35.18')

4 . 0 5 5 346 (93.17') -0.830 437 (146.14') 0.554 356 (56.33')

LH 0.984 459 (10.12') MH 0.173 059 (80.03') NH 0.029 859 (88.29')

The H-C-H Plane 0.170 457 (80.19') -0.982 533 (169.28') 0.074 649 (85.72')

4 . 0 4 2 257 (92.42') 0.068 399 (86.08') 0.996 763 (4.61')

The (C-O-H)ll Plane L ~ i l -0,123 835 (97.1 1') 0.991 028 (7.68') M ~ l l -0.077 754 (94.46') 0.040 819 (87.66') NHII 0.989 252 (8.41') 0.127 266 (82.69')

-0.050 275 (92.88') 0.996 136 (5.04') 0.072 002 (85.87')

Lll -0.033 450 (91.92') Mil -0.060 645 (93.48') NII 0.997 598 (3.97')

The (COO)li Plane 0.845 819 (32.24') 0.530 017 (57.99') 0.060592 (86.53')

-0,532 418 (122.17') 0.845 814 (32.24') 0.033 582 (88.08')

The (C-O-H)I Plane 0.490 785 (60.61') L H I 0.771 198 (39.54') M H I -0.61 1 334 (127.69') 0.393 328 (66.84') N H -0.177 ~ 552 (100.23') 0.777 447 (38.97')

4.405 443 (113.92') -0.686 704 (133.37') 0.603 367 (52.89')

Data from Robert G.Delaplane, unpublished results. The fractional coordinates are only accurate to four or five significant figures, and the data throughout should be used accordingly. Unit vector from atom A to B. Distance from atom A to B. Center of symmetry is at 1.874 056,2.326 261, 3.190 989. We designate the normal to a plane by the letter N, the bisector of the three atoms which define the plane by M, and the perpendicular to these two by L.

Radicals in Malonic Acid Single Crystals carbons, the small magnetic moment of !3C, and a C-C bond length of 1.5 A, would lead us to expect the contributions of spin density on the neighboring carbons to be negligible. Thus, we conclude that the motional averaging of the RCHR radical nicely resolves the problem associated with earlier studies of the I3Chfi tensor. The values of the I3C hfi tensors for RCHR reported by Bonazzola et al.,38are somewhat different from those of Heller and Cole used above. If one uses the same procedure as above to estimate the spin density based on the Bonazzola et al., hfi tensor values, one obtains p = 0.7,a value significantly lower than that obtained above. However, if one were to accept their values instead of the Heller and Colevalues, then the procedure outlined aboveagain leads togood agreement with theexperimental results, but now with 0 = 18O. Their analysis of the I3Cresults in RCHR was hampered because they were not aware of the two site averaging of the RCHR radical at high temperature. On the other hand, their analysisof the librational averaging in the RCH2 radical seems to be more straightforwardand gives good agreement with experiment. 3. The TemperatureDependenceof B(RCHR). Wesuggested above that the high-temperature proton hfi tensor values arise from dynamic averaging of the low-temperature values. Therefore, we should be able to predict [approximately] the room temperature values for the proton hfi tensor elements. If we average the four A tensors (Table I) before diagonalizing, and subtract the trace, we obtain the values Bpred= (1.55, -32.85, +3 1.30)MHz from our low-temperature data. For convenience, we will refer to the three diagonal tensor elements in terms of B, for the largest positive value, B, for the largest negative value, and B, for the intermediate value. These values are in excellent agreement with the room temperature ESR data which yield, for the anisotropic components, the values Bcxp= (1.3, -31.7, +30.3) MHz.lo Thus the observed hyperfine splittings at room temperature are a result of the dynamic averaging of the rigid lattice values, and should not be taken as a precise representation of the >C-H fragment anisotropy. The average rigid lattice anisotropyvalues for RCHR are B42 = (0.15,-32.85, 32.75) MHz, essentially perfectly nonaxial. This is the direct, static average of the 4.2K measured values for the four radicals. By contrast, other ENDOR studies at 4.2Kof-CH-R radicals yield B tensors with a middle element (B,) of 1.5-2.5 MHz, a value also suggested for CH3.39 It is possible that significant electron delocalizationonto the (COO)I carboxyl group of RCHR in malonic acid, compared to the-CH2groups of succinic52 and glutaric accounts for this difference. By comparing the low temperature rigid latticevalues (static average) with the room temperature (motionally averaged) values of the model above, we see that the Bi and B, values are changed by about 1.5 MHz, as one might expect from a predominant wagging motion about the CI-C2 direction. If we now scale the values of Bpredby 0.965,we obtain B’ = (1.5,-3 1.9, 30.4)MHz, which is virtually the same as the observed values (certainly well within the experimental accuracy). This ratio of 0.97 may represent additional vibrational contributions, bond lengthening, or other minor changes in structure (which would affect the spin density) that could occur between 4.2K and room temperature. It should be noted, however, that the experimental accuracy of the ESR results probably does not warrant such detailed comparisons. Thus, in summary, we find that the >C-H fragment in malonic acid has two symmetrically disposed potential minima in the crystal and that the room temperature spectra represent motionally averaged spectra. Thus, the previously reported data for this system are actually only approximate values because of the motional averaging that occurs at room temperature. In thecase of the proton anisotropy, the difference due to the motional averaging is only a few percent. B. The RCH2 Radical System. RCH2 Radicals. As has been shown by Kikuchi et aLzothe primary oxidation product of the

The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2897

C

b*

Figure 9. Qualitative representation of movement of BI/CI fragments upon radical formation. The double dashed lines indicate the position of the original C2 CObond. The solid line indicates the direction of the C2 CO bond in the radical. The BI’ICI’ pair shows similar rearrangements. However, Bl’shifts by 1 l o and CI’by 14’. The extent of rotation about the C2 Co bond can be seen in Figure 10.

- -

-

irradiation process, after transferring a proton to a neighboring molecule, can decarboxylate to form an RCH2 radical. Since there are two carboxyl groups which are oriented parallel (11) and perpendicular (I)to the C-C-C plane we will discuss the resulting radicals separately. The (RCH2)L radicals were first reported by Horsfield, Morton, and Whiffen’s and have been studied primarily using conventional ESR methods. However, similar radicals have been observed in many other 1 . The Parallel Radicals (RCH2)ll. If the (COOH)I group is eliminated, we are left with the (RCH2)li radicals. Again, because of the slight inequivalenceof the inversion pair, there art two magnetically inequivalent molecules each with two protons, for a total of four distinct tensors. The hyperfine tensors for the (RCH& radicals, designated D and E, are given in Table 11. The entire radical lies essentially parallel to the b+c plane (within < 5 O in all cases). Two points are immediately apparent. First, the agreement between the diagonalized tensor elements is excellent. The average trace is 60.61 MHz with the largest deviation f0.07 MHz. Second, the trace (60.61 MHz) is 2-3% higher than the (59.05MHz) trace for the RCHR radical. The observed H-C-H angles are the same (1 19.30° and 1 19.40°)for both radicals in the unit cell. The directions of the Bi elements are within 0.3” of each other for the D and D’ protons (the B, and B, elements are virtually identical as well). For the E and E’ protons, the Bi (and Bp) elements are twisted apart by 2.4O (the B, elements are essentially parallel). This suggests that the twist occurs about an axis roughly parallel to the c axis. The anisotropic tensors for D and E are slightly though distinctly different, and we will address this observation later. 2. The Perpendicular Radicals (RCHJ.. There are at least five distinct sets of (RCH2)I radicals designated the B/C proton pairs. Each pair corresponds to a different orientation of the radical fragment that is formed. Two additional pairs were analyzed and are reported in Table VI1 as the B21,/C2b pairs. These tensors are not reported in the tables because it could not be established unequivocally that the two protons belonged to the same radical. We now examine each of the B/C pairs in turn. Figures 9 and 10 provide a pictorial representation of how each of the pairs has reoriented upon radical formation.

McCalley and Kwiram

2898 The Journal of Physical Chemistry, Vol. 97, No. 12, 1993

The B and C lines are likely to contain more fitting error than the D and E lines and exhibit greater sensitivity to proper 'intersection" of the three data planes. This is they exhibit considerableoverlap, and because the tensors are skewed relative to the three data axes a*b*c. In other words, the maximum and minimum ENDOR frequencies are not found in any of the three data planes (plane l', a*b*, comes closest). The line-tracking and matching problems were nontrivial (although satisfactorily resolved for these 10lines), which may give rise to some systematic errors in the data for these radicals. Nevertheless, we believe the following observations regarding (RCH2) are significant. 1. The H-C-H angles for (RCH2) I fall in the range 1 17.6118.2', which differs noticeably from the more accurately determined 119.3' of (RCH&. 2. The average trace of 60.26 MHz (with u = 0.25) is 0.4 MHz lower than the 60.67 MHz ( u = 0.07) of the four (RCH2)ll lines. 3. Note that the 2pr direction for the BI/CIpair lies roughly in the b*c plane and at 45.2' from b*. For [BI'ICI'], this angle is 48.2', a 3' difference. Thestrongest lines(oftheB/Cset)arefrom theBI/CIradicals, and the resulting tensors are most like the D/E average of the (RCH2)1l radicals. The traces are about 0.4 MHz smaller, while the B1and C I anisotropiesare virtually identical to the E and D anisotropiesrespectively except for a 0.5 MHz averaging of the B, and B, elements. 3. Spin Density on the Oxygens in the RCHz Radicals. The resolution provided by the ENDOR experiment allowsus to extract even more detailed information about the electronic structure of the RCH2 radical. Although one might expect the hfi tensors for the two protons in this radical to be identical, a closer examination of the anisotropic elements reveals that the magnitude of the anisotropy is 0 . 8 4 9 MHz smaller for the D proton (the one on the same side as the carbon-oxygen double bond) than for the E proton. Theoriginofthisdifferencecanbe traced tothedifference in the spin density on the two oxygen atoms. (By symmetry,spin density on the carbons will not give rise to a difference between the two proton tensors.) If we take the difference between the elements of the diagonalized tensors for the D and E protons we obtain

2 L because

n2 I

I* I

.

.

.

I

.

.

.

a. The BI/C1 set. The four hyperfine tensors and direction cosines for this complete set (2 protons per radical and two inquivalent radicals per unit cell) are given in Table 111. The hfcc should be the same in first order for the two protons on the same carbonand this is the case (-60.44and -60.36 for an average of -60.40 MHz). The "symmetry-related" pair yields values of -60.04 and -59.90 for an average of -59.97 MHz. The small difference of 0.4 MHz between these averages may represent slightly different spin delocalizationdue to a minor twist in one partner to be discussed later. The average for all four protons is -60.20 MHz. To understand the nature of the radicals more easily, Figure 9 shows the original hydrogen-bonded chain of malonic acid molecules on the left and directly to the right shows how theradicalsareorientedwithrespect to theiroriginal positions in the crystal. Several points are worth noting. First, the plane of the resulting radical "moves away" from the (CO2H) moiety to which it had been bound. (It's as though the original CO-C, bond acted like a spring under tension, and once broken, the resulting fragment was allowed to relax into a more stable conformation away from its former position.) In addition to this motion (approximately a ccw rotation about a* by lo'), the radical has also reoriented about the CO C2 direction cw by about 15'. This is most easily seen by referring to Figure 10which showsthe 2pr orbital direction with respect to the plane of the original (COO)I group. Thus, the 2pr direction for the BI/C1 pair lies 5' above the horizontal, and therefore has been "rotated" 15' since the normal to the (COO), plane lies at about 10' below the horizontal. b. The Bz/Cz Set. The B2/C2 set is very similar to the BI/CI set except that the rotation about CO C2 is only about 5' cw instead of the 15' noted for BI/CI. Note, however, that the orientation of the CO C2 bond is nearly identical to that in the BI'IC,' pair, but the angle of rotation about the bond is different. c. The B J / CSet ~ and the B4/G Ser. For the B& set there seems to be relatively little reorientation of the radical plane about a*, but a substantial ccw rotation about Co- C2of roughly 10' is observed. The (B4/C4) pair is rotated cw by 20'. Each of these radicals exhibits a skewed anisotropydue to the different spin densitiesontheoxygens,in a manner virtually identical to the (RCH& case.

-

-

-

AB(E-D),,,

= (0.08,-0.48,0.39) f 0.05 MHz

We can now calculate the contributions to the anisotropic elements for the two protons due to spin density on O I 1and on 0 1 2 . We assume that the spin densities PI and p2 are represented by Slater 2p, orbitals on oxygens 0, I and on OIz,respectively. The bond lengths used for the radical are based on the neutron diffraction data but allow for the rearrangement of the H atoms as a result of radical formation. After integratingover the Slater 2p,orbita142 using the refinements developed by D e r b y ~ h i r eand ~ ~Barfield,44 to obtain the anisotropic contributions to the tensor elements in an axis system with x perpendicular to the molecular plane, and z aligned along the direction joining the spin density and the proton of interest, we transformed the resulting tensor contributions into the axis system in which the Ho and H E tensors respectively are diagonal. The results for the four cases are (neglecting the off-diagonal element in each case) B,(D)

(-3.20,4.65, -1.45)pl

B, (E) = (-1 30,-1.06,2.96)p, AB,(E-D) = (1.40, -5.71, 4.41)pl AB~(E-D),,,, = (1.0,4.1,3.1) Similarly, the effect of spin density on 0 1 2 is

Radicals in Malonic Acid Single Crystals B,(D) = (-1.80, -1.30,3.14)p2

ABz(E-D) AB2(E-D),,,,

(-1.73,6.94, -5.24)pZ

= (-1.0,4.0, -3.0)

In the tensors listed above, Bi(D)designates theanisotropic tensor for proton D due to spin density on oxygen i where 1 and 2 represent OI1and 0 1 2 , respectively. Note that the normalized values are essentially identical in magnitude but opposite in sign. Consequently, we will only be able to determine the differencebetween pIand p2, since p2 will partially (but uniformly) cancel the effects of p I . Because of this, we can combine the two sets of equations above and write an approximate expression for the difference AB(E-D),,,,

= (1.40, -5.71, 4.41)A12

(2) where A12 H P I -fp2 is approximately equal to the difference in the spin densities on the two oxygens, and f = lB2ii/AB1iil.The average value off for i = x, y, z yieldsf E 1.2. [If the magnitude of A B 2 were equal to that of AB1, then A12 would be exactly equal to p I - p2.1 Note that we have simply used ABI as our starting values in eq 2. We can now extract an approximatevalue for A12 by comparing the largest element (Ey,,) in AB(E-D)ca~cand in AB(E-D)exp. ThisyieldsA12= 0.084. Ifwemultiplythetherestoftheelements in AB(E-D),,l, by this value we obtain45 AB(E-D),,,,

(0.12, -0.48,0.37)

AB(E-D),,,

= (0.08, -0.48,0.39)

Thus, the difference in anisotropy for the two protons suggests that A12, and therefore the difference in spin density on the two oxygens, should be about 0.084.09. It is of interest to compare this prediction with the results of ab initio calculations on this free radical which were carried out subsequently by D a v i d ~ o nand ~ ~co-workers. The Mulliken net population47on 011is 0.0956 and on 0 1 2 is 0.0165 yielding a difference of 0.08, in excellent agreement with the results determined experimentally. If we accept the theoretical value and set p2 a! 0.02, then p I N 1.2~2+ 0.084 H 0.11. (The ab initio values are obtained for the isolated molecule. It is likely that the hydrogen bonding in the carboxyl dimer will tend to make the difference in the spin density on 011 and 0 1 2 slightly smaller.) The difference in anisotropy for the BI/CIpair is AB(B,-C,) = (0.36, -0.78, +0.42) MHz and is similar to the (E-D) anisotropy discussed above. Indeed, all the B/C pairs show this general behavior, although less cleanly, with the overall average being AB(B's-C's) = (+0.54, -4.61,0.07) MHz The negative difference on the E, element seems to be the most unvarying manifestation of the predicted anisotropy difference between the two protons on an RCH2 radical. The E, elements are probably the most accurately-known of the a-proton tensor elements, because they correspond to the well-fitted ENDOR maxima. Clearly, all the "B" protons are in the "E-position" of RCH2, while all the "C" protons are in the "D-position"; i.e., all the B's are on the same side of the radical as the carboxyl -OH bond. Thus the crystallographic position of the -OH group of the perpendicular ("I ") carboxyl dimer agrees with the hyperfine tensor placement of the C-H direction for the B and C protons;

The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2899 i.e., the carboxylic proton remains on the original oxygen of the parent molecule, as was also found for the (RCH2)n radical. One might have expected that some isomerization of the carboxyl protons might have occurred upon formation of the radical, but theclear associationofthe B/C lines intodistinct groupanalogous to the E/D groups shows this not to be so. Thus, the H-bonding patterns in the crystal seem to persist in the damage sites. 4. Spin Density on Co. The average value of the isotropic hfcc for (RCH2)11is 60.61 MHz. This result is quite similar to the value of 59.10 MHz obtained for RCHR which would suggest that the spin density on the "centraln carbon atom (CO)in the two radicals is nearly the same. The similarity of the anisotropic tensors would also suggest this. However, we note from solution studies that Q for these two radical types should differ by 5-1O%.l5J6 Moreover, the ab initio calculation for RCHz yields a value of 0.884 for the net Mulliken population on the methylene carbon (and a net population on the carboxyl carbon of about 4.01). If we accept this value as correct, then one can estimate the value for Q(CCH2) as 60.67/0.884 = 68.6 MHz (or 24.5 G). This value of Q(CCH2) is indeed about 10%lower than the value for Q(C2CH) discussed earlier, consistent with the estimates of Q(CCH2) summarized by B01ton.I~ Thus, we conclude that the spin density distribution on (RCH2)ll is given by p(C0) = 0.88, p(OI1) = 0.11, p(OI2)= 0.02, and with p(Cl) N 4 . 0 1 , However, if we accept these differences in the spin density (and in Q)for the two radicals, then we are left with the problem of how to reconcile the anisotropic tensor results. As already indicated, the elements of the anisotropichfi tensor for the RCHR proton has essentially the same magnitude as the hfi tensor elements for the RCH2 protons. This would not be consistent with a 10% difference in the spin densities. We turn now to a discussion of how these contradictions might be resolved. 5. The a-Proton Anisotropy Calculation for the >C-H Fragment. a. Comparisons of Theory and Experiment. Our task is to rationalize the ENDOR results for the anisotropy of the a-proton hfi tensor for the >C-H fragment in the two types of radicals discussed above (RCHR and RCH2) and to compare these data with theoretical dipole tensor calculations using the McConnell andStrathdee equations.lI Webegin by summarizing the experimental data for the three protons in these two radicals. (Wechooseonlythe(RCH2)11in thelattercase,since these yielded the most precise experimental data.) RCHR:

B,,,(RCHR) = (0.15, -32.90,32.75) MHz

RCH,:

Bexp(RCH2)D (1 -02,-32.88, 31.87) MHz

RCH,:

B,,,(RCHJ,

= (1.10, -33.36,32.26) MHz

The results of integrating over a 2p, Slater orbital (for p = 1.0) using the McConnell equations yields (for rC-H = 1.0694 N 1.07

A) b*,,,(>C-H)

= (-3.75,-40.00,43.75) MHz

where we use lower case b to designate the tensor due to spin density in a single (2pr) orbital and the asterisk to indicate that the values are for unit spin density. If we now adjust these values for the estimated spin density on the two radicals, we obtain 0.78b,,,(RCHR) = (-2.9, -3 1.2, 34.1) MHz 0'88b,h,(RCH2)D,E= (-3.3, -35.2,38.5) MHz Note that the 10% difference in the spin density on the two different radicals shows up as a 0.4-4 MHz difference in the Bii. This is clearly not consistent with the experimental results, and

McCalley and Kwiram

2900 The Journal of Physical Chemistry, Vol. 97, No. 12, 1993

including the contributions of spin density in other orbitals does not resolve the discrepancy. How can this dilemma be resolved? b. Eflects of Libration on the Anisotropic Proton Tensor Elements. Our calculations of the anisotropic tensor elements above were predicated on the assumption that the radicals are static. However, one would expect that the RCHR radical will undergosignificantlibrational motion (about the Cl-C2 direction) in the shallow potential well(s) we discussed earlier. How would such librational motion affect the anisotropic proton hfi tensor elements? For simplicity, we begin with RCHR and consider libration only about the y axis. This will leave the -40.0-MHz element unchanged and reduce the magnitude of the other two. Using a simple-jump model once again as in eq 1, but now with ( B z z ) = 34.1 cos2 8 - 2.9 sin28, we find that for 8 = f 10" (L designates the results under librational averaging) 0~78bth,(RCHR)L= (-1.78, -31.20,32.98) M H z

Figure 11. Projections onto b*c of the malonic acid atomic framework, and showing the direction in the paralleldimerof the major (Bp) element of the hfi tensor for selected protons. Arrows are scaled as ( B p ) - i / 3so that the length coincides roughly with the center of the spin density primarily responsible for the interaction.

compared to B,,,(RCHR)

(0.15, -32.90,32.75) MHz

This agreement is reasonablegiven that spin density contributions from other centers in the radical have not been included in b, and we have used an arbitrary though plausible value of t9 and have neglectedotherzeropointvibrations. Increasing8 bya few degrees improves the results even further, especially for B,. We now consider the case of the RCH2 radical. We would expect the RCH2 radical to experience significant librational motion about the C-C bond direction. Since we have good values for the spin densities in RCH2 from the ab initio calculations, we can correct the values of the experimental anisotropic hfi tensors by removing the estimated contributions due to spin density on the oxygens. (The spin density on the carboxyl carbon is -0.01 from the ab initio calculations and can be neglected.) In the RCH2 case, one also has to take into account the fact that the proton tensor axes are skewed with respect to the axis of libration.38 This calculation yields, for the experimental tensors due only to spin density on the proximate carbon (CO),the following values for the tensor elements for protons D and E and for the average,

(b) '~"b, = (1.47,-33.39,31.92) M H z

= (1.46, -33.46,3 1.99) M H z '.'*(b) = (1.5, -33.4, 32.0) M H z

If we now calculate the effect of libration on the (-3.75, -40.00, 43.75) MHz tensor we find the best agreement for 0 = f25". The results for this degree of librational motion are (for p = 0.88)

0~88(b)t~,(250)= (0.9, -33.6,32.7) MHz The agreement is reasonable given the simplicity of the model (other zero point vibrations, as well as minor spin density terms have been neglected). One could argue that the f25" libration is arbitrary and serves merely as an adjustable parameter. However, it must be kept in mind that we have to satisfy the values of two independent parameters consistent with different spin densities on two distinct radicals. The librational model provides one way of doing this with fairly realistic values for the degree of motion. Although further refinements of these calculations are possible, they do not seem warranted at this time given the uncertainties in detailed spin densities, geometries and theoretical models. C. Tbefl-Proton Radical System. In addition to the ENDOR lines from protons on r a n d u radicals known from earlier studies of malonic acid, an unexpected complex of relatively isotropic lines was also observed (Table V). These lines are associated

-1

-3

-2

-1

0

1

2

3

Figure 12. Projections onto the plane containing the C&I bond and I* and showing the direction of the major ( B p ) element of the hfi tensor for selected protons. Lengths are scaled the same as in Figure 11.

with another family of radicals which appear similar to, but more stable than, the reduction productst2 which have been observed both in X-irradiated carboxylic acids48 and amino acids.41.49 The anisotropic behavior of the hyperfine tensors suggests that six of these lines are protons on three conformations of a single type of free radical in which the spin density, primarily on a carboxyl carbon, interacts with two methylene protons located near their original position in the malonic acid crystal. The K and L lines of Table V arise from two conformations of the radical with spin density on C I in the (COO),l group, while the M and N lines may arise from a radical with spin density on C2 in the (COO), group. The isotropicand anisotropiccomponents of these tensors fall within the ranges observed by Box and coworkersSoin their collection of the properties of "anionn radicals formed by one-electron reduction (and possible protonation) of carboxylic acid groups. A number of related radicals have also been investigated.5'-58 The experimental hfi tensors are given in Table V and are identified with the letters K,L, M, and N, where the first pair is associated with spin density on C I and the second with spin density on C2. Within a pair such as K and L, the first letter is likewise associated with proton 1 and the second with proton 2. The experimental results are represented in Figures 11 and 12 by drawing vectors from H i and H2 in the direction of Bp with a length roughly proportional to B,-'/3. This immediately suggests that dominant spin density centers for the K and L tensors are associated with the (COO)11 group (and for M and N probably with the (COO)L group). We can put this into somewhat more quantitative terms by comparing the associated direction cosines of the major principal axis, B,, with the calculated values due to spin density in a single 2pr orbital residing on the carboxyl carbon atom and oriented perpendicular to the respective carboxyl plane. The neutron diffraction coordinates for the parent molecule were used for all

The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2901

Radicals in Malonic Acid Single Crystals

CHART I11

CHART I

HI(K) H2 (L)

experiment

calculated

atom-atom

-0.2299 (103.3) -0.8046 (143.6) -0.5476 (123.2) 0.4104 (65.8) -0.8273 (145.8) -0.3836 (112.6)

-0.1976 (101.4) -0.8070 (143.8) -0.5565 (123.8) 0.3927 (66.9) -0.6866 (133.4) -0.6119 (127.7)

-0.3119 (108.2) -0.7827 (141.5) -0.5387 (122.6) 0.5083 (59.4) -0.6415 (129.9) -0.5745 (125.1)

experiment

calculated

atom-atom

-0.5478 (123.2) -0.7304 (136.9) 0.4080 (65.9) 0.6358 (50.5) -0.7238 (136.4) 0.2683 (74.4)

-0.2848 (106.5) -0.6827 (133.0) 0.6729 (47.7) 0.5347 (57.7) 4 . 5 3 8 6 (122.6) 0.6511 (49.4)

-0.2693 (105.6) -0.7346 (137.3) 0.6228 (51.5) 0.5388 (57.4) -0.5993 (126.8) 0.5921 (53.7)

CHART 11

HI(M) Hz (N)

calculations, and the corresponding direction cosines (see Chart I) (and the angles) for the Cl-Hi (atom-atom) direction are also given (in the atom-atom column). The results for the C r H i interactions are given in Chart 11. The agreement between the observed directions of the major (positive) axis of the anisotropic hfi tensor and the calculatedvalues for thedominant contribution expected from the spin density on the respective carboxyl carbon is excellent. The results are also consistent with the directions derived from the neutron diffraction values for the atom-atom directions. Indeed, the agreement between the calculated and experimental values for the CI-HI case is deceptively good if one recognizes that spin density in other orbitals also contribute to the magnitude and direction of the principal axes of the tensor. The close agreement in this case is due in part to the special position of the H I proton with respect to the nodal plane of the 2pr orbital on C I . These data provide strong evidence for the hypothesis that these tensors arise from a radical formed from a relatively intact malonic acid molecule. It is worth pointing out, when making comparisons between the experimental and calculated direction cosines, that the direction of the major positive tensor element typically lies at about 5' less than the angle formed between the nodal plane of the 2pn orbital and the C-H direction (for deviations around 10-20O). This is reflected in the C1 case if one compares the 101.4O calculated value and the 108.2" value for the actual CI-HI direction. In other words, the agreement in this case is within just one or two degrees. The same can be said for the 66.9' versus 59.4O for the C I - H ~direction. If one were to compare the experimental and calculated direction cosines for the minor axes of the hfi tensors for these protons assuming that only the 2p, orbital on C I ( x is roughly perpendicular to the C-C-C plane in this context) contributed to the hfi tensor, then one would find less satisfactory agreement. In other words, spin density (even if only a few percent) in the other atomic orbitals on CO.on Cz and on the other atoms in the radical, will have a significant effect in shifting the directions of the minor axes. For example, even 5-10% spin density on C2 in a 2px orbital is enough to reuerse the minor axis directions for the H I tensor. On the other hand, spin density in the 1s orbital of H2 cannot change the direction cosines of the principal axes of the H I tensor as can be seen by inspection (given that the HI-H2 direction lies essentially along the same direction as the 2px orbital on CI, and given that the dipolar tensor due to spin density in an 1s orbital is axially symmetric). These effects can be seen from simple geometric models. Without ab initio level calculations on these radicals to determine the spin densities precisely, it is not productive to try to calculate in detail the anisotropic hfi interaction for each of the four hfi tensors by including all the minor spin density contributions from throughout the radical. However,given below are the angles corresponding to the direction cosines for all three

experiment calculated

B"

B,

B

103.3 143.6 123.2 97.4 140.4 128.7

116.3 114.5 31.3 123.7 117.8 46.5

30.0 115.1 74.9 34.7 115.8 68.4

principal axes calculated for the K tensor under the following assumptions about the spin densities.

+

+

B = 0.5B[2px(C,)] 0.05B[2px(C,)] 0.015B[ ls(H,)] - 0.022B[2px(Co)] - 0.015B[2p,(Co)] 0.008B[2py(CJ] - 0.008B[2,(Co)]

-

where B[u(v)] designates the anisotropic hfi tensor contribution from atomic orbital u located on atom v, and the coefficients represent theestimated spindensities (including sign). The results for the CI-HI interaction are given in Chart 111, where the three columns are associated with the positive element, the least negative and the most negative elements, (6.4, -2.6, -3.8) MHz, respectively. This agreement is remarkably good (within an average of about 5 O for each value listed above) considering that we are using crude estimates for the spin density in the various orbitals, do not know the precise geometry of the radical, are neglecting three and four center terms, and are neglecting spin density on all oxygen atoms since they are further away from the H I proton. Such calculations can be refined using spin densities from ab initio calculations. The calculations for the L tensor give similar results, but will not be repeated here. Because the Hz proton lies farther from the nodal plane of the 2px orbital on CI, small spin densities in other orbitals have a greater effect on the direction cosines of the principal axes than in the case of the K tensor. This situation becomes even more extreme in the case of the M and N tensors where we assume that an unpaired electron is associated with the perpendicular carboxyl group. In this case the anisotropic tensor becomes essentially nonaxial and behaves like an a-proton tensor (in terms of its anisotropy). However, the relative magnitude of the isotropic and anisotropiccomponents immediately eliminates the possibility that this is an alpha proton interaction. It should also be noted that there are nocorresponding primed tensors for the M and N tensors. This is probably due to the fact that the perpendicular carboxyl group is less subject to the 3O twist discussed earlier. It is possible, however, that the M and N tensors are due to radicals of the form ( R C H I C I O ) ~ . So far we have focused on the orientational question regarding these hfi tensors in order to establish the nature of these radicals. We now turn to a consideration of the magnitude of the isotropic and anisotropic elements of the tensors. The average isotropic values for the K tensor (CI-HI) and the L tensor (CI-H~)are 66.09 and 57.26 MHz, respectively. Since we are assuming that these two j3 protons are on the same radical, we can make an estimate of the primary spin density on C1 using the general empirical relation4

ai = A,

+ A , cos' Bi = 10 + 140 cos'

Bi

for i = 1, 2 (3)

A rotation about the C& bond by 4O gives (for a1 - a2 = 8.83 MHz) a value of p of about 0.52. Since the isotropic value for H I is actually the larger of the two, this means that 81 is actually the smaller of the two. This is opposite to the situation in the parent molecule where 81 is actually larger by about 2O. The simplest assumption is that there has been roughly a 6O relative twist upon formation of the radical. The magnitude of the anisotropicinteractionsare alsogenerally consistent with the picture outlined above. For example, the major axis of the (K K') hfi tensor has a value of B, = 6.41 MHz for HI. The calculated value of this same element, due to unit spin density in 2pxon C,, is 14.8 MHz. When contributions

+

2902 The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 from the other orbitals are included, this value generally drops to about 13 MHz. Thus a spin density of roughly 0.5 would be more or less consistent with the corresponding value of the anisotropic term. Again, a detailed comparison would require precisevalues for the spin densities as well the coordinates of the atoms in the radical. If we compare the results of the calculation outlined above using estimated spin densities in the various atomic orbitals with experimental values we obtain the following results for K: experiment (6.4, -3.8, -2.6) for (K + K’)/2; calculated (6.4, -3.9, -2.5) MHz. This excellent agreement can be viewed as either remarkable or fortuitous depending on the degree of confidence one wishes to place on the estimated values of the spin densities and the approximate nature of the coordinates used, the neglect of spin density on the oxygens, and the neglect of all three and four center terms that appear in the full density matrix calculation of the dipolar interaction. For purposes of this work, we feel we have established the general identity of the isotropic free radicals, K and L. One can cite one other minor piece of evidence in support of our hypothesis. The spin density in Cl should also give rise to a measurable interaction with the hydroxyl hydrogen on that carboxyl group. Indeed, the properties of one of the weakly coupled proton lines (observed outside the congested weakly coupled region in some orientations and designated W in Figure 6) suggest that it is a candidate for this interaction in the case of the parallel carboxyl group. The anisotropy is consistent with the values expected. What remains uncertain is thedetailed character of the radicals. As already indicated, we believe the evidence is consistent with a simple electron addition to the neutral molecule. This extra electron resides in the 2p, orbital of the carboxyl carbon, where i is roughly in the direction normal to the carboxyl plane. A similar radical has been observed in irradiated succinic acid59 where it was found to be stable at temperatures not much lower than room temperature. In terms of radical formation mechanisms, these one electron reduction radicals can decay directly to either RCHzC=O or RCHR (via HzOloss and H transfer).21 Most reports $0 date indicate that the negative ion is not very stable but is converted rapidly to the protonated anion. Indeed, Kikuchi et reported the protonated form of the radical in malonic acid, and their tensors are clearly different from those we report here. In particular, they report that B, = 10.33 and 11.76 MHz for the two protons on the radical with the unpaired electron located on the (COO)I group. These values suggest a spin density on CZof roughly 0.849compared to our estimates of 0 . 5 4 6 for the radicals we observe. The higher value would be expected for the protonated anion radical, whereas the lower value would be consistent with the (unprotonated) anion radical which should exhibit greater delocalization of the spin density over the carboxyl group. (They do not report values for the (COO)11 case since the lines were not sufficiently resolved.) It is not clear why two different radical types were observed in these twoexperiments. Theonlyobvious differenceis that their crystals were deuterated at roughly the 99% level compared to ours at 75%, and they irradiated at low temperatures whereas irradiation in our case was done at room temperature. This question remains to be explored. The tensor designated F is also relatively isotropic and apparently involves a single proton located roughly in the C-C-C plane of the parent molecule. The dipolar tensor data for the F tensors suggests that the primary spin density is located in a 2p7r orbital on the (COO)Lgroup. One candidate considered for these data is a radical of the form H3C-COOH- (or a variant thereof). If we assume that the methyl group is rotating, then the observation of only a single ”proton” interaction would be explained.@Q61 The isotropic value measured for proton F is slightly lower than the values observed for radicals K and L. The estimated spin density on the carboxyl carbon is roughly 0.5 as before. In

McCalley and Kwiram this case, an additional ENDOR transition is observed that behaves as though it belongs to the same radical. Analysissuggests that the hydroxyl hydrogen on the perpendicular carboxyl group fits the observed G tensor elements (Table V) in both magnitude and relative orientation. However, other evidence from the quadrupole splittingson the deuteronENDOR lines (not reported here) is not entirely consistent with a methyl radical model. The identity of this radical remains uncertain at this time. D. The u-Radicrl System. The u-radical tensors are given in Table VI. The results are very similar to those obtained in the original ESR study of this radical, and we refer the reader to the earlier article21 for a discussion of this unusual species. V. Conclusions The prototypical malonic acid system is wonderfully simple and extraordinarily complex. We have provided an overview of the rich diversity of just the most prominent radical species. The discovery of the two sites for the RCHR radical at low temperature was surprising, but it helps to explain some puzzling observations that have caused difficulties over the years for those who sought to forge coherent interpretations of hfi tensors for these basic radicals. Therecognitionof the two low-temperaturesitesallowed us to explain the earlier uncertainty regarding the asymmetry of the 13Cresults and to confirm that the spin density on the central carbon of RCHR is between 0.75 and 0.80. Likewise, using the precision possible with the ENDOR technique, we were able to extract informationabout the spin densityon the carboxyl oxygens in the RCH2 radicals, in excellent agreement with ab initio calculations. Finally, the radicals with isotropic proton tensors raise an interesting question about the solid state reaction mechanism which apparently yields “reduction” products somewhat different in structure than those previously observed in malonic acidZoand considerablymore stable at room temperature than any previous radicals of this type. Note Added in hoof. An extensive compilation of ENDOR data for organic free radicals studied in single crystals can be found in “ENDOR Data Tables” (Chapter VI) by: Goslar, J.; Piekara-Sady, L.; Kispert, L. In ESR Handbook;Poole, Jr., C.P., Farach, H. A., Eds.; American Institute of Physics: New York, in press. Ackoowledgment. Professor Ernest R. Davidson and his coworkers have been especially helpful in providing us with the results of their calculations on the RCHz radicals. Dr. Jerzy Krzystek has been very helpful at the later stages in the preparation of this manuscript and in checking some critical measurements including variable-temperature experimentsto confirm the nature of the phase transitions in malonic acid. Support from the National Science Foundation for the early stages of this work carried out at Harvard University is gratefully acknowledged. References and Notes ( I ) McConnell, H. M.; Heller, C.; Cole, T.; Fessenden, R. W. J. Am.

Chem. Soc. 1960, 82, 766-775.

(2) Heller, C.; McConnell, H. M.J. Chem. Phys. 1960,32,1535-1539. (3) Carrington, A.; McLachlan, A. D.Introduction to Magnetic Resonance, 2nd ed.; John Wiley and Sons: New York, 1979.

(4) Wcrtz, J. E.; Bolton, J. R. EIecrronSpin Resonance; McGraw-Hill: New York, 1972. ( 5 ) Gordy, W.Theory and Applications of Electron Spin Resonance; In Techniques of Chemisrry; Weissberger, A,; Ed.; John Wiley & Sons: New York, 1980 Vol. XV, Chapter VI, pp 198-304. (6) Feher, G. Phys. Reo. 1956, 103, 500-501, 83435. (7) Kwiram, A. L. Annu. Reu. Phys. Chem. 1971, 22, 133-170. (8) Kevan, L.; Kispert, L. D.Electron Spin Double Resonance Spectroscopy; John Wiley and Sons: New York, 1976. (9) (a) McConnell, H. M. J . Chem. Phys. 1956, 24, 764-766. (b) McConnell, H. M.;Chestnut, D. B. J . Chem. Phys. 1958.28, 107-1 17. (c) Weissman, S. 1. J. Chem. Phys. 1956, 25, 890-891. (d) Bersohn, R. J. J. Chem. Phys. 1956, 24, 1066-1070.

(IO) Cole, T.; Heller, C.; McConnell, H. M. Proe. Narl. Acad. Sei. U.S.A.

1959, 45, 525-528. (1 1) McConnell, H. M.;Strathdee, J. Mol. Phys. 1959. 2, 129-138.

Radicals in Malonic Acid Single Crystals (12) Wewillusethisconvention throughoutthe paper. Diagonalhyperfine tensors will be represented as (Azx,A,, Ax*),where the x, y , z axes are the local axes which diagonalize the hfi tensor. (1 3) McConnell, H. M.; Fessenden, R. W. J. Chem. Phys. 1959,31,1688. (14) Cole, T.; Heller. C. J. Chem. Phys. 1961, 34, 1085-86. (15) Bolton, J. R. Electron Spin Densities. In Rudicul Ions; Kaiser, E. T., Kevan, L., Eds.; Interscience Publishers: New York, 1968; pp 1-33. (16) Fcsscnden, R. W.; Schuler, R. H. Electron Spin Resonance Spectra of Radiation-ProducedRadicals. In Aduunces in Rudiution Chemistry;Burton, M., Magee, J.L., Eds.; Wiley-Interscience: New York, 1970;Vol.2. pp 1-176. (17) Karplus, M.; Fraenkel, G. K. J. Chem. Phys. 1961, 35, 1312-23. (18) Horsfield, A.; Morton, J. R.; Whiffen, D.H . Mol. Phys. 1961, 4, 327-332. ( 19) everidge, D. L.; McIver, J. W. J. Chem. Phys. 1971,54,468 14690. (20) Kikuchi, M.; Leray, N.; Roncin, J.; Joukoff, B. J. Chem. Phys. 1976, 12, 169-176. (21) McCalley, R. C.; Kwiram, A. L. J. Am. Chem. Soc. 1970,92,144142; J. Chem. Phys. 1970, 53, 2541-42. (22) Box, H. C. Rudiurion E//ecrs; Academic Press: New York. 1977. (23) (a) McCalley, R. C. Ph.D. Thesis, Harvard University, 1971; Diss. Absrr. Inr. B 1972,32,6955. (b) McCalley, R. C.; Kwiram, A. L. Phys. Rev. Lerr. 1970. 24. 1279-81. (24) Kwiram, A. L. J . Chem. Phys. 1971,55.2484-2495. (25) Suzuki. I. J. Phys. Soc. Jpn. 1974,37, 1379. (26) Derbyshire, W.; Gorvin, T. C.;Warner, D. Mol. Phys. 1969, 17, 401-407. (27) Gotdkoop, J. A.; MacGillavry, C. H. Acru Crysrullogr. 1957, 10, 125-127. (28) The (100)/(010) dihedral angle is obruse (96O) in Figure 1 even though the interaxial angle between a and b is acute ( S o ) . Mounting a crystal without awareness of this paradoxical situation could result in an effective reversal of the c direction from that of Figure 1 (unless other faces such as 01 1, are also utilized in the orientation). Such a reversal would interchange thecarboxyl groups between the twoendsof malonicacid, perhaps accountingfor anunusualclaimmadein theonginalESRstudyofthe( R C H Z ) ~ radical.'* (29) Two Cartesian axis systems based on the external morphology of malonic acid crystals have been described: ( I ) Honfield et al., 1961, based their coordinate system on the (010) cleavage face and its intersection axis with the (102) face, and (2) Derbyshire et al., 1969, based theirs on the (001) plane and its intersection axis b with the (100) cleavage. An internal axis system (based on the C-C-C local symmetry plane of the malonic acid molecules) was used by McConnell et al., 1960, in the pioneering study of the ReHR radical and more recently by Haeberlen et al., 1977. Although such a choice is convenient for the direct relation of the data to the molecule, it necessitates X-ray orientation for each crystal and places undue reliance on the exactness of the X-ray atomic coordinates. (30) (a) Sagnowski,S.F.; Aravamudhan, S.;Haeberlen, U.J. Mugn. Res. 1977, 28, 271-288. (b) Miiller, C.; Idziak, S.;Pislewski, N.; Haeberlen, U. J. Mugn. Res. 1982, 47, 227-239. (31) (a) Delaplane, R. Private communication. (b) McMullan, R. K. Private communication. (32) Hosaka, A.; Sugimori, A.; Genka, T.; Tsuchihashi, G. Bull. Chem. SOC.Jpn. 1967, 40, 1799-1806. (33) Dalton, L. D.; Kwiram, A. L.; Cowen, J. A. Chem. Phys. Lerr. 1972, 14,77-81. (34) Iwasaki, M. J . Mugn. Reson. 1974, 16,417-423. (35) Krzystek, J.; Kwiram, A. L. Unpublished results. (36) (a) Pigenet, C.; Lucazeau, G.; Novak, A. In Moleculur Spectroscopy o/ Dense Phuses; Grossman, M., Elkomoss, S. G., Ringcissen, J., Eds.;

The Journal of Physical Chemistry, Vol. 97, No. 12. 1993 2903 Elsevier: Amsterdam, 1976;pp 31 1-314. (b) Ganguly, S.;Fernandcs, J. R.; Dcsiraju, G. R.; Rao, C. N. R. Chem. Phys. Lett. 1980, 227. (37) Budzinski, E. E.; Box, H. C. J. Chem. Phys. 1978,68, 5296-97. (38) Bonazzola, L.; Hesse-Bezot, C.; Roncin, J. Chem. Phys. 1975, 9, 213-221. (39) (a) Cole, T.; Pritchard, H. 0.;Davidson, N.R.; McConnell, H. M. Mol. Phys. 1958, 1, 406. (b) Toriyama, K.; Nunome, K. Iwasaki, M. J. Chem. Phys. 1976, 64,2020-2026. (40) Jeevarajan, A. S.;Carmichael, I.; Fcsscnden, R. W. J. Phys. Chem. 1990.94, 1372-76. (41) Box, H. C.; Budzinski. E. E.;Freund. H. G. J. Chem. Phys. 1969, 50.2880-84. (42) Marcellus, D. H. Ph.D. Thesis, Harvard University, 1973. The calculations were carried out using programs developed by D. Marcellus. A carbon Slater orbital with Z,= 3.18 was used; for oxygen,Z. = 4.45 was used. (43) Derbyshire, W. Mol. Phys. 1962, 5, 225-231. (44) Barfield, M. J. Chem. Phys. 1970, 53, 383631343. (45) One of the uncertainties in these calculations is the precise geometry of the free radical. We used the neutron diffraction results for the above discussion. However, we also carried through the calculation using the optimized values of the structure obtained in the UHF calculation for the isolated molecule. The final results are essentially identical whether we use the neutron diffraction structure or the UHF structure. (46) Davidson, E. R. Private communication. (47) It could be asked whether the gross or net Mulliken population is a more appropriate measure. The gross population includes the overlap populations. Sincetheoverlap populatiomare smallto begin with and represent spin density closer to the C-C axis, their contribution to the anisotropy difference would be significantly smaller than the larger populations directly on the oxygen atoms. Although one could carry out a refined calculation to compare the two approaches, the close agreement with either choice does not seem to warrant the additional refinement, since the result of the ab initio calculation for the gross population is 0.066. (48) Box, H. C.; Freund, H. G.; Lilga, K. T. J . Chem. Phys. 1965, 42, 1471-74. (49) Sinclair. J. W.: Hanna. M. W. J. Phvs. Chem. 1967. 71. 84-88. (50) Box, H. C.; Freund, H.'G.; Lilga, K.T.; Budzinski, E. E.'J. Chem. Phys. 1975,63, 2059-2063. (51) Box, H. C.; Budzinski, E. E.; Potter, W. J . Chem. Phys. 1971, 55, 315-319. (52) Budzinski, E. E.; Box, H. C. J . Chem. Phys. 1975,63,4927-4929. (53) Wells, J. W. J. Chem. Phys. 1970, 52, 4062-64. (54) Iwasaki, M.; Muto, M. J. Chem. Phys. 1974,61, 5315-20. (55) Close, D. M.; Fouse, G. W.; Bemhard, W. A.; Andersen, R. S.J. Chem. Phys. 1979, 70,2131-2137. (56) (a) Muto, M.; Nunome, K.; Iwasaki, M.J. Chem. Phys. 1974,61, 1075-1077. (b) Muto, M.;Inoue, T., Iwasaki, M. J. Chem. Phys. 1972,57, 3220-3227. (57) Muto, M.; Nunome, K.; Iwasaki, M. J. Chem. Phys. 1974,61,531115. (58) Tamura. N.; Collins, M. A.; Whiffen, D. H. Trans. Furuduy Soe. 1966,62, 2434-43. (59) Schwartz. R. N.; Hanna, M. W.; Bales, B. L. J. Chem. Phys. 1969. 51,4336-40. (60) Toriyama, K.; Iwasaki, M.; Nunome, K.; Muto, H. J. Chem. Phys. 1981.75, 1633-1638. (61) Toriyama, K.; Nunome, K. Iwasaki, M. J. Chem. Phys. 1976,64, 2020-2026.