J. Phys. Chem. 1996, 100, 9605-9609
9605
High-Field Electron Spin Resonance Study of a Nitroxide Biradical, 1,4-Bis(4′,4′-dimethyloxazolidin-N-oxyl)cyclohexane Serge Gambarelli, Daniel Jaouen, and Andre´ Rassat* De´ partement de Chimie de l’Ecole Normale Supe´ rieure (URA CNRS 1679), 24 Rue Lhomond F-75231 Paris Cedex 05, France
Louis-Claude Brunel SerVice National des Champs Intenses, CNRS, B.P. 166X, F-38042 Grenoble Cedex, France
Claude Chachaty DRECAM/SCM, Centre d’Etudes Nucle´ aires de Saclay, F-91191 Gif-sur-YVette Cedex, France ReceiVed: December 21, 1995X
1,4-Bis(4′,4′-dimethyloxazolidine-N-oxyl)cyclohexane (1), a “fast exchange” biradical in which the principal directions of the g and D tensor are different, has been studied by ESR at low temperature at 245 and 294 GHz. These frequencies correspond to an “intermediate high field” (δgµBB ≈ |D|), i.e., such that the powder spectrum is neither dominated by the anisotropy of the g tensor (as at “very high field”) nor by that of the dipolar D tensor (as at “low field”). As B increases from low field to very high field, the canonical directions do not simply rotate from the principal directions of D to those of g but split into “pseudocanonical directions” at intermediate fields. The principal values of the magnetic tensors and their relative orientations were obtained by computer simulation. They are more accurate for the g tensor than those determined at low field; the dipolar parameter D is negative. Magnetization and ESR studies show that 1 is a ground-state singlet with an exchange interaction 2J/k ) -25 ( 2 K.
Introduction In biradicals and other triplet species, when the dipolar D and the molecular g tensors have different principal directions, the general shape of the dilute frozen solution spectrum (“powder spectrum”) is expected to be dominated by the anisotropy δg of g at very high field B (δgµBB . |D|) and of D at low field (δgµBB , |D|) (the symbols have their usual meaning1). We present here a study of the intermediate case.
In a biradical such as 1 and because of the symmetry (C2h) of the molecule2-6 (Figure 1) the local gi as well as the local Ai tensors (i ) a, b, nitroxide moiety) are each identical and all have the same principal directions (x, y, z) (Figure 1). Because 1 is a “fast exchange” case,3,4 the spin Hamiltonian can safely be written7 in terms of the total electronic S ) S(1) + S(2) (1 and 2 refer to the two unpaired electrons) and nuclear I ) Ia + Ib spins and of the molecular tensors g (≡gi) and A (≡Ai).
H ) µBB‚g‚S + 1/2I‚A‚S + S‚D‚S The principal directions (X, Y, Z) of the D tensor are such that by symmetry Y is parallel to z, while the angle γ ) (X,x) * Author to whom correspondence should be addressed. E-mail address:
[email protected]. X Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(95)03788-9 CCC: $12.00
Figure 1. Projection of biradical 1 on its molecular symmetry plane showing the direction of the principal axes of the magnetic tensors situated in this plane: x and y are parallel to principal axes of the local g and A tensors; X and Z are the principal axes of the dipolar D tensor. The z and Y axes are perpendicular to this plane.
Figure 2. Definition of the angle used in the discussion: when Bz ) 0 the polar angles of B are (θ ) π/2 and φ) or (Θ and Φ ) 0).
) (Z,y) [)23,5°3] is symmetry-independent (Figure 1). (A similar case (biradical 2) with γ ) 13° has been reported in a pioneering study.8) Since γ is the only parameter defining the relative orientation of the magnetic tensors, the changes occurring in the powder spectra at high magnetic field can be analysed in a quite simple manner. As the resonance frequency increases, the Y(||z) canonical direction common to D and g is conserved but the other © 1996 American Chemical Society
9606 J. Phys. Chem., Vol. 100, No. 23, 1996
Gambarelli et al.
Figure 3. Experimental (245 GHz) spectrum of biradical 1 dissolved in ethanol (a) at 50 K; (b) at 30 K; (c) at 15 K; (d) at 5.8 K. B in tesla, intensity in arbitrary units.
canonical orientations do not simply rotate continuously from X and Z at low field to respectively x and y at high field (see Appendix): at intermediate field, accumulation of spectra does not occur for two orthogonal directions of the magnetic field + but for two pairs (φ+ 0 , φ0 ) and (φ0 + (π/2), φ0 + (π/2)) of “pseudocanonical” directions φ ) (B,Ox) (Figure 2) of the magnetic field B, such that
tan(2φ( 0 - γ) )
1(λ tan γ 1-λ
or
tan2(δφ0) )
2λ sin 2γ 1 - λ2
where δφ ) φ+ 0 - φ0
λ ) 2δgµBB/3|D| ) δgB/3|D′| and
geµBD′ ) D (+ and - refer to the high- and low-field lines of the pair), the ) [hν corresponding resonance fields being B( 0 ( )]/µ g(φ ), where D(φ) and g(φ) are the dipolar interD(φB 0 0 action and the g factor for an orientation φ of the magnetic field. For any value of γ, the separation δφ0 between the pseudocanonical directions is maximum and equal to 45° for λ ) 1. For biradical 1 where δg (≈gxx - gyy ≈ gyy - gzz) ) 0.003 and 2|D| ) 684 MHz (2|D′| ) 244 G),3-6 λ ) 1 corresponds to B0 ) 12 T (and to B0 ) 3.5 T for 2 where the study8 was made at 5.4 T, i.e., λ ) 1.54). Except for λ ) 1, δφ0 is maximum for γ ) 45°. The sin 2γ factor reduces the value of tan 2δφ0 by 0.7 and 0.4 for γ ) 23.5° and 13°, respectively: the spectral changes associated with 1 are more sensitive than with 2.
When λ , 1 or λ . 1, φ+ 0 ) φ0 but for other λ (in + particular λ = 1), B0 and B0 occur for different angles φ0: except for the B || z || Y transition, B+ 0 - B0 is not proportional to D(φ0), dipolar interaction for a single canonical orientation φ0 of the magnetic field, and D and g have to be determined by computer simulation. This has been observed in the frozen solution spectrum of biradical 1 at 245 and 294 GHz (8.73 and 10.5 T at g ) 2, λ ) 0.72 and 0.86, respectively). A variable-temperature study at high field has determined the sign of D9-12 and suggested that biradical 1 has a singlet ground state. This was confirmed by X-band and magnetization studies.
Experimental Section X-band ESR spectra were obtained on a E 300 Brucker spectrometer equipped with a variable-temperature accessory (Oxford Instrument) and a data acquisition system. Intensity measurements were performed using a dual-sample cavity with a crystal of 4-hydroxy-2,2,6,6-tetramethylpiperidin-1-oxyl as reference. Absence of saturation was checked, especially at low temperature. The solution samples were degassed by a freezepump-thaw cycle and sealed in vacuo. High-field ESR spectra were obtained with a home-built spectrometer13 using a M/200 solution of 1 in an ethanol glass at four different temperatures (5.8, 15, 30, and 50 K) (245 GHz) and at 15 K (294 GHz). A sample of phosphorus-doped silicium for which giso ) 1.998 50 was used as a field standard. The exchange interaction (2J) of biradical 1 (M/200 solution in o-terphenyl) was obtained through two different methods: (a) the magnetization of this solution was recorded on a SQUID spectrometer working at 1 T. The static susceptibility χpara of 1 was calculated by subtracting the diamagnetic contribution extrapolated for infinite temperature on a χ vs 1/T graph. (b) The relative temperature dependence I/Iref of the intensity I of the |∆m| ) 1 and |∆m| ) 2 transitions at X-band compared to the intensity Iref of the reference sample was recorded as a function of temperature T. The temperature variation of the static suceptibility χpara of a polycrystalline sample of undiluted 1 was similarly determined
High-Field ESR Study of a Nitroxide Biradical
J. Phys. Chem., Vol. 100, No. 23, 1996 9607
Figure 4. Experimental (294 GHz) spectrum of biradical 1 dissolved in ethanol at 15 K. B and intensity as in Figure 3.
Figure 6. Temperature dependence of χparaT (emu K mol-1) (O) (and of χpara-1 (1)) (a) and TI/Iref (O) (and of Iref/I (1) (b) of pure crystal of biradical 1 (in arbitrary units). The theoretical curves were calculated for the Bleany-Bowers and Curie-Weiss expressions with 2J/k ) -34 K (a); -36 K (b) and θ ) -9.7 K (a); -30 K (b). Part a also gives an effective magnetic moment per molecule µ ) 1.95 µB at high temperature.
and of the X-band ESR intensity of absorption of a diluted sample (Figure 5). Best fits to the Bleaney-Bowers equation14
Q ) T[3 + exp(-1J/kT)]C-1
Figure 5. (a) Temperature dependence of χparaT (O) (and of χ-1 (1)) (arbitrary units) of a M/200 of biradical 1 in o-terphenyl glass. (b, c) Temperature dependence of TI/Iref (O) (and of Iref/I (1)) (arbitrary units) (b) of the |∆m| ) 1 ESR absorption and (c) of the |∆m| ) 2 of the same solution (in arbitrary units). The theoretical curves were calculated for the Bleany-Bowers and Curie-Weiss expressions with 2J/k ) -25 K (a); -42 K (b); -26 K (c) and θ ) -5.64 K (a); -10 K (b); -9.24 K (c).
(a) on the SQUID spectrometer and (b) by recording the intensity of the ESR |∆m| ) 1 line at the X-band. Results and Discussion Intramolecular Exchange Interaction. 1 is a “strongexchange” case, i.e., |2J ( 2D| . |Azz| and the exact value of 2J and its sign has no influence on the ESR spectrum. However from the temperature dependence of the signal-to-noise ratio at high field (Figure 3), it may be concluded that biradical 1 has a singlet ground state. This is confirmed by the temperature dependence of the paramagnetic part χ of the static susceptibility
(Q is χ-1 (SQUID) or Iref/I(ESR), and C is Curie constant (SQUID) or a constant depending on the spectrometer (ESR)) were obtained for 2J/k ) -25 ( 1 K (SQUID), -42 ( 3 K (|∆m| ) 1) and -26 ( 2 K (|∆m| ) 2). The |∆m| ) 1 value is probably less precise. In pure crystal (Figure 6) the same pair model gives 2J/k ) 34 ( 0.5 K (SQUID) and 36 ( 2 K (ESR). A value 2J ) -335 J/mol (2J/k ) -43 K) has been reported for 1 in pure crystals.15 Frozen Solution ESR Spectra. The magnetic parameters are such that we expect well apparent pseudocanonical directions: δφ0 ) 23° and 33° at 245 and 294 GHz, respectively (much larger than in 2 where δφ0 ) 12°). Figures 3 and 4 give the ESR spectra recorded at 245 GHz (at 50, 30, 15, and 5.8 K) and at 294 GHz, respectively; even at 5.8 K where the Curie-law dependence increases the sensitivity of detection for a monoradical compared to a singlet ground-state biradical, no monoradical impurity can be detected around g ) 2.0056 on the 50, 30 and 5.8 K spectra. The 15 K spectrum was recorded a few days after the other ones, and the small signal on the right of the B peak (Figure 3c) can be attributed to a monoradical impurity (slow decomposition of 1 in ethanol solution). The presence of a ca. 15 G structure (corresponding to Azz ) 32 G3,4 on the C and D peaks (Figure 3c) identifies them as the low- and high-field lines of the B || z || Y spectra (lY and hY), with a dipolar splitting |D′| ) 117 ( 7 G, in agreement with low-field results |D′| ) 122 ( 3.3-6 As explained earlier, any assignement of the other lines can only be approximate. For instance (see Figure 3c), neglecting the angle γ (so that y ) Z, x ) X), A could be assigned to a superposition of the hyZ and lxX lines, B to hxX and C to a superposition of the hyZ and lzY lines, but the splittings between A and C (277 ( 15 G) and between A and B (153 ( 12 G) are much larger than 2|D′| and |D′|.
9608 J. Phys. Chem., Vol. 100, No. 23, 1996
Gambarelli et al.
Figure 7. Best simulated 245 GHz spectra at various temperature, (corresponding to Figure 3), using the parameters reported in Table 3 with program (b). (a), (b), (c), (d) as in Figure 3, B and intensity as in Figure 3.
Sign of the Dipolar Interaction. Since the two B || Y lines are unambiguously assigned, the temperature dependence of the ratio (Il/Ih)Y of the (lY) line clearly shows9 D < 0, in agreement with the presence of two localized spins.10,11 This was confirmed by the computer simulation. (Qualitatively, i.e., taking γ ) 0, the temperature dependence of the other lines is also consistent with D < 0.) Hyperfine Splitting. The Azz/2 splittings are the only ones present on the B || z lines, the other splittings in the xy plane (Axx/2 ≈ Ayy/2 ≈ 3 G)3,4 being too small to be observed. When hyperfine interactions are of the order of the nuclear Zeeman splitting, second-order effects may occur at high field,16 but not when the magnetic induction is parallel to a principal axis of the hyperfine A tensor. This situation is obtained here even for the pseudocanonical directions because the A tensor is nearly cylindrical, and so the principal directions of D and g are either parallel or perpendicular to the principal axes of A. Computer Simulation. Two programs have been used: a program (a) already described17 written in APL for PC, in which γ is set to zero, and a program (b)18 written in Microsoft FORTRAN for PC 486/DX2. For each orientation of B in the molecular frame, program (b) diagonalizes (Jacobi method) the matrix of the spin Hamiltonian in the three triplet state functions. This program provides the possibility to vary the relative orientation of g and D. The nuclear Zeeman term is neglected and the hyperfine terms are introduced as first-order perturbation. The temperature dependence is explicitly taken into account. The 10 parameters to be introduced are the angle γ, the principal values of g, A, and D, and the temperature T. Starting with the low-field values as a first guess, best fits (Figures 7 and 8) were obtained for the values given in Table 1. The temperature dependence could only be reproduced with a negative value for D. Conclusion This ESR study of biradical 1 at “intermediate” high field (λ ≈ 1) has provided a determination of the structural parameter γ and of the principal values of the magnetic tensors in agreement with the low-field results. The principal values of
Figure 8. Best simulated 294 GHz spectra at 15 K, (corresponding to Figure 6), using the parameters reported in Table 3 with program (b). B and intensity as in Figure 3.
TABLE 1: Magnetic Parameters Obtained at Low Field and High Field low field
gxx gyy gzz god 2D′ (G) E′ (G) A′xx (G) A′yy (G) A′zz (G) a′ (G)d γ (deg)
300 Ka
77 Kb
high fieldc
2.0090 ( 3 × 10-4 2.0058 ( 3 × 10-4 2.00221 ( 3 × 10-4 2.0057 ( 3 × 10-4 (()246 ( 3 2 ( 0.5 5(1 5(1 33 ( 0.5 14.3 ( 0.8 23.5 ( 2
2.0088 ( 2 × 10-4 2.0058 ( 2 × 10-4 2.0023 ( 2 × 10-4 2.0056 ( 2 × 10-4 (()242 ( 2 3.5 ( 1 6(1 6(1 32 ( 1 14.7 ( 1
2.00860 ( 2 × 10-5 2.00580 ( 2 × 10-5 2.00210 ( 2 × 10-5 2.00550 ( 2 × 10-5 - 244 ( 1 + 2.5 ( 1 6(6 6(6 34 ( 1 15.3 ( 10 25 ( 1
a In single crystal at 300 K.3 b In ethanol solution at 77 K. The values here given have been recalculated from ref 4 taking into account second order corrections with γ ) 23.5°.3 c High-field values in ethanol solution (best fit were obtained at the different temperatures with these parameters and with line widths δxx ) δyy ) 7 G, δzz ) 7.9 G). d Average of the three principal values.
the g matrix were obtained with a better accuracy than at X-band and the sign of the dipolar interaction D was found to be negative. It has been shown that the concept of canonical directions vanishes at “intermediate” high fields (λ ≈ 1) and reappears at very high field (λ . 1). Biradical 1 has been shown
High-Field ESR Study of a Nitroxide Biradical to be a ground state singlet with a low-lying excited triplet state (2J/k ) -25 ( 2 K). Appendix In the (x, y) ≡ (X, Z) plane the two resonance fields B((φ) for an orientation φ ) (B, Ox) or δ ) (B, OX) ) φ - γ (Figure 1) are
B((φ) )
J. Phys. Chem., Vol. 100, No. 23, 1996 9609 At X-band for biradical 1, λ ) 3 × 10-3, the canonical directions are those of the D tensor but second-order corrections19 are not negligible.3 For other values of λ, the directions of accumulation (such that dB(/dφ ) 0) (pseudocanonical directions) cannot be the same for the two B+ and B- transitions: defining ζ so that φ ) ζ + γ/2 (and δ ) ζ - γ/2) (Figure 2), B+ (or B-) is extremum for ζ+ 0 (or ζ0 ) such that
d(δ) hν µBg(φ) µBg(φ)
tan 2ζ( 0 )
1(λ tan γ 1-λ
or, if
with
δζ0 ) ζ+ 0 - ζ0
g2(φ) ) gxx2 cos2 φ + gyy2 sin2 φ
tan 2δζ0 )
and
2d(δ) ) D(3 sin2 δ - 1) + 3E cos2 δ ) D + 3E 3 + (- D + E) cos 2δ 2 2
( Thus, transition from the low-field regime (ζ( 0 ) γ/2, φ0 ) ( ( γ) to the high-field regime (0 ) -γ/2, φ0 ) 0) is quite continuous. When λ ) 1 (in biradical 1, By ≈ 12 T)
ζ+ 0 ) π/4
Since for biradical 1
ζ0 )0
η ≡ (gxx - gyy)/gyy ≡ δg/gyy ) 1.5 × 10-3 neglecting second-order terms,
g-1(φ) ) gyy-1(1 - η cos2 φ) and
B((φ) ) By(1 - η cos2 φ) - d(δ)/2βe or
B((φ) ) B( 0 - K cos 2φ ( L cos 2δ with
B( 0 ) By(1 - η/2) - (D′ + 3E′)/4 K ) Byη/2 L ) (3/4)(- D′ + E′) and
hν ) gyyµBBy The characteristic parameter λ is thus
λ)
By δgBy K 2 δg ) ≈ L 3 gyy (- D′ + E′) 3(- D′)
As λ varies from very small (,1) to very large values (.1), the extrema of B(φ) change from the principal direction of D tensor for both B+ and B- to those of the g matrix, for both B+ and B- again.
2λ sin 2γ 1 - λ2
(+kπ/2) (+kπ/2)
and
δζ0 ) π/4(+kπ/2) i.e., the pseudocanonical orientations in the xy (or XZ) plane differ by π/4. References and Notes (1) Atherton, N. M. Principles of electron spin resonance; Ellis Horwood: New York, 1993. (2) Gleason, W. B. Acta Crystallogr. 1973, B29, 2959. (3) Rohde, O.; Van, S. P.; Kester, W. R.; Griffith, O. H. J. Am. Chem. Soc. 1974, 96, 5311. (4) Michon, P.; Rassat, A. J. Am. Chem. Soc. 1975, 97, 696. (5) Rohde, O.; Griffith, O. H. J. Magn. Reson. 1975, 17, 324. (6) Gleason, W. B.; Barnett, R. E. J. Am. Chem. Soc. 1976, 98, 2701. (7) Geschwind, S. In Electron Paramagnetic Resonance; Geschwind, S., Ed.; Plenum Press: New York, 1972; p 456. (8) Ondar, M. A.; Dubinskii, A. A.; Grinberg, O. Ya.; Grigor’ev, I. A.; Volodarskii, L. B.; Lebedev, Ya. S. Zh. Strukt. Khim. 1981, 22, 59. English translation: J. Struct. Chem. 1982, 22, 525. (9) Atherton, N. M. Electron Spin Resonance, Theory and Applications; Ellis Horwood: Chichester, U.K., 1973; p 170. (10) Chemerisov, S. D.; Grinberg, O. Ya.; Tipikin, D. S.; Lebedev, Ya. S.; Kurreck, H.; Mobius, K. Chem. Phys. Lett. 1994, 218, 353. (11) Tipikin, S.; Lebedev, Ya. S.; Poluektov, O. G.; Schmidt, J. Chem. Phys. Lett. 1993, 215, 199. (12) Hornig, A. W.; Hyde, J. S. Mol. Phys. 1963, 6, 33. (13) Barra, A. L.; Brunel, L. C.; Robert, J. B. Chem. Phys. Lett. 1990, 165, 908. (14) Bleaney, B.; Bowers, D. K. Proc. R. Soc. London A 1952, 11, 303. (15) Miller, T. M.; Waszczak, J. Y.; Mujsce, A. M.; Schneemeyer, L. Abstract ORGN 348; 203rd ACS National Meeting, San Francisco, April 5-10, 1992. (16) Reference 1, p 175. (17) Chachaty, C. J. Chim. Phys. 1985, 82, 621; and in: Logiciels pour la chimie; Socie´te´ Franc¸ aise de Chimie: Paris, 1991; p 76. (18) Available on request. E-mail:
[email protected]. (19) Hutchison, C. A.; Mangum, B. W. J. Chem. Phys. 1961, 34, 908.
JP953788U
