ENDOR Study of 14N Hyperfine and Quadrupole Couplings of ...

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2618 J. Phys. Chem. A, Vol. 106, No. 11, 2002 Itagaki et al. Figure 1. X-band EPR spectra of an X irradiated Li(N2D5)SO4 single crystal recorded at 240 K. The external magnetic field is parallel to the a, b, and c crystallographic axes, respectively. The crystals were irradiated at room temperature for 1 h using an X-ray tube with tungsten anode operated at 70 kV and 20 mA (approximate dose rate 250 Gy/min). The irradiated crystals were mounted to the goniometer head of a Weissenberg X-ray diffraction camera, and the crystallographic axes were aligned with the rotation axis of the camera within 1.0° using oscillation diagrams. The crystals were transferred to a quartz rod for EPR and ENDOR measurements. X-band EPR and ENDOR spectra were recorded using a Bruker ELEXSYS E580 spectrometer in CW-mode equipped with an EN 801 ENDOR cavity. The ENDOR spectra were obtained with a Bruker E250 ENDOR accessory and an ENI RF 500 amplifier. The RF modulation depth for ENDOR measurements was 190 kHz. A Bruker VT4111 temperature controller using cold nitrogen gas flow regulated the sample temperature. The nitrogen hyperfine and quadrupolar coupling tensors were determined using the program NQENDFIT 13 assuming isotropic g tensor. The DFT calculations were performed using the Gaussian 98 program packages 17 on the Cray computer server at the NSC (National Supercomputer Center) in Linköping. The single-point calculation used the B3LYP hybrid functional, and the 6-31G(d,p) basis set based on an optimized structure was evaluated using the MP2 method with the 6-31++G(d,p) basis set, as previously reported. 9 Results 1. EPR and ENDOR Spectra of the N2D4 •+ Cation. EPR spectra measured along each of the crystallographic axes for X-irradiated LiDzS crystals at room temperature are shown in Figure 1. Because X-irradiation of LiHzS crystals yields the Figure 2. ENDOR spectra obtained from X irradiated Li(N2H5)SO4 and Li(N2D5)SO4 single crystals. The external magnetic field is parallel to the crystallographic c axis. N2H4 •+ cation, 9 the radical species formed in the LiDzS crystals is expected to be the N2D4 •+ cation. Along the b and c axes, five lines that are due to the two equivalent nitrogens are observed. This simple spectrum is predicted when the protons of the cation are replaced by deuterons to be the N2D4 •+ species and the hfc is reduced by a factor of 1/6.5. Along the a axis, however, an unresolved spectrum appears, because of the small 14N hfc (aN ) 0.65 mT). Figure 2 shows the 1-50 MHz ENDOR spectra at 240 K recorded along the c axis for LiHzS and LiDzS crystals. It is striking that in the LiDzS crystal the 14N ENDOR lines (marked with a stick diagram in the figure) were clearly observed around 25 MHz (although the lowfrequency part of the 14N resonance is partially obscured by the proton signal), whereas these signals were not at all observable in the LiHzS crystal. The ENDOR spectra obtained with the external magnetic field along each of the crystallographic axes of a LiDzS crystal X irradiated at room temperature and measured at 240 K are shown in Figure 3. Although minor splittings are observed along the b and c axes because of small misalignments of the crystal, essentially four 14N-ENDOR lines are observed at each axis. This indicates that the two nitrogens in the N2D4 •+ cation are magnetically equivalent. The four 14N-ENDOR lines are ascribed to doublets with splitting virtually equal to twice the 14N nuclear Zeeman frequency (ca. 1.1 MHz) and centered at half the 14N hfc, with each of these doublet lines further split into another doublet by the nqc, i.e., 2 × 2 lines. 13-16 Thus, the four ENDOR transitions are due to m s : |+1/2〉, m I : |-1〉 S |0〉, |+1〉 S |0〉 m s : |-1/2〉, m I : |-1〉 S |0〉, |+1〉 S |0〉 (1) Here the four transitions are denoted as (+ 1 /2, -1), (+ 1 /2, +1), (- 1 /2, -1) and (- 1 /2, +1), respectively. These first-order ENDOR transitions are to be observed at 13,18 ∆E ) G(ms ) + P(ms ) G 2 (ms ) 3(mI - 1/2) (2)
ENDOR Study of N2D4 •+ J. Phys. Chem. A, Vol. 106, No. 11, 2002 2619 Figure 3. ENDOR spectra of an X irradiated Li(N2D5)SO4 single crystal recorded at 240 K with the external magnetic field along the crystallographic a, b, and c axes, respectively. In each case, the field was locked to the center of the corresponding EPR spectrum in Figure 1. The lines marked by * are the 2nd harmonic of a real line because if the nonlinearity of the rf power amplifier. where G(m s ) ) ηb( m s g′ g‚T - ν I E)( m s g′ T‚g - ν I E)ηb P(m s ) ) ηb( m s g′ g‚T - ν I E)Q( m s g′ T‚g - ν I E)ηb g′ ) ηb‚g‚g‚ηb (3) where ηb is the direction of the external magnetic field, g is the g tensor, T is the hyperfine coupling tensor, Q is the quadrupolar coupling tensor, νI is Larmor frequency of 14 N, and E is the unit tensor (Eij ) δij). The sharp and intense signals at around 5 MHz are attributable to strongly coupled deuterons (D1 and D2). The hfc determined from these lines are perfectly corresponding to 1/6.5 ()γD/γH) of the strongly coupled protons, supporting the notion that the radical formed in the LiDzS crystal is N2D4 •+ . The nqc of 2 D is too small to be observed under the present experimental conditions. The ENDOR signals of the strongly coupled protons in N2H4 •+ (H1 and H2) were intensely observed even in LiDzS, and the resonance frequencies of the signals are the same as in LiHzS. 9 The presence of these lines is probably due to imperfect deuteration of the crystal. It appears, however, that the ENDOR transitions of the protons are enhanced in the partially deuterated crystals. This is further commented below. TABLE 1: Orientation of the Symmetry-Determined Coordinate System XYZ with Respect to the Unit Cell Axes 〈abc〉, Calculated from the 1H hfc Tensor Data Reported in Ref 9 〈a〉 〈b〉 〈c〉 X 0.2461 -0.7677 -0.5922 Y -0.5550 0.3870 -0.7364 Z 0.7942 0.5099 -0.3306 2. ENDOR Data Fitting. The 14 N-ENDOR lines were observed at most field orientations throughout the three orthogonal planes, , , and . The ENDOR spectra are, however, more complicated than outlined above because of site splitting from the two magnetically inequivalent sites in the orthorhombic crystal. Consequently, a total of two sets of four lines (eight lines) are observed at all orientations except for along the crystallographic axes. To use the program NQENDFIT, 13 based on eqs 2-3 above, the quantum numbers ms and transitions mI f mI (1 for each 14 N-ENDOR line must be assigned. This is usually accomplished by an educated guess. However, in the present case, the assignment did not become clear until some model calculations had been performed. Therefore, the first step in this process consisted in estimating theoretical hyperfine and quadrupolar tensors for the radical. To calculate the 14 N-hyperfine coupling and quadrupolar coupling tensors, the orientation of the radical in the unit cell must be known. The proton couplings in the • N2H4 + radical were studied by Itagaki et al. 9 On the basis of their observations, the symmetry-determined reference frame 〈XYZ〉, as defined above, relative to the crystal unit cell system, 〈abc〉, can be determined and is given in Table 1. Now, the spin density distribution of the radical was estimated using the SCF RHF/CI INDO MO method. 19 The nitrogen dipolar coupling tensor is mainly due to spin localized in the nitrogen 2p orbitals. The central coupling is mostly from the spin in the 2px orbital, calculated to be F2px ) 0.4988. In addition, small spin densities in the 2py (0.0086) and 2pz (-0.0014) and the spin in the 2px orbital at the neighboring nitrogen atom, FR, contribute. The dipolar coupling tensor with unit spin density in 14 N 2p orbitals was reported by Morton et al. 20 and employed in this work. When the 2px orbital is located on a nitrogen atom, the coupling to an R- 14 N is given by (-1.15, -2.04, 3.18) MHz (calculated with Z* ) 3.90, R ) 1.315 Å, and the nuclear g factor for 14 N, 0.4038). The isotropic value of the 14 N coupling is obtained by scaling the calculated 2s orbital spin density (0.020) with the constant 1811 MHz 20 yielding 36.2 MHz. Together with the dipolar coupling tensor calculated above, the estimated hyperfine coupling tensor is obtained and is given in Table 2 in the experimental frame of reference. To calculate the 14 N-quadrupolar coupling tensors, the method previously described 21 was used. With the 14 N nuclear quadrupole moment being Q ) 193 × 10 -32 m 2 , 22 the required factor of proportionality 21 e 2 Q4πɛ02I(2I - 1)ha0 3 equals 2.27 MHz. In the literature, values between 2.0 and 2.5 MHz have also been used. 23
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