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ENDOR studies of X-irradiated naphthalene single crystals
15 December 1972
CHEWCAL PHYSICSLE’l-l-ERS
Volume 17, number 4
ENDOR STUDIES OF X-IRRADIATED
NAPHTHALENE
SINGLE CRYSTALS
U.R. BGHME and H.C. WOLF Pirysikdisches
Institut der Universitiit Stuttgart,
Ted 3, Stuttgart. Gertnarry
Received 25 September 1972
Detailed ENDOR studies in the crhydronaphthyl radical have led to the determination hyperfme principal axes and values of the dipole-dipole interaction of all CH and CH?
image a-hydronaphthyl equivalent CHz groups.
radicals show different
concentrations
because of a different
of spin density distribution, protons in the radical. Mirror
crystal surrounding
of chemically
I. Introduction When
irradiating naphthalene single crystals by X-
LA*
LB’
SA" ;
i
rays or by partic!es such as neutrons or electrons,
I
paramagnetic radicals are formed. Irradiation at nitrogen temperatures results in abstraction of a hydrogen atom from a naphthalene molecule. The products of this reacTion - the hydrogen atom and
the remaining waphthyl
radical - can be observed by ESR [l] and by optical measurements [2]. Men warming
up the sample both radicals disappear. It
has been assumed that one a-naphthyl radical and one naphthalene molecule form a binaphthyl radical 131. The atomic hydrogen on the other hand adds to a naphthalene molecule forming an a-hydronaphthyl radical [4]. This radical can also be obtained by irradiation at room temperature. Its existence has been shown by ESR experiments [S]. Since ESR spectra are not we!1 resolved only a few large hyperfine interactions could be found by this method [6]. Furthermore, the determination of the hyperfine tensors cannot be performed with high accuracy because of the superposition of so many different hyperfine interactions present. For this reason ENDOR investigations have been made in order to study in detail all hyperfine interactions in the ar-hydronaphthyl radical. :. 2. Experimental The naphthalene crystal is monoclinic ancl contains ‘:ja2
.
‘-
28’
“Hz
CH2
b
\
24
I/ fi 37
-
%EHWR/HH=
Fig. 1. Part of an EhTDOR spectrum of X-irradiated naphthalene single crystals. Bo is rotated in the Lx’-plane of the crystal, Bo and axis b form an angle of 7.5 degrees. Two types of radicals are formed which are denoted by ’ and “. A and B refer to the two mo1ecuk.s in the unit cell of naphthalene; numbers stand for different protons in the radical (see fig. 5).
hvo molecules per unit cell 171. Crystals were purified by hot chromatography and grown by the Bridgman method. Samples 5 X 5 X 2 mm3 in size were X-irradiated at a temperature of -20°C in order to avoid sublimation. The maxima! X-ray dose was about lOI1 rantgen. About one in 104 molecules is converted into a radical. To obtain the dependence of the hyperfine
interaction
on the direction
of the static
magnetic field B,, crystals were rotated around all three crystal axes. Measurements were performed with a Varian ESR spectrometer in the 10 GHz range as described elsewhere [8].
:.
Volume 17, number 4
CHEMICAL
PHYSICS
LETTERS
number
21,5
t
15 December
c?f proton
i972
rosition 7 unit refl
21
uENDOR/MHz ,x,5
6
20
A
t9,5
6
I9
A
6
18,5
46
18 17,s
5
A
f
: A
2
17 16,s
6 A
16
i.B
?5,5
B” A
fS
8
Fig. 2, Angular dependence of ENDOR lines in tie bc’-plane. For illustration of the numbering see fig. 5. A measured ENDOR spectrum is shown in fig. 1. The MHz scale indicates the nuclear transition frequencies which correspond to the hyperfine interactions of the protons, Measurements have been made in the frequency range from 15 to 50 MHz. 45 ENDOR lines have been found but only 30 could be observed for
axes. For B, partied to the crystal axes these different molecules become equivatent. This symmetry was used to check the orientation of the sample in the cavity.
all directions of B, relative to the crystal axes. The line width of the ENDOR lines varies in the range
3. Theory
from 150 to 700 kHz. When inducing a nuclear resonance the ESR signal diminishes, i.e., the ENDOR
The spin Hamilton operator of a system of electron spin S = $ and nuclear spin I = 4 is given by the expression
sign is opposite to, for instance, WI ENDOR signal of the. F-center in alkali-halides 191. The ENDOR sign is the same as in the corresponding hydrogen addition radical of anthracene [8]. The change of the ESR signal amounts to about 1% of the total ESR signal height. Fig. 2 shows the measured angular dependence in one of the crystal planes, in the frequency range from 15 to 21 MHz. Because of the two magnetically inequivalent molecuies A and B per unit cell the line. positions are symmetrical with respect to the crystal
HS=gs~,BO.S-gl~~Bg.j+~.A.P.
(0
whereg,pB is the magnetic moment of the electron, gigk the magnetic moment of the proton, B, the static magnetic field, g the electron spin operator. 1 the nuc!ear spin operator, and A the symmetrical hyperfine tensor. When the electron spin is quantized along BO, i.e., for high magnetic fiefd B,, m, is a good. quantum number. The energy of the system is then
583
VoIume 17, number 4
E=c$g
p B sB0
*‘g*f
15 December 1972
CHEMICAL PHYSICS LETTERS
I-(
k
lB,+
I’
(3
with B,ff = k-A/g1 & T BOk and k standing for the direction of the magnetic field Bg. This expression shows that t!!e nuclear magnetic moment is quantized along an effective magnetic field Beff which is formed by the static magnetic field B0
and a lo& magnetic field k-A which describes the hyperfiie interaction. With the selection rules for
nuclear transitions, Am, = 0 and Am1 = 1, one obtains for the ENDOR
energy
= ;Ik-A%lvJCBOkl ,
%NDOR
or in frequency ‘ENDOR
transition
Fig. 3. ehydronaphthyl additicn to an a-position
radical originating of a naphthalene
from hydrogen molecule.
(3)
units
= &bTTVkkl
)
(4)
where vk is the Zeeman frequency of the proton and 7 the hypertine tensor in frequency units. The symmetrical hyperfine tensor ? has six independent elements which can be determined by the measuremenr of ENDOR frequencies for six different directions off?, relative to the crystal axes. For this purpose ENDOR frequencies for B, parallel to the crystal ayes and under an angle of 45 degrees are used to calcuIate the values of the hyperfine tensor. This means one must coIve a non.linear system of 6 equations for the 6 unknown elements of the tensor. Diagonalisation of the hyperfine tensor gives the eigenvalues and the eigenvectors of the tensor. The eigenvalues give information about the spin density distribution in the radical, the eigenvectors about sym-
metry and orientation of the radical in the crystal en-
5. Spin density distribution From the experimental isotropic hyperfine interone obtains from the McConnell relation an experimentally determined spin density distribution of the sp2 hybridized carbon atoms. QC_H = -25.? G has been used according to the Qc_,I value in the cyclohexadienyl radical which has been measured by Fessenden and Schuler [ lo]. For the CH, protons it has been assumed that unit spin density in the 1s orbital of hydrogen produces a hyperfine interaction of action
504 G. Calculations of the sp’~ndensity distribution using McLachIarr’s SCF MO method. The CH, group was treated as consisting of two heteroatoms C(sp3) and H,. Parameters were = -0.1 and kC(T3)_H2 = 2.5. lZH12 = 0.5, hCisp3) have been performed
Table
1 shows the experimental
and the calculated
spin density distribution.
vironment. 5.1. Direction of pnhcipni 4. Results and discussion In accordance with ESR experiments performed by Okubo and co-workers [4] all measured hyperfine tensors can be understood if one assumes the formation of an a-hydronaphthyl radical as shown in fig. 3. This radical is formed by addition of a hydrogen atom to an a-position of the naphthalene molecule. The carbon atom which formerly was~sp2 hybridized is now changed to an sp3 formation. Since its geometry is no longer pianar the CH2 protons are no longer located iri the radical plane.
axes
ALIhyperfine tensors of CH protons or aromafic
protons have one principal axis in common which is perpendicular to the radical’s plane. This plane coincides with the plane of the undamaged naphthalene molecule which proves that the radical is embedded in the crystal like a normal naphthalene molecule. Deviations are smaller than 3 degrees. Another principal axis of each tensor coincides with the direction of the CH bonding. This is true very precisely for the protons 2,4. and 7 (see fig. 4) which are bonded to carbcns with positive spin densities.
Deviations up to about 20 degrees can be seen at
Volume
17, number 4
CHEhlICAL
PHYSICS
Table I Experimental and calculated spin density distribution in the *hydronaphthyl mined. In the McConnell relation QC_H = -25.7 G has been used [9] Proton
I
1’
2
43p
0.064
0.070
0.419
Pcalc.
0.063
0.063
0.455
number
3
15 December
LEMERS
radical. In the experiment
only I pl
can
1972
be deter-
4
0.107 -0.132
0.506
0.104
0.432
0.111
0.029 -0.045
0.039
0.120 0.094
-0.045
Tnblc 2 Dipole-dipole interaction of the arcmatic protons in the (r hydronaphthyl radical compared with the calculations of Atkins [ 111. Calculated values are given in brackets. Agree ment is good for positive spin densities nt the corresponding arbor. atoms and for small angles of hypertine axis and C-H bonding direction.
All D-values are given in MfIz Angle of hf-axis
Proton
D,
theory 2
-38.2 -16.53 (-15.95)
*CM
Fi_g. 4. Direction
of hyperfine principal ases compared C-H-bonding direction. At each carbon, experimental densities are indicated.
with spin
and protons 3,6 and 8. At proton 5 this can he understood quantitatively if one takes into account the influence of the high spin density at carbon 4. Deviations at the other protons 3,6 and 8 result from the fact that these protons are bonded to carbons with negative spin densities. This negative spin density results from a polarisation of the a-electrons of the carbon skeleton whose influence on the local magnetic field must be included. The dipole-dipole interaction of the CH, protans with the unpaired electron is very small since their next neighbour is the sp3 hybridized carbon which carries no spin density. Furthermore the ENDCR lines of the CH2 protons are very broad. Line widths of 700 kHz are typical for CH2 ENDOR lines whereas ENDOR lines of aromatic protons have a line width of 150 to 300 kHz. So it is rather difficult to determine the direction of the hyperfine principal acres and the values of the hyperfine interaction with high precision. One axis is nearly parallel to the long axis of the radical, the others form an angle of about 30 and 60 degrees with the radical plane. This corresponds to. proton
5
3
3.80 (3.95)
4
-20.08 (-19.30)
5 6
-4.8
(18.06)
(-2.01)
1.16
1.00 0.419
and C-H direction 0” 0’ 1”15’
0.12 (-4.50)
-3.92 (0.55)
19.17 (31.80)
0.88 (-3.50)
0.506
2”41’
0.104
17”54’
-2.09
3.56
-1.47
(4.50)
(-0.52)
0.23
-1.41
-5.12 (-4.55)
8
43.0 15.36
(-3.98) 1.18 (1.48)
I
Spin density
k
(-1.68) 4.76 (5.20)
2.35
-0.81
(1.48)
(-1.68)
-0.107
-OS!39
9O24’
9” 28’
(0.20) 0.34 (-0.65) -1.54
0.120 -0.039
1°IS’ 19O 0’
(0.20)
the fact, that the CH, protons are not situated in the radical plane according to the tetragonal structure of the sp3 hybridized carbon. Errors may be in the range of 15 degrees.
5.2. V&es
of the magnetic dipole-dipole
interaction
The magnetic dipole-dipole
interaction of a proton and an unpaired electron in a p-drbital of a carbon atom can be calculated [ 1 I]. Since all aromatic protons in the Ir-hydronaphthyl radical are bonded in the same way to a carbon atom with unpaired spin in J
585
15 December 1972
CHEhJICAL PHYSICS LETTERS
-Volume 17, numbei 4
Table 3 interaction of CHz-protons in the cr-hydronaphfhyl radical and for comparison dition radical of imidazole [ 131. All values are given in MHz Dipole-dipok
Substance
Proton
a-hydronaphthyl
1 1’
irnidazole
2 2’
its p-orbital,
experimental dipoIe interactions can be refers to.the principal axis parallel to the W-bonding
Isotropic hfs I____ 101.78 90.43
and calculated dipolecompared, see table 2. DC, of the hyperfine tensor direction, D, to the direc-
hydrogen
ad-
DCH
Dx
-2.80 -3.03
4.10 4.27
-1.28 -1.25
-3.96 -3.84
5.35 5.15
-1.40 -1.30
D,
i44.09 127.08
in the corresponding
---
hybridized and therefore spin density carrying carbon atom. In table 3 isotropic and anisotropic hyperfine interaction of the CH, protons in o-hydronaphthyl and, for comparison, in the corresponding imidazole
tion paraiiel to the carbon p-orbital. It can be seen
radical [ 131, are listed. OX refers to the principal axis
that for the carbon atoms with positive spin density (2,4 and 7) agreement is very good. As mentioned
near the long axis of the radical and DCfj to the hyperfine axis which forms an angle of 30 degrees with the radical plane. From the table, one can see that the
above,
at these
protons
one principal
axis coincides
well with the CH-bonding
ratio of the isotropic to the anisotropic hyperfine in-
direction. Deviations are found at proton 5 because of the influence of the large spin density at the next nearest carbon 4. At carbons with negative spin densities no agreement with the calculated-values can be found because of the influence of polarised u-electrons which contribute to the IocaI magnetic field. Again at these protons the coincidence of the CH-bonding direction and the principal axis is not good. From this, it foliows that agreement with theory is very good if the spin density at the carbon is positive arid the influence of the next nearest neighbour can be neglected. At the same time exact coincidence of the CH-bonding direction and one principal hyperfine axis is found. For riegative spin densities at the carbon this model cannot be used since it assumes that the unpaired electron is only localized in a carbon p-orbital. Because of the polarisation of the cr-electrons this is not the case. Because of hyperconjugation [ 121 the isotropic hyperfiie interaction for Chr, protons is much larger thafi for aromatic protons. In the case of the c+hydronsphthyl radical, the hyperfine interaction of the two protons is not identical: its values are 10 1.78 MHz and 90.45 MHz. This has also been found in the cor-
tensors it is found in the radical there are two types of hyperfme tensors whose principal values are almost identical. One tensor can be transferred into the other merely by reflecting its principal axes with respect to the,yz plane of the radical. This indicates the existence of two types of radicals, see fig. 5. They differ by the position of the hydrcgen addition. Because of the inversion symmetry of the molecule position 1 and 5 of the naphthalene molecule are equivalent to position 4 and 8. But the crystal surrounding of the CH2 protons in position 1 and 5
responding hydrogen addition radical of imidazofe 1131. it may be due to a slight distortion of the CH2 group. In spite of the large isotropic splitting dipolcdipole interaction is very small. This comes from the great distance from the CH, protons to the next sp2
differs from that of osition 4 and 8. The existence of both types of ra P &Is is confirmed by the two complete sets of ENDOR lines which show all hyperfine interactions of the radica!‘s protons. When studying COrreSpOnding ENDOR lines of
teraction
is very similar
tar all protons. Furthermore protons of the CH2 group show very similar behaviour if one takes into account that different spip densities in the surrounding of the CH~ group lead to different absolute values of the hyperfine interaction. CalcuIations of the anisotropic hyperfine interaction by Derbyshire [ 141 show onIy qualitative agreement with the experimental values in Lu-hydronaphthyl and imidazole radicals.
the two non-equivalent
5.3. Line intensities From analysis
of the hyperfine
that fqr each of the nine protons
::
Volume 17, number
Fig. 5.
4
CHEMICAL PHYSICS LETTERS
a-hydronaphthyl radicals with mirror image symmetry.
type I and type II radicals it has been found that their intensities are not equal. Since the intensity of ENDOR lines depends strongly on the direction of the static magnetic field B0 relative to the crystal axes it is difficult to compare FND3R intensities of different lines. For this reason corresponding lines of type I and type II radicals have been compared for all possible orientations of the crystal in the magnetic field Bo. Ail ENDOR lines which correspond to type I radical have been found to be 1.5 to 5 times stronger than the corresponding lines of type II radical. This is considered to be due to different concentraGons of both radicals, i.e., the forming rate of the two radicals is different: When irradiating naphthalene at low temperatures the first reaction products are hydrogen atoms which are abstracted from naphthalene molecules. These hydrogen atoms can move freely in the crystal. At temperatures above lOOoK they react with naphthalene molecules forming a-hydronaphthyl radicals. Obviously this addition is favoured in position 1 and 5 by the crystal environment so that this type of radical is more frequent than the type II radical.
15
December 1972
types of cr-hydronaphthyl radicals which differ by the position of the hydrogen addition. While these positions in the moIecuIe are chemically equivalent, its crystal surrounding is different. This leads to different concentrations cf the two radicals. Comparison of the measured and the calculated spin density distribution in both radicals shows good agreement. The mag netic dipole-dipole interactions have been measured for all CH and CH, protons. Thus it has been confirmed that the ar-hydronaphthyl radical is situated in the naphthalene crystal like a normal naphthalene molecule.
Acknowledgement This work has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich
67.
References [I] Y. Akasaka, K. Masuda and S. Namba, J. Phys. Sot. Japan 30 (1971) 1686.
[ 2] Y. Akasaka, K. Murakami, K. hfasuda and S. Namba, Mol. Cryst. Liquid Cryst. 15 (1971) 37. [3] T. Chong and N. Itoh, Mol. Cryst. Liquid Cryst. 11 (1970) 315. 141 T. Okubo, N. Itoh and T. Suita, ~101. Cryst. Liquid Mol. 6 (1969) 227. (51 J.A. Lconeand W.S. Koski, J. Am. Chem. Sot. 88 (1966) 656. [6] N. Itoh and T. Okubo, Mol. Cryst. Liquid Cryst. 17 (1972) 303. [7] D.W.J. Cruickshank, Acta Cryst. 10 (1957) 504. [8] U.R. BBhme and G.W. Jesse, Chem. Phys. Letters 3
(1969) 329.
6. Conclusion It has been shown that X-irradiation of naphthalene single crystals at room temperature produces two
[9] H. Seidel and H.C. WoX, Phys. Stat. Sol. 11 (1965) 2. [lo] R.W. Feaenden and R.H. Schuler, J. Chem. Phys. 39 (1963) 2147. [ 111 P.W. Atkins, Thesis, Univ. Leicester (1966 ). 1121 J.P. Colpa and E. de Boer, Mol. Phys. 7 (1963) 333. [I3] B. L3mottc. Thesis, Univ. Grenoble (1968). [ 141 W. Derbyshire, Mol. Dhys. 5 (1962) 225.
587
CHEWCAL PHYSICSLE’l-l-ERS
Volume 17, number 4
ENDOR STUDIES OF X-IRRADIATED
NAPHTHALENE
SINGLE CRYSTALS
U.R. BGHME and H.C. WOLF Pirysikdisches
Institut der Universitiit Stuttgart,
Ted 3, Stuttgart. Gertnarry
Received 25 September 1972
Detailed ENDOR studies in the crhydronaphthyl radical have led to the determination hyperfme principal axes and values of the dipole-dipole interaction of all CH and CH?
image a-hydronaphthyl equivalent CHz groups.
radicals show different
concentrations
because of a different
of spin density distribution, protons in the radical. Mirror
crystal surrounding
of chemically
I. Introduction When
irradiating naphthalene single crystals by X-
LA*
LB’
SA" ;
i
rays or by partic!es such as neutrons or electrons,
I
paramagnetic radicals are formed. Irradiation at nitrogen temperatures results in abstraction of a hydrogen atom from a naphthalene molecule. The products of this reacTion - the hydrogen atom and
the remaining waphthyl
radical - can be observed by ESR [l] and by optical measurements [2]. Men warming
up the sample both radicals disappear. It
has been assumed that one a-naphthyl radical and one naphthalene molecule form a binaphthyl radical 131. The atomic hydrogen on the other hand adds to a naphthalene molecule forming an a-hydronaphthyl radical [4]. This radical can also be obtained by irradiation at room temperature. Its existence has been shown by ESR experiments [S]. Since ESR spectra are not we!1 resolved only a few large hyperfine interactions could be found by this method [6]. Furthermore, the determination of the hyperfine tensors cannot be performed with high accuracy because of the superposition of so many different hyperfine interactions present. For this reason ENDOR investigations have been made in order to study in detail all hyperfine interactions in the ar-hydronaphthyl radical. :. 2. Experimental The naphthalene crystal is monoclinic ancl contains ‘:ja2
.
‘-
28’
“Hz
CH2
b
\
24
I/ fi 37
-
%EHWR/HH=
Fig. 1. Part of an EhTDOR spectrum of X-irradiated naphthalene single crystals. Bo is rotated in the Lx’-plane of the crystal, Bo and axis b form an angle of 7.5 degrees. Two types of radicals are formed which are denoted by ’ and “. A and B refer to the two mo1ecuk.s in the unit cell of naphthalene; numbers stand for different protons in the radical (see fig. 5).
hvo molecules per unit cell 171. Crystals were purified by hot chromatography and grown by the Bridgman method. Samples 5 X 5 X 2 mm3 in size were X-irradiated at a temperature of -20°C in order to avoid sublimation. The maxima! X-ray dose was about lOI1 rantgen. About one in 104 molecules is converted into a radical. To obtain the dependence of the hyperfine
interaction
on the direction
of the static
magnetic field B,, crystals were rotated around all three crystal axes. Measurements were performed with a Varian ESR spectrometer in the 10 GHz range as described elsewhere [8].
:.
Volume 17, number 4
CHEMICAL
PHYSICS
LETTERS
number
21,5
t
15 December
c?f proton
i972
rosition 7 unit refl
21
uENDOR/MHz ,x,5
6
20
A
t9,5
6
I9
A
6
18,5
46
18 17,s
5
A
f
: A
2
17 16,s
6 A
16
i.B
?5,5
B” A
fS
8
Fig. 2, Angular dependence of ENDOR lines in tie bc’-plane. For illustration of the numbering see fig. 5. A measured ENDOR spectrum is shown in fig. 1. The MHz scale indicates the nuclear transition frequencies which correspond to the hyperfine interactions of the protons, Measurements have been made in the frequency range from 15 to 50 MHz. 45 ENDOR lines have been found but only 30 could be observed for
axes. For B, partied to the crystal axes these different molecules become equivatent. This symmetry was used to check the orientation of the sample in the cavity.
all directions of B, relative to the crystal axes. The line width of the ENDOR lines varies in the range
3. Theory
from 150 to 700 kHz. When inducing a nuclear resonance the ESR signal diminishes, i.e., the ENDOR
The spin Hamilton operator of a system of electron spin S = $ and nuclear spin I = 4 is given by the expression
sign is opposite to, for instance, WI ENDOR signal of the. F-center in alkali-halides 191. The ENDOR sign is the same as in the corresponding hydrogen addition radical of anthracene [8]. The change of the ESR signal amounts to about 1% of the total ESR signal height. Fig. 2 shows the measured angular dependence in one of the crystal planes, in the frequency range from 15 to 21 MHz. Because of the two magnetically inequivalent molecuies A and B per unit cell the line. positions are symmetrical with respect to the crystal
HS=gs~,BO.S-gl~~Bg.j+~.A.P.
(0
whereg,pB is the magnetic moment of the electron, gigk the magnetic moment of the proton, B, the static magnetic field, g the electron spin operator. 1 the nuc!ear spin operator, and A the symmetrical hyperfine tensor. When the electron spin is quantized along BO, i.e., for high magnetic fiefd B,, m, is a good. quantum number. The energy of the system is then
583
VoIume 17, number 4
E=c$g
p B sB0
*‘g*f
15 December 1972
CHEMICAL PHYSICS LETTERS
I-(
k
lB,+
I’
(3
with B,ff = k-A/g1 & T BOk and k standing for the direction of the magnetic field Bg. This expression shows that t!!e nuclear magnetic moment is quantized along an effective magnetic field Beff which is formed by the static magnetic field B0
and a lo& magnetic field k-A which describes the hyperfiie interaction. With the selection rules for
nuclear transitions, Am, = 0 and Am1 = 1, one obtains for the ENDOR
energy
= ;Ik-A%lvJCBOkl ,
%NDOR
or in frequency ‘ENDOR
transition
Fig. 3. ehydronaphthyl additicn to an a-position
radical originating of a naphthalene
from hydrogen molecule.
(3)
units
= &bTTVkkl
)
(4)
where vk is the Zeeman frequency of the proton and 7 the hypertine tensor in frequency units. The symmetrical hyperfine tensor ? has six independent elements which can be determined by the measuremenr of ENDOR frequencies for six different directions off?, relative to the crystal axes. For this purpose ENDOR frequencies for B, parallel to the crystal ayes and under an angle of 45 degrees are used to calcuIate the values of the hyperfine tensor. This means one must coIve a non.linear system of 6 equations for the 6 unknown elements of the tensor. Diagonalisation of the hyperfine tensor gives the eigenvalues and the eigenvectors of the tensor. The eigenvalues give information about the spin density distribution in the radical, the eigenvectors about sym-
metry and orientation of the radical in the crystal en-
5. Spin density distribution From the experimental isotropic hyperfine interone obtains from the McConnell relation an experimentally determined spin density distribution of the sp2 hybridized carbon atoms. QC_H = -25.? G has been used according to the Qc_,I value in the cyclohexadienyl radical which has been measured by Fessenden and Schuler [ lo]. For the CH, protons it has been assumed that unit spin density in the 1s orbital of hydrogen produces a hyperfine interaction of action
504 G. Calculations of the sp’~ndensity distribution using McLachIarr’s SCF MO method. The CH, group was treated as consisting of two heteroatoms C(sp3) and H,. Parameters were = -0.1 and kC(T3)_H2 = 2.5. lZH12 = 0.5, hCisp3) have been performed
Table
1 shows the experimental
and the calculated
spin density distribution.
vironment. 5.1. Direction of pnhcipni 4. Results and discussion In accordance with ESR experiments performed by Okubo and co-workers [4] all measured hyperfine tensors can be understood if one assumes the formation of an a-hydronaphthyl radical as shown in fig. 3. This radical is formed by addition of a hydrogen atom to an a-position of the naphthalene molecule. The carbon atom which formerly was~sp2 hybridized is now changed to an sp3 formation. Since its geometry is no longer pianar the CH2 protons are no longer located iri the radical plane.
axes
ALIhyperfine tensors of CH protons or aromafic
protons have one principal axis in common which is perpendicular to the radical’s plane. This plane coincides with the plane of the undamaged naphthalene molecule which proves that the radical is embedded in the crystal like a normal naphthalene molecule. Deviations are smaller than 3 degrees. Another principal axis of each tensor coincides with the direction of the CH bonding. This is true very precisely for the protons 2,4. and 7 (see fig. 4) which are bonded to carbcns with positive spin densities.
Deviations up to about 20 degrees can be seen at
Volume
17, number 4
CHEhlICAL
PHYSICS
Table I Experimental and calculated spin density distribution in the *hydronaphthyl mined. In the McConnell relation QC_H = -25.7 G has been used [9] Proton
I
1’
2
43p
0.064
0.070
0.419
Pcalc.
0.063
0.063
0.455
number
3
15 December
LEMERS
radical. In the experiment
only I pl
can
1972
be deter-
4
0.107 -0.132
0.506
0.104
0.432
0.111
0.029 -0.045
0.039
0.120 0.094
-0.045
Tnblc 2 Dipole-dipole interaction of the arcmatic protons in the (r hydronaphthyl radical compared with the calculations of Atkins [ 111. Calculated values are given in brackets. Agree ment is good for positive spin densities nt the corresponding arbor. atoms and for small angles of hypertine axis and C-H bonding direction.
All D-values are given in MfIz Angle of hf-axis
Proton
D,
theory 2
-38.2 -16.53 (-15.95)
*CM
Fi_g. 4. Direction
of hyperfine principal ases compared C-H-bonding direction. At each carbon, experimental densities are indicated.
with spin
and protons 3,6 and 8. At proton 5 this can he understood quantitatively if one takes into account the influence of the high spin density at carbon 4. Deviations at the other protons 3,6 and 8 result from the fact that these protons are bonded to carbons with negative spin densities. This negative spin density results from a polarisation of the a-electrons of the carbon skeleton whose influence on the local magnetic field must be included. The dipole-dipole interaction of the CH, protans with the unpaired electron is very small since their next neighbour is the sp3 hybridized carbon which carries no spin density. Furthermore the ENDCR lines of the CH2 protons are very broad. Line widths of 700 kHz are typical for CH2 ENDOR lines whereas ENDOR lines of aromatic protons have a line width of 150 to 300 kHz. So it is rather difficult to determine the direction of the hyperfine principal acres and the values of the hyperfine interaction with high precision. One axis is nearly parallel to the long axis of the radical, the others form an angle of about 30 and 60 degrees with the radical plane. This corresponds to. proton
5
3
3.80 (3.95)
4
-20.08 (-19.30)
5 6
-4.8
(18.06)
(-2.01)
1.16
1.00 0.419
and C-H direction 0” 0’ 1”15’
0.12 (-4.50)
-3.92 (0.55)
19.17 (31.80)
0.88 (-3.50)
0.506
2”41’
0.104
17”54’
-2.09
3.56
-1.47
(4.50)
(-0.52)
0.23
-1.41
-5.12 (-4.55)
8
43.0 15.36
(-3.98) 1.18 (1.48)
I
Spin density
k
(-1.68) 4.76 (5.20)
2.35
-0.81
(1.48)
(-1.68)
-0.107
-OS!39
9O24’
9” 28’
(0.20) 0.34 (-0.65) -1.54
0.120 -0.039
1°IS’ 19O 0’
(0.20)
the fact, that the CH, protons are not situated in the radical plane according to the tetragonal structure of the sp3 hybridized carbon. Errors may be in the range of 15 degrees.
5.2. V&es
of the magnetic dipole-dipole
interaction
The magnetic dipole-dipole
interaction of a proton and an unpaired electron in a p-drbital of a carbon atom can be calculated [ 1 I]. Since all aromatic protons in the Ir-hydronaphthyl radical are bonded in the same way to a carbon atom with unpaired spin in J
585
15 December 1972
CHEhJICAL PHYSICS LETTERS
-Volume 17, numbei 4
Table 3 interaction of CHz-protons in the cr-hydronaphfhyl radical and for comparison dition radical of imidazole [ 131. All values are given in MHz Dipole-dipok
Substance
Proton
a-hydronaphthyl
1 1’
irnidazole
2 2’
its p-orbital,
experimental dipoIe interactions can be refers to.the principal axis parallel to the W-bonding
Isotropic hfs I____ 101.78 90.43
and calculated dipolecompared, see table 2. DC, of the hyperfine tensor direction, D, to the direc-
hydrogen
ad-
DCH
Dx
-2.80 -3.03
4.10 4.27
-1.28 -1.25
-3.96 -3.84
5.35 5.15
-1.40 -1.30
D,
i44.09 127.08
in the corresponding
---
hybridized and therefore spin density carrying carbon atom. In table 3 isotropic and anisotropic hyperfine interaction of the CH, protons in o-hydronaphthyl and, for comparison, in the corresponding imidazole
tion paraiiel to the carbon p-orbital. It can be seen
radical [ 131, are listed. OX refers to the principal axis
that for the carbon atoms with positive spin density (2,4 and 7) agreement is very good. As mentioned
near the long axis of the radical and DCfj to the hyperfine axis which forms an angle of 30 degrees with the radical plane. From the table, one can see that the
above,
at these
protons
one principal
axis coincides
well with the CH-bonding
ratio of the isotropic to the anisotropic hyperfine in-
direction. Deviations are found at proton 5 because of the influence of the large spin density at the next nearest carbon 4. At carbons with negative spin densities no agreement with the calculated-values can be found because of the influence of polarised u-electrons which contribute to the IocaI magnetic field. Again at these protons the coincidence of the CH-bonding direction and the principal axis is not good. From this, it foliows that agreement with theory is very good if the spin density at the carbon is positive arid the influence of the next nearest neighbour can be neglected. At the same time exact coincidence of the CH-bonding direction and one principal hyperfine axis is found. For riegative spin densities at the carbon this model cannot be used since it assumes that the unpaired electron is only localized in a carbon p-orbital. Because of the polarisation of the cr-electrons this is not the case. Because of hyperconjugation [ 121 the isotropic hyperfiie interaction for Chr, protons is much larger thafi for aromatic protons. In the case of the c+hydronsphthyl radical, the hyperfine interaction of the two protons is not identical: its values are 10 1.78 MHz and 90.45 MHz. This has also been found in the cor-
tensors it is found in the radical there are two types of hyperfme tensors whose principal values are almost identical. One tensor can be transferred into the other merely by reflecting its principal axes with respect to the,yz plane of the radical. This indicates the existence of two types of radicals, see fig. 5. They differ by the position of the hydrcgen addition. Because of the inversion symmetry of the molecule position 1 and 5 of the naphthalene molecule are equivalent to position 4 and 8. But the crystal surrounding of the CH2 protons in position 1 and 5
responding hydrogen addition radical of imidazofe 1131. it may be due to a slight distortion of the CH2 group. In spite of the large isotropic splitting dipolcdipole interaction is very small. This comes from the great distance from the CH, protons to the next sp2
differs from that of osition 4 and 8. The existence of both types of ra P &Is is confirmed by the two complete sets of ENDOR lines which show all hyperfine interactions of the radica!‘s protons. When studying COrreSpOnding ENDOR lines of
teraction
is very similar
tar all protons. Furthermore protons of the CH2 group show very similar behaviour if one takes into account that different spip densities in the surrounding of the CH~ group lead to different absolute values of the hyperfine interaction. CalcuIations of the anisotropic hyperfine interaction by Derbyshire [ 141 show onIy qualitative agreement with the experimental values in Lu-hydronaphthyl and imidazole radicals.
the two non-equivalent
5.3. Line intensities From analysis
of the hyperfine
that fqr each of the nine protons
::
Volume 17, number
Fig. 5.
4
CHEMICAL PHYSICS LETTERS
a-hydronaphthyl radicals with mirror image symmetry.
type I and type II radicals it has been found that their intensities are not equal. Since the intensity of ENDOR lines depends strongly on the direction of the static magnetic field B0 relative to the crystal axes it is difficult to compare FND3R intensities of different lines. For this reason corresponding lines of type I and type II radicals have been compared for all possible orientations of the crystal in the magnetic field Bo. Ail ENDOR lines which correspond to type I radical have been found to be 1.5 to 5 times stronger than the corresponding lines of type II radical. This is considered to be due to different concentraGons of both radicals, i.e., the forming rate of the two radicals is different: When irradiating naphthalene at low temperatures the first reaction products are hydrogen atoms which are abstracted from naphthalene molecules. These hydrogen atoms can move freely in the crystal. At temperatures above lOOoK they react with naphthalene molecules forming a-hydronaphthyl radicals. Obviously this addition is favoured in position 1 and 5 by the crystal environment so that this type of radical is more frequent than the type II radical.
15
December 1972
types of cr-hydronaphthyl radicals which differ by the position of the hydrogen addition. While these positions in the moIecuIe are chemically equivalent, its crystal surrounding is different. This leads to different concentrations cf the two radicals. Comparison of the measured and the calculated spin density distribution in both radicals shows good agreement. The mag netic dipole-dipole interactions have been measured for all CH and CH, protons. Thus it has been confirmed that the ar-hydronaphthyl radical is situated in the naphthalene crystal like a normal naphthalene molecule.
Acknowledgement This work has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich
67.
References [I] Y. Akasaka, K. Masuda and S. Namba, J. Phys. Sot. Japan 30 (1971) 1686.
[ 2] Y. Akasaka, K. Murakami, K. hfasuda and S. Namba, Mol. Cryst. Liquid Cryst. 15 (1971) 37. [3] T. Chong and N. Itoh, Mol. Cryst. Liquid Cryst. 11 (1970) 315. 141 T. Okubo, N. Itoh and T. Suita, ~101. Cryst. Liquid Mol. 6 (1969) 227. (51 J.A. Lconeand W.S. Koski, J. Am. Chem. Sot. 88 (1966) 656. [6] N. Itoh and T. Okubo, Mol. Cryst. Liquid Cryst. 17 (1972) 303. [7] D.W.J. Cruickshank, Acta Cryst. 10 (1957) 504. [8] U.R. BBhme and G.W. Jesse, Chem. Phys. Letters 3
(1969) 329.
6. Conclusion It has been shown that X-irradiation of naphthalene single crystals at room temperature produces two
[9] H. Seidel and H.C. WoX, Phys. Stat. Sol. 11 (1965) 2. [lo] R.W. Feaenden and R.H. Schuler, J. Chem. Phys. 39 (1963) 2147. [ 111 P.W. Atkins, Thesis, Univ. Leicester (1966 ). 1121 J.P. Colpa and E. de Boer, Mol. Phys. 7 (1963) 333. [I3] B. L3mottc. Thesis, Univ. Grenoble (1968). [ 141 W. Derbyshire, Mol. Dhys. 5 (1962) 225.
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