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Proton-NMR study on chemisorption of ethylene on platinum powder
Surface Science 154 (1985) L215-L219 North-Holland, Amsterdam
L215
SURFACE SCIENCE LETTERS PROTON-NMR STUDY ON C H E M I S O R P T I O N OF ETHYLENE ON PLATINUM POWDER Takashi SHIBANUMA and Toshiji MATSUI Research Institute for Catalysis, Hokkaido University, Sapporo 060, Japan Received 4 September 1984; accepted for publication 17 December 1984
The high-temperature phase of ethylene on surfaces of Pt powder has been studied by proton-NMR in order to decide whether the surface species is the ethylidyne species (CH3-C -=) proposed by Kesmodel et al. or the multiple-bonded species (-CH2-CH=) proposed by Demuth. The observed NMR spectrum is not attributable to CH3-groups on the surfaes, but can be interpreted as the superposition of two signals, one originating from CH2-groups and the other from CH-groups. In other words, the results suggest that the surface species is the multiple-bonded species.
Investigations of the bonding character of simple hydrocarbon molecules adsorbed on metal surfaces are important for understanding the surface reactions and catalytic processes on these surfaces. From this viewpoint, the adsorption of ethylene on platinum surfaces, especially on the (111) face, has been studied with various techniques by many authors in the recent years [1-6]. Two kinds of stable adsorption phases of ethylene, a low-temperature phase and a high-temperature phase, have been shown to be present on the P t ( l l l ) face below and above room temperature, respectively. Regarding the low-temperature phase, there has been an agreement on the surface species among various authors; the surface species is di-o-bonded C 2H 4 species with its C - C bond axis parallel to the surface. On the other hand, the nature of the surface species of the high-temperature phase is still open to argument. An ethylidyne s p e c i e s ( C H 3 - C ~=) with the C - C bond axis nearly normal to the surface has been suggested by Kesmodel et al. [1] as being most consistent with the result of LEED I - V curve analysis. The ethylidyne species has been supported by Steininger et al. [3] on the basis of Ibach's ELS results [2], which agree fairly well with IR results for the ethylidyne group in the organometallic complex, C H 3 C C o 3 ( C O ) 9 with respect to vibrational frequencies and the mode assignment [7]. A multiple-bonded species, - C H 2 - C H = with the C - C bond axis almost parallel to the surface, on the other hand, has been proposed by Demuth [4] from an UPS investigation and a re-examination of Ibach's ELS
0039-6028/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
L216
T. Shibanuma, T. Matsui / N M R of chernisorbed C2H 4 on Pt
data [2]. In this letter, results of a proton-NMR study carried out to decide between the ethylidyne and the multiple-bonded species is presented. The CH3-grou p and CH2-grou p in these species should be observed as a proton 3-spin system and a proton 2-spin system, respectively, in NMR. The platinum sample was prepared as follows; fine platinum powder was precipitated from aqueous solution of chloroplatinic acid by reduction with formalin, reduced in a flowing hydrogen stream for 30 h at 420 K, and then evacuated to 1 × 10 -6 Torr at 420 K. The BET area of a typical sample was found to be about 7 m2/g. A platinum crystallite is usually believed to be surrounded mostly by the (111) faces. The sample thus prepared was transferred, without being exposed to air, to a spectrometer equipped with a gas handling system. The low- and high-temperature phases were found to be formed at the gas phase pressure, 7.2 × 10 -1 Torr and 182 K, and at 1.3 Torr and 296 K, respectively. Assuming the density of molecules at O = 1 to be 1.5 × 1015 molecules/cm 2, the coverages 0 in the former and the latter cases were estimated to be 0.21 + 0.02 and 0.17-0.18, respectively. N M R measurements were performed by using a Varian broad-line N M R spectrometer (model WL-112) operating at a fixed frequency of 34.06 MHz. The N M R signal was recorded by scanning the magnetic field modulated with a frequency of 35 Hz and was accumulated several tens of times. From the spectrum thus obtained, the blank spectrum, i.e., the spectrum observed for a sample without adsorbed species but otherwise under the same condition, was subtracted, and the N M R spectrum of adsorbed species was obtained.
o) Low-temperature phase
-8
-6
-4
b) High-temperature p
I -8
-6
I -4
'
-2
h
c
I -2
0
l
s
e
I 0
2
~
Hm
2.5G
4
,
6
H;
• G
2
4
8
[G]
I
6
8 [G)
Fig. 1. Spectra of adsorbed ethylene: (a) low-temperature phase (182 K); (b) high-temperature phase (296 K). R: reference position. Modulation amplitude and number of accumulation: (a) 2.5 G, 60 times; (b) 1.6 G, 60 times. The dashed line in (a) represents calculated spectrum for the 2-spin system (spin 1/2) with spin-spin distance of ].'/8 .~. The ordinates (a) and (b) are in arbitrary units.
L217
72 Shibanuma, 7". Matsui / N M R of chemisorbed C2H ~ on Pi
Fig. la shows the N M R spectrum observed for the low-temperature phase at 182 K and with a modulation amplitude of 2.5 G. The spectrum, except for a small rise a r o u n d the reference position, i.e., the zero (R) of the abscissa in fig. la, consists of two peaks widely separated and is characteristic of a 2-spin system with spin 1 / 2 [8]. The dashed line in fig. l a displays the calculated spectrum for the CH2-grou p, where the same modulation amplitude is assumed and the two protons are assumed to be 1.78 ,~ apart, the distance being appropriate for the sp3-hybridized carbon atom. If the carbon atom is in the sp 2 hybridization, the separation between these two peaks would decrease to 86% of that in fig. la. The origin of the small rise is not understood, but even if it is due to an u n k n o w n adsorption species, its a m o u n t must be rather small. The conclusion is therefore that the observed spectrum orginates from C H 2groups where the carbon atom is almost sp3-hybridized. This is in good agreement with the idea of the di-o-bonded C2H 4 species, which has been concluded from various experiments. Fig. l b shows the spectrum obtained for the high-temperature phase at 296 K. As seen from the figure, a narrow, intense peak develops around the reference position; otherwise the spectrum is similar to that for the low-temperature phase, fig. la. The high-temperature phase once formed at r o o m temperature is believed to remain unchanged after it is cooled down to 150 K, because its ELS spectrum is unaffected by the cooling [2]. Thus the system was cooled down to 152 and 251 K, and the spectra shown in figs. 2a and 2b with a
a) High-temperature phase
.~-,~",
/
|
-8
-6
-4
-2
b) High-temperature phase at 251 K
-8
-6
-4
0
2
4
~ //7
-2
~',,
0
'
2
4
6
8
[G]
Hm 1.6G '
6
8 [G]
Fig. 2. Spectra for the high-temperature phase. The spectra observed at 152 and 251 K arc shown by the solid lines in (a) and (b), respectively. R: reference position. Modulation amplitude and number of accumulation: (a) 1.6 G, 90 times; (b) 1.6 G, 80 times. The dotted line in (a) and the dashed lines in (a) and (b) represent the calculated spectra for the ethylidyne species and for the multiple-bonded species, respectively. The ordinates of (a) and (b) are in arbitrary units.
L218
T. Shibanuma, T. Matsui / N M R
of chernisorbed C , H 4 on Pt
solid line were taken. It is observed that as the temperature is raised the spectrum becomes sharper owing to molecular motion on the surface. Therefore the spectrum at 152 K in fig. 2a is taken to be a standard spectrum to be compared with the calculated one in which a rigid configuration of adsorption species is considered (see below). If the surface species in the high temperature phase is the ethylidyne species, CH3-C~= as proposed by Kesmodel and Ibach, the spectrum is expected to show characteristic features of the 3-spin system with spin 1/2, which was studied in detail by Andrew and Bersohn [9]. They calculated the N M R spectrum of the CH3-grou p in polycrystalline C H 3 C C I 3 at 90 K, at which the rotation of the CH~-group is frozen, and showed that the spectrum consists of three peaks and the separation between the two side peaks is - 13 G. The spectrum of fig. lb and those observed at lower temperatures, figs. 2a and 2b as well do not exhibit such a feature. The hindering energy for the internal rotation of the CH3-grou p as deduced from various chemical compounds does not exceed 4 kcal/mol. We therefore calculate the spectrum for rotating CH3-groups [10] on the P t ( l l l ) face, and show the calculated spectrum in fig. 2a with a dotted line. In this calculation, the surface species are assumed to be in the ( 2 x 2) structure on the (111) face [2], and the intermolecular broadening of the proton lines for the rotating CH3-grou p is calculated by placing three protons at each (2 x 2) lattice site. Also the effect of the modulation with amplitude 1.6 G is taken into account. The above configuration of protons leads to intermolecular line broadening of about 1 gauss, which is considerably smaller than that in bulk solids. In fig. 2a, it is found that the calculated spectrum (dotted line) does not resemble the observed spectrum (solid line). Now, the other species, - C H 2 - C H = proposed for the high-temperature phase, is considered. The observed spectrum should be compared with a spectrum calculated for an isosceles triangular configuration of three hydrogen atoms. This calculation was made for the first time by Andrew and Finch [11] and further developed by Doremieux-Morin [12]. However, to compare with the spectra obtained in the present experiment, which employed a rather large modulation amplitude (1.6 G), the following approximation seems to be satisfactory: The spectrum is calculated as the superposition of the 2-spin spectrum due to the CH2-groups and the 1-spin spectrum due to the CH-groups, both being calculated by taking account of the modulation amplitude. Actually, it was confirmed that Doremieux-Morin's spectrum calculated for the isoceles triangular model with her parameter values, ~ = 1.5 and fl/a = 0.2 [12] (this set of parameter values is appropriate for the multiple-bonded species) and without taking account of the modulation effect agrees, at least qualitatively, with the spectrum calculated by the present approximate method. The obtained spectrum shown in fig. 2a with a dashed line does not have dips on the both sides of the peak in contrast with the spectrum for the ethylidyne species shown by the dotted line in fig. 2a. The spectrum for the multiple-
T. Shibanuma, T. Matsui / N M R
of chemisorbed C2H ~ on Pt
L219
b o n d e d species (dashed line) is calculated using following parameters: the intensity ratio of 2 . 1 for the spectrum of the CH2-grou p to that of the CH-group, a - 1 0 % increase in distance between c a r b o n atoms than the normal value (1.54 ,~) and - 15% smaller intermolecular line broadening than that calculated for the (2 x 2) structure of the surface species. Since the coverage of 0.17-0.18 in the high-temperature phase is smaller than that for the (2 × 2) structure, this smaller broadening is plausible. These parameter values were chosen to give a good fit of the calculated spectrum to the experimental one. Of course, one can not attach too much significance to these values because the SN ratio of the observed spectra is not very good and the calculation uses the approximation. As mentioned earlier, the sharper spectrum in fig. 2b as c o m p a r e d with that in fig. 2a is due to decrease in the intermolecular dipolar interactions at a higher temperature. It is interesting to see if the calculated spectrum (dashed line) is made to reproduce the spectrum in fig. 2b by changing the width parameter in the Gaussian broadening function used. The result is the dashed line in fig. 2b, which is rather satisfactory. After all, it is concluded that the surface species in the high-temperature phase of C 2 H 4 on platinum powder is the multiple-bonded species, - C H 2 - C H = rather than the ethylidyne species, CH3-C-~. We wish to thank Professor T. N a k a m u r a for a critical reading of the manuscript and a n u m b e r of useful comments.
References [1] L.L. Kesmodel, L.H. Dubois and G.A. Somorjai, J. Chem. Phys. 70 (1979) 2180. [2] H. Ibach and S. Lehwald, J. Vacuum Sei. Technol. 15 (1978) 407. [3] H. Steininger, H. Ibach and S. Lehwald, Surface Sci. 117 (1982) 685. [4] J.E. Demuth, Surface Sci. 93 (1980) L82. [5] M.R. Albert and L.G. Sneddon, Surface Sci. 120 (1982) 19. [6] J.R. Creighton and J.M. White, Surface Sci. 129 (1983) 327. [7] P. Skinner, M.W. Howard, I.A. Oxton, S.F.A. Kettle, D.B. Poweli and N. Sheppard, J. Chem. Soc. Faraday Trans. II, 77 (1981) 1203. [8] G.E. Pake, J. Chem. Phys. 16 (1948) 327. [9] E.R. Andrew and R. Bersohn, J. Chem. Phys. 18 (1950) 159. [10] H.S. Gutowsky and G.E. Pake, J. Chem. Phys. 18 (1950) 162. [11] E.R. Andrew and N.D. Finch, Proc. Phys. Soc. (London) 70B (1957) 980. [12] C. Doremieux-Morin, J. Magnetic Resonance 33 (1979) 505.
L215
SURFACE SCIENCE LETTERS PROTON-NMR STUDY ON C H E M I S O R P T I O N OF ETHYLENE ON PLATINUM POWDER Takashi SHIBANUMA and Toshiji MATSUI Research Institute for Catalysis, Hokkaido University, Sapporo 060, Japan Received 4 September 1984; accepted for publication 17 December 1984
The high-temperature phase of ethylene on surfaces of Pt powder has been studied by proton-NMR in order to decide whether the surface species is the ethylidyne species (CH3-C -=) proposed by Kesmodel et al. or the multiple-bonded species (-CH2-CH=) proposed by Demuth. The observed NMR spectrum is not attributable to CH3-groups on the surfaes, but can be interpreted as the superposition of two signals, one originating from CH2-groups and the other from CH-groups. In other words, the results suggest that the surface species is the multiple-bonded species.
Investigations of the bonding character of simple hydrocarbon molecules adsorbed on metal surfaces are important for understanding the surface reactions and catalytic processes on these surfaces. From this viewpoint, the adsorption of ethylene on platinum surfaces, especially on the (111) face, has been studied with various techniques by many authors in the recent years [1-6]. Two kinds of stable adsorption phases of ethylene, a low-temperature phase and a high-temperature phase, have been shown to be present on the P t ( l l l ) face below and above room temperature, respectively. Regarding the low-temperature phase, there has been an agreement on the surface species among various authors; the surface species is di-o-bonded C 2H 4 species with its C - C bond axis parallel to the surface. On the other hand, the nature of the surface species of the high-temperature phase is still open to argument. An ethylidyne s p e c i e s ( C H 3 - C ~=) with the C - C bond axis nearly normal to the surface has been suggested by Kesmodel et al. [1] as being most consistent with the result of LEED I - V curve analysis. The ethylidyne species has been supported by Steininger et al. [3] on the basis of Ibach's ELS results [2], which agree fairly well with IR results for the ethylidyne group in the organometallic complex, C H 3 C C o 3 ( C O ) 9 with respect to vibrational frequencies and the mode assignment [7]. A multiple-bonded species, - C H 2 - C H = with the C - C bond axis almost parallel to the surface, on the other hand, has been proposed by Demuth [4] from an UPS investigation and a re-examination of Ibach's ELS
0039-6028/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
L216
T. Shibanuma, T. Matsui / N M R of chernisorbed C2H 4 on Pt
data [2]. In this letter, results of a proton-NMR study carried out to decide between the ethylidyne and the multiple-bonded species is presented. The CH3-grou p and CH2-grou p in these species should be observed as a proton 3-spin system and a proton 2-spin system, respectively, in NMR. The platinum sample was prepared as follows; fine platinum powder was precipitated from aqueous solution of chloroplatinic acid by reduction with formalin, reduced in a flowing hydrogen stream for 30 h at 420 K, and then evacuated to 1 × 10 -6 Torr at 420 K. The BET area of a typical sample was found to be about 7 m2/g. A platinum crystallite is usually believed to be surrounded mostly by the (111) faces. The sample thus prepared was transferred, without being exposed to air, to a spectrometer equipped with a gas handling system. The low- and high-temperature phases were found to be formed at the gas phase pressure, 7.2 × 10 -1 Torr and 182 K, and at 1.3 Torr and 296 K, respectively. Assuming the density of molecules at O = 1 to be 1.5 × 1015 molecules/cm 2, the coverages 0 in the former and the latter cases were estimated to be 0.21 + 0.02 and 0.17-0.18, respectively. N M R measurements were performed by using a Varian broad-line N M R spectrometer (model WL-112) operating at a fixed frequency of 34.06 MHz. The N M R signal was recorded by scanning the magnetic field modulated with a frequency of 35 Hz and was accumulated several tens of times. From the spectrum thus obtained, the blank spectrum, i.e., the spectrum observed for a sample without adsorbed species but otherwise under the same condition, was subtracted, and the N M R spectrum of adsorbed species was obtained.
o) Low-temperature phase
-8
-6
-4
b) High-temperature p
I -8
-6
I -4
'
-2
h
c
I -2
0
l
s
e
I 0
2
~
Hm
2.5G
4
,
6
H;
• G
2
4
8
[G]
I
6
8 [G)
Fig. 1. Spectra of adsorbed ethylene: (a) low-temperature phase (182 K); (b) high-temperature phase (296 K). R: reference position. Modulation amplitude and number of accumulation: (a) 2.5 G, 60 times; (b) 1.6 G, 60 times. The dashed line in (a) represents calculated spectrum for the 2-spin system (spin 1/2) with spin-spin distance of ].'/8 .~. The ordinates (a) and (b) are in arbitrary units.
L217
72 Shibanuma, 7". Matsui / N M R of chemisorbed C2H ~ on Pi
Fig. la shows the N M R spectrum observed for the low-temperature phase at 182 K and with a modulation amplitude of 2.5 G. The spectrum, except for a small rise a r o u n d the reference position, i.e., the zero (R) of the abscissa in fig. la, consists of two peaks widely separated and is characteristic of a 2-spin system with spin 1 / 2 [8]. The dashed line in fig. l a displays the calculated spectrum for the CH2-grou p, where the same modulation amplitude is assumed and the two protons are assumed to be 1.78 ,~ apart, the distance being appropriate for the sp3-hybridized carbon atom. If the carbon atom is in the sp 2 hybridization, the separation between these two peaks would decrease to 86% of that in fig. la. The origin of the small rise is not understood, but even if it is due to an u n k n o w n adsorption species, its a m o u n t must be rather small. The conclusion is therefore that the observed spectrum orginates from C H 2groups where the carbon atom is almost sp3-hybridized. This is in good agreement with the idea of the di-o-bonded C2H 4 species, which has been concluded from various experiments. Fig. l b shows the spectrum obtained for the high-temperature phase at 296 K. As seen from the figure, a narrow, intense peak develops around the reference position; otherwise the spectrum is similar to that for the low-temperature phase, fig. la. The high-temperature phase once formed at r o o m temperature is believed to remain unchanged after it is cooled down to 150 K, because its ELS spectrum is unaffected by the cooling [2]. Thus the system was cooled down to 152 and 251 K, and the spectra shown in figs. 2a and 2b with a
a) High-temperature phase
.~-,~",
/
|
-8
-6
-4
-2
b) High-temperature phase at 251 K
-8
-6
-4
0
2
4
~ //7
-2
~',,
0
'
2
4
6
8
[G]
Hm 1.6G '
6
8 [G]
Fig. 2. Spectra for the high-temperature phase. The spectra observed at 152 and 251 K arc shown by the solid lines in (a) and (b), respectively. R: reference position. Modulation amplitude and number of accumulation: (a) 1.6 G, 90 times; (b) 1.6 G, 80 times. The dotted line in (a) and the dashed lines in (a) and (b) represent the calculated spectra for the ethylidyne species and for the multiple-bonded species, respectively. The ordinates of (a) and (b) are in arbitrary units.
L218
T. Shibanuma, T. Matsui / N M R
of chernisorbed C , H 4 on Pt
solid line were taken. It is observed that as the temperature is raised the spectrum becomes sharper owing to molecular motion on the surface. Therefore the spectrum at 152 K in fig. 2a is taken to be a standard spectrum to be compared with the calculated one in which a rigid configuration of adsorption species is considered (see below). If the surface species in the high temperature phase is the ethylidyne species, CH3-C~= as proposed by Kesmodel and Ibach, the spectrum is expected to show characteristic features of the 3-spin system with spin 1/2, which was studied in detail by Andrew and Bersohn [9]. They calculated the N M R spectrum of the CH3-grou p in polycrystalline C H 3 C C I 3 at 90 K, at which the rotation of the CH~-group is frozen, and showed that the spectrum consists of three peaks and the separation between the two side peaks is - 13 G. The spectrum of fig. lb and those observed at lower temperatures, figs. 2a and 2b as well do not exhibit such a feature. The hindering energy for the internal rotation of the CH3-grou p as deduced from various chemical compounds does not exceed 4 kcal/mol. We therefore calculate the spectrum for rotating CH3-groups [10] on the P t ( l l l ) face, and show the calculated spectrum in fig. 2a with a dotted line. In this calculation, the surface species are assumed to be in the ( 2 x 2) structure on the (111) face [2], and the intermolecular broadening of the proton lines for the rotating CH3-grou p is calculated by placing three protons at each (2 x 2) lattice site. Also the effect of the modulation with amplitude 1.6 G is taken into account. The above configuration of protons leads to intermolecular line broadening of about 1 gauss, which is considerably smaller than that in bulk solids. In fig. 2a, it is found that the calculated spectrum (dotted line) does not resemble the observed spectrum (solid line). Now, the other species, - C H 2 - C H = proposed for the high-temperature phase, is considered. The observed spectrum should be compared with a spectrum calculated for an isosceles triangular configuration of three hydrogen atoms. This calculation was made for the first time by Andrew and Finch [11] and further developed by Doremieux-Morin [12]. However, to compare with the spectra obtained in the present experiment, which employed a rather large modulation amplitude (1.6 G), the following approximation seems to be satisfactory: The spectrum is calculated as the superposition of the 2-spin spectrum due to the CH2-groups and the 1-spin spectrum due to the CH-groups, both being calculated by taking account of the modulation amplitude. Actually, it was confirmed that Doremieux-Morin's spectrum calculated for the isoceles triangular model with her parameter values, ~ = 1.5 and fl/a = 0.2 [12] (this set of parameter values is appropriate for the multiple-bonded species) and without taking account of the modulation effect agrees, at least qualitatively, with the spectrum calculated by the present approximate method. The obtained spectrum shown in fig. 2a with a dashed line does not have dips on the both sides of the peak in contrast with the spectrum for the ethylidyne species shown by the dotted line in fig. 2a. The spectrum for the multiple-
T. Shibanuma, T. Matsui / N M R
of chemisorbed C2H ~ on Pt
L219
b o n d e d species (dashed line) is calculated using following parameters: the intensity ratio of 2 . 1 for the spectrum of the CH2-grou p to that of the CH-group, a - 1 0 % increase in distance between c a r b o n atoms than the normal value (1.54 ,~) and - 15% smaller intermolecular line broadening than that calculated for the (2 x 2) structure of the surface species. Since the coverage of 0.17-0.18 in the high-temperature phase is smaller than that for the (2 × 2) structure, this smaller broadening is plausible. These parameter values were chosen to give a good fit of the calculated spectrum to the experimental one. Of course, one can not attach too much significance to these values because the SN ratio of the observed spectra is not very good and the calculation uses the approximation. As mentioned earlier, the sharper spectrum in fig. 2b as c o m p a r e d with that in fig. 2a is due to decrease in the intermolecular dipolar interactions at a higher temperature. It is interesting to see if the calculated spectrum (dashed line) is made to reproduce the spectrum in fig. 2b by changing the width parameter in the Gaussian broadening function used. The result is the dashed line in fig. 2b, which is rather satisfactory. After all, it is concluded that the surface species in the high-temperature phase of C 2 H 4 on platinum powder is the multiple-bonded species, - C H 2 - C H = rather than the ethylidyne species, CH3-C-~. We wish to thank Professor T. N a k a m u r a for a critical reading of the manuscript and a n u m b e r of useful comments.
References [1] L.L. Kesmodel, L.H. Dubois and G.A. Somorjai, J. Chem. Phys. 70 (1979) 2180. [2] H. Ibach and S. Lehwald, J. Vacuum Sei. Technol. 15 (1978) 407. [3] H. Steininger, H. Ibach and S. Lehwald, Surface Sci. 117 (1982) 685. [4] J.E. Demuth, Surface Sci. 93 (1980) L82. [5] M.R. Albert and L.G. Sneddon, Surface Sci. 120 (1982) 19. [6] J.R. Creighton and J.M. White, Surface Sci. 129 (1983) 327. [7] P. Skinner, M.W. Howard, I.A. Oxton, S.F.A. Kettle, D.B. Poweli and N. Sheppard, J. Chem. Soc. Faraday Trans. II, 77 (1981) 1203. [8] G.E. Pake, J. Chem. Phys. 16 (1948) 327. [9] E.R. Andrew and R. Bersohn, J. Chem. Phys. 18 (1950) 159. [10] H.S. Gutowsky and G.E. Pake, J. Chem. Phys. 18 (1950) 162. [11] E.R. Andrew and N.D. Finch, Proc. Phys. Soc. (London) 70B (1957) 980. [12] C. Doremieux-Morin, J. Magnetic Resonance 33 (1979) 505.