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Hydrogen bonding in liquid amides studied by low frequency raman spectroscopy.
Journal of Molecular Structure, 175 (1988) 251-256
251
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
HYDROGEN BONDING IN LIQUID AMIDES STUDIED BY LOW FREQUENCY RAMAN SPECTROSCOPY.
O. FAURSKOV NIELSEN Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen (Denmark)
ABSTRACI Low frequency Raman spectra-(lO-400 cm -I) in the R(~)-representation are used to investigate N-ethylformamide in the liquid state. Polarization measurements are performed. Spectra are also obtained of Nd-ethylformamide. The results are compared to similar investigations of formamide, N-methylformamide and N,Ndimethylformamide, acetamide~ N-methylacetamide and N,N-dimethylacetamide. A band observed around lO0 cm -± is assigned to vibrations of atoms in intermolecular hydrogen bonds of chain-like species. An approximate description of this mode is given.
INTRODUCTION Low frequency vibrational spectra (10-200 cm -I) are difficult to obtain for liquids and solutions. Even with Fourier-transform techniques serious problems are encountered in the far infrared (FIR) region. The absorption coefficient of water is very high and FIR-spectroscopy is not suited for aqueous solutions. The Raman spectrum of water is weak, but in the low-frequency region the intense and broad Rayleigh line obscures the low-frequency features of the spectrum. In order to overcome this problem we have used the so-called R(~)-representation of the low-frequency Raman spectrum (refs. 1-3). The applications and advantages of the R(5)-representation have recently been thoroughly discussed (ref. 4). The R(~)- representation was originally introduced in order to compare FIR and lowfrequency Raman spectra of molecular liquids (refs.l-3). This representation was also very useful to reveal otherwise unobservable features in aqueous solutions or gels of larger molecules including agarose and a-carrageenan (ref. 5), cellulose (ref. 6), nucleosides (ref. 7), nucleotides (refs. 8-10), nucleic acids (ref. ll) and proteins (ref. 12). In order to explain the bands observed below 200 cm -1 the solvent water has been investigated (ref. 13). The original results for water (ref. 13) have now been confirmed by other authors (refs. 14-15). A number of smaller molecules, which can be considered as model systems for larger molecules, have been investigated. In the context of biologically interesting molecules spectra of liquid amides are of special interest. In the neat liquid state all these molecules containing an N-H group form linear bonded species. Low frequency spectra of formamide, N-methylformamide, N,N-dimethyl-
0022-2860/88/$03.50
© 1988 Elsevier Science Publishers B.V.
252
formamide, acetamide, N-methylacetamide, and N,N-dimethylacetamide have been investigated (refs. 12, 16-20). The present contribution will present lsw-frequency Raman spectra of N-ethylformamide in the liquid state. Results for all the amides investigated so far will be summarized and an assignment will be given for the band observed around lO0 cm -1 for hydrogen bonded amides.
METHODS Materials The sample of N-ethylformamide was purchased from Merck. A rather strong fluorescense was observed in a spectrum obtained directly from the commercial sample. However, this fluorescense disappeared after distillation in vacuo. Nd-ethylformamide was synthesized by a repeated treatment of N-ethylformamide with D20. Each time the water was evaporated in vacuo. The Raman spectrum of the final product showed no evidence of a remaining N-H group.
Instrumental. Raman spectra in the Stokes side was recorded from i0 to 400 cm -I. The spectrometer was a DILOR Z24 triple monochromator equipped with a cooled Centronix P4283 PM-tube. Data collection was performed with an IBM AT3 computer coupled to a Hewlett Packard model 7550A plotter. Perpendicular illumination was used in a horizontal scattering plane. The exciting scource was the green 514.5 nm line from a Spectra-Physics model 165 argon ion laser with an output of 350 mW. Spectra were obtained in either the IVV or the IVH configuration. A quarterwave plate was placed before the monochromator entrance slit to assure circularly polarized light. All spectra were obtained at room temperature. In some cases the spectra were smoothed by a Savitzky Golay procedure (ref. 21). Spectral slit widths were from 2 to 4 cm -l.
RESULTS AND DISCUSSION The R(5)-representation. As in previous work (refs. 1-3) this representation was calculated directly from the intensity data in the Stokes side of the Raman spectrum, I(~):
R(~) ~ ~[ l-exp(-h~c/kT)] I(g)
(i)
where ~ is the Raman shift in cm -I, h is Planck's and k is Boltzmann's constant, T is the absolute temperature and c is the velocity of light.
Neat liquid N-ethylformamide. Fig. ] shows the Raman spectrum at different gains for N-ethylformamide.
A
253
I
'
I~
l
I
I
.",l,J
'/
RI )
300
400
200
100
Fig. i. Raman spectra (I(~) and R(~)-representations) liquid state at room temperature. IvH-configuration.
cm -1
0
of N-ethylformamide
in the
band is observed at i00 cm -1 as a shoulder on the intense Rayleigh line. This shoulder is observed as a well-resolved band in the R(~)-spectrum,
and the maxi-
mum is found at 105 cm -l. The bands observed at 229, 283 and 310 cm -I are assigned to intramolecular
vibrations.
of the R(9)-representation Polarization measurements
Fig. 1 clearly demonstrates
the advantage
in the low-frequency part of the Raman spectrum. are shown in Fig. 2. Evidently the low-frequency band
at 105 cm -1 is depolarized.
I
'
I
'
I
'
I
I
I
I 200
L
I 100
I cm -~
z
I 400
l
1 300
Fig._2. R(~)-spectra of N-ethylformamide IVH-configuration (lower curve).
in Ivv-configuration
0
(upper curve) and
254
I
'
I 400
L
I
~
l
f
I
I
I 100
I
_z
i 300
L
i 200
, c m -~
0
Fi 9. 3. R(i~)-spectra of N-ethylformamide (upper curve) and Nd-ethylformamide (lower curve). Both spectra were obtained in the IVH-configuration.
Nd-ethylformamid~. R(~)-spectra of Nd-ethylformamide are shown in Fig. 3 together with the spectrum of N-ethylformamide. The bands in Nd-ethylformamide are all shifted towards lower frequencies, lhe shift found for the band around lO0 cm -1 is only 3 cm -1. lhe magnitude of this shift is comparable to previous observations for nitrogen deuterated formamide (ref. 17), N-methylformamide (ref. 12) and Nmethylaeetamide (ref. 20).
Comparison of low frequency spectra of amides. Intermolecular hydrogen-bonded amides all show a band around lO0 cm -1 in the neat liquid state. Frequency maxima for these bands are given in Table I.
TABLE i Frequency maxima for the band observed around lO0 cm -1 in some amides in the liquid state, a Compound
Frequency Maximum (cm -1)
ref.
110 112 105
17 12,16 this work
10] 100
22 20
Formamide N-methylformamide N-ethylformamide Acetamide N-methylacetamide
ca.
aAll spectra were obtained at room temperature, except for acetamide (89oc) and N-methylacetamide (30oc).
255
Assignment of the band found around i00 cm
-1
in liquid amides.
Table 1 shows that substitution of hydrogen by an alkyl group on either the carbon or the nitrogen atom in formamide results in only a small shift downward in frequency. This indicates, that these substituents only participate slightly in the vibrational mode. Isotopic substitution of nitrogen bound hydrogen by deuterium also causes only a small frequency shift (Fig. 2 and refs. 12, 17 and 20). The assignment of the band at lO0 cm -1 to an intermolecular hydrogen bond, is supported by the fact that the band disappears in N,N-dimethylformamide (ref. 16) and N,N-dimethylacetamide
(ref. 22). For liquid formamide isotopic
substitution by nitrogen-15 was also performed (ref. 17). The shift in frequency was of the
same order of magnitude as found for deuterium substitution,
indi-
cating a major contribution of nitrogen displacement in the vibration.
® O ......
® ®/R H-N\ ® / C = ' O ...... R'
® ®/R H-N\ ®
® ®/R ® R"~"C=~ ...... H
/ C = O ...... H - N , .
R'
(~
R=H, CH3 ; R'=H.CH3,CH2CH 3 Fig. 4. An approximate description of the mode giving rise to the band around lO0 cm -1. The plus and minus signs refer to motion in and out of the plane, respectively.
The vibrational mode in Fig. 4 could explain the observed experimental data. Furthermore a preliminary ab initio calculation on a dimer of formamide (ref.23) supports this description. This mode includes a torsion around the CN-bond as previously proposed for N-methylacetamide by Fillaux et al. (ref. 24). Further calculations are planned in order to obtain a more precise description of the vibration. Preliminary results were obtained for N-ethylformamide in solutions of either water or dimethylsulfoxide N-ethylformamide.
(DMSO). Concentrations ranged from 5 to 75% (v/v) of
The band around lO0 cm -1 appears in both solvents indicating
the presence of chain-like intermolecular hydrogen-bonded species at the concentrations investigated. The amides can be considered as model systems for more complicated molecules of biological interest. Larger molecules are extremely difficult to investigate experimentally, but our preliminary results for nucleic acids (ref. ll) and proteins (ref. 12) indicate the presence of a mode corresponding to the one shown in Fig. 4. This mode might be involved in the breaking of hydrogen bonds and thus
286
be of importance for a description of biomolecular activity on a molecular level.
Acknowled9ements.
The author is grateful to the Danish Natural Science Research
Council for partially financing the Raman equipment and to Irving Bigio, Los Alamos National Laboratory, USA for helpful discussions and a careful reading of the manuscript.
REFERENCES l
2 3 4 5 6 7 9 8 9 i0 11 12 13 14 15 16 17 18 19 20 21 22
23 24
O. Faurskov Nielsen, D.H. Christensen, P.-A. Lund and E. Praestgaard, Proc. 6th Intern. Conf. Raman Spectrosc., E.D. Schmid, R.S. Krishnan, W. Kiefer and H.U. Schr6tter (Editors), Heyden, London-Philadelphia-Rheine, 1978, Vol. 2, pp. 208-209. O. Faurskov Nielsen and E. Praestgaard, Chem. Phys., 2B (1978) 167-173. O. Faurskov Nielsen, P.-A. Lund and E. Praestgaard, J. Chem. Phys., 75 (1981) 1586-1587. M.H. Brooker, O. Faurskov Nielsen and E. Praestgaard, O. Raman Spectrosc., in press. O. Faurskov Nielsen, P.-A. Lund and F.M. Nicolaisen, Acts Chem. Scand., A34 (1980) 749-754. O. Faurskov Nielsen, T. Lindstr~m and P.-A. Lund, Acts Chem. Scand., A36 (1982) 623-625. O. Faurskov Nielsen, P.-A. Lund and E. Praestgaard, J. Raman Spectrosc., (1980) 286-290. P.-A. Lund and E. Praestgaard, J. Raman Spectrosc., ii (1981) 92-95. O. Faurskov Nielsen, P.-A. Lund and S.B. Petersen, J. Raman Spectrosc., ll (1981) 493-495. O. Faurskov Nielsen, P.-A. Lund and S.B. Petersen, J. Am. Chem. Soc., 104 (1982) 1991-1995. O. Faurskov Nielsen, P.-A. Lund, L. S. Nielsen and E. Praestgaard, Biochem. Biophys. Res. Comm., iii (1983) 120-126. O. Faurskov Nielsen, D.H. Christensen and E. Praestgaard, Adv. Life Sciences, Ser. D. (1987) in press. O. Faurskov Nielsen, Chem. Phys. lett., 60 (1979) 515-517. M.H. Brooker and M. Perrot, J. Chem. Phys., 74 (1981) 2795. S. Krishnamurthy, R. Bansil and J. Uiafe-Akenten, J. Chem. Phys., 79 (1983) 5863. 8. Faurskov Nielsen and P.-A. Lund, Chem. Phys. Lett., 78 (1981) 626-628. O. Faurskov Nielsen, P.-A. Lund and E. Praestgaard, J. Chem. Phys., 77 (1982) 3678-3683. O. Faurskov Nielsen, D.H. Christensen and E. Praestgaard, J. Chem. Phys., 82 (1985) i183-i185. J. Halding Jensen, P.L. Christisnsen, O. Skovgaard, 0. Faurskov Nielsen and I. Bigio, Phys. Lett., A., 117 (1986) 123-126. O. Faurskov Nielsen, I.J. Bigio, I. Olsen and J.M. Berquier, Chem. Phys. tett., 132 (1986) 502-506. A. Savitzky and M.J.E. Golay, Anal. Chem., 36 (1964) 1627. O. Faurskov Nielsen, I.J. Bigio, C. Johnston and S.P. Layne, Spectrose. of Biological Molecules, A.J.P. Alix, L. Bernard and M. Manfait (Editors), John Wiley and Sons, Chichester-New York-Brisbane-Toronto-Singapore, 1985, pp. 193-194. B. Pierce, Hughes Aircraft Corp., California, USA, personal communication. F. Fillaux, M.H. Baron, C. LeLoz~ and G. Sagon, J. Rsman Speetrosc., 7 (1978) 244.
251
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
HYDROGEN BONDING IN LIQUID AMIDES STUDIED BY LOW FREQUENCY RAMAN SPECTROSCOPY.
O. FAURSKOV NIELSEN Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen (Denmark)
ABSTRACI Low frequency Raman spectra-(lO-400 cm -I) in the R(~)-representation are used to investigate N-ethylformamide in the liquid state. Polarization measurements are performed. Spectra are also obtained of Nd-ethylformamide. The results are compared to similar investigations of formamide, N-methylformamide and N,Ndimethylformamide, acetamide~ N-methylacetamide and N,N-dimethylacetamide. A band observed around lO0 cm -± is assigned to vibrations of atoms in intermolecular hydrogen bonds of chain-like species. An approximate description of this mode is given.
INTRODUCTION Low frequency vibrational spectra (10-200 cm -I) are difficult to obtain for liquids and solutions. Even with Fourier-transform techniques serious problems are encountered in the far infrared (FIR) region. The absorption coefficient of water is very high and FIR-spectroscopy is not suited for aqueous solutions. The Raman spectrum of water is weak, but in the low-frequency region the intense and broad Rayleigh line obscures the low-frequency features of the spectrum. In order to overcome this problem we have used the so-called R(~)-representation of the low-frequency Raman spectrum (refs. 1-3). The applications and advantages of the R(5)-representation have recently been thoroughly discussed (ref. 4). The R(~)- representation was originally introduced in order to compare FIR and lowfrequency Raman spectra of molecular liquids (refs.l-3). This representation was also very useful to reveal otherwise unobservable features in aqueous solutions or gels of larger molecules including agarose and a-carrageenan (ref. 5), cellulose (ref. 6), nucleosides (ref. 7), nucleotides (refs. 8-10), nucleic acids (ref. ll) and proteins (ref. 12). In order to explain the bands observed below 200 cm -1 the solvent water has been investigated (ref. 13). The original results for water (ref. 13) have now been confirmed by other authors (refs. 14-15). A number of smaller molecules, which can be considered as model systems for larger molecules, have been investigated. In the context of biologically interesting molecules spectra of liquid amides are of special interest. In the neat liquid state all these molecules containing an N-H group form linear bonded species. Low frequency spectra of formamide, N-methylformamide, N,N-dimethyl-
0022-2860/88/$03.50
© 1988 Elsevier Science Publishers B.V.
252
formamide, acetamide, N-methylacetamide, and N,N-dimethylacetamide have been investigated (refs. 12, 16-20). The present contribution will present lsw-frequency Raman spectra of N-ethylformamide in the liquid state. Results for all the amides investigated so far will be summarized and an assignment will be given for the band observed around lO0 cm -1 for hydrogen bonded amides.
METHODS Materials The sample of N-ethylformamide was purchased from Merck. A rather strong fluorescense was observed in a spectrum obtained directly from the commercial sample. However, this fluorescense disappeared after distillation in vacuo. Nd-ethylformamide was synthesized by a repeated treatment of N-ethylformamide with D20. Each time the water was evaporated in vacuo. The Raman spectrum of the final product showed no evidence of a remaining N-H group.
Instrumental. Raman spectra in the Stokes side was recorded from i0 to 400 cm -I. The spectrometer was a DILOR Z24 triple monochromator equipped with a cooled Centronix P4283 PM-tube. Data collection was performed with an IBM AT3 computer coupled to a Hewlett Packard model 7550A plotter. Perpendicular illumination was used in a horizontal scattering plane. The exciting scource was the green 514.5 nm line from a Spectra-Physics model 165 argon ion laser with an output of 350 mW. Spectra were obtained in either the IVV or the IVH configuration. A quarterwave plate was placed before the monochromator entrance slit to assure circularly polarized light. All spectra were obtained at room temperature. In some cases the spectra were smoothed by a Savitzky Golay procedure (ref. 21). Spectral slit widths were from 2 to 4 cm -l.
RESULTS AND DISCUSSION The R(5)-representation. As in previous work (refs. 1-3) this representation was calculated directly from the intensity data in the Stokes side of the Raman spectrum, I(~):
R(~) ~ ~[ l-exp(-h~c/kT)] I(g)
(i)
where ~ is the Raman shift in cm -I, h is Planck's and k is Boltzmann's constant, T is the absolute temperature and c is the velocity of light.
Neat liquid N-ethylformamide. Fig. ] shows the Raman spectrum at different gains for N-ethylformamide.
A
253
I
'
I~
l
I
I
.",l,J
'/
RI )
300
400
200
100
Fig. i. Raman spectra (I(~) and R(~)-representations) liquid state at room temperature. IvH-configuration.
cm -1
0
of N-ethylformamide
in the
band is observed at i00 cm -1 as a shoulder on the intense Rayleigh line. This shoulder is observed as a well-resolved band in the R(~)-spectrum,
and the maxi-
mum is found at 105 cm -l. The bands observed at 229, 283 and 310 cm -I are assigned to intramolecular
vibrations.
of the R(9)-representation Polarization measurements
Fig. 1 clearly demonstrates
the advantage
in the low-frequency part of the Raman spectrum. are shown in Fig. 2. Evidently the low-frequency band
at 105 cm -1 is depolarized.
I
'
I
'
I
'
I
I
I
I 200
L
I 100
I cm -~
z
I 400
l
1 300
Fig._2. R(~)-spectra of N-ethylformamide IVH-configuration (lower curve).
in Ivv-configuration
0
(upper curve) and
254
I
'
I 400
L
I
~
l
f
I
I
I 100
I
_z
i 300
L
i 200
, c m -~
0
Fi 9. 3. R(i~)-spectra of N-ethylformamide (upper curve) and Nd-ethylformamide (lower curve). Both spectra were obtained in the IVH-configuration.
Nd-ethylformamid~. R(~)-spectra of Nd-ethylformamide are shown in Fig. 3 together with the spectrum of N-ethylformamide. The bands in Nd-ethylformamide are all shifted towards lower frequencies, lhe shift found for the band around lO0 cm -1 is only 3 cm -1. lhe magnitude of this shift is comparable to previous observations for nitrogen deuterated formamide (ref. 17), N-methylformamide (ref. 12) and Nmethylaeetamide (ref. 20).
Comparison of low frequency spectra of amides. Intermolecular hydrogen-bonded amides all show a band around lO0 cm -1 in the neat liquid state. Frequency maxima for these bands are given in Table I.
TABLE i Frequency maxima for the band observed around lO0 cm -1 in some amides in the liquid state, a Compound
Frequency Maximum (cm -1)
ref.
110 112 105
17 12,16 this work
10] 100
22 20
Formamide N-methylformamide N-ethylformamide Acetamide N-methylacetamide
ca.
aAll spectra were obtained at room temperature, except for acetamide (89oc) and N-methylacetamide (30oc).
255
Assignment of the band found around i00 cm
-1
in liquid amides.
Table 1 shows that substitution of hydrogen by an alkyl group on either the carbon or the nitrogen atom in formamide results in only a small shift downward in frequency. This indicates, that these substituents only participate slightly in the vibrational mode. Isotopic substitution of nitrogen bound hydrogen by deuterium also causes only a small frequency shift (Fig. 2 and refs. 12, 17 and 20). The assignment of the band at lO0 cm -1 to an intermolecular hydrogen bond, is supported by the fact that the band disappears in N,N-dimethylformamide (ref. 16) and N,N-dimethylacetamide
(ref. 22). For liquid formamide isotopic
substitution by nitrogen-15 was also performed (ref. 17). The shift in frequency was of the
same order of magnitude as found for deuterium substitution,
indi-
cating a major contribution of nitrogen displacement in the vibration.
® O ......
® ®/R H-N\ ® / C = ' O ...... R'
® ®/R H-N\ ®
® ®/R ® R"~"C=~ ...... H
/ C = O ...... H - N , .
R'
(~
R=H, CH3 ; R'=H.CH3,CH2CH 3 Fig. 4. An approximate description of the mode giving rise to the band around lO0 cm -1. The plus and minus signs refer to motion in and out of the plane, respectively.
The vibrational mode in Fig. 4 could explain the observed experimental data. Furthermore a preliminary ab initio calculation on a dimer of formamide (ref.23) supports this description. This mode includes a torsion around the CN-bond as previously proposed for N-methylacetamide by Fillaux et al. (ref. 24). Further calculations are planned in order to obtain a more precise description of the vibration. Preliminary results were obtained for N-ethylformamide in solutions of either water or dimethylsulfoxide N-ethylformamide.
(DMSO). Concentrations ranged from 5 to 75% (v/v) of
The band around lO0 cm -1 appears in both solvents indicating
the presence of chain-like intermolecular hydrogen-bonded species at the concentrations investigated. The amides can be considered as model systems for more complicated molecules of biological interest. Larger molecules are extremely difficult to investigate experimentally, but our preliminary results for nucleic acids (ref. ll) and proteins (ref. 12) indicate the presence of a mode corresponding to the one shown in Fig. 4. This mode might be involved in the breaking of hydrogen bonds and thus
286
be of importance for a description of biomolecular activity on a molecular level.
Acknowled9ements.
The author is grateful to the Danish Natural Science Research
Council for partially financing the Raman equipment and to Irving Bigio, Los Alamos National Laboratory, USA for helpful discussions and a careful reading of the manuscript.
REFERENCES l
2 3 4 5 6 7 9 8 9 i0 11 12 13 14 15 16 17 18 19 20 21 22
23 24
O. Faurskov Nielsen, D.H. Christensen, P.-A. Lund and E. Praestgaard, Proc. 6th Intern. Conf. Raman Spectrosc., E.D. Schmid, R.S. Krishnan, W. Kiefer and H.U. Schr6tter (Editors), Heyden, London-Philadelphia-Rheine, 1978, Vol. 2, pp. 208-209. O. Faurskov Nielsen and E. Praestgaard, Chem. Phys., 2B (1978) 167-173. O. Faurskov Nielsen, P.-A. Lund and E. Praestgaard, J. Chem. Phys., 75 (1981) 1586-1587. M.H. Brooker, O. Faurskov Nielsen and E. Praestgaard, O. Raman Spectrosc., in press. O. Faurskov Nielsen, P.-A. Lund and F.M. Nicolaisen, Acts Chem. Scand., A34 (1980) 749-754. O. Faurskov Nielsen, T. Lindstr~m and P.-A. Lund, Acts Chem. Scand., A36 (1982) 623-625. O. Faurskov Nielsen, P.-A. Lund and E. Praestgaard, J. Raman Spectrosc., (1980) 286-290. P.-A. Lund and E. Praestgaard, J. Raman Spectrosc., ii (1981) 92-95. O. Faurskov Nielsen, P.-A. Lund and S.B. Petersen, J. Raman Spectrosc., ll (1981) 493-495. O. Faurskov Nielsen, P.-A. Lund and S.B. Petersen, J. Am. Chem. Soc., 104 (1982) 1991-1995. O. Faurskov Nielsen, P.-A. Lund, L. S. Nielsen and E. Praestgaard, Biochem. Biophys. Res. Comm., iii (1983) 120-126. O. Faurskov Nielsen, D.H. Christensen and E. Praestgaard, Adv. Life Sciences, Ser. D. (1987) in press. O. Faurskov Nielsen, Chem. Phys. lett., 60 (1979) 515-517. M.H. Brooker and M. Perrot, J. Chem. Phys., 74 (1981) 2795. S. Krishnamurthy, R. Bansil and J. Uiafe-Akenten, J. Chem. Phys., 79 (1983) 5863. 8. Faurskov Nielsen and P.-A. Lund, Chem. Phys. Lett., 78 (1981) 626-628. O. Faurskov Nielsen, P.-A. Lund and E. Praestgaard, J. Chem. Phys., 77 (1982) 3678-3683. O. Faurskov Nielsen, D.H. Christensen and E. Praestgaard, J. Chem. Phys., 82 (1985) i183-i185. J. Halding Jensen, P.L. Christisnsen, O. Skovgaard, 0. Faurskov Nielsen and I. Bigio, Phys. Lett., A., 117 (1986) 123-126. O. Faurskov Nielsen, I.J. Bigio, I. Olsen and J.M. Berquier, Chem. Phys. tett., 132 (1986) 502-506. A. Savitzky and M.J.E. Golay, Anal. Chem., 36 (1964) 1627. O. Faurskov Nielsen, I.J. Bigio, C. Johnston and S.P. Layne, Spectrose. of Biological Molecules, A.J.P. Alix, L. Bernard and M. Manfait (Editors), John Wiley and Sons, Chichester-New York-Brisbane-Toronto-Singapore, 1985, pp. 193-194. B. Pierce, Hughes Aircraft Corp., California, USA, personal communication. F. Fillaux, M.H. Baron, C. LeLoz~ and G. Sagon, J. Rsman Speetrosc., 7 (1978) 244.