The SPASIBA force field of aldehydes. Part I: Structure and vibrational wavenumbers of methanal, ethanal and propanal

Journal of Molecular Structure 476 (1999) 261–270

The SPASIBA force field of aldehydes. Part I: Structure and vibrational wavenumbers of methanal, ethanal and propanal A. Zanoun a, b, V. Durier b, A. Belaidi c, G. Vergoten b,* b

a Institut de Physique, Universite´ d’Oran Es-Senia, Algeria CRESIMM, Bat. C8 Universite´ des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq, France c De´partement de Ge´nie-Electrique, E.N.S.E.T. d’Oran, Algeria

Received 19 June 1998; accepted 28 July 1998

Abstract The SPASIBA vibrational spectroscopic force field has been developed for the aldehyde function. The tested molecules are methanal, ethanal, propanal and some of their deuterated analogues. The parameters have been obtained by fitting calculated and observed vibrational wavenumbers. A set of 34 independant force constants has been found to correctly describe the structure and vibrational spectra. The average error between predicted and observed vibrational wavenumber is 16 cm ⫺1. 䉷 1999 Elsevier Science B.V. All rights reserved. Keywords: SPASIBA potential energy function; Aldehydes vibrational wave numbers

1. Introduction The carbonyl group present in the molecules of aldehyde, ketone, carboxylic acids, esters, amids and other types of compounds plays a major role in many biological processes and is often of great interest for industrial purposes. Experimental aldehyde-based compounds are discussed in many reviews [1] but only a few theoretical works have been dedicated to this subject [2–4]. With the evolution of computational means, new computational techniques have been developed such as the molecular mechanics force field (MM3) [5]. The limits of these techniques originate in the use of an empirical molecular energy expression, where the

* Corresponding author. Tel.: ⫹ 33-320-337150; Fax: ⫹ 33320-337279.

associated parameters are determined to reproduce experimental quantities (structure and thermodynamic properties). Checking the force field efficiency is performed with the help of vibrational spectra. The SPASIBA potential energy function [6] has been developed and parameterized in our laboratory. The present force field consists of mixing a molecular mechanics force field (derived from the AMBER package) [7] and the Urey–Bradley–Shimanouchi spectroscopic force field [8]. Several classes of molecules have been parameterized: alkanes [9], alkenes [10], lipids [11], aliphatic ethers [12], alcohols [13] and esters [14]. In the course of the present work, force field parameters have been developed for the aldehyde function. The main goal is that the obtained force constants should be transferable to molecules with the same chemical function in order to reproduce the different properties. These constants are mainly

0022-2860/99/$ - see front matter 䉷 1999 Elsevier Science B.V. All rights reserved. PII: S0022-286 0(98)00551-1

262

A. Zanoun et al. / Journal of Molecular Structure 476 (1999) 261–270

After comparison with experimental results, force field parameters that could be transferred from one molecule to another in the concerned series have been carefully checked. All the results obtained in this work were found with a dielectric constant equal to 1, the electrostatic interactions were completly taken into account and the 1–4 Van-der Waals interactions were weighted by a factor of 0.5. The computations were performed on a DEC alpha 3400 computer. The following molecules were thus parameterized: R–CHO with R ˆ H, CH3, CH2CH3. It should be noted SPASIBA force field parameters taken from previous studies [6, 9, 14] were directly transferred without further adjustment. Fig. 1 gives the different molecules with their atom types and atomic charges. Residual charges have been obtained through ab initio calculations at the Becke3LYP/6-31G* level of theory using the Gaussian 94 program [15]. The equilibrium geometric parameters and the force constants are displayed in Table 1.

3. Results and discussions 3.1. Moments of inertia and dipole moments Fig. 1. Atom types and charges.

determined by the use of vibrational spectra, adjusting the calculated to the observed wavenumbers in order to obtain the best agreement. Use of the SPASIBA database helped us to determine the new parameters for each molecule under study. Vibrational spectra were computed with a mean error lower than 16 cm ⫺1.

A comparison between the experimental and calculated values for each molecule is depicted in Table 2. We notice that the calculated values are in good agreement with the experimental ones. The deviation is of the order of 0.10 D for the dipole moment and ˚ ⫺2 for the moments of inertia. 0.99 amu A 3.2. Structures and energies The structural data for the three compounds are summarized in Table 3.

2. Computational method The force constant optimization for each molecule was performed according to the following main stages: • computation of the minimal energy geometry; • computation of the vibrational wavenumbers; and • minimization of the mean deviation between the calculated and observed vibrational wavenumbers.

3.2.1. Methanal The structure of methanal has been studied using microwave spectroscopy [17] and electron diffraction [20]. The calculated molecular structure fits well with the observed values (Table 3). The average deviations between the observed and calculated parameters are ˚ and 1.11⬚ for the bond lengths and bond 0.05 A angles, respectively.

A. Zanoun et al. / Journal of Molecular Structure 476 (1999) 261–270

263

Table 1 Parameters of the SPASIBA potential Stretching

˚ ⫺2) K (kcal mol ⫺1 A

CyO C–HY C–HX C–C3 C3–HC C3–H1 C2–HM C2–CT CT–HC

780.0 270.0 265.0 144.0 331.0 337.0 308.0 165.0 320.0

Angular bending

H (kcal mol ⫺1 rad ⫺2)

OyC–HY HY–C–HY OyC–HX C3–C–HX C3–CyO C–C3–H1 C–C3–HC H1–C3–HC HC–C3–HC C2–C–HX C2–CyO C–C2–HM HM–C2–HM CT–C2–HM CT–C2–C C2–CT–HC HC–CT–HC Torsion X–C3–C–O X–C3–C–HX X–C2–C–O X–C2–C–HX X–C2–CT–X X–C2–CT–X Out-of-plane bending X–C3–C–HX X–C2–C–HX X–HY–C–HY

21.5 26.0 20.5 15.0 23.5 10.0 22.0 26.0 29.0 14.0 24.0 18.0 27.0 17.5 14.0 17.5 29.6 Vn/2 (kcal mol ⫺1) 0.15 0.01 0.10 0.32 0.01 0.22 Vn/2 (kcal mol ⫺1)

7.7 4.8 10.2

˚) r0 (A 1.213 1.115 1.113 1.520 1.100 1.100 1.100 1.530 1.110 ˚ ⫺2) F (kcal mol ⫺1A

u0 (⬚)

145.0 0.01 97.0 67.0 65.0 26.0 67.0 19.0 10.0 66.0 98.0 66.0 05.0 58.0 49.0 79.0 10.07

121.0 118.0 121.1 117.2 123.8 109.0 109.5 108.3 108.6 115.5 124.5 110.5 108.5 111.5 110.0 109.5 108.5

g

n

180.0 0.0 180.0 0.0 0.0 0.0 g

180.0 180.0 180.0

3.2.2. Ethanal Ethanal has been studied by electron diffraction [20], microwave [21] and combined methods [22]. For the hydrogen in the CHO plane, a particular type of hydrogen (H1) has been defined, (its charge

3.0 3.0 3.0 3.0 3.0 3.0 n

2.0 2.0 2.0

differs from the two others). The most stable conformer corresponds to the eclipsed form. A detailed study on the rotation barrier of this compound has been reported by Wilberg [23]. The results obtained using the SPASIBA force field are presented

264

A. Zanoun et al. / Journal of Molecular Structure 476 (1999) 261–270

Table 2 Dipole moments (m) and moments of inertia (IX,Y,Z) of some aldehydes Compound

Expt

Ref.

Calc.

Diff.

%

(m) in Debye Methanal Ethanal Propanal

2.339 2.690 2.73

[16] [18] [19]

2.325 2.805 2.790

0.014 0.115 0.060

(IX,IY,IZ) Methanal

IX IY IZ

1.850 13.017 14.876

[17]

1.841 13.110 14.952

0.009 0.093 0.076

0.48 0.71 0.51

Ethanal

IX IY IZ

8.933 49.741 55.553

[18]

9.354 48.747 54.827

0.421 0.994 0.726

4.71 1.99 1.30

Propanal

IX IY IZ

30.827 85.779 109.920

[19]

30.941 86.469 110.925

0.114 0.690 1.005

0.34 0.80 0.91

in Table 4. The rotation barrier given by our calculations (1.22 kcal mol ⫺1) is in good agreement with the experimental value (1.162 kcal mol ⫺1) [18]. Souter and Wood [24] also measured the infrared spectrum and assigned the torsional transitions. Combining microwave and far-infrared data, these authors have determined new values for the barrier to internal rotation (1.128 kcal mol ⫺1). Munoz-Caro et al. [25] calculated the torsional energy in ethanal at the MP2/6311G(d,p) level (1.164 kcal mol ⫺1). The calculated bond distances and bond angles of the stable conformer (eclipsed) are listed in Table 3. The average deviation between the observed and ˚ for the bond lengths calculated parameters is 0.008 A and 1.266⬚ for the bond angles, respectively.

This skew conformer corresponds to a 133.1⬚ dihedral angle (Fig. 2), (the experimental value is 131⬚) [19]. A conformational study of propanal by Raman spectroscopy confirms that both conformers exist in the vapor and liquid states. This study revels a high energy skew conformer [28]. The results obtained with the SPASIBA force field (Table 4) are in good agreement with those observed. The calculated structures of the cis conformer are compared with observed structures in Table 3. The average deviation between ˚ and the observed and predicted parameters is 0.01 A 1.05⬚ for the bonds lengths and bond angles, respectively.

3.2.3. Propanal The microwave spectrum of propanal was measured some years ago [19]. A complete study using electron diffraction, microwave and infrared was performed by Van Nuffel [26]. The isomer of lowest energy has a structure in which the methyl group is cis with respect to the carbonyl group [27]. Another stable conformer (skew) has been calculated at 1.05 kcal mol ⫺1 above the cis form. The experimental value is 0.95 kcal mol ⫺1 [19].

3.3. Vibrational wavenumbers The vibrational wavenumbers have been calculated for methanal, ethanal and propanal. Six molecules (H2CO, D2CO, CH3CHO, CH3CDO, CD3CDO and CH3CH2CHO) where optimized using the SPASIBA force field leading to 81 fundamental wavenumbers. For these molecules, the average root mean square (rms) deviation between observed and calculated wavenumbers (Table 5) is 16 cm ⫺1, showing a good

A. Zanoun et al. / Journal of Molecular Structure 476 (1999) 261–270 Table 3 Calculated and observed structures of aldehydes a Parameter

Expt

Methnal Cy0 C–HY OyC–H H–C–H

1.208 1.116 121.74 116.52

Ethanal Cy0 C–C3 C–HX C–H1 C3–H OyC–C HX–C–C C–C–HC C–C–H1 H–C3–H H1–C3– CyO Propanal Cy0 C2–C C2–CT C–HX C2–HM CT–HC OyC–C OyC–H C2–C– HX C–C–C C–C2–H CT–C–H H–C2–H C–CT–H H–CT–H OyC–C– C

Ref.

Table 4 Relative energies (kcal mol ⫺1) of the aldehyde conformations

Calc.

Diff.

1.203 1.115 121.0 118.0

⫺ 0.005 ⫺ 0.001 ⫺ 0.740 1.480

[17]

[18] 1.211 1.509 1.113 1.100 1.100 121.6 121.2 109.8 109.8 109.8 0.0

⫺ 0.005 0.008 0.001 0.014 0.014 ⫺ 2.3 1.03 0.6 ⫺ 0.9 1.5 0.0

1.209 1.513 1.521 1.131 1.125 1.127 124.50 120.80 114.70

1.213 1.512 1.530 1.114 1.111 1.110 124.50 120.49 114.61

0.004 0.001 0.009 ⫺ 0.017 ⫺ 0.014 ⫺ 0.017 0.0 ⫺ 0.31 ⫺ 0.09

113.80 108.50 111.80 101.80 111.10 107.80 0.0

112.45 108.61 110.12 106.70 110.12 108.91 0.0

⫺ 1.31 0.11 ⫺ 1.68 4.90 0.02 1.11 0.0

1.216 1.501 1.114 1.086 1.086 123.9 117.5 109.2 110.7 108.3 0.0

265

[19]

˚ ), bond angles (in deg.), dihedral angles (in Bond lengths (in A deg.). a

transferability of the force field parameters among the selected molecules. 3.3.1. Methanal This simplest carbonyl compound has a C2v symmetry with six normal modes 3A1, 1B1 and 2B2. The calculated vibrational wavenumbers of the

Expt

SPASIBA

Ethanal a Cis (0⬚) Gauche (60⬚)

0.0 1.162

0.0 1.22

Propanal b Cis (0⬚) Gauche (60⬚) Skew (120⬚) Trans (180⬚)

0.0 2.10 0.95 1.55

0.0 2.05 1.05 1.56

a b

Ref. [18]. Ref. [19].

methanal are compared with the observed one in Table 6. The potential energy distribution (PED) of each vibration is also listed. The rms deviation between the predicted and observed frequencies is 14.4 cm ⫺1. The assignments of normal modes of vibration are in accordance with previous studies [31]. The rms deviation of the deuterated derivatives of D2CO is 17.6 cm ⫺1 (Table 7). This increase in rms arises partly from the fact that the same geometry as for H2CO has been kept. 3.3.2. Ethanal Ethanal has been the subject of many studies, infrared spectra in gaseous phase and Raman spectra in the liquid phase [29]. The infrared study of five Table 5 RMS errors (cm ⫺1) between the observed and calculated wavenumbers of some aldehyde compound using SPASIBA Molecule

nf a

Methanal H2CO D2CO

6 6

14.4 17.5

Ethanal CH3CHO CH3CDO CD3CDO

15 15 15

11.2 17.3 25.1

Propanal CH3CH2CHO

24

10.6

a

SPASIBA

The number of fundamental wavenumbers taken into account.

266

A. Zanoun et al. / Journal of Molecular Structure 476 (1999) 261–270

Fig. 2. Rotational barrier for propanal.

deutered isotope species in gas phase has been carried out by Hollenstein [32]. This compound has a Cs symmetry with 15 normal modes in two symmetry blocks, 10A 0 and 5A 00. Table 8 lists the experimental and calculated wavenumbers of ethanal, together with the PED using the SPASIBA force field. The rms deviation is 11.9 cm ⫺1. Moreover, the rms deviations of the deuterated derivatives of ethanal are 17.8 and

25.2 cm ⫺1 for CH3CDO and CD3CDO (Table 9). Here also the rms increase is partly due to the fact that the same geometry was kept for deuterated compounds, although the latter may vary [5]. 3.3.3. Propanal The gaseous infrared and liquid Raman spectra were previously assigned for propanal [26]. This

Table 6 Comparison of observed (no) and calculated (nc) wavenumbers of methanal Species

No.

no (cm ⫺1) a

nc (cm ⫺1)

Dn c

Assignment (PED) c

A1

n1 n2 n3

2780 a 1744 1504

2815 1742 1505

35 ⫺2 1

ns CH (99%) n CO (83%) d HCH (48%), n CO (23%), d OCH (20%)

B1

n4

1167

1171

4

g OCH (100%)

B2

n5 n6

2875 1247 b rms(cm ⫺1)

2875 1246

0 ⫺1 14.4

na CH (100%) d OCH (92%)

a

Ref. [29]. Ref. [30]. c The abbreviations used are: na, antisymmetric stretching; ns: symmetric stretching; d: in-plane bending, g: out-of-plane bending coordinates.Dn ˆ nc ⫺ no. b

A. Zanoun et al. / Journal of Molecular Structure 476 (1999) 261–270

267

Table 7 Comparison of observed and calculated wavenumbers of methanal and its deuterated derivative H2CO

D2CO

no (cm ⫺1)

nc (cm ⫺1)

Dn

no (cm ⫺1) a

nc (cm ⫺1)

Dn

2874 2780 1744 1504 1247 1167

2875 2815 1742 1505 1246 1171 rms (cm ⫺1)

1 35 ⫺2 1 ⫺1 ⫺4 14.4

2160 2056 1700 1106 990 938

2122 2061 1682 1099 994 938

⫺ 38 5 ⫺ 18 ⫺7 4 0 17.6

a

Ref. [29].

Table 8 Comparison of observed and calculated wavenumbers of ethanal Species

No

no (cm ⫺1) a

nc (cm ⫺1)

Dn

Assignment (PED) b

A0

n1 n2 n3 n4 n5 n6

3010 2967 2822 1743 1441 1400

3008 2971 2824 1738 1451 1380

2 4 2 ⫺5 10 ⫺ 20

n7 n8 n9 n10

1352 1113 919 509

1334 1129 904 502

⫺ 18 16 ⫺ 15 ⫺7

na CH3 (100%) ns CH3 (99%) n CHX (99%) n CO (90%) da CH3 (80%), d CCH (14%) d OCH (36%), d CCH (22%), d HCH (15%) ds CH3 (59%), d CC3HC(16%) n CC (80%), d OCC (9%) n CC (80%), d OCC (9%) d OCC (55%), d HXCC (12%)

n11 n12 n13 n14 n15

3010 1420 867 763 150 rms (cm ⫺1)

3024 1426 848 764 162

14 6 ⫺ 19 1 12 11.9

A 00

a b

Ref. [29]. wag: wagging.

na CH3 (100%) da CH3 (90%) wag CH3 (82%) g CHX (92%) t CC (100%)

268

A. Zanoun et al. / Journal of Molecular Structure 476 (1999) 261–270

Table 9 Comparison of observed and calculated wavenumbers of ethanal and its deuterated derivatives CH3CHO

CH3CDO

CD3CDO

no (cm ⫺1)

nc (cm ⫺1)

Dn

no (cm ⫺1) a

nc (cm ⫺1)

Dn

no (cm ⫺1) a

nc (cm ⫺1)

3010 2967 2822 1743 1441 1400 1352 1113 919 509 3010 1420 867 763 150 rms (cm ⫺1)

3008 2971 2824 1738 1451 1380 1334 1129 904 502 3024 1426 848 764 162

2 4 2 ⫺5 10 ⫺ 20 ⫺ 18 16 ⫺ 15 ⫺7 14 6 ⫺ 19 1 12 11.9

3014 3014 2970 2071 1743 1442 1420 1353 1109 1043 849 802 668 500 145

3024 3008 2970 2077 1708 1450 1426 1343 1124 1051 867 840 637 498 157

10 ⫺6 0 6 ⫺ 35 8 6 ⫺ 10 15 8 18 38 ⫺ 31 ⫺2 12 17.8

2265 2225 2130 2060 1737 1151 1045 1028 1028 938 747 670 573 436 116

2242 2234 2130 2077 1703 1097 1047 1020 1019 911 798 684 600 445 123

a

Dn ⫺ 23 9 0 17 ⫺ 34 ⫺ 54 2 ⫺8 ⫺9 ⫺ 27 51 14 27 9 7 25.2

Ref. [29].

molecule has a Cs symmetry with 24 fundamental wavenumbers distributed over 15A 0 and 9A 00. We carried out the computation of cis conformer in Table 10. The PED of each vibration is also listed. The rms error of the SPASIBA calculation is 10.6 cm ⫺1.

4. Conclusion From the present work it can be seen that the SPASIBA force field is quite able to reproduce the conformational energies, observed structures and normal vibrational modes. The geometric parameter

deviations between the observed and calculated struc˚ for bond lengths and 1.13⬚ for tures are 0.008 A valence angles. The reproducibility of the vibrational wavenumbers is supported by a calculated rms of 16 cm ⫺1. From comparison with previous works in molecular mechanics, done on the same compounds, it clearly appears that the SPASIBA potential energy function reproduces the spectroscopic properties quite well. The main advantage of the SPASIBA force field is to give a correct description of the vibrational wavenumbers [33] and, at the same time, good structures and energies. This supports the confident use of the SPASIBA force field in molecular dynamic simulations of such compounds.

A. Zanoun et al. / Journal of Molecular Structure 476 (1999) 261–270

269

Table 10 Comparison of observed and calculated wavenumbers of propanal (cis) Species

No

no (cm ⫺1) a

nc (cm ⫺1)

Dn

Assignment (PED) b

A0

n1 n2 n3 n4 n5 n6 n7 n8

2991 2940 2905 2808 1753 1467 1421 1387

2981 2926 2903 2818 1742 1467 1439 1387

⫺ 10 ⫺ 14 ⫺2 10 ⫺ 11 0 18 0

n9 n10 n11

1380 1334 1136

1371 1328 1119

⫺9 ⫺6 ⫺ 17

n12 n13 n14 n15

1010 846 646 272

1037 844 633 284

27 ⫺2 ⫺ 15 12

na CH3 (94%) ns CH3 (74%), ns CH2 (25%) ns CH2 (73%), ns CH3 (26%) n CHX (99%) n CO (90%) da CH3(87%) ds CH3 (56%), ds CH2 (33%) sci CH2 (40%), d OCHX (18%), d HXCC2 (12%) wag CH2 (53%), d OCHX (11%) tw CH2 (31%), r CH2 (26%) d C2CTHC(45%), d HCTH(21%) n C2CT (68%), n CC2 (18%) n CC2 (67%), n C2CT (18%) d OCC2 (43%), d CC2CT (13%) d CC2CT (48%), d OCC2 (22%)

n16 n17 n18 n19

2991 2951 1467 1253

2980 2949 1469 1258

⫺ 11 ⫺2 2 5

n20

1097

1101

4

n21 n22 n23 n24

896 664 255 145

A 00

a b

884 664 257 141 rms (cm ⫺1)

⫺ 12 0 2 ⫺4 10.6

na CH3 (99%) na CH2 (94%) da CH3 (88%) d CC2HM (47%), d HMC2CT (44%) d C2CTHM (18%), wag CH3 (16%) g CHX (53%), d C2CHX (46%) g CHX (89%) t C2CT (93%) t C2C (100%)

Ref. [26]. sci: scissoring; r: rocking.

References [1] C.E. Suter, J. Am. Chem. Soc. 101 (1979) 6481. [2] M.R. Peterson, G.R. Demare, G. Csiz-Madia, O.P. Straust, J. Mol. Struct. 92 (1983) 239. [3] N.G. Rondan, M.N. Paddon-Ron, P. Caramella, K.N. Houk, J. Am. Chem. Soc. 103 (1981) 2436. [4] B.W. Kenneth, E. Martin, J. Am. Chem. Soc. 107 (1985) 5035. [5] N.L. Allinger, K. Chen, M. Rahman, A. Pathiaseil, J. Am. Chem. Soc. 113 (1991) 4505. [6] P. Derreumaux, G. Vergoten, J. Chem. Phys. 102 (1995) 8586. [7] S.J. Weiner, P.A. Kollman, D.J. Nguyen, D.A. Case, J. Comput. Chem. 7 (1986) 230. [8] T. Shimanouchi, in: Physical Chemistry VII Molecular Properties, Chapter 6, New York, 1970, p. 233.

[9] P. Derreumaux, P. Lagant, G. Vergoten, J. Mol. Struct. 295 (1993) 223. [10] M. Chhiba, G. Vergoten, J. Mol. Struct. 326 (1994) 35. [11] M. Chhiba, G. Vergoten, J. Mol. Struct. 384 (1996) 55. [12] F. Tristram, V. Durier, G. Vergoten, J. Mol. Struct. 377 (1996) 47. [13] F. Tristram, V. Durier, G. Vergoten, J. Mol. Struct. 378 (1996) 249. [14] M. Chhiba, F. Tristram, G. Vergoten, J. Mol. Struct. 405 (1997) 113. [15] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, Keith, G.A. Peterson, J.A. Montgomery, K. Raghavachari, M.A. Allaham, V.G. Zakrewski, J.V. Ostiz, J.B. Foresman, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Anders, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J.

270

[16] [17] [18] [19] [20] [21] [22] [23] [24]

A. Zanoun et al. / Journal of Molecular Structure 476 (1999) 261–270 Defrees, J. Baker, J.P. Stewart, M. Head Gordon, G. Gonzalez, J.A Pople, Gaussian, Inc. Pittsburg PA, 1995. A.L. McClellan, Tables of Experimental Dipole Moments, H. Freeman and Company, El Cerrito, CA, 1965. K. Takagi, T. Oka, J. Phys. Soc. Jpn 18 (1963) 1174. R.W. Kilb, C.C. Lin, E.B. Wilson Jr, J. Chem. Phys. 26 (1957) 1695. S.S. Butcher, E.B. Wilson Jr, J. Chem. Phys. 40 (1964) 1671. C. Kato, S. Konaka, T. Iijima, M. Kimura, Bull. Chem. Soc. Jpn 42 (1969) 2148. J.D. Swalen, C.C. Costain, J. Chem. Phys. 31 (1959) 1562. T. Iijima, M. Kimura, Bull. Chem. Soc. Jpn 42 (1969) 2159. K.B. Wilberg, E. Martin, J. Am. Chem. Soc. 107 (1985) 107. C.E. Souter, J.L. Wood, J. Chem. Phys. 52 (1970) 674.

[25] C. Munoz-Caro, A. Nino, D.C. Moule, J. Mol. Struct. 350 (1995) 83. [26] P. Van Nuffel, L. Van Den Enden, C. Van Alsen, H.J. Geise, J. Mol. Struct. 116 (1984) 99. [27] H.M. Pickett, D.G. Scroggin, J. Chem. Phys. 61 (1974) 3954. [28] A. Chapput, B. Roussel, G. Fleury, J. Raman Spectrosc. 2 (1974) 117. [29] P. Cosse, J.H. Schachtschneider, J. Chem. Phys. 44 (1966) 97. [30] T. Oka, K. Suchiya, S. Iwata, Y. Morino, Bull. Chem. Soc. Jpn 37 (1964) 4. [31] A. Chapput, B. Roussel, G. Fleury, J. Raman Spectrosc. 1 (1973) 507. [32] H. Hollenstein, Hs.H. Gu¨nthard, Spectrochim. Acta 27 (1971) 2027. [33] G. Vergoten, Biospectroscopy, in press.