the intermolecular stretching vibration of some hydrogen-bonded complexes

Sp&~&,&a Ah, 1967, Vol. 23A, pp. 611 to 625. Pergamon Press Ltd. Printed in Northern Ireland

The intermolecular stretching vibration of some hydrogen-bonded complexes

S. G. W. GINN and J. L. WOOD Department of Chemistry, Imperial College of Science and Technology,

Imperial Institute Road, South Kensington, London SW.7

(Received 20 Aj+? 1966)

Abstract-The intermolecular stretching vibrations Y a of the hydrogen-bonded complexes (a) phenol-trimethylamine, (b) phenol-triethylamine and (c) phenol-pyridine are observed in the far i&a-red at 143 cm-l, 123 cm-l and 134 cm-l respectively. The bands shift to 141 cm-l, 120 cm-1 and 130 cm-1 in the deuterium bonded complexes. The band in solutions of phenol in Ccl4 at 150 cm-l (143 cm-l in phenol-OD) is ascribed to the intermolecular vibration of (d) phenol cyclic trimer, or of phenol polymer. Normal co-ordinate calculations determine KH. . . B, the stretching force constant of the hydrogen bond as (a) 0.27, (b) O-19, (c) 0.23 and (d) 0.29 mdyn/A, which become for the corresponding deuterated complexes (a) 0.27, (b) 0.18, (c) 0.23 and (d) 0.30 mdyn/k. Having regard to the approximations involved, these results are consistent with no change in the stretching force constant on deuteration.

THE FORMATION of a weak intermolecular complex from two constituent molecules leads to the generation of six intermolecular vibrations which have no counterparts in the separated molecules. At the same time 3 rotations and 3 translations in the individual molecules disappear. The intermolecular modes can be described approximately as one stretching, four bending and one torsional mode. The stretching mode, designated v, in hydrogen bonded complexes by PIMENTEL and MCCLELLAN [l] will have the highest frequency, and be expected in the far infra-red range (50- 200 cm-l).

Previous low frequency studies have been almost entirely confined to complexes formed by self-hydrogen bonding in a single component, i.e. dimers or polymers [l-6]. In such cases it may be difficult to establish unequivocally that a band assigned to v. is due to the complex, and is not present in the component alone. It is also desirable to avoid crystalline systems, where lattice and intermolecular modes can neither be distinguished in principle, nor often, in practice, unambiguously assigned. We have therefore chosen some phenol-amine systems for examination in the liquid phase. Brief notification of some of the experimental results has been given previously [7].

[l] G. P~ENTEL and A. L. MCCLELLAN, The Hydrogen Bond, Freeman, San Francisco (1960). [2] T. MIY~ZAWA and K. S. PI~ZER, J. Am. Chtm. Sot. 81, 74 (1969). [3] Y. NAKAI and K. HIROTA, Bull. Chem. Sot. Japan 32, 709 (1959). [4] Y. NAEAI and K. HIROTA, Nippon Kugaku Zwahi 81, 881 (1900). [5] A. E. STANEVICH, Opt. Spectq 16,425 (1964). [6] R. J. JACOBSEN and J. W. BREECH, Spctrochim. Acta 21, 1753 (1965). [7] S. G. W. GINN and J. L. WOOD, Proc. Chews. Sot. 370 (1964), idem., C&m. Comrnun. 628

(1965).

611

612 S. G. W. GINN and J. L. WOOD

EXPERIMENTAL

Materials

Analar phenol was used from freshly opened bottles as supplied. Phenol-OD was

prepared by exchange. G.P.R. triethylamine was dried over BaO for three days, refluxed over fresh BaO and carbon for 1 hr, and fractionated. AnalaR pyridine was dried with BaO and fractionated. G.P.R. anhydrous trimethylamine was distilled on the vacuum line.

Solutions

Water was excluded by preparing all solutions in the dry box or on the vacuum line. All spectra were obtained within 1 hr of solution preparation. Trimethylamine slowly reacts with CC&. This is to be compared with the similar behaviour of.triethylamine (2 M in Ccl,) which reacts to the extent of 2 per cent in 3 days [S]. Fortunately the decomposition appears to be prevented in the presence of phenol.

I I I I I 100 140 180

cm-’

Spectra

Fig. 1. - ~2 M PhOH + -5M MeSN in Ccl, ---- -5 M Me3N in Ccl,.

These were recorded with a single beam vacuum grating far infra-red spectro- meter constructed in the department. Solutions were examined in sealed thin

polythene bags. Comparison backgrounds were run under identical operating conditions immediately before or afterwards, thinner samples of the same solution rather than the empty cell being used to eliminate interference effects. The bags, which were suspended from a cold finger, were cooled when necessary but not frozen.

[S] R. F. COLLINS, Chem. and Ind. 704 (1957).

The intermolecular stretching vibration of some hydrogen-bonded complexes 613

Fig. 2. A - ~2 M PhOH + ~5 M MeaN in Ccl, *- -2 M PhOD + ~7 M Me3N in CCI, ---- -5M Me,NinCC14.

B ~ 2.8 M PhOH in Et,N +- -3 M PhOD in Et,N

- - - - liquid Et,N. C-- 2.8 M PhOH in pyridine

* __ -3.5 M PhOD in pyridine - - - - liquid pyridine.

D ~ 2.7 M PhOH in Ccl, * ~ 2.8 M PhOD in Ccl,

- - - - liquid Ccl,.

To establish the band centres and contours, many independent pairs of runs were made, with both the mixtures, and the separate components (e.g. Fig. 1). The resulting spectra are shown in Fig. 2. Since the low frequency spectra of phenol and phenol-OD complexes are so similar, the isotopic composition was confirmed by examining the 2000-3500 cm-l region.

Assignment

DISCUSSION

The solutions of phenol in each of the three amines all show a medium or strong band below 150 cm-l absent in the unmixed components, which can be confidently


assigned to the intermolecular vibration v,. All the internal vibrations of the components can be accounted for by bands at higher frequency. Strong solutions of phenol in Ccl,, examined for comparison, show a broad and weak band around 150 cm-l. This cannot be an internal fundamental, and results from hydrogen bonding association [5, 61.

The nature of the associated species can be established more exactly from the spectra in the OH stretching region. Dilute ((O-025 M) solutions of phenol in Ccl, show a single sharp band at 3611 cm-l, assigned to the monomer. Between O-025 and 0.20 M a second, quite well defined band at 3485 cm-l becomes prominent. Its assignment to the dimer is supported by equilibrium constant studies based on the reduction in the intensity of the monomer band [9], or its overtone [lo]. These studies imply that there is no contribution to the 3611 cm-l band from any terminal OH groups. Since the OH stretching frequency of terminal OH groups is little affected by action of the oxygen as an H-bond acceptor [ll], one can infer that the dimer is cyclic. In more concentrated phenol solutions a broad band around 3340 cm-’ becomes prominent. In these solutions there is no evidence for the presence of free terminal OH groups-the small residual band at ~3600 cm-l is accounted for by the small proportion of free monomer present. Molecular weight studies (to be regarded with reserve) indicate trimer, and this must then be cyclic. Open ended polymers are only possible if the proportion of free OH groups is small, i.e. if the molecular weight is large.

When excess base is present, the 3340 cm-l band disappears, and is replaced by a complex absorption band around 3100 cm-l, showing the entire replacement of phenol by the base as acceptor. Quantitative intensity studies [12]-which are limited to more dilute solutions-show the association is 1 phenol : 1 base ; there is no indication of any other association in the more concentrated solutions which were required for the far infra-red studies. It is therefore concluded that the low frequency intermolecular vibrations relate to the stretching modes of the 1: 1 phenol/base complexes, and for phenol itself to the cyclic trimer, or possibly higher polymers. The resulting assignments are shown in Tables 1 and 2.

The H-bond stretching force constant

Recently attempts have been made to obtain a hydrogen bond stretching force constant from v,, using a diatomic model [5, 61. These attempts encounter the difficulty of assigning an effective reduced mass to the attached molecules. The mass of the entire molecules, or of the immediately attached atoms, have been suggested, and lead to widely differing values. It is obvious that both these models are com- pletely unsatisfactory. Taking the entire mass of the molecule into account is equivalent to setting all the internal force constants and frequencies equal to infinity [ 131; taking only the mass of the directly attached atoms is equivalent to

[9] J. J. Fox and A. E. MARTIN, Proc. Roy. Sot. 162A, 419 (1937). [IO] M. M. MACUJIRE and R. WEST, Spectrochim. Acta 17, 369 (1961).

[ll] Ref. [l], p. 96-7. [12] A. HALL and J. L. WOOD, unpublished work. [13] E. B. WILSON, J. C. DECTUS and P. C. CROSS, MoZecuZm Vibrations, McGraw-Hill, New

York (1955).

The intermolecular stretching vibration of some hydrogen-bonded complexes

Table 1. Far infrared spectra of phenol and phenol-OD in amines

616

Solvent Frequency

(cm-‘) Awignment

PhOH-pyridine 134 m 143 sh 208 w 242 m

343 sh 363 sh

vo(H- -N) vo(H- -N) ? (solvent) 0 out-of-plane

deformation (solvent) (solvent)

PhOH-Et,N 123 m 200 m 224 sh 240 m

310 B

vo(H- -N) (mlvent) (solvent) 0 out-of-plane

deformetion (solvent)

PhOH-Me,N in Ccl, 143 B 243 m

278 w P 312 mw Increaidng abeorption above 340

vo(H- -N) 0 out-of-plane

deformation (MeaN) f (CCl,)

(MeaN)

PhOD-pyridine 130 m vo(D- -N) 139 sh YU(D- -N)?

PhOD-Et,N

PhOD-Me,N in CCI,

120 m vo(D- -N)

141 8 v,(D- -N)

8 = strong; m = medium; w = weak; sh = shoulder.

Table 2. Far infrared spectra of phenol and phenol-OD

Solvent

Frequency of bands

(cm-l) Assignment

PhOH 160 w, vbr 260 m

360 ms, vbr

va(O- -H) 0 out-of-plane deformation OH torsion?

PhOD CCI, 143 w, vbr 220 m, br

250 m

270 sh 310 mw ~380 s

v,(O- -D) OD torsion (monomer)? 0 out-of-plane deformation OD torsion? (solvent) 0 m-plane deformation

8 = strong; m = medium; w = weak; vbr = very broad; ah = shoulder.

Force constants relating to internal displacements are also shown in the Appendix Table A. Those for the trimethylamine moiety are transferred from the free molecule [I81 and differ only slightly from the extreme hydrogen bonding case of MeaNHCl

l-191. ~,,(vW is chosen by comparison, the value representing some double bond character in CO [20]. F,,(vPh’C) and F,,(6Ph’CO) were then estimated by treating phenol as a triatomic system Ph’CO [17]. The small value of P,, reflects the ring bending contribution to the flexibility. B’,,(vOH) is lowered from the free phenol value (7.84 mdyn/A) [2l] by hydrogen bonding, and is obtained from the shifted vOH. B’J8 COH) is taken equal to the bending constant in water [22] or in formic acid monomer [23]. The hydrogen bond bending constants and all interaction constants were taken as zero. To take advantage of the C, symmetry, transformation to symmetry co-ordinates is effected, the G and F matrices similarly transformed (details are given in the Appendix) and F,, (the v,(H- - -N) force constant) computed using the observed frequency shown in Table 1. The procedure was repeated for the phenol-OD complex. Results are given in Table 3. For comparison, values of the extreme diatomic model representations are also included. It is apparent that neither provides a satisfactory approximation.

_ P41 WI [I61 [I71 WI [I91 [201

Ref. [l], p. 87.

[211 [221 ~231

R. SCHROEDER and E. R. LIPPINCOTT, J. Phys. Chem. 61, 921 (1957). J. C. EVANS, Spectrochim. Acta 16, 1382 (1960). D. R. LIDE JR. and D. E. MANN, J. Chem. Phye. 28, 572 (1958). J. R. BARCEL~ and J. BELLANATO, Spectrochim. Acta 8, 27 (1956). J. T. EDSALL, J. Chem. Phys. 5, 225 (1937). Ref. [13], p. 175. L. G. BONNER, J. Chem. Phys. 5,293 (1937); T. KOJIMA, J. Phya. Sot. Japan 15,284 (1960). W. GORDY, J. Chem. Phys. 14, 305 (1946). Ref. [13], p. 176. Ref. [2], p. 77.


setting the internal force constants and frequencies equal to zero. It is apparent from the vibrational spectrum that most of the internal force constants in the associated molecules are little changed from their values in the free species. A good estimate of the modified OH stretching force constant can be made. Consequently the internal flexibility of the molecules forming the complex can be quantitatively accounted by a normal co-ordinate analysis. This has been done, and details are now given.

Phenol-trimethylamine

The model structure (shown in the Appendix, Fig. A) is chosen to take account of the following features. The linearity of O-H- - -N conforms with the structure usual in open complexes [ 11. The O---N distance is taken from an empirical correlation with AvOH [14], and the O-H distance similarly chosen [15]. The C-O distance is chosen by comparison with crystalline phenols [16]. Since CC0 bending can be expected to have an appreciable influence, some account of this is taken by attaching the u-carbon to a Ph’ unit of mass 65 units, at the centre of mass of the five replaced CH groups. Trimethylamine dimensions were adopted from the free molecule [IT]. The dimensions are collected in Appendix Table A. Me groups were represented by point masses of 15 units. The Me,N C, symmetry axis was taken

’ to coincide with the O---N direction.


Table 3. Hydrogen-bond stretching force constants (mdyn@), phenol-amine complexes

Simplified normal Diatomic Diatomic

co-ordinate model model

Phenol-trimethylamine 0.271 017_Nl4 0.09 (-J94-N59 0.44 Phenol-OD-trimethylamine 0.274 0’*-N14 < 1 y0 lower 0g5-N59 3 % lower

Phenol-triethylamine Et = 15 0.192 017_--*4 0.07 094-N59 0.33 Phenol-OD triethylamine Et = 15 0.179 01*-N14 2.5% lower 0g5-N59 5% lower

Phenol-triethylamine Et = 30 0.236 017_Nl4 0.07 094-PO’ 0.44 Phenol-OD-triethylamine E = 30 0.220 018-N14 2.5 y0 lower 0 95-N101 5 y0 lower

Phenol-pyridine Phenol-OD-pyridine

0.229 0”-N14 0.08 094_N79 0.45 0.227 @E-N14 3.5% lower 0g5-N79 6% lower

Phenol-triethylamine

It is not practicable to take into account the effect of the torsional orientation of the ethyl groups, which are therefore represented by point masses. The model is then identical with that for the trimethylamine complex. The computation was carried out representing the ethyl groups by point masses of 15 or 30 a.m.u., which span the effective range. The resulting values of P,, are also shown in Table 3.

Phenol-pyridine

The model structure is based on a linear hydrogen bond (shown in the Appendix Fig. B). Phenol dimensions are as before. The pyridine dimensions (Appendix Table Bl) are from the free molecule [24]-these are only slightly different from those of the hydrochloride [25]. It was assumed that the nitrogen lone pair orbital is directed along the H-bond, i.e. the C, axis of pyridine coincides with the O-H- - -N direction. The torsional orientation of the pyridine ring is undetermined so the plane was chosen normal to the phenol plane, as this reduces the complexity of the computation. Force constants for the phenol moiety were as before, and those of the pyridine moiety, adpoted from the free molecule 1261 are also given in the Appendix Table Bl. Symmetry coordinates were again formed, based on C, symmetry, the G and P matrices transformed, and P,, determined as before. (Details are given

in the Appendix.) Values for the phenol and phenol-OD complexes are also shown in Table 3.

Phenol polymer

Various models have been explored; a planar cyclic trimer (C,, symmetry), a cyclic dimer (C,, symmetry), and dimer and trimer units of an open chain polymer.

Cyclic trimer. The model structure is shown in the Appendix (Fig. C). Dimen- sions were based on empirical correlations [l] and are also included in the Appendix.

Since it is not possible to maintain the linearity of OH- - -0 and at the same time form the bond in the direction of maximum electron density of the oxygen, the OH--O

[24] B. BAK et al., J. Mol. Spectry 2, 361 (1968). [25] C. RERAT,A&zC~?J~~. 15,427 (1962). [26] V. I. BEREZIN, Opt.Spechy 15, 167 (1963).


bond was not assumed to be linear, the OH--O angle being treated as a variable parameter. All interaction force constants were taken as zero as were the O-H- - -0 and H-O- - -H bending force constants, while the Ph-0 and OH stretching force constants, and the PhOH bending constant were varied over the ranges given in Appendix Table C 1.

The in-plane normal vibrations of the cyclic trimer divide into the A’ and E’ species, only the latter being infra-red active. The nine in-plane ring modes may be described as follows :

Description A’ E’

OH stretching Vl V2) v3

H- - -0 stretching v4 % %

OH- -0 bending % % % Putting the bending force constants equal to zero results in zero frequency for

the v,, vs and v9 modes. The 150 cm-l band is identified with the vs, vg mode. Figure 3

0.6

F( Ph-O-H 1: A 0.4 md. A

B 0.6 md.8

C 0.0 md. ii

D I.0 md. A o-o ; I I I I 1

60 100 140 0

L (O-H--O)

Fig. 3. Dependence of the hydrogen bond stretching force constant on the angle (O-H- -0) for phenol oyclio trimer.

shows computed values of the P,, (0- - -H), (v~), stretching force constant for a range of O-H- -0 angles and PhOH bending force constants (for details see Appendix). The values are not sensitive to variations over reasonable values of the Ph-0 and OH stretching force constants.

The phenol-phenol hydrogen bond is shown by displacement to be weaker than the phenol-amine bond. Consequently the large values of F,, (0- -H) for inter- mediate values of LOHO are unreasonable. The low range of LOHO is physically


not plausible, although the force constant is reasonable. It is therefore inferred that if the cyclic trimer is present, the OH0 angle is nearly linear. On repeating the computation with the PhOD data, the F,, (0- - -D) constant remains close to the F,, (O---H) value only when the bond is linear. The resulting values, which are then also independent of Fl,,,, (6 PhOH), are included in Table 4.

Table 4. Hydrogen bond stretching force constants (mdyn/A), phenol polymer*

Phenol polymer

L(O-H- -0)

L(O-:- -0)

(deg)

L (H-O- -H) F(O- -H)

i.(D--o;;- -D) F(OE --D)

(deg) (mdynl&

cyclic trimer-H 180 60 0.29

cyclic trimer-D 180 60 0.30

cyclic dimer-H 90 90 0.76 cyclic dimer-D 90 90 0.76 open trimer-H 180 120 o-11, 0.29 open trimer-D 180 120 0.11, 0.29

open trimer-H 180 60 0.27, 0.28 open trimer-D 180 60 0.27, 0.28 open dimer-H 180 120 0.16

open dimer-D 180 120 0.17 open dimer-H 180 60 0.27

open dimer-D 180 60 0.27

Force constants used: F(Ph-0) = 6 mdyn/& F(O-H) and F(O-D) = 6 mdyn/A, F(Ph-O-H) and F(Ph-O-D) = 0.7 mdyn/A.

Cyclic Amer. The stretching force constant F(O- -H) has also been calculated for the cyclic dimer (C, point group). Details are given in the Appendix. Even for the most favourable choice of parameters, the F,, (O--H) force constant is im- plausibly large (Table 4) and it can be confidently concluded that the band observed (Table 2) is not due to the cyclic dimer.

Open dimer and trimer. An open polymer is also possible. The mechanics of open dimer and trimer models have been examined (details are given in the Appendix Fig. D). Results for the dimer are given in Table 4. In the open trimer two infra- red active vibrations result from O---H stretching. When either of these is identified with the observed band, reasonable force constants are obtained (Table 4).

Phenol-pyridine band structure. The doublet structure of the phenol-pyridine y0 band (Fig. 2) is securely substantiated by repeated runs (Fig. 4). The band contour is unchanged on deuteration, the entire band moving to some 3 cm-l lower frequency. The doublet is therefore not due to hydrogen tunnelling. On addition of Ccl, to the solution, the higher frequency component disappears, indicating that it could originate from a polar species, i.e. v, of PhO-- - -HN+Py. Work in progress has not yet provided confirmation of this suggestion-thus it has not so far been possible to definitely identify the NH+ stretching band of PyN+H, which would be expected in the range 2500 cm-l to 2800 cm-l [27].

[27] R. C. LORD and R. E. MERRIFIELD, J. Chena. Phya. 21, 166 (1953). R. H. NUTTALL et al., J. Chem. Sot., 4965 (1960). D. COOK, Can. J. Chem. 89, 2009 (1961).


t

Fig.

cm -I

4. __- PhOH in pyridine (~2.8 * ___ PhOD in pyridine (-3.5 - - - - liquid pyridine.

M) Ml

CONCLUSIONS

Relative strength of hydrogen and deuterium bonds

The present examination shows that there is no change in the 0- - -H stretching force constant on deuteration-in this precise sense, the hydrogen and deuterium bonds in the systems examined are of the same strength. This conclusion is valid even if substantial approximations have been introduced. Reference to Table 3 shows that even with the extreme approximation of diatomic models, the change in the stretching force constant is small.

Linearity of the hydrogen bond

It has been suggested that the observation of only a small decrease in v, on deuteration implies linearity of the hydrogen bond [6]. The present results must not be understood as necessarily supporting this view. They show, that with an unchanged force field, the change in v0 is consistent with a linear bond. However, calculations carried out with bent bond models [28] show that, with a physically reasonable, unchanged force field, v, may also exhibit only a slight drop. Consequently, for open systems, more detailed knowledge of the intermolecular force field is required before attempting to decide the linearity of the hydrogen bond. Within the scope of the present calculations, it appears probable that if a phenol cyclic trimer of C,, symmetry is present, the bonds are linear.

Acknowledgements-We wish to thank the Science Research Council for enabling this work to be carried out by providing a Grant for a Special Research.

[28] S. G. W. GINN and J. L. WOOD, unpublished data.


APPENDIX

SO3

o,, S’H_S”

s J S5 “ST

0% S,

/

Me

Fig. -4. Internal co-ordinates of 1: 1 phenol-trimethylamine complex.

Table A. Structural parameters and force constants, phenol. trimethylamine complex

Structural unit

Length or angle

(4 (de4 Force const .

(mdyn/h

PW-c 1.68 1.5

C-O 1.36 6.0

O-H l-00 6.0

H- -N 1.75 -

N-Me 1.47 4.0

Ph’--C--0 180 0.53

CO-H 120 0.7

O-H- -N 180 0.0

H- -N-Me 111 0.0

Me-N-Me 108 0.86

622 8. G. W. GINN and J. L. WOOD

Fig. B. Internal co-ordinates of 1: 1 phenol-pyridine complex.

Table Bl. Structural parameters, pyridine moiety of phenol-pyridine complex

Structural unit Length (A) or angle

N-C, 1.34

Ca--cfl 1.39 q-c,, 1.39 H-N-C, 121”35’ C,-N-C, 116”50’ N-C,--CB 123”53’ c,-c~-c, 118”32’

%--C,--c, 1 lS”20’

Table B2. Symmetry force constants, pyridine moiety of phenol-pyridine complex

8.00 mdyn/A F 89 6.38 mdyn/A F 8.10

F lo.lo ~GW mdyn/A F 9.10 2.93 mdyn-A F 8,ll 2.64 mdyn-A F 8.16

z;*;;

F’ 10.11 F 10.15 F 11.16

0.13 mdyn/A -0.60 mdyn/A

0.13 mdyn/A 1.59 mdyn

-1.13 mdyn -0.53 mdyn -0.53 mydn -1.13 mydn

1.59 mdyn - I.24 mdyn-A


Table B3. In-plane (A’) symmetry co-ordinates S in terms of internal co-ordinates 8 of phenol-amine complexes

symmetry -trimethyltmine and co-ordin8t3 Sk -triethylmnine (Fig. A)

-pyridine (Fig. B)

81 = Sl

sp = 8%

s* = S*

84 = S.4

s, = 4

86 = 4

8, = 87

sg = SS

89 = &.s. + f&l)

4

S*

4

84

85

4

s, 1

-

42 (S8 -I- 4,)

32 - (4 + 4,)

z (S,, + S,,)

S 14 1

812 = S 10

-

SlS = $2 WI, + S,,)

814 = S16 =

Ji (S,, + 4,) - $2 (S,, + 4,)

1

The redundancy condition in the smetry a mkbix srisig from the me, angles ia (approximately) :

%,,I + Or.14 + ~/(h + %lJ - 0. This condition w&s used 8s a aheck. The thma mdundtmay conditions arising from the pyridine moiety am:

9.n+ ~za,.,, = 0

Qt.11 + am + G%,, + 4.1.) = 0

Gkrls + 0*0310C+a,a - 0.8237&,, + 0~8119C+,,,

- 0.36780,,,, + 1.0822C+b,,, = 0.

me ccmrdinetm thus eliminated exe S,,, S,, and S,,

Ph

Fig. C. In-plane

I SI

Ph internal co-ordinates of phenol cyclio model).


Table Cl. Structural parameters and cyclic trimer

Structural Length or angle unit (A) (deg)

force constants, phenol

Range of force constants

md/A (stretching) md-A (bending)

Ph-O 1.36 0, 6, IOOt O-H 1.00 3-q O--H 1.75 --

Ph-O-H 120 0-1.07

O-H- -0 60-180 0.0

H-O- -H 180-60 0.0

Ph-O- -H 60-180 0.0

t Same ranges taken for corresponding parameters in phenol cyclic dimer. The (O-H- -0) angle varied over range 60-150”.

Table C2. The E, symmetry co-ordinatest Sk of phenol cyclic trimer

- Sa = 43 (8, + ES, + @S,)

1

s4 = 113 (S,, + ES,1 + &*s,,) 1

Q5 = 7; (4, + ES,, + &*s,,)

QB = 43 w,, + ES,, + E’S,*) 1 -

s, = 43 (S,, + Eszo + c*S,,) where E = $w, @ = e--2ni/3.

t The two E’ representations of the C,, group are labelled E,,‘, E,’ where

c sn E c, csz 0, 4 h6

El%’ 1 E &* 1 F &* -%’ 1 &* E 1 &* E

The two redundancy conditions in E,’ are:

Qa.4 + %, + %B = 0 %,a + M&s,, + oGr,e + da,,, = 0

where a, b, o and d am in general complex numbers. (It is necessmy to 1188 compkxx symmetry co-ordinates for molecules belonging to the ayclic point groups, C,, Clzhr (n > 3) a~ has been recently confirmed by R. W. MOONEY et al. [29]).

[29] R. W. MOONEY et al., J. Chem. Phys. 42, 3741 (1965). R. W. MOONEY et al., Acta Chem. Stand. 19, 1031, 1749 (1965).


Ph

Ph

S5 I

Fig. D. In-plane internal co-ordinates for phenol cyclic dimes and phenol open dimer and trimer. (Bond lengths are the same aa those given in Table Cl. For bond

angles see Tables 4 and Cl.)

Table C3. The B, symmetry co-ordinates of phenol cyclic dimer

8, = -$ (S, - S,) 8s = -$ (S, - S,)

sa = $ (S, - S,) s* = 5 (S, - S,)

the intermolecular stretching vibration of some hydrogen-bonded complexes

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