Geometric structure and vibrational spectrum of tetrahydrofuran

1844 J. Phys. Chem. 1993,97, 7844-7856

Geometric Structure and Vibrational Spectrum of Tetrahydrofuran

Beniamino Cadioli' and Enzo Gallinella Dipartimento di Chimica, Universitb di Modena, via G . Campi 183, I41100 Modena, Italy

Christian Coulombeau LEDSS, Universitb Joseph Fourier, F38041 Saint- Martin-d'HPres, France

Her& Jobic Institut de Recherches sur la Catalyse, 2 av. A . Einstein, F69626 Villeurbanne, France

Gaston Berthier' Ecole Normale Supbrieure, 24 rue Lhomond. F75005 Paris, France, and Institut de Biologie Physico- Chimique, 13 rue Pierre et Marie Curie, F75005 Paris, France

Received: February 1 , 1993; In Final Form: April 27, 1993

Ab initio calculations for the symmetric C2, C,, and CZ, forms and for two unsymmetric C1 forms of tetrahydrofuran were performed both at the SCF level and accounting for electron correlation by full second-order Maller- Plesset perturbative treatment. The standard STO-3G, 6-31G, and 6-31G** bases and a 6-31G* basis with different exponents for polarization functions on oxygen and carbons were applied to a complete optimization of the geometrical parameters within each given molecular symmetry. The most reliable computations have given the C2 conformation on the absolute energy minimum, the C, structure on a transition state, only 0.3 kcal mol-' higher, and the CZ, form on an energy maximum, 4.7 kcal mol-' high. While bond lengths appear nearly conformation-independent, angles and dihedrals show a marked flexibility in the delicate balance between bond-angle strain and ring-angle torsion that governs the interconversion between the different forms. The puckering amplitude q is seen to be nearly constant, a t 39.5 pm, for both the C2 and C, structures. The vibrational spectrum was reinvestigated by recording the infrared spectrum of the vapor and the infrared and Raman spectra of solutions in apolar solvents and of the liquid and the solid a t different temperatures. The spectrum of the solid between 30 and 120 K was investigated for the first time by neutron inelastic scattering experiments. With the guide of the computed spectrum as predicted at the MP2/6-31G* level of theory, all the normal modes have been identified and assigned in terms of symmetry coordinates. Experimental evidence strongly suggests that in solid tetrahydrofuran the pseudorotational motion becomes a large-amplitude ring- deformation vibration with a fundamental frequency of about 140 cm-'.

Introduction

The structural properties of tetrahydrofuran (THF) have long been investigated, both in view of its important role as structural unit of carbohydrates and biological molecules and in the context of a general interest in conformation and ring puckering of small- membered rings.' In a microwavestudy? the rotationalconstants and the dipole moments for the ground and several excited states were measured and a potential energy function along the pseudorotational coordinate 4 at a constant value of the radial coordinate r was derived, which exhibited two equivalent minima at about 4 = 45O and 4 = 135O, with the forms C2 (4 = 90,270') and C, (4 = 0,180°) lying on maxima, 70 and 170 cal mol-1 high, respectively, suggesting the Occurrence of a nearly free pseudorotation. From consideration of the variation of the dipole moment with the pseudorotational states, a twisted conformation was indicated to be the stable form of the molecule in the ground state.2 A very similar one-dimensional potential, expanded in terms of cos 24 and cos 44, was derived from assignment of the very complicated far-infrared spectrum of thevapor.3 Later works used more sophisticated potentials for this assignment below 300 cm-1 and evidence was acquired for the need of a two-dimensional Hamiltonian.4-5 Ring inversion through planarity was estimated from microwave2 and far-infrared4 studies to be hindered by a potential barrier ranging from 3.5 to 3.9 kcal mol-', respectively. As a proof of the molecular pliability along the angular coordinate, only three principal bond lengths (C-0, C-C, and C-H) were

0022-365419312097-7844$04.00/0

obtained from electron-diffraction structural analyses, and the radial distribution could not be resolved in terms of any static c~nformation.~*~ A symmetric twisted conformation has been proved for the ground state of the molecule by a single-crystal X-ray structure analysis, from which bond lengths and bond and torsional angles have been determined.* A more detailed structure analysis confirming the C2 conformation of solid THF has been performed very recently for the deuterated species by high- resolution neutron powder diffraction (HRNPD).g

Information about the equilibrium conformation and structural parameters of the free molecule has also come from theoretical calculations. Early ab initiocomputations with theSTO-3G basis predicted a C, envelope form as the stable conformation of THF, while at the 4-31G level the energy minimum was found for a twisted C2 conformer, with a pseudorotational barrier corresponding to the Cs-Cz energy difference of 1.33 kcal mol-1.10 Using the 6-31G* basis, this barrier height was lowered to 0.74 kcal mol-' in the independent particle SCF model11 and to 0.54 kcal mol-' after a Mdler-Plesset second-order perturbative (MP2) treatment of electron correlation.12 With respect to the C2 form, the energy of the C, conformation (coplanar ring atoms) was predicted tobe2.65and3.45 kcalmol-1 higherattheSCF4-31GIO and 6-3 1G*" levels, respectively. In all these calculations, only few bond parameters were energy-optimizedlOJ1 or all of them were optimized only at the SCF 3-21G level.12 Molecular mechanics, too, was used to calculate the intramolecular potential

0 1993 American Chemical Society

Structure and Spectrum of Tetrahydrofuran

function and the structural parameters of THF;l3 in the most recent paper, the results of the SCF 6-31G* computations by Cremer11 appear to be quite closely reproduced. Monte Carlo statistical mechanics simulations carried out for liquid THF have indicated a distribution of the molecules over all the possible conformers with 0’ I 4 I 180° and a probabiiity maximum for the C2 form.14

Despite this great deal of interest on conformation, structure and ring-puckering vibrations of THF, no satisfactory elucidation of, the gross vibrational spectrum of the molecule has been accomplished so far. On inspection of the infrared and Raman literature, it appears that only sparse and incomplete investigations have been devoted to the recording and analysis of the spectra of THF, and no consistent and complete vibrational assignment has been put forward for this molecule up to now. To our knowledge, there is no Raman spectrum reported in literature after that of 1940 by Kohlrausch and Reitz;15 infrared spectra and tentative partial assignments were reported early in 1952,16 1960,’’ and 1969.18 However, both for the Raman spectrum of the liquid and for the infrared spectra of the liquid and the vapor, less than a half of the fundamentals were observed; the assignments of refs 17 and 18 were mainly based on the infrared spectrum of the solid phase, for which a higher number of lines were reported. In subsequent works, normal-coordinate treatments were proposed. Eyster and Prohofsky19 used the previous incomplete experimental data and made the assumption of a Ckconformation. Derouault et alU2o later reexamined the Raman spectrum of the liquid and the infrared spectra of solutions in apolar solvents; the spectra were not reported; they simply used a set of frequencies taken from Raman and infrared for different aggregation states to assign the 1500-280-cm-l region, using the correct C2 symmetry.

In view of the incompleteness of the observed fundamentals and of the inconsistency of the proposed assignments, we felt that a reappraisal of the Raman and infrared spectra under better conditions of sensitivity and resolution might yield more experimental data to serve as a basis for a more accurate interpretation of the vibrational spectrum of THF, and that an assignment as complete as possible could be attained through the support of accurate ab initio calculations. To this end, we started a more detailed investigation and recorded the Raman and infrared spectra for the various aggregation states and a t different temperatures. Moreover, neutron inelastic scattering (NIS) experiments were carried out at different temperatures from 30 to 120 K, giving independent information on the vibrational frequencies for the spectrum of the crystal below 1500 cm-l. Finally, in combination with the experimental work, Hartree- Fock and MP2 calculations of the total energies and of the vibrational spectra of the C2, C,, CZ, and of two C1 conformations were performed with several basis sets up to inclusion of polarization functions on all atoms.

Computational Methods

Complete geometrical optimization within each symmetry group was pursued at every level of ab initio computation, with 17, 17, and 10 independent parameters for the CZ, C,, and CZ, molecular symmetries, respectively. Furthermore, two nonsym- metric C1 forms were taken into consideration within a constrained geometrical model, characterized by 32 variational parameters; these forms, denoted B2 and B3 following Laane,’ describe bent conformations of THF with an a- or 8-carbon as “unique” atom, respectively, i.e., with an CY- or 8-carbon puckered with respect to the plane of the other four atoms of the ring. The following atomic bases were used at the HartreeFocklevel: standard STO- 3G, 6-31G, and 6-31G**, and a 6-31G* basis with exponents 0.85 and 0.75 for the six Cartesian polarization functions on oxygen and carbons, respectively. Full-MP2 computations of geometries and vibrational spectra were made using the standard

The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 7845

6-31G and 6-31G** bases anda 6-31G* one with split exponents of 0.85 and 0.75 on the five 3d polarization functions on oxygen and carbons, respectively. This last basis proved to be well balanced and gave the most reliable results in the computation of the vibrational frequencies. Both GAUSSIAN 9021 and GAMESSZ packages were used on a Sun Sparc Station 2. Owing to the very low energy differences and to some very weak force constants involved, in some cases the precaution was taken of repeating the same calculations with both packages, with starting geometries defined in Cartesians or by suitable 2-matrices and with lower thresholds than the default values; in these cases practically identical values of final energies and geometrical parameters were obtained. In the MP2/6-3 1G* optimization of the geometry and numerical computation of the vibrational spectra, the maximum residual Cartesian force was less than 10-5 hartree bohrl. The puckering parameters were derived using the RING program.23 The vibrational analysis was performed by means of a modified version of the “General Vibrational Analysis System”.z4 The normal modes of vibration were inspected on a personal computer with use of the VIBMOL program.2s The analysis of the NIS data was carried out by reference to a synthetic spectrum generated with a computer simulation program.26

Experimental Section Tetrahydrofuran of high purity (anhydrous, 99.9%) was pur-

chased from Aldrich Chimica, Italy, and stored under inert atmosphere.

All the infrared spectra were taken on a Bruker IFS 113v FT spectrometer, with 5 pm KBr and 6 pm Mylar beamsplitters and a DTGS detector. The spectra of the liquid at low temperature and of the solid were taken using the liquid nitrogen cryostat of Specac, U.K., equipped with a vacuum tight cell with AgCl windows and 50 and 25 pm path lengths. For the liquid, several runsweremadeat temperaturesfrom 183 to 155 K, under 1 .O-cm-l resolution and accumulating 20 scans each time. For the solid, after annealing of the sample, the spectrum was taken at 90 K, under 0.5-cm-l resolution and accumulating 100 scans. From one run to another, only minor changes were noticed in the appearance of the solid phase; since this was obtained by freezing a liquid film, the possibility of an oriented growth of at least a portion of the solid can not be excluded. The spectrum of the vapor was taken under 0.1-cm-l resolution and accumulating 100-400 scans. The sample was transferred via a vacuum line in a 20-cm path length cell, where it was kept very effectively desiccated over calcium hydride.

The Raman spectra were recorded on a Jobin-Yvon HG 2 s spectrophotometer equipped with a Spectra-Physics 165 Ar+ laser source. The 488.0-nm line was used as exciting radiation and a spectral slit width of 3 cm-1 was used throughout; details of interest were reinspected at 1 S-cm-l resolution. Samples were prepared by transfer through a vacuum line and sealing in a 5 mm 0.d. glass tube. The sample cell was put in a modified Oxford Instrument DN 1754 liquid nitrogen cryostat; the temperature was monitored by an automatic controller and an independent chromel-alumel thermocouple. The accuracy of the reported temperature was better than 2 K. Depolarization ratios were measured as p = Iv~/Zvv. The spectra of the liquid were taken at 165 and 205 K and, besides, at 298 and 340 K. The spectra of the solid were recorded at 85 and 150 K. The solid at 150 K, a little below the melting point of the substance, was seen in the cell tube as a translucent mass; at 85 K, after repeated annealing, it appeared as a translucent mass embedded with minute white granules of microcrystalline nature. In the recorded spectra, these apparent inhomogeneities and imperfect order in the solid samples might have been responsible for lines of slightly different frequencies between 150 and 85 K, and for widely different relative line intensities not only between 150 and 85 K spectra but also between repeated runs at 85 K.

7846 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993

TABLE I: Energies of the CZ, C, and CZ, Forms of Tetrahydrofuran, As Computed at Several Levels of Accuracy'

Cadioli et al.

level HFIST0-3Gd HF/3-21@ HF/4-31Gf HF/6-3 lGd MP2/6-3 lGd HF/6-31G*g HF/6-3 1 G*//HF/3-2 1 Ge MP2/6-3lG*//HF/3-2lGe HF/6-31G*(6D)dvh HF/6-3 1G**(6D)dJ MP2/6-3 1G*( 5D)da MP2/6-31Gt*(6D)d.'

C22 -228.149 828 -229.699 16 -230.634 59 -230.874 81 1 -231.357 205 -230.973 91 -230.973 61 -231.668 27 -230.976 690 -230.988 720 -231.677 391 -231.758 009

-0.737 1.24 1.33 1.081 1.027 0.74 0.50 0.54 0.383 0.428 0.308 0.401

2.391

2.65 2.725 3.461 3.45

3.375 3.410 4.738 4.833

Complete geometrical optimization, unless otherwise indicated. Absolute energies in au. Relative energies in kcal mol-' above the C2

energy. d Present results. e Reference 12. /Reference 10, partial geometrical optimization. g Reference 1 1, partial geometrical optimization.

The polarization functions over oxygen and carbons have exponents of 0.85 and0.75,respectively. Standardexponentsfor polarization functions on oxygen, carbon and hydrogen.

For NIS experiments, a sample of THF, initially dried over calcium hydride then heated under reflux over sodium during distillation, was put into a thin-walled aluminum container. The spectra were obtained at 30, 60, 90, and 120 K with the spectrometer TFXA,27 on the ISIS pulsed neutron source a t the Rutherford Appleton Laboratory, U.K. This spectrometer is a time-of-flight instrument with an inverse geometry and a time- focusing analyser; it gives good counting rates and good energy- transfer resolution (M/E = 0.02) over a wide range of energy transfer. The estimated absolute accuracy is A10 cm-1.

Results and Discussion Molecular Geometry. Total and relative energies obtained at

several computational levels of theoretical models for the three molecular symmetries C2, C,, and Cb are given in Table I, together with some results of ab initio computations by other authors. The energies of the B2 and B3 forms, which are intermediate between those of the C2 and C, forms, will be discussed later. Partial geometrical optimization with the STO-3G basis had given 0.65, 0.0 (reference) and 2.30 kcal mol-' as relative energies of the C2, C,, and Cb forms, respective1y;'O complete optimization leads to 0.74, 0.0, and 2.39 kcal mol-', respectively (our calculations) and, further, 4-3 1 G single-point energy computations using STO- 3G optimized parameters gave even worse results, 4.5,0.0, and 1.9 kcal mol-', respectively;2* this is contrary to any experimental indication and to the results of all the more sophisticated computations. As seen in Table I, the present result at the SCF 6-31G* level for the C2 structure is about only 1.7 kcal mol-' lower than that of a similar computation with partial optimization of bond parameters and with standard exponents of polarization functions;" our result for the C2 form at full-MP2/6-31G*(5D) is lower by more than 16 kcal mol-' than the frozen-core MP2/ 6-31G*(6D) treatment byMcKeeet~l.'~performedon the3-21G optimized geometry. On looking at the whole of the results, the following points

emerge. (i) The stability sequence C2 > C, > C, is constantly obtained, the only changes affecting the energy differences. (ii) The energy minimization and the computation of the harmonic force field show that the C2 structure is on the absolute minimum of the potential surface (no imaginary frequencies), the C, structure lies on a transition state (one imaginary frequency), and the Cb one on a relative maximum (two imaginary frequencies). These features are at variance with the one- dimensional potentials along the pseudorotational coordinate 4, as derived from assignment of the far-infrared and Raman spectra, where both the C2 and C, forms lie on relative energy maxima.293 (iii) Within the independent particle model, the CsC2 energy

TABLE Ik Theoretical and Experimental Geometrical Parameters for Tetrahydrofuran'

MP2/6-3 lG*(5D) parameter C2 C, Cb X-raybCz HRNPDCCz

143.53 152.58 152.80 109.96 109.52 109.42 109.57 109.30 106.17 101.12 109.32 108.38 110.93 113.59 108.36 112.89 110.38 113.78 110.18 108.37 118.66

121.31 -1 19.00

-1 16.76 -12.88

-39.07 32.94

36.21 35.32

-43.63 39.49

142.53 153.67 154.68 109.28 110.21 109.33 109.41 104.10 105.34 103.19 109.98 107.68 110.71 114.29 108.71 111.92 110.48 112.81 110.71 107.75 118.85

-1 18.00 120.96

-118.21 42.58

-25.30 0.00

-24.92 -28.01 0.00

39.74

142.70 153.89 154.08 109.72 109.72 109.34 109.34 111.76 108.63 105.49 108.44 108.44 111.73 111.73 107.77 110.94 110.94 111.20 111.20 107.13 119.58

-1 19.58 120.35

-120.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00

143.5(5) 153.1 (10) 153.1( 10) 109(5) 109(5) 109(5) 109(5) 109.8(3) 106.7(4) 101.9(3)

-1 1.7(3)

-35.2(4) 29.6(3)

3 5 4 4)

143.8(3) 151.6(3) 151.6(3) 1 10.1(4) 109.4(4) 109.4(4) 109.6(4) 109.9(3) 106.4(2) 102.6(2) 108.1 (2) 108.4( 3) 1 11.0(3) 112.1(3)

-11.3(2)

-34.5( 2) 28.8(2)

34.3(2)

MP2/6-3 1G*(5D) rotational wnst (MHz) C2 C, CZ, microwaved Cz

A 7120.2 7171.1 6999.6 7096.87 B 7005.2 6924.4 6890.4 6976.02 C 4029.8 4017.2 3800.6 4008.01 Kc 0.9256 0.8436 0.9317 0.9218 dipole moment ( D ) 1.896 1.682 1.932 1.75

a Bond lengths in pm, angles in degrees. Electron diffraction studies gave: rco = 142.8, rcc = 153.6, rCH = 111.5, and q = 38 pm (ref 6); r a = 142.8, rm = 153.8, and rCH = 111.0 pm (ref 7). bAt 148 K ref 8. High-resolution neutron powder diffraction, at 5 K ref 9. d From microwave, ground state; ref 2. Asymmetry parameter K = (2B - A - c)/U - c).

difference shows a regular trend with basis extension and tends to a value of about 0.4 kcal mol-'. At this level, polarization functions are needed to lower this difference below 1 kcal mol-', and only allowance for a complete geometrical relaxation with the polarized basis is able to reduce this difference below 0.5 kcal mol-'. In this particular respect, electron correlation effects are relatively unimportant and appear to be nearly basis-independent; moreover, their consideration can ameliorate the results only if applied to the geometrical structures optimized with an extended basis. Although a direct comparison of the Cs-C2 energy difference is not possible with experimental data, the present computations agree with the general experimental indication of a nearly free pseudorotational path (an overall pseudorotational barrier of about 150 cal mol-' has often been indicated or assumed). (iv) Instead, the Cb-Cz energy difference is raised both by basis extension within each model and by consideration of the electron correlation effects for each particular basis set. The best SCFand MP2 results, 3.4and 4.8 kcal mol-' respectively, lie around the experimental estimates of this barrier, 3.5-3.9 kcal mol-'.2,4 (v) Within each computational model, both C,-C2 and Cb-C2 energy differences fall into a relatively narrow range, although the individual bond parameters may vary largely from one model to another. For instance, the optimized C-O distance in the C2 structure is 144.41 pm a t the SCF/6-31G level, 149.28

Structure and Spectrum of Tetrahydrofuran The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 7847

TABLE III: Relative Energies and Conformational Parameters of Four Conformers of Tetrabydrofurao aloa tbe Pseudorotational Path as Computed at the MP2/631C*f5D) Level'

\ Y,

Q P

Figure 1. Atom numbering and definition of internal coordinates for the C2 conformation of tetrahydrofuran.

pm after full-MP2 treatment, 140.89 pm at SCF/6-31G*(6D) and 143.53 pm at MP2/6-31GS(5D); the bond parameters are not varied significantly by further addition of polarization functions on hydrogens.

Besides the electronic energies computed at the extrema of the potential surface, it is interesting to consider the zero-point vibrational energies (ZPVE). By computing the vibrational spectra for the C2 and C, structures at the MP2/6-31G* level, one finds ZPVE to be 75.183 and 75.262 kcal mol-', respectively. The further small stabilizing effect of the C2 structure corresponding to occupation of the ground vibrational state is in contradiction with the result of an SCF 3-21Gcalculation12 which gives78.72and78.69 kcalmol-',respectively. AttheSCF6-31G1 level, the ZPVE has practically the same value for the two structures, 78.914 and 78.913 kcal mol-', respectively. The energies for the C2 form include the contribution from the lowest normal mode (pseudorotation), quite overestimated by the harmonic approximation, 98 and 57 cal mol-' at the SCF and MP2 levels, respectively.

The results of the geometrical optimizations performed for the C2, C,, and C, structures at the full-MP2/6-31G*(5D) level are given in Table 11, together with the available experimental data (see Figure 1 for atom numbering). Analysis of the changes of individual equilibrium bond parameters on passing from one conformation to another reveals that ring angles C30C2,OC2C4, and C2C4C5 and dihedrals between ring bonds C3OC2C4, OC2C4C5, and C2C4CsC3, as described by the ab initio computations, are affected by substantial changes on passing from the C2 to the C, and C, structures of THF. A comparison between the individual parameters from electron diffraction and the calculated ones is not very meaningful. In fact, ab initio calculations refer to equilibrium configurations, while electron- diffraction data for THF represent a kind of average over molecules variously distorted on Occurrence of the pseudorotational motion, the distortion being dependent on the particular level that is Occupied. This is demonstrated by the considerable differences in the rotational constants measured for several excited states.2 Moreover, the differences between the bond legnths computed for the three forms are quite small. X-ray and HRNPD structure analyses have been the only other experimental sources of information on the configuration of the molecule. Both analyses

B1 39.74 0.00 107.686 B2 40.11 37.38 50.309 B3 39.61 73.20 7.461 T1 39.49 90.00 0.000

a Complete geometrical optimization, within a constrained model. bNames of conformers taken from Laane (ref 1). B1 and T1 coincide with the CS and Cz-symmetry forms, respectively; B2 and B3 represent bent forms with an a- or @-carbon, respectively, out of the plane of the other ring atoms. e The angular coordinate q5 for B2 and B3 is not exactly 36O and 72O, respectively, because theTHFring is nota regular pentagon.

establish that the molecule possesses C2 symmetry, but the bond parameters from the two sources do not match one another very precisely and appear to be temperature dependent to different extents. However, only minor changes with temperature are seen in geometric parameters most strictly controlling the molecular symmetry, Le., the ring-bond and torsional angles. On comparing experimental geometrical parameters with the theoretical ones for the C2 structure, only a few points deserve some comment. The experimental value of the dihedral angle C2C4CsC3, 35.0°, is definitely lower than that indicated by the ab initio calculation, 39.1O. This means that the THF molecule in the crystal is quite flatter than the isolated molecule depicted theoretically. A measure of the flatness of the molecule is given by the parameter q for the total puckering amplitude. This is defined by q2 = E,$, where the ZI are the Cartesian displacements of the atoms of the ring from their mean planeeZ9 A constant q is required as a necessary, though not sufficient, condition for a perfect separation between angular and radial normal modes, say for a circular and not an elliptic path in molecular inversion through pseudorotation in a (r, 4) coordinate system. From our calculations, q has nearly the same value for the C2 and C, forms, 39.5 and 39.7 pm, respectively. Experimental estimates of q cover a fairly wide range of values, the lower limit being found for the solid phase: 34.3 pm from HRNPDg and 35.5 pm from X-rays;s a similar value is found in a Monte Carlo simulation of the liquid.14 A value of 38 pm was inferred from electron diffraction: an average estimate of 44 pm was derived from far-infrared spectroscopy?O and 42 pm were obtained in a calculation of the vibrational levels using a nonfactored Hamil t~nian.~

A more meaningful insight into the overall molecular configuration of THF comes from analysis of the rotational constants, since they respond sensitively to even small changes in the whole geometry. These observables were obtained with great precision by microwave measurements for several pseudorotational states. If we compare our computed values for re with those determined for the ground state,z we find a particularly good agreement for the C2 structure; moreover, the C2 shape of the THF molecule, as depicted by the energy calculations, is the only one fitting the asymmetry parameter derived from the measured rotational constants.

The calculated dipole moment for the C2 form is 1.90 D, all along the C2 axis, while the experimental value in the ground pseudorotationalstateis 1.75 f 0.02 D.2 Engerholm etal.2pointed out that the absence of experimental evidence of a dipole-moment component po out of the mean plane of the ring is consistent with both of two indistinguishable possibilities, that of a low or zero pseudorotational barrier, and that of a high barrier with such a phase that the THF molecule assumes a twisted configuration having C2 symmetry. The present calculations are consistent with the former possibility; our overestimate of the experimental dipole moment by an 8% may be ascribed to a nonperfectly described electron charge distribution and to differences between equilibrium (re) and ground-state values, which can be of particular relevance in such a case of large-amplitude motion.


TABLE I V Observed Vibrational Swctra of Liauid and Gaseous Tetrahydrofuran.

Cadioli et al.

~~

Raman infrared liquid liquid

165 K 298 K D 173 K 298 K vapor assignment

2966.5 S

2940.0 8

2913 sh 2874.1 8

2719.0 mw

2662.0 W

1490.0 mw 1477.0 w 1463.0 W

1448.0 mw

1366.0 Vw

1335.5 vw

1291.3 vw

1242.0 mw

1233 sh

1175.5 vw

1142.0 Vw

1066.3 w

1031.0mw

955.0 vw 919.0 S

910 sh

2984 sh 2972.0 wb 2962.0 S

2941.0 s

2913.5 m

2860 sh 2875.5 s

2719.5 mw

2660.3 w

1488.0 mw

1462 sh

1449.5 mw

1477.0 W

1364.3 vw

1334.0 vw

1292.0 VW

1244 sh

1227.0 mw

1 1 7 8 . 0 ~ ~

1142.0 VW

1070.0 vw

1029.0 mw

913.oVS

0.05

0.05

0.05

0.10 0.05 0.05

dP

0.05

0.05

0.5

0.7 dP

dP

0.15

0.7

dP

dP

0.5

0.6

0.2

0.75

0.55

dpC

dFf

0.05c

2987 sh 2971 ms

2951 sh

2935 ms 2908 sh 2871 vs

2864 sh 2848 s

2717.0W 2684.2 vw

2654.3 W

1550 sh 1491 sh 1480 sh 1461.6mW

1448.0 W

1365.6 W

1334.5 vw 1306.3 vw 1290.9 W

1241.6 W, br

1210.~ vw 1190 sh

1175.7 mw, br

1131.3 VW 1071 vs

1030.8 mw

952 sh 917 ms

910 sh

2976.0 s

2952 sh

2934 sh 2912 sh 2876 sh

2858.0 s

2718.oW 2682.5 vw

2654.3 w

1559.0 vw 1492 sh

1460.6 W

1449.5 vw

1364.9 W

1333.2 vw

1290.1 vw 1308 sh

1241 .O VW, br

1181.3 w, br

1070.0 VS

10314w

895 sh 0. I f 896 m 869.1 w 839.4 W

865 sh dpc 840.0 VW 840 sh pC

805 sh

867 sh 838 sh 804 sh

2981.3 br

2870.8 br

2862.2 2854.3 br 2851.7

1463.8 1463.2 1453.3 1452.1 1412.1 1367.7 1367.1 1366.6

1294.0 1291.1 1285.9 1273.1 1271.9 1271.2 1268.9 1255.3 1253.4 1250.7 1249.9 1240.1 1239.7 1238.1 1237.6 1192.7 1203.2 1202.4 1175.6 1175.1 1174.3

1128.7

1087.8 1084.8 1026.0 1025.6 1003.0 999.0 975.8

932.3 931.6 921.7 921.2 920.0 919.1 917.5 916.1 915.1

868.8 835.6 802.7

Structure and Spectrum of Tetrahydrofuran The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 7849

TABLE IV (Continued) ~~

Raman infrared liquid liquid

165 K 298 K P 173 K 298 K vapor assignment 800.9 799.1

644.0

574.3

664.0 vw 657.0 vw 0.7 662.8 mw 658 w 644.4 VI6

580.5 vw 591.0W 0.7 580.5 vw 575.0 V32

285.5 vw 286.0 vw 0.75 290.0 w, br 260.2d VI7 75 mw, br dipolar band

a Frequencies in cm-1. The depolarization ratios have been measured at 295 K. IR relative peak intensities have been estimated from absorbance recordings. For the vapor-phase bands only the frequencies of the central Q-lines are reported (see text). From ZVH trace. Measured on the liquid at 165 K. At 295 K, the 913-cm-l band yields an overall depolarization ratio of 0.03. dAccording to refs 4 and 5.

As concerns the pseudorotational path, the energies of the B2 and B3 forms can be used together with those of the C, and C2 forms to describe the potential-energy curve to ring inversion, V’(q, 4). The MP2 results, resumed in Table 111, depict a very small change in the q coordinate as 4 goes from Oo (C, form) to 90° (Czform). As a first approximation, onecould take a constant q value and derive the following potential:

V(4) = 43.322 + 51.129 cos 24 + 10.521 cos 44 + 2.714 cos 104 cm-1 where we have chosen to include the cos 104 term in order to keep a trace of the parent molecule, cyclopentane, where that term is the first nonzero contribution to the potential. The coefficients of cos24 and cos44 are in phase, like those derived by several authors in a tentative reproduction of the observed splittings of the two first pairs of pseudorotational levels and in the vibrational assignment of the far-infrared spectrum by a one- dimensional appro~imation.~,3.~ But their relative weights, 5 1 and 11 cm-’, respectively, are quite different from those derived by Greenhouse and Strauss (27 and 40 cm-l),’ by Engerholm et al. (30 and 40 cm-l)* and by Sont and Wieser (36 and 40 cm-l, in an expansion where the cos64 coefficient is 13 cm-l).’ Using the same one-vibration approximation with the above-quoted MP2 potential and a fixed pseudorotational constant, 3.19 cm-I,3 we did not succeed in a close fitting of the observed pseudorotational transitions and, above all, of the reported splittings in the two low-lying pairs of levels. This failure may be due to insufficiencies of the ab initio computations, to the approximations of the fixed q and effective mass and, mainly, to the one-vibration model itself, without coupling with rotation and normal modes of higher energy.

Infrared and Raman Spectra. The infrared and Raman spectra for liquid and gaseous THF are reported in Table IV, and those for the solid phase are in Tables V and VI. The infrared and Raman spectra for the liquid phase at room temperature display numerous weak, broad, and overlapping bands; we found these features quite consistent with the theoretical prediction of several fundamentals occurring in almost degenerate pairs or distributed closely together in clusters, and of an absorption spectrum of widespread weak intensity. A very satisfactory resolution was attained only at low temperature, near the freezing point of the substance: by taking full advantage of the natural line-narrowing effect and of the quenching of the pseudorotational motion, we eventually were able to obtain very detailed infrared and Raman spectra, with sharp lines and some evident shoulders, where all the fundamentals expected between 3000 and 200 cm-l, but one, were identified and attributed (Figure 2).

The spectra of the solid strictly relate to those for the liquid at low temperature and together they form the firm experimental basis on which the attribution of the fundamentals was carried out. Besides, although nearly uninfluential in the search for the normal frequencies, the spectra of the solid happened to be marked with intriguing features. In fact, on comparing infrared and Raman frequencies, they appear to be subjected to the rule of mutual exclusion; Le., the frequencies of the absorption and

scattering lines generally do not coincide but are just some wavenumbers apart. This is an effect of the crystal field: THF crystallizes in the monoclinic system, space group C 2 / c , with four molecules in the unit cell located on the twofold axis of the space group.6 Consequently, the selection rules for the crystal in the presence of a factor C2h predict splitting of the free-molecule normal modes into two components: A - A,, A, and B - B,, B,. One of these is Raman active, and one is infrared active, according to the g and u symmetry of the unit-cell modes. Detailed inspection of our spectra, however, demonstrated that these rules, although they were generally fulfilled, were not sufficient to explain all the main features. In the Raman spectra, almost all the fundamentals appeared in single lines, but in a few cases the Occurrence of sharp doublets had to be admitted. A more varied scene was met in the infrared: a number of fundamentals appeared in single lines and one in a sharp doublet, but the majority manifested themselves in single lines with a secondary multiplet structure; Le., they were accompanied with other unresolved or slightly resolved weak lines superimposed on the main absorption profile. We did not understand the origin of this fine structure. Infrared line half-widths, moreover, were of various magnitude, ranging from about 3 to 15 cm-I (e.g., the ~ 3 2 and vlo, respectively) and the b’28 mode appeared in a band with a modulated contour of more than 50 cm-1 half-width. We could not make out what the origin of such a variable fine structure would be, nor of the great variability of the relative intensities of the Raman lines, nor of the widely different half-widths of the infrared lines. Since THF has a very flexible structure and at the temperatures reached in our experiments the molecules may not have been rigid enough to allow a perfect crystallization, we feel that for the purpose of a better comprehension of the spectra of the solid it would be necessary to inspect the optical spectra down to the lowest temperatures.

The infrared spectrum for the vapor represents a special case. On theone hand, it mostly displays ill-defined absorption envelopes merging with one another, where the band centers are often seen with difficulty or not seen at all. On the other hand, under 0.1 cm-1 resolution and below 1500 cm-l, a striking multitude of closely and unequally spaced sharp weak lines, superimposed on several band absorption profiles or aside from them, was brought to light. Since their features are by no means amenable to ordinary rotational structure, we have been led to attribute them to pseudorotational structure in summation or difference tones between mid-frequency modes and the ring-puckering vibration of lowest frequency, Le., the ring-puckering motion along which the free molecule experiences the inversion. Thus, the mid- infrared spectrum of the vapor is invaded by the marks of the most peculiar motion of the molecule. We are convinced that, owing to the large band overlaps above mentioned, there is not much hope of succeeding in picking out the line sequences belonging to the various tones; nevertheless, there is one exception to this, and is represented by the weak isolated band q6, attributed to the A-species ring-angle bending mode of higher frequency


TABLE V Observed Vibrational Suectra of Solid Tetrahvdrofuran.

Cadioli et al.

Raman infrared NIS 30 K 85 K b 150 K 90 Kb 90 Kc assignment

1498

1480

1450

1388

1323 1289

1258

1193

1150

2996 sh 2988.0 s 2987.0 s 2988.9 ms

2986.5 ms 2980.0 w 2979.0 vw 2978.2 m

2974.5 m 2971.5 m

2878.0 W 2879.0 vw

2859.0 vs 2860.5 VS

1508.5 w 1494.0 W 1484.3 vw

1472.5 m 1464.0 m

1373.5 W

1342.5 W 1313.5 W 1302.0 W

1252.0 mw

1242.5 mw 1188.5 mw 1178.5 vw, br

1144.0 W

1057.5 w

1508.0 W 1495.0 w 1484.5 YW

1472.5 m 1464.0 w

1144.5 W

1060.5 w

1046 1038.0 m 1039.0 mw

97 1 959.5 w 9 6 1 . 0 ~

889 883.0 vs 877.0 W

886.5 vs 880.5 w

2960.3 m 2955.2 m 2950.7 m 2944.6 ms 2936.9 m 2935.4 m 2921.5 s 2912 sh 2906 sh 2882.0 s, br

2862 sh 2858.9 s 2854 sh 2852 sh 2845 sh

1497.5 vw, br 1490.0 m 1486.0 m 1478.2 vvw 1464.9 m

1441.0 s

1418.9 w 1368.9 m 1365.5 sh 1337.8 w 1320.9 m 1304.0 m 1295.1 vw 1247.5 sh 1245.1 s

1180.0 ms, br

1162.0 sh 1151.1 w 1141.5 vvw 1130.8 ww 1115sh 1092.0 vvw 1070.0 w 1054.5 ms 1049.2 vvw 1030.0 vvw 1025 sh 1039.2 s

987.5 ww 980.4 w, br

954.1 ms 95 1.5 sh 947.5 sh 925.5 sh 922.9 ms 919.5 w 910.4 m 909.5 sh 904.2 vvw 895.5 w 891.1 ms 889 sh 880.7 vvw 879.5 ww

3000 sh 2986.8 s

2978.3 mw

2966.8 m 2959.3 m

2945.0 ms, br 2934.5 m

2921.2 s 2913 sh 2906 sh 2884.8 sh 2879 ms, br 2874 sh 2859.0 vs

2842.6 w

1497.2 vw 1489.0 mw 1487.5 mw

1467.3 mw 1463 sh 1447 sh 1440.9 s 1419.1 w 1369.0 mw 1366 sh 1337.7 w 1320.2 mw 1304.9 mw, br 1295.0 vw 1251 sh 1244.7 vs

1183.2 s 1180.8 s 1162.5 sh 1151.5 w 1141.5 w w 1 1 3 1 . 0 ~ ~ 1113 w, br 1092.3 w, br 1072 sh 1030.3 vw 1020 sh

1 0 4 2 . 0 ~ ~ *

1038.8 vs 1036.8 s 987.2 vw 911 w, br 973.5 w 953 mw, br

926.4 w 919.4 w

912.5 sh 909.8 ms

895.8 vw 886.6 w, br 879.5 sh 877.0 s


TABLE V (Continued)


Raman infrared NIS 30 K 85 Kb 150 K 90 Kb 90 Kc assignment

847

877.0 w

864.1 ww 8 5 3 . 7 ~ ~

866.5 w 866.5 vw, br 872.2 ms, br

840.3 w 841 .o vw 841 sh 838.2 ms, br 826.5 vvw 805 sh 727.5 w, br 693.5 vw 681 sh

670 666.5 w 665.5 w 665.5 m 650.5 w w

589 587.5 w 587.5 W 584.8 m

872.0 sh Y3 I 868.5 sh 864.0 vw 853.6 vw 841.9 m, br V I 3 836 sh 826.6 vw 803 w, br

693.0 vw 682 sh

650.6 vw

727.8 w, br 0 2 + v33

666 mw, br VI6

584.9 mw v31

a Frequencies in cm-I. IR relative peak intensities have been estimated from absorbance recordings. b Annealed solid. Direct solid.

TABLE VI: Neutron Inelastic Scattering, Raman and Infrared Low-Frequency Spectra of Solid Tetrahydrofuran.

NIS Raman infrared 30 K 60 K 90 K 120 K 85 Kb 150 K 90 Kb assignment

301 298 298 293 299.0 vw, br 295 vw, br 289.8 vw, br VI7 255 255 252 242 242 vw, br 240 sh 2 - 0 Y33

229 vvw, br 218 vvw, br 208 vvw, br 200 ww, br 165 sh 160 sh 152.5 VW 149.0 vw 144.0 vw, br

143 139 137 134 135 vw, br 131.5 ww 0 3

126 124 124 118 125.0 W 117.0 w, br 121 sh lattice 108 108 105 103 w 104.0 W 118.5 vw, br

76 75 69.5 w 64.0 vw, br 97.5 vw, br 68 67 61 57 38.5 w 87.5 vvw, br 57 57 14.5 vw 80 vw

Frequencies in cm-'. IR relative peak intensities have been estimated from absorbance recordings. Annealed solid.

vibrations 100 98 97 95 80.0 vw 72.5 VW 107.5 w

(Figure 3). Line sequences are seen both in the high- and in the low-frequency side of the whole band. However, when we tried to explain them as belonging to summation and difference transitions as mentioned above and we took the band center at 644.4 cm-', we did not succeed in recognizing the line sequence seen in the far-infrared spectrum and attributed to the transitions for the pure pseudorotational This departure would indicate that some interaction occurs between pseudorotation and higher-frequency vibration modes, which is equivalent to admitting that when the molecule passes in the first-excited level of these, even a slight interaction can remodulate the weak potential hindering molecular inversion through the C, form. The sequence in the summation tone might also be complicated by the presence of a difference tone between ~ 1 3 or ~ 3 0 and Y17; however, the sequence in the low-frequency side of the band Y16, as a difference tone, should be related to the exact levels of the pure pseudorotation.

The previous Raman and infrared spectra for liquid THF bear only a rough relation to those presented in this work. In the early Raman spectrum by Kohlrausch and Reitz,*s only 13 lines are reported that can match, within 10 cm-I, lines of the present spectrum; three more, at 1104,964, and 215 cm-1, of which we did not find any trace in our recordings, must be considered spurious. Infrared spectra of liquid THF were published by Tschamler and Voetter16 and by Palm and Bissell'' for the 3000450-~m-~ region, where 11 and 12 fundamentals, respectively, are reported, with near frequencies (within 8-6 cm-l) to those of bands recorded in our spectrum. Nine of them are to

be considered as counterparts of Raman lines. Infrared spectra of solid THF were reported by Palm and Bissell for the 3000450-~m-~ region" and by Fore1 et al. for the 1500450-cm-1 interval.'* For the interval in common, they practically give the same lines, with only small differences in the tabulated frequencies. Their spectra are also substantially similar to ours; our spectra, however, cover the full rangeof interest, 3OOO-8Ocm-1, and display the effect of the crystal field. No Raman spectrum of solid THF has thus far been reported in literature and that presented in this work represents quite a new contribution. The only infrared spectrum for gaseous THF is that by Palm and Bissell reported for the 3000450-cm-1 region.17 Its resolution appears to be exceedingly low, so that the frequencies indicated for 11 fundamentals now come out to be rather unreliable; in particular, a band given at 1238 cm-1, and classified as strong, does not appear at all in our spectra.

In our work, we have also recorded the infrared and Raman spectra of 10% mixtures of THF in CCI, and CS2, which were useful for a better examination of minute details and broad absorption envelopes of the liquid. We have observed that in CC14 no appreciable frequency shift happened, whereas CSz acted more as a solvent, with diffuse downward frequency shifts. These were more apparent, of the order of 6-8 cm-1, in the CH-stretching region, where, besides, both solvents gave far better resolution in comparison with the spectrum of the pure liquid.

NIS Spectra. One of the main characteristics of neutron spectroscopy is the absence of selection rules so that all the vibrational modes can be observed, albeit with different intensities.


2 . 8 2 . 6 2 . 4 2 . 2 2 . 0

t 1 . 8 5 1 . 6 w 1 . 4 2 1 . 2 a p 1 . 0

v)

0.8 0 . 6 0 . 4 0 . 2 - 0 . 0 - 0 . 2

m

Cadioli et al.

Figure 2.

2 . 1

1.9

Lo 1 . 7 I- * 1.5

1 . 3

1 . 1

0 .9

0 .7

0 . 5

0 . 3

0 . 1

3

u

m

Lo

Infrared spectra WRVENUMBER CM-1

of liquid THF at 173 K (A) and of the annealed solid at 90 K (B). of liquid THF at 173 K (A) and of the annealed solid at 90 K (B).

1 0 0 . 0 +

6 5 . 0 4 6 0 . 0 4 I c

740 720 700 680 660 640 620 600 580 560 WRYENUMBER C M - I

Figure 3. The IR ring-bending band Y16 of gastous THF showing pseudorotational structure. The line at 667.6 cm-l belongs to COz.

The spectra have, however, to be recorded at low temperature to minimize the effect of the Debye-Waller factor. This factor, exp(-QZ( uz)), reduces band intensities with increasing momentum transfer Q (on a spectrometer of the type used in this work, QZ is proportional to the energy transfer). The influence of the Debye-Waller factor is particularly striking for large mean-square displacements ( u2) , which is the case for THF. The NIS spectra were therefore recorded for the solid phase, the aim being to check the vibrational assignment of the modes above 400 cm-l and to find out the position of the lowest ring-puckering vibration. The NIS spectrum was simulated only for the part above 400 cm-l, for the harmonic motions, the pseudorotational mode becoming a large-amplitude ring-deformation vibration in the solid (see below). The simulation of the NIS spectrum was accomplished by calculating the intensity including the contributions from the fundamentals and from the multiphonon processes due to the lattice modes, according to the method described in ref 26. Theoretical data were used as inputs in the present work, i.e., the MP2/6-3 1G* vibration frequencies uni- formly scaled by a factor of 0.95 and the hydrogen mass-weighted

1

sm tm Ism um 5m I m , Ism 2000

Energy transfer (a") Energy m s f e r (cm-')

Figure 4. NIS spectra of solid THF between 400 and 2000 cm-'. Experimental: 30 K (A), 60 K (B) and 120 K (C); simulattd: 30 K (D), 60 K (E) and 120 K (F). Intensities are given in arbitrary units.

displacements, the carbon and oxygen atoms being neglected because of their much smaller incoherent cross section. The effect of the Debye-Waller factor and the instrumental resolution were taken into account. The calculated spectra are shown in Figure 4 for temperatures of 30,60, and 120 K, the agreement with the experimental spectra being satisfactory. The fundamentals have a sharper appearance at the lowest temperature (Figure 4A), and in the energy range from 400 to 1500 cm-1 the sequence of NIS peaks turnsout to bein fair agreement with the opticalvibrational frequencies. Because of the instrumental resolution, in some instances NIS peaksmay be connected, in Table V, with frequency pairs in the optical spectrum.

In the low-frequency region, Figure 8, the lattice modes are easily distinguished from the intramolecular ones by the fact that they are less sensitive to a temperature rise in the solid phase. The peak positions of the intramolecular modes are tabulated in Table VI.

Vibrational Assignment. The 33 normalvibrations of the THF molecule are distributed into A and B species according to the


1 2 . 0 it

' V 3 . 0

1100 1095 1090 1885 1080 1 0 7 5 1070 WRYENUMBER C M - 1

Figure 5. The center of the IR v&OC band Y28 of gaseous THF.

irreducible representation I'(C2) = 17A + 16B. Our attribution of the fundamentals has been based on a comprehensive examination of the infrared and Raman spectra for the various aggregation states, on discrimination of the A and B species by measurement of the Raman depolarization ratios and on strict consideration of the normal-frequency spectrum calculated from the ab-initio force field. Owing to the diffuse band overlaps and the Occurrence of pseudorotational fine structure, no useful analysis could generally be carried out in terms of A- and B + C-type gas-phase absorption envelopes of an asymmetric rotor, nor in terms of parallel- and perpendicular-like bands of a nearly oblate rotor. In this respect, we only mention the appearance of a parallel-like rotational structure near the center of the strong infrared band v28, (Figure 5 ) , where the components are likely to be splitted by Coriolis interaction and their intervals rapidly increase from 0.42 to 0.51 cm-l on passing from the R- to the P-branch (to be compared with a value for A + B of 0.469 cm-l as derived in the rigid-molecule approximation from the ground- state rotational constants of ref 2). Of all the spectra for the various aggregation states, that for the vapor has been the least useful for the search for the fundamentals. Therefore, for most normal vibrations of THF it has not been possible to know the frequencies of the free molecule, and, for the presentation of the complete set of the normal frequencies, it has been necessary to resort to the spectra of the condensed phases. In the assignation table (Table VIII) we have preferred to present the Raman frequencies for the liquid; in a few instances, where the Raman lines are missing, the infrared frequencies have been introduced.

In the 3000-cm-1 region, the infrared and Raman spectra of the liquid have quite a complementary character and the theoretical prediction of the Occurrence of A- and B-species vibrations in nearly degenerate pairs is confirmed. The variable- temperature study on the Raman spectra showed the rapid disappearance, on cooling, of two pronounced humps on the lines v1 and v4, respectively (Figure 6). These had the same polarization as v1 and v4 and, in the spectra of the apolar solutions, they appeared as resolved lines. No like behavior was observed in the rest of the spectrum and we had no reasons to explain the pair character of V I and v4 either as manifestation of conformational equilibrium or as effect of pseudorotational dynamics. The Occurrence of Fermi doublets seemed to us the only possible alternative explanation.

Below 1500 cm-l, there is almost a complete correspondence between the spectra of the liquid at low temperature and those of the solid. The most difficult correlation happens for the CH2- bending vibrations v5, v22, V6, and ~ 2 3 , where large differences are seen between the frequencies of the IR and Raman spectra of the solid and between these and the ones of the liquid. As concerns the attribution of the other fundamentals, a few points are worthy


I , 3100 2900 2700

lJ m - 1

Figure 6. Raman spectrum of liquid THF in the 3000-~m-~ region: A at 340 K, B at 165 K. The two sharp lines inserted at 3095.0 and 2813.3 cm-l are Ne calibration lines.

to be mentioned. As counterparts of the three fundamentals vl0, ~ 2 7 , and v11 predicted by the ab initio calculations in that order with close frequencies, there occur in the IR and Raman only two bands; owing to their depolarization ratios, these must be attributed to the v10 and v11 vibrations. The broadness of the infrared band Y ~ O , both in the liquid and in the solid, might justify taking ~ 2 7 as nearly degenerate with vlo; the attribution to ~ 2 7 of a very weak and unresolved line at 1162.0 cm-I, on the low- frequency side of the infrared line v10 in the solid, seemed to us preferable on account of the indications of the computed spectrum.

The most intriguing case of near-degeneracy in the whole spectrum of THF is certainly that concerning the ring-stretching vibrations ~13, ~30, and ~ 1 4 , that in the liquid at room temperature appear to be cast in a single band, at 9 1 1 cm-1 in infrared and 9 13 cm-I in Raman. On cooling, a progressive resolution takes place, and near the freezing point of the substance the three components become fairly visible, with quite differentiated frequencies. At the same time, the temperature lowering brings out the appearance and resolution of three additional close and weak bands, ~29, ~ 3 1 , and ~15, attributed to modes of prevailingly CH2-rocking character (Figure 7). Thus, a major difficulty in interpreting the spectrum of liquid THF at room temperature has been overcome, by showing the "hidden" presence between 800 and 1000 cm-l of six fundamentals around a single apparent band. The frequencies of the vibrations ~ 1 3 , ~ 3 0 , and ~ 1 4 diverge furthermore in the solid, and a similar behaviour is observed for the other two ring-stretching vibrations v28 and v12. For instance, the frequency v28, 1084.8 cm-' in the vapor, passes to 1070 cm-l in the liquid and to 1054.5 cm-1 in the solid. We believe that the observed frequency shifts, which are particularly considerable for the ring-stretching vibrations, cannot be ascribed solely to variations of the intermolecular forces from one phase to another but must also depend on alteration of the nuclear configuration accompanying the phase changes and measured with the parameter q (see above).

For the present vibrational assignment, the 33 normal modes have been expressed in terms of symmetry coordinates (Table VII); 29 of them are simple combinations of classical bond-stretch

7854 The Journal of Physical Chemistry, Vol. 97, No. 30,1993

0 1000 900 I

LJ / cm-1 I

Figure 7. IVV (A) and IVH (B) Raman recordings of liquid THF at 165 K in the ring-stretching and CH2-rocking region, and corresponding Raman spectrum of the annealed solid at 85 K (C).

and angle-deformation coordinates, with assumption of a local symmetry in the CH2 groups. The remaining four coordinates, two for each symmetry type, are intended to describe the two ring-angle bending vibrations and the two ring puckering modes. The coefficients of the individual ring-bond angles and ring-bond torsions were obtained by normalization of the eigenvectors corresponding to the two highest eigenvalues of each of the two Wilson G-matrices built over the five ring-angle bendings and ring-bond torsion^.^' The ratios between individual coefficients are rather different from those of a regular and planar pentagon, as given by Pulay et ala3*

The observed fundamentals and the proposed assignment are reported in Table VIII. In order to gain a high accuracy in the calculated spectrum, we overcame the independent particle SCF model through a perturbative treatment of the electron correlation at the MP2 level, a procedure already seen to ensure a definite improvement in the prediction of the vibrational spectra of small molecule^.^' The calculated spectrum, characterized by an overestimate of the normal frequencies gradually diminishing from a 7% to a 4% between 3000 and 800 cm-1, can be considered of satisfactory precision, and in fact the indication it yields of the distribution of the fundamentals was of invaluable help as a guide for the search of these during the recording of the spectra. The preliminary SCF computation with the same polarized basis had given overestimates ranging from 12 to 8% and, moreover, a somewhat different sequence of the normal modes and diffuse differences in the potential energy distribution.

The spectrum is dominated by the manifestations of the C-H motions. The normal-coordinate description reveals that a-CH2 and &CH2 stretching and bending vibrations are separated to a high extent, and the other C-H deformation vibrations becomes increasingly mixed on passing from wagging to twisting and rocking. The separation between ar-CHz and @-CH2 motions had already been qualitatively indicated;19 however, the present treatment shows that stretching vibrations in @CH2 are faster than in a-CH2 and that the reverse happens for the bending motions. In an analogous manner, the C-C and C-O stretching motions appear to be almost unmixed. Thus, there does not exist a genuine breathing vibration; the motion most resembling it is that of the mode ~ 1 3 , concentrated on the CCCC frame. Such

Cadioli et al.

TABLE W: Symmetry Coordinates for Tetrahydrofuran' coordinate description

a(CH2) wag

B(CH2) wag

a(CH2) twist

B(CH2) twist

a(CH2) rock

W H d rock

COC sym stretch C.C# sym stretch C&p stretch ring bend

ring pucker

a(CH2) sym stretch a(CH2) asym stretch B(CH2) sym stretch B(CH2) asym stretch a(CH2) bend

W H d bend

a(CH2) wag

B(CH2) wag

a(CH2) twist

B(CH2) twist

a(CH2) rock

B(CH2) rock

COC asym stretch c&# asym stretch ring bend

ring pucker

a See Figure 1 for definition of internal coordinates.

a description is peculiar to the MP2 treatment; with the SCF force constants, the C-O stretchings enter this mode with a certain weight (10%). The ring-bond stretchings are responsible for the most intense Raman bands ~ 1 3 and ~ 1 4 and the mid-infrared band Yza.

Of the two ring-puckering vibrations, the radial one has a computed frequency of 279.8 cm-l that compares favorably with the 260-cm-1 frequency proposed for this fundamental in the vapor pha~e;~ysJ~ this success of the harmonic approximation may be explained by the considerable depth of the two equivalent potential wells along the inversion track of the Cz form through the planar CZ, conformer, correctly described by the form of the computed normal coordinate. For the angular mode, governed by a periodic and very flat potential, the energy prediction by the harmonic approximation meets with a complete failure. Further, this very particular mode is pictured in that approximation


TABLE MI: Vibrational Assignment of THF’

The Journal of Physical Chemistry, Vol. 97. No. 30, 1993 7855

computed MP2/6-31G* observed I P o o / w c assignmentb

3181.2 3153.2 3119.6 3077.6 1595.9 1553.1 1438.5 1387.4 1293.9 1229.8 1207.1 1071.9 967.3 940.6 872.5 674.7 279.8

3191.2 3152.6 3120.2 3073.5 1583.4 1543.8 1402.6 1348.5 1294.5 1213.5 1143.5 997.7 943.7 914.3 584.9 (39.5)h

2962.0 2941 .o 2913.5 2875.5 1488.0 1462 1364.5 1308 shC 1227.0 1178.0 1142.0 1029.0 919.0 Sd

840.0 Wd 657.0

895 shd

286.0~

2972.0 w.f 2934 shc 2912 she 2858.0 sc 1477.0 1449.5 1334.0 1292.0 1244 1 16L0 shg

910 shd 865 shd

1070.0 955.0 Wd

591.0

A Species 210 0.05 200 0.05 110 0.10 220 0.05 25 0.5 sh 0.7 5 0.15

25 0.5 3 br 0.6 1 0.2 30 0.55 350 0.03

0.1 P

3 br 0.7 4 br 0.75

B Species dP

23 dP sh dP

1 br dP 2 br 0.7

22 br dp

6 br 0.75 dP dP dP

3 br 0.7

0.93 1 0.933 0.934 0.934 0.932 0.941 0.949 0.943 0.948 0.958 0.946 0.960 0.950 0.952 0.963 0.974 1.022

0.93 1 0.93 1 0.933 0.930 0.933 0.939 0.95 1 0.958 0.961 0.958 0.936 0.957 0.964 0.946 1.010

a Observed Raman frequencies, in cm-l, for liquid THF at 298 K, unless otherwise indicated; br broad, s strong, sh shoulder, w weak, dp depolarized and p polarized (estimated); I apparent relative peak intensity; p depolarization ratio IvH/Iw; w,, and w, observed and calculated frequencies. Scc Table VI1 for definition of the symmetry coordinates. In the assignment, the potential energy matrix is calculated from the potential energy distribution function proposed by Morino and Kuchitsu (refs 24 and 35); contributions less than 5% are omitted. Infrared frequency (liquid). d The six lines from 955 to 840 cm-1 are neatly resolved only with the liquid at 165 K at room temperature one only line of overwhelming intensity is present, at 913 cm-l, and shoulders at 895 and 840 cm-1 are seen with difficulty. Intensity and depolarization ratio of vi3 actually refer to the room temperature line.e 260.2 cm-1 in the vapor phase (ref 5 ) . J From the IVH Raman trace. g Infrared frequency of the solid phase. Pseudorotational mode, as estimated in the harmonic approximation (see text).

essentially as an out-of-phase torsion around the two C-C bonds that brings the oxygen atom up and down the ring mean plane, which neither by symmetry nor by form does match the pseudorotational path going from one enantiomeric form C2 to the other through the C, structure.

The Low-Frequency Spectrum of the Solid Phase. In addition to a few narrow lines attributable to lattice vibrations, the low- frequency Raman spectrum of solid THF below 150 K exhibits the rise of two new broad and weak lines a t about 240 and 135 cm-1, of which the intensity increases on lowering temperature. A very weak and broad absorption at about 240 cm-’ and a weak and broad line a t 144 cm-I are seen as the infrared counterparts. The two Raman lines had already been observed by Aleksanyan and Antipov who followed the low-frequency Raman spectrum down to 20 K.36 At this temperature, a new line, the process of formation of which occurred reversibly between 150 and 40 K, was observed at 249 cm-l, and they assigned it to an out-of-plane skeletal vibration in a restricted nonplanar conformation, the restriction being “due to a change of molecular potential caused by intermolecular forces”. No particular attention, however, was paid to the other line, reported at 141 cm-1 together with lattice frequencies.36

Two peaks in the frequency intervals 242-255 and 134-143 cm-1 have been observed between 120 and 30 K in our NIS experiments (Figure 8). Their intensity is strongly increasing on cooling, so their attribution to latticevibrations must be discarded. As already mentioned, the Debye-Waller factor has an increasing

1 I

I I I 0 100 200 300 400

Energy transfer (cm-1) Figure 8. NIS spectra of the lattice and low-frequency modes of THF between 0 and 400 cm-’. 30 K (A), 60 K (B), 90 K (C) and 120 K (D). Intensities are given in arbitrary units.

effective influence as the temperature increases, by redistributing the intensity of the lattice modes around the intramolecular modes. In this case, it is responsible of the decrease of intensity of the lowest-frequency internal mode.

7856 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 Cadioli et al.

Accordingly, it appears to us quite reasonable to assign the two Raman lines at 242 and 135 cm-1 (85 K) and the corresponding NIS peaks at 252 and 137 cm-* (90 K) to the 2 - 0 and 1 - 0 transitions of the large-amplitude ring-deformation vibration substitute in the solid THF for the pseudorotational motion of the free molecule. Moreover, the attribution of the 135-cm-1 Raman line to an intramolecular fundamental mode is strongly supported by the fact that the corresponding infrared line at 144 cm-1 taken as fundamental represents the sole possibility to explain a line at 727.5 cm-1 in the infrared spectrum of the solid: ~ 3 2 + v33 = 585 + 144 = 729 cm-1. In a very recent paper, results of incoherent neutron scattering experiments on solid cyclopentane are reported3’ that evidence the Occurrence of two low-frequency peaks, 270 and 136 cm-1 at 5 K; these are assigned to the 2 +

0 and 1 + 0 jumps of the ring deformation vibration to which in the solid the free pseudorotation is reduced by intermolecular forces.

There are important variations of the mean square amplitude, from 0.010 at 30 K to 0.030 at 120 K for the hydrogen atoms due to the lattice modes and from 0.010 at 30 K to 0.022 at 120 K for the hydrogen atoms due to the internal modes. This property agrees with a similar observation by HRNPD for the deuterated m~lecu le .~ The increase of the mean square amplitude of the internal modes, unexpected in this range of temperature for the rigid molecules, indicates an unusual extent of nuclear mobility of THF even at the lowest temperature.

Acknowledgment. This work was supported in part by CNR funds and performed with the facilities of the Centro di Calcolo (CICAIA) and Centro Strumenti (CIGS), Modena University. Helpful discussions with Prof. M. G. Giorgini (Bologna Uni- versity) are gratefully acknowledged. The authors thank Dr. J. Tomkinson and the Rutherford Appleton Laboratory staff for their technical assistance in recording the spectra on the TFXA spectrometer.

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Geometric structure and vibrational spectrum of tetrahydrofuran

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