J. Phys. Chem. 1994,98, 4998-5009
4998
IR Transition Moments of 1,3-Dimethyluracil: Linear Dichroism Measurements and ab Initio Calculations Anders Holm&,' Anders Broo," and Bo Albinssonlb Department of Physical Chemistry, Chalmers University of Technology, 41 2 96 Gcteborg, Sweden Received: January 12. 19940
The vibrational transition moment directions of 1,3-dimethyluracil (DMU), 1,3-dimethyluraciI-5-d (DMU5 - 4 , and 1,3-dimethyluracil-6-d ( D M U - 6 - 4 have been determined from measurements of polarized I R spectra on samples partially aligned in stretched poly(viny1 alcohol) and by ab initio calculations at the HF/6-31G' level of approximation. The agreement between experiments and theory is good. I R spectra of DMU, DMU5-d, and DMU-6-d in KBr and in D 2 0 form, together with the calculated spectra and the I R polarizations, the basis for some reassignments. Special attention is paid to the double-bond region, where the high-frequency carbonyl stretching mode is assigned to an in-phase vibration of the C40 and the C20. This vibration is polarized in a direction almost bisecting the angle between the two carbonyl bonds, in agreement with an in-phase assignment. The low-frequency mode is the out-of-phase vibration of the two carbonyl groups, and it is consequently polarized perpendicular to the high-frequency mode. In order to determine the orientation axisof D M U in the polymer matrix, theUVlineardichroism (LD) spectrum was measuredand the polarizations of theelectronic transitions wereestimated froma semiempiricalself-consistent reaction field (SCRF) calculation including solvent effects. Thecombined information from IR LDand UV LDshows that themolecular orientation axis in the stretched film experiment is parallel to the first I + I* transition in DMU.
Introduction The vibrational spectra and force fields of the pyrimidine bases have attracted much attention during the last 40 years. The reason for this is of course the importance of the pyrimidines as building blocks in the nucleic acids. The experimental investigations on the pyrimidines have been mainly concerned with vibrational assignments of the bases in the solid state or in solution." Later, the matrix isolation technique has been widely employed to study the vibrational spectra of several uracils and ~ytosines.~"There has also been a tremendous development of ab initiocalculations which accurately describe the ground-state wave function of several medium-sized molecules. In the case of the pyrimidine bases, the calculations have led to earlier assignments being questioned, but also to new experiments being encouraged.'"' Vibrational transition moments have not attracted much attention, compared to UV transition moments, possibly because of the relative difficulty associated with the measurement of polarizcd IR spectra. The IR polarizations of some small lowsymmetry molecules have been recently determined in studies by Professor Michl's group."25 The information derived from polarized IR measurements on the pyrimidine bases can be expected to become very useful in the future for understanding the nature of the normal modes, but also for structural interpretations of vibrational spectra of polynucleotides. In addition, vibrational circular dichroism (VCD) is increasingly used to investigate polynucleotides, and theinterpretationofsuch measurements depends on detailed knowledge of vibrational transition moments.2628 We have chosen to concentrate this work on a specific pyrimidine derivative, and the choice of 1.3-dimethyluracil (DMU) (Figure 1) requires some comments. The main goal is to describe the vibrational properties of the uracil base when bonded to the sugar backbone of a nucleic acid. A logical choice is then to study 1-methyluracil since the methyl group should have approximately the same effect as the sugar moiety in the naturally occurring base. However, 1-methyluracilhas the ability to form dimers via hydrogen bonding, which could complicate *Abstract published in Advance ACS Abslmcfs. April 15. 1994.
0022-3654/94/2098-4998.$04.50/0
--+ Y'
Figure 1. 1,3-Dimethyluracil molecule with atomic numbering and molecular mrdinate system used in this study. The z' axis is parallel to the N I X , axis. The angle 6 defines an in-plane angle and is positive when wuntcd from the z' axis toward NI.
the analysis of the experimental data. As a starting point for our studies on the pyrimidine bases, we have instead chosen to study DMU, for which self-association is limited. This article presents the polarized IR spectra of DMU, DMU5-d, and DMU-6-d oriented in stretched films of poly(viny1 alcohol). The orientation of DMU in the polymeric host is determined by UV lineardichroismmeasurementscombined with a semiempirical self-consistent reaction field calculation of the electronic spectrum. To the best of our knowledge, this is the first calculation of theelectronically excited states ofa pyrimidine base where specific solvent effects have been accounted for. The experimental IR transition moments arecompared with ab initio calculatedtransition moments,andasweshallsee,theagreement between experiments andcalculationsis satisfactory. In addition to the IR moments, the vibrational assignments of DMU are discussed since there is still some controversy about the origin of the bands observed in the carbonyl region. Szczesniak et a/.'0 studied DMU isolated in a low-temperature argon matrix and
0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 19, 1994 4999
IR Transition Moments of 1,3-Dimethyluracil assigned the high-frequency band to have mainly C40 stretch character and the low-frequency band to have mainly C20 stretch character. By contrast, Graindourze et a1.13 reassigned the two carbonyl fundamentals to appear in the reversed order from a matrix study of DMU. Their reassignment was basedon observed wavenumber shifts when the argon matrix was doped with water. We found the use of IR polarizations to give conclusive information on the coupling between the two carbonyl stretching vibrations in DMU. Our results indicate that both the high-energy mode and the low-energy mode are due to a mixture between C40 and C20 stretching motions.
3Syy ILD' (in-plane) I3Sz,
s,
+ syy+ s,, = 0
(7) (8)
For overlapping transitions the observed LDris a weighted average of the LDf values of the contributing tran~itions2~
LDr(A) =
(9)
Materials and Experimental Methods Chemicals. DMU, DMU-5-d, and DMU-6-dwere synthesized by Bodil Gustavsson under the supervision of Dr. Ingmar Nilsson, AB Astra Hlssle. Poly(viny1 alcohol) (PVA) was obtained as a powder from E. I. du Pont de Nemours Co. (Elvanol). All aqueous solutions were prepared with deionized water (Millipore). Film Preparation. A 10%(w/w) solution of PVA was prepared by dissolving PVA in water under heating to 100 "C.Portions of 5 mL were taken, and 3 mL of water solution of DMU, DMU5-d, and DMU-6-d were added, each containing 0.3 mg (UV measurements) or 10-30 mg (IR measurements) of substance. The mixtures were gently poured on horizontal glass plates and left to dry in a dust-free environment for 48 h. The films were then removed with a spatula and stretched mechanically 5 times their original length under the hot air from a hairdryer (-80 "C). Linear dichroism (LD) is defined as
LD = Ail - A ,
(1)
where All and A l are the absorbances measured with plane polarized light respectively parallel and perpendicular to the macroscopicalsampleaxis (the stretchingdirection). The reduced linear dichroism, LD', is defined as
LD' = (k,, -A,)/&
(2)
where Ai, is the absorbance of a corresponding isotropic sample. For a uniaxial orientation of the sample molecules, such as in a polymer matrix, Aiso can be calculated from the polarized components as29 Ais0
= '/3(~ll+ 2 ~ , )
(3)
The LD' of a pure transition i can be related to the direction of the absorbing transition dipole moment by30 (4)
where S,,, Syy,and S,, are the Saupe orientation parameters31 for the diagonal in-plane axes z and y , and the out-of-plane axis x, characterizing the orientation of the solute molecules. The e l s are the diagonal elements of the extinction coefficient tensor. For a pure in-plane polarized transition i the LDr can be related to the angle Bi between the transition moment and the preferred molecular orientation axis z according to LDf = 3(Sy,,sin2 8,
+ S,, cos2 Oi)
(5)
For an out-of-plane transition the LDr is
LDj = 3Sxx For an in-plane polarized transition the LDr can have values between 3S,, and 3Syy and the orientation parameters are interrelated according to
where A,@) is the absorbance associated with transition i at wavelength A. The pure reduced linear dichroism LDf is determined by the TEM method.32.33 This method is based on forming linear combinations of the type ,411 - dAl with varying valuesof the substractioncoefficientd. The subtractioncoefficient di, for which a specific spectral feature i disappears, is related to the LDf of the transition containing that feature by34
di- 1 di + 2
LD; = 3-
IR measurements were performed on a Perkin-Elmer 1800 Fourier transform spectrometer. To obtain polarized IR radiation, a KRS-5 polarizer (IGP225 Cambridge Physical Science) was placed in front of the sample. The spectral resolution was 4 cm-1 and each spectrum an average of 300 scans. A resolution of 1 cm-l was tested for comparison but no difference in absorption spectra or in evaluated LD; values could be detected. A baseline for PVA was recorded similarly and subtracted on an interfaced computer. The LDf values were obtained by the TEM method. Given the orientation parameters, the polarizations of the IR transition moments relative to the molecular orientation axis were calculated using eq 5. The angle Bi is related to the angle ai within the molecular framework and to the angle (a)that specifies the direction of the orientation axis by hi = a f led
(11)
where hi and a are the angles between the z' axis (Figure 1) and the transition dipole moment directions and the orientation axis, respectively. Measurements of DMU, DMU-54, and DMU6-d in D20 (Merck) were performed using a 25-pm AgCl cell. The sample concentrations were 5 X 1V M. IR spectra of polycrystalline DMU, DMU-5-d, and DMU-6-d in KBr tablets were also measured. UV measurements were performed on a CARY 2300 spectrophotometer. The spectrophotometer was interfaced with a computer and five data points per nanometer were collected with a spectral bandwidth of 1 nm. Polarized measurements were made with a Glan air-space calcite polarizer in both sample and reference beam. The LDr was calculated using eqs 2 and 3. The UV measurement of DMU in water was obtained in a square quartz cell with l-cm path length. Quantum Chemical Calculations The UV transition moments were calculated using a semiempirical self-consistent reaction field method (SCRF).3S The excited states were obtained from a configuration interaction calculationwhere all possible single and double excitations (CISD) were taken into consideration. The actual CI space was then restricted to the 300 configurationswith lowest energy. The SCRF method was used to include solvation effects in the calculation of the absorption spectrum of DMU in water. The geometry of DMU with the first solvation layer of four water molecules was taken from a molecular dynamics simulation (MD).36 The
5000
Holmen et al.
The Journal of Physical Chemistry, Vol. 98, No. 19. 1994
FiynZ. HF/6-31G* and MP2/6-3IGo(bold) optimized C,geomelries of 1,3-dimethyluracil. At both the HF/STO-3G and HF/6-3lG levels, the methyl group bonded to NI has its "in-plane" hydrogen pointing
toward theC2carbonyloxygen. Theswitchofminimumconformerwhen HF/6-31G* theory is used is probablydue to an increasedoverlapbctween the hydrogens and the d-orbitals on the CIcarbonyl oxygen.
starting geometry and the atomic charges were taken from the MP2/6-31G8 calculation in this work. The concentration of DMU in the MD simulation was 114 mM. The DMU/water complex was simulated during 61 ps, and the final geometry of the complex was used in the SCRF calculation. The solvation radius was set to 6.5 A. With this solvation radius, DMU and the first layer of hydrogen-bonded water molecules are within the solute cavity. This procedure diminishes the problem with the solvation radius entering in the SCRF method25 In a CISD calculation of the DMU/water complex in the gas phase, about 90% of the solvent shift was accounted for. The SCRF 'super molecule" treatment thus accounts for the remaining 10%. All ab initio calculations of the geometries and IR spectra were performed using the GAUSSIAN 90"'. and GAUSSIAN 92"b program packages. The geometry of DMU was optimized assuming C, symmetry, using both Hartree-Fock (HF) theory and second-order Moller-Plesset perturbation theory (MP2).'8 We used three standard basis sets: the minimal STO-3G basis the split valence 6-31G basis s e t P and the 6-31G* basis set.41 Thevibrational spectrum wascalculated for each geometry except for the MP2/6-31G* geometry due to lack of disk space at the CRAY XMP/48. We were therefore unable to check if the calculated geometry at the MP2/6-31G* level corresponds to the global minimum. The geometries calculated at the HF/ 6-31G* and the MP2/6-31G* levels are depicted in Figure 2. Our results support the findings by Banerjee and co-workers" that both methyl groupsin DMU have Weir "in-plane" hydrogens pointing away from the Cz carbonyl oxygen. The vibrational transition moment directions were calculated from the dipole moment derivatives.".'3 Previousexperiencehas shown that thedifferencein calculated wavenumbers in going from H F theory to MP2 theory using the same basis set could be as large as l O W . 4 5 and that the basis set dependenceof calculated IR transition momentsisquitestrong~' Thecalculatedspectrausedin thisstudythus havetobeconsidered asrough guides for theinterpretationof the experimentalspectra.
Results and Discussion
In this section, we first present the results from the polarized IR measurements on DMU, DMU-5-d, and DMU-6-d, giving the IR polarizations relative to the molecular orientation axis. Second, we describe how the results from UV LD measurements combined with calculated electronic transition moment directions provide informationabout theorientation of DMU in the stretched PVA film. Third, we use the combined results from IR LD and UV LD toestablish theabsoluteIR transitionmomentdirections relative to the molecular framework. For each vibrational transition there are two possible transition moment directions obtained from the experiments. In order to find the correct polarization for each vibration, we compare the experimental polarizations with IR moments from ab initio calculations.
1800 1600 1400 1200 1000
800
600
Wavenumber (cm-' ) Figwe 3. Polarized IR spectrum of 1,3-dimethyluracilis stretched poly(vinyl alchol). Finally, we discuss vibrational assignments on the basis of the present work and compare these to previously published assignments. IR Linear Dichroism. To obtain the IR transition moment directions relative to the molecular coordinate system x', y', and figure 1). wehavemeasured thepolarizedIRspectraof DMU, DMU-5-d, and DMU-6-d in stretched PVA. The polarized IR spectraofDMUareshownin Figure 3. Thedata evaluated from the polarized spectra for the three isotopomers are presented in Table I . Theassignmentsarediscussedat theendofthissection. Experience has shown that in a uniaxial medium, like a polymer film, molecules orient on average with their smallest cross section perpendicular to the stretching direction.29." As DMU is a lowsymmetry molecule with no pronounced "long" in-plane axis, it is difficult to make an a priori prediction of how the molecule orients in the stretched film. The value of the out-of-plane orientation parameter, S,,, is determined from the LD'values of the out-of-plane transitions, polarized perpendicular to the molecular plane. These transitions are characterized by their large negative LD'values. Todetermine the in-plane parameters, we have to rely on an approximate method. For DMU, DMU5-d, and DMU-6-d, which are assumed to have the same degree of alignment," we have evaluated the IR LD for 41 in-plane vibrational transitions and we expect at least one of these to be polarized either closely parallel or perpendicularto the orientation axis. The corresponding LDr value of this transition, which is an extremein-planevalue, gives an approximation of theappropriate orientation parameter (either S, or Syy). The remaining inplaneorientation parameter isdetermined fromeq8. Theextreme LD' values are shown in boldface in Table 1. Theout-of-plane parameterforall threesubstances iscalculated as a mean of the LDr values for the out-of-plane modes, which gives S,, = 4 . 2 1 . All three substances have the same in-plane minimum value, LD' = 0, giving S, = 0. This corresponds to S, = 0.21. The largest in-plane LD'vaIue for DMU (0.63) also yields S, = 0.21. We now have IR polarizations related to the direction of the orientation axis (Table 1). What we want to establish is the IR moment directions related to the molecular framework defined in Figure 1. To be able to do so, the direction of the orientation axis related to the molecular framework must be deduced. This is described in the next section. Estimation of the Direction of the Orientation Axis. In Figure 4 the UV absorption and LD' spectra of DMU in stretched PVA are shown. The LD' shows a small variation over the first band, probably due to vibronicborrowing from higher lying, differently polarized, transitions. It is not trivial todecide which LD'value should beusedintheevaluationofthetransitionmomentdirection. WechoseaLDrvaluefromthe(0.0) region(35 46O~m-~)'~from thefact that thisgivesthedirectionofthepureelectronictransition
IR Transition Moments of 1,3-Dimethyluracil
The Journal of Physical Chemistry, Vol. 98, NO. 19, 1994 SO01
TABLE 1: Observed Vibrations in 1,3-Dimethyluracil, 1,3-Dimethyluracil-5-d, and 1,3-Dimethyluracil-6-d in PVA Film, Their LDr and Polarization DMU
DMU-5-d
DMU-6-d
i , cm-1
LD*
18)"
i , cm-l
LD'
1704 1666 1654 1628 1485 1456 1439 1402 1376
0.13 0.32 0.38 0.52 0.02
63 44 39 25 80 90 77 54 56
1704 1660 1647 1620 1485 1453 1439 1397
0.13 0.33 0.38 0.52
63 43 39 25 90 76
0.03
77
1358 1340
0.38 0.57
39 17
1226
0.56
19
1139
d
1013 980
0.04 0.55
1340 1234
c
0.03 0.22 0.20 0.52
0.63c
25 0
1166 1144
d
1004
0.03
77
934
0.06
72
806
764
d
-0.6lC
-0.64c
WP
WP
718
-0).63c
OOP
685
0.37
40
517 482
0.20 0.05
56 74
c 0.04 c
0.27
778
-0.64c
WP
761
-0.62c
WP
0.43 0.23 0.03
LDr
1704 1670 1646 1612 1484 1450 1432 1395
0.13 0.22 0.36 0.48
w*
0.06
63 54 41 29 90 90 90 72
1365
0.55
21
1224
0.55
21
1020
0.12
65
932 908
0.38 0.41
39 36
790
0.31
45
766
-0).63c
WP
708 684
-0.6lC 0.43
WP 34
517 482
0.20 0.06
56 72
c c c
assignmentb U C ~ OvC20 , 'in-phase" (43) Fermi resonance band (sh) 4 0 , vC4O 'out-of-phase" (100) VCSCS (27) L C H (Med, 6,CH (Men) (17) v(ring) (16) 6,CH (Mel), 6,CH ( M e d (17) 6,CH (Me,), 6,CH (Med (17) v(ring), bCsH, 6CsH (1 1) u(ring), bCsH, 6CsD (15) u(ring), GCsH, 6CsD (14) 6C6H, v(ring) (1 5) vN-Mel, bCsH, vN-Me3 (8) vN-Mel, 6C6H, vN-Me3 (8) vN-Me,. 6CsH. vN-Mel(8)
76 21
800
676 517 482
i , cm-1
49
34 53 77
Transition moment direction in degrees relative to the orientation axis. w p = out-of-plane vibration. The assignments are discussed in the text. 6,, 7,and p denote in-plane stretching, in-plane-bending, asymmetric bending, symmetric bending, out-of-plane bending, and rocking, respectively. The numbers in parentheses denote relative intensities related to the vibration uC20, vC40 at 1654 cm-I, which has arbitrarily been given the intensity 100. c Boldface numbers denote the LD' values that have been used to determine the orientation parameters. The LD' could not be evaluated due to too strong baseline absorption in the perpendicular component. a
v, 6,b,,
08
I
01
00 45bOO
40000
35WO
Wavenumber (cm ')
Figure 4. Reduced UV linear dichroism (-)
and absorption (spectra of 1,3-dimethyluracil in stretched poly(viny1 alcohol).
Wavenumber (cm-')
- -)
moment vector. The value of 0.63, corresponding to S,, = 0.21, is the largest in-plane value observed. The same S,, value was determined from the IR LD measurements. The direction of the orientation axis is therefore parallel to the polarization of the first ?r ?r* transition in DMU. The polarization of the second transition is harder to evaluate. We were not able t o measure the polarized spectra over the whole second band, and the transition moment direction for this transition is therefore slightly more uncertain. The LDr spectrum is nearly constant throughout the red edge of the second band, with an average value of 0.27. This is consistent with an angle of 49O between the second transition moment and the orientation axis. There remains to determine the direction of the orientation axis within the molecular framework. To this end we have calculated the electronic spectrum and the electronic transition
-
Figure 5. Experimental absorption spectrum of 1,3-dimethyluracil in water and theelectronic transitions from theSCRFcalculation. Oscillator strengths U,and transition moment directions (6) aregiven in parentheses (Jb). Transitions with an oscillator strength lower than 0.005 are not shown. The calculation yields three transitions below 37 000 cm-1, all r* character, with oscillator strengths lower than 0.005. having n
-
moments of DMU in water using a semiempirical SCRF method,35 as outlined previously under the section Quantum Chemical Calculations. The experimental spectrum and calculated transitions of DMU in water are shown in Figure 5. The first band observed in water is centered around 37 900 cm-' followed by an almost equally strong band a t 49 260 cm-1. Clark et al.49 have extended the measurements into the vacuum UV for DMU in water and found one more band at 53 480 cm-l. The calculation predicts three strong ?r r* transitions, each of these transitions corresponding to the main component of one of the three experimentally observed bands. The first strong calculated
-
5002 The Journal of Physical Chemistry, Vol. 98, No. 19, 1994 TABLE 2
Holmen et al.
In-Plane IR Transition Moment Directions for 1,3-Dimethyluracil, 1,3-Dimethyluracil-ld,and 1,3-Dimethyluracil-6d DMU DMU-5-d DMU-6-d ~
6"
6"
mode 9 10 11 12
15 17 18 19 19 19 20 22 22 22
i , cm-l
exp.6
1704 1654 1628 1485 1456 1439 1402 1376
49 or -77 25 or 3 l l o r -39 66 or 3 76 63 or 89 40 or 68 42 or -70
1340 1234
11 o r 2 -14
cake 56 -3 1 -5
-86 -8 9 65 -64
i , cm-1
1704 1647 1620 1485 1453 1439 1397
exp.6 49 - or -77 25 or -53 11 or -39 76 62 or 3
76 63 or 89
'6
cake 59 -30 -2
-89 85 -8 6 -8 1
i , cm-1
1704 1646 1612
exp.6 49 -or -77
27 or -55
15 or -43
1450 1432 1395
76 76 76 58 or -86
1365
7 or -35
1484
cake 56
assignmentd
-32 -1 1
89 82 -8 8 -80
45 -15 -22
1358 1340
25 or -53 3or-31
27 -1 6
1226
5or-33
-2 1
13
1224 7 or -35 -3 28 1020 51 o r 2 -55 1004 63 or 89 69 1013 62 or 90 62 28 -25 980 7or-35 23 77 58 or -86 934 30 932 25 or -53 -14 30 22 or 3 -37 908 25 800 35 or -63 -1 7 32 31 or -59 -9 790 32 684 26 or -54 -41 685 -41 20 or -48 35 676 20 or -48 -39 35 39 or 3 517 -53 517 42 or -70 -60 517 42 or -70 -60 37 63 or -89 482 60 or -88 -8 3 482 58 or -86 -84 482 -83 38 Transition moment direction in degrees relative to the z' axis. Accuracy estimated to be within f10'. The preferred solution is underlined. Calculated at the HF/6-31G* level. See text for discussion of the assignments. v, 6 , 6,,, 6,, and p denote in-plane stretching, in-plane bending, asymmetric bending, symmetric bending, and rocking, respectively. transition lies a t 37 980 cm-I. The transition density is localized mainly to the c5-C~double bond, and the transition polarized at -14' from the z' axis, i.e. nearly parallel to the c5-c,5double bond. The next strong transition is found at 48 520 cm-I and is polarized at +38'. The third strong transition lies at 55 420 cm-* and is polarized at -33'. From the LD measurements we found the orientation axis to be parallel to the polarization of the first electronic band. The calculated polarization of this band is -14' with respect to the z' axis, in good agreement with both experimental and other calculated values found in the literature for uracil and 1-methyluracil.5C-55 Therefore, we conclude that the orientation axis for DMU in stretched PVA makes approximately an angle of -14' to the z' axis. The observed polarization of the second A T * transition is then either -63' or +35', according to experiment. The +35' value is in good agreement with the calculated value of +38'. With thedirectionoftheorientation axis known, theIRmoment directions can now be given within the molecular framework. IRTransitionMoment Directions. Experimental and calculated IR polarizations are presented in Table 2. The accuracy of the experimental directions is limited by the accuracy of the orientation axis direction and is estimated to be within &lo0.For each direction there are two possible values of the angle 6, and with the present material there is no possibility to experimentally distinguish between these. To resolve this ambiguity, we compare the experimental directions with calculated ones. Most calculated directions at the HF/6-31G* level of theory agree within 10-30' with one of each experimental value. However, for three modes, the difference between calculated and observed polarizations is larger than 30°. One of these is the very weak mode ~ 3 in 0 DMU6-d. It is a complex mode consisting of almost equal amounts of v N-Me3, E D , and 6CH. The remaining two modes are the ring vibration ~ 3 in2 both DMUJ-dand DMU-6-d. Thisvibration is also a very complex mode with large displacements of all atoms in the ring. The general disagreement between experiment and theory is probably caused by the combination of experimental
-
uncertainty and the limitations of the computational method. It should be noted that our calculations are performed for a single molecule in the gas phase while the experiments are performed with the samples dissolved in a polar matrix that forms hydrogen bonds to the solute molecules. The perturbations introduced by the solvent have not been accounted for in any way, and this is of course one reason for the discrepancies between experimental and calculated moment directions. Previous studies have also shown that it is quite difficult to accurately calculate IR moment directions. Arnold and co-workersZ4have calculated IR transition moments for s-trans-1,3-butadiene and tested different levels of theory. Their results show that even quite large basis sets, 6-311G**56 and D95V**57, at the MP2 level give transition moment directions that differ 10-20' from experimental directions. Radziszewski et al.23 also tested different basis sets in calculating IR polarizations for ethylene4 and found that it is especially difficult to calculate IR moment directions for normal modes that are dominated by bending motions. However, we believe that the calculated directions are sufficiently accurate to distinguish between the two experimental results for most of the modes. The best choice for some of the transitions is shown in Figure 6 and in Table 2. If the assignments for v9 and v10 are correct, we have an indication that these modes are due to the strong coupling of vC~0 and vC40. In this case, the twocarbonyl stretching motions should give rise to one in-phase stretching vibration and one outof-phase stretching vibration. For DMU this should yield an IR moment direction for the in-phase vibration that bisects the angle between the two carbonyl groups and an out-of-phase moment almost perpendicular to the in-phase moment, and these are, in fact, the observed moment directions (Figure 6). The observed moment directions are thus in agreement with a strong coupling of vC20and vCIO in DMU. Further argument for the case of strong coupling can be found in an article by Rostkowska et a1.12 They found the difference in energy to be very small (
