4560
J . Phys. Chem. 1985, 89, 4560-4565
position of the Pd+-Oy complex are proposed as the two different oxygen species stable in Pd-Ca-X zeolite.
grateful to the Energy Laboratory of the University of Houston for equipment support.
Acknowledgment. This research was supported by the National Science Foundation and Robert A. Welch Foundation. We are
Registry NO. C6H6, 71-43-2; C2H4, 74-85-1; CH,OH, 67-56-1; Pd, 7440-05-3; O,, 7782-44-7; H20, 7732-18-5.
Solid State Studies. 29. Crystalline Urea: Evidence for Vibrational Delocalization K. Liapis, U. A. Jayasooriya, S. F. A. Kettle,* School of Chemical Sciences, University of East Anglia, Norwich NR4 7TJ, U.K.
J. Eckert, J. A. Goldstone, and A. D. Taylort Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received: March 21, 1985)
A comparison of single-crystal and mixed-crystal isotopomeric Raman, incoherent inelastic neutron scattering, and infrared data on crystalline urea indicates the inadequacies of an isolated-molecule approach to the interpretation of these spectra.
The resolution available with modem instrumentation has made it clear that it is almost invariably a poor approximation to interpret the vibrational spectra of crystalline materials as those of the isolated molecular or ionic units. When infrared and Raman data are taken together additional features are usually observed which are associated either with a site splitting of degenerate vibrations, with the weak appearance of features forbidden in the isolated unit (to be treated by the site group model), or with interunit vibrational coupling (to be treated by the factor group or unit cell group models). Although the site-group model may be appropriate for some internal vibrations, as far as we are aware, every case which has been examined in detail with the number of molecular units per primitive unit cell, z 2 2 , has required the use of the factor group model to explain the features associated with at least some internal vibrations. Such factor group splittings are most readily examined by single-crystal methods, either infrared or Raman. However, it is not necessarily true that intermolecular vibrational coupling is made manifest by the observation of factor group splitting. When a unit cell is occupied by a single structural unit ( z = 1) there can be no factor group splitting. Instead, as we have recently illustrated,] intermolecular vibrational coupling leads to a frequency dispersion over k space and not to an observable at the center of the Brillouin zone. For centrosymmetric crystals with z = 2 factor group splitting is revealed by a comparison of infrared and Raman spectra and not by a study of either alone for individually they may be interpreted by the site group model. For noncentrosymmetric crystals with z = 2 one would intuitively expect that any factor group effects would be more evident-perhaps by factor group features appearing in both infrared and Raman so that neither is amenable to a site group interpretation. In fact, the opposite can be true, as we show in the present paper for the case of a noncentrosymmetric crystal, that of urea; here z = 2, infrared and Raman considered separately are predicted to provide no information on factor group effects, and a comparison of the two is predicted to reveal only that associated with totally symmetric, A,, molecular modes. Single-crystal infrared data are predicted to be a barren source. Single-crystal Raman spectra may provide evidence for factor group effects but, again, only on molecular A, modes. We now detail the basis for these generalizations. In the c r y ~ t a l ,urea ~ . ~ is a planar molecule with C2, symmetry and occupies a C,, site; the space group is Old (P421m)with z ‘On leave from Neutron Division, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX1 1 OQX, U.K.
0022-3654/85/2089-4560$01.50/0
TABLE I: Comparison of Site and Factor Group Infrared Activities in Ureaa
site (C2”)
factor (&)
a Infrared silent modes are omitted. The different axis sets are distinguished.
TABLE I 1 Comparison of Site and Factor Group Raman Activities in Urea“ A, (x’x’, y’y’, z’z’) A2 (x‘y?
BI
(~’2’3
B2 (~‘2’) a
A,
(22,
xx
+ Y V ) + B,(xy)
(xx - YY) E (xz, YZ) E ( x z ,Y Z ) Bl
Raman silent modes are omitted
= 2. It is of interest to compare the site and factor group infrared spectral predictions for urea. This comparison is made in Table I. At first sight it would appear from Table I that there is a clear distinction between site and factor group predictions for (local) x’ and y ’ dipole-active vibrations. This apparent distinction is illusory. It has to be remembered that site group axes are local whereas factor group axes are crystal. Since z = 2 there are two sets of site group axes; because of the crystal S4 axis these two sets are related by a 90’ rotation about z (local or crystal). It therefore follows that B, site group modes have an isotropic infrared absorption in the xy crystal plane, as have also the B,. The site and factor group models of urea are therefore indistinguishable by infrared spectroscopy. The analogous comparison of site and factor group predictions for Raman spectral activities is given in Table 11. Because of the relationship between local and crystal axes the Raman activities of molecular A,, B,, and B2 modes do not provide a distinction between the two models, even by single-crystal studies. The presence or absence of in(1) R. Durman, U. A. Jayasooriya, S. F. A. Kettle, S. Mahasuverachai, R. Mortimer, and L.-J. Norrby, J . Chem. Phys., 81, 5247 (1984). (2) P. Vaughan and J. Donohue, Acta Crystallogr., 5, 530 (1952). (3) (a) J. Worsham, Jr., H. Levy, and S . W. Peterson, Acra Crystallogr., 10, 319 (1957); (b) A. W. Pryor and P. L. Sanger, Acta Crystallogr., Part. A, 26, 543 (1970).
0 1985 American Chemical Society
Crystalline Urea termolecular vibrational coupling in these modes cannot be determined by normal vibrational spectroscopic techniques. It is only in the case of molecular A I modes that the presence of such coupling is determinable. Fortunately, as readily shown by tensor addition, both A, and B2 factor group modes are expected to show significant intensity. Single-crystal Raman spectra may, then, be expected to provide direct evidence of intermolecular vibrational coupling on molecular A, modes by the appearance of (factor group) A I B2 pairs. Further, on several grounds, it is reasonable to expect that these pairs may show significant splitting. This, however, is a simplistic view. The space group of urea is Did and so noncentrosymmetric. It follows that those modes which are infrared active may also be Raman active and so, assuming a dominant dipolar coupling mechanism, may exhibit LO - TO splitting. These effects will be confined to factor group modes of B2 and E symmetry (Table I). It must be recognized that it is unusual to observe LO-TO splitting on internal modes in Raman spectroscopy. Its observation would indicate rather strong intermolecular vibrational coupling. The factor group Al modes will not show LO-TO splitting but only the (12) spectra will be pure Al; the ( x x ) and b y ) spectra will show both Al and B, features. This is not the end of the complications. Although molecules of DZdsymmetry cannot be optically active, crystals based on this symmetry may be. This complicates single-crystal Raman measurements-the planes of polarization of incident and scattered beams may be less well defined than is desirable. In the present paper we concern ourselves with the single question, does intermolecular vibrational coupling between internal modes occur in the urea lattice? The answer to this question does not require a complete discussion of the urea single-crystal Raman data, only a comparison of the spectra revealing the A, and B2 features, and these are all that we discuss in this paper. Urea is one of the crystalline species most studied by vibrational spectroscopy, no doubt because its site and molecular symmetries are identical. Many normal coordinate analyses of the vibrations of urea have been reported,e1o based largely on the infrared spectral data, and there is no doubt that it is possible to obtain a good fit, although details of the assignments, force fields, and force field parameters differ. Although some infrared data on dissolved urea are extant,” they are limited because of solvent absorption and it may be that the planarity of urea molecule observed in the crystal may not persist in solution. In practice, all reported normal coordinate analyses of urea have made use of infrared data obtained on crystalline materials; as is evident from Table I, and the associated discussion, the infrared spectra can be interpreted on an isolated molecule approach, even if intermolecular vibrational coupling occurs. However, the status of all extant normal coordinate analyses is questionable if this coupling does, indeed, occur. It is therefore the purpose of the present paper to explore this question. Historically, little use has been made of Raman data on urea;12-19 single crystal data have not been available and, although
+
(4) A. Yamaguchi, T.Miyazawa, T. Shimanouchi, and S. Mizushima, Spectrochim. Acta, 10, 170 (1957). (5) Y. Saito, K. Machida, and T. Uno, Spectrochim. Acta, Part A , 27,991 (1971). (6) J. L. Duncan, Spectrochim. Acta, Part A , 27, 1197 (1971). (7) B. Ya. Shteinberg, Yu. I. Mushkin, and A . I. Finkelshtein, Opt. Spectrosc., 33,589 (1972). (8) D. Hadzi, J. Kidric, Z. V. Knezevic, and B. B a r k Spectrochim. Acta, Parr A , 32,693 (1976). (9) G . Diaz and M. Campos, Specrrosc. Lett., 14, 365 (1981). (10) J. F. Anenas, F. Manquez, and A. Cardenete, Spectrochim. Acta, Purr A , 40, 1033 (1984). (11) I. Laulicht, S. Pinchas, E. Petreanu, and D. Samuel, Spectrochim. Acta, 21, 1487 (1965). (12) K. W. F. Kohlrausch and A. Pongratz, 2.Phys. Chem., Abt. B, 27, 176 (1934). (13) J. T.Edsall, J . Chem. Phys., 4, 1 (1936). (14) K. W. F. Kohlrausch and A. Pongratz, Monutsh. Chem., 70, 226 (1937). (15) R. Ananthakrishnan, Proc. Indian Acud. Sci., Sect. A , 5, 200 (1937). (16) A. W.Reitz and J. Wagner, Z . Phys. Chem., Ab?. B, 43,339 (1939). (17) J. W. Otvos and J. T.Edsall, J . Chem. Phys., 7, 632 (1939).
The Journal of Physical Chemistry, Vol. 89, No. 21, 1985 4561
372 m 376 m 544 s
544 s
544 s
562 w 573 w(sh) 007 vs
007 vs
563 s 573 w 1007 vs
172 m
175 m
537 m 517 m
535 s 577 w
1464 vw 1532 m 1576 w
1605 vw 1645 s
1644 m
1605 m 1641 s
372 m 555 s
1166
1007 vs 1147 vw
m 1535 vw 1573 vw 1590 w 1645 w 1672 m
1700 w
1700 vw
3234 m 3240 m 3320 s 3347 s
3240 m 3313 w(sh) 3350 s 3422 s
3240 m 3315 w 3320 m 3350 s
3430 m
3430 w
3460 w
3465 m
3350 s 3447 m
‘vs = very strong; s = strong; m = medium; w = weak; vw = very weak; sh = shoulder.
solution studies have been reported in the early literature, the information they provide has not been greatly used. Although polarization data are available from these solution studies the question of whether the structure of urea in solution is the same as in the solid is unresolved. In that urea is only soluble in strongly hydrogen-bonding solvents such a structural change is entirely possible and means that the applicability of the solution polarization data to solid-state assignments has to be established. In the present investigation we have therefore confined our studies to the Raman spectra of crystalline urea. In addition to Raman data, we report the incoherent inelastic neutron scattering spectrum (IINS) of urea. By probing the whole of k space this spectrum tests for the existence of dispersion on internal modes of urea; the observation of such dispersion would be indicative of intermolecular vibrational coupling. The IINS spectra also provide an indication of the parentage of the individual modes, since IINS intensities in protonic materials are related to the amplitude of proton motion. This motion could result from motion within the NH2 unit or from the unit moving as a whole. Finally, we have recorded the infrared and Raman spectra of mixtures of isotopomers of urea. When strong intermolecular vibrational coupling occurs between corresponding modes of isotopomers in the same lattice only a single peak is observed, its frequency being a function of the composition of the mixed crystal (the “one-mode” limit). In the absence of any coupling two spectral features are observed (the “two-mode” limit). Formally, of course, the k = 0 selection rule is lost in such mixed crystals; this is important away from the one- and two-mode limits and results in multiple-headed broadened peaks. For the purpose of the present work the important observation would be a failure to observe two-mode behavior in isotopomeric crystals. This failure is an immediate indicator of intermolecular vibrational coupling; strong coupling will lead to the one-mode limit and the appearance of sharp, composition-dependent features. One may comment that such one-mode behavior is likely to be associated with the observation of factor group and LO-TO splittings in the single-crystal Raman spectra and dispersion in the IINS. (18) J. R. Ferraro, J. S. Ziomek, and G. Mack, Spectrochim. Acta, 17, 802 (1961). (19) W. Kutzelnigg, R.Mecke, B. Schrader, F. Nerdel, and G. Kresse, Z . Electrochem., 65, 109 (1961).
4562
The Journal of Physical Chemistry, Vol. 89, No. 21, 1985
I /
1
Ni i
n
1400 1200
900 600 300cm-' Figure 1. Single-crystalRaman spectra of urea. Nomenclature used is that given in ref 20. 3500
3100
1700
TABLE IV: Symmetry Species and Frequency Ranges Associated with Internal Coordinates in Urea and Deuteriourea freq range, cm-l symmetry internal coordinate under C,,, (NH,LCO (ND,LCO In-Plane Vibrations 2597-2438 2(Al + B2) 3485-3352 v(N-H,D) stretches 1590-888 A, + B2 16 15-1 003 v(C-N) stretch -1590 A, 16 15-1003 v(C=O) stretch 1255-1 155 A, + B, 1678-161 5 G(HNH, DND) bend 1000-475 A, + B2 -1153 p(HNH, DND) rock -475 A, -558 6(NCN) bend 1475-520 B2 1463-575 p(NCN) rock Out-of-Plane Vibrations 785-500 r(C0) out of plane def B, B, + A2 785-500 w(HNH, DND) wag 719-555 T(HNH, DND) torsions B, + A2
776-375 776-375 -510
Results and Discussion The single-crystal Raman data are particularly useful in highlighting those frequency regions in which intermolecular vibrational coupling occurs in urea. The urea crystal is biaxial and it is necessary to propagate along suitable indicatrix axes if optical rotation effects are to be avoided. Because of the finite collection angle this requirement cannot be obeyed for the scattered light and so measurements such as z(yy)x and x(yy)z must be expected to differ. In practice, the differences were found to be small; however, we only report features common to such pairs. The relevant single-crystal Raman data are presented in Table 111 and some spectral regions shown in Figure 1. These data have to be interpreted in the light of the correlation between molecular, site, and factor group symmetries (Tables I and 11) and the frequency regions associated with the internal mode vibrations (Table IV). Considering only the spectral region above, i.e. that associated with internal modes, nine peaks and a weak shoulder are observed in the zz spectrum compared with the seven A, predicted. The "extra" peaks are in the 3000-cm-' region, where three peaks and a weak shoulder are observed but only two predicted. The additional peaks are undoubtedly that at 3240 cm-' and the weak shoulder at 33 13 cm-' probably originating in Fermi resonance. Four features are predicted in the 1000-1700-~m-~region but five observed. The weakest is at 1577 cm-' and we assign it as an
Liapis et al. anharmonic. This spectral region is rich in anharmonic features. That this is so is evident from the B, spectra (actually, y y / x x z z ) . Because no molecular A, frequency is expected above ca. 780 cm-I, all fundamental crystal Bl features (which correlate with molecular A,) must be below ca. 800 cm-I. Weak B, peaks at 1605 and 1700 cm-' must therefore be anharmonic (there are no strong peaks in other polarizations which could lead to breakthrough). Similarly, B, peaks at 3320, 3430, and 3460 cm-' are probably too strong to be breakthrough and are assigned as anharmonic with some intrinsic intensity. We may comment that the only clear B, fundamentals are at 562 and 372 cm-', the latter being a surprisingly low frequency. We now turn to the crystal B2 modes; in looking for the effects of intermolecular vibrational coupling, besides comparing B2 and A, spectra it is necessary to consider simultaneously both LO-TO splitting and anharmonic featurs in the former. Above 200 cm-' there are 13 peaks in the y ( x y ) x spectrum (which is TO, the x(yx)y is similar). Only seven are predicted. An isolated anharmonic peak is unlikely to show either factor group or LO-TO splittings. Weak peaks coincident in all B, spectra and noncoincident with A, fundamental features are therefore excluded. We thus eliminate B, peaks at 3234 and 3315 cm-I. It is clear that LO-TO splitting does not occur on the strong Raman peak at 1007 cm-'. The coincidence of A, and B2 frequencies confirm the absence of intermolecular vibrational coupling effects on this peak. Similar arguments apply to peaks at 1535 and 3350 cm-' and also to that at 1573 cm-I. The latter is the weakest peak in both mixed LO and T O and T O B, spectra and so could well be a B2 anharmonic just as the A, has been assigned to an anharmonic. If so, coincidence with A, could result from a free molecule combination mode involving ca. 1007 (v(C-N) and ca. 560 cm-' (G(NCN)). Only the 1007, 1535, and 3350 cm-l are therefore assigned as vibrationally insulated B2 modes. Corresponding to (mixed LO and TO) B2 features between 544 and 563 cm-' is a T O peak at 555 cm-'. The corresponding A, frequency is 544 cm-]. Clearly, intermolecular vibrational coupling occurs on this mode. Similarly, the A, mode at 1175 cm-' is clearly separated from the B2 (TO) mode at 1147 cm-' and the B, (mixed LO and TO) at 1166 cm-'. Again, intermolecular vibrational coupling must be the common origin of these phenomena. There is a peak at ca. 1644 cm-' in all B, and in the A, spectra. In the (mixed LO, TO) B, spectra it is the strongest peak in this spectral region and is at 1641 cm-]. However, in one T O B2 spectrum it is weak and at 1645 cm-I, the strongest peak in this region being at 1672 cm-l. In view of this and the LO-TO splitting generally evident in this region we conclude that the ca. 1644-cm-' coincidences are accidental, there being one B2 fundamental in this region which exhibits both LO-TO and factor group effects, complicated by anharmonic features which, as noted above, are common in this region. The strongest B2 peak in the 3300-cm-' region is at 3350 cm-I, shows no LO-TO effects, and is coincident with the strong A, peak. It seems clear that it should be assigned as a vibrationally isolated mode. In a single-crystal infared study it has been reported at 3362 cm-1.21 A complicated LO-TO/ factor group/anharmonic pattern extends from 3422 to 3500 cm-'. However, the B2 mode at 3447 cm-' (3449 cm-' in the singlecrystal infrared),2' arising from v(N-H) internal coordinates, shows both factor group splitting (the A, is at 3422 cm-I) and ~ significant LO-TO splitting. That is, in the 3 3 0 0 - ~ m -region where there are two A,-B, pairs derived from molecular A, modes the pairs differ, one shows intermolecular vibrational coupling, one does not. As is evident, it is possible to use infrared data in the discussion for some spectral regions. Unfortunately, in general, the infrared bands are (Figure 2) broad and not very informative, particularly in polycrystalline samples. However, it is possible to use some of these other infrared data to comment on the above discussion. In particular, we note the absence of a strong infrared peak at 1645 cm-l (strong peaks occur at 1610 and 1680 cm-') (20) S . P.S. Porto, J. A. Giordmaine, and T. C. Damen, Phys. Reu., 147, 608 (1966). (21) R. D. Waldron and R . M. Badger, J . Chem. Phys., 18, 566 (1950).
The Journal of Physical Chemistry, Vol. 89, No. 21, 1985 4563
Crystalline Urea
1
I
4000
3000
I
1
1200
800
1
1
1600 Wavenumber /cm -I
2001)
400
Figure 2. Infrared spectrum of urea (KBr disk). (A comparative study of urea in nujol with that in alkaline halide pellets has been reported by Ste~art.2~)
5f
IINS
1649 X
L
1.r.
I
I I
Raman
I.. I
I
I. ,
I
"
1dOO
1400
12b0
I,
I
I
I
1800
I
lob0
I
d0
I
600
I
.
acm-'
Figure 3. Incoherent inelastic neutron scattering spectrum of urea (ca. 15 K), together with polycrystalline infrared and Raman spectra as bars, for comparison.
supporting the interpretation we have given for this region. Secondly, recognizing that isolated-molecule Al modes will normally be infrared active we may use the above discussion and the infrared spectra to compile a partial listing of molecular AI modes with some confidence (we use our Raman frequencies). These modes are those at 1006, 1535, and 3350 cm-'; the other A, modes lie at ca. 550, 1160, ca. 1645, and ca.3430 cm-' (these four being complicated by solid-state and other effects). One significant feature of this list is that in none of the normal coordinate analyses reported in the literature has a peak near the 1535-cm-' region been assigned as an A, fundamental. The single-crystal Raman data indicate that intermolecular vibrational coupling occurs on peaks in the 550-, 1160-, and 3430-cm-I regions. We now seek an independent check on these conclusions. Further, since these conclusions relate solely to molecular A, modes, it is of interest to see whether modes of other than A, molecular symmetry species falling in these frequency regions are also intermolecularly vibrationally coupled.
Inelastic Neutron Scattering Studies To a first, very good, approximation, the only peaks apparent in the IINS of urea will be those involving proton motion, either
because the protons participate in a normal coordinate or because they "ride" on other vibrating units. IINS explores the whole of k space so that if a peak is significantly displaced from, or broadened with respect to, its infrared or Raman counterpart, dispersion is implicated. The IINS spectrum reveals the density of states, so that if dispersion-change of frequency with k-is important an IINS peak may be significantly displaced from the corresponding infrared/Raman, which explore only k 0. However, the relatively low resolution of IINS must not be overlooked. Thus, in the 1100-cm-l region in our system the width of the peak at half-height is ca. 60 cm-l, improving at lower frequencies and worsening at higher. This change in resolution accounts for the peak shape changes seen across Figure 3. The 1649-cm-' IINS peak in Figure 3 presumably corresponds to the Raman peaks at 1644 cm-' but is too broad to throw any additional light on the complications-particularly the participation of anharmonics-in this region. However, we note the IINS peak at 1540 cm-' is coincident with Raman peaks which we have concluded are vibrationally insulated, showing neither factor group nor LO-TO splittings. In the 1100-cm-' region we have concluded that there is a vibrationally isolated mode at 1016 cm-'; this is in accord with
-
4564
The Journal of Physical Chemistry, Vol. 89, No. 21, 1985
the observation of an IINS peak at this frequency. However, we have also concluded that peaks in the 1140-1 150-cm-' region show both factor group and LO-TO splittings. In support of this, the corresponding IINS peak is at 1128 cm-I, indicating that dispersion also occurs. We have also concluded that vibrational coupling, manifest in factor group and LO-TO effects, occurs in the 540-570-cm-' region. In agreement with this, whereas one IINS peak-that at 544 cm-'-coincides with peaks in the infrared/Raman spectra that at 598 cm-' has no counterpart in either. It is the density of vibrational states which is relevant to IINS so that peak maxima may differ appreciably from those observed at k = 0. This comment applies equally to the IINS peak at 1128 cm-I, which lies outside the region in which coupling is manifest at k = 0 of 1140-1 180 cm-'. The IINS data therefore support our conclusions derived from the single-crystal Raman data with the exception of those in the 3000-cm-I region, for which no IINS data are available. There are three other peaks in the IINS spectrum. That at 787 cm-' coincides with an infrared peak whereas that at 729 cm-' is slightly displaced from a corresponding infrared absorption. This vibration is Raman silent. The sharpness and intensity of the IINS peak lead us to assign this to a fundamental which, in view of the frequency range and spectral activity, must correlate with a molecular mode of B, symmetry. It appears that this mode exhibits some small dispersion, notwithstanding its weak dipole and zero quadrupole activity. The IINS peak at 448 cm-' is sharp and relatively intense. It therefore almost certainly corresponds to a vibrationally isolated fundamental. It has no counterpart in either the infrared or Raman within ca. 50 cm-I. Molecular A2 or B, modes may appear in this region; in that the former are infrared inactive and could be, fortuitously, extremely weakly Raman active we incline to assign it as an A2 molecular fundamental. We note that no extant normal coordinate analysis of urea has placed a fundamental in this frequency region. There is one final comment relevant to the assignment of the 729- and 448-cm-I IINS peaks. As is evident from Table IV, if we ignore mixing of internal coordinates, five or six IINS molecular peaks are predicted below 800 cm-' (in either one or two motions the protons "ride"; in the others they are intimately involv.ed). Five peaks are observed; in view of the limited resolution involved the actual number present may well be greater than this. It is to be noted that several cases already exist where the inclusion of IINS data have led to substantially revised vibrational assignments and thus normal coordinate analysis.22 Urea may well be a further case. particularly in view of some of the conclusions reached above.
Isotopic Studies We have carried out a wide range of studies of the infrared and Raman spectra of polycrystalline samples of isotopomeric urea species involving D and ISN but include only those which are immediately relevant to the question of the existence of intermolecular coupling in normal urea. These observations not only provide additional data on such coupling on molecular A, modes but also on molecular B, and B2 (both subtending the E irreducible representation of the factor group). In Figure 4 we show the most clear-cut example of the value of isotopic mixed-crystal studies. Peaks are observed at slightly different frequencies in the ca. 550-cm-l region for C0('4NH2)2 and C0(I5NHJ2; this difference is evident in the Raman of a physical mixture of crystals of these two isotopomers. On recrystallization of this mixture, so that the isotopomers are randomly distributed over a common lattice, only a single peak occurs (one-mode behavior), clearly demonstrating the existence of intermolecular vibrational coupling in conformity with the conclusions reached above. In general, the corresponding Raman data for the other spectral regions in which we have concluded that intermolecular vibrational coupling occurs support these conclusions, although the fact that the peaks are not as sharp as those (22) Y . Brunel, C. Coulombeau, C. Coulombeau, M. Month, and H. Jobic, J . Am. Chem. SOC.105, 6411 (1983).
Liapis et al.
600
500 cm!
Figure 4. A comparison of the Raman spectra of a (A) ca. 1:l physical and CO('JNH2)2and (B) the same sample comixture of CO(14NH2)2 crystallized.
of Figure 4 means that these Raman data alone are not sufficient to establish this coupling without supporting evidence.
Conclusions When intermolecular vibrational coupling is excluded from consideration, crystalline urea represents a relatively simple vibrational problem. Inclusion of this coupling represents a considerable complication. However, by a combination of techniques which have not previously been applied to urea, single-crystal and mixed-isotope Raman together with IINS, it has proved possible to establish that intermolecular vibrational coupling does, indeed, occur. The factor group model indicates that observation of this coupling should be confined to features originating in molecular A , modes; of the seven sets of such AI-derived peaks we have established that intermolecular vibrational coupling is of importance for four. Further, it seems likely that intermolecular vibrational coupling affects some of the features originating in molecular B, and B2 (and, possibly, A2) modes since the pattern set by the molecular A , modes is probably followed. Experimental Section hormal urea and i5h'-substituted urea (99.6% "N) were purchased from B.O.C. Limited. Deuterated samples were made by repeated recrystallizations from deuterium oxide (99.8% D) purchased from Fluorochem Limited. Infrared spectra were run on a Perkin-Elmer 577 double-beam grating infrared spectrophotometer. Raman spectra were recorded with a Spex 1401 double monochromator spectrometer and a Spectra Physics Ar ion laser. The 488.0-nm laser line was used with about 30 mW of laser power incident on the sample. Crystal axes were determined and aligned by X-ray diffraction techniques. Incoherent inelastic neutron
J . Phys. Chem. 1985,89, 4565-4569 scattering spectra were obtained on the filter difference spectrometer (FDS) at the Los Alamos pulsed neutron Source. The FDS23is an inverted geometry time-of-flight spectrometer, which utilizes the polycrystalline cutoffs of beryllium and beryllium oxide to select a band of final energies from the scattered neutron beam. A “white” neutron beam is incident on the sample, and the total time-of-flight for each event in the detectors is recorded. Sub(23) A. D. Taylor, E. J. Wood, J. A. Goldstone, and J. Eckert, Nucl. Inst. Methods, 221, 408 (1984). (24) J. E. Stewart, J . Chem. Phys., 26, 248 (1957).
4565
traction of the fixed final flight time determined by the band-pass filters then determines the energy transfer to the sample.
Acknowledgment. We are grateful to Professor E. W. J. Mitchell, of the Department of Physics, Clarendon Laboratory, University of Oxford, who kindly provided the single crystal of urea used in the single-crystal Raman studies. Work at Los Alamos was supported in part by the Division of Basic Energy Sciences, U S . Department of Energy. Registry No. Neutron, 12586-31-1; urea, 57-13-6.
Spectroscopic Studies of Chemically Liberated “Free” -OH Groups in Aqueous N2H4, NH,, and CH,NH2 Solutions C. Austen Angel]* and Dana L. Fields Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: March 25, 1985)
As a contribution to understanding and identifying the nature of the disputed “broken” hydrogen bond in aqueous solutions we have sought to compare the spectroscopic character of “free”-OH groups produced by chemical means at constant temperature with that of the putative “free” -OH produced in pure water alcohols, etc. by temperature increases. “Free”, or at least very weakly bonded, -OH groups have been produced quasi-stoichiometrically at room temperature by displacing bound -OH groups from OH-0 bonds previously free with previously free -NH groups, the competitive status of which has been abruptly increased by protonation of the amine group. The sharp overtone bands of the unbonded -NH groups necessarily present in amine + H 2 0 solutions (due to the excess of protons over lone pairs) disappear stoichiometrically on protonation using HC104, and an equivalent number of weakly bonding -OH groups are produced. The spectroscopic signature of the chemically liberated -OH group is almost indistinguishable from that of the group liberated thermally, and a well-defined isosbestic point at 1442 nm (close to the approximate isosbestic point at 1440-1450 nm in the heated water spectra) implies that the same mechanism of “exciting across the centroid” (a (strong bond) (weak bond) exchange within a continuum model) is involved in each case.
-
Introduction There has been much controversy in the literature on water and other hydrogen-bonded systems concerning the appropriateness of the concept of “breaking” of hydrogen bonds. This is widely assumed by solution chemists, particularly in biological circles, to be a valid description of processes occurring in aqueous systems during composition and temperature changes. By contrast, all computer simulation studies on aqueous and alcoholic systems, irrespective of the form of the pair potential employed, have the common feature of denying the reality of any simple two-state “on”-“off“ picture of hydrogen bonds in these media. Instead of continuous and monotonic distribution of hydrogen bond energies is found.] The force of these latter studies, even allowing for the fact that most have not included non-pairwise-additive terms in the potential function, is sufficient to virtually rule out the simple two-state models of hydrogen-bonded systems (which, in any case, are incapable of dealing simultaneously with the observed responses to pressure and temperature variations2$). One of the most plausible arguments for two-state descriptions of hydrogen bonding has been the existence of isosbestic points in the spectra of H-bonded systems undergoing temperature or composition variation^.^-^ These do not, however, withstand (1) (a) W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys., 79, 926 (1983); (b) D. L. Beveridge, M. Mezei, F. T. Marchese, G. Ravishan, T. Vasau, and S. Swaminat, Adv. Chem. Sec. 16, 204, 297 (1983). (2) W. Kauzmann in “Water and Biological Systems”, Editions CNRS, Paris, 1976, p 37. (3) C. A. Angell, J . Phys. Chem., 75, 3698 (1971). (4) W. A. P. Luck and W. Ditter, 2.Nuturforsch. E. 24, 482 (1969). (5) W. A. P. Luck and W. Ditter, J . Phys. Chem., 74, 3687 (1970). (6) (a) G. E. Walrafen, J. Chem. Phys., 52, 4176 (1970); (b) G. E. Walrafen, “Water, a Comprehensive Treatise”, F. Franks, Ed., Plenum, New York, 1971, Chapter 6, and references therein.
0022-3654/85/2089-4565$01.50/0
detailed analysis insofar as the spectra cannot be described by the sums of two Gaussian components of varying intensities. ~ , ~a major one of these, Rather three or more are r e q ~ i r e d ,and as first shown by Luck and Ditter,s proves almost invariant under temperature change. A related phenomenon is seen in computer simulation studies, of both aqueous1’ and alcoholicI2 systems. In these, the population of hydrogen bonds of intermediate energy VH = 3.0 kcal/mol remains invariant, while populations of weaker and stronger bonds change. This led Stillinger and Rahmanll to the description “exciting across the centroid”, and Angell and Rodgers9 recently showed that the behavior of the overtone IR spectra of normal and supercooled water was consistent with this concept. The latter authors showed by short extrapolation how the overtone spectrum of water should appear when the weak bond population is minimized by vitrification. A broad band of frequencies extending from 6200 to 7200 cm-I (1 390 to 1610 nm) is identified out of which grows a relatively narrow band of frequencies at the short wavelength edge 6900-7200 cm-’ (1390-1450 nm) as the system is excited. The “weak-bond”-“strong bond” exchange, which can be sustained within the continuum model of water, thus seems a viable replacement for the evidently untenable two-state models. The present contribution is intended to strengthen this view by showing how the same relatively narrow band of “weak bond” frequencies can be grown systematically at the expense of a narrow band of “free” -NH frequencies as a result of a titration procedure which (7) W. C. MacCabe, S.Subramanian, and H. F. Fisher, J . Phys. Chem., 74, 4360 (1970).
(8) G. R. Chopin and K. Buijs, J. Chem. Phys., 39, 2042 (1963). (9) C. A. Angell and V. Rodgers, J . Chem. Phys., 80, 6245 (1984). (10) C. A. Angell, Annu. Reo. Phys. Chem., 34, 593 (1983). (11) F. H. Stillinger and A. Rahman, J . Chem. Phys., 57, 1281 (1972). (12) W. L. Jorgensen, J. Am. Chem. SOC.,103, 335 (1981).
0 1985 American Chemical Society
