Bpe&mchbiorr Acta, Vol. 278, pp. 1197 to 1206. Pergamon Preen 1971. Printed In Northern Ireknd

Normal coordinates for the planar vibrations of urea using 16N and 180 frequency shift data

J. L. DUNCAN Department of Chemistry, University of Aberdeen,

Old Aberdeen, Al39 2UE, Scotland

(Receieted 14 i&z& 1970)

&&&---A foroe constant refinement calculation to the observed planar vibration frequencies of OC(NH&, and OC(ND,), and simultaneously to the observed frequency shift data of l*OC(NH& and 0C(16NH,)e has enabled the normal coordin&es for the planar vibrations of ures to be determined with some degree of precision in terms of twenty-one independent force con&s&s. The accuracy of the determined force field is tested by its ability to reproduce the observed 16N frequency shifts of 0C(14NH,)(1SNH,), the lower symmetry of whioh causes the A, and B, species vibrations of the symmetric molecule to combine into one symmetry species containing 8ll thirteen vibrations. The observed r5N frequency shift on the week absorption at 1066 cm-l, coupled with the oslculationa of this paper, con&m that this band arises from the B, species NH, rocking mode, ss originally assigned by WALDRON end by STEWART, but reas- signed by Y~~.AQUCHI et al. The corresponding absorption in urea-D4 is observed at 850 cm-l, in excellent agreement with the product rule.

TELE MOLECULE urert is of some considerable interest in organic chemistry as the simplest diamide, and in inorganic chemistry ss one of the simplest molecules capable of forming transition metal complexes. On both counts, accurate descriptions of the force field and of the resulting forms of the normal coordinates would be of much value, as well as being of assistance in the determination of reliable normal coordirmtes for the molecules thiourea and selenourea, for which much less spectro- scopic information is currently available. The necessary calculations have been carried out with some degree of assurance by employing recent data on the l*O [l] and r6N [z] frequency shifts of urea-Elp, in addition to the H4 and D4 frequency data [3-51 (which in themselves are insufficient to determine reliable information).

Recently, it has been demonstrated that heavy isotope frequency shifts are generally much more sensitive functions of the normal coordinates of a molecule, and hence of its force field, than the H and II isotopio frequencies [S]. The use of such frequency shifts enables the force field to be determined to a considerably higher accuracy than in their absence [7]. The reasons for this are twofold. Firstly,

[I] I. LUJTLIOHT, S. PINCHaS, E. PETREANU end D. S-L, Spectrochim. Acta 21, 1487 (1905). [2] R. PARELLIIDA and J. F. ARENAS, to be published; paper 82 at the Xth European Congress

of Molecular Spectroscopy, Liege (1909). [3] R. D. WALDRON, Ph.D. thesis, California Institute of Technology (1951); R. D. WALD~ON

and R. M. BILDQER, J. Chtvn. Php3.26, 255 (1957). [4] J. E. STEWART, J. Chew FiQJ8.26, 248 (1957). [S] A. Y~uuom, T. MNA~AWA, T. SHI~OUOHI and 8. Mrxusm, Spxtrochim. Acta 10,

170 (1957). [S] A. A. Cm- and D. C. Mom, Spectrochim. Acta 22, 251 (1966); D. C. MoKnm,

Spctrochim. Acta %$269 (1966). [7] J. L. DUNCE, D. C. MoKE~LN and A. ti, Mol. phy8.18,289 (1970).

1197

1198 J. L. DUNCAN

the small frequency shifts are relatively free from the effects of anharmonicity, which are at their maximum when H and D frequencies are employed. Secondly, the uncertainty of a frequency shift is very much smaller than that which arises when the two frequencies are treated independently; accordingly, the weighting factors are enhanced and the force field is thus determined with greater precision. The availability of reasonably precise IsO and 16N frequency shift measurements on urea-H, in the solid phase has prompted this investigation as an attempt to determine with some degree of accuracy the forms of the planar normal vibrations of urea.

A previous normal coordinate analysis of the planar vibrations has been carried out by YAXAMJCHZ et al. [5], employing a Urey-Bradley force field, and fitted to H and D frequency data only. These authors appear to have omitted the NH, stretching vibrations from their analysis, and the fit to the frequencies is not very good. In addition, their reassignment of the B, species NH, rocking vibration in urea-H, is neither supported by the observed 15N isotope shift data, nor by the present calcula- tions, which give a very much better simultaneous fit to all the data with the original assignment.

DEFINITION OF COORDINATES

Urea belongs to the point group C,,, in terms of which the thirteen planar vibrations factorize according to 7Ar + 6B,. A set of internally consistent valence symmetry coordinates is given in Table 1 in terms of the valence displacement coordinates of Fig. 1. These coordinates contain no angle redundancies. They correspond closely to those of YAMAGUC~~ et al., whose bending coordinates do involve angle redundancy relations, and which therefore differ from those here, the precise factors being :

sZfcmmation z fi * s~fomtion/G; gcging = 1/;z. As&~@

where Y refers to the symmetry coordinates of YAMA~UCHI et aZ., and D to those of this paper. Algebraic formulae for the QI elements are given in [6], and may be simply transformed to the coordinate system here by using the above relations. Apart from one trivial typographical error, these elements have been checked in this work. The equilibrium geometry employed here is that of the crystalline state, determined by WORSEAM et al. [S], and given by rN_n = O-99, R&N = 1.36,

D ~0 = 1.24 A, au- = 122’, 6NcN = 117’. Bond lengths are considered accurate to better than f0.01 A, and angles to better than f lo. The NH, groups are assumed to be symmetrically disposed about the CN bonds, and the NH bonds to be of the same length. The small differences observed in the NH bond lengths and in the HNC bond angles lie within the overall experimental errors in their determination. The effect of these small asymmetries on the results presented here is quite negligible, and it was not considered worth complicating the issue by taking them into account, particularly when the precision of the experimental frequency data (discussed below) is assessed.

[8] J. E. WORSHABI, H. A. LEVY and S. W. PETERSON, Acta Cqat. 10, 319 (1967).

Normal coordinates for the planar vibrations of ma 1199

Table 1. Internal valence symmetry coordinates for the planar vibrations of urea*

8, = 2-l(&; + &a + Br, + ha) 6.9, = 2-q&r1 - dr, - csr, + &i-d)

s,, = 2-l(aq + &, - 8r, - 6r,)

S, = 2-‘( 6R, + 8R,) s,,

i

= 2--1(&l - al.8 + a?-, - &A)

A,

i

S, = 6D R S,, = 21’a(8R1 - 6R,)

1 S, = F’*A(6a, + da,)

s,, = Zl’*A(6al - Baa)

$l z y’;$& - W,) 2, 5 ~~‘;Awl + vz)

7 * 16 'V

* Symmetry coordinates involving angle bending displacements are scaled by I Angstrom, thus enabling all force constants to have units mdyn A-1.

Y

5 / I l+- & HP

/ Rl

X

2 s Ydown

Fig. 1. Numbering of atoms and labelling of internal valence coordinates for urem.

OBSERVED DATA

The frequency end frequency shift data have been taken from Refs. [l-a]. The assigument of only one frequency has been questioned. In the B, species, the predominantly NH, rocking vibration, Q, of urea-H, was originally assigned to a weak band at ~1060 cm-l [3,4]. On the evidence of polarized infrared spectra, and by comparison with the spectrum of the guanidinium ion, YAMA~TJCHJ et al., preferred to reassign this vibration as underlying its A, species counterpart at 1164 cm-l, and assigned the corresponding B, species vibration in urea-l>, as coincident with its A, species counterpart et 886 cm-l [S]. This assignment introduces a rather serious product rule discrepancy in the B, species (H/D theoretical = 3.570, HID observed = 3.690), which is in the opposite direction to that normally encountered, i.e. it infers negative anharmonicity corrections. Because of this discrepancy, none of our calculations are able to give a good fit either to these frequencies alone or in conjunction with the observed l*O and 15N frequency shifts. When the alterna- tive assignment of 1060 cm-i to yr4 is used, the product rule predicts its counterpart in urea-D, to lie at -d350 cm-l, precisely where a band is found in the spectra. of

1209 J. L. DUNCAN

ANGELL and SHEPPARD [9] and of WALDRON [3]. This evidence, coupled with the observation of a ibN frequency shift of 10 cm-l on the 1060 cm-l band [2], in exact agreement with that predicted for the B, species rocking mode, would seem to strongly support the assignment originally proposed by WALDRON [3] and STEWART [4]. Accordingly, vi4 vibration frequencies of 1056 cm-l (the accurately measured value of PARELLADA and ARENAS [2]) for urea-H, and of 850 cm-l for urea-D4 are accepted for the purposes of the refinement. Uncertainties of 1 o/o have been allowed on all frequencies to cover the effects of experimental error and anharmonicity, as well as those which may arise from hydrogen bonding effects and Fermi resonance perturbations. From the fit achieved to the frequency data, it would appear that the latter two effects are not a major source of trouble.

The uncertainties associated with the frequency shifts are a little more difficult to assess. As well as the effects of hydrogen bonding in the solid state, which may affect some of the shifts, but can not be accounted for in the calculations, there is also the di0iculty associated with the measurement in many cases of band centres of broad and ill-defined bands in order to estimate the shifts. An indication of the difficulty may be had from the observation of LAULICHT et al. [l] that on l*O substitution, the NH, stretching frequencies apparently incPeme by 4 cm-l, a result probably of both the above effects. Accordingly, a minimum uncertainty of 2 cm-l was allowed on all shifts, but for larger shifts ( >8 cm-l) uncertainties of between 20 and 30% were allowed. The observed data and uncertainties allowed are given in Table 2. In the refinement calculations, the data were weighted according to l/ai2, where Us is the uncertainty in the ith datum.

RESULTS OF REFIXEYENT CALCULATIONS

The A, and B, species refinements were treated quite separately, and no trans- ference of force constants or constraints between the two species were found necessary. By orbital following arguments the signs of certain off-diagonal force constants can be predicted. With the definition of coordinates in Table 1, it is anticipated that in the A, species F3,4 and Pa,, should be positive, while P,,, and F,,, should be negative; in the B, species F12,16 should be positive and F,,,,, negative. It is most pleasing that in the refinements performed, all these force constants are calculated with the anticipated signs and with what appear to be reasonable magnitudes. Unfortunately, the 16N frequency shifts on the NH, stretching vibrations are not of sufficient accuracy to determine any NH, stretch interaction force constants with significance. All NH, stretch interaction force constants are therefore constrained to be zero. Considering the high degree of factorization of such stretching vibrations, our inability to determine any such interaction force constants should have very little effect on the remainder of the force constants and a negligible effect on the forms of the normal coordinates.

A, species

In the A, species, a successful refinement was first performed to all diagonal force constants and to the four off-diagonal force constants, the signs of which are

[S] C. L. ANQELL and N. SHEPPARD, unpublished results; C. L. ANOELL, Ph.D. thesis, University of Cambridge, 1968.

Normal coordinates for the planar vibrations of urea 1201

Table 2. Observed wavenumbers and uncertainties, IY, calculated wavenumbers and error ve&ora, E, for the planar vibrations of urea

WNW, OCPD,), Ohs a Cal0 & Obs (I Cd0 E

Vl 3449 35 3468 VP 3362 34 3361

V’a 1683 17 1689 V( 1603 16 1600 rz % 1164 12 1167 -3 V6 1003 10 1006 -3 17 661 6 667 0 co 3436 34 3463 -17 Vll 3342 33 3363 -11 %a 1626 16 1623 +3 V11) 1463 16 1463 0 VU 1066 11 1066 VlS 673 6 672

2689 26 2428 24 1628 16 1242 12 999 10 886 9 476 6

2686 26 2433 24 1488 16 1162 12 860 9 612 6

2680 $9

2429 1626 r:

1242 993 t-i 884 474 ::

2671 +16

2426 1486 $i

1166 849 ;: 612 0

0C(16NH ) II =OC(NH,), ObS u Cd0 E Obs u Cal0 E

9.6 3 12.4 -2.9 -10 10 4.4 +6*6

4.3 2 2.9 +1*4 2.1 2 3.2 -1.1 6.6 2 7.6 -2.0

21.1 4 20.7 +0*4 6.3 2 9.2 -2.9 9.6 3 12.1 -2.6

-10 10 4.4 +6*6 8.7 3 12.0 -3.3 3.6 2 3.8 -0.3

10.0 3 10.6 -0.6 6.1 2 6.2 -0.1

- - 9.6 3

lb.0 4 10.0 3 - -

2.0 2 - - -

2.0 z 0.0 2

- -

-18 6

o-0 0.0 9.6

16.6 11.6 9.7 3.8 0.0 0.0 0.1 0.8 I.0

13-3

- -0.1 - I.6 - 1.6

- -1.8

-

+T9 -0.8

+Y7

predictable. These concern the interactions between CN, stretching/CO stretching (F3,4), CN, stretching/NH, deformation (F&, CN, stretching/CN, deformation (F3,,), and CO stretching/CN, deformation (F4,,). Each of the remaining six inter- action force constants could be significant, so the improvement in the fit to the observed data was found on releasing each in turn. (Releasing more than one, along with the other eleven parameters, csused the c&uiletion to become ill-conditioned.) Five of these force constants, F4,5, F4,e, F5,B, F5,, and F6,7, refined to very small values (IFrrl < O-05 mdyn 8-l) and gave little improvement in the fit. However, permitting the CN, stretching/NH, rocking interaction force constant, F3,@, to refine gave a significant improvement in the fit to the frequency shift data. Accordingly, the data were assumed to be sensitive to this force constant, and relatively insensitive to the others, and this la-parameter refinement was accepted as the best result consistent with the data. As seen in Table 2, the reproduction of the frequency data is excellent, and all frequency shifts are reproduced to within a reasonable estimate of the uncertainty in their measurement. The 16N frequency shift on the symmetric NH, stretching vibration must always be less than the shift on the antisymmetric stretching vibration for HNH angles greater than 90°, as can be seen by inspection of the respective G elements. The experimentally observed shift of -10 cm-l cannot be reproduced by any force field, and may well arise out of hydrogen bonding effects or difliculty in the accurate location of the band centres.

All force constants (listed in Table 3) appear to have reasonable values. A not

1202 J. L. DUNCAN

inconsiderable CO stretching/CN, stretching interaction is predicted ($‘a,4 = +2*507 mdyn 8-i), as might be expected from the possible resonance forms of this molecule. The CO stretching force constant of 11.4 mdyn 8-l is less than that found in formaldehyde (rco = 1.205 8) of ~13.0 mdyn A-l, and in carbon dioxide and ketene (rco = 1.16 d) of ~16.0 mdyn A-l, reflecting the weaker and longer CO bond in urea (rco = l-24 A). In all planar molecules containing the XYZ, group, for the definition of symmetry coordinates of Table 1, a large and negative value for the X Y stretching/ YZa deformation interaction force constant is found necessary to fit the frequency data, and is reproduced here in the force constants F,,, and E”,,,. In agreement with orbital following arguments, F3,, is calculated to be positive, although it is not very well defined.

The force field determined here is rather different from that of YAMAGUCHI et al., particularly with respect to the diagonal elements representing the CN, stretching and CO stretching coordinates, for which they found FCNSatreech = S-07, PO0 stretch = 8.69 mdyn 8-l. Although this latter force field gives a tolerable fit to the H and D frequencies [5], it will reproduce practically none of the heavy isotope frequency shifts. These, of course, were not available at the time of its determination. How- ever, it is hoped that the usefulness of such data as a means towards the achievement of a greater accuracy in force constant calculations and hence in the determination of the actual forms of the normal coordinates of a molecule is demonstrated here.

B, species In the B, species, it was found possible to reproduce the two lowest vibration

frequencies in the H4 and Da species only on releasing the NH, rocking/CN, rocking interaction force constant, F,,,,,. The two interaction force constants, CN, stretch- ing/NH, deformation, F12,13, and CN, stretching/CN, rocking, Fla,ls, the signs of which may be predicted from orbital following arguments, were also allowed to vary, and this g-parameter refmement was found to give a good fit to all the data. None of the remaining three force constants, F12,14, F13,14, F13,15, on being allowed to refine, was found to give any significant improvement in the fit. Therefore, this g-parameter set of force constants was accepted as the best set consistent with the data. The excellence of the overall fit to the data in Table 2, and in particular the reproduction of the observed 16N frequency shift on vi4 of urea-H, seem to be con- vincing evidence that the assignment used here for the B, species vibration fre- quencies is the correct one.

Combined results

The accepted sets of force constants for the A, and B, species of urea with their standard deviations are given in Table 3, along with the associated potential energy distributions for urea-H, and -D4. Further data, in the form of L, L-l, Jacobian matrix elements, and Cartesian displacement coordinates are available on request from the author. Since it is considered that the actual forms of the normal co- ordinates for the planar vibrations of urea are determined with some degree of precision in these calculations, the atomic displacements in each normal coordinate are depicted in Fig. 2, where all displacements are for 5 x a unit displacement in the normal coordinate, except for the NH, stretching vibrations, where the displace- ments are for a unit displacement in the normal coordinate.

&0*61-

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o-

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‘6

J. L. DUNCAN

Fig. 2. Calculated carte&n displacements for the planar vibrations of urea-H,, (a) A, species, (b) B, species. The arrows correspond to 5 x a unit displacement in the corresponding normal coordinate, except for the hydrogen stretching vibrations where they correspond to 1 x a unit displacement. The normal coordinatee shown are those for the force field of Table 3 of this work. (The frequency assoaiated with the second last normal vibration in (b) should be

1056 cm-l.)

Normal ooordinates for the planar vibrations of urea 1206

From the two sets of force constsnts determined in this work, the NH and CN stretch valence force constants are calculated to be fNH = 6.40 and fcN = 6.82 mdyn A-l. The former is slightly lower than that found, 666 mdyn A-l, for the observed frequency data of ammonia, and equal to that found for methylamine [lo]. The latter is considerably larger then the corresponding valence force con&s&s in methylamine of 4.9 mdyn 8-l [lo] an in methyl &cyanide of 5.4 mdyn A-1 [Ill, d reflecting the grester double bond character of the CN bonds in urea (roN methyl- amine = 1’474 A, rcN methyl isocyanide = l-427 A, roN urea. = 1.35 A). The small differences found for the NH, deformation and rocking force constants in the 8, and B, species indicates that a small but significant interaction occurs between the two NH, groups in urea.

Table 4. Observed frequency shifts for 0C(14NHs)(16NHe) and values calculated using the force field of Table 3

Obs CMC Obs talc

4 -6 2.2 ko -5 10.1

A% -6 1.7 41 45 2.7

A% 3.2 1.3 A912 6.7 6.7

A94 1.6 1.9 A%8 I.7 1.9

A% 2.2 3.7 &a - 4.9

Avs 10-B 10.8 % 2.6 2.6

A+ 3.2 4.6

As a test of the force field, the frequency shifts arising from mono 16N substituted urea were calculated and compared with the observed values [2]. The asymmetric substitution of only one 14N atom by its 15N isotope causes the A, and B, species of the C,, point group to combine into one species containing all thirteen planar vibrations. It was considered that an adequate test of the accuracy of the derived force field would be its ability to reproduce all the observed frequency shifts of 0C(14NHz)(‘SNHz). As can be seen in Table 4, with the exception of the NH, stretching vibrations, the shifts on which are not measured to high accuracy, most of the experimentally observed shifts are reproduced to within a few tenths of a wavenumber. This pleasing result gives an indication of the accuracy to which the normal coordinates are determined from the data available, within the limitations of the harmonic oscillator approximrttion.

Note added in proof--To conform with the MULLIKEN convention [J. Chem. Phya. 83, 1997 (IQ!%)] the (2, y, z) axes in Fig. 1 should be replaced by (-y, z, e). The planar vibrations of a molecule belonging to the point group OsV are then of symmetry speoies A, and B,. If this convention is followed, then throughout this paper Bl should be replaced by B,. The vibration frequencies vlo - vls then becomeg rn, - rrs, and the force constants Fn,, etc. become E;s.rs etc.

Acknowledgment-The author would like to thank Dr. R. PARE-A, Prof. N. SHEPPARD and Prof. R. M. BADGER for most helpful correspondence, and Drs. P~L~E~AD A and ARENAS for making their results on the rsN frequency shifts of ~rea-E~ available prior to publication.

[lo] E. L. Wu, G. ZEXBI, 5. CALIBANO and B. CRAw.rOnD, J. Chem. Phye. 86,206O (1981). [ll] J. L. D~CAN, Spectrochim. Acta $30, 1197 (1964).