ELSEVIER Journal of Molecular Structure (Theochem) 312 (1994) 93-100

THEOCHEM

Ab initio studies on tetramethylurea and tetramethylthiourea

Katalin T6tha, Philippe BOppb, Mikael PeriikyliiC, Tapani A. Pakkanenc

, Gabor Jancs6*,a'Central Research Institute/or Physics, Atomic Energy Research Institute, P.O. Box 49, H-1525 Budapest, Hungary

b1nstitut /iir Physikalische Chemie, Rheinisch- Westfalische Technische Hochschule, D- W-52056 Aachen, Germany<University 0/Joensuu, Department o/Chemistry, P.O. Box 111, 80101 Joensuu, Finland

(Received 25 October 1993; accepted 21 January 1994)

Abstract

Ab initio molecular orbital theory at the HF and MP2leveis was applied to study the structures oftetramethylurea andtetramethylthiourea and to carry out a conformational analysis of these molecules. The calculated structural parametersare in good agreement with the experimental observations and correctly describe the deviations of the moleculargeometries from the planar structures. Conformational analysis shows that the rotational motions about the Csp2-Nbond are less hindered than the analogous motions in dimethylformamide and dimethylthioformamide. The methylgroups can rotate quite freely around the C-N bond in both the molecules studied here.

1. Introduction

Tetramethylurea (TMU) is one of the few ureaderivatives that are liquid at room temperature. Itis miscible in all proportions with water, while thesolubility of tetramethylthiourea (TMTU) in wateris rather low (about 2.6 g per 100 cm3 at 20DC).TMU-H20 mixtures exhibit a number of anoma­lies in their physico-chemical properties [1] whichreflect the changes with concentration in theirstructure and intermolecular interactions. Recently,we have used different neutron-scattering tech­niques to obtain information about the structureand dynamic properties of aqueous TMU solu­tions [1-3]. As a first step to understanding thesolute-solute and solute-solvent interactions inthe solutions, we attempted in the present work

*Corresponding author. Present address: Laboratoire de Spec­troscopie Moleculaire et Cristalline, Universite de Bordeaux I,F-33405 Talence Cedex, France.

to elucidate the structure of the free TMU andTMTU molecules by using ab initio techniques.

Originally, the structures of urea and its deriva­tives were believed to be planar [4], because theC-N bond has partial double-bond character.Experimental X-ray and neutron-diffraction datashow a planar structure for the urea molecule inthe crystal phase [5-7], whereas in the gas phasethe microwave spectrum of urea [8] indicates a non­planar structure, which was later confirmed by anab initio study [9]. No experimental study is avail­able on the molecular structure ofTMU in the solidstate. An early electron diffraction (ED) study ofTMU in the gas phase, carried out by Vilkov et al.[10], yielded a nearly planar configuration of thenitrogen atoms, but this result was revised byFernholt et al. [11], using the ED method, whofound a pyramidal (sp3) configuration about thenitrogen atoms for both TMU and TMTU.

The aim of the present study was not onlyto determine the molecular structures by means

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94 K. T6th et al./J. Mol. Struct. (Theochem) 312 (1994) 93-100

Fig. I. Numbering of the atoms in TMU (TMTU). ¢ and 7 aretorsional angles defined as: ¢I> LXIC2N3C4; ¢2, LXIC2N3C5;71, LC2N3C4H; 72, LC2N3C5H. ¢ is equal to 0° when N3-C4 issyn to C=X, and 7] and 72 are equal to 0° when C4-He/C5-Heare syn to C2 - N) (He is the closest hydrogen atom in therespective methyl group to the C=X group).

ofelaborate ab initio calculations, but also to carryout confonnational analyses and to study thebarriers to internal rotations. The other interestingpoint, we consider, is the effect of substitutingoxygen by sulphur on the molecular properties.

2. Computational methods

Ab initio molecular orbital calculations wereperfonned using GAUSSIAN 90 (12] and GAUSSIAN 92

[13] on CRAY Y-MP, SNI-Fujitsu S600/20, andStardent 3040 computers. Geometry optimiza­tions assuming C2 symmetry were carried out atthe Hartree-Fock (HF) level using the standard4-31G and 6-3IG* basis sets (split-valence basissets; the asterisk indicates inclusion of d orbitalson the heavy atoms) and Huzinaga's minimalbasis set MINI-I [14]. The electron correlationwas considered by employing the second-orderMeller-Pleset perturbation (MP2) correction,using the frozen core approximation, with the6-31 G* basis set (MP2/6-31 G*). Complete geom­etry optimization was also carried out for the MP2case. In order to study the barriers to internal rota­tions, the geometries were fully optimized for dif­ferent fixed internal rotation angles at the HF level.The potential energy profiles used for the detenni-

nation of the rotational barriers of internalrotation are described by Fourier-type expansionof the potential function with the fonn [15]:

IV = yO +"2 L Vn[1 - cos(nT)]

(n= 1,3)

+ L V; sin(nT) (I)(n=I,2)

where T is the particular dihedral angle and yO isthe energy corresponding to the T = 00 angle.

3. Results and discussion

3.1. Geometries and Mulliken charges

A sketch of the molecules TMU (X = 0) andTMTU (X = S) is shown in Fig. I where the num­bering of the atoms and the internal coordinatesare defined. In Table I we compare the calculatedand experimental geometrical parameters,obtained by gas electron diffraction (ED) [10, II]and liquid X-ray diffraction (XR) methods [16], forthe TMU molecule. The molecular geometryobserved in the more recent and complete ED[11] study was used as the initial values for dipolemoment calculations and for comparison with theresults of our calculations. Complete structureoptimization at the MINI-I level gives longer equi­librium bond lengths and slightly smaller bondangles than the corresponding experimentalvalues. While the 4-31 G split-valence basis setoffers an improved description of bond lengths,the bond angles are in less good agreement withthe experiment than are the ones obtained withMINI-I. The 6-3IG* polarization basis set leadsto a real improvement in the bond angles andlengths. The mean absolute deviation of the6-31G* bond angles and bond lengths from experi­ment are thus 0.8 0 and 2.3 pm, respectively. Elec­tron correlation (MP2/6-3IG*) gives structuralparameters which are very close to the experimen­tal values: all bond lengths and angles are nowwithin 1.3 pm and 0.7 0 of the experimental values.The degree of pyramidality about the nitrogenatoms (i.e. the magnitude of the non-planarity)can be described by the out-of-plane bending of

K. T6th et al.jl. Mol. Struct. (Theochem) 312 (1994) 93-100 95

Table IThe calculated and experimental (ED, electron diffraction; XR, X-ray diffraction) geometrical parameters for TMU; atom-numberingcorresponds to Fig. I

HFj4-3IG HFj6-3IG* HFjMINI-I MP2j6-3IG* MNDO ED ED XR[19] [II] [10] [16]

Bond length (pm)C=O 123.0 120.2 127.1 123.4 122.7" 124.0 121.5 123C2-N3,6 137.1 138.0 145.2 139.4 142.6 139.7 133.8 137N3-C4,5 145.6 145.2 149.5 145.8 146.8 146.1 145.4 146C-H 108.1 108.3 120.0 109.4 111.7 110.0

Bond angle (deg)LXCN 121.4 122.0 122.8 122.7 122.1 122.3 120.0 119.3LC2N3C4 117.7 115.5 113.8 114.7 118.9 114.3 117.5 114.0LC2N3C5 123.4 121.0 117.6 119.9 120.4 119.8 117.5 119.7LNCH 110.3 110.4 110.5 110.1 110.9 110.0

q,l -13.3 -7.0 -3.0 -4.4 -31.7 -4.8 -7q,2 143.7 136.7 133.3 135.7 125.9 138.3 144.271 -28.1 -42.6 -44.3 -42.272 5.2 22.8 31.5 24.0XN 23.0 36.3 43.7 39.9 22.4 36.9 28.8

"Some values are averages of the calculated ones obtained without assuming C2 symmetry.

the nitrogen atom (XN); this ranges from 0° forplanar Sp2 to 60° for tetrahedral Sp3 nitrogen [17].The values of XN, calculated according to Ref. 17and listed in Table 1, show that the pyramidal con­figuration about the nitrogen atoms are welldescribed in all cases except with the 4-31G basis set.

It is worth mentioning that there are no signifi­cant differences between the experimental struc­tural parameters determined in the gas and liquidphases, with the exception of XN, the values ofwhich indicate that the pyramidal configurationof the nitrogen atom in TMU is more pronouncedin the gas phase than in the liquid phase. Thiscontrasts with the behaviour found for smallamides (the TMU can be considered as a deriva­tive of dimethylformamide). There an elongationof the carbonyl bond and a shortening of thec-N bond distance in the crystal was observed,compared with the gaseous state [18]. The struc­tural analysis done by Radnai and Ohtaki [16]indicates a certain kind of ordering between neigh­bouring TMU molecules in the liquid phase, sup­posing the formation of loose dimers due todipole-dipole interaction in the liquid.

As far as we know, ab initio studies on TMU andTMTU have not been carried out so far; only semi-

empirical MNDO [19] and AMI [9] results areavailable in the literature. The MNDO structuralparameters for TMU are listed in Table 1, fromwhich it can be seen that the MNDO methodunderestimates the amount of pyramidality andoverestimates the torsion around the CSp2 - Nbonds «/>i, 4>2) compared with the values obtainedby ED and our ab initio calculations. The AM 1study reported in Ref. 9 is limited to the calculationof the torsional angles 4>, and 4>2; the values of 1.4°and 148.4° are quite close to the experimental ones.

The calculated and gas ED [11] experimentalstructural parameters for the TMTU molecule arecollected in Table 2. The thionyl bond distance isoverestimated by the MINI-l and 4-31G basis sets,but is well represented by 6-31 G* one, which showsthe importance of the d functions on sulphur [20].Errors in the lengths determined for other bondsare consistent with the corresponding results forTMU and need not be discussed. MINI-l bondangles are in surprisingly good agreement withthe experimental values, with the exception of the4>, torsional angle which is much smaller than theexperimental value and is underestimated even bythe 4-31 G and 6-31 G* basis sets. The pyramidalityof the nitrogen atoms seems to be overestimated by

96 K. Toth et al./J. Mol. Struct. (Theochem) 312 (1994) 93-100

Table 2The calculated and experimental (ED, electron diffraction) geometrical parameters for TMTU; atom numbering corresponds to Fig. 1

HF/4-3IG* HF/6-3IG* HF/MINI-I MP2/6-31G* ED"

Bond length (pm)C=S 173.2 168.0 178.3 166.4 167.6C2-N3,6 135.2 135.9 140.7 138.1 138.8N3-C4,5 146.2 145.6 149.5 145.9 146.1C-H 108.0 108.2 112.0 109.3 111.2

Bond angle (deg)LXCN 121.7 122.4 122.3 123.4 122.2LC2N3C4 120.6 120.2 118.7 118.5 118.9LC2N3C5 122.7 121.6 121.8 120.1 122.3LNCH 110.1 110.2 110.3 109.9 110.9

r/>1 -14.8 -12.5 -7.6 -8.9 -23.8

r/>2 144.8 140.9 144.3 137.4 140.171 -36.7 -41.9 -41.7 -45.172 -1.0 6.5 4.4 14.0XN 20.4 26.6 28.1 33.7 16.1

"Ref. 11.

all calculations compared with the experiment. Theslightly less pyramidal configuration in TMTUcompared with TMU is, however, reproduced.The experimental Csp2 - N bond length is slightlyshorter in TMTU than in TMU, which is wellreproduced by the calculations. A similar shorten­ing of the Csp2 - N bond length has also beenobserved for thioamides [18]. This bond-length

shortening can be interpreted by considering thepyramidalization of nitrogen atoms in TMU andTMTU: an increase in the planarity about thenitrogen atom is accompanied by a decrease inthe Csp2 - N distance because the resonance formof the molecule, in which the Csp2 - N has double­bond character, becomes more dominant.

Table 3 shows the calculated dipole moments

Table 3Calculated" atomic charges (with hydrogen atoms summed into heavy atoms) and dipole moments for TMU and TMTU; atomnumbering corresponds to Fig. 1

X=o X=S

HF/MINI-I HF/4-31G HF/6-3IG* HF/MINI-l HF/4-3IG HF/6-31G*

Atomic chargeb (e)XI -0.401 -0.667 -0.650 -0.282 -0.Q75 -0.315C2 0.416 1.106 0.995 0.132 0.354 0.464N3 -0.251 -0.820 -0.655 -0.220 -0.804 -0.608C4 0.126 0.319 0.248 0.155 0.338 0.277C5 0.118 0.304 0.235 0.140 0.326 0.257N6 -0.251 -0.820 -0.655 -0.220 -0.804 -0.608C7 0.126 0.319 0.248 0.155 0.338 0.277C8 0.118 0.304 0.235 0.140 0.326 0.257

Dipole moment (D)2.815 3.575 3.532 5.418 4.968 5.200

"Experimental equilibrium geometries [11] were used.be = 1.602177 x 10-19 C.clD = 3.336 x 10-30 Cm.

K. T6th et al.jJ. Mol. Struct. (Theochem) 312 (1994) 93-100 97

40

35

30

:::- 250

.E....~ 20>-E'..cw 15

10

5

0

0 30 60 90Dihedral Angle (deg)

120 150 180

Fig. 2. Torsional profiles of the dihedral angle '1>1 ofTMU by using MINI-l C&) and 6-3IG* (.). Fits to Eq. (1) for MINI-I (-) and6-3IG* (- - -).

and net Mulliken charges on heavy atoms for theTMU and TMTU molecules. Experimental equi­librium geometries were used [11]. The calculatedcharges are extremely sensitive to basis set [20] andthus a comparison of the results obtained with thesame basis sets shows that the sulphur atom is lessnegative than the oxygen atom and the Csp2atom isless positive in TMTU than in TMU. The calcu­lated dipole moments ofTMU, except that obtainedwith the MINI-1 basis set, fit into the range ofexperimentally observed values (3.28-3.66 D) [21].We could not find any experimentally observeddipole moment for TMTU in the literature; how­ever, it is known that the thiourea and substitutedthioureas (sym-diphenylthiourea [22] and N, N'­dimethylthiourea [23]) have slightly higher dipolemoments (0.33-0.11 D) than the correspondingureas. It is interesting that the calculated dipolemoment of TMTU is much higher than that ofTMU. The dipole moment of urea is larger thanthat of TMU by about 1.2 D, which is themesomeric contribution to the dipole moment[24]. By assuming that for TMTU the mesomericcontribution is about as large as for thiourea (whichis reasonable because in TMTU the formation ofresonance structures is less hindered than in TMU

due to the more planar structure of the former) oneexpects that TMTU has a slightly higher dipolemoment than does thiourea (4.89 D) [22].

3.2. Conformational analysis and torsional barriers

Conformational analysis has been performed forTMU and TMTU by studying the rotation aboutthe Csp2-N and C-N bonds (torsional angles <PI>and 71 and 72, respectively, see Fig. 1). The energiescalculated at 30° intervals of the dihedral angle <PI,by using the MINI-l and 6-31G* basis set forTMU, are plotted in Fig. 2. The energy profilecan be represented in the form of Eq. (1) and thecorresponding curves are drawn in Fig. 2 as solidand dashed lines for the MINI-l and 6-31G* basissets, respectively. The polarization function doesnot have a significant effect on the torsional pro­file; it just increases the rotational barrier from 35.7to 37.2 kJ mol-I. There is quite a large differencebetween the available experimental data on thisbarrier; while Stilbs and Moseley [25] obtained avalue of 25.5 ± 0.4 kJ mol-I from Fourier trans­form measurements of nuclear spin relaxation atabout -120°C, Martin et al. [26] predicted avalue of 48.5 kJ mol-I based on a correlation

K. T6th et a/.(l. Mo/. Struct. (Theochem) 312 (1994) 93-10098

80

70

60

:=- 500

.E.,:!!. 40>-f'..~ 30

20

10

0

0 30 60 90

Dihedral Angle (deg)

120 150

•

180

Fig. 3. Torsional profile of the dihedral angle (PI ofTMU by using MINI-l and considering the -N(CH3h group as rigid. The line is a fitto Eq. (2).

between 15N chemical shifts and measured barrierheights for various dimethylamino derivatives. Theparameters of the equation given in Ref. 26 werecomputed with respect to the hindered rotational

10

9

8

7

6'0~ 5:!!.>-f' 4!w 3

2

barrier of dimethylformamide as reference; the lat­ter is a planar molecule, and thus Martin et al.'sequation might overestimate the rotational barrierin TMD.

'.o +---+---+"7'"-+..,.....:--+--f----j,.----1f==:....I--I--+--+--+---f---+--'+--+.-:-."'---r-----l

·130 60 90 120 150 180

Dihedral Angle (deg)

Fig. 4. Torsional profiles of the dihedral angles 71 (.) and 72 (..) ofTMU by using MINI-I. The solid and dashed lines are fits to Eq. (I).

K. Toth et al.jl. Mol. Struct. (Theochem) 312 (1994) 93-100

45

99

·'0

35

30

10

5

•

O+-----l_-1-_+----"I---+_-r-_-I--+_+-_+----+--f--+---==f""""'=:::::!:o,..L.+---1r--i

-530 60 90

Dihedral Angle (deg)

120 150 180

Fig. 5. Torsional profile of the dihedral angle rPl of TMTU by using MINI-\. The line is a fit to Eq. (1).

are shown in Fig. 3. This treatment of the motionsmakes the energy profile very smooth, but gives anunreliably high (71.48 kJ mol-I) rotational barrier.

Another interesting point is to investigate howeasily the -CH3 group can rotate about the C-Nbond. The results of the rotational analysis consid­ering 71 and 72 are displayed in Fig. 4. The curvesshow a C3 symmetry corresponding to the local C3

During the conformational analysis of the mol­ecules the bond length changed very little (e.g. theC2-N3,6 bond by ±0.8 pm) between the steps, butthe bond angles LC2N3C4 and LC2N3C5 and theother torsional angles altered significantly, whichsuggests that the rotation about the Cspz-N bondis strongly coupled with the nitrogen inversion.(The optimized geometry parameters belonging toeach step are available from the authors onrequest.) In order to separate the rotation and theinversion motion, the -N(CH3h group was con­sidered to be rigid during conformational analysis.The calculated energies and energy profile of therotational motion in the form of

IV = VO + 2: L Vn[l - cos(n7)]

(n=I,3)

(2)

symmetry of the -CH3 group. As can be seen fromthe figure, the methyl groups can rotate quite freelyand there is no significant difference between therotational barriers of 8.5 and 9.2 kJ mol-I for themethyl group positioned on the carbonyl side andthe methyl group situated on the other side of themolecule.

Finally, the rotation about the Cspz-N bond inTMTU was also investigated and the results areshown in Fig. S. The basis set applied was MINH.The energy profile obtained is quite similar to thoseobtained for TMU (see Fig. 2). The rotationalbarrier is higher (40.8 kJmol- l

) than that ofTMU (35.7kJmol- l

) which is in disagreementwith the value predicted by Martin et al. [26](13.4kJmol- I). Conversely, our result is consist­ent with the tendency observed for dimethylforma­mide (DMF) and dimethylthioformamide(DMTF). In these the rotational barriers werefound to be 86.24 and 92.11 kJfmol, respectively[27, 28]. If one considers the TMU as a derivativeofDMF, it is very interesting to observe how dras­tically the rotational barrier decreases on replacingthe hydrogen atom by the -N(CH3h group. Thiscan be due to the loss of planarity in the case ofTMU.

100 K. T6th et alp. Mol. Struct. (Theochem) 312 (1994) 93-100

Acknowledgements

K.T. and G.J. acknowledge the financial supportfrom the Hungarian Research Fund under grantNo. OTKA-1846. P.B. acknowledges a Heisen­berg Fellowship from DFG and support byFonds der Chemischen Industrie, Frankfurt.Grants of computer time on the CRAY Y-MPand SNI-Fujitsu S600/20 computers are alsoacknowledged.

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