Journal of Molecular Structure 612 (2002) 315±324
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The microwave Stark and Fourier transform spectra, structure and quadrupole coupling constants of 1,2-dicyanocyclobutene q D. Petitprez a,1, G. Wlodarczak a, H. Lignier a, J. Demaison a, A. de Meijere b, A.G. Steiniz b, H. Mùllendal c,* a
Laboratoire de Physique des Lasers, Atomes et MoleÂcules, Universite des Sciences et Technologies de Lille, FR-59655 Villeneuve d'Ascq Cedex, France b Institut fuÈr Organische Chemie der Georg-August-UniversitaÈt GoÈttingen, Tammannstrasse 2, DE-37077 GoÈttingen, Germany c Department of Chemistry, The University of Oslo, P.O. Box 1033, Blindern, NO-0315 Oslo, Norway In honor of Professors Helmut Dreizler and Paolo Favero for their many contributions to science Received 17 July 2001; revised 30 November 2001; accepted 30 November 2001
Abstract The microwave spectrum of 1,2-dicyanocyclobutene, C4H4(CN)2, has been investigated using a Stark microwave spectrometer in the 11.0±34.0 GHz spectral region, and a Fourier transform microwave spectrometer in the 6±18 GHz region. The ground and several vibrationally excited states of the parent species have been assigned, as have the ground state of several 13C and 15N isotopomers. The nuclear quadrupole coupling constants of the 14N nucleus have been determined for several species. The effective (r0) structure of the molecule has been derived. The substitution (rs) structure of the heavy atoms has also been calculated. An anomalously short carbon±carbon double bond of 132.6(2) pm was found by the substitution method. This short bond length is shown to be unreliable. Advanced quantum chemical calculations have been carried out for the title compound as well as for the cyclobutene prototype. An accurate estimate of the equilibrium (re) structures of cyclobutene as well as of 1,2dicyanocyclobutene based on quantum chemical calculations has been made. q 2002 Elsevier Science B.V. All rights reserved. Keywords: 1,2-Dicyanocyclobutene; Microwave spectroscopy; Structure; Nuclear quadrupole coupling constants; Quantum chemical calculations
1. Introduction The rather unique structure of gaseous cyclobutene q
This paper is dedicated to Professor Paolo G. Favero and Professor Helmut Dreizler in appreciaton of their signi®cant contributions to the ®eld of microwave spectroscopy. * Corresponding author. Tel.: 147-22-85-56-74; fax: 147-22-8541-54. E-mail addresses:
[email protected] (D. Petitprez),
[email protected] (H. Mùllendal). 1 Also corresponding author. Tel.: 133-3-20-43-49-05; fax: 1333-20-33-70-20.
was determined about 30 years ago by Bak et al. [1] by microwave spectroscopy (MW). The compound was found to have a planar carbon skeleton. The C±C±C bond angles are close to 908. The carbon±carbon single bond opposite to the carbon±carbon double bond was found to be as long as 156.6(3) pm by the isotopic substitution method (rs-distance) [2]. It is likely that such a long and presumably weak bond would be easily in¯uenced by substituents. Bastiansen and Derissen [3] investigated cis-3,4dichlorocyclobutene by electron diffraction (ED) and found a long distance of 158.3(13) pm, an
0022-2860/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0022-286 0(02)00102-3
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increase of almost 2 pm compared to cyclobutene itself. In a related compound, 1,2-dichlorotetra¯uorocyclobutene, an even longer bond (rg value 1.599(10) pm) was found [4]. Interestingly, in tetra¯uorocyclobutene [5] the corresponding bond length was found to be 153.9(6) pm (rs-distance), nearly 3 pm shorter than in the prototype compound and 6 pm shorter than in its `cousin' 1,2-dichlorotetra¯uorocyclobutene. Several investigations have been made for hexa¯uorocyclobutene with con¯icting results. The C±C distance was found to be 159.5(16) in the ®rst ED investigation [6] and 158.1(11) pm (ra-distance) in the second [7]. However, a MW study yielded a much smaller value of 155.2(6) pm [8]. The discrepancy of about 3 pm motivated a new investigation in which the rotational constants were included with the ED ®t [9]. The result was 158.2(8) pm (ra0-value). There is thus an unresolved controversy regarding this distance in hexa¯uorocyclobutene obtained by MW spectroscopy and ED. The origin of this difference is unclear [9]. A recent ab initio investigation [10] (MP2/631 1 G p and LDA 1 BP/TZP levels of theory) yielded results that are in better agreement with the combined ED±MW result [9] than with the MW ®nding [8]. The investigations referred to above have indeed revealed that the long carbon±carbon bond length is sensitive to its substitutents, as it varies from about 154 [8] to approximately 160 pm [4]. This is not the only structural parameter that apparently varies considerably for cyclobutenes. Rather different values have been reported for the carbon±carbon double bond as well. A long double bond of 135.9(9) pm has been reported for 1,2-dichlorotetra¯uorocyclobutene [4], whereas a short bond of 132.5(24) pm was determined for hexa¯uorocyclobutene [9]. In other investigations [3,5,6,8] bond lengths between these two extremes were derived. The in¯uence of the cyano group on the structure of the cyclobutene ring has not been investigated before, and this was one motivation to carry out the present MW and theoretical study. Moreover, the title compound presented us with some additional challenges as well. Using the Lille Fourier transform spectrometer it should be possible to resolve and hopefully assign the complicated hyper®ne structure
caused by quadrupole coupling with the overall rotation of the spins of the two 14N nuclei in the parent species. It was also hoped that using this instrument it would be possible to obtain and analyze the spectra of mono-substituted 13C and 15N isotopomers in natural abundance, allowing the full substitution structure of the ring to be determined, thus avoiding complicated and expensive chemical syntheses. The fact that 1,2dicyanocyclobutene has an unusually large dipole moment (roughly 20 £ 10 230 C m; note units) and hence a relatively strong spectrum, indicated that our objections with regard to these less abundant isotopomers might be within reach. It was also decided to carry out high-level quantum chemical computations for several reasons: these calculations produce fairly accurate rotational constants that would facilitate assignments. The predicted dipole moment and the vibrational fundamental frequencies are helpful in the assignment procedure. These calculations are now so advanced that it should be possible in this case to calculate a rather reliable and accurate equilibrium structure that could be compared with experimentally derived structures both for the cyclobutene prototype molecule as well as for the title compound.
2. Experimental 2.1. Synthesis The sample utilized in this work was synthesized according to the procedure of Bellens et al. [11]. 2.2. Stark spectrometer experiment The MW spectrum was ®rst studied using the Oslo spectrometer, which is brie¯y described in Ref. [12]. The 11±34 GHz spectral region was investigated at room temperature. The pressure was about 2±4 Pa when the spectra were recorded and stored electronically using the computer programs written by Waal [13]. The lines were rather broad because of the rather high dipole moment. Quadruple coupling arising from the two nitrogen nuclei may also have contributed to the broadness. The accuracy of the spectral measurements is presumed to be no better than ^0.12 MHz for this reason.
D. Petitprez et al. / Journal of Molecular Structure 612 (2002) 315±324
2.3. Fourier transform experiment The MWFT spectrometer in Lille [14] was then used in the 6±18 GHz spectral range to record some lines at a higher spectral resolution and also to study some isotopic species. A newly built heated nozzle was used to increase the line intensities [15]. The optimal operating temperature was found to be around 40 8C. Neon was used as the carrier gas, at a pressure behind the nozzle of 1.5 £ 10 5 Pa (1.5 atm). The 13C and 15N species were observed in natural abundance. The accuracy of the measurements is as large as 2 kHz, partly owing to the complex hyper®ne pattern caused by the two nitrogen nuclei. 2.4. Method of calculations All the calculations were performed with the molpro2000 2 [16] or gaussian 94 [17] programs. The 6-31111G pp basis set as implemented in gaussian 94 was used for the ®rst prediction of the rotational constants and the dipole moment components. Electron correlation was included using the second order Mùller±Plesset (MP2) perturbation theory [18]. This procedure was selected because use of a relatively large basis set in the MP2 procedure is known to give fairly accurate geometries [19], and hence rotational constants. It was neither assumed that the molecule has C2v symmetry in these MP2/631111G pp re®nements, nor that the heavy atoms lie in one plane. However, the computations converged to an energy minimum (all vibrational frequencies computed to have positive values [20]) having C2v symmetry. For the ®nal calculations of the structure, different methods and basis sets were used. Besides the MP2 method, density functional theory with the hybrid functional B3LYP (Becke's three parameter functional employing the Lee, Yang and Parr correlation functional), [21] was also used. This method has been shown to be often in better agreement with experiment 2
molpro2000 is a package of ab initio programs written by H.-J. Werner, P.J. Knowles, with contributions from R.D. Amos, A. Bernhardsson, A. Berning, P. Celani, D.L. Cooper, M.J.O. Deegan, A.J. Dobbyn, F. Eckert, C. Hampel, G. Hetzer, T. Korona, R. Lindh, A.W. Lloyd, S.J. McNicholas, F.R. Manby, W. Meyer, M.E. Mura, A. Nicklass, P. Palmieri, R. Pitzer, G. Rauhut, M. SchuÈtz, H. Stoll, A.J. Stone, R. Tarroni, T. Thorsteinsson.
317
than the MP2 method and at a lower cost [22]. However, to obtain a reliable structure, it is recommended to use the coupled-cluster method with single and double excitations [23] augmented by a perturbational estimate of the effects of the connected triple excitations [CCSD(T)] [24] with a correlation-consistent polarized core-valence basis set [25] of at least quadruple zeta quality. In most cases, the CCSD(T) method is believed to yield results close to the exact n-particle solution within the given basis set [26]. However, for a molecule as large as dicyanocyclobutene, the computation time would be prohibitive and the CCSD(T) method was used with only a small double zeta basis set. The well known Dunning's correlation-consistent polarized valence basis sets, cc-pVnZ [27] where n D, T, Q were used in the ®nal calculations together with the frozen core approximation.
3. Results 3.1. Stark spectrum and assignment of the ground vibrational state The Stark spectrum of 1,2-dicyanocyclobutene was very rich with absorptions occurring every few MHz throughout the entire MW range. The reason for this is the fact that the molecule has a b-type spectrum and rather small rotational constants and ®ve normal modes with wave numbers less than 300 cm 21 according to the MP2/6-31111G pp computations. None of the absorption lines are very strong in spite of the fact that the dipole moment is as large as about 20 £ 10 230 C m (from the same theoretical calculations). The peak absorption intensities of the strongest lines in this spectral region were roughly 2 £ 10 27 cm 21. The reason for this relative weakness is primarily the very large number of available quantum states (a large partition function) rendering relatively few molecules in each state. The MP2/6-31111G pp rotational constants (A 2715; B 1837; and C 1111 MHz) indicate that the compound is very asymmetrical
k < 20:09: Searches were ®rst made in the 11±15 GHz region for the relatively strong series of high-J b-type Q-branch transitions using these rotational constants as the
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Table 1 Spectroscopic constants (A-reduction; I r-representation [28]; uncertainties represent one standard deviation) of 1,2-dicyanocyclobutene obtained using the Stark spectrometer (further sextic constants pre-set at zero in least-squares ®t) Vibrational state No. of transitions R.m.s. dev. a (MHz)
Ground 261 0.103
First ex. in-plane bend 165 0.128
Second ex. in-plane bend 74 0.103
First ex. out-of-plane bend 134 0.156
Av (MHz) Bv (MHz) Cv (MHz) D J (kHz) D JK (kHz) D K (kHz) d J (kHz) d K (kHz) F KJ (Hz) F K (Hz)
I a 1 Ib 2 Ic c (10 220 u m 2)
2742.8942(29) 1855.3542(27) 1121.5628(27) 0.837(13) 24.1772(74) 5.901(13) 0.37535(82) 20.1097(56) 20.135(17) 0.172(46) 6.03727(60)
2746.6112(70) 1861.2139(67) 1122.2294(67) 0.901(37) 24.105(16) 5.831(26) 0.3915(17) 20.133(12) 20.289(31) 0.563(84) 5.1980(14)
2750.314 3(76) 1867.0227(70) 1122.8625(68) 0.845(25) 24.210(21) 5.901(13) 0.3865(22) 20.066(14) 20.0887(54) ±b 4.3594(14)
2736.8161(65) 1856.5564(63) 1122.4102(64) 0.804(25) 24.130(20) 5.804(32) 0.3742(23) 20.041(15) 20.238(38) 0.43(10) 6.6103(15)
a b c
Root-mean-square deviation. Pre-set at zero. Principal moments of inertia. Conversion factor: 505 379.05 £ 10 220 MHz u m 2.
starting point in the analysis because these transitions were predicted to be the strongest ones in this part of the spectrum. These attempts were soon successful. It was then easier to extend the assignments up to a maximum value for the quantum number J 53: The R-branch transitions were searched for next using a trial and error procedure. These transitions were found after some trials. Attempts to resolve the quadrupole hyper®ne struc-
ture failed because the Stark spectrometer has insuf®cient resolution. A total of 261 transitions were ultimately assigned for the ground vibrational state. A full listing is available from H.M. upon request. The spectroscopic constants obtained using the Stark spectrometer (A-reduction, I r-representation [28]) are given in Table 1. Two of the sextic centrifugal distortion constants had to be included in the least-squares ®t
Table 2 Ground state spectroscopic constants (A-reduction; I r-representation [28]; uncertainties represent one standard deviation) obtained using the Fourier transform spectrometer Species No of transitions R.m.s a (kHz)
Parent 85 1.6
13 C1 32 2.0
13 C2 26 1.8
13 C3 29 1.6
15 N1 45 1.2
A0 (MHz) B0 (MHz) C0 (MHz) D J b (kHz) x aa (MHz) x bb (MHz) x cc (MHz)
Ia 1 Ib 2 Ic d (10 220 u m 2)
2742.8914(2) 1855.3499(1) 1121.5563(1) 0.809(5) 21.079(1) 21.148(1) 2.227(1) 6.0289
2741.5144(2) 1852.373(1) 1120.2386(1) 0.809 c 21.067(1) 21.148(2) 2.215(2) 6.0357
2694.9957(2) 1850.994(1) 1111.8885(1) 0.809 c 21.066(1) 21.151(2) 2.217(2) 6.0330
2735.4480(2) 1836.954(1) 1113.5746(1) 0.809 c 21.076(1) 21.150(2) 2.226(2) 6.0349
2710.9240(2) 1814.0271(4) 1101.0654(1) 0.805(2) 20.801(3) 21.415(3) 2.216(3) 6.0278
a b c d
Root-mean-square deviation. Further quartic constants preset at the values shown in Table 2 for the ground vibrational state; see text. Kept constant at this value in the least-squares ®t. Principal moments of inertia. Conversion factor: 505 379.05 £ 10 220 MHz u m 2.
D. Petitprez et al. / Journal of Molecular Structure 612 (2002) 315±324
319
assigned, as shown in Table 2. A further decrease of Ia 1 Ib 2 Ic is seen in this case, as expected. In the last column of Table 2 the spectroscopic constants of the ®rst excited state of the lowest outof-plane vibration are listed. It is seen that Ia 1 Ib 2 Ic increases relative to the value for the ground state vibration upon excitation, which is typical for outof-plane modes [29]. The calculated frequency (same theoretical level as before) is 142 cm 21 is again in agreement with rough relative intensity measurements. Fig. 1. A model with atom numbering of 1,2-dicyanocyclobutene projected in the a±b principal axes plane.
in order to get a root-mean-square deviation comparable to the experimental uncertainty of the frequency measurements (^0.12 MHz). It is seen in Table 2 that Ia 1 Ib 2 Ic 6:03727
60 £ 10220 u m2 (Ia, Ib and Ic are the principal moments of inertia). This is close to the typical value found for molecules possessing four out-of-plane hydrogen atoms attached to two sp 3-hybridized carbon atoms (6.4; same units). It is somewhat less than that found for cyclobutene (6.39296(7) £ 10220 u m 2) [1]. The reason for this difference is presumed to be caused largely by the low-frequency in-plane bending vibration [29] of the cyano group which was found to be 99 cm 21 in the MP2/6-31111G pp calculations. It was not possible to determine the dipole moment because of the weakness of the low-J transitions. 3.2. Vibrationally excited states The ground state spectrum was accompanied by several satellite spectra that could be ascribed to vibrationally excited states. Three excited states belonging to two different normal modes were ultimately assigned, as shown in Table 1. The most intense satellite is presumed to belong to the ®rst excited state of the lowest in-plane bending vibration of the cyano group. Typical for this excited state is the fact that Ia 1 Ib 2 Ic 5:1980
14 £ 10220 u m2 decreases upon excitation [29]. Rough relative intensity measurements are in agreement with 99 cm 21 calculated for this normal, as already mentioned. The second excited state of this mode was also
3.3. Fourier transform studies The search for the lines observed with the MWFT spectrometer was quite straightforward due to the good quality of the available predictions. These predictions were made using the previous results from the analysis of the Stark spectrum coupled with the ab initio calculations described earlier. Nevertheless, the hyper®ne structure caused by the two nitrogen nuclei was not easy to analyze. In the ®rst step we analyzed the spectra of the 15N 14N species: the hyper®ne structure due to a single 14N nucleus was easier to analyze and provided us the diagonal elements of the quadrupole coupling tensor. These values were used in a second step to predict the hyper®ne structure for the parent species. For the species containing two 14N nuclei, the calculation programs from Pickett [30] were used for the prediction and the analysis of the spectra. The identi®cation of the complex patterns in these spectra was then possible. The analysis of the spectra was made using the symmetric coupling scheme: I I1 1 I2 FJ1I where I1 and I2 are the nuclear spins of the two nitrogen nuclei, coupled to form a total nuclear spin I, which then couples with the rotational angular momentum J to form the resultant total angular momentum F. This coupling scheme is usually retained for molecules containing two identical nuclei. Many lines are blended, preventing a complete resolution of the spectrum. In the ®tting procedures
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Fig. 2. Two hyper®ne components of the JK 2,K 1 22,1 Ã 11,0 transition of 13C2-1,2-dicyanocyclobutene. Each component is a doublet due to the Doppler effect and is denoted by I 0 ,F 0 Ã I,F. Recording conditions: molecular pulse width: 620 ms; MW pulse width: 1 ms; MW power: 20 mW; sample interval: 100 ns, 1024 data points; number of cycles averaged: 500.
we retained only the well isolated or well resolved hyper®ne components. The three different 13C species were then treated in the same way. When possible we tried to observe the same isolated hyper®ne components as those observed for the parent species. Fig. 1 shows some hyper®ne components of the JK 2 ;K 1 22;1 Ã 11;0 transition belonging to the 13C(1) species (Fig. 2). In the ®tting procedure, the rotational constants were ®tted together with the diagonal quadrupole coupling constants. The quartic centrifugal distortion constants were kept ®xed to the values obtained from the Stark analysis (see Table 1), except D J, which was also ®tted for the parent species. It was the less well determined constant in the Stark analysis (Table 2) and the ®t was slightly improved when this constant was unconstrained. For the other isotopic species, D J was then ®xed at this value. The determined molecular parameters (A-reduction, I r-representation [28]) are reported in Table 2 for all the observed species. The measured frequencies are available from the authors (D.P. or G.W.) upon request. Several attempts were made to observe the monodeuterated species in natural abundance but all failed. The fact that the four hydrogen atoms are equivalent should enhance the spectral intensity. The high value of the dipole moment is also a favorable condition for the observation of such spectra, but it seems that the corresponding line
intensities are still below the sensitivity limit of our spectrometer. 4. Structure determination 4.1. Structure of cyclobutene As cyclobutene is signi®cantly smaller than dicyanocyclobutene, it is more easily amenable to highlevel ab initio calculations. For this reason, the structure of cyclobutene was ®rst calculated at the CCSD(T) level of theory, but the expensive calculation at the CCSD(T)/cc-pVQZ level was replaced by simpler calculations because it is known that the variation from CCSD(T)/cc-pVTZ to CCSD(T)/ccpVQZ may be accurately predicted at the MP2 level, as was found previously for the CC bond [31]. The following approximation formula was used: CCSD
T=cc-pVQZ < CCSD
T=cc-pVTZ 1 MP2=cc-pVQZ 2 MP2=cc-pVTZ:
1
The coupled cluster T1 diagnostic [32] which is 0.0099 at the CCSD(T)/cc-pVTZ level indicates that nondynamical electron correlation is not important and that the CCSD(T) results should be reliable.
D. Petitprez et al. / Journal of Molecular Structure 612 (2002) 315±324
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Table 3 Structure of cyclobutene (distances in pm, angles in degrees) Method
rs [1]
Basis set C1±C1 0 C1±C2 C2±C2 0 C1±H C2±H C1 0 ±C1±C2 C1±C2±C2 0 C2±C1±H C1±C2±H C1 0 ±C1±C2±H a b c
134.2(4) 151.7(3) 156.6(3) 109.4(5) 94.2 85.8 ±c ±c ±c
MP2
B3LYP
CCSD(T)
re a
cc-pVTZ
cc-pVQZ
cc-pVTZ
cc-pVDZ
cc-pVTZ
cc-pVQZ b
134.49 151.33 156.53 108.13 108.93 94.18 85.82 133.36 115.68 115.29
134.24 151.04 156.22 108.05 108.84 94.17 85.83 133.33 115.68 115.30
133.44 151.54 156.96 108.19 109.15 94.45 85.55 133.43 115.91 115.47
136.10 153.27 158.30 109.84 110.68 94.15 95.85 133.41 115.66 115.45
134.59 152.19 157.45 108.29 109.19 94.31 85.69 133.46 115.68 115.27
134.34 151.90 157.14 108.21 109.10 94.30 85.70 133.43 115.68 115.28
134.0 151.6 156.8 108.1 109.0 94.3 85.7 133.4 115.7 115.3
CCSD(T)/ccpVQZ 1 core correlation correction, see text. Calculated with CCSD(T)/cc-pVQZ < CCSD(T)/cc-pVTZ 1 MP2/cc-pVQZ-MP2/cc-pVTZ. Not given in Ref. [1].
Improving the basis set from cc-pVTZ to cc-pVQZ shows that convergence is almost achieved and further justi®es the use of Eq. (1). In order to estimate the core and core-valence correlation effects on the computed molecular geometry, it was assumed that this correction is constant for a given bond and was taken from our work on the CC bond, i.e. 20.32 pm for the CC bond and 20.15 pm for the CH bond [31]. The ®nal structure is given in Table 3 . It is to be noted that it is in very good agreement with the experimental rs structure. 4.2. Substitution structure of the heavy atoms of 1,2dicyanocyclobutene All atoms in 1,2-dicyanocyclobutene are relatively far (more than 30 pm) away from a principal inertial axis. This is ideal for a structure determination by the substitution method [2] provided the zero-point vibrational effects are small, which turned out not to be the case for the title compound. The rotational constants obtained in the Fourier transform experiment (Table 2) were used because they are more accurate than the ones obtained in the Stark experiment (Table 1) and have been obtained in a consistent manner. 1,2-Dicyanocyclobutene was assumed to have C2v symmetry. The a- and b-axis Cartesian coordinates found using Kraitchman's equations [33] are listed in Table 4. The c-coordinates of the heavy atoms were assumed to
be exactly zero owing to the symmetry of the molecule. It is of course possible to calculate the standard deviations of the Kraitchman coordinates from the standard deviations of the rotational constants. However, standard deviations obtained this way are unrealistically small by at least one order of magnitude owing to the zero-point vibrational effect. Instead, Costain's way of estimating the uncertainty [2] of a coordinate was employed. In this procedure the uncertainty of a Kraitchman coordinate x is given by s
x K=uxu; where K is a constant that depends on the atom in question. The values of K given by van Eijck [34] were used. In our case, K 0:08 for carbon and 0.11 pm 2 for nitrogen [34]. Kraitchman's coordinates of the heavy atoms with van Eijck uncertainties are given in Table 4. The structure of the heavy atoms (see Table 5) was calculated from the entries in this table. The uncertainties of the bond distances and angles (Table 5) Table 4 Kraitchman's coordinates [33] (pm) with van Eijck uncertainties [34] of 1,2-dicyanocyclobutene Atom C1 C2 C3 N1
a
b
^ 66.33(12) ^ 78.88(10) ^ 165.22(5) ^ 247.63(4)
230.57(26) 2182.22(4) 72.14(11) 153.60(7)
c 0.0 0.0 0.0 0.0
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Table 5 Structure of dicyanocyclobutene (distances in pm, angles in degrees). The CCSD(T)/cc-pVDZ results have not been included in this table. They were in qualitative agreement with the other results, but the cc-pVDZ basis set is too small to draw any quantitative conclusions
C1±C1 0 C1±C2 C2±C2 0 C1±C3 C3±N1 C2±H C1 0 ±C1±C2 C1±C2±C2 0 C2±C1±C3 C1±C3±N1 b C1±C2±H C1 0 ±C1±C2±H a b
B3LYP
MP2
cc-pVTZ
cc-pVTZ
cc-pVQZ
134.92 151.71 156.57 141.15 115.36 108.91 94.09 85.91 133.87 177.77 114.88 115.63
135.82 151.33 156.31 141.42 117.55 108.79 93.88 86.12 133.35 178.23 114.66 115.75
135.57 151.06 156.03 141.25 117.24 108.70 93.88 86.12 133.30 178.18 114.65 115.76
re a
rs
r0
135.4 151.6 156.6 142.1 115.9 108.8 93.9 86.1 133.3 178.2 114.7 115.8
132.6(2) 152.2(3) 157.8(2) 142.6(2) 115.9(1)
136.1 151.5 156.7 142.0 115.7 108.8 93.9 86.1 133.3 178.2 114.7 115.8
94.7(2) 85.3(1) 178.6(12)
MP2/cc-pVQZ with offset correction, see text. Bent outwards.
have been calculated from the van Eijck uncertainties (shown in Table 4) by the familiar formula for propagation of errors. The C1±C3xN1 bond angle of 178.68 has an uncertainty of 1.28. This indicates that the C1C3N1 chain of atoms may not be entirely linear, but slightly bent. It is possible to ®nd out in which direction this bending occurs. Accurate values for the C1 0 C1C3 and C1 0 C1N1 angles can be calculated from the entries in Table 4. The values are 133.9(2) and 134.6(1)8, respectively. The increase of about 0.78 in the C1 0 C1N1 angle in comparison with the C1 0 C1C3 angle is taken as evidence that the C1C3N1 link of atoms is not entirely linear but bent slightly outwards by approximately 1.58. 4.3. Ab initio structure of 1,2-dicyanocyclobutene When the rs structure of 1,2-dicyanocyclobutene given in Table 5 was compared with the rs structure of cyclobutene (Table 3) and with the MP2/631111G pp structure of 1,2-dicyanocyclobutene, it was found that the rs(C1yC1 0 ) of the double bond of the title compound was abnormally short, only 132.6(2) pm (Table 5). This unreasonably short rs double bond length prompted advanced quantum chemical calculations because it should be within reach to derive an accurate
theoretical equilibrium structure for this compound. The structures of cyclobutene and 1,2-dicyanocyclobutene were then calculated using the following methods: MP2/cc-pVTZ, MP2/cc-pVQZ, B3LYP/ccpVTZ, and CCSD(T)/cc-pVDZ. It was now assumed that both molecules have C2vsymmetry and that the heavy atoms lie in one plane. All the methods give compatible results (Table 5). In fact, the C1yC1 0 double bond is calculated about 0.13 pm longer in 1,2-dicyanocyclobutene than in cyclobutene. Comparison of the MP2/cc-pVTZ and MP2/ccpVQZ results show that convergence is almost achieved at the cc-pVQZ level. Comparison of the MP2/cc-pVTZ and B3LYP/cc-pVTZ results indicates that the angles should be accurate within 0.38. An approximate equilibrium structure was estimated from the MP2/cc-pVQZ results. The MP2/cc-pVQZ angles were assumed to be identical to the equilibrium angles [35]. The bond lengths of the ring were corrected using offsets estimated from cyclobutene. For the C3xN1 and C1±C3 bond lengths, the offset was estimated from cyanoacetylene, HCxC±CxN [36]. The C1±C3 bond length is likely to be less accurate because it is known that for such a bond length between a double bond and a triple bond, the offset is not constant at the MP2 level [31]. The estimated equilibrium structure is found in Table 5.
D. Petitprez et al. / Journal of Molecular Structure 612 (2002) 315±324
4.4. Effective structure It seems that the failure of the rs structure is due to the fact that the substitution coordinates of the C1 atoms are rather small. A similar dif®culty was already encountered in a few other heavy molecules: t-butyl chloride [37], phosgene [38], and probably also hexa¯uorocyclobutene [9]. For instance, the coordinate of the central carbon atom is 43.9 pm in t-butyl chloride, which is usually not considered as a small coordinate, but it appears that the variation of the rovibrational correction upon isotopic substitution is not negligible compared to the variation of the moments of inertia with isotopic substitution (which is quite small). A similar situation presumably exists for the title compound. In this case, the simple effective structure (r0 structure) might be more accurate. The problem is that the available rotational constants do not allow us to determine the complete r0structure. To overcome this dif®culty, the procedure of the predicate observations method described in Ref. [39] was used as follows: in the least-squares ®t, the ab initio bond angles and the re(C±H) bond length with appropriate weights were employed as input data together with the experimental moments of inertia. It was furthermore assumed that the ab initio bond angles are accurate to within 18 (which is rather pessimistic) and that the re(C±H) bond length is accurate to within 0.2 pm. The values that were obtained in the least-squares ®t for the bond angles and the re(C±H) bond length were almost identical to the input data. This indicates that the ab initio bond angles and the re(C±H) bond length are compatible with the observed moments of inertia. Moreover, the least-squares ®t was well behaved and the determined r0 structure shown in Table 5 was found to be in satisfactory agreement with the ab initio equilibrium structure, con®rming the de®ciency of the substitution method in this case.
5. Conclusions It is seen in Tables 3 and 5 that the equilibrium C1± C2 and C2±C2 0 bond lengths are practically the same in cyclobutene and 1,2-dicyanocyclobutene, whereas the C1yC1 0 double bond is 1.4 pm shorter in cyclobutene than in 1,2-dicyanocyclobutene. The cyano
323
group substituents thus lead to an elongation of the double bond with little effect on other structural parameters. Calculations were also carried out for ethylene, acrylonitrile and cis-dicyanoethylene in order to see if the introduction of the cyano group leads to an elongation of the double bond in this case as well. Indeed, a similar elongation was found for this series of compounds. The results were (in pm at the MP2/ccpVQZ level): ethylene 132.94; acrylonitrile: 133.50; cis-1,2-dicyanoethylene: 134.38. Then C1±C3yN1 chain of atoms is slightly nonlinear and bent outwards. This is similar to previous ®ndings [40,41]. The length of the C3N1 triple bond (115.9 pm) is also typical [40]. Finally, it should be stressed that rs parameters (even as long as 66 pm) can be quite unreliable when the molecules are heavy and has low-frequency normal mode(s). The resulting uncertainties of the structural parameters are not encompassed in van Eijck's way [34] of estimating error limits, as shown in the present case of the C1yC1 0 double bond length. In such cases the r0 structure may be more accurate than the rs structure. Acknowledgements H.M. is grateful to the Universite des Sciences et Technologies de Lille for a grant as visiting professor. Anne Horn is thanked for assistance. This work has received support from The Research Council of Norway (Programme for Supercomputing) through a grant of computer time. References [1] B. Bak, J.J. Led, L. Nygaard, J. Rastrup-Andersen, G.O. Sùrensen, J. Mol. Struct. 3 (1969) 369. [2] C.C. Costain, J. Chem. Phys. 29 (1958) 864. [3] O. Bastiansen, J.L. Derissen, Acta Chem. Scand. 20 (1966) 1089. [4] H. Thomassen, K. Hedberg, J. Phys. Chem. 94 (1990) 4847. [5] A.M. Andrews, S.L. Maruca, K.W. Hillig, R.L. Kuczkowski, N.C. Craig, J. Phys. Chem. 95 (1991) 7714. [6] C.H. Chang, R.F. Porter, S.H. Bauer, J. Mol. Struct. 7 (1971) 89. [7] A.G. CsaÂszaÂr, K. Hedberg, J. Phys. Chem. 94 (1990) 3525. [8] I.W. Xu, M.E. Klausner, A.M. Andrews, R.L. Kuczkowski, J. Phys. Chem. 97 (1993) 10346.
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