Journal of Molecular Structure 612 (2002) 315±324
www.elsevier.com/locate/molstruc
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: denis.petitprez@univ-lille1.fr (D. Petitprez),
harald.mollendal@kjemi.uio.no (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
316
D. Petitprez et al. / Journal of Molecular Structure 612 (2002) 315±324
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 ˆ 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 ˆ 2715; B ˆ 1837; and C ˆ 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
318
D. Petitprez et al. / Journal of Molecular Structure 612 (2002) 315±324
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 ˆ 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 ˆ
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 ˆ 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 ˆ I1 1 I2
FˆJ1I
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
320
D. Petitprez et al. / Journal of Molecular Structure 612 (2002) 315±324
Fig. 2. Two hyper®ne components of the JK 2,K 1 ˆ 22,1 à 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 ˆ 22;1 à 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
321
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† ˆ 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 ˆ
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
322
D. Petitprez et al. / Journal of Molecular Structure 612 (2002) 315±324
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.
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