The molecular structure of 1,1-dicyanocyclopentane from gas electron diffraction data and ab initio calculations

Article abstract of DOI:10.1016/S0022-2860(02)00089-3

The molecular structure of 1,1-dicyanocyclopentane (DCCP) has been investigated by means of gas-phase electron diffraction and ab initio calculation. Although the electron diffraction data could be fairly good reproduced by a C_s (envelope) model we found it more pertinent to apply a pseudorotation model to account for the dynamic and large amplitude motion in DCCP. Based on this model we analyzed the dependency of the ring geometric parameters and vibrational mean amplitudes on the phase angle φ. For a better elucidation of this distinct dependency we developed particular equations which describe the dependency of the distribution of the delocalized net charges throughout the ring on the phase angle φ. For the purpose of a more systematical study of the substituent effect exerted by the cyano group we also investigated the structure and conformational stability of monocyanocyclopentane (MCCP) by means of various quantum mechanical methods. The MP2 method in combination with the basis sets 6-311 + G(2df,2pd), 6-311 + G(d,p), and 6-31 G(d,p) favors the axial conformer which is in contradiction to earlier results which were obtained from electron diffraction data [J. Mol. Struct., 116 (1984) 29]. Using the same basis sets but the DFT/B3PW91 method, however, leads to a more stable equatorial conformer. This striking behavior is discussed in this paper. The joint electron diffraction and ab initio study has led to the following r_α structural parameters of DCCP: r(C≡N) = 1.152(2) A?, r(C42≡) = 1.472(5) A?, average r(C-C)_ring = 1.549(3) A?, ∠(C5-Cl-C2) = 103.6(26)°, ∠(NC-C-CN) = 109.0(35)°, ∠(C-C≡N) = 175.2(33)°, and ∠(H-C-H) = 112.7(23)°. The puckering amplitude for the five-membered ring was determined to be q = 0.434(45) A?. The quantum mechanical calculations were carried out by utilizing the Hartree-Fock, density functional B3PW91, and perturbation MP2 methods and applying the basis sets: 6-31 G(d,p), 6-311 G(df,pd), 6-311 + G(d,p) and 6-311 + + (2df,2pd). In contrast to the Mulliken poulation analysis the natural population analysis provided clear evidence for the electronic interaction and bond conjugation within the geminally substituted cyano groups.

Full text of DOI:10.1016/S0022-2860(02)00089-3

Journal of Molecular Structure 612 (2002) 181±197
www.elsevier.com/locate/molstruc
The molecular structure of 1,1-dicyanocyclopentane from gas
electron diffraction data and ab initio calculationsq
a,
b
*
Marwan Dakkouri , Volker Typke
a
È
Department of Electrochemistry, Universitat of Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
b
È È
Universitatsrechenzentrum, Universitat Ulm, D-89069 Ulm, Germany
Received 7June 2001; accepted 31 August 2001
Abstract
The molecular structure of 1,1-dicyanocyclopentane (DCCP) has been investigated by means of gas-phase electron diffrac-
tion and ab initio calculation. Although the electron diffraction data could be fairly good reproduced by a Cs (envelope) model
we found it more pertinent to apply a pseudorotation model to account for the dynamic and large amplitude motion in DCCP.
Based on this model we analyzed the dependency of the ring geometric parameters and vibrational mean amplitudes on the
phase angle f. For a better elucidation of this distinct dependency we developed particular equations which describe the
dependency of the distribution of the delocalized net charges throughout the ring on the phase angle f.
For the purpose of a more systematical study of the substituent effect exerted by the cyano group we also investigated the
structure and conformational stability of monocyanocyclopentane (MCCP) by means of various quantum mechanical methods.
The MP2 method in combination with the basis sets 6-311 1 G(2df,2pd), 6-31111G(d,p), and 6-31G(d,p) favors the axial
conformer which is in contradiction to earlier results which were obtained from electron diffraction data [J. Mol. Struct., 116
(1984) 29]. Using the same basis sets but the DFT/B3PW91 method, however, leads to a more stable equatorial conformer. This
striking behavior is discussed in this paper.
The joint electron diffraction and ab initio study has led to the following ra structural parameters of
Ê
Ê
Ê
DCCP: rꢀCxN† ˆ 1:152ꢀ2† A, rꢀC±Cx† ˆ 1:472ꢀ5† A, average rꢀC±C† ˆ 1:549ꢀ3† A, /ꢀC5±C1±C2† ˆ 103:6ꢀ26†8;
ring
/ꢀNC±C±CN† ˆ 109:0ꢀ35†8; /ꢀC±CxN† ˆ 175:2ꢀ33†8; and /ꢀH±C±H† ˆ 112:7ꢀ23†8: The puckering amplitude for the
Ê
®ve-membered ring was determined to be q ˆ 0:434ꢀ45† A.
The quantum mechanical calculations were carried out by utilizing the Hartree±Fock, density functional B3PW91, and
perturbation MP2 methods and applying the basis sets: 6-31G(d,p), 6-311G(df,pd), 6-311 1 G(d,p) and 6-31111(2df,2pd).
In contrast to the Mulliken poulation analysis the natural population analysis provided clear evidence for the electronic
interaction and bond conjugation within the geminally substituted cyano groups. q 2002 Elsevier Science B.V. All rights
reserved.
Keywords: 1,1-Dicyanocyclopentane; Monocyanocyclopentane; Pseudorotation; Non-linearity and conjugation of geminal cyano groups;
Charge distribution and natural population analysis versus Mulliken poulation analysis
q
ªThis paper is dedicated to Professor Paolo G. Favero and
Professor Helmut Dreizler in appreciaton of their signi®cant contri-
1. Introduction
butions to the ®eld of microwave spectroscopyº.
* Corresponding author. Tel.: 149-731-502-2873; fax: 149-731-
As a continuation of our efforts to contribute to a
502-2872.
better understanding of the effects of substituents on
E-mail address: marwan.dakkouri@chemie.uni-ulm.de
the geometry and dynamics of cyclic systems we
(M. Dakkouri).
0022-2860/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved.
PII: S0022-2860(02)00089-3

182
M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
Scheme 1.
investigated the structure of 1,1-dicyanocyclopentane
(DCCP) by means of electron diffraction and ab initio
calculations. Static (rigid) one-conformer (for each
the Cs and C2 forms) and two conformers (Cs plus
C2) model as well as a model considering the pseu-
dorotational motion have been used to ®t the experi-
mental data.
Major reasons for initiating the present study are:
(1) To obtain additional pertinent results which may
contribute to a more complete and perhaps detailed
understanding of the pseudorotational motion in ®ve-
membered rings. (2) To explore the in¯uence of the
geminal cyano groups on the pseudorotational para-
meters of the ®ve-membered ring, the phase angle f
and the puckering amplitude q. (3) To extend our
earlier investigations of the reasons leading to the
non-linearity of geminally substituted cyano groups
and whether this structural peculiarity is the result
of direct conjugation and/or steric interaction. (4) To
elucidate the role of the electrophylic cyano group by
the stabilization of the envelope (Cs) or half-chair (C2)
conformation.
2. Synthesis and experimental data
According to the scheme shown above the reaction
between tetrahydrothiophane and tetracyanoethylene
epoxide provided the corresponding sulfoniumdicyano-
methylide. The subsequent transylidation of triphenyl-
phosphine with the ylide gave DCCP [1] (Scheme 1).
Recordings of the diffraction patterns at two camera
distances were obtained with the apparatus of the
Hungarian diffraction group in Budapest. Two sets
of data were obtained at approximate camera
distances of 19 and 50 cm. The experimental condi-
tions are summarized in Table 1, and the intensity data
are deposited as supplementary material. Our usual
data reduction and re®nement procedures were used
[2,3], and the atomic scattering amplitudes and phases
of Haase [4] were applied.
3. Ab initio calculations
The ab initio computations were carried out on
various levels of theory using the programs gaussian
98 [5] and spartan [6]. The following methods were
applied: HF/6-31Gpp, B3PW91/6-31111G(df,pd),
It has been long recognized that the potential func-
tion for the hindered pseudorotation in substituted
cyclopentanes depends substantially on the charge
af®nity of the substituent and the kind of electronic
interaction with the ring system. In this context DCCP
with its cyano groups as strong p- and s-electron
acceptors in geminal arrangement represents undoubt-
edly a unique testing example in this respect.
B3PW91/6-31Gp,
B3PW91/6-3111G(2df,2pd),
MP2/6-31Gpp, and MP2/6-3111G(2df,2pd). All these
methods, particularly the perturbation methods,
provided results which are in good agreement with the
experiment.
Table 1
Experimental conditions of the diffraction experiment
Ê
Wavelength (A)
Ê 21
s range (A )
Camera distance (mm)
Temperature nozzle (8C)
501.278
192.189
126
126
0.049087
1.875±14.25
5±36.205.0490878.7

Table 2
Optimized geometrical parameters of DCCP by using different levels of theory
HF/6-31G(d,p)
Cs C2
B3PW91/6-31G(d)
B3PW91/6-311 1 G(2df,2pd)
MP2/6-31G(d,p)
MP2/6-311 1 G(2df,2pd)
Cs
C2
Cs
C2
Cs
C2
Cs
C2
Ê
Bond distances (A)
C1±C2
1.5493
1.5385
1.5513
0.414
1.5710
1.5309
1.5284
0.419
1.5562
1.5380
1.5523
0.421
1.5782
1.5303
1.5293
0.421
1.5525
1.5331
1.5477
0.413
1.5736
1.5254
1.5258
0.415
1.5470
1.5364
1.5510
0.440
1.5706
1.5281
1.5263
0.436
1.5443
1.5338
1.5497
0.443
1.5675
1.5256
1.5248
0.446
C2±C3
C3±C4
qa
C1±C6
1.4807
1.4754
1.1343
1.0832
1.4778
1.4778
1.1344
1.4730
1.4673
1.1606
1.4697
1.4697
1.1607
1.4674
1.4613
1.1499
1.4636
1.4636
1.1500
1.4716
1.4656
1.1824
1.4686
1.4686
1.1824
1.4643
1.4580
1.1707
1.4607
1.4607
1.1708
C1±C8
±CxN
kC±Hlb
1.08371.0942
1.0948
1.0898
1.0904
1.0896
1.0902
1.0882
1.0889
Bond angles (8)
C1±C2±C3
C2±C3±C4
C5±C1±C2
NC±C±CN
H±C2±H
104.1
106.2
104.8
104.0
104.8
104.2
106.3
101.7104.9
109.6
107.9
106.9
123.0
127.3
40.2
105.0
103.4
105.9
105.0
110.1
108.4
107.3
121.8
128.1
43.1
104.5
103.3
105.9
104.4
103.4
105.2
108.4
107.8
107.7
125.8
125.8
106.2
101.6
109.5
108.0
107.0
122.9
127.6
40.9
103.4
104.8
108.8
107.7
107.6
125.6
125.6
103.5
102.9
101.4
109.2
108.0
107.9
125.4
125.4
102.6
102.1
109.1
108.0
107.1
123.2
127.7
40.5
101.5
104.9
109.1
107.7
107.5
125.5
125.5
110.3
108.5
107.3
121.8
127.9
43.5
109.3
108.2
108.1
125.3
125.3
H±C3±H
c
b6
d
b8
ae
hf
2.1
2.2
2.2
2.2
2.4
2.5
2.6
2.4
2.72.5
Dihedral angles (8)
C1±C2±C3±C4
C4±C5±C1±C2
C2±C3±C4±C5
DEg
24.9
40.0
0.0
±
234.9
13.3
25.2
40.4
235.6
24.9
234.8
26.4
236.4
26.6
±
237.2
12.739.8
0.0
13.2
43.6
42.5
0.0
13.8
45.6
42.8
0.0
14.2
46.6
43.70.0
0.993
44.1
±
0.572
±
0.287
±
1.523
1.049
a
Puckering amplitude for the ring, calculated with program ring [26,27].
Average value.
b
c
d
e
f
Angle between the bond C6±C1 and the plane C5C1C2.
Angle between the bond C8±C1 and the plane C5C1C2.
Angle between the C5C1C2 plane and C2C3C4C5 plane (¯ap angle).
Bending angle (outwards) of the C±CxN chain.
DE ˆ EꢀC2† 2 EꢀCs† (kcal/mol).
g

184
M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
Fig. 1. Atomic numbering of MCCP and DCCP.
Table 2 lists the most prominent structural para-
meters of DCCP as predicted by the latter four ab
initio methods. For atomic numbering see Fig. 1.
31Gpp method for both the Cs and the C2 forms. The
procedure we applied for the determination of these
amplitudes has been described previously [7]. It is
worthwhile to note that initially the values for several
calculated vibrational amplitudes of non-bonded
distances were unreasonably high. The subsequent
elimination of the contributions from the lowest vibra-
tional frequency, the pseudorotation, however, has led
to generally plausible values.
At this stage of the present electron diffraction
study it became evident that by applying static models
the geometry of DCCP is most properly described
when the envelope form (Cs symmetry) was used.
Neither the C2 conformer nor a combination of
different ratios of the Cs and C2 conformers could be
adequately described by the electron diffraction data.
This result also supports the signi®cant changes in the
ring C±C bond lengths in going from Cs to C2
symmetry which were obtained in the ab initio calcu-
lations. This was introduced into the subsequent large
amplitude treatment. The predominance of the Cs
form is consistent with the results predicted by all
ab initio methods that have been applied for this
study (Table 2).
The ®nal results of the structural analysis gained
from the re®nement of the static Cs model are
shown in Table 3. In Tables 3 and 5 the different s
values have the following meaning: s1 is the single
standard error of the ®tting procedure, s2 is the error
propagated from the estimated uncertainties of the
®xed parameters, and stotal is the combined ®nal
error estimate. The method to calculate the propa-
gated error s2 and the total error stotal has been
described in Refs. [7±9].
4. Static models
Initially we started the analysis of the electron
diffraction data by applying static models of
symmetry Cs and/or C2. Since not all the independent
structural parameters of DCCP can be determined
from the electron diffraction intensities, the following
assumptions were introduced for the data re®nement:
(1) all geometrical parameters of the C±CxN
moieties are equal; (2) all C±H bond distances
were assumed to be equal; (3) all H±C±H bond
angles were assumed to be equal; and (4) local C2v
symmetry was assumed for the CH2 groups. In
addition the overall molecular symmetry implies
the constraints rꢀC1±C2† ˆ rꢀC1±C5†; rꢀC2±C3† ˆ
rꢀC4±C5†;
/ꢀC2±C3±C4† ˆ /ꢀC3±C4±C5†: Further we have
for Cs symmetry
/ꢀC1±C2±C3† ˆ /ꢀC4±C5±C1†;
and
/ꢀC2±C3±C4±C5† ˆ 0;
/ꢀC1±C2±C3±C4† ˆ 2/ꢀC3±C4±C5±C1†;
/ꢀC4±C5±C1±C2† ˆ 2/ꢀC5±C1±C2±C3†; and for C2
symmetry
/ꢀC1±C2±C3±C4† ˆ /ꢀC3±C4±C5±C1†
and /ꢀC4±C5±C1±C2† ˆ /ꢀC5±C1±C2±C3†: When
attempting to ®t different ratios of Cs and C2
conformations it was also assumed that the ring
C±C bond distances have the same values in both
conformations.
To obtain reasonable values for the vibrational
amplitudes lij a normal coordinate analysis has been
conducted using the force ®elds provided by the HF/6-

M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
185
Table 3
Structural parameters (ra) of DCCP as obtained from the ®t of the
static Cs model, with different kinds of uncertainties
cular distances for several pairs of atoms change by
Ê
up to 2 A. This indicates that the analysis of the
experimental data using a large amplitude treatment
of the pseudorotation should be more appropriate than
a static model allowing only for Cs symmetry.
In 1,1 disubstituted ®ve-membered rings the pseu-
dorotational motion is characterized by a potential
function of the form (neglecting higher terms)
a
b
c
ra
s1
s2
stotal
Ê
Bond distances (A)
C1±C2
1.554
1.544
1.560
1.474
1.165
1.088
0.003
0.003
®x
0.003
0.004
0.009
0.010
C2±C3
C3±C4
C±Cx
0.001
0.001
®x
0.001
0.001
0.004
0.002
Vꢀf† ˆ 12 V2ꢀ1 2 cos 2f† 1 1 V4ꢀ1 2 cos 4f†
2
CxN
C±H
where f is the phase of the pseudorotation. This gives
stable con®gurations of Cs symmetry at f ˆ 0;
^p; ^2p; ¼; and stable con®gurations of C2
symmetry at f ˆ ^p=2; ^3p=2; ¼ The energy differ-
ence between the minima of the potential function is
given by the constant V2. Fig. 2 shows the potential
function for 1,1-dicyanocyclopentane.
Bond angles (8)
NC±C±CN
gd
107.6
41.6
0.6
0.6
0.1
0.6
0.8
0.5
0.8
1.1
2.1
2.3
0.5
2.7
C2±C3±C4
H±C±H
he
1f
106.8
111.3
5.8
0.2
1.3
0.72.3
0.4
1.8
1.5
To account for large amplitude motions in the
analysis of gas-phase electron diffraction data the
assumption is made that the large amplitude motion
is a slow motion, and the reduced total molecular
intensity sMꢀs† can be written as [13,14]
Ê
Vibrational amplitudes (A)
lC±Cring
lC±Cx
lC±H
0.056
0.044
0.078
0.031
0.070
0.068
0.2670.020
0.090
0.114
0.344
0.121
0.095
0.156
0.111
2.02
0.001
0.002
0.002
0.000
0.017
0.008
0.001
0.002
0.002
0.001
0.019
0.012
0.002
0.005
0.006
0.002
0.053
0.028
lCxN
lC2´´´C5
lC2´´´C6
lC3´´´C6
lC3´´´C8
lC2´´´N7
lC3´´´N7
lC3´´´N9
lC6´´´N9
lN´´´N
Z2p
Z2p
sMꢀs†
ˆ
wꢀf†sMꢀs; Rꢀf††df=
wꢀf†df ꢀ1†
0.023
0.064
total
0
0
0.005
0.002
0.012
0.0070.005
0.042
0.005
0.019
where R(f) designates the geometry of the molecule
at the phase angle f. The weight function w(f) at
temperature T with normalizing factor N is given by
0.025
0.001
0.111
0.012
0.0070.006
0.015
0.019
0.013
0.001
0.044
0.004
wꢀf† ˆ N expꢀ2Vꢀf†=RT†
lC1´´´H10
g
Rlong
0.002
To apply these formulas to DCCP various problems
have to be solved. Most importantly the dependency
of the geometry on the phase angle f should be
analyzed. Inspection of Table 2 shows that the ring
C±C bond distances as obtained from ab initio
calculations depend strongly on the phase angle f:
g
Rshort
3.59
a
s1 is the single standard error of the ®t.
s2 is the propagated error [7±9].
b
c
d
p
The angle between the C5±C1±C2 plane and the C2C3C4C5 plane
:
stotal
ˆ
6s12 1 3s22
(¯ap angle).
e
Ê
the C1±C2 distance increases by about 0.023 A in
going from f ˆ 0 to p=2 and thereby the C3±C4
Bending angle (outwards) of the C±CxN chain.
f
Rocking angle of the NC±C±CN group.
1=2
P
P
R ˆ 100‰ wiD2i = ꢀwis2Mi2ꢀobs††Š
;
g
Ê
distance decreases by 0.024 A. We would like to
where Di ˆ sMiꢀobs† 2 sMiꢀcalc†:
note that similar calculations for 1,1-dichlorocyclo-
pentane [15] show an analogue behavior. With a slight
modi®cation of Eq. (2) this procedure has proven to be
also applicable to ®ve-membered rings including
heteroatoms like Silacyclopentane [16]. However, in
the large amplitude analysis of the diffraction patterns
it is required to establish the ring geometry for any
phase angle f. Therefore we rationalize this observa-
tion by using the following model: in contrast to the
5. Large amplitude treatment
Saturated ®ve-membered rings are known to
undergo a special form of vibrational motion, the
pseudorotation [10±12]. A close examination of the
variation of non-bonded distances during one cycle of
pseudorotation shows that in DCCP the intramole-

186
M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
Fig. 2. Potential function of pseudorotation for 1,1-dicyanocyclopentane (angles in radian). V2 ˆ 1050 cal=mol is the energy difference between
the Cs and the C2 con®guration as calculated by MP2/6-311 1 G(2df,2pd), V4 ˆ 1629 cal=mol is the ®nal ®tted value from the ra ®t.
localized electron density distribution the density distri-
bution of the delocalized net charges which represents
the overall distribution of charges throughout the ring
depends markedly on the phase angle f. Assuming that
this dependency for the Cs and C2 conformers can be
described by a function of the form shown in Fig. 3 we
may write for the density distribution
Assuming a regular pentagon in the mean plane of the
®ve-membered ring the integral can be easily evalu-
ated. If we neglect the differences in the puckering
amplitudes q resulting for the Cs and C2 forms and
adjust the parameters rCC, d1, d2, and df to the ab initio
distances for both symmetries by applying a least
squares procedure we obtain the results listed in
Table 4. It can easily be seen from Table 2 and Eq.
(3) that rCC is the mean value of the ring C±C bond
distances.
dꢀa; f† ˆ d1 cos a 1 d2 cos 2a 1 df cos a cos 2f
ꢀ2†
where a designates the angle between the axis from the
center of the ring to atom C1 and every position along
the ring, both projected to the mean plane as de®ned by
Cremer and Pople [27]. The coef®cients d1, d2, and df
are adjustable parameters. Therefore, the contribution
of the delocalized net charges to the bond distance Ci±
Cj can be written as
Since the largest deviation from the ab initio values
Ê
is 0.001 A we adopted the coef®cients d1, d2, and df as
a
R
well as the values of the integrals j cos a da and
ai
R
a
j cos 2a da for ®tting the geometry by using the
ai
electron diffraction data. The ring distances were
calculated according to
r12 ˆ rCC 1 0:951057d1 2 0:293893d2
Za
j
rij ˆ rCC
1
dꢀa; f†da
ꢀ3†
1 0:951057df cos 2f
ꢀ4†
ai

M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
187
Fig. 3. Density of delocalized net charge distribution for f ˆ 0 (------) and f ˆ p=2 (± ± ±) (angles in radian).
the conformations with Cs and C2 symmetry. This was
taken into account by using
r23 ˆ rCC 2 0:363271d1 1 0:769421d2
2 0:363271df cos 2f
ꢀ5†
ꢀ6†
a512ꢀf† ˆ a512ꢀCs† 1 d512ꢀ1 2 cos 2f†=2
ꢀ7†
r34 ˆ rCC 2 1:175571d1 2 0:951057d2
2 1:175571df cos 2f
To set up the geometry of the ring we additionally
made use of the formula given by Kilpatrick et al.
[17] for the z coordinates of the ring atoms
Further inspection of Table 2 shows that the bond
angle C5±C1±C2 ˆ a512 differs by more than 38 for
Table 4
p
zi ˆ 2=5q cosꢀf 1 4pꢀi 2 1†=5†
i ˆ 1; ¼; 5 ꢀ8†
Fitted constants from Eq. (2) and ring C±C bond distances calculated from Eqs. (4)±(6) for 1,1-dicyanocyclopentane
HF/6-31G(d,p)
B3PW91/6-31G(d)
MP2/6-31G(d,p)
MP2/6-3111G(2df,2pd)
Fitted constants
rCC
d1
1.54561(54)
0.01205(61)
1.54868(53)
0.01591(62)
1.54413(60)
0.01245(68)
1.54166(49)
0.01188(56)
d2
20.00862(76)
20.01041(58)
20.01137(76)
20.01047(58)
20.00963(84)
20.01126(64)
20.01000(69)
20.01126(53)
df
C±C distances calculated from Eqs. (4)±(6)
Cs
C2
Cs
C2
Cs
C2
Cs
C2
C1±C2, C1±C5
C2±C3, C4±C5
C3±C4
1.5497
1.5384
1.5519
1.5695
1.5308
1.5274
1.5572
1.5380
1.5531
1.5771
1.5303
1.5285
1.5481
1.5363
1.5519
1.5695
1.5281
1.5254
1.5452
1.53371.5256
1.5504
1.5666
1.5240

188
M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
The same q was used for all values of f. The calcula-
tion of the ring geometry is completed using a coor-
dinate system with the x and y axes lying in the ring
mean plane: the coordinate system is chosen such, that
the projection of atom C1 into the mean plane, lies on
the x axis, and the origin is positioned so that all
angles from one edge of the planar pentagon to an
adjacent edge is 728. Thus, if we ®x d1, d2, and df
to the values given in the last column of Table 4
and d512 to the ab initio value, only rCC, a512, and q
are free parameters at a given phase angle f for ®tting
the ring geometry.
l(N7´´´H14) and the corresponding distances. We
therefore decided to use the differences lijꢀf ± 0† 2
lijꢀf ˆ 0† of the calculated vibrational amplitudes:
these were introduced into the analyzing programs
as constants to be added to the vibrational amplitudes
of the most stable conformer (symmetry Cs at f ˆ 0).
This limits the possibility to adjust the vibrational
amplitudes in the least squares procedure to cases
where the scatter of the calculated amplitudes is suf®-
ciently small. Values at intermediate f are obtained
by interpolation.
To calculate sMꢀs†
from Eq. (1) we used the
total
Further, we observed a strong dependency of the
C1±Cx distance as well as the C(CxN)2 rocking angle
r on the phase angle f. The difference in the axial and
equatorial C1±Cxbond distances is found to be
usual assumption that the integral can be appoximated
suf®ciently well by ®nite sums. Therefore the
geometry of the molecule was set up for various
values of the phase angle f, and the corresponding
Mꢀs; Rꢀf†† was calculated. For symmetry reasons it is
suf®cient to use an interval width of p. We used a step
width of df ˆ 58 in the interval 2135 # f # 1458;
giving a total of 37intermediate conformers.
Ê
,0.006 A, and the rocking angle ,2.78 in Cs form.
However, the twisting t of the C(CxN)2 group in the
C2 conformer is only ,0.38. These dependencies were
taken into account by applying the following equa-
tions:
Attempts have been undertaken to extract the
potential constants V2 and V4 from the experimental
gas electron diffraction data. However, it turned out,
that the dependence of the data on V2 and V4 is very
poor. Therefore, the constant V2 was ®xed at the ab
initio energy difference between the conformers of Cs
and C2 symmetry, and only V4 was adjusted.
Using the pseudorotational model two different
types of ®tting schemes have been applied to deduce
the molecular structure from the electron diffraction
patterns: in a ®rst attempt an ra structure was ®tted
under the assumption that the ra parameters are
geometrically consistent. Though the overall ®t is
acceptable, several problems cannot be solved suf®-
ciently well, however. In particular the discrepancy
between the experimental and theoretical radial distri-
rC ±Cx ˆ rCCx ^ drCCx cos f;
rꢀf† ˆ r cos f;
1
tꢀf† ˆ t sin f
A dependency of the geometry of the methylene
groups on f, though present in the ab initio results,
was not taken into consideration because the sensi-
tivity of the diffraction data on these parameters is
too small: the rocking, wagging, and twisting angles
were ®xed to zero, and all C±H distances were
assumed to be equal.
A second problem to be solved is the correlation
between the root mean square amplitudes lij and the
phase angle f. Using the scaled quadratic ab initio
force ®elds for both stable conformations Cs and C2
we have calculated the vibrational amplitudes within
the range 2p # f , 1p with a step width of df ˆ
98: Following Hilderbrandt et al. [18] we tried to
establish with these data a dependency of the vibra-
tional amplitudes on f of the form
Ê
bution curve in the region at 4.0 A (Fig. 6) is too large,
and also the deviation of the C±CxN chain from line-
arity by 6.98 is not acceptable. Since it is well known
that in molecules containing linear chains the perpen-
dicular vibrational amplitudes contribute signi®cantly
to the non-bonded ra distances, we decided to ®t the ra
geometry, which is geometrically consistent by de®-
nition. The required corrections ꢀra 2 ra† were calcu-
lated along with the vibrational amplitudes by using
the force ®eld provided from the HF/6-31Gpp calcula-
tions. These data were entered as additional constants.
The results of both types of ®tting are listed in Table 5.
lij ˆ l0ij 1 aꢀ1 2 cos f†
However it turned out that there is no such simple
dependency for most of the lij. This is demonstrated
for some examples in Fig. 4 utilizing the vibrational
amplitudes l(C3´´´N7), l(C4´´´N7), l(N7´´´H12), and

Fig. 4. Dependency of selected vibrational amplitudes (upper row) and corresponding distances (lower row) on phase angle f. Calculations were performed with the scaled ab initio
force ®elds obtained at f ˆ 08 (Cs symmetry, ±±±) and at f ˆ 2708 (C2 symmetry, ± ± ±).

190
M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
Table 5
Final model parameters (ra, ra) and errors for 1,1-dicyanocyclopentane using the pseudorotational model. The parameters d1, d2, and df are the
respective coef®cients in Eqs. (4)±(6)
ra ®t
ra ®t
a
b
c
a
b
c
Value
s1
s2
stotal
Value
s1
s2
stotal
Ê
Geometrical parameters (distances in A, angles in 8)
C±Cring
d1
1.552
0.0119
20.0100
20.0113
0.419
0.001
0.001
0.003
1.549
0.001
0.001
0.003
®x
®x
®x
0.0119
20.0100
20.0113
®x
®x
®x
d2
df
qd
C±Cz
dC±Cz
C´N
0.016
0.002
0.020
0.001
0.002
1.0
0.0170.049
0.002
0.014
0.001
0.001
1.1
0.434
0.018
0.014
0.051
1.472
0.006
0.055
0.002
0.004
3.2
1.472
20.0065
1.152
0.002
0.002
0.005
20.011
1.164
®x
®x
0.001
0.002
1.1
0.001
0.001
0.9
0.002
0.004
3.1
C±H
C5±C1±C2
d512
1.085
1.068
104.6
103.6
3.50
®x
3.50
NC±C±CN
H±C±H
C±C´N
re
108.9
0.8
1.0
1.2
1.4
0.5
0.9
7
3.1
109.1
1.2
1.2
3.7
113.1
2.7112.6
3.2
0.9
0.5
2.3
173.1
26.72.3
0.31
175.2
24.1
0.31
1.2
2.1
0.9
1.4
3.4
5.6
2.4 .0
t f
®x
®x
Ê
Fitted vibrational amplitudes (A)
lC±Cring
lC±C z
lC±H
0.054
0.041
0.079
0.030
0.064
0.068
0.073
0.101
0.113
0.112
0.001
0.005
0.003
0.001
0.012
0.009
0.005
0.008
0.009
0.002
0.001
0.002
0.001
0.000
0.008
0.010
0.004
0.012
0.004
0.001
0.004
0.012
0.007
0.002
0.032
0.055
0.041
0.076
0.029
0.071
0.001
0.002
0.002
0.001
0.013
0.001
0.002
0.001
0.000
0.017
0.003
0.006
0.006
0.002
0.044
lC´N
lC2´´´C4
lC2´´´C8
lC3´´´C8
lC2´´´N9
lC3´´´N9
lC1´´´H10
00.0270.07 0.008
0.010
0.026
0.002
0.014
0.029
0.022
0.006
0.075
0.005
0.004
0.008
0.002
0.013
0.104
0.111
0.111
0.0070.015
0.003
0.020
0.005
0.001
Potential constants (cal/mol)
V2
1050
1469
®x
865
1050
1629
2.89
3.81
®x
1150
V4
945
2677
963
3274
Rlong
Rshort
3.41
3.99
a
s1 is the single standard error of the ®t.
s2 is the propagated error [7±9].
b
c
d
e
f
p
Puckering amplitude.
:
stotal
ˆ
6s12 1 3s22
Rocking angle of the NC±C±CN group at Cs symmetry.
Twisting angle of the NC±C±CN group at C2 symmetry.
Figs. 5 and 6 show the experimental and theoretical
reduced molecular intensity sMꢀs†; and the experi-
mental and theoretical radial distribution function
from the pseudorotational model, respectively. Table
6 shows a comparison of the geometrical parameters
which have been obtained from the electron diffrac-
tion investigation with those obtained from the ab
initio calculations at the MP2/6-311 1 G(2df,2pd)
level.
The electron diffraction intensity data, the calcu-
lated vibrational amplitudes and the corrections ꢀra 2
ra† are deposited as supplemental data.

M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
191
Fig. 5. Experimental ( £ ) and theoretical (Ð) reduced molecular intensity sMꢀs† for DCCP.
6. Discussion
cyano groups we found it reasonable to carry out ab
initio calculations on monocyanocyclopentane
(MCCP) and to compare the results with those of
DCCP. For a proper comparison we used the same
methods and basis sets we employed in the case of
Searching for the factors affecting the ring
geometry and the symmetry of the ®ve-membered
ring in DCCP as a result of the substitution by geminal
Fig. 6. Experimental ( £ ) and theoretical (Ð) radial distribution function from pseudorotational model for DCCP.

192
M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
Table 6
Comparison of ra distances, bond angles and dihedral angles of 1,1-dicyanocyclopentane (DCCP) as obtained from electron diffraction and ab
initio calculations (MP2/6-311 1 G(2df,2pd))
Cs only
ra ®t
ra ®t
Ab initio
Cs
Cs
C2
Cs
C2
Cs
C2
Ê
Bond distances (A)
C1±C2
C2±C3
C3±C4
qa
1.554
1.544
1.560
0.418
1.474
1.474
1.165
1.088
1.556
1.577
1.536
1.535
0.419
1.472
1.472
1.164
1.085
1.555
1.576
1.535
1.536
0.434
1.475
1.475
1.164
1.083
1.5443
1.5338
1.5675
1.5256
1.545
1.561
0.419
1.482
1.461
1.164
1.085
1.548
1.558
0.434
1.482
1.469
1.165
1.084
1.54971.5248
0.443
0.446
C1±C6x
C1±C8x
±CxN
kC±Hlb
1.4643
1.4580
1.1707
1.0882
1.4607
1.4607
1.1708
1.0889
Bond angles (8)
C1±C2±C3
C2±C3±C4
C5±C1±C2
NC±C±CN
H±C±H
102.3
.0106.7107
104.0
101.8
104.3
102.5
102.0
103.6
103.0
103.3
102.6
104.4
106.6
105.9
104.6
108.9
113.1
118.8
108.1
108.9
113.1
125.6
103.6
109.1
112.6
121.4
107.1
109.1
112.6
125.5
101.4
110.3
107.9
121.8
104.9
109.3
108.2
125.3
107.6
111.3
c
b6
128.6
d
b8
122.7132.3
41.6
125.6
129.5
125.5 .9
127
125.3
43.5
2.72.5
ae
hf
41.9
6.9
±
43.1
4.8
±
±
5.8
6.9
4.8
Dihedral angles (8)
C1±C2±C3±C4
C4±C5±C1±C2
C2±C3±C4±C5
24.724.6
40.6
0.0
2 34.5
42.0
44.5
25.6
0.0
2 35.8
42.8
45.8
26.6
0.0
2 37.2
40.713.1
0.0
13.6
14.2
46.6
a
Puckering amplitude for the ring.
Average value.
b
c
d
e
f
Angle between the bond C6±C1 and the plane C5C1C2.
Angle between the bond C8±C1 and the plane C5C1C2.
Angle between the C5C1C2 plane and C2C3C4C5 plane (¯ap angle).
Bending angle (outwards) of the C±CxN chain.
DCCP. Additionally, the optimized geometry of
MCCP by using the basis set 6-31111G(2df,2pd)
and the B3PW91 and the MP2 methods has been
calculated.
tively, and thus being the more stable conformer. In
contrast, the Hartree±Fock method UHF/6-31G(d,p)
has suggested the equatorial conformer to be more
stable by 0.360 kcal/mol. Similarly, the density func-
tional (DFT) hybrid method B3PW91 in combination
with the basis sets 6-31111G(df,pd) and 6-
31111G(2df,2pd) favors the equatorial conformer
by 0.361 and 0.466 kcal/mol, respectively. This result
is interesting because it re¯ects the confusion that
took place concerning the conformational stability
of MCCP as it was found by the experimental studies.
A microwave investigation carried out by Choe and
Harmony [19] could not provide clear cut evidence for
the preference of one or the other conformer and,
Before comparing the ab initio results we would
like to discuss very brie¯y the conformational prefer-
ence in MCCP and to address the controversy which
has arisen about the occurrence of the axial and equa-
torial conformers in this molecule. The second order
Mùller±Pleset perturbation theory by using the basis
sets 6-31G(d,p), 6-311 1 G(2df,2pd), and 6-
31111G(d,p) has shown that MCCP exists in axial
and equatorial forms with the axial conformer lower
in energy by 0.415, 0.370, and 0.535 kcal/mol, respec-

M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
193
Table 7
Optimized geometrical parameters of MCCP (envelope Cs symmetry)
a
HF/6-31G(d,p)
B3PW91/6-31111G(2df,2pd)
eq ax
MP2/6-31G(d,p)
eq ax
MP2/6-311 1 G(2df,2pd)
eq ax
Exp.
eq
ax
Ê
Bond distances (A)
C1±C2
C2±C3
C3±C4
qc
1.5372
1.5393
1.5403
1.5514
0.398
1.5378
1.5351
1.5492
0.412
1.5403
1.5363
1.5481
0.395
1.5362
1.5372
1.5513
0.431
1.5377
1.5381
1.5334
1.5351
1.5356
1.5362
1.544(1)b
1.5394
1.5524
0.414
1.55071.5505
1.5497
0.432
0.426
0.439
1.4537
0.426(28)
1.477(7)
1.160(2)
C±Cx
±CxN
C1±H
kC±Hl
1.4713
1.1356
1.0866
1.0852
1.4771
1.1358
1.0839
1.0840
1.4531
1.1512
1.0954
1.0908
1.4592
1.1514
1.0921
1.0905
1.4616
1.1817
1.0944
1.0901
1.4672
1.1818
1.0913
1.0900
1.4597
1.1706
1.0894
1.1704
1.0931
1.08871.0886
1.102(6)
Bond angles (8)
C1±C2±C3
C2±C3±C4
C5±C1±C2
H±C1±Cx
C2,5±C1±Cx
kH±C±Hl
103.5
104.6
106.0
102.5
107.1
111.2
107.7
125.2
127.6
39.1
103.7104.7103.3
106.2
103.8
103.1
105.9
102.4
108.2
113.9
107.4
130.4
121.4
103.7
105.8
106.1
102.9
107.2
113.8
107.2
130.5
122.4
41.2
106.1
102.3
107.3
111.6
107.2
125.9
126.8
38.8
105.8
105.7
102.8
101.9
108.5
110.5
107.6
123.8
127.7
102.1
108.3
113.8
107.5
129.9
121.8
101.7
108.5
110.3
107.7
123.4
128.1
107.4
114.1
112.1(13)
107.2(32)
107.0
d
b6
130.9
e
b8
af
121.7
40.8
42.742.0
43.5
42.6
26.1
Dihedral angles (8)
C1±C2±C3±C4 24.9
C4±C5±C1±C2 40.6
24.1
38.8
24.8
40.2
24.0
38.5
25.9
42.0
25.726.4
41.5
42.9
42.1
a
Pseudorotating model given in Ref. [18] (rg values).
b
c
d
e
f
Single average C±C bond.
Puckering amplitude for the ring,calculated with program ring [26,27].
Angle between the bond C6±C1 and the plane C5C1C2.
Angle between the bond H8±C1 and the plane C5C1C2.
Angle between the C5C1C2 plane and C2C3C4C5 plane (¯ap angle).
Ê
therefore, the authors suggested that both conformers
might be energetically equally favored. However,
Hilderbrandt et al. [18] concluded from their electron
diffraction data that the equatorial conformer is by
180(330) cal/mol preferred over the axial form.
Based on our ab initio results presented in this work
we conclude that the axial conformer in MCCP is
energetically more stable and the prediction by the
HF and DFT methods are less reliable. Perhaps it is
of interest to indicate that the predicted dipole
moments for the axial and equatorial conformers
differ only by about 0.3 D.
length in MCCP is about 0.02 A longer than predicted
by the MP2/6-311 1 G(2df,2pd) and B3PW91/6-
31111G(2df,2pd) methods. On the other hand the
Ê
experimental value for the CxN bond is by 0.01 A
shorter than that produced by the MP2 method and
Ê
by 0.01 A longer than it has been predicted by the
Ê
DFT method. The value of 1.1356 A for this bond
as predicted by the HF/6-31G(d,p) calculations is de®-
nitely too low.
Overall, based on the ab initio results presented in
this work a closer scrutiny of the conformational
analysis by the experiment seems to be warranted.
Consistently, all ab initio methods we applied show
that the ring geometrical parameters remain almost
unchanged upon going from the axial to the equatorial
conformer. It is also remarkable that the exocyclic
Further discrepancies between the electron diffrac-
tion and the quantum mechanical results are visible
from the C±Cx and CxN bond lengths. As it is shown
in Table 7the experimentally determined C±C x bond

194
M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
angle H±C1±Cx and the bond lengths within the C±
CxN moiety are negligibly different in both confor-
mers. Only the ¯ap angle is approximately 18 smaller
in the axial conformer. All these ®ndings explain the
uncertainty of the microwave and electron diffraction
experiments by the determination of the conforma-
tional stability for MCCP.
From Table 2 it is evident that for DCCP the agree-
ment between the values produced by the ab initio
methods we used in the present study is fairly good.
Nevertheless, a closer consideration of the various
parameters shown in Table 2 indicates that the C1±
C2 bond is slightly overestimated by the DFT method
and both the DFT and HF/6-31Gpp methods overesti-
mate the C1±C6 bond. It is also worthwhile to note that
the HF/6-31Gpp level of theory overestimates the C1±
C8 bond length but it drastically underestimates
(rather more than the DFT method) the CxN bond
distance.
triple bond is signi®cantly shortened. This bond short-
ening has been the focal point of controversial discus-
sions and various concepts of rationalizations have
been proposed. Based on Mulliken electron charge
density distribution analysis Politzer et al. [20] have
found that a signi®cant fraction of the p-electrons of
the carbon triple bond is spread over the neighbouring
regions (denoted `outer' p charge). Conclusively, the
strengthening of the adjacent single bond is attributed
to addition of partial p bonding to the single bond.
Although this concept neglects a probable charge
polarization effect exerted by the attached substituents
it seems to be applicable to the C±Cx bonds in DCCP.
From the experimental and the ab initio results
listed in Tables 2 and 5 it can be easily concluded
that the simultaneous lengthening of the CxN bonds
and shortening of the C±Cx bonds are adequately
describable by the notion of Politzer et al. [20].
Taking this notion into consideration the subsequent
electronic contact of the outer p charges in the single
bond regions leads to a conjugative or resonance inter-
action between the geminal cyano groups. Such kind
of interaction results in a reduction of the C±Cx
bonds and elongation of the CxN bonds as it has
been observed in DCCP.
A comparison between the ab initio results which
have been produced by the MP2/6-311 1 G(2df,2pd)
method for the envelope form of DCCP and the predo-
minant axial conformer of MCCP (Tables 2 and 7)
leads to the following conclusions: (i) While the
vicinal ring carbon±carbon bond increases by about
Ê
0.01 A upon going from MCCP to DCCP the
remaining ring C±C bonds, however, stay almost
unchanged. (ii) The equatorial C±Cx bond in DCCP
From Tables 2 and 5 it can also be seen that there is
quite good agreement between the calculated and the
experimental values for the puckering amplitude q.
The relatively large exocyclic xC±C±Cx angle is
probably the result of the steric repulsion between the
geminal cyano groups. Also it is most likely that this
repulsive interaction is responsible for the outward
bending of the C±CxN chains by about 2.3 and 4.88
as provided by the theory and experiment, respec-
tively. It is important to indicate that this consistency
between theory and experiment demonstrates that this
bending angle is not the consequence of vibrational
effects.
From all the foregoing it may be concluded that the
insertion of a second cyano group in geminal position
into MCCP does not lead to drastical changes in the
geometrical parameters of DCCP. Only the C±C bond
distances and bond angles associated with the central
atom C1 are in¯uenced by the geminal substitution.
The widening of the xC±C±Cx angle and the devia-
tion of the C±CxN groups from linearity are due to
internal steric repulsion within the NxC±C±CxN
moiety.
Ê
is slightly shorter (by 0.006 A) than that in axial posi-
tion and this difference parallels the difference
between the axial and equatorial C±Cx distance in
MCCP. (iii) The computed CxN bond does not vary
on moving from MCCP to DCCP. (iv) The puckering
amplitude q for DCCP is larger than that for MCCP.
From Table 2 it can be easily seen that by applying
the MP2 method and the augmentation of the basis set
using triple zeta basis set and adding diffuse functions
to the heavy atoms and orbitals of higher angular
momentum to the heavy atoms and the hydrogens
leads generally to a reduction of all bond distances
in DCCP. On the other hand, all bond angles remain
almost unchanged upon the extention of the basis set.
Moreover, it is noticeable that the contraction of the
bond lengths within the cyano groups is evident. The
C±Cx and CxN bonds shorten by about 0.007and
Ê
0.012 A, respectively, due to the augmentation of the
basis set.
It is well known that a single bond adjacent to a

M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
195
In order to ®nd more pertinent reasons for the non-
linearity of the C±CxN moiety in DCCP we
performed a natural population analysis (NPA) [21±
23] and Mulliken population analysis (MPA) for the
Cs and C2 symmetric forms of DCCP as well as for the
axial and equatorial conformers in MCCP. For this
purpose we applied the MP2/6-31111G(2df,2pd),
ment and ab initio calculations provide values for the
xC±C±Cx angle which are close to the magnitude of
the tetrahedral angle and the bending angle is rela-
tively small. The charge distribution N2xC1±C2±
C1xN2 according to NPA elucidates unambiguously
these results and justi®es the predicted conjugation
between the geminally substituted cyano groups. In
this case the attractive Coulombic interaction between
the positively charged carbon of one cyano group and
the negatively charged nitrogen of the other cyano
group compensates partially for the repulsive interac-
tion between equally charged atoms in the cyano
groups. Such intramolecular interaction antagonizes
larger xC±C±Cx and C±CxN angles.
Focusing on the most stable envelope (Cs) confor-
mation, the average value for the ring C±C bond
distances in DCCP emerging from the ab initio calcu-
lations (Table 2) agree well with the ra value resulting
from the experimental and ab initio joint analysis. It is
also worth to recognize that the averaged C±Cx bond
MP2/6-3111G(d,p), MP2/6-311G(d,p),
B3PW91/6-3111G(2df,2pd) methods.
and
Without
going into further details we summarize the results
as follows: As it was anticipated both analyses
provided inconsistent charge distributions. For brevity
we would like to focus only on the charge distribution
on the atoms within the C(CxN)2 fragment. While the
MPA places negative charges on both atoms in the
CxN group and positive charge on the anchor atom
C1, the NPA predicts that the terminal atoms in the C±
CxN group are negatively charged and the middle
carbon atom is positively charged. It is worthwhile
to note that similar contradictory charge distribution
was observed for the C±CxN group in both the axial
and equatorial conformers in MCCP.
It is generally accepted that the MPA exhibits
various fundamental de®ciencies [24,25]. One of the
major weaknesses of MPA is its dependence on the
kind and size of the basis set in use, and one further
considerable de®ciency is that it partitions in some
cases the electronic charges in such a way that nega-
tive orbital population occurs. Moreover, in many
cases the MPA overestimates the covalent character
of a bond although it is ionic. The latter shortcoming
of MPA is evident in the equatorial form of MCCP.
While the charge distribution for the C±CxN group
(using the MP2/6-3111G(d,p) method) according to
MPA is C(11.91)±C(20.66)xN(20.22), the NPA,
however, results in C(20.27)±C(10.34)xN(20.33).
From this example it is evident that in contrast to NPA
the MPA suppresses the ionicity of the CxN bond.
Perhaps the most intriguing feature which emerges
from this population analysis for DCCP is the
following: Taking the Mulliken charge distribution
within the C(CN)2 fragment into consideration
(N2xC2±C1±C2xN2) we may conclude that a
considerable repulsive steric interaction due to the
negatively charged cyano groups would be dominant
leading to a distinct widening of the xC±C±Cx angle
and to a more accentuated bending of the C±CxN
chain. However, in the present study both the experi-
Ê
distance provided by the MP2 method is 0.01 A
shorter than that obtained from the experiment,
whereas the average value produced by the DFT
method agrees fairly well with the experimental
value. The application of the MP2 method and the
basis sets 6-31G(d,p) and 6-311 1 G(2df,2pd) leads
to a CxN bond length which is considerably longer
Ê
than the experimental value by 0.030 and 0.018 A,
respectively. The HF/6-31G(d,p) method, however,
Ê
provides a value for this bond which is 0.018 A
shorter than the experimentally determined one.
This odd result demonstrates that the CxN bond
length is not reasonably predicted by the theory, at
least not by the ab initio methods we applied in this
work.
It is perhaps of particular interest to indicate that the
observed rg mean values for the ring carbon±carbon
distances in cyclopentane, MCCP and DCCP are
Ê
Ê
Ê
1.546(1) A [28], 1.544(1) A [18], and 1.555(3) A
(this work), respectively. Although the variation in
the averaged C±C bond distance is non-systematical,
the lengthening of this bond in DCCP by 0.009 and
Ê
0.011 A in comparison to cyclopentane and MCCP,
respectively, indicates that the geminal substitution of
cyclopentane by cyano groups leads to a general elon-
gation of the ring C±C bonds. Considering the distinct
s and p electron acceptor property of the cyano group
this bond change appears to be minor. However, this

196
M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
might be the consequence of competing effects like s-
charge withdrawal by the cyano group and ring strain.
It remains to point out that the observed puckering
in MCCP by an additional cyano group, in general,
does not substantially affect the ring geometry.
Perhaps the most intriguing result of this work is
that evidence for the bond conjugation within the
C(CN)2 linkage could be derived from the NPA. In
contrast to the MPA, based on the charge distribution
provided by th NPA we could rationalize the moderate
xC±C±Cx angle widening and the C±CxN angle
bending by attractive and repulsive electrostatic inter-
action between the alternatively negatively and posi-
tively charged atoms within the NxC±C±CxN
fragment.
Ê
amplitudes q of 0.427(15) A [28], 0.426(28) A [18],
Ê
Ê
and 0.434(45) A (this work) for cyclopentane, MCCP
and DCCP, respectively, indicate that this parameter
seems to be less sensitive to direct substitution on
cyclopentane.
7. Summary and conclusions
In summary, from the presented experimental and
ab initio results the following conclusions may be
derived:
8. Supplementary data
The electron diffraction data could be properly
reproduced after the application of a dynamic pseudo-
rotation model instead of a static model. To determine
the pseudorotational potential function in more accu-
rate fashion we had to account for the distinct depen-
dency of the geometrical parameters as well as the
vibrational amplitudes on the phase angle f in
DCCP. For a better justi®cation of the pseudorotation
model we found it more pertinent to include the
dependency of the delocalized net charge distribution
within the ®ve-membered ring on the phase angle f.
Assuming similar puckering amplitudes for the Cs and
C2 symmetric forms and a regular pentagon we devel-
oped a charge distribution function which allows for
the determination of the contribution of the deloca-
lized net charges to a certain bond distance within the
®ve-membered ring (Eqs. (2) and (3)). As to the best
of our knowledge such kind of treatment of the
pseudorotation motion in ®ve-membered ring has
not been employed before.
To calculate the reduced total molecular intensities
within the frame of the pseudorotation model a total of
37intermediary conformers in the range of 2135 #
f # 1458 were incorporated into the structural
analysis. Taking into account that large amplitude
motions play an eminent role within DCCP (particu-
larly the C±CxN groups) the experimental data could
be best described by applying a ra ®t. For this purpose
we adopted the necessary perpendicular vibrational
amplitudes for the ra 2 ra corrections from the quad-
ratic force ®eld produced by the HF/6-31Gpp method.
From the present structural analysis of DCCP we
found that the substitution of the hydrogen atom on C1
Supplementary material has been depsited with the
British Library Document Supply Centre as supple-
mentary publication number sup 26686.
Acknowledgements
The authors are grateful to Prof. I. Hargittai for
recording the patterns and collecting the data for
DCCP. M.D. gratefully acknowledges the ®nancial
support from the Fonds der Chemischen Industrie.
References
[1] K. Wallenfels, K. Friedrich, J. Rieser, Justus Liebigs Ann.
Chem. (1976) 656.
[2] V. Typke, M. Dakkouri, H. Oberhammer, J. Mol. Struct. 44
(1978) 85.
[3] H. Oberhammer, W. Gombler, H. Willner, J. Mol. Struct. 70
(1981) 273.
[4] J. Haase, Z. Naturforsch. Teil A 25 (1970) 936.
[5] gaussian 98, Revision A.7, M.J. Frisch, G.W. Trucks, H.B.
Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G.
Zakrzewski, J.A. Montgomery, Jr., R.E. Stratmann, J.C.
Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N.
Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M.
Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S.
Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui,
K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari,
J. B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B.
Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.
Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham,
C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe,
P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres,
C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople,
Gaussian, Inc, Pittsburgh, PA, 1998.

M. Dakkouri, V. Typke / Journal of Molecular Structure 612 (2002) 181±197
197
[6] W.J. Hehre, spartan, Release 5.0.3, Wavefunction, Inc,
Irvine, CA, 1994.
[18] R.L. Hilderbrandt, H. Leavitt, Q. Shen, J. Mol. Struct. 116
(1984) 29.
[7] M. Dakkouri, V. Typke, J. Mol. Struct. 320 (1994) 13.
[8] V. Typke, M. Dakkouri, M. Schiele, Z. Naturforsch 35a
(1980) 1402.
[19] J. Choe, M. Harmony, J. Mol. Spectrosc. 81 (1980) 480.
[20] P. Politzer, S.D. Kasten, J. Phys. Chem. 80 (1976) 283.
[21] A.E. Reed, R.B. Weinstock, F. Weinhold, J. Chem. Phys. 83
(1985) 735.
[9] M. Dakkouri, V. Typke, J. Mol. Struct. 550±551 (2000) 349.
[10] B. Fuchs, in: E.L. Eliel, N.L. Allinger (Eds.), Topics in Stereo-
chemistry, vol. 10, 1978, p. 1.
[22] A.E. Reed, F. Weinhold, J. Chem. Phys. 83 (1985) 1736.
[23] A.E. Reed, P.v.R. Schleyer, Chem. Phys. Lett. 133 (1987) 553.
[24] A.E. Reed, P.v.R. Schleyer, J. Am. Chem. Soc. 108 (1986)
3586.
[11] J. Laane, in: J.R. Durig (Ed.), Vibrational Spectra and
Structure, vol. 1, 1972, p. 25.
[12] H.L. Strauss, Ann. Rev. Phys. Chem. 34 (1983) 301.
[13] J.H.M. ter Brake, F.C. Mijlhoff, J. Mol. Struct. 77 (1978) 109.
[14] M. Dakkouri, V. Typke, R. Bitschenauer, J. Mol. Struct. 355
(1995) 239.
[25] A.E. Reed, P.v.R. Schleyer, J. Am. Chem. Soc. 112 (1990)
1434.
[26] D. Cremer, Program ring, QCPE Program No. 288, Indiana
University, Bloomington, IN, 1975.
[15] V. Typke, M. Dakkouri, T. Schauwecker, Manuscript in
preparation.
[27] D. Cremer, J.A. Pople, J. Am. Chem. Soc. 97 (1975) 1358.
[28] W.J. Adams, H.J. Geise, L.S. Bartell, J. Am. Chem. Soc. 92
(1970) 5013.
[16] M. Dakkouri, V. Typke, To be published.
[17] J.E. Kilpatrick, K.S. Pitzer, R. Spitzer, J. Am. Chem. Soc. 69
(1947) 2483.