Barriers to internal rotation around the C-N bond in 3-(o-aryl)-5-methyl- rhodanines using NMR spectroscopy and computational studies. Electron density topological analysis of the transition states

Article abstract of DOI:10.1039/b406556e

We have investigated the pairs of rotational isomers for six 3-(o-aryl)-5-methyl-rhodanines (Z = H, F, Cl, Br, OH, and CH₃) using NMR spectroscopy and density functional theory (DFT) calculations. Electron density topological and NBO analysis h

Full text of DOI:10.1039/b406556e

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A R T I C L E
Barriers to internal rotation around the C–N bond in 3-(o-aryl)-
5-methyl-rhodanines using NMR spectroscopy and computational
studies. Electron density topological analysis of the transition
states
Yeliz Aydeniz,a Funda Oğuz,a Arzu Yaman,a Aylin Sungur Konuklar,a Ilknur Doğan,a
Viktorya Aviyente*a and Roger A. Kleinb
a
Department of Chemistry, Boğazici University, Bebek, Istanbul, Turkey.
E-mail: aviye@boun.edu.tr
Institute for Physiological Chemistry, University of Bonn, Germany.
b
E-mail: klein@institut.physiochem.uni-bonn.de
Received 4th May 2004, Accepted 2nd July 2004
First published as an Advance Article on the web 4th August 2004
We have investigated the pairs of rotational isomers for six 3-(o-aryl)-5-methyl-rhodanines (Z = H, F, Cl, Br, OH, and CH3)
using NMR spectroscopy and density functional theory (DFT) calculations. Electron density topological and NBO analysis
has demonstrated the importance of non-covalent interactions, characterised by (3, −1) bond critical points (BCPs),
between the oxygen and sulfur atoms on the thiazolidine ring with the aryl substitutents in stabilizing the transition states.
The energetic activation barriers to rotation have also been determined using computational results; rotational barriers for
3-(o-chlorophenyl)-5-methyl-rhodanine (3S) and 3-(o-tolyl)-5-methyl-rhodanine (6S) were determined experimentally
based on NMR separation of the diastereoisomeric pairs, and the first-order rate constants used to derive the value of the
rotational barrier from the Eyring equation.
appearance of a potential barrier resulting in hindered rotation is
Introduction
to carry out an ab initio quantum-mechanical calculation of the
Thiazolidinediones and rhodanines are known to possess pharma-
total energy of the molecule as a function of the dihedral angle, at
cological activity1 and to be very effective in improving glycaemic
a sufficiently high level of theory. The difference between neigh-
control in diabetic patients, potentiating the action of insulin and
bouring maxima and minima is the energy barrier during hindered
thus lowering blood glucose levels. Rhodanines have both antiviral
rotation. In the ground state the two ring systems are orthogonal
and antibacterial activity.2 The 3-(o-aryl)-5-methyl-rhodanines that
to one another, or very nearly so. There are two transition states
we have analysed consist of a five-membered ring bonded to a
with geometries corresponding to the Z group on the same side
phenyl ring, i.e. a 5/6 ring skeleton (Fig. 1).
or opposite side to the carbonyl or thiocarbonyl group with the
two ring systems nearly coplanar, such that rotation is sterically
hindered. These compounds possess both a chiral centre and a chiral
axis; the chiral centre is the methyl-substituted carbon atom C5 and
the C–N bond forms the chiral axis. Thus, four stereoisomers, S–P,
S–M, R–M and R–P4 coexist as shown in Fig. 1. S–P/R–M and S–
M/R–P are enantiomeric pairs, whereas S–P/S–M and R–M/R–P
are diastereomers interconvertible through 180° rotation around the
C–N bond. In this study, sulfur-containing compounds (rhodanine
derivatives) with S–P and S–M configurations have been modelled
computationally.
The N-aryl-2-thioxo-4-oxazolidinones, as well as N-(o-aryl)-
rhodanines with CH3 and Cl substituents, have been synthesized
Fig. 1 Hindered internal rotation around the Caryl–Nsp2 bond in ortho-aryl-
and the barriers to rotation by thermal racemization determined by
substituted rhodanines.
Dogan et al.5 A study by Colebrook6 investigated conformational
The existence of hindered rotation around C–C single bonds
has drawn attention to the potential energy surfaces of these com-
pounds. Although in the late 1910s it was thought that free rotation
could occur around any carbon–carbon single bonds, as time passed
evidence was obtained that free rotation was hindered in many com-
pounds and that these molecules existed as equilibrium mixtures of
a number of preferred rotational isomers.3 The hindered rotation
around the C–N bond of the 3-(o-aryl)-rhodanines can be thought
of as representing a model for the rotational equilibrium around the
C–N bond in 5/6 ring skeletons (Fig. 1).
The compounds studied are shown in Fig. 2. The Z group rep-
resents the substituents, i.e. H, F, Cl, Br, OH, or CH3. It is known
that rotation about the N-(phenyl) bond is restricted both by the size
of the ortho-substituent and the presence of an exocyclic S and O,
causing a rotational barrier between the stereoisomers S–P/S–M
and R–M/R–P (Fig. 1). The most obvious way of explaining the
isomerism in 1-aryl, 3-aryl and 3-aryl-2-thio-hydantoins with H, F,
Cl, Br, CH3 substituents. They found stationary points at 50° and
120° with a small barrier at 90°. The transition states observed at
0° and 180° are higher in energy compared to the transition state at
90°. The influence of F, Cl, Br, NH2, and OCH3 substituents on the
rotational energy barrier for 2,2-disubstituted biphenyls has been
studied by König et al. and dynamic gas chromatography has been
used to determine the energy barriers for atropisomeric biphenyls.7,8
In 1997, Cui et al.9 reported studies on aromatic polyimides with 6/6
and 5/6 ring systems. They found the minimum energy conformers
for these two adjoining ring systems at 90° and 46° using MP2
(Møller-Plesset-2) and HF (Hartee–Fock) methods, respectively.
In 1998, Rang et al.10 described studies of the stereochemistry
and conformational analysis of 3-(alkyl)- or 3-(aralkyl)-5-(methyl/
phenyl)-rhodanines using X-ray crystallography, UV spectroscopy
and molecular mechanics.
2 4 2 6
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6
T h i s j o u r n a l i s © T h e R o y a l S o c i e t y o f C h e m i s t r y 2 0 0 4

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1H and 13C NMR spectra were recorded on a Bruker AC-250
(250 MHz, 20 °C) spectrometer, 2D-NOESY spectra were taken on
a Varian-Mercury (VX-400 MHz-BB, 30 °C) spectrometer. J values
are given in Hz. Melting points were recorded using Fisher Johns
melting point apparatus. Elemental analyses were performed on
Carlo Erba 1100. Thermal interconversion studies have been done
keeping the sample in the NMR cavity at a constant temperature
(sensitivity is ±0.1) and recording the spectra over time.
Computational
The potential energy surface for free rotation around the C1′–N3
bond of the 3-(o-aryl)-5-methyl-rhodanines with H, F, Cl, Br, OH
and CH3 ortho-substituents on the aryl ring was sampled in each
case with PM3 using the SPARTAN 5.1.1 package.12 The local min-
ima and the transition structures located with PM3 were then opti-
mized at the B3LYP/6-31G* level using Gaussian-98.13 Vibrational
frequency analysis was carried out in order to confirm the nature of
the stationary points. The vibrational frequencies have been utilized
to calculate the zero-point energy (ZPE) and thermal energy correc-
tions. Wavefunction files were generated in Cartesian coordinates
using the Gaussian option 6D 10F; the use of the option scf = tight
was important to prevent ‘charge leakage’ as described by Pope-
lier.14 Electron density topology was analysed using Biegler-König’s
AIM2000 and Popelier’s MORPHY98 programs.14,15 Natural bond
orbital (NBO) theory was applied to selected compounds in order
to understand their structural features.16 For the compounds mod-
elled, the stereocenter C5 had the S-configuration and structures are
denoted as S–M with the C4–N3–C1′–C2′ dihedral angle positive,
or as S–P with the C4–N3–C1′–C2′ dihedral angle negative. The
acronyms TS and TS′ refer to the transition structures where the
substituent interacts with oxygen or sulfur respectively (Fig. 2).
Fig. 2 Atom numbering and the compound naming for 3-(o-aryl)-5-
methyl-rhodanines.
In this paper, we focus on the conformational behaviour of
the 3-(o-aryl)-5-methyl-rhodanines with H, F, Cl, Br, OH, CH3
substituents. The CH3 and Cl derivatives have been synthesized
and the barriers to rotation have been determined experimentally.
Rationalisation of the effect of substituents on the hindered rota-
tion, together with DFT calculations followed by electron density
topological analysis of the wavefunction, enables us to understand
better the nature of the interactions present in each compound and
their transition states. Comparison of the computational results with
the experimental observations provides support for the conclusions
drawn.
Results and discussion
Experimental
Methodology
Experimental determination of the rotational barriers was
carried out for 3-(o-tolyl)-5-methyl-rhodanine (6S) and 3-(o-chloro-
phenyl)-5-methyl-rhodanine (3S). Synthesis yielded a mixture of
the four stereoisomers, S–M, S–P, R–M and R–P (Fig. 1). The
1H NMR spectrum consisted of superimposed spectra for two dia-
stereomers, one for the S–M/R–P enantiomeric pair and one for
the S–P/R–M pair. In the case of 3-(o-tolyl)-5-methyl-rhodanine,
the ratio of the diastereomers was found to be 1:3.2, based on the
signal intensities of the well resolved ortho-methyl signals (Fig. 3a).
When this isomeric mixture was kept at constant temperature and
Experimental
3-(o-Chlorophenyl)-5-methyl-rhodanine, 3S, was synthesized
by reacting ammonium o-chlorophenyl dithiocarbamate, prepared
from 0.3 mol of CS2 and 0.2 mol o-chloroaniline in 25% ammonia
solution, with the sodium salt of 2-chloropropionic acid (0.15 mol)
in aqueous sodium hydroxide solution.11 The product was purified
by column chromatography over silica using 1:3 v/v CHCl3/
petroleum ether as the eluting solvent (1.25 g, 3%), mp 93 °C.
(Found: C, 47.46; H, 3.28; N, 5.39%. Calc. for C10H8NOS2Cl: C,
46.60; H, 3.11; N, 5.43%). H (250 MHz; C6D6; Me4Si) 3.40, 3.54
[H, quartet, J = 7.3, 7.3, C(5)H, one for each diastereomer], 1.07,
1.19 [3 H, doublet, J = 7.3, 7.3, C(5)Me, one for each diastereo-
mer], 7.22–7.58 (4 H, multiplet, Ph); C (62.5 MHz; C6D6; Me4Si)
198.8 (thiocarbonyl carbon in heterocycle), 175.4 (carbonyl carbon
in heterocycle) 46.0, 45.8 (methine carbon in heterocycle, one for
each diastereomer), 18.5, 17.5 (methyl carbon attached to C-5 of the
heterocycle, one for each diastereomer), 133.4, 132.8, 130.8, 130.2,
127.7 (aromatic carbons).
3-(o-Tolyl)-5-methyl-rhodanine, 6S, was synthesized by react-
ing racemic ethylthiolactate (0.02 mol) with o-tolylisothiocyanate
(0.02 mol) in the presence of a catalytic amount of sodium metal
in toluene.11 At the end of 5 h of refluxing, toluene was removed
by evaporation and the product purified by recrystallization from a
petroleum ether–ethanol mixture (1.8 g, 33%), mp 81 °C. (Found:
C, 55.98; H, 4.83; N, 5.76%. Calc. for C11H11NOS2: C, 55.70; H,
4.64; N, 5.90%). H (250 MHz; C6D6; Me4Si) 3.36, 3.43 [1 H,
quartet, J = 7.3, 7.3, C(5)H, one for each diastereomer], 1.08,
1.11 [3 H, doublet, J = 7.3, 7.3, C(5)Me, one for each diastereo-
mer], 1.88, 1.94 (3 H, singlet, o-Me, one for each diastereomer),
6.79–7.00 (4 H, multiplet, Ph); C (62.5 MHz; C6D6; Me4Si) 176.2
(carbonyl carbon in heterocycle) 45.7 (methine carbon in hetero-
cycle), 18.5, 17.3 (methyl carbon attached to C-5 of the heterocycle,
one for each diastereomer), 18 (o-Me), 135.2, 136.5, 131.3, 129.9,
129.1, 127.3 (aromatic carbons).
1
the H NMR spectrum recorded over time, the intensity of the
lower intensity signal increased and that of the higher intensity
signal decreased until equilibrium was reached. At an equilibrium
temperature of 333 K, the diastereomeric ratio changed to 1.4:1
(Fig. 3d). This change in relative intensity of the signals was due
to the first-order transformation of the S–M/R–P to S–P/R–S
diastereomers via 180° rotation around the C–N bond (Fig. 1), the
equilibrium constant, K, being 1.4 at 333 K. The rate constants k1
and k−1 for this conversion (Fig. 1) have been found by following the
reversible first-order kinetics.17 The negative slope of the straight
line obtained from plotting ln([A]t − [A]eq/[A]0 − [A]eq) against time
yielded rate constants from which the magnitude of the rotational
barrier could be obtained using the Eyring equation.17
The conformations of the rotational isomers of 3-(o-tolyl)-5-
methyl-rhodanine have been determined using through-space
connectivities derived from 2D-NOESY experiments. The 2D-
NOESY spectrum of the compound showed a crosspeak between
the ortho-methyl signal of the higher intensity diastereomer with
the C5 methyl signal of the same diastereomer (Fig. 4). This NOE
relationship is only possible for the S–M or R–P structures where the
closest distance between the hydrogens of the methyl groups is found
to be 3.515 Å by DFT calculations as described later. Therefore the
higher intensity stereoisomer has been assigned to the S–M (or R–P)
structure. Thus the kinetics followed for determination of the rate
constants refer to the conversion of the S–M/R–P pair to S–P/R–M.
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6
2 4 2 7

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Table 1 Experimentally determined kinetic and thermodynamic parameters Go (kcal mol−1), Ho (kcal mol−1) and So (cal mol−1) for the thermal intercon-
version process between the diastereomers of 3S and 6S determined by following the change in the 1H NMR signals. Solvent: C6D6
Compound
T/K
Go/kcal mol−1
Ho/kcal mol−1
So/cal mol−1
k1/s−1
k−1/s−1
G#/kcal mol−1
3S
333
0.24
−1.27
−4.5
1.51 × 10−6
2.19 × 10−6
a28.47
b28.20
c28.80
318
333
0.17
−0.22
6S
0.53
2.2
1.16 × 10−5
8.37 × 10−6
d27.10
e27.32
c27.64
318
304
−0.18
−0.15
a Gibbs free energy of activation for the conversion of the higher intensity diastereomer to the lower intensity one. b Gibbs free energy of activation for the
conversion of the lower intensity diastereomer to the higher intensity one. c Calculated value. d Gibbs free energy of activation for the conversion of S–M (R–P)
to S–P (R–M). e Gibbs free energy of activation for the conversion of S–P (R–M) to S–M (R–P).
3S the initial higher intensity signal ended up as the thermodynami-
cally more stable diastereomer at equilibrium. Whereas for 6S the
initial lower intensity signal turned out to be more populated at
equilibrium, both 3S and 6S being equilibriated at 333 K, in the
NMR cavity. For 6S it is certain that the obtained kinetic and thermo-
dynamic values (Table 1) refer to the conversion of S–M (R–P) to
S–P (R–M) (Fig. 1), based on the NOESY results. However, for 3S,
since it was not possible to do the isomeric assignment, the reported
k1 and k−1 values are only relative.
The Go values, the Gibbs Free energy difference between the
diastereomers, have been determined using the equilibrium constant
values, K = k1/k−1, via Go = −RTlnK. For 6S, the S–P (R–M) pair
has been found to be slightly more stable (by about 0.2 kcal mol−1)
than the S–M (R–P) pair. This difference may be due to the steric
repulsion between the two methyl groups in the cisoid S–M (R–P),
whereas no such repulsion is present in the transoid S–P (R–M)
conformations. The Ho and So values have been determined
from the slope and the intercept respectively of the plot of lnK vs.
1/T assuming that Ho and So are constant over the temperature
range studied.
Geometrical features
For 3-(phenyl)-5-methyl-rhodanine (1S), two minima, which are
virtually isoenergetic, have been located on the potential energy
surface at 89.0° (1S–M) and −89.3° (1S–P) (Fig. 5). The clock-
wise direction of the C2′–C1′–N3–C4 dihedral angle is considered
as positive. In both these structures, the N lone-pair electrons
are delocalized towards S7, as the CS group is able to interact
strongly with strong electron donors. The N3–C2 (1.390 Å) distance
is shorter than the N3–C4 distance (1.405 Å) and C2–S7 (1.643 Å)
is longer than the reference value (1.600 Å)11 (Table 2). Transition
structures (1S–TS or 1S–TS′) have been located at 2.7° and 178.0°
from the carbonyl side of the rhodanine plane. At these stationary,
first-order saddle points, the two rings are flat and coplanar because
of electron delocalization. Six-membered O8–C4–N3–C1′–C2′–H
Fig. 3 250 MHz 1H NMR signals of 3-(o-tolyl)-5-methyl-rhodanine, 6S,
and S7–C2–N3–C1′–C6′–H rings based on electron density topo-
for which diastereomeric signals were observed at 333 K in C6D6: a) at t = 0
logy are formed by the OH and SH hydrogen bonds. Topologi-
cal studies show that the hydrogen bonds formed between the two
s; b) t = 9000 s; c) t = 83400 s; d) t = 94200 s.
In the case of the 3-(o-chlorophenyl)-5-methyl-rhodanine (3S)
stereoisomers, M and P conformations could not be assigned to the
higher and lower intensity diastereomers because no NOE through-
space connectivity could be established between the ortho-H and
C5–H or CH3 protons, since the proton–proton distances are of the
order of ca. 4 Å or greater. Analysis of the reversible first-order
ring systems in these transition states are characterised by bond
critical points (BCPs) of correct (3, −1) topology with a Laplacian
of rho, 2(), which is positive and in the correct range, typical of
closed-shell interactions – see discussion below. The C2′–H and
C6′–H distances shorten from 1.086 Å in 1S–M or 1S–P to 1.076
and 1.075 Å in 1S–TS and 1S–TS′, respectively. Along the reaction
coordinate for this transition, the positive charge on Z = H (on C6′)
increases from 0.0700 a.u. (atomic units) to 0.1086 a.u. In 1S–TS,
electrons contribute to bonding with the neighbouring atoms (O)
associated with a decrease in electron density for the hydrogen
atoms bonded to C6.
1
kinetics derived from the change in the H NMR signal for the
C5–CH3 protons yielded the rate constants and rotational barriers
for this compound. The experimentally determined kinetic and
thermodynamic constants for 3-(o-tolyl)-5-methyl-rhodanine (6S)
and 3-(o-chlorophenyl)-5-methyl-rhodanine (3S) are summarised
in Table 1.
For both 3S and 6S the kinetics of the thermal interconversion
process have been studied by following the conversion of the higher
intensity 1H NMR signal to the lower intensity one. In the case of
In the case of 3-(o-fluorophenyl)-5-methyl-rhodanine (2S),
there are two minima located on the potential energy surface at
72.8° (2S–M) and −71.9° (2S–P). These two minima are virtually
isoenergetic within the calculation error, with the global minimum
2 4 2 8
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6

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Table 2 Selected geometrical parameters for the compounds 1S, 2S, 3S, 4S, 5S and 6S (B3LYP/6-31G*)
C1′–N3
N3–C2 N3–C4 C2–S7 C4–O8 S1–C5 S1–C2 C2′–Z
C4–C5
C5–C6
S7–H O8–H
C4–N3–C1′–C2′
1S–M
1S–TS
2S–M
2S–TS
2S–TS′
3S–M
3S–TS
3S–TS′
4S–M
4S–TS
4S–TS′
5S–M
5S–TS
5S–TS′
6S–M
6S–TS
6S–TS′
1.444
1.467
1.434
1.447
1.457
1.435
1.445
1.456
1.434
1.445
1.456
1.443
1.473
1.475
1.446
1.461
1.472
1.390
1.407
1.391
1.400
1.415
1.391
1.403
1.414
1.390
1.403
1.412
1.382
1.419
1.388
1.389
1.403
1.404
1.405
1.430
1.406
1.457
1.442
1.406
1.461
1.453
1.406
1.459
1.453
1.417
1.418
1.459
1.404
1.447
1.452
1.643
1.653
1.642
1.651
1.639
1.642
1.649
1.636
1.642
1.649
1.635
1.655
1.648
1.664
1.643
1.651
1.644
1.210
1.210
1.209
1.199
1.208
1.209
1.198
1.205
1.209
1.199
1.205
1.207
1.22
1.839
1.815
1.840
1.832
1.826
1.840
1.843
1.831
1.840
1.844
1.832
1.836
1.826
1.828
1.839
1.838
1.825
1.770
1.768
1.768
1.777
1.778
1.768
1.778
1.786
1.768
1.778
1.786
1.763
1.769
1.772
1.770
1.778
1.786
1.086
1.075
1.345
1.343
1.339
1.751
1.757
1.751
1.904
1.918
1.913
1.363
1.353
1.345
1.508
1.517
1.515
3.919 3.570
1.986
3.539 3.957
2.432
2.082
3.732 3.679
2.459
2.184
3.788 3.645
2.474
2.211
4.502 2.903
2.316
89.3
2.7
1.527
1.519
1.519
1.528
1.516
1.517
1.526
1.516
1.518
1.527
1.516
1.517
1.528
1.518
1.518
1.533
1.535
1.527
1.533
1.523
1.526
1.535
1.523
1.526
1.533
1.527
1.525
1.532
1.524
1.536
72.8
−5.5
172.0
84.3
7.9
166.7
84.0
9.3
164.4
114.1
−4.1
175.9
82.7
3.7
1.204
1.211
1.203
1.205
2.059
3.704 3.760
2.411
2.139
−169.5
Fig. 4 2D-NOESY spectrum of 3-(o-tolyl)-5-methyl-rhodanine, 6S, in pyridine-d5 at 303 K.
2S–M being more stable than 2S–P by ca. 0.04 kcal mol−1. This
may be due to favorable interactions between the C5 methyl group
and F that are syn to each other at a distance of 3.207 Å. Because
of favorable interactions between O and F in the transition state
2S–TS, an inter-atomic interaction path results characterised by a
(3, −1) BCP and a positive value for 2(), typical of a closed-shell
interaction. Fluoroacetaldehyde also shows a definite preference for
the syn conformer with the FCCO dihedral angle equal to 0°.18 Simi-
larly, an early experimental study by Cantacuzene and co-workers
demonstrated that the axial–equatorial distribution for 2-fluoro-
cyclohexanone was 55% in favour of the equatorial isomer.19 In
the examples cited above, special stabilizing interactions between
oxygen and fluorine have been postulated. The same type of inter-
actions would be present in FONO2, whose molecular structure has
been studied computationally using coupled-cluster theory.20 In this
study the molecule was found to be planar allowing an interaction
between F and O. The electron density topological analysis reported
in this paper provides additional evidence for a marked closed-shell
interaction, in the sense defined by Bader21 between the fluorine and
oxygen atoms in the fluorophenyl-rhodanine derivative transition
states studied (see Table 5 and Fig. 6). In structure 2S–M the N3–C2
(1.391 Å) distance is shorter than the N3–C4 (1.406 Å) distance
and C2–S7 (1.642 Å) is longer than the reference value 1.600 Å10
(Table 2). The transition states for this compound are located at
dihedrals corresponding to −5.5° (2S–TS) and 172.0° (2S–TS′)
with the two rings nearly coplanar. 2S–TS′ (23.32 kcal mol−1) is
less stable than 2S–TS (20.94 kcal mol−1) because, with the dihedral
equal to 172.2°, the fluorine atom is close to a sulfur atom that is less
electronegative and larger than oxygen, resulting in higher steric
repulsion. The thiocarbonyl group interacts with the lone pairs on
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6
2 4 2 9

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Table 3 Energetics for compounds 1S–6S. E0 and G0 are the electronic
and Gibbs free energies of activation with ZPE corrections (kcal mol−1)
Compound
C4′–N3–C1′–C2′/°
Conformation
E0
G0
1S
2.7
89.0
178.0
−89.3
1S–TS
1S–M
1S–TS′
1S–P
11.26
0.00
11.26
0.00
13.15
0.00
13.15
0.00
2S
3S
4S
5S
6S
−5.5
72.8
172.0
−71.9
2S–TS
2S–M
2S–TS′
2S–P
20.94
0.00
23.32
0.04
22.53
0.00
24.86
0.04
7.9
84.3
166.7
−83.4
3S–TS
3S–M
3S–TS′
3S–P
27.13
0.02
33.42
0.00
28.80
0.05
34.90
0.00
9.3
84.0
164.4
−85.8
4S–TS
4S–M
4S–TS′
4S–P
28.32
0.00
34.95
0.23
29.90
0.00
36.28
0.12
−4.1
114.1
175.9
5S–TS
5S–M
5S–TS′
5S–P
16.96
0.00
19.41
0.03
18.20
0.00
20.71
0.12
−115.1
3.7
82.7
−169.5
−83.0
6S–TS
6S–M
6S–TS′
6S–P
25.80
0.00
32.10
0.04
27.64
0.05
33.73
0.00
Fig. 5 Structures corresponding to the global minima for the compounds
1S [3-(phenyl)-5-methyl-rhodanine], 2S [3-(o-fluorophenyl)-5-methyl-
rhodanine], 3S [3-(o-chlorophenyl)-5-methyl-rhodanine], 4S [3-(o-bromo-
phenyl)-5-methyl-rhodanine], 5S [3-(o-hydroxyphenyl)-5-methyl-rhodanine],
6S [3-(o-tolyl)-5-methyl-rhodanine].
N3, with the result that N3–C2 is shorter than N3–C4 and C2–S7
is longer than the reference value for both 2S–TS and 2S–TS′
structures (Table 2).
In the case of 3-(o-chlorophenyl)-5-methyl-rhodanine (3S),
there are two minima located symmetrically on the potential energy
surface at dihedral angles of 84.3° (3S–M) and −83.4° (3S–P). Their
energies are very close to each other, however, with the minimum
at −83.4° (3S–P) ca. 0.05 kcal mol−1 more stable compared to the
other minimum, i.e. indistinguishable at the level of the calculation
accuracy. Two transition structures are located at dihedrals of 7.9°
(3S–TS) and 166.7° (3S–TS′), with the rings quite some way from
Fig. 6 Structures corresponding to the transition-state structures for
the compounds 1S [3-(phenyl)-5-methyl-rhodanine], 2S [3-(o-fluoro-
phenyl)-5-methyl-rhodanine], 3S [3-(o-chlorophenyl)-5-methyl-rhodanine],
4S [3-(o-bromophenyl)-5-methyl-rhodanine], 5S [3-(o-hydroxyphenyl)-5-
methyl-rhodanine], 6S [3-(o-tolyl)-5-methyl-rhodanine].
2 4 3 0
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6

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coplanarity. The sulfur atom (S7) is larger than the oxygen (O8), so
that the S7Cl dipolar repulsion is stronger than the O8Cl repul-
sion, as evidenced by larger deviations from planarity in the case of
3S–TS′. As a consequence, 3S–TS′ has a higher rotational energy
barrier than 3S–TS, 33.42 kcal mol−1 compared to 27.13 kcal mol−1,
respectively. Owing to steric interactions between the sulfur and the
chlorine atoms, the Cl group is pushed out of the plane of the phenyl
ring. In 3S–TS, N3 donates its electrons towards S7. As a result,
N3–C2 (1.403 Å) is shorter than N3–C4 (1.461 Å) and C2–S7 is
longer than the reference value 1.600 Å (Table 2). Two ring systems,
consisting of O8–C4–N3–C1′–C2′–Cl and S7–C2–N3–C1′–C6′–H,
are formed one on either side. In 3S–TS the distance between H and
S7 is 2.459 Å, which is suitable for HS bonding15 as evidenced
from the topological analysis. The C2′–Cl distance lengthens
from 1.751 Å (3S–M) to 1.757 Å (3S–TS). In 3S–TS′, two rings,
S7–C2–N3–C1′–C2′–Cl and O8–C4–N3–C1′–C6′–H, are formed
one on either side. The positive charge on S7 increases from 0.0807
in 3S–M to 0.3019 in 3S–TS′. In 3S–TS′, the S7 electrons are
delocalized towards the C2–S7 bond which shortens from 1.642 to
1.636 Å (Table 2).
towards the thiocarbonyl group causes ring formation involving
O8–C4–N3–C1′–C6′–H to take place on the O8 side, O8 donating
its electrons to the C6′–H bond. The O8H5′ distance is 2.059 Å
and the atoms are able to form a hydrogen bond interaction.
For the 3-(o-tolyl)-5-methyl-rhodanine (6S), the minimum with
a dihedral of 82.7° (6S–M) is 0.05 kcal mol−1 less stable than the
global minimum (6S–P). Transition structures are located at di-
hedrals of 3.7° (6S–TS) and −169.5° (6S–TS′). In 6S–TS′, owing
to the bulkiness of the S and CH3 groups, these two groups repel
each other. In 6S–M the methyl groups are 3.515 Å away from each
other, whereas for 6S–P this distance is 5.330 Å.
Energetics
The relative electronic energies with zero-point corrections (E0)
and the Gibbs free energies (G0) for compounds 1S–6S are re-
ported with respect to the most stable minimum energy conformer
(Table 3). The transition structures (TS′) around 180° (substituent
Z faces S) exhibit higher energy barriers to rotation compared to the
transition structures (TS) around 0° (substituent Z faces O). H, F,
OH, CH3 substituents have smaller energy barriers to rotation than
Cl and Br due to delocalization of electrons in the transition struc-
tures for compounds 1S, 2S, 5S, 6S. This delocalization stabilizes
the transition states and decreases the energy barriers. Owing to
the size of Cl and Br, the transition structures for these substituents
are not planar and the dihedral angles between the five-membered
heterocycle and the phenyl ring are larger (ca. 10°) than those for
Z = H, F, OH and CH3 (ca. 4°).
If only the atomic size were to be taken into account, the energy
barrier to rotation would be expected to increase with the substitu-
ents in the order H, F, Cl, Br, OH, CH3. The actual order is, however,
H, OH, F, CH3, Cl and Br. In compound 6S the C5–CH3H–CH2
distance is 4.100 Å for 6S–TS, in compound 3S the C5–CH3Cl
distance is 4.885 Å, in 3S–TS and in 4S the C5–CH3Br distance
is 4.936 Å in 4S–TS. Although the destabilizing interactions are
higher in 6S–TS, the barrier is lower than expected. The order of
dipole repulsion is in agreement with the above result. The dipolar
repulsion for either OBr or OCl is higher than for OCH3.
In compound 5S (Z = OH), the H bonding observed between the
carbonyl group and the OH substituent stabilizes the transition
state. The experimentally determined rotational energy barriers for
3S and 6S are 28.47 and 27.03 kcal mol−1, respectively (Table 3).
These energy barriers are for the rotation of the Z group from the
less sterically crowded environment containing carbonyl group
(C4–O8). This refers to the TS approached from the carbonyl side.
Our calculations have shown that the free energy of activation for
these compounds is 28.80 and 27.64 kcal mol−1, in good agreement
with the experimental results. Thus B3LYP/6-31G* can be used
with confidence for the calculation of the free energy barriers in
3-(o-aryl)-5-methyl-rhodanines.
For the 3-(o-bromophenyl)-5-methyl-rhodanine, 4S, the struc-
ture corresponding to the energy minimum located at 84.0° (4S–M)
is 0.12 kcal mol−1 more stable than that at −85.8° (4S–P). The
two transition structures are located at 9.3° (4S–TS) and 164.4°
(4S–TS′). Among the substituted rhodanine compounds studied, a
bromine substituent causes the largest deviation from the planarity
in the transition-state structures, presumably because of its size. The
bond distances for 4S–M follow the same trend as those in 2S–M
and 3S–M. In 4S–TS, rings consisting of O8–C4–N3–C1′–C2′–Br
and S7–C2–N3–C1′–C6′–H are formed, with (3, −1) BCPs and
positive Laplacians of 2() for the OBr and HS non-bonded
interactions. The distances between O8Br and S7H are 2.474
and 2.839 Å, respectively. In 4S–TS′, the six-membered rings
S7–C2–N3–C1′–C2′–Br and O8–C4–N3–C1′–C6′–H are formed.
In3-(o-hydroxyphenyl)-5-methyl-rhodanine, 5S, the energy-min-
imised structure (5S–M) with a dihedral of 114.1° is 0.12 kcal mol−1
more stable than that with a dihedral of −115.1° (5S–P). In 5S–M,
the H of the OH group is tilted towards the S7 atom (C1′–C2′–O–H:
44.9°) and the O–HS distance is 2.394 Å. In both structures the
hydroxy group is directed towards the sulfur atom (S7) and away
from the C5–CH3 group (d > 4 Å). We have located another geom-
etry corresponding to a stationary local minimum structure (5S–M′)
in which the OH group is tilted towards the oxygen (O8) with the
dihedral C4–N3–C1′–C2′ = 56.8° and C1′–C2′–O–H = −47.1°.
Although 5S–M′ lies 0.40 kcal mol−1 below 5S–M on the PES,
it is 0.28 kcal mol−1 less stable on the free energy surface. In this
structure the H of the hydroxy group is stabilized by O8 (O–HO8
1.866 Å); this is confirmed by topological analysis which shows
a (3, −1) BCP with a positive Laplacian – see Table 5. In 5S–M′
the hydrogen of the hydroxy group is in relatively close proximity
to the C5–CH3 group (d = 3.729 Å and d = 3.827 Å), destabiliz-
ing this structure on the free energy surface. The transition-state
structures are located at dihedrals of −4.1° (5S–TS) and 175.9°
(5S–TS′). 5S–TS′ (19.41 kcal mol−1) is less stable than 5S–TS
(16.96 kcal mol−1). O–HO bonding in 5S–TS is more effective
than O–HS bonding in 5S–TS′,17 as shown by electron density
topological analysis. In 5S–TS, the N3–C2 and N3–C4 distances
are very similar. As rotation towards the carbonyl group occurs, the
negative charge on O8 increases from 0.0830 a.u. to 0.2298 a.u. as
a result of H-bonding. The C1′–N3 distance lengthens from 1.443
to 1.473 Å. The N3–C2 distance lengthens while N3–C4 does not
change. The distance between S7H is 2.316 Å and results in a
closed-shell atomic interaction.15 Thus a six-membered ring forms
consisting of the S7–C2–N3–C1′–C6′–H atoms. The C2′–OH dis-
tance shortens from 1.363 to 1.353 Å because the OH group donates
its electrons towards the C2′–OH bond. In 5S–TS′, the N3–C2 bond
(1.388 Å) has its shortest value. N3 donates its electrons towards
S7 and, because of stabilization by S7H–O on the C2–S7 side,
N3 donation is high and the C2–S7 bond length is at its longest
value compared to the other TS′ structures (1.664 Å). Rotation
NBO analysis
Natural bond orbital (NBO) analysis originated as a technique for
studying hybridization and covalency effects in polyatomic wave
functions, based on local block eigenvectors of the one-particle
density matrix.16a The filled NBOs are well adapted to describing
covalency effects in molecules; the antibonds represent unused
valence-shell capacity. Small occupancies of the antibonds corre-
spond to small, non-covalent corrections to the picture of localized
covalent bonds. The energy associated with the antibonds can be
numerically assessed by deleting these orbitals from the basis-
set and recalculating the total energy to determine the associated
variational energy lowering.16b In this way one obtains a decompo-
sition of the total energy into components associated with covalent
and non-covalent contributions. Hyperconjugative interactions
play a highly important role in NBO analysis. They represent the
weak departures from a strictly localized natural Lewis structure.
Energy stabilizations are examined in terms of delocalizations of
electron density from almost filled orbitals to neighboring almost
empty orbitals.16c Energy effects of delocalizations are expressed
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6
2 4 3 1

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Table 4 NBO energies (kcal mol−1) corresponding to the main interactions in compounds 1S–TS, 2S–TS, 2S–TS′, 5S–TS, 5S–TS′
1S–TS
2S–TS
2S–TS′
5S–TS
5S–TS′
lpS1→*(C2–S7)
lpS7→*(S1–C2)
lpS7→*(C2–N3)
lpO8→*(C5–C4)
lpO8→*(C4–N3)
lpN3→*(C2–S7)
lpN3→*(C1′–C2′)
lpN3→*(C4–O8)
lpC2′→*(C1′–N3)
lpC2′→*(C3′–C4′)
lpO(OH)→lp(C2′)
lpC6′→*(C1′–N3)
lpC2′→*(C4′–C5′)
lpO(OH)→lp(C6′)
34.63
10.29
3.30
19.83
30.35
61.27
23.21
42.75
32.70
10.73
13.74
20.39
35.65
56.24
27.66
19.41
31.93
10.45
15.92
20.42
31.80
47.64
26.79
27.65
33.32
10.26
14.25
20.59
22.58
—
—
—
446.05
51.85
48.3
33.06
11.11
7.00
20.59
33.54
—
—
—
487.98
50.44
60.51
as perturbations to the Fock matrix. In the present work, delocal-
izations with lone pairs as donors are considered, Table 4. In the
transition structures for the compounds of interest, the electron flow
in the thiazolidine structure is from the lone-electron pairs on S1
towards the C2–S7 antibonding orbitals, resulting in the elegation
of this bond as seen in Table 2. The repulsion of the two rings which
causes an elongation of the C1′–N3 bond is due to different factors
based on the nature of the Z substituent. In the case of compounds
1S–TS, 2S–TS and 2S–TS′ the lone pairs on nitrogen interact with
the vicinal antibonding orbitals; however, when Z = OH (5S–TS
and 5S–TS′) the elongation of the C1′–N3 bond is due to the inter-
actions of the hydroxy group with the vicinal antibonding orbitals.
The C1′–N3 bond length is 1.467, 1.447, 1.457, 1.473 and 1.475 Å
in the compounds 1S–TS, 2S–TS, 2S–TS′, 5S–TS and 5S–TS′,
respectively. The highly-pronounced delocalization of electrons
towards the *(C1′–N3) bond stabilizes 5S–TS and 5S–TS′ and
justifies the relatively low rotational barriers for compound 5S as
compared to 2S.
much shorter, associated with a higher value for the electron density
and its Laplacian.
Calculated values for the ‘hydrogen bond energy’, derived from
the properties of the (3, −1) BCP, which are predominantly electro-
static in origin,23 are shown in Table 6. As would be expected, the
HS interaction is somewhat weaker than that for HO, with
significant structural effects dependent on the substitution of the
aromatic ring.
We used both atomic basin integration and natural bond orbital
(NBO) analysis of the antibonding orbital electron occupancies to
analyse further the quantitative charge transfer involved in these
non-covalent interactions. The NBO results have been discussed
in the previous section. Atomic basin integration was carried out
using MORPHY9814 and AIM200015 software, yielding values for
the atomic charge (actually the first electrostatic moment derived
from a Buckingham-type multipole analysis rather than single-
point atomic charges), q(), the dipolar polarisation, (), and
the atomic volume, vol(). Both the atomic charge, q(), and the
atomic volume, vol(), were estimated out to the 0.001 a.u. electron
density contour. The values obtained are shown in Table 7 for the six
title compounds studied.
Electron density topological analysis
We have analysed and characterised the electron density topology
of all the transition states discussed above using Biegler-König’s
AIM2000 and Popelier’s MORPHY98 programs,14,15 as described
in the Methodology section. The electron density () and the value
of the Laplacian of (), 2(), are shown together with relevant geo-
metrical data, for both rotational transition states for each of the six
title compounds studied, in Table 5. Typical electron density maps
through the plane of the two ring systems are shown for the 3-(o-
fluorophenyl)-5-methyl-rhodanine [structures 2S–TS and 2S–TS′ –
Fig. 7(a) and (b)] and for 3-(o-hydroxyphenyl)-5-methyl-rhodanine
[structures 5S–TS and 5S–TS′ - Fig. 7(c) and (d)]. Electron density
contour plots are shown with contours plotted at 0.001, 0.002,
0.004, 0.080, 0.020… atomic units (a.u.). Molecular graphs for the
3-(o-fluorophenyl)- and 3-(o-hydroxyphenyl)-5-methyl-rhodanine
transition states are shown in Fig. 8(a–d).
The non-bonded closed-shell interactions can be separated into
two distinct categories. The first consists of a classical hydrogen
bond between the activated ortho-hydrogen on the aromatic ring
and either the sulfur or oxygen substituent on the five-membered
thiazolidine ring. The values for the electron density and its Lapla-
cian at the (3, −1) bond critical point (BCP), together with the geo-
metrical parameters d and , indicate moderately strong hydrogen
bonding comparable to that observed for the water dimer, for 1:1
water–ethanediol complexes or hydrated glucopyranose.22
Charges derived by AIM theory atomic basin integration have
been shown to be amongst the most accurate and to be preferred
over other methods.22,24 Mulliken charges are not as useful and are
markedly dependent on the basis-set but less so on the correla-
tion functional used, with 6-31+G(d) giving higher charges than
6-311+G(2d,p). Charges derived from atomic basin integration are
more stable, showing variations in the third or fourth significant
figure for the different levels of theory.22 Guerra et al.25 have pointed
out recently that both the AIM and NPA electron density partition-
ing schemes seem to yield unrealistically large atomic charges,
especially for oxygen, implying a greater ionic character than is
‘chemically reasonable’, in comparison to the Hirshfeld or Vor-
onoi deformation density procedures, which these authors prefer.
Nonetheless, charges derived from the use of the AIM partitioning
scheme can be recommended for comparative purposes, as in the
present case, where changes in charge distribution, i.e. charge trans-
fer, rather than absolute values are important. Values for the two
starting structures in each case are shown as an average since these
were found to be substantially conformer-independent, with differ-
ences being observed only in the fourth or fifth significant figure.
A comparison of the 3-(o-fluorophenyl)-, 3-(o-chlorophenyl)-
and 3-(o-bromophenyl)-5-methyl-rhodanine transition state
structures for compounds 2S, 3S, 4S is instructive. The dipolar
polarisation, (), of the sulfur and oxygen atoms attached to
the thiazolidine ring is markedly greater in either TS or TS′ as
compared to the reference values, 0.8902 ± 0.0225 and 0.4573 ±
0.0053 a.u., respectively. The dipolar polarisation for the oxygen
atom increases when it interacts with the halogen rather than
with the aromatic ortho-hydrogen atom by +0.0516 a.u. (F);
+0.0276 a.u. (Cl); and +0.0221 a.u. (Br). This is also true for the
sulfur atom: +0.0204 a.u. (F); +0.0137 a.u. (Cl); +0.0076 a.u.
(Br). The aromatic ortho-hydrogen, on the other hand, shows
The second type of non-bonded interaction is characterised by
a BCP of (3, −1) topology and a positive value for its Laplacian,
occurring between the o-aryl substituent, i.e. H, F, Cl, Br, OH or
CH3, and either the sulfur or oxygen atom on the thiazolidine ring,
depending on the transition state. These interactions show similar
values of electron density, (), and its Laplacian, 2(), to the HO
or HS interactions, with the exception of the 3-(o-hydroxyphenyl)
compound, in which the OH–O or SH–O separation distance is
2 4 3 2
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6

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Fig. 7 Electron density contour maps through the plane of the rings for the transition states TS and TS′ for 3-(o-fluorophenyl)-5-methyl-rhodanine (2S) [(a)
and (b)], and for 3-(o-hydroxyphenyl)-5-methyl-rhodanine (5S) [(c) and (d)]. Electron denisty contours are shown at 0.001, 0.002, 0.004, 0.008, 0.020,
0.040… a.u. Atoms are colour coded (carbon, hydrogen = black; oxygen = red; nitrogen = blue; halogens = green or brown).
a reduction in dipolar polarisation compared to the reference
value of 0.1413 ± 0.0007 a.u. when it interacts with oxygen or
sulfur, corresponding to observations in other hydrogen-bonded
systems.21 The difference in ortho-hydrogen dipole polarisation
between HO and HS is influenced by the o-halogen substitu-
ent, i.e. +0.0128 a.u. (F); +0.0086 a.u. (Cl); and +0.0065 a.u. (Br).
Upon interaction, oxygen becomes more negatively charged and
sulfur more positively charged compared to the reference values
of −1.1263 ± 0.0035 and +0.0787 ± 0.0041 a.u., respectively, the
larger numerical values being associated with interaction with the
o-halogen in the order F > Cl > Br. The other feature highlighted by
the data in Table 7 is that the atomic volume decreases sharply upon
non-covalent interaction and this is reflected in marked increases
in the average nuclear charge density [data not shown but equal to
q()/vol()].
The o-hydroxyphenyl-derivative is characterised by a TS with
a short, strong, hydrogen bond between the OH hydrogen and
the rhodanine oxygen atom, with values for the electron density,
(), and its Laplacian, 2(), at the bond critical point of 0.0563
and +0.1956 a.u., respectively, and an O–HO distance of 1.61 Å
(see Table 5). The OH hydrogen atom in 5S–TS has increased posi-
tive charge (0.0351 a.u.) and a considerably reduced dipolar polari-
sation (−0.0313 a.u.), together with a marked diminution in atomic
volume, all of which are typical for the *+…*− charge transfer seen
in strong hydrogen bonding.22 In 5S–TS′, in which the OH group is
hydrogen bonded to the sulfur atom, these effects are qualitatively
similar but smaller in magnitude.
Conclusions
Our results demonstrate very clearly that the quasi-planar transi-
tion structures for the rotational equilibrium around the C–N bond
joining the two ring systems in the o-aryl-substituted 5-methyl-
rhodanines studied, are stabilized by non-bonded, closed-shell
interactions between the o-substituent, Z = H, F, Cl, Br, OH and
CH3, and the o-hydrogen atom with the pendant S and O atoms of
the rhodanine ring; these interactions are characterised by (3, −1)
BCPs and positive values for Laplacian of the electron density at
the critical point, thus satisfying Bader’s criteria for the closed-
shell type.21 It is interesting to note that, in the much simpler un-
substituted biphenyl system, a transition state also exists in which
the two rings are coplanar and stabilized by HH non-bonded
interactions which are of the closed-shell variety with a (3, −1)
BCP and a positive value for the Laplacian of the electron density
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6
2 4 3 3

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Fig. 8 Molecular graphs for the same structures as in Fig. 7(a–d). BCPs are shown as small red dots and RCPs as yellow dots.
at the critical point [ = 0.0155 a.u.; (), 2() = +0.0607 a.u.].
The energy difference between the coplanar transition state and
the global energy minimum in which the two benzene rings are
orthogonal to one another is approximately 2.5–3.0 kcal mol−1
(R. A. Klein, unpublished data). Although surprising at first glance,
hydrogen–hydrogen interactions, which appear to stabilize the
coplanar biphenyl transition state, have been described as the ‘di-
hydrogen bond’ in other systems.26
Detailed analysis of these non-bonded, closed-shell interactions
using atomic basin integration techniques together with NBO
analysis, has provided insights into the nature of these interac-
tions and the role of charge transfer. Of particular interest are the
interactions between sulfur and oxygen with the halogens, fluorine,
chlorine and bromine, as discussed in the previous section. There
is both experimental and theoretical evidence in the literature for
oxygen–oxygen non-bonded closed-shell interactions in inter-
and intra-molecular complexes.27,28 Evidence is also available for
similar fluorine–fluorine interactions.29
Although the presence of a (3,−1) bond critical point (BCP) and an
inter-atomic bond path in a structure at its electrostatic equilibrium
goemetry has been considered30 to be proof of a bonding inter-
action, it seems implausible chemically to classify the closed-shell
interactions described above as bonding in the classical sense. Rather
they are quantum-mechanical interactions between the electron dis-
tributions of the atoms involved which possess topological proper-
ties shared by classically bonded systems but are of the closed-shell
type with a positive Laplacian of the electron density (), 2(), at
the BCP and interaction energies at least an order of magnitude
smaller than for a ‘normal’ covalent bond. It is these interactions
that stabilize the rotational transition states studied in this paper.
Calculation of the height of the barriers to rotation using B3LYP/
6-31G* gives results which are in remarkably good agreement with
those obtained experimentally using NMR spectroscopy, supporting
the use of computationally efficient DFT methods for problems of
this type.
2 B. C. C. Contello, D. S. Eggleston, D. Haigh, R. C. Haltiwanger, C. M.
Heath, R. M. Hindley, K. R. Jennings, J. T. Sime and S. R.Woroneicki,
J. Chem. Soc. Perkin Trans. 1, 1994, 3319–3324.
3 Internal Rotation in Molecules, W. J. Orville-Thomas, ed., John Wiley
and Sons, New York, 1974, pp. 1–7.
4 R. S. Cahn, C. K. Ingold and V. Prelog, Angew. Chem., Int. Ed., 1966, 5,
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2 4 3 4
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6

View Article Online
Table 6 Electrostatic interaction energies (kcal mol−1) calculated from the
properties of the (3, −1) bond critical point (BCP) as described in the text
Compound
HS
HO
OZ
SZ
1S
2S
3S
4S
5S
6S
−5.97
−4.37
−4.10
−3.98
−5.81
−4.61
−7.60
−5.98
−4.89
−4.70
−6.24
−5.34
—
—
−6.76
−4.87
−4.47
−16.84
−4.66
−5.92
−3.89
−3.55
−11.98
−3.17
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
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6
2 4 3 5

View Article Online
Table 7 Atomic basin integration for the interacting atoms in the compounds studied: atomic charge, q(); dipole polarisation, (); and atomic volume,
vol(), are given, in atomic units
S
O
H
Z
1S–TS (1S–TS′)
q()
()
vol()
1S–M
q()
0.2192
1.1712
219.29
−1.1714
0.5761
118.38
0.1086
0.1291
35.70
0.1193
0.1216
34.73
0.0737
0.8986
233.58
−1.1293
0.4540
133.09
0.0700
0.1425
47.07
0.0701
0.1425
47.58
()
vol()
2S–TS
q()
0.2216
1.1693
221.85
−1.1319
0.6420
117.76
0.1006
0.1395
37.47
−0.6404
0.3274
92.61
()
vol()
2S–TS′
q()
0.3070
1.1897
214.15
−1.1654
0.5904
118.29
0.0938
0.1267
36.76
−0.6559
0.3192
94.43
()
vol()
2S–M
q()
0.0772
0.8980
232.51
−1.1248
0.4562
131.37
0.0805
0.1409
46.67
−0.6493
0.2717
107.73
()
vol()
3S–TS
q()
0.2282
1.1718
222.15
−1.1424
0.6308
117.37
0.0874
0.1398
38.00
−0.1793
0.1891
198.42
()
vol()
3S–TS′
q()
0.3019
0.8999
214.84
−1.1592
0.6032
118.96
0.0719
0.1312
38.46
−0.1808
0.1777
199.01
()
vol()
3S–M
q()
0.0807
0.8999
233.35
−1.1275
0.4573
132.45
0.0786
0.1409
46.61
−0.1818
0.1735
214.57
()
vol()
4S–TS
q()
0.2298
1.1726
222.17
−1.1471
0.6265
117.34
0.0850
0.1388
38.25
−0.0383
0.3555
241.83
()
vol()
4S–TS′
q()
0.3000
1.1802
213.90
−1.1591
0.6044
119.13
0.0673
0.1323
38.83
−0.0377
0.3469
242.09
()
vol()
4S–M
q()
0.0830
0.9018
233.13
−1.1290
0.4579
133.24
0.0797
0.1407
46.56
−0.0410
0.3847
254.07
()
vol()
5S–TS
q()
0.2505
1.1740
218.48
−1.1749
0.5479
114.00
0.0950
0.1307
35.95
0.6173
0.1172
11.85
()
vol()
5S–TS′
q()
0.1792
1.1105
215.30
−1.1543
0.6062
117.89
0.0831
0.1252
36.67
0.5653
0.1382
14.52
()
vol()
5S–M
q()
0.0231
0.8443
225.78
−1.1208
0.4668
130.22
0.0695
0.1416
46.34
0.5822
0.1485
17.91
()
vol()
6S–TS
q()
0.2235
1.1743
221.78
−1.1585
0.6068
116.25
0.0834
0.1372
37.58
0.0642a
0.1356a
41.12a
()
vol()
6S–TS′
q()
0.2456
1.1737
215.57
−1.1591
0.6059
120.05
0.0696
0.1301
39.15
0.0551a
0.1452a
42.63a
()
vol()
6S–M
q()
()
vol()
0.0705
0.8983
233.62
−1.1319
0.4513
132.87
0.0672
0.1434
47.49
0.0437b
0.1502b
48.28b
a Hydrogen-bonded CH3 hydrogen. bAverage for all non-bonded CH3 hydrogens.
2 4 3 6
O r g . B i o m o l . C h e m . , 2 0 0 4 , 2 , 2 4 2 6 – 2 4 3 6