VALISA: A new procedure for total lineshape analysis of NMR spectra. Conformational analysis of trans-1,2-dibromocyclopentane

Article abstract of DOI:10.1023/A:1020948412771

A new strategy of total lineshape analysis of the multiplet structure of NMR spectra was proposed and a VALISA program was developed to implement the computational procedure. Evaluation of the new technique taking a solution of several test problems and the complete analysis of the ¹H NMR spectrum of trans-1,2-dibromocyclopentane as examples showed its high efficiency. Using a complete set of vicinal spin-spin coupling constants, detailed conformational analysis of this molecule was carried out and a more correct model for the description of conformational interconversions of the five-membered cycles was proposed. Conformational behavior of trans-1,2-dibromocyclopentane molecule can be reasonably described assuming large-amplitude molecular vibrations along a sector of the pseudorotation path, containing mostly diequatorial conformations.

Full text of DOI:10.1023/A:1020948412771

1222
Russian Chemical Bulletin, International Edition, Vol. 51, No. 7, pp. 1222—1230, July, 2002
Physical Chemistry
VALISA: a new procedure for total lineshape analysis of NMR spectra.
Conformational analysis of transꢀ1,2ꢀdibromocyclopentane
ꢀ
S. V. Zubkov, S. S. Golotvin, and V. A. Chertkov
Department of Chemistry, Lomonosov Moscow State University,
Leninskie Gory, Moscow 119899, Russian Federation.
Fax: +7 (095) 932 8846. Eꢀmail: chertkov@org.chem.msu.su
A new strategy of total lineshape analysis of the multiplet structure of NMR spectra was
proposed and a VALISA program was developed to implement the computational procedure.
Evaluation of the new technique taking a solution of several test problems and the complete
1
analysis of the H NMR spectrum of transꢀ1,2ꢀdibromocyclopentane as examples showed its
high efficiency. Using a complete set of vicinal spinꢀspin coupling constants, detailed conforꢀ
mational analysis of this molecule was carried out and a more correct model for the description
of conformational interconversions of the fiveꢀmembered cycles was proposed. Conformaꢀ
tional behavior of transꢀ1,2ꢀdibromocyclopentane molecule can be reasonably described asꢀ
suming largeꢀamplitude molecular vibrations along a sector of the pseudorotation path, conꢀ
taining mostly diequatorial conformations.
Key words: analysis of highꢀresolution NMR spectra, total lineshape analysis, conformaꢀ
tional analysis of cyclopentanes, pseudorotation.
Recently, some new techniques for automated extracꢀ
and spinꢀspin coupling constants from experimental specꢀ
tra3). Exact solution of this problem requires the use of
iterative procedures with stepꢀbyꢀstep control, which inꢀ
cludes calculations of the theoretical spectrum (using the
current set of spectral parameters), its comparison with
the experimental spectrum, and the corresponding changes
in the set of parameters based on the results of comꢀ
parison.
In the case of NMR spectroscopy, such iterative proceꢀ
dures can be implemented using two principal approaches,
namely, the approach by Castellano and BothnerꢀBy4
and the total lineshape analysis.5 The fundamental differꢀ
tion of information from complex NMR spectra have
been proposed (see Ref. 1). They are based on the use of
multipulse sequences and multidimensional Fourier transꢀ
form. However, most of these methods are efficient only
when analyzing the firstꢀorder nuclear spin systems (for
the definition of this concept, see Ref. 2). Nevertheless,
higherꢀorder effects can manifest themselves even when
using NMR spectrometers with high and ultrahigh magꢀ
netic fields and studying relatively small molecules. Interꢀ
preting such spectra is a classical example of the inverse
spectral problem (determination of the chemical shifts
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1129—1136, July, 2002.
1066ꢀ5285/02/5107ꢀ1222 $27.00 © 2002 Plenum Publishing Corporation

Highꢀresolution NMR lineshape analysis
Russ.Chem.Bull., Int.Ed., Vol. 51, No. 7, July, 2002
1223
ence between them concerns the method of processing
the spectral data and comparing the calculated and exꢀ
perimental spectra. The method proposed by Castellano
and BothnerꢀBy includes separation of the frequencies, fi,
of all observed transitions from the experimental specꢀ
trum and their assignment to theoretical transitions ψi
(assignment stage). In the course of the iterative proceꢀ
dure the parameters of this method are changed in such a
way that the residual functional be minimum
long time. In particular, convergence is complicated by
noise, impurity signals, and by distortions of the base line,
phase, and some other lineshape parameters. In addition,
2
the hypersurface of the χ functional of a typical NMR
spectrum exhibits numerous narrow and deep local
minima, which strongly hampers the search for a global
minimum.
In this case, the convergence problem appears to be
the most important, since the procedure for total lineshape
analysis requires the choice of a highly accurate initial
approximation (in other words, one should a priori know
the desired values of the spectral parameters to be found).
Stephenson and Binsch5 proposed a satisfactory method
of attacking this problem and practically implemented it
in two programs, DAVINS5 and DAISY.11a They emꢀ
ployed a free matrix transformation of the total spectral
contour represented as a vector, which smoothes the hyꢀ
persurface of the functional to be minimized in such a
manner that ideally we get only one, global, minimum
(strictly speaking, it can differ from true minimum). If the
iterative procedure finds this minimum, the transformaꢀ
tion is repeated using the matrix with reduced offꢀdiagoꢀ
nal elements and smaller smoothing factor, so that the
new global minimum is slightly shifted from the precedꢀ
ing one. Iterations are repeated until a unity transformaꢀ
tion matrix is obtained and the global minimum of the
transformed functional matches the true minimum. One
sequence of the iterative cycles is called a grand cycle.5
Such a roundabout procedure, which is methodologiꢀ
cally similar to the use of integral transforms, does allow
one to find a solution for a large number of spectra irreꢀ
spective of the choice of the initial approximation for the
–
2
χ
LAOCOON (p) =
,
(1)
–
where N is the number of the allowed transitions and p is
the vector of parameters which includes the chemical
shifts, νi, and the spinꢀspin coupling constants, Jij.
This approach is applicable to the vast majority of
relatively well resolved NMR spectra with a simple mulꢀ
tiplet structure. Indeed, the procedures based on the clasꢀ
sical LAOCOON program4 are successfully used at preꢀ
sent, since they are known to be reliable and provide fast
convergence. However, this technique has some drawꢀ
backs. First, the assignment of the frequencies to particuꢀ
lar theoretical transitions is too laborꢀconsuming and reꢀ
quires skills in the art. Recently,6 considerable advances
have been made in solving this problem using a pattern
recognition formalism. Second, deconvolution results in
a small set of numerical data. When using functional (1),
a considerable body of information is lost prior to starting
the iterative process. This concerns, in particular, the
crossꢀcorrelations of the estimates of the frequencies and
amplitudes of the spectral components obtained after
deconvolution (offꢀdiagonal elements of the covariation
matrix). Our experience suggests that these values are of
great importance for correct description of poorly resolved
multiplets. This loss can to some extent be compensated
by using different weighting factors for different spectral
lines or, generally, using the integral transforms.7—10
Though this approach extends the capabilities of analysis,
the fact that some parameters have no physical meaning
hampers statistical estimation of the results obtained.
The second classical approach called the total lineꢀ
shape analysis is a priori free from all drawbacks inherent
in the aboveꢀmentioned methods. The experimental and
theoretical spectrum are compared using the entire freꢀ
quency range and the residual functional has the form
–
vector p. Nevertheless, the choice of the matrix elements
involved in the transformation remains a nontrivial probꢀ
lem. In addition, execution of the sequence of iterative
cycles is still too laborꢀconsuming for most applications
and provides no possibility of visual control of the conꢀ
vergence process. These reasons seem to be responsible
for little use of the algorithm by Stephenson and Binsch.
We developed and evaluated a new procedure for solvꢀ
ing the convergence problem in the total lineshape analyꢀ
sis of highꢀresolution NMR spectra. The technique uses a
convolution with a Lorentzian line of prescribed width as
the smoothing transformation. In essence, this is a stanꢀ
dard procedure leading to uniform broadening of all specꢀ
tral lines, which is often used in NMR spectroscopy for
improving the signalꢀtoꢀnoise ratio (see Ref. 1). At a sufꢀ
ficiently large broadening, one can always get a spectrum
with one or several flattened maxima that will correspond
to minima of the χ2 functional. Variation of the line broadꢀ
ening has no effect on the position of minimum, and
theoretically (in the absence of noise) one could find a
correct solution at this step. However, the global miniꢀ
mum can be so flat that the numerical algorithms stop
before reaching it. Then, a new iterative cycle is perꢀ
–
2
χ
lineshape (p) =
,
(2)
–
where the vector of parameters, p , also includes the
lineshape parameters (halfwidth L and the amplitude scale
factor S). In this case, no line assignment is required and
the spectrum can be processed in fully automated mode.
Of course, there have also been a number of problems,
which hindered the extension of this approach for a rather

1224
Russ.Chem.Bull., Int.Ed., Vol. 51, No. 7, July, 2002
Zubkov et al.
Calculations using the VALISA program were carried out on
formed with a less broadened spectrum (and less flattened
global minimum of the χ2 functional) and so forth until
the initial nonꢀbroadened spectrum is considered. This
approach seems to be more attractive, since it uses a transꢀ
formation with clearer physical meaning, which allows
visual control of the convergence process, wellꢀsubstantiꢀ
ated choice of the parameters to be varied, and estimation
of adequacy of the solution thus obtained. Evaluation
revealed improved convergence and performance of the
new procedure (often, obtaining a correct solution reꢀ
quires execution of a small number of the grand cycles).
A representative example of problems that need exact
total lineshape analysis of NMR spectra is the conformaꢀ
tional analysis of cyclic hydrocarbons (in particular, fiveꢀ
membered cycles). Modern formalism of conformational
analysis of these compounds is based on the study by
Cremer and Pople12 who proposed a concept of pseudoꢀ
rotation. NMR spectroscopy provides a unique possibility
of experimental determination of the molecular geometry
in solutions. Valuable information can be extracted from


a PC with a Pentium MMX CPU operated at a frequency of
250 MHz. Typical computing time of one grand cycle was ∼0.8 s
for pyridine (spin system AA´BB´C, 3000 points in the specꢀ
trum, and 11 varied parameters) and ∼5 min for dibromoꢀ
cyclopentane (spin system AA´BB´CC´DD´, 20000 points in
the spectrum, and 22 varied parameters).
Theoretical spinꢀspin coupling constants were calculated
using Eq. (3) and a homeꢀmade Newkarpl program. The geomꢀ
etries and energies of the theoretically possible conformations of
transꢀ1,2ꢀdibromocyclopentane molecule were calculated using
the Gaussian 94W 17 program suite.
Results and Discussion
Program complex VALISA. Using the aboveꢀmenꢀ
tioned new strategy of total lineshape analysis, we develꢀ
oped a VALISA (VAriable LIne Shape Analysis) program
complex. The array of input data includes the digitized
unbroadened spectrum, description of the spin system
(number of spins, information on the chemical and magꢀ
netic equivalence of the nuclei, initial approximation for
the chemical shifts and spinꢀspin coupling constants),
description of strategy (sequence of line broadenings and
parameters to be varied), and some additional parameters
(in particular, convergence control parameters, the maxiꢀ
mum number of iterations, the operating frequency of the
spectrometer, etc.). Following the prescribed strategy, the
VALISA program convolves the spectrum with the referꢀ
ence line of a given width and executes a search for a
3
the JH,H vicinal constants, which are related to the
H—C—C—H torsion angles (ϕ) by relationships similar
to the Karplus equation.13 Therefore, measurements of
the spinꢀspin coupling constants allows determination of
the averaged conformational state of a particular molꢀ
ecule. In this case, completeness of spectral analysis is of
crucial importance, since each new coupling constant
allows one to consider a larger number of conformations.
By analogy with cyclohexane derivatives, most of earlier
studies used a simplified twoꢀconformation model for
analysis of the fiveꢀmembered cycles (see, e.g., Refs. 14
and 15). With an efficient method of processing the NMR
spectra in hand we performed conformational analysis of
the transꢀ1,2ꢀdibromocyclopentane molecule taking into
account all significant conformations according to the
model by Cremer and Pople12 and compared our results
with those obtained using the simplest twoꢀconformation
approach.
2
minimum of the χ functional.
In each grand cycle, the minimization procedure uses
the Levenberg—Marquardt modification of the Newꢀ
ton—Raphson gradient method, which acts under condiꢀ
tions of strongly correlated spectral parameters. Earlier,
this method has proved itself in the analysis of NMR
spectra. It is employed both in the classical total lineshape
analysis program NMRCON18 and modern program comꢀ
plex PERCHit19 developed for spectral analysis using the
integral transforms. In addition, the damping parameter
controlling the correlation elimination mechanism is reꢀ
duced in each iteration step within the same grand cycle
following the procedure developed for the NMRCON
program. If the next step leads to an increase in the χ2
value, the program uses a procedure for linear search for a
minimum by the golden section along the direction of the
gradient.20
After finding the best approximation to the minimum
at a given line broadening the width of the reference line
is changed, the initial spectrum is convoluted with the
new reference line, and the iterative procedure is exꢀ
ecuted again.
Convergence problem. Stephenson and Binsch proꢀ
posed a number of tests for evaluating the efficiency of the
total lineshape analysis algorithms.21 In particular, the
program should find correct values of the chemical shifts
Experimental
1
H NMR spectra of degassed 2 M solutions of transꢀ1,2ꢀdiꢀ
bromocyclopentane in C6D6, CD3CN, and CCl4 were recorded
on a Varian VXRꢀ400 spectrometer (operating frequency is
1
400 MHz for H nuclei) at 303 K. Slight experimental distorꢀ
tions of the base line were eliminated using a previously develꢀ
oped algorithm.16 The model 1H NMR spectrum of pyridine
was calculated for a Lorentzian line with a halfwidth of 0.32 Hz.
The level of white noise added was 2.5%, 10%, and 40% of the
peak amplitude of the most intense signal. The digital resolution
was 0.04 Hz per point.
transꢀ1,2ꢀDibromocyclopentane was synthesized by bromiꢀ
nation of cyclopentene in CCl4 solution in the cold. After addiꢀ
tion of a necessary amount of bromine the solvent was removed
and the product was distilled. The yield was 66.5%, b.p.
95—97 °C (35 Torr) (cf. Ref. 11b: b.p. 74 °C (17 Torr)).

Highꢀresolution NMR lineshape analysis
Russ.Chem.Bull., Int.Ed., Vol. 51, No. 7, July, 2002
1225
Table 1. Chemical shifts (∆ν/Hz) and spinꢀspin coupling constants (J/Hz) of the test systems of the ABCD type
Number of test
system
∆ν
∆ν
∆ν
∆ν
J1,2
J1,3
J1,4
J2,3
J2,4
J3,4
1
2
3
4
1
2
3
4
12
22
22
33
6
8
3
4
2
4
11
3
11
7
2
1
4
7
5
6
7
3
3
7
6
2
2
27
37
20
21
11
22
15
28
27
20
10
35
9
and spinꢀspin coupling constants in four different, strongly
coupled ABCD systems (see Fig. 1 and the parameters in
Table 1) by sequentially using the parameters of each of
the other three test systems as initial approximation. As
can be seen in the typical plot of changes in the spectral
parameters (Fig. 2), our algorithm finds the global miniꢀ
mum in the stage where the linewidth becomes compaꢀ
rable with the smallest spinꢀspin coupling constants. Unꢀ
til then the changes in small coupling constants have little
effect on the functional (2), so they can vary over a rather
wide range. Indeed, the spinꢀspin coupling constants vary
nearly randomly at a broadening of 10 Hz (see Fig. 2).
The results obtained using the VALISA program are
listed in Table 2. The figures in this Table represent the
numbers of the grand cycles required to find the correct
solution. As can be seen in Table 2, the VALISA system
solved all the twelve tests, eight of them being solved after
execution of one grand cycle. For comparison, the proceꢀ
dure by Stephenson and Binsch20 solved a total of ten
tests and only three of them required one grand cycle. We
believe that combining the new approach proposed in this
work and modern optimization methods allows one to
exclude this class of problems from the "hardꢀtoꢀsolve"
category.
0
10
20
30
40
ν/Hz
Fig. 1. NMR spectra of test systems of the ABCD type in the
spectral region from 0 to 50 Hz.
Stability problem. To evaluate the solution stability in
the presence of typical disturbing factors, we chose a
strongly coupled, fiveꢀspin AA´BB´C system, which corꢀ
responded to the 1H NMR spectrum of pyridine. This is a
wellꢀknown test developed for the LAOCOON program.4
It was also used in evaluating the efficiency of the
∆ν, J/Hz
1
35
30
25
2
3
Table 2. Number of the grand cycles necessary for execution of
the tests taken from Ref. 21 by the VALISA (I, this work) and
DAVINS programs (II, see Ref. 21)
4
20
15
10
5
5
Number of target
test
Number of initial
test system
6
7
8
system
I
II
9
10
0
1
2
3
4
1
2
3
4
50
100
150
Iteration step
1
2
3
4
*
2
1
1
1
*
1
1
2
3
*
1
1
2
1
*
*
2
1
2
—
*
2
2
2
*
1
1
2
*
Fig. 2. Variations of parameters in different stages of solution of
the test system 4 using the parameters of the test system 2 taken
as initial approximation: ∆ν (1), ∆ν (2), ∆ν (3), ∆ν (4), J1,3 (5),
4
3
2
1
4
—
J2,3 (6), J1,2 (7), J2,4 (8), J3,4 = J1,4 (9), and L (10).

1226
Russ.Chem.Bull., Int.Ed., Vol. 51, No. 7, July, 2002
Zubkov et al.
1
Conformational analysis of cyclopentane derivatives. In
the case of cyclic hydrocarbons typical H NMR spectra
1
410
430
450
470
490
∆ν/Hz
exhibit strongly overlapped complex multiplets while obꢀ
taining information on the torsion angles requires knowlꢀ
edge of exact values of as many vicinal spinꢀspin coupling
2
1
constants as possible. For instance, the H NMR specꢀ
trum of transꢀ1,2ꢀdibromocyclopentane (Fig. 4) exhibits
a total of nearly 300 discernible lines grouped into four
multiplets from the H(1) and H(2), H(3) and H(4), H(5)
and H(6), and H(7) and H(8) protons (Fig. 4). Using the
total lineshape analysis procedure with the threeꢀstep adꢀ
ditional broadening of 0.5, 0.2, and 0.1 Hz, we obtained
the estimates of all conceivable chemical shifts and proꢀ
ton—proton spinꢀspin coupling constants for this comꢀ
pound. We compared these values with the vicinal spinꢀ
spin coupling constants corresponding to theoretically
possible conformations and calculated from the torsion
angles (ψ) using the generalized Karplus equation
1
Fig. 3. H NMR spectrum of pyridine with the highest noise
level (1) and solution obtained by the VALISA program (2).
PAREMUS program complex.6 In the case of the VALISA
program white noise was added to the spectrum under
study, while the initial approximation was the same as
that used in Ref. 4. The level of white noise added was
2.5, 10, and 40% of the amplitude of the most intense
signal. The halfwidth of each spectral line was 0.36 Hz
and an additional line broadening of 3, 1, and 0.5 Hz was
used during the iterative process. The results obtained are
presented in Table 3. As can be seen in Fig. 3, even at very
high level of noise in the spectrum the iterative process
overcomes numerous noiseꢀinduced local minima and
finds a rather correct solution. This is possible owing to
substantial improvement of the effective signalꢀtoꢀnoise
ratio in the intermediate (broadened) spectra at the cost
of a loss of resolution. In fact, the broadening procedure
used by the program complex VALISA represents a comꢀ
monly accepted noise reduction technique that is used in
routine NMR spectroscopy in those cases when a small
additional broadening of spectral components causes no
loss of information on the multiplicity of the system unꢀ
der study.
3
JH,H = P1cos2ψ + P2cosψ + P3 +
+ Σ∆χ {P4 + P5cos2(ξ ψ + |∆χ |)},
(3)
i
i
i
where ∆χi is the electronegativity difference between the
substituent (bromine) and hydrogen, ξi is the sign correꢀ
sponding to the relative orientation of the substituent,
and Pi (i = 1, 2, ..., 5) are the empirical constants depenꢀ
dent on the number of nonꢀproton substituents.23
The molecule of a substituted cyclopentane can adopt
a total of twenty classical conformations (Fig. 5) that can
undergo interconversions during pseudorotation.12 In the
case of unsubstituted cyclopentane they correspond to
two symmetrical conformations, namely, the twist and
1
Table 3. Spectral parameters (∆ν, J/Hz) used as initial approximation and the results of analysis of simulated H NMR
spectrum of pyridine
Parameters
Initial
values
S/N
True
values
0.025
0.1
0.4
∆ν = ∆ν
516.0
427.0
450.0
5.0
2.0
1.0
–0.1
8.0
1.5
516.5055(4)
427.4345(5)
450.1466(9)
4.9507(6)
1.82422(7)
1.0193(7)
–0.0418(4)
7.6277(9)
1.4680(2)
516.506(2)
427.433(2)
450.153(4)
4.948(3)
1.825(3)
1.017(3)
–0.04(2)
7.631(4)
516.499(5)
427.429(7)
450.12(1)
4.960(9)
1.83(1)
1.02(1)
–0.04(5)
7.63(1)
516.506
427.435
450.148
4.950
1.824
1.019
–0.043
7.627
1.466
1
5
4
∆ν = ∆ν
2
∆ν
3
J1,2 = J4,5
J1,3 = J3,5
J1,4 = J2,5
J1,5
J2,3 = J3,4
J2,4
1.466(7)
1.49(2)

Highꢀresolution NMR lineshape analysis
Russ.Chem.Bull., Int.Ed., Vol. 51, No. 7, July, 2002
1227
4.250
2.375
2.250
2.125
2.000
1.875
1.750
1.625
δ
Fig. 4. 1H NMR spectrum of 2 M solution of transꢀ1,2ꢀdibromocyclopentane in CD3CN.
envelope conformations with C2 and CS symmetry, reꢀ
spectively. We performed conformational analysis of the
transꢀ1,2ꢀdibromocyclopentane molecule. Symmetry
considerations allowed reduction of the number of differꢀ
ent molecular conformations down to eleven. These
1
are five envelope conformations, namely, E(ϕ = 72),
4
2
E5(ϕ = 36), E(ϕ = 0), E3(ϕ = 324), E(ϕ = 288) and six
1
1
twist conformations, namely, T2(ϕ = 90), T5(ϕ = 54),
Fig. 5. Canonical conformations of disubstituted cyclopentanes. Figures inside the circle denote the phase angles of pseudorotation.

1228
Russ.Chem.Bull., Int.Ed., Vol. 51, No. 7, July, 2002
Zubkov et al.
E/kcal mol–1
3
2
1
3
2
0
60
120
180
240
300 ϕ/deg
Fig. 6. Pseudorotation potential of transꢀ1,2ꢀdibromocycloꢀ
pentane molecule.
4T5(ϕ = 18), T3(ϕ = 342), T3(ϕ = 306), T1(ϕ = 270),
where ϕ is the phase angle of pseudorotation. The fact
that the number of different molecular conformations is
less than that of the vicinal spinꢀspin coupling constants
(a total of 13) allowed simultaneous consideration of all
theoretical conformations, thus excluding the determinaꢀ
tion of the more or less significant conformations. The
geometry of each conformation was optimized by the ab
initio HF/6ꢀ31G* method. The pseudorotation potential
of transꢀ1,2ꢀdibromocyclopentane molecule presented in
Fig. 6 is a smooth curve with two broad minima correꢀ
sponding to the classical twist conformations.
The parameters of the 1H NMR spectrum of dibromoꢀ
cyclopentane recorded in a C6D6 solution22 and refined
using the PAREMUS program6 (Table 4) were chosen as
initial approximation. Most of the spinꢀspin coupling conꢀ
stants calculated by the VALISA program were found to
be rather close to those obtained using the PAREMUS
4
2
2
1
4.263
4.262 4.261 4.260 4.259
δ
Fig. 7. The same region of the 1H NMR spectrum of transꢀ1,2ꢀdiꢀ
bromocyclopentane: experimental (1), calculated using the
PAREMUS program (2), and calculated using the VALISA proꢀ
gram (3).
program; however, the values of four spinꢀspin couꢀ
pling constants changed by ∼0.2 Hz and one of them
(JH(3),H(6) = JH(4),H(5)) changed its sign. Detailed analysis
of the spectra showed that the new total lineshape analysis
program corrected some discrepancies between the exꢀ
perimental and theoretical spectra, which are clearly seen
only in the region of combinatorial lines of low intensity
at δ 4.258—4.263 (Fig. 7). Then, the PAREMUS proꢀ
gram and the corrected set of parameters were used to
Table 4. Chemical shifts (δ) and spinꢀspin coupling constants (Ji,j) of transꢀ1,2ꢀdibromocyclopentane in C6D6 obtained from
calculations using the PAREMUS (P) and VALISA (V ) programs
Atom
δ
Program
Ji,j/Hz
H(1)
.—
H(2)
H(3)
H(4)
H(5)
H(6)
H(7)
H(1)
H(2)
H(3)
H(4)
H(5)
H(6)
H(7)
H(8)
4.2747
4.2747
2.2811
2.2811
1.8137
1.8137
1.6118
1.6118
P
V
P
V
P
V
P
V
P
V
P
V
P
V
P
V
1.647(4)
1.631(1)
.—
–0.570(4)
–0.5696(7)
5.620(4)
5.6154(8)
.—
5.620(4)
1.196(4)
1.1726(7)
1.876(4)
1.9118(7)
–15.205(8)
–14.990(1)
0.203(4)
–0.011(1)
.—
1.876(4) –0.382(9)
1.9118(7) –0.486(1)
.—
5.6154(8)
–0.570(4)
–0.5696(7)
–0.576(4)
–0.573(1)
.—
1.647(4)
1.631(1)
–0.570(4)
–0.5696(7)
5.620(4)
5.6154(8)
1.196(4)
1.1726(7)
1.876(4)
1.9118(7)
–0.382(9)
–0.486(1)
0.480(9)
0.337(1)
1.196(4)
1.1726(7)
0.203(4)
–0.011(1)
–15.205(8)
–14.990(1)
–0.134(4)
–0.551(1)
.—
0.480(9)
0.337(1)
10.170(8)
10.173(1)
7.402(8)
7.400(1)
3.909(8)
3.930(1)
8.960(8)
8.951(1)
.—
.—
5.620(4)
5.6154(8)
–0.570(4)
–0.5696(7)
1.876(4)
.—
–0.576(4)
–0.573(1)
–15.205(8)
.—
0.203(4)
–0.011(1)
–15.205(8)
–14.990(1)
7.402(8)
7.400(1)
10.170(8)
10.173(1)
1.9118(7) –14.990(1)
.—
1.196(4)
1.1726(7)
0.480(9)
0.337(1)
–0.382(9)
–0.486(1)
0.203(4)
–0.011(1)
10.170(8)
10.173(1)
7.402(8)
–0.134(4)
–0.551(1)
3.909(8)
3.930(1)
8.960(8)
8.951(1)
.—
8.960(8)
8.951(1)
3.909(8) –13.430(8)
3.930(1) –13.221(7)
.—
7.400(1)

Highꢀresolution NMR lineshape analysis
Russ.Chem.Bull., Int.Ed., Vol. 51, No. 7, July, 2002
1229
1
2
Table 6. Relative contributions (in per cent) of the T2 and T1
conformations of transꢀ1,2ꢀdibromocyclopentane molecule in
solvents with different dielectric constants (ε) obtained using the
twoꢀconformation model
revise the results obtained. The new results virtually coinꢀ
cided with those obtained using the VALISA program.
Discrepancies of the order of some hundredth of Hz beꢀ
tween a number of coupling constants, which lie outside
the boundaries of the confidence interval in both models,
can be due to both the errors of deconvolution (a necesꢀ
sary preliminary step for the PAREMUS procedure) and
the lineshape distortions left out of consideration in the
current version of the VALISA program. Indeed, our atꢀ
tempt at analyzing a spectrum of this complex system
with strongly distorted base line showed that the VALISA
program can find an incorrect solution. Namely, a numꢀ
ber of spectral components of low intensity are placed in
positions corresponding to the "rotation" satellites instead
of being included in the main multiplet; however, the
contours of more intense spectral lines match one another
Solvent
ε
1T2
2T1
RMS
error/Hz*
CD3CN
C6D6
CCl4
37.5
2.3
2.2
83(8)
93(8)
99(8)
18(8)
7(8)
0(8)
1.1
1.1
1.0
* Root mean square deviation of experimental and calculated
spinꢀspin coupling constants.
Table 7. Relative contributions (in per cent) of statistically sigꢀ
nificant conformations 1E, 1T5, 4T5, 4E, and 2T1 of transꢀ1,2ꢀdiꢀ
bromocyclopentane in different solvents
1
almost exactly. The H NMR spectra of transꢀ1,2ꢀdiꢀ
bromocyclopentane recorded in other solvents were anaꢀ
lyzed using the parameters obtained for the H NMR
Solvent Computaꢀ
tional
1E
1T5
4T5
4E 2T1 RMS
error
1
spectrum of transꢀ1,2ꢀdibromocyclopentane in C6D6 soꢀ
lution as initial approximation.
Procedure
/Hz*
CD3CN VALISA
46(6) 35(4) 15(5) 8(5) 6(4) 0.49
The contributions of each of the eleven molecular
conformations to the averaged conformational state of
the transꢀ1,2ꢀdibromocyclopentane molecule were calꢀ
culated using a total of thirteen vicinal spinꢀspin coupling
constants obtained for solutions in CCl4, C6D6, and acꢀ
etonitrile (Table 5). Statistical significance of the contriꢀ
butions of particular conformations was determined by
the least squares method; the functional to be minimized
had the form
C6D6
VALISA
PAREMUS* 52(7) 43(4) 13(5)
VALISA 58(9) 41(5) 8(6)
52(7) 43(4) 12(5)
—
—
—
—
—
—
0.58
0.59
0.73
CCl4
* See the note in Table 6.
diaxial conformation 1T2 (the second classical conformaꢀ
tion) was observed in the full model. Instead, different
neighboring conformations (1E, 4E, 4T5, and 1T5) arranged
on the "walls" of the global minimum are involved in
the conformation equilibrium. This can be rationalꢀ
ized in terms of largeꢀamplitude vibrations along the
pseudorotation coordinate (phase angle). In fact, the
transꢀ1,2ꢀdibromocyclopentane molecule occupies the
global minimum position for a short time; rather, it oscilꢀ
lates when moving along the sector of the pseudorotation
path. Thus, a large number of accurately determined exꢀ
perimental vicinal spinꢀspin coupling constants allowed
the use of a full conformation model. As can be seen, a
conventional treatment of the conformational state of the
disubstituted cyclopentane as an equilibrium between the
diaxial and diequatorial twist conformations is sufficient
for qualitative description of changes in the properties;
however, actually the dibromocyclopentane molecule
spends much longer time in other conformations. We also
showed that other disubstituted cyclopentanes behave
analogously.22
2
χ
=
,
(4)
inhabit
where Jiexp is the ith experimental spinꢀspin coupling conꢀ
stants, xk is the relative population of the kth conformaꢀ
tion, Jik is the ith spinꢀspin coupling constants for the kth
conformation calculated using Eq. (3), and N is the numꢀ
ber of theoretical conformations.
The results obtained in the experiments with different
solvents using the twoꢀconformation and full models are
listed in Tables 6 and 7, respectively. As can be seen, the
solution of transꢀ1,2ꢀdibromocyclopentane in CD3CN (a
solvent of the highest polarity) is characterized by high
population of the diequatorial conformation 2T1, which is
consistent with the published results.14 However, no
Table 5. Vicinal spinꢀspin coupling constants of transꢀ1,2ꢀdiꢀ
bromocyclopentane (Ji,j/Hz) in different solvents
Thus, in this study we performed a detailed analysis of
some convergence and solution stability problems as apꢀ
plied to the total lineshape analysis of highꢀresolution
NMR spectra. This allowed us to develop a new strategy
of analysis of the multiplet structure of complex NMR
spectra and to evaluate its parameters using the VALISA
program. The possibilities of the new computational techꢀ
Solvent
J1,2
J1,4
J2,3
,
J1,6
J2,5
,
J3,7
J4,8
,
J3,8
J4,7
,
J5,7
J6,8
,
J5,8
J6,7
,
C6D6
CCl4
CD3CN
1.631 5.615 1.912 10.173 7.400 3.93 8.951
1.171 5.446 1.395 10.314 7.594 3.635 8.918
2.352 5.877 2.685 10.002 7.087 4.346 9.053

1230
Russ.Chem.Bull., Int.Ed., Vol. 51, No. 7, July, 2002
Zubkov et al.
11. a. U. Weber and H. Thiele, Proc. of the 12th Eur. Experimenꢀ
tal NMR Conf., Oulu (Finland), 1994, 302.
b. C. Altona, H. R. Buys, and E. Havinga, Rec. Trav. Chim.,
1966, 85, 983.
12. D. Cremer and J. A. Pople, J. Am. Chem. Soc., 1975, 97, 1354.
13. M. Karplus, J. Chem. Phys., 1959, 30, 11.
14. C. Altona, Tetrahedron Lett., 1968, 2325.
15. M. Polak, B. Mohar, J. Kobe, and J. Plavec, J. Am. Chem.
Soc., 1998, 120, 2508.
nique were demonstrated taking a complete interpretaꢀ
tion of the 1H NMR spectrum of transꢀ1,2ꢀdibromocycloꢀ
pentane as an example. The accuracy and reliability of the
spinꢀspin coupling constants obtained using the VALISA
program made it possible to carry out the conformational
analysis taking into account all conformational states deꢀ
scribed by pseudorotation of the fiveꢀmembered cycle.
The VALISA program was also successfully employed for
solving other complicated structural24 and conformaꢀ
tional25 problems.
16. S. Golotvin and A. Williams, J. Magn. Reson, 2000, 146, 122.
17. GAUSSIAN 94, Revision E.1, M. J. Frisch, G. W. Trucks,
H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A.
Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A.
Montgomery, K. Raghavachari, M. A. AlꢀLaham, V. G.
Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B.
Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng,
P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S.
Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S.
Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Headꢀ
Gordon, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Pittsꢀ
burgh (PA), 1995.
18. J. Heinzer, J. Magn. Reson., 1977, 26, 301.
19. R. Laatikainen, M. Niemitz, U. Weber, J. Sundelin,
T. Hassinen, and J. Vepsalainen, J. Magn. Reson. A,
1996, 120, 1.
20. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P.
Flannery, Numerical Recipes in C: The Art of Scientific Proꢀ
gramming, CUP, Cambridge, 1993, 994 pp.
21. D. S. Stephenson and G.Binsch, J. Magn. Reson., 1980,
37, 409.
22. S. S. Golotvin, Ph.D. (Chem.) Thesis, M. V. Lomonosov
Moscow State University, Moscow, 1998, 160 pp. (in
Russian).
23. C. A. G. Haasnoot, F. A. A. M. de Leeuw, and C. Altona,
Tetrahedron, 1980, 36, 2783.
24. V. A. Chertkov, S. V. Zubkov, A. A. Ovcharenko, A. V.
Karchava, and M. A. Yurovskaya, Khim. Geterotsikl. Soed.,
1999, 11, 1500 [Chem. Heterocycl. Compd., 1999, 11 (Engl.
Transl.)].
This work was financially supported by the Russian
Foundation for Basic Research (Project No. 97ꢀ03ꢀ
33794).
References
1. T. D. W. Claridge, HighꢀResolution NMR Techniques in Orꢀ
ganic Chemistry, Pergamon, Amsterdam, 1999, 382 pp.
2. J. A. Pople, W. G. Schneider, and H. J. Bernstein, High
Resolution Nuclear Magnetic Resonance, McGrawꢀHill, New
York, 1959, 501 p.
3. N. M. Sergeev, Spektroskopiya YaMR [The NMR Spectrosꢀ
copy], Izdꢀvo MGU, Moscow, 1981, 279 pp. (in Russian).
4. S. M. Castellano and A. A. BothnerꢀBy, J. Chem. Phys.,
1964, 41, 3963.
5. D. S. Stephenson and G. Binsch, J. Magn. Reson., 1980,
37, 395.
6. S. S. Golotvin and V. A. Chertkov, Izv. Akad. Nauk, Ser.
Khim., 1997, 444 [Russ. Chem. Bull., 1997, 46, 423 (Engl.
Transl.)].
7. P. Diehl, S. Sykora, and J. Vogt, J. Magn. Reson.,
1975, 19, 67.
8. R. Laatikainen, J. Magn. Reson., 1990, 92, 1.
9. E. Kolehmainen, K. Laihia, R. Laatikainen, J. Vepsalainen,
M. Niemitz, and R. Suontamo, Magn. Reson. Chem., 1997,
35, 463.
25. S. V. Zubkov, S. S. Golotvin, and V. A. Chertkov, Proc.
15th Eur. Experimental NMR Conf., 2000, 42.
10. J. Pulkkinen, R. Laatikainen, J. Vepsalainen, and
M. Ahlgren, Magn. Reson. Chem., 1999, 37, 119.
Received February 1, 2002