371
Research Article
Received: 6 August 2008 Revised: 29 September 2008 Accepted: 3 December 2008 Published online in Wiley Interscience: 5 February 2009
(www.interscience.com) DOI 10.1002/mrc.2397
A systematic approach for the generation and
verification of structural hypotheses
Mikhail Elyashberg,a Kirill Blinova and Antony Williamsb∗
During theprocess ofmolecular structure elucidation the selection of themost probable structural hypothesismay be based on
chemical shift prediction. The prediction is carried out using either empirical or quantum-mechanical (QM) methods.When QM
methods are used, NMRprediction commonly utilizes theGIAOoption of theDFT approximation. In this approach the structural
hypotheses are expected to be investigated by scientist. In this article we hope to show that themost rationalmanner bywhich
to create structural hypotheses is actually by the application of an expert system capable of deducing all potential structures
consistent with the experimental spectral data and specifically using 2D NMR data. When an expert system is used the best
structure(s) can be distinguished using chemical shift prediction, which is best performed either by an incremental or neural
net algorithm. The time-consuming QM calculations can then be applied, if necessary, to one or more of the ‘best’ structures to
confirm the suggested solution. Copyright c© 2009 John Wiley & Sons, Ltd.
Supporting information may be found in the online version of this article.
Keywords: NMR; 1H; 13C; 15N; expert system; GIAO; neural nets; increments
Introduction
The problem of molecular structure elucidation continues to be
a major challenge and an important problem in the domain of
organic chemistry and molecular spectroscopy. If a researcher
is engaged in the investigation of a chemical reaction, then
one of his or her primary aims is to determine the structure
of the reaction product(s). In the domain of natural products
the isolation and elucidation of chemical structures can be
a major challenge. In both cases the structure determination
process, in general, is reduced to forming some structural
hypothesesand then their subsequentverification. Thegeneration
of structural hypotheses is the initial step in theprocessof structure
elucidation.
Each hypothesis is the result of the comprehensive logical treat-
ment of available spectral and chemical information associated
with the structure under analysis. Nowadays the main source of
spectral information is a combination of 1D and 2D NMR spec-
tra complemented by the molecular formula and fragmentation
ions determined from one of the many variants of MS.[1] The
information obtained from 2D NMR data is frequently rather
complicated and fuzzy by nature. During the interpretation of
2D NMR data several structural hypotheses are often produced,
each of them fitting the experimental data and commonly other
available information. Hypothesis generation by humans offers
a series of evident difficulties: (1) there is no guarantee that all
possible hypotheses will be enumerated; (2) there are no criteria
allowing the selection of the most credible hypotheses. As a re-
sult, articles revising previously reported chemical structures can
be quite common. A very interesting review reporting a great
number of such cases was published recently by Nicolaou and
Snyder.[2] The main objective of the article was to demonstrate
to the chemical community that molecular structure elucida-
tion is not a routine problem, and for the final decision it is
frequently necessary not only to comprehensively utilize both
spectral and X-ray data but also to confirm the structure via to-
tal synthesis. Different research teams offer different conclusions
since investigators working in a traditional manner have no ac-
cess to an exhaustive list of all possible candidate structures.
We suggest that it is necessary to utilize a method that will sys-
tematically generate all possible structural hypotheses as well as
identifying the most probable for this series. Choosing several
of the most probable structures can drastically reduce the num-
ber of hypotheses which should be examined and finally verified
and can both reduce the time consumed by highly qualified
specialists as well as reduce the number of potential errors of
misinterpretation.
Such methods already exist under the guise of computer-aided
structure elucidation (CASE) techniques. A series of CASE expert
systems have been described previously.[3–6] When these systems
are used the relationships between spectral data and structural
information are treated as a set of assumptions (‘axioms’).[7] CASE
programs derive all logical consequences (structures) from the
set of axioms to solve the task which the spectroscopist performs
when elucidating a structure without computational assistance.
In other words, the initial assumptions and postulates form an
axiomatic theory adjusted to solve a given analytical task. Any
changes in the set of axioms (varying assumptions, adding new
assumptions, etc.) influence the set of final structural hypotheses.
Alternatively, if somenewhypothetical structures are addedby the
researcher to an earlier set of candidate structures, it is necessary
to verify that they are in agreementwith the initial axioms. If a new
candidate structure contradicts the initial axioms then either the
∗ Correspondence to: Antony Williams, ChemZoo Inc., 904 Tamaras Circle,Wake
Forest, North Carolina 27587, USA. E-mail: antony.williams@chemspider.com
a Advanced Chemistry Development, Moscow Department, 6 Akademik Bakulev
Street, Moscow 117513, Russian Federation
b ChemZoo Inc., 904 Tamaras Circle, Wake Forest, North Carolina 27587, USA
Magn. Reson. Chem. 2009, 47, 371–389 Copyright c© 2009 John Wiley & Sons, Ltd.

372
M. Elyashberg, K. Blinov and A. Williams
newsuggestion iserroneousor thegivenaxiomsshouldberevised.
For example, a new candidate structure with a molecular formula
or molecular mass differing from the experimentally determined
values is only feasible when the corresponding MS data are in
doubt.
An expert system can produce an output file contain-
ing many thousands and even tens of thousands of struc-
tures. All of them may formally meet the criteria and con-
straints provided by all of the 2D NMR correlations, but the
chemical shift assignments of the carbon and hydrogen nu-
clei for the majority of structures usually contradict a num-
ber of the spectrum–structure correlations. A credible final
structure or set of structures containing the correct struc-
ture can be distinguished from the full set of candidates
using NMR spectrum prediction. The efforts of many groups
of researchers have been focused on the development of al-
gorithms for chemical shift prediction using different empiri-
cal approaches.[8–12]
Recently we developed two fast calculation algorithms,[13–15]
one ofwhich is based on additivity rules, the so-called incremental
approach, and the other employs artificial neural networks.
These algorithms provide a calculation speed of 3000–10 000
13C chemical shifts per second with the average deviation
between calculated and experimental chemical shifts equal to
d = 1.8 ppm. The maximum calculation speed is achieved
using the incremental approach. For a file containing tens
of thousands of structural isomers the calculation time by
either of the two methods is no longer than several minutes.
Both algorithms are implemented in the CASE expert system
Structure Elucidator,[16–18] and their high speed and accuracy has
strongly influenced the CASE strategy.[19] The third algorithm
included into the set of system predictors is based on a
fragment method.[1] Although this method is not as fast
as the other two, it allows the user to obtain a detailed
explanation as to how each predicted chemical shift was
calculated. These calculations use a hierarchical organization of
spherical environments (HOSE)-code-based prediction approach
(see review[1]) and employ a database containing 175 000
structures with assigned 13C and 1H chemical shifts. For each
atom within the candidate structure the related structures used
for the prediction can be shown with their assigned chemical
shifts and this allows the user to understand the origin of the
predicted chemical shifts. All three methods can be used for 1H,
13C, 15N, 19F and 31P NMR chemical shift prediction and all of
them are implemented within the Structure Elucidator software
program.
During the lastdecade therehasbeena significantgrowth in the
number of publications devoted to the application of quantum-
mechanical (QM) chemical shift calculations for identifying the
most credible structure(s). It has been shown[20–25] that a QM
approach provides a calculation accuracy that is, in general,
enough for the successful validation of candidate structures and,
in particular, for the revision of structures which were originally
determined incorrectly. One of the most recent and striking
examples of the successful application of the QM approach was
described by Rychnovsky[26] who refuted the incorrect structure
of hexacyclinol proposed by Grafe et al.[27] and suggested another
structure which was then unambiguously proved by synthesis
and X-ray analysis.[28] A systematic method to confirm the
structure of hexacyclinol using Structure Elucidator was also
described elsewhere.[29] QM chemical shift prediction is rather
time consuming relative to other approaches. Different authors
report different time costs for such calculations depending on the
molecules size, flexibility and the number of possible conformers
for which chemical shifts should be predicted. The processor time
can vary from several hours to several tens of hours. It is therefore
necessary to reduce the number of candidate structures to which
QM calculations should be applied as much as possible before
starting a series of calculations. It is natural to expect that prior
to performing QM chemical shift calculations a minimum set of
candidate structures shouldbechosenonthebasisof fast chemical
shift prediction by empirical methods. Structure generation and
subsequent ranking of the candidate structures in descending
order of their probability consumes only a few minutes on a
modern processor using today’s expert systems.[18] Obviously the
application of QM methods can play a decisive role in such cases
when the analyzed structures contain ‘exotic’ fragments that
were absent from the training set. Another situation whereby
QM prediction could help to identify a preferable structure
may occur when the differences between the experimental
NMR chemical shifts and those calculated by empirical methods
for several ‘best structures’ are too small to enable a certain
choice.
In many publications the potential of QM methods was
evaluated on molecules for which the number of heavy atoms
was most frequently around 20 and rarely reached 30 atoms.
Meanwhile, for example, many natural product molecules contain
40–100 or more heavy atoms, and the prediction of chemical
shifts for such molecules is not attainable by QM methods as yet.
For large molecules we can only rely on empirical methods for
chemical shift prediction.
It is worthy to note that some publications (for example[30])
devoted to structure elucidation assisted by QM chemical shift
prediction frequently do not mention empirical methods at all.
In many cases it is seemingly alleged that the QM approach
is the unique predictive method for proving or disproving a
proposed structure. Other works (for example[31,32]) compare the
accuracy of QM methods with the accuracy of older versions of
empirical approaches[33] that do not appropriately represent the
performance of contemporary programs.[8,15,34–36] To the best of
our knowledge the capabilities of thenewer empiricalmethods for
identifying the most probable structure within a set of proposed
structures have not been compared with results attained using
QM methods until this publication.
With this in mind we selected a series of articles where the
QM approach was successfully used for selection of the right
structure among a series of suggested molecules or for revising
the originally hypothesized chemical structure. For each case
if 2D NMR data were available then we made an attempt
to solve the problem systematically using the expert system
Structure Elucidator[16,17] which is capable of enumerating all
possible structural hypotheses. We found that the right structure
was also assigned as the most probable one in the examples
considered by both QM and fast empirical NMR chemical
shift predictions,[8,13] while alternative and incorrect structures
suggested by researchers were ranked lower. Securitization
of the examples studied enabled us to suggest a general
approach where the most probable structure is established as
a result of the joint application of a CASE expert system in
combination with both empirical and QM methods for chemical
shift prediction.
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373
Generation and verification of structural hypotheses
Results and Discussion
Problems solved in Common Mode of expert system
There are two main modes for operating the Structure Elucidator
(StrucEluc) expert system: the Common Mode and the Fragment
Mode. In the Common Mode the program uses atoms included
into the molecular formula and connectivities derived from 2D
NMR spectra, with the atoms characterized by both their chemical
shifts and their properties if available. The properties may include
atomvalence, hybridization, the possibility of having heteroatoms
as neighbors, the number of hydrogen atoms attached to carbons
adjacent to CH, CH2 and CH3 groups, etc. The program infers all
logical consequences (structures) resulting from the data outlined
above. This mode of operation resembles, to a certain extent,
an ‘ab initio’ approach. In the Fragment Mode of the program
‘free’ atoms and structural fragments are utilized as the basis of
structure generation. The fragments can be found in a database
or proposed by the chemist. This mode is especially effective
in those cases where there is a lack of COSY or/and HMBC
correlations.
In this section we will consider several examples in which
the preferred structure should be selected on the basis of NMR
spectrum prediction. These problems were used by different
researchers to examine the possibilities of QM methods to be
used as an analytical tool. We used spectral data presented in the
corresponding publications to demonstrate how the problems
could be solved using the StrucEluc system operating in the
Common Mode.
Example 1. Boletunones A and B
Kim et al.[37] separated two new natural products and attributed
them to Boletunone A (1) and Boletunone B (2) using 1D and 2D
NMR data. Both structures are presented with the 13C chemical
shift assignment suggested by authors:[37]
CH3
17.00
CH3
21.70
CH3
58.40
28.10
68.60
71.50
29.80
45.90
73.20
76.20
146.5056.00
106.30 133.10
171.30 198.70
OH
OO
O
O O
OH
1
H3C15.00
CH3
15.20
CH3
21.00
30.10
66.60
27.60
46.00
71.90
77.40
145.00
54.50
107.00
131.70
173.00 198.60
OH
HO O
O
O
O
2
Steglich and Hellwig[38] have shown that structures 1 and 2 are
wrong, and the following alternative structural formulae for these
compounds, 3 and 4, were offered and proved:
H3C17.00
CH3
21.70
H3C58.40
28.10
68.60
71.50
29.80 45.90
73.20
76.20
146.50
56.00
106.30
133.10
171.30
198.70
OH
O
O
O
O
O
OH
CH3
15.00
CH3
15.20
H3C21.00
30.10
66.60 27.60
46.00
71.90
77.40
145.00
54.50
107.00
131.70
173.00
198.60
OH
OH
O
O
O
O
3 4
For Boletunone A, we have shown[19] that application of StrucEluc
allowed reliable determination of the right structure 3 in 0.15 s.
We also demonstrated how the problem of Boletunone B could
be solved very quickly and correctly in a systematic way. Since the
Boletunone B story was used by Bagno et al.[20] for challenging
DFT chemical shift calculations used as an analytical tool, we will
explain here the solution of this problem in more detail.
Bagno et al.[20] showed that QM-based NMR chemical shift
prediction was capable of distinguishing between the structural
hypothesesof2 and4, and coulddetermine thegenuine structure.
It was demonstrated that a quantum-chemical approach could be
used to resolve disputes regarding the acceptance or rejection of
different isomeric structures.
Tocalculate the 1Hand13C spectra forboth theoriginalproposal
2and the revisedstructure4, thegeometrieswereoptimizedat the
B3LYP/6–31G(d,p) level in the gas phase, and the NMR properties
were calculated with B3LYP/cc-pVTZ both in the gas phase and
with a solvent reaction field of DMSO.
To make a choice as to the most favorable of the two structures,
the following statistical characteristics were used: the parameters
a and b for the linear regression equation δcalcd = a + bδexptl;
the correlation coefficient, R2; the mean absolute error (MAE)
defined as n|δcalcd − δexptl|/n; the corrected MAE, CMAE, defined
as n|δcorr − δexptl|/n, where δcorr = (δcalcd − a)/b and therefore
corrects for systematic errors. The corrected chemical shifts are
referred to the scaled shifts.
The authors[20] found that for the correct structure (4)
MAE(13C) = 7.2 ppm, CMAE(13C) = 1.9 ppm and R2 = 0.9984,
while for the wrong structure, 2, these values were equal to
6.0 ppm, 3.7 ppm and 0.9952 correspondingly. These parameters
indicate that structure 4 is preferable. The calculation of the 1H
chemical shifts and coupling constants confirmed that the revised
structure 4 is in better agreementwith the experimental spectrum
than the originally proposed structure 2. An attempt to improve
prediction accuracy by optimizing the structures at the MP2/cc-
pVDZ level indicated that the changes in geometrywere very small
and NMR properties were very similar.
For systematic elucidation of the Boletunone B structure, we
input the 1D and 2D NMR data associated with Boletunone B into
the StrecEluc software. The 1H signal multiplicities determined by
Kim et al.[37] were introduced for all methyl groups and for two
CH groups [δC = 77.4, δH = 4.34(d) and δ = 71.9, δH = 3.77(s)].
The multiplicities of these groups had been determined with
sufficient reliability. During the first program run ‘Strict Structure
Generation’[17] was performed. This meant that the absence of
Magn. Reson. Chem. 2009, 47, 371–389 Copyright c© 2009 John Wiley & Sons, Ltd. www.interscience.wiley.com/journal/mrc

374
M. Elyashberg, K. Blinov and A. Williams
H3C
CH3
CH3
OHHO O
O
O
O
1
H3C
H3C
H3C
OH
HO
O O
O
O
2
H3C
CH3
H3C
HO OH
O
O
O
O
dN(13C): 5.010dN(13C): 4.740dN(13C): 3.869
3
Figure 1. The first three structures of the file produced by Strict Structure Generation from the NMR data measured for Boletunone B. The structures are
ranked in ascending order of average deviation dN(13C).
the so-called non-standard correlations[39] in the 2D NMR data
was assumed, non-standard correlations (NSC) defined as those
for which the distance between intervening nuclei in the COSY
and HMBC spectra is longer than three bonds. The program
generated 142 structures in 3.8 s, 57 structures were retained after
spectral filtering and no structures were removed after checking
the structures for duplicates. The result can be symbolized in the
following way: k = 142 → 57 → 57, tg = 3.8 s.
Neither the2nor4 structurewas foundamong the 57 structures
since the presence of one NSC in the HMBC NMR data was
postulatedboth in theoriginal and revised structures. 13Cchemical
shift prediction was performed for all structures in the output file
using the neural net (NN) approach discussed previously and all
structureswere ranked in ascending order of the average chemical
shift deviation dN(13C) calculated for each structure. A lower index
N denotes that the prediction was performed by the NN method.
The top structures contained within the ranked structure file are
presented in Fig. 1.
The average deviation value of the first ranked structure is
twice as large as the average deviation of the NN method
(1.8 ppm), which indicates a need to repeat structure generation
in Fuzzy Mode.[18] Structure generation was repeated in this
mode allowing one NCS in the HMBC data as assumed by
both groups of investigators.[37,38] This gave the following result:
k = 1211 → 383 → 374, tg = 14 s
The top-ranked structures in the file are shown in Fig. 2.
Figure 2 shows that the revised structure is identical to the
‘best’ structure and the difference between the average deviations
calculated for the second and first structures is significant.[18] The
original structure 2was not found in the output file since structure
2 contradicts the multiplicity of the 1H signal δ = 3.77 ppm; a
singlet is observed in the 1H spectrum, while a doublet should be
expected if structure 2 was correct. Fuzzy Structure Generation
was performed without taking into account the multiplicities
(k = 32814 → 8621 → 7533, tg = 1 min 10 s) produced
structure 2 and it was ranked in third position in the resulting
structure file (dN 13C is equal to 3.08 ppm for this structure). Direct
comparison of the linear regression parameters calculated for
structures 2 and 4 shows that R2(4) = 0.999 and R2(2) = 0.995,
and these parameters are practically the same as those found by
Bagno et al. The application of the systematic approach outlined
here would allow researchers to immediately identify the correct
structure that could then be further justified and investigated in
more details by quantum-chemical calculations if it were deemed
necessary.
Theregression linesassociatedwithstructures2and4areshown
in Figs 1S and 2S (see Supporting Information). These figures show
the difference in point scattering corresponding to the original
and revised structures.
Example 2
Although there are articles devoted to the evaluation of DFT
chemical shift calculation as a potential tool for identification of
the proposed structure, there are also publications where this
approach has been applied to solving real chemical problems.
Recently Sanz et al.[30] employed 13C and 15N chemical shift
calculations by the GIAO approximation of the DFT method to
choose between the structures forming two pairs of isomers (5 or
6) and (7 or 8):
N N
N
F
F
N N
N
F
FF
5 6
F
N N
NS
F
F
S
N N
N
F
FF
7 8
F
The authors[30] synthesized and separated two samples, #1 and
#2, with molecular formulae of C19H12F3N3 (1) and C17H10F3N3S
(2). For the purpose of structure determination and confirmation,
1D NMR spectra (1H, 13C, 15N and 19F) in combination with 1H–13C
gs-HMBC and 1H–15N gs-HMBC data were used. The authors[30]
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375
Generation and verification of structural hypotheses
derived the two pairs of alternative isomers shown above and the
problem was reduced to selection of the correct structure within
each of the isomer pairs. For this purpose the authors calculated
both the 13C and 15N chemical shifts using the GIAO method of
DFT approximation for two model compounds:
H3C
CH3
N N
N
F
F
CH3
CH3
N N
N
F
FF
9 10
F
The model compounds 9 and 10 were used in order to simplify
the QM computations. Linear regressions of the calculated
versus experimental 13C chemical shifts, the latter assigned for
the proposed structures, allowed the authors[30] to confirm
configuration 9 as the most preferable [R2(9) = 0.998; R2(10) =
0.984]. 15N chemical shift prediction resulted in R2(9) = 0.992 and
R2(10) = 0.991 values for the corresponding model structures
and only slightly supports model 9 as the preferred structure.
In order to show how the problem could be solved without
utilizing model structures and QM calculations, we repeated
the structure elucidation process for both samples using our
systematic approach.
The experimental 1D and 2D NMR data and the molecular
formulae obtained for the two samples were input into the
StrucEluc system, and the two problems, 1 and 2, were solved. For
the structure elucidation process both 1H–13C and 1H–15N HMBC
correlations were used as initial data.
Problem 1. Strict Structure Generation gave the following result:
k = 106 → 44 → 20, tg = 27 s. For all structures 1H, 13C and
15N chemical shifts were calculated using the NN approach and,
following thegeneral StrucEluc strategy, the resulting structurefile
was ranked in ascending order of dN(13C). The first three structures
of the ranked file are presented in Fig. 3.
The figure shows that all average deviations-dN(13C), dN(1H),
dN(15N) and dI(13C) – indicate that structure 5 is themost probable
one. The values R2(5) = 0.984 and R2(6) = 0.895 calculated for
13C prediction by the NN method support our assignment and the
conclusion of Sanz et al.[30]
Problem 2. The first program run was executed using the
Strict Mode of structure generation. Only one structure, 11, was
produced in 7 s. The very large values of the calculated average
deviations [dN(13C) ∼ 9 ppm, dN(15N) ∼ 65 ppm] suggested that
structure 11 was likely incorrect and, consequently, non-standard
HMBC connectivities might exist within the 2D NMR data.
N
N
N
S
F
F
F
11
As mentioned earlier, according to the general strategy of CASE
developed by us,[16–18,40] fuzzy structure generation[40] should
be carried out in such a case. Fuzzy structure generation was
performed under the conditions m = 1–15, a = x, that is the
possible number of NSCs is allowed to be between 1 and 15,
and lengthening of connectivities is replaced by their removal
during structure generation. This mode allows problems to be
solved when 2D NMR data contain an unknown number of NSCs
having unknown lengths. The following result was obtained:
k = 1481 → 415 → 164, tg = 11 min.
Chemical shift prediction and structure ranking promoted
structure 7 to the first ranked position while structure 8 was
ranked as fourth. Both structures with average deviations are
presented in Fig. 4.
In this case the preferable structure was also indicated by all
NMR shift predictions having the lowest deviations as well as the
calculated values of R2(7) = 0.974 and R2(8) = 0.807. Additional
evidence for structure 7 is the need for a seven bond NSC in
structure 8.
In the examples discussed in this section empirical methods
of chemical shift prediction are not only dramatically faster but,
in definite cases, are even more reliable because no structural
models simplifying the calculations were utilized. Nevertheless,
the coincidence of structural assignments made by both QM
and empirical approaches shows that researchers can choose
the method that is more attractive for them. Graphs of linear
regression and the associated scattering of points calculated
for both problems can be found in the Supporting Information
(Figs 3S–6S).
Problems solved in Fragment Mode
The analytical process taken by experts for molecular structure
elucidation from 2D NMR data has been described in a series
of books (for example[41–43]). The spectroscopist usually tries
to assemble some fragments from atoms and their spectral
signals and then commonly combine the fragments using HMBC
correlations until a complete molecular structure or set of
plausible structures are constructed. As previously discussed
there is no guarantee that all possibilities will be taken into
account by the process of manual structure assembly. Moreover,
some superfluous structural hypotheses may be suggested. If
selection of the right structure is performed by QM chemical shift
prediction then additional time will be consumed for checking
these structures. In this sectionwewill demonstrate howan expert
system supplied with new empirical chemical shift prediction
methods can be used to assist the spectroscopist in obtaining the
right solution in an optimal manner.
Magn. Reson. Chem. 2009, 47, 371–389 Copyright c© 2009 John Wiley & Sons, Ltd. www.interscience.wiley.com/journal/mrc

376
M. Elyashberg, K. Blinov and A. Williams
H3C
CH3
CH3
OHHO O
O
O
O
dN(13C): 2.167
1
CH3
H3C
H3C
HO
HO
O
O
O
O
dN(13C): 3.457
2
H3C
CH3
CH3
OH
HO
O
O
O
O
dN(13C): 3.972
3
Figure 2. The top-ranked structures in the output file resulted from Fuzzy Structure Generation using the NMR data obtained for Boletunone B. The
top-ranked structure is identical to the revised structure 4.
N
N
N
F
F F
dI(13C): 1.745
dN(13C): 1.221
dN(1H): 0.143
dN(15N): 5.026
1 5
N N
N
F
F
F
dI(13C): 2.821
dN(13C): 2.264
dN(1H): 0.202
dN(15N): 10.109
2
N
N
N
F
F
F
dI(13C): 3.707
dN(13C): 3.715
dN(1H): 0.326
dN(15N): 24.891
6
3
Figure 3. The first three structures of the ranked structural file produced as a solution for Problem1. The right structure is confirmedby average deviations
calculated for 1H, 13C and 15N spectra. dI(13C) denotes the average deviation found when the incremental method of chemical shift prediction was
employed.
N N
N
S
F F
F
dI(13C): 2.016
dN(13C): 1.639
dN(1H): 0.107
dN(15N): 3.566
1 7
N N
N
S
F
F
F
dI(13C): 3.689
dN(13C): 3.178
dN(1H): 0.166
dN(15N): 13.355
4 8
Figure 4. Structures 7 and 8 proposed in the work of Sanz[30] with their
calculated average deviations. The arrows show long-range 1H–15NHMBC
correlations of 5JNH for structure 7 and 7JNH for structure 8. For these
structures values of R2(7) = 0.974 and R2(8) = 0.807 were calculated.
Example 1
Balandina et al.[22] synthesized a novel quinoxaline and deter-
mined its molecular formula C16H10N2O2 from the MS data
(m/z = 262(M+) combined with elemental analysis data. To
HC
128.02
CH
128.07
HC
128.68
C
140.92
CH
128.07
C
138.16
N
N
HC
128.76
CH
128.73
HC
128.73
CH
124.81
CH
124.81
C
128.80
C
144.42
C
134.68
C
138.29
C
151.04
O OH
Figure 5. Initial structure information for the generation of structural
hypotheses.
elucidate the structure of this compound, authors used 1H, 13C
and 15N NMR spectra. Assignment of the 1H and 13C NMR spectra
was accomplished using data derived from DEPT, 2D COSYGP,
HSQC and HMBC experiments. Analysis of the NMR data provided
two fragments containing H, C and N atoms with assigned chem-
ical shifts. Three quaternary carbons (151.04, 138.29 and 134.68)
without HMBC correlations, one hydrogen atom and two oxygen
atoms were not assigned to either of the fragments. The initial
data for forming structural hypotheses are presented in Fig. 5.
Using these data and some additional chemical considerations
the authors suggested six structures which are presented in Fig. 6.
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Generation and verification of structural hypotheses
N
N
H
O
O N
N
H
O
O
N
N
OH
O
N
N
O
O
N
N+
O
H O-
N
N O
O
12 13 14
15 16 17
Figure 6. Six suggested structures derived from the experimental data. Structure 14 corresponds to the correct structure.
N
N
OH
O
dI(13C): 1.451
dN(13C):1.619
dN(1H): 0.101
dN(15N): 9.591
1
N
H
N
O
O
dI(13C): 6.003
dN(13C): 4.054
dN(1H): 0.322
dN(15N): 82.976
2
N
N
OHO
dI(13C): 7.309
dN(13C): 6.313
dN(1H): 0.129
dN(15N): 92.817
3
N
N
OH
O
dI(13C): 9.275
dN(13C): 7.866
dN(1H): 0.149
dN(15N): 88.670
414
Figure 7. Output structural file ranked by dN(13C) deviation.
To select the right structure, 1H, 13C and 15N chemical
shifts were predicted for structures 12–17 using the DFT
framework and using a hybrid exchange-correlation function,
GIAO B3LYP, at the 6–31G(d) level. Full geometry optimizations
were performed under ab initio RHF/6–31G conditions. Linear
correlation coefficients of the experimental versus calculated 13C
chemical shifts (R2), root-mean-square (rms) errors, slope (a),
standard deviations (sd) and mean absolute deviations [MAD
= (|δexp − δcalc|)/n] for structures 12–17 were computed.
As a result structure 14 was identified as the most probable
(R2 = 0.9758, rms = 1.16 ppm, sd = 1.2 ppm, MAD = 7.03 ppm).
Other proposed structures were rejected by the authors due to
smaller R2 values (R2 = 0.01–0.57) and larger deviations. It should
be noted that the R2 values have a reasonable interpretation only
in those cases when experimental chemical shifts are assigned to
the atoms of competing structures. Otherwise, selection of the
preferable structure can be attained only by simple comparison
of the experimental with the calculated spectrum and based on
determiningoutliers.Obviously theapplicationofanexpertsystem
for structure elucidation provides chemical shift assignments that
agreewith the2DNMRcorrelationsandconsequently theselection
of the best structure occurs automatically.
To solve this problem using a CASE approach, spectral data
presented in the work[22] were entered into the StrucEluc system.
Fragments andatoms shown in Fig. 5were eventually transformed
into a molecular connectivity diagram (MCD).[16] The atomic
properties for three carbon atoms not included into the fragments
were automatically set as sp2/not defined (atom hybridization
is sp2, possibility of neighboring heteroatoms is not defined).
Structure generation was performed in the automatic mode and
Fuzzy Structure Generation was allowed. The following result was
obtained: k = 247 → 16 → 4, tg = 1 s.
Empirical chemical shift prediction was performed for all nuclei.
Subsequent structural ranking by dN(13C) deviation resulted in the
structure ordering shown in Fig. 7:
Structure 14 is the best structure according to the shift
predictions for all nuclei presented in Fig. 7. Moreover, the
deviations for structure 14 are dramatically smaller than those
for the next (#2) ranked structure for all nuclei, and suggest a high
reliability for the solution.[18] Note that the dN(13C) deviation for
structure14 is almost four timessmaller than theaveragedeviation
calculated by the GIAO approach. Figure 8 shows the chemical
shift assignments performed for structure 14 and deduced by the
authors[22] and listed with deviations calculated by us.
All deviation values calculated for the new assignment
(including the deviations d(15N)) are smaller than those found
for the former assignment. The largest errors are related to the
carbons at 151.4 and 138.29 ppm, differences of 11 and 16.5 ppm.
It is also interesting to note that all suggested structures 12–17
except structure 14 were not generated by the program since
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378
M. Elyashberg, K. Blinov and A. Williams
128.02
128.07
128.68 128.07
128.76
128.73
128.73
124.81
124.81
140.92
138.16
128.80
144.42
134.68
138.29
151.04
N
300.18
N
261.11
HO
O
dI(13C): 1.451
dN(13C): 1.619
dN(15N): 9.591
dI(15N): 2.918
This article
128.02
128.07
128.68 128.07
128.76
128.73
128.73
124.81
124.81
138.16
140.92
128.80
144.42
134.68
151.04
138.29
N
261.11
N
300.18
HO
O
dI(13C): 2.842
dN(13C): 3.158
dN(15N): 48.661
dI(15N): 36.152
Ref.[22]
Figure 8. The chemical shift assignments for structure 14 automatically determined in this article and deduced by the original article authors.[22] The
deviation values indicate that some chemical shifts assigned on the basis of QM prediction should be exchanged.
Figure 9. Correlation plots of 13C chemical shift values predicted for structure 14 (our assignment) by the DFT and NN methods versus the experimental
shift values. The target line Y = X is shown. The coordinates of some points are shown in frames where the first value designates the experimental
shift and the second represents the calculated shift. The regression parameters are: R2(NN) = 0.905, R2(QM) = 0.937, rms(NN) = 2.54 ppm and
rms(QM) = 1.89 ppm.
the atom property correlation table (APCT) prevents the assembly
of structures whose atoms would have chemical shifts differing
dramatically from the experimental shifts.
For completeness we repeated structure generation with both
the APCT and Filters (structural and spectral) switched off.
Finally, 59 non-isomorphic structures were generated including
structures12and13 characterizedby 13C chemical shift deviations
of 6–8 ppm. Structures 15 and 17 could not be generated
because according to the initially postulated conditions themono-
substituted benzene ring is connected to the carbon atom with a
shift of 144.42 ppm whose hybridization was assigned as sp2 (sp3
is necessary for 15 and 17).
Using the 13C chemical shift values predicted for structure 14
by DFT and NN methods we calculated linear regressions for the
experimental shift values based on our shift assignments relative
to the assignments suggested by the authors[22] (Fig. 9).
Figure 9 shows that for chemical shifts calculated by the NN
algorithm the regression line is very close to the Y = X line. The
DFT line lies 7 ppm below the Y = X line. We can observe that
the value of R2(DFT) suggests only an acceptable linear correlation
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Generation and verification of structural hypotheses
Figure 10. The correlation plots of the 13C chemical shift values predicted for structure 14 (assignment given in Ref. [22]) by DFT and NN methods versus
the experimental shift values. The target line Y = X is shown. The coordinates of some points are shown in frames where the first value designates the
experimental shift and the second represents the calculated value. The regression parameters are R2(NN) = 0.551, R2(QM) = 0.538, rms(NN) = 5.54 ppm
and rms(QM) = 5.10 ppm.
200 190 180 170 160 150 140 130 120 110 100 90 80 70 60
200 190 180 170 160 150 140 130 120 110 100 90 80 70 60
200 190 180 170 160 150 140 130 120 110 100 90 80 70 60
200 190 180 170 160 150 140 130 120 110 100 90 80 70 60
200 190 180 170 160 150 140 130 120 110 100 90 80 70 60
200 190 180 170 160 150 140 130 120 110 100 90 80 70 60
200 190 180 170 160 150 140 130 120 110 100 90 80 70 60
Exp
13
14
15
16
17
12
Figure 11. Experimental 13C chemical shifts in comparison with the chemical shifts predicted by the NN algorithm for proposed structures 12–17.
between the experimental and predicted shifts. However, it does
not characterize the true quality of prediction. Consequently, the
R2 criterion should not be considered as a measure of intrinsic
prediction precision for a given method. As our experience shows
theaveragedeviation is aneffective and rather reliable criterion for
selection of the most probable structure. The difference between
the DFT- and NN-regression lines can be accounted for systematic
errors in the calculations performedwith the GIAO approximation.
These errors may be different for different molecules, different
versions of the DFT-based programs and for different ranges of
13C NMR spectrum. Figure 10 confirms the conclusion regarding
the chemical shift assignment given in Ref. [22]: both NN and QM
chemical shift predictions indicate that theassignment is incorrect.
As the article doesnot contain anatom-numbering schememaybe
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380
M. Elyashberg, K. Blinov and A. Williams
N
N
N
N
O
O
O
ON
N
N
N
O
O
ON+
N
H
N
N
O ON+
NH
N
N
O
O
N+
N
N
N
O
N
N
N
N
O O
18: C27H23N4O2 20:C27H23N4O219 : C27H23N4O2
21:C27H22N4O2 22:C27H22N4O3 23:C27H22N4O3
Figure 12. Structures suggested in the work.[32] .
some confusion in the carbon atom labeling arose when spectral
information was listed in the article.[22]
Since the authors[22] do not report how the 13C experimental
chemical shifts were assigned to the carbons of all proposed
structures 12–17 (except structure 14), it was not possible
to calculate the linear regressions for the NN-calculated shifts
for all supposed structures. Therefore, we predicted the 13C
NMR chemical shifts for structures 12–17 and then graphically
compared the predicted spectra with the experimental one as
shown in Fig. 11.
The difference between the experimental and NN-predicted
spectra is dramatic for all structures except structure 14.
All incorrect structures could be immediately rejected before
performing QM calculations and the right structure would be
quickly identified if hypotheses were offered by a human expert.
The authors[22] note that ‘an attempt to predict 1H and 13C NMR
shifts values of structure 14 based on additivity rules. . . would
be totally unsuccessful’ because ‘estimation of chemical shifts
according to the additive scheme implemented in the ‘‘estimate’’
utility of CambridgeSoft’s ChemDraw Program[33] gives very poor
prediction of 13C chemical shifts’. With a more appropriate
prediction algorithm,[8,9,34–36] this comment is obviously invalid.
We share the authors’ enthusiasm regarding progress in QM
methods applied to chemical shift prediction. With our results
described above, however, the conclusion that ‘non-empirical
calculations of chemical shifts are very cheap in the sense of
computational costs and most of the researchers can run them
easily on their desk computers (3–5 hper one isomer on aPentium
4 2.8 GHz processor with 512 MB RAM)’ provides a less-than-ideal
situation relative to the use of other computational approaches
for NMR prediction.
The same group of authors[32] reported the application of
a more complex molecule structure elucidation strategy that
was described in their work.[22] A novel organic compound was
investigated by 1D and 2D NMR experiments (DEPT, NOESY,
COSY, HSQC, HMBC, and HMBC 1H–15N). El mass spectra were
recorded on a TRACE MS instrument (Finnigan MAT) and a MALDI
mass spectrum was also obtained. From the MS data a molecular
formula of C27H22N4O3 was established. 2D NMR data analysis
allowed the authors to assemble three fragments with chemical
shifts assigned to 1H, 13C and 15N nuclei. Two quaternary C atoms,
one N atom and three O atoms remained unassigned.
The authors[32] suggested two structural hypotheses (22 and
23), which are both in accordance with the molecular formula
C27H22N4O3 and four other structures (18–21) with a molecular
formulaediffering fromthatdetermined fromtheMSdata (Fig. 12):
To identify the best structure from among the suggestions
18–23, Balandina et al. calculated the 13C chemical shifts for all
candidate structures using QM methods. As a result of statistical
processing of the data, structure 23 was selected as the most
preferable structure since its correlation coefficient of R = 0.996
was the highest in value and the MAD = 5.65 ppm was the
minimum.
We attempted to solve this problem by employing the usual
strategy for the StrucEluc system to elucidate unknown structures
using the FragmentMode. On the basis of spectral data presented
in the article,[32] the program produced the MCD shown in Fig. 13
The atom corresponding to the chemical shift of 157.77 ppm
was introduced with the property sp2/not defined, while the
atom corresponding to 117.38 ppm was assigned the property
of not defined/not defined as the indicated chemical shift can be
observed either for sp2 or sp3 (O–C–O) hybridized carbons. HMBC
connectivities are marked by arrows in Fig. 13.
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Generation and verification of structural hypotheses
CH2
38.33
H2C40.92
CH2
44.18
CH261.63
CH
115.82
CH
117.31
HC
121.89
C
122.16
CH
126.91
C
129.71
C
154.90
C
157.77
N
N
N
C
117.38
CH
127.30
HC
127.30
HC
127.85
CH
129.34
CH
129.34
C
132.72
C
143.70
CH
128.77
HC
128.77
CH
129.16
CH
129.16
HC
129.94
C
131.61
C
144.01
N
O
O
O
C
A B
Figure 13. The molecular connectivity diagram containing the three fragments derived by Balandina et al.[32] The arrows denote HMBC correlations.
N
N
N
N
O
O
O
dI(13C): 2.740
dN(13C): 2.278
1
NN
NNO
O
O
dI(13C): 3.310
dN(13C): 3.747
2
N
N
N
N
O
O
O
dI(13C): 3.535
dN(13C): 4.208
323
Figure 14. The output structural file ranked by dN(13C) deviation.
Structure generation accompanied by Structural Filtering was
performed under standard conditions. To reduce the output file,
three- and four-membered cycleswere forbidden, and aGeometry
option was enabled to exclude deliberately ‘ugly’ structures. The
results gave: 411 → 44 → 25, tg = 0.9 s. For all structures,
13C chemical shifts were calculated by NN and incremental
approaches. The first three structures of the ranked file are shown
in Fig. 14.
Comparison of the best structure #1 of the ranked file with
the suggested structures establishes structure #1 as identical to
structure 23. Therefore, structure 23 corresponds to themolecular
formula and the constraints graphically represented in the MCD.
Structure 23 and the largest fragment C depicted in the MCD
contains a chain –N–CH2CH2 –N–, while this fragment is absent
from the structure 22. Structure 22 is possible only if the initial set
of constraints is changed. In this case it wouldmean that the chain
part of the large fragment which is well confirmed by 1H–13C
and 1H–15N HMBC correlations has been determined incorrectly.
There is however no grounds for revision of the mentioned chain.
For structures18–21 all havemolecular formulae differing from
that determined experimentally. Though possible it is unlikely.
In addition structure 19 contains a fragment that contradicts
the side chain of the core fragment C discussed previously.
Structure 20 would show a doublet signal for the carbonyl
group and, consequently, can be rejected for this reason. Finally,
the carbon atom at 154.9 ppm in structure 21 has to be sp3
hybridized and this is impossible. The structural suggestions are
therefore not appropriate. The authors[32] nevertheless discussed
all six structures as part of their methodological analysis in the
publication.
Since structures 18 (C27H23N4O2) and 21 (C27H22N4O2) contain
fragment C we performed the structure elucidation process using
these molecular formulae to obtain all consequences of replacing
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382
M. Elyashberg, K. Blinov and A. Williams
Figure 15. A comparison of the experimental chemical shifts with those
calculated for selected atoms using the NN and QM approaches. The
numbers in brackets correspond to the structure numbers.
these constraints. New MCDs were created and the following
results were obtained:
Structure 18. k = 88, tg = 2.5 s, with structure 18 selected
as the best with dN(13C) = 4.24 ppm. Structure 18 should
be rejected as the deviation is almost twice as large as that
obtained for structure 23.
Structure 21. Fuzzy Structure Generation was run with the
APCT and Spectral Filters switched off since structure 21would
not be generated with these filters switched on.
Result: k = 13826 → 13569 → 271, tg = 61 s. 13C chemical
shifts for the resulting 13 569 structures were calculated using the
incrementalmethod in 77 s. Structure21was again selected as the
best structure with dN(13C) = 4.81 ppm and dI(13C) = 6.07 ppm.
The deviation values are large enough to suggest that, in this
case, structure 21 has been ‘forcibly’ derived from the available
NMR experimental data. It is worthy to note that the predicted
chemical shift for the carbon atom at 154.90 ppm differs from the
experimental value by >70 ppm.
Balandina et al. again compared their resultswithNMRchemical
shift prediction contained within the CambridgeSoft ChemOffice
program. They stated that ‘information on the chemical shifts
for the carbon atom of the N+ = C–O fragment is lacking in
the database of ChemOffice program package. . . Hence, if these
structures were formed in the course of the reaction, they could
not be established in terms of this empirical approach’. Based on
the data obtained for structure 18 the current study showed that
this limitation was not present in our program.[8,15] In spite of the
fact that theexamplesemployed for justificationof amethodology
based on QM NMR calculations seem to be rather weak, we agree
with authors’[32] conclusion that the ‘combined use of modern
2D NMR experiments and ab initio chemical shift calculations is
efficient’. This approach may be the only computational approach
if a molecule contains exotic substructures that are unknown for
a program based on empirical methods of spectrum prediction.
At the same time CASE expert systems supplied with fast and
accurate algorithms for empirical chemical shift prediction can
frequently help the researcher to avoid time-consuming QM
computations.
Selection of the correct structure without using
a CASE application
As shown in previous sections the application of a CASE expert
system allows one to obtain a full set of possible structures for
which all experimental 13C and 1H chemical shifts are assigned
to the atoms composing the structures. Nevertheless, there are
situations when 2D NMR data cannot unambiguously solve a
problem and it is necessary to make a choice between isomers
of very similar structures. In such situations it is obviously
desirable to find the best candidate structure without additional
experimentation, for example X-ray analysis. NMR spectrum
prediction canbeattractive for thispurpose. So, again thequestion
arises: are modern empirical methods of chemical shift prediction
capable of delivering a solution with appropriate confidence?
Here we consider several examples where a solution to a problem
was found using both QM and empirical predictions applied
independently.
Example 1
The structures of two new isomeric quinoxalines, 24 and 25, with
molecular formula C21H13N5O2 were established in the reported
work:[31]
8a
4a
8
5
6
2
3
N
N
6′
5′
7′
4′
7a′
3a′
NH
2′
N
1′′
2′′
6′′
3′′
5′′
4′′
N+
O-
O
24
8a
4a
8
5
7
3
N
N
6′
5′
7′
4′
7a′
3a′
NH
2′
N
1′′
2′′
6′′
3′′
5′′
4′′
N+
O-
O
25
2
Both isomers had almost identical 1H NMR spectra, but different
13C spectra. In order to determine the correspondence between
the spectral data and the structures the authors used 13C
NMR chemical shift prediction using the DFT method. The
authors suggested that the spectra could be attributed to the
corresponding structures (24 or 25) by assuming mutual trends
in the calculated and experimental shifts for atoms which are
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383
Generation and verification of structural hypotheses
R2(NN)=0.985
Database : Proposed Structures
Chemical Shifts (13C) : QM Calc. (ppm) (Current Record) (12 pts)
Chemical Shifts (13C) : NN Calc. (ppm) (Current Record) (17 pts)
155150145140135130
Chemical Shifts (13C) : Value (ppm)
120
125
130
135
140
145
150
155 A
dN=1.45 ppm
R2(QM)=0.969
dQ=7.97 ppm
Figure 16. Correlation plots of the 13C chemical shift values predicted for the structure 24byDFT (circles) andNN (triangles)methods versus experimental
shift values. The target line Y = X is shown.
most sensitive to the position of the –NO2 group. In this case
atoms C-2, C-3, C-4a and C-8awere allocated as themost sensitive.
The trend was discovered by comparing the 13C chemical shifts
calculated by the QM methods with the experimental shifts of
the corresponding pairs of atoms. As a result the experimental
spectrum of substance 1 was related to isomer 25 and spectrum 2
to isomer 24.
The authors stated: ‘If the molecular fragments are simple and
linked by one bond, empirical chemical shift increments can be
exploited to predict the influence of neighboring groups and in
this way to establish the overall structure. However, there are
many cases where fragments are bonded by two or even three
bonds. In such cases simple empirical rules cannot be deduced
to take into account the influence of the vicinal fragments’. We
agree that simple empirical rules can be challenging to apply
successfully for the prediction of accurate chemical shifts in such
highly conjugated systems such as isomers24 and25. However, in
the process of developing our algorithms[13,15] we placed high
emphasis on taking into account the effects of conjugation.
Therefore, the particular problem discussed here was used by
us as an example to challenge our program. We attempted to
establish a one-to-one correspondence between the structures
and spectra using 13C chemical shift prediction performed using
our NN algorithm.
For the 13C spectra of substances 1 and 2 we compared the four
experimental chemical shifts related by the authors[31] to the four
‘representative’ atoms (C-2, C-3, C-4a and C-8a) in both isomers.
These chemical shifts were compared with those calculated
by QM and NN approaches. The initial data are presented in
Table 1.
Table 1. Experimental and calculated chemical shifts in ppm related
to the four carbon atoms of isomers 24 and 25
Exp1 Exp2 DFT 24 NN 24 DFT 25 NN 25
147.56 147.12 141.69 147.13 141.94 148.14
156.97 157.65 149.8 155.22 149.38 154.56
143.78 144.87 136.75 145.01 135.92 143.29
141.33 140.12 132.29 138.8 133.17 143.3
Table 2. Results of comparison of four experimental chemical shifts
taken from each of the two spectra with corresponding calculated
chemical shifts
Spectra DFT 24 NN 24 DFT 25 NN 25
1 R2 = 0.9746 R2 = 0.9428 R2 = 0.9755 R2 = 0.9711
SE = 1.46 SE = 1.99 SE = 1.38 SE = 1.11
2 R2 = 0.9719 R2 = 0.9785 R2 = 0.9497 R2 = 0.9149
SE = 1.54 SE = 1.22 SE = 1.97 SE = 1.91
Using these data we calculated the R2 and standard errors
(SE) for all eight combinations of spectra and structures. In
other words we checked how each of the spectra 1 and 2
correlates with structures 24 and 25. The results are shown in
Table 2.
The table shows that according to both methods of spectrum
prediction, the chemical shifts of isomer 24 correlate more
strongly with spectrum 2, whereas the chemical shifts of isomer
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384
M. Elyashberg, K. Blinov and A. Williams
Figure 17. The correlation plots of 13C chemical shift values predicted for structure 25 by DFT (circles) and NN (triangles) methods versus experimental
shift values. The target line Y = X is shown.
25 correlate with spectrum 1. This agrees with the conclusion
made by the authors.[31] Fig. 15 demonstrates that the most
important chemical shifts calculated using the NN approach are
closer to the experimental values that those obtained by the QM
calculations, while both approaches are capable of revealing the
general trend.
Figures 16 and 17 allow us to compare the accuracy of
chemical shift prediction performed by both methods. It is
evident that the precision of chemical shift prediction by the
NN method provides the possibility to utilize calculated 13C NMR
spectra of large enough conjugated molecules which contain
a significant number of heteroatoms. It should be noted that
the NN prediction of 15N chemical shifts suggests that the
nitrogen atom in the position meta to the NO2 group in isomer
24 will have a chemical shift equal to ∼320 ppm, while a
chemical shift ∼303 ppm is expected for the nitrogen atom
in the para-position. It is predicted that for isomer 25 both
N atoms would have close chemical shifts near 315 ppm. We
expect that these spectral features would also be very useful for
confirmation of the spectral assignments made for isomers 24
and 25.
Example 2
Barone et al.[23] investigated the possibility of structure validation
of natural products by the QM GIAO calculations of 13C NMR
chemical shifts. We selected two examples given in this work
where the analyzed structures are absent from the ACD/Labs
database and consequently the results of empirical NMR spectrum
prediction were not influenced.
Different groups of researchers suggested the following
structures and chemical shift assignments for a natural product
magnolialide:
41.90
126.30
77.70
128.90
27.00
33.20
23.00
49.60
38.10
83.10 139.00
170.40O
CH2
118.60
O
CH3
19.60
OH CH3
18.40
33.20
126.30
41.90
128.90
27.00
77.70
23.00
49.60
38.10
83.10
139.00
170.40O
CH2
118.60
O
CH3
18.4
CH3
19.60
HO
26 27
33.20
27.00
139.00
49.60
126.30
77.70
38.10
83.10 41.90
23.00
O 128.90
170.40
O
CH2
118.60
H3C
18.40
H
H3C19.60 OH
28
It was experimentally established that structure 26 was the
correct structure. GIAO-based chemical shift calculation allowed
authors[23] to confidently reject structure 28. In spite of the
similarity in plots showing the differences between experimental
and predicted shifts for structures 26 and 27, it was found that
these differences were slightly larger for 27. This observation,
together with the correlation coefficient, led to the assignment of
structure 26 to magnolialide. In the article,[23] all calculations were
performed with and without chemical shift scaling, so the results
can be compared.
The authors noted that they could discriminate between and
assign the chemical shift values δ = 128.90 and 126.30 ppm
for two of the carbon nuclei which had not been unequivocally
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Generation and verification of structural hypotheses
Table 3. Statistical parameters calculated for structures 26–28
26 27 28
R2(QM) 0.9975 0.9925 0.9844
R2(NN) 0.9975 0.9931 0.9944
dQ, ppm 1.82 3.51 4.99
dN, ppm 2.06 3.32 3.36
assigned previously. The scaled (29) and not scaled (30) chemical
shifts of structure 26 are shown below:
44.90
131.50
79.80
131.30
24.70
32.90
23.80
49.00
37.50
82.00 138.60
165.10O
CH2
117.80
O
CH3
17.60
OH CH3
18.00
39.60
1 31. 10
72.40
133. 40
27.20
34.60
24.70
44.50
36.50
75.00 138.70
166.20O
CH2
125.70
O
CH3
23.30
OH CH3
21.90
29 30
We see that the scaled chemical shifts for the corresponding
atoms are almost the same (29, 131.3 and 131.5, bold), while
there is a difference for the non-scaled set of chemical shifts (30,
133.4 and 131.1, bold). The problem concerning which chemical
shifts should be used for checking assignments likely careful
investigation.
The results of 13C chemical shift prediction for structures
26–28 by NN and DFT approaches are shown in Table 3, as
well as in Figs 7S–9S (see Supporting Information) where plots are
computed for both methods of prediction. For comparison scaled
chemical shifts were used as these are closer to the experimental
values.
Table 3 andFigs 7S–9S show that bothmethodsprovide almost
the same accuracy for chemical shift prediction. Correct selection
of the right structure is provided not only by R2 values, but
by the average deviations dN and dQ. In accordance with our
experiences examining hundreds of structures elucidated using a
CASEapproach,[18] thedifferencesbetweentheaveragedeviations
calculated for structures 26–28 allow us to confidently state that
structure 26 is indeed genuine.
Example 3
Another example considered by Barone et al.[23] is the case when
predicted 13C chemical shift values for the correct and incorrect
structures are very similar. The structures are shown as 31, the
correct structure, and 32, the incorrect structure.
133.20
130.00
128.10
27.50
125.20
31.10
154.40
126.60
107.40
127.80
O
141.60
116.50
CH3
19.50
CH3
14.00
CH3
11.30
133.20
130.00
27.50
31.10
125.20
128.10
154.40
126.60
107.40
127.80
O
141.60
116.50
CH3
19.50
CH3
14.00
CH3
11.30
31 32
The incorrect structure (32) differs from the correct structure
(31) only by the position of a double bond. The authors conclude
that neither the chemical shift value, nor the δ analysis, allows
an unambiguous assignment. We were interested to compare the
predictions of both QM and NN approaches for these very similar
conjugated structures. The results are presented below and in
Figs 10S–11S (Supporting Information):
Structure 31: R2(QM) = 0.9988, R2(NN) = 0.9991, dQ =
1.56 ppm, dN = 1.64 ppm
Structure 32: R2(QM) = 0.9980, R2(NN) = 0.9982, dQ =
2.05 ppm, dN = 2.18 ppm
The regression plots and parameters characterizing the quality
of correlationcalculatedbybothmethodsareverysimilar,butboth
methods indicate the correct structure and again the differences
in average deviations (0.5 ppm) for both structures are acceptable
in terms of confirming the choice made.
The combined application of empirical and non-empirical
methods of chemical shift assignment
BagnoandSaielli[21] publishedan interestingoverviewofadvances
in quantum-chemical prediction of NMR spectra and their
parameters.AsanexampleofNMRspectrumpredictionperformed
for natural products, they reported a computational study of the
molecule of nimbosodione 33.
10
5
1
4
2
3
8
7
9
6
13
14
12
11
CH318
H3C19
CH320
O
15
OH
16
21
O
17
CH322
33
Compound 33 was originally isolated and identified by Ara
et al.[44] from spectral data, but as a result of the total synthesis of
nimbosodione and careful analysis of its NMR spectra Li et al.[45]
showed that the original NMR spectral data and their assignment
were incorrect. Even though Li et al.[45] measured the 1H and
13C NMR spectra of nimbosodione accurately, they failed to
complete a new spectral assignment. Bagno et al.[21] calculated
the 1H and 13C NMR chemical shifts of structure 33 using a DFT
approach and clearly showed that the spectral assignment and
chemical shifts of several definite atoms reported by Ara et al were
incorrect. The absence of a correct spectral assignment prevented
the authors[21] from comparing the predicted and experimental
chemical shifts.
In order to allow this we performed a search in the ACD\Labs
NMR Database[8] for structures having the framework similar
to that of nimbosodione. The database contains more than
290 000 structures with chemical shifts assigned to both carbon
and hydrogen atoms. Five structures were found as a result of
the search. These structures (ID 2–6) and their assigned 13C
chemical shifts are presented in Fig. 18. Comparison of the found
structures with the nimbosodione structure allowed us to assign
the chemical shifts of the compound under investigation (ID 1)
Magn. Reson. Chem. 2009, 47, 371–389 Copyright c© 2009 John Wiley & Sons, Ltd. www.interscience.wiley.com/journal/mrc

386
M. Elyashberg, K. Blinov and A. Williams
38.53
48.45
37.40
33.24
18.56
41.32
123.10
197.40
164.24
35.69
117.64
131.35
166.19
112.79
CH3
32.58
H3C21.26
CH3
22.76
O
OH
204.41
O
CH3
26.43
1 (ID:1) Nimbosodione
38.24
49.77
37.92
33.22
18.96
41.47
123.58
197.97
157.17
36.02
133.58
126.23
160.78
109.76
OH
26.88
CH3
22.37
CH3
22.37
CH3
24.74
O
H
CH3
32.37
H3C21.19
2 (ID:2)
37.10
49.61
37.91
33.33
18.93
41.38
127.53
199.34
151.96
36.03
124.02
130.80
160.01
109.62CH3
23.20
H
OH
CH3
15.35
CH3
32.62
H3C21.42
O
3 (ID:3)
38.00
49.00
35.90
37.70
24.00
79.80
155.60
125.30
35.30
197.60
104.00
162.60
129.80
123.60
H3C23.40
H
H3C15.60
CH3
27.50
O
170.80
H3C21.20
O
O
CH3
16.10
O
CH3
55.60
4 (ID:4)
37.90
48.80
36.20
38.80
27.50
78.00
123.80
197.90
155.30
35.50
125.60
135.50104.50
161.60
H3C
14.90
CH3
27.40
H
26.50
CH3
22.35
CH3
22.35
O
H3C23.20
HO
H3C55.30
5 (ID:6)
39.30
48.90
42.80
34.60
68.70
46.20
155.00
123.50
35.60
198.40
109.50
159.50
126.90
133.70
CH3
32.40H3C22.00
O
171.10
O
H3C
21.40
H3C23.90
H
O
HO
26.70
CH3
23.02
H3C23.02
6 (ID:7)
Figure 18. The structure of nimbosodione (ID:1) assigned in accordance with the experimental NMR spectra reported by Li et al.[45] The assignments of
carbon atoms of the reference structures (ID 2–6) found in the ACD/NMR DB were used.
Table 4. A comparison of experimental and calculated 13C chemical
shifts for nimbosodione
Atom Exp.[44] Exp,[45] our assignment Calc. QM[21] Calc. NN
C1 37.95 37.4 41.75 36.8
C2 18.90 18.56 23.78 19.38
C3 41.37 41.32 45.41 40.92
C4 33.31 33.24 41.19 33.87
C5 36.03 48.45 39.53 49.38
C6 49.58 35.69 53.63 37.25
C7 198.60 197.4 201.75 197.77
C8 157.08 123.1 128.25 125.46
C9 159.08 164.24 173.26 161.31
C10 33.31 38.53 46.34 38.89
C11 109.62 112.79 117.47 111.48
C12 159.15 166.19 177.21 165.79
C13 157.42 117.64 122.09 119.57
C14 130.78 131.35 139.49 131.98
CI8 15.10 32.58 34.35 29.17
C19 23.22 21.26 23.06 26.49
C20 21.31 22.76 25.07 27.53
COCH3 32.59 26.43 28.07 29.48
COCH3 198.62 204.41 212.84 205.42
as shown in Fig. 18. To check the assignment, both the 1H and
13C chemical shifts of nimbosodione were calculated using an NN
approach.[15]
The two sets of both old and new assigned experimental 13C
chemical shifts and the corresponding values calculated by DFT
and NN approaches are collected in Table 4.
Statistical analysis of the data gave the following average
chemical shift deviations and R2 values for the old and new
assignments:
(1) Oldassignment – R2(DFT) = 0.979;R2(NN) = 0.981;d(DFT) =
10.48 ppm, d(NN) = 7.87 ppm.
(2) New assignment – R2(DFT) = 0.994; d R2(NN) = 0.999;
(DFT) = 6.26 ppm, d(NN) = 1.72 ppm.
Both methods of chemical shift calculation provide evidence
that the old nimbosodione assignment is incorrect. The old (34)
and new (35) measured chemical shifts and their assignments are
shown on structures 34 and 35.
33.31
36.03
37.95
33.31
18.90
41.37
157.08
198.60
159.08
49.58
157.42
130.78
159.15
109.62
CH3
15.10
H3C23.22
CH3
21.31
O
OH
198.62
O
CH3
32.59
38.53
48.45
37.40
33.24
18.56
41.32
123.10
197.40
164.24
35.69
117.64
131.35
166.19
112.79
CH3
32.58
H3C21.26
CH3
22.76
O
OH
204.41
O
CH3
26.43
34 35
The difference between the regression plots calculated for
the both new and old assignments can be visually evaluated
from Figs 19 and 20. For the old assignment both methods
of chemical shift prediction show significant scattering of
the calculated chemical shifts and a significant deflection of
both plots from the target line. The application of both
methods of chemical shift prediction in combination with the
data stored in a database containing structures accompanied
www.interscience.wiley.com/journal/mrc Copyright c© 2009 John Wiley & Sons, Ltd. Magn. Reson. Chem. 2009, 47, 371–389

387
Generation and verification of structural hypotheses
Figure 19. Correlation plots of 13C chemical shift values predicted for the new nimbosodione assignment by DFT (circles) and NN (triangles) methods
versus experimental shift values. The NN-regression line almost coincides with the target line Y = X.
Figure 20. Correlation plots of 13C chemical shift values predicted for the old nimbosodione assignment by DFT (circles) and NN (triangles) methods
versus experimental shift values. Both methods of chemical shift calculation show significant scattering of the calculated chemical shifts and significant
deflection from the target line.
by their assigned NMR spectra allowed us to confidently
determine full chemical shift assignment which was previously
impossible.
Experimental
All calculations were performed on a PC (OS Windows 2000, SP4)
with a 2.8 GHz processor and 2 GB of memory.
Conclusions
The elucidation of chemical structures from spectral data is one of
the primary applications of molecular spectroscopy. Nowadays a
combinationof 1D and2DNMRdata is used as theprimarydata for
this purpose. The two most important stages in solving a structure
elucidation problem are the creation of structural hypotheses
from the spectral data and verification of the hypotheses by
Magn. Reson. Chem. 2009, 47, 371–389 Copyright c© 2009 John Wiley & Sons, Ltd. www.interscience.wiley.com/journal/mrc

388
M. Elyashberg, K. Blinov and A. Williams
chemical shift prediction. When conventional methods are used
the structural hypotheses are derived by the researcher. Due to
the biases of the investigators different researchers can suggest
different structures. One consequence of this is that articles very
frequently appear where previously suggested structures have
been revised.
The selection of the right structure is usually attained by using
chemical shift prediction for all suggested structures and the best
structure is determined by structure ranking in an ascending
order of deviation between the experimental and predicted
NMR spectra. Until recently, empirical methods of NMR spectrum
prediction were used, namely fragment-based, incremental and
NN algorithms.[1] During the last decade it was shown that the
GIAOoption of aQMDFT approximation could also be successfully
used for this purpose.
This article considered a series of examples where several
possible structures were derived from the NMR data by the
investigators. When 2D NMR data were available we used the
expert system Structure Elucidator[16,17] for the generation of
structural hypotheses, and the best structures were distinguished
by empirical methods of chemical shift prediction implemented
into the system. Results were comparedwith structures suggested
by one or more groups of researchers and with the results of
the most probable structure selection obtained when the QM
methods were employed.
This work has shown that a systematic approach based on CASE
principles allowed us to determine all structures which do not
contradict the experimental data: the 1D and 2D NMR spectra
and the molecular formula. Genuine structures are distinguished
using a procedure of ranking structures in an ascending order of
deviation between the experimental and calculated NMR spectra.
Erroneous structures suggested by other researchers are also
generated and are ranked lower in the ordered output file if
the structures do not contradict the initial set of constraints. The
programautomatically rejects structures suggestedby researchers
that cannot be considered as consistent with the initial data. We
believe that our observation that average chemical shift deviations
found by our NN approach (or incremental one) are frequently
less than ones found by QM approach which can be explained
in the following way: the NNs are trained using experimental
NMR spectra which were recorded from molecules that likely
exist in the most probable spatial configurations or in ‘average
conformations’. As a result the chemical shifts calculated by both
methods are close for rigid structures and can also be close for
flexible molecules.
When QM methods are used for structure elucidation it
is desirable to reduce the set of structures as much as
possible to prevent superfluous human labor and computational
expenses. Minimization of a set of candidate structures and
justification of structural hypotheses is achieved by application
of Structure Elucidator. We conclude that the optimal way
to solve the spectrum-structural problem is the creation of
structural hypotheses using a 2D NMR-based expert system and
revealing the most probable structure(s) by empirical methods
of chemical shift prediction. For additional verification of the
preferred structures the application of QM prediction methods is
very useful. Moreover, non-empirical methods can play a decisive
role if the verified structures contain fragments which are absent
from the database utilized for training the empirical methods of
prediction. If 2D NMR data are not available then the application
of fast but accurate incremental and NN based algorithms[13,15]
for preliminary probability estimation of each structure suggested
by a researcher can be extremely helpful. We suggest that a
systematic approach based on an expert system application for
structure elucidation from NMR data is the most practical and
rational way for approaching the problem. We believe that the
most convincing evidence of the effectiveness of the QM method
as a tool for molecular structure elucidation could be examined if
thesemethodswere compared to the 2–3 top structures of output
files produced by an expert system such as Structure Elucidator.
Supporting information
Supporting information may be found in the online version of this
article.
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