219
Research Article
Received: 23 October 2009 Revised: 22 December 2009 Accepted: 30 December 2009 Published online in Wiley Interscience: 27 January 2010
(www.interscience.com) DOI 10.1002/mrc.2571
Empirical and DFT GIAO quantum-mechanical
methods of 13C chemical shifts prediction:
competitors or collaborators?
Mikhail Elyashberg,a Kirill Blinov,a Yegor Smurnyy,a Tatiana Churanovaa
and AntonyWilliamsb∗
Theaccuracyof 13Cchemical shiftpredictionbybothDFTGIAOquantum-mechanical (QM)andempiricalmethodswascompared
using 205 structures for which experimental and QM-calculated chemical shifts were published in the literature. For these
structures, 13C chemical shifts were calculated using HOSE code and neural network (NN) algorithms developed within our
laboratory. In total, 2531 chemical shifts were analyzed and statistically processed. It has been shown that, in general, QM
methods are capable of providing similar but inferior accuracy to the empirical approaches, but quite frequently they give
largermean average error values. For the structural set examined in this work, the followingmean absolute errors (MAEs) were
found: MAE(HOSE) = 1.58 ppm, MAE(NN) = 1.91 ppm and MAE(QM) = 3.29 ppm. A strategy of combined application of both
the empirical and DFT GIAO approaches is suggested. The strategy could provide a synergistic effect if the advantages intrinsic
to eachmethod are exploited. Copyright c© 2010 JohnWiley & Sons, Ltd.
Supporting information may be found in the online version of this article.
Keywords: NMR; 13C NMR; chemical shift prediction; GIAO; DFT; HOSE code; neural nets
Introduction
Different methods of 13C NMR spectrum calculation have been
developed over the years to provide a reliable choice for the
most probable structural hypothesis, assist in the process of
spectral signal assignment and to aid in the determination
of stereochemistry for complex organic molecules. The first
prediction algorithmswere basedon additive rules and referred to
as an incremental method. They were intended for the empirical
prediction of 13C NMR chemical shifts and implemented in a
series of programs.[1–4] The programs[5–9] utilizing a fragmental
approach and HOSE codes[10] as well as efficient artificial neural
net algorithms (NN) were developed.[11,12] These algorithms are
based on empirical methods, run fully automatically and require
no user intervention. As the programs were required by expert
systems for the purpose of computer-aided structure elucidation
(CASE),[13] they were implemented into the most advanced CASE
systems.[14–16]
Automated chemical shift prediction methods are under
constant improvement.[17–19] Recently, it has been shown[18] that
programs based on NN algorithms and additive rules are capable
of predicting 13C chemical shifts for diverse classes of organic
molecules with a mean absolute error (MAE) value of 1.6–1.8 ppm
andataspeedof6000–10 000shiftsper second.Programsutilizing
HOSE codes[7,9] provide similar or better accuracy. This approach
alsoprovides facilitieswhich showall reference structures involved
in a particular chemical shift calculation for a given atom. Visual
analysis and comparison of atom environments in a reference
structure and in the structure under investigation can be used
to understand how the chemical shift was calculated. The
shortcoming of these programs is that they are not very fast with
the prediction speed varying between several seconds and tens
of seconds depending on the size and complexity of a chemical
structure.
Thepredictionof 13Cchemical shiftsusingquantum-mechanical
(QM) methods has become the focus of many researchers.
There is extensive literature devoted to the development and
application of different QM approaches. The discussion of all
approaches is beyond the scope of this article which is focused
on the GIAO approximation of the DFT approach which has been
increasingly applied to NMR spectral calculations. The reason for
wide applicability of the GIAO DFT calculations is the relatively
low computational costs and the potential possibility to provide
high enough accuracy to solve many problems for organic and
analytical chemistry. Almost all practicing chemists use different
modifications, most frequently the B3LYP functional variant of this
method, when a QM prediction seems necessary. The important
advantage of this approach is that it takes into account electron
correlation effects. Additional consideration is given to electron
correlation by perturbation theory. The calculation of shielding
constants at MP2 level (perturbation theory of second order) is
available,but thesecomputationsare tootime-consumingandthis
is the reason why they are applied only to small molecules. There
is an N3 dependence in computational time for the DFT approach
and N5 for MP2, where N is the number of basis functions. The
∗ Correspondence to: AntonyWilliams, Royal Society of Chemistry, USOffice, 904
Tamaras Circle,Wake Forest, NC 27587, USA. E-mail: tony27587@gmail.com
a Advanced Chemistry Development, Moscow Department, 6 Akademik Bakulev
St, 117513 Moscow, Russian Federation
b Royal Society of Chemistry, US Office, 904 Tamaras Circle, Wake Forest, NC
27587, USA
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220
M. Elyashberg et al.
Hartree–Fock method is not very computationally expensive but
it also does not take into account the electron correlation effects
so much larger errors in predicted chemical shifts are expected to
be associated with the Hartree–Fock method than to the B3LYP
method when electronegative and heavy atoms are present in a
molecule. Therefore, theGIAODFT-basedmethodsof 13C chemical
shift prediction will be compared with empirical methods in our
article. The ‘QM’abbreviationused in this article specifically implies
the DFT GIAO approximation.
During the last decade, many publications were devoted to the
13C chemical shift prediction of organic molecules using the GIAO
approach.[20–38] It is possible to distinguish the following goals of
these works:
• Search for the most successful combinations of density
functionals and basis sets (calculation protocols) capable
of providing a prediction of geometry and chemical shifts
for sets of organic molecules characterized by structural
diversity[20–22];
• Search for appropriate calculation protocols leading to accept-
able predicted chemical shift values for a given compound or
class of compounds[23–25];
• Detailed investigation of the structural and electronic proper-
ties for a singlemoleculeor a seriesof selectedmolecules[26–28];
• Selecting the most probable structural hypothesis in the
process of molecular structure elucidation[29–38] and, once
the genuine structure is determined, choosing its preferable
stereochemical configuration.
There are a lot of examples demonstrating that successfully
chosen GIAO calculation protocols lead to close coincidence
between the predicted chemical and experimental shifts. It is
rather common that the functionals and basis sets selected for
geometryoptimizationdiffer fromthoseused for thechemical shift
calculation which hampers guessing the best protocol. Attempts
have been made to select an optimum protocol that fits for the
purposeof 13C calculation forboth rigidandflexiblemolecules. For
instance, Cimino et al.[20] tested about 50 protocols and concluded
that the best prediction of the experimental 13C values is obtained
at the mPW1PW91 level using the 6-31G(d,p) basis set both for the
geometry optimization and chemical shift calculation.
Nevertheless, the search for new approaches leading to
improved calculation accuracy continues. Recently, for instance,
Sarotti and Pellegrinet[39] suggested using for GIAO-based 13C
chemical shift calculation a multi-standard method (MSTD). When
the MSTD approach is employed, two reference compounds
should be used: (i) methanol – for the prediction of chemical
shifts of sp3-hybridized carbon atoms and (ii) benzene – for
sp and sp2-hybridized ones. The authors concluded that the
mPW1PW91/6-31G(d) protocol constituted a level of theory that
provides maximal reliability and MAE values around 1.5 ppm at
minimal computational cost when applying the MSTD approach.
This approach looks attractive, and requires further investigation
and testing.
Accessibility to programs performing QM calculations encour-
aged non-specialists in quantum chemistry to use them for the
interpretation of different experimental data. Some authors[40]
treat the GIAO chemical shift calculation as an almost routine
method that can be easily utilized by organic chemists. However,
the scattering of observed chemical shift MAE values found by dif-
ferent researchers is evidence that such generalities are not borne
out in practice. Theoreticians developing QM-based methods of
chemical shift calculations[41] note that ‘using to full advantage
these (GIAO) interpretative potentialities requires perhaps a larger
dose of theoretical experience’. Experienced researchers also com-
ment that ‘since the quality of the results obtaineddepends on the
functional and basis set used, their choice must be made wisely
and with great attention’. We suppose that creation of an expert
system capable of helping organic chemists to choose the appro-
priate protocol applied to a specific molecular structure could be
useful.
The results of QM 13C NMR shift predictions performed for
organicmoleculesofdifferentchemicalcompositionsanddifferent
classes have been published in many articles. As far as we know,
the results have not yet been generalized, and QM computational
errors determined for a large enough structural set were not
compared with those obtained from the empirical methods. It is
worthy to note that the empiricalmethods of NMR shift prediction
are either almost not mentioned at all in the articles devoted
to QM-based computations of chemical shifts or the accuracy
attained using QM approach is commented on without taking
into account the latest achievements[7–9] in the field of empirical
methods.
Meanwhile, examples of the application of empirical methods
for molecular structure elucidation and the determination of
relative stereochemistry in parallel with QM methods have been
considered.[42–44] The examples show that QM calculations, which
are far more computationally expensive in comparison with
empirical ones, are frequently used in such cases when empirical
shift prediction allows one either to rapidly and reliably find the
correct solution of a problem or to suggest one to three structural
hypotheses to be finally discerned by determining additional
experimental data and theoretical considerations.
In this connection, it would be worthy to cite the following
quotation from Dirac’s recollections[45]: ‘The engineering training
which I received did teach me to tolerate approximations. . . If
I had not had this engineering training, I should not have had
any success with the kind of work that I did later on. . . Engineers
were concerned onlywith getting equationswhichwere useful for
describingnature. Theydidnotverymuchmindhowtheequations
were obtained. Once they got them they proceeded to use them
with their slide rules, andget resultswhichwere necessary for their
work. And that led me of course to the view that this outlook was
really the best outlook to have’. We suggest that Dirac’s comment
should be taken into account when choosing an appropriate
method for 13C chemical shift prediction. It is quite probable that
in many cases an ‘engineering outlook’ represented by empirical
methods can be successfully utilized without the additional work
associated with the application of QM calculations. Speaking
figuratively, it is possible to say that the empirical methods supply
practicing chemistswith a predictive tool thatworks automatically
like an ‘engineering slide rule’.
The necessity of developing ‘engineering approaches’ to
improve the accuracy of NMR chemical shift prediction was also
recognized by theoretical chemists who suggested procedures
for scaling non-empirically predicted chemical shifts[29] or scaling
calculated isotropic tensorsofmagnetic shielding.[46] Aliev et al.[47]
suggested an universal equation for scaling 13C chemical shifts
calculated with the GIAO B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d)
protocol, whichmarkedly reduces MAE values. Scaling procedures
empirically take into accountdifferent effects (electron correlation,
relativistic effects, interaction with solvent, etc.) influencing
calculation accuracy. Reducing prediction errors is the main
purposeof thescalingprocedures. TheMSTDapproachmentioned
above was also developed having in mind the same goal.
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Empirical and DFT GIAO methods of 13C shifts prediction
One may say the non-empirical methods are indeed ‘semi-
empirical’ ones.[40,46] The theoreticians conclude that ‘the choice
of empirically scaled parameters could be mainly determined by
an ‘‘aesthetic drive’’, i.e. owing to the wish to consider apparently
smaller values of the medium average error’.[20]
Inour study,wemadeanattempt tocompare theaccuracyof 13C
chemical shift prediction attained by QM and empirical methods
for a largenumberof organicmolecules. For thisgoal,weextracted
data from over 100 articles in the literature data associated with
QM calculations published by different research groups over the
last decade and compared the results with those obtained for the
same structures using our HOSE code and ANN-based algorithmic
approaches. We have shown that, in general, QM methods are
capable of providing the same accuracy as empirical approaches,
but quite frequently they give larger MAE values, a situation that
can be accounted for by the difficulties associated in selecting the
appropriate calculation protocols. A strategy for the combined
application of both empirical and QM approaches is suggested.
Results and Discussion
Data selection and processing
For our computational experiments, we have found 205 structures
for which both assigned experimental and QM-calculated 13C
chemical shifts were published in the literature. Most of the data
were obtained from the Journal of Molecular Structure, Magnetic
Resonance in Chemistry and other related journals. Only examples
where the 13C experimental spectra were of high quality were
chosen for analysis. At the selection stage, we observed that some
authors[48] used for the evaluation of QM methods experimental
spectra which differed significantly from the available reference
spectra. In such cases, we used the reference experimental 13C
NMR spectra which are present in the ACD/Labs database or in the
Aldrich spectral atlas.[49]
Almost 50% of the structures contained 10 or less carbon
atoms and approximately 85% of the structures contained less
than 20 carbon atoms. This distribution reflects the fact that QM
chemical shift calculations were applied mostly to molecules of
small and modest sizes, and the calculations are applicable to
molecules with 20–30 carbon atoms, a common situation for
natural products. Moreover, 13C NMR prediction for a molecule of
the size and complexity of Taxol has been reported recently.[47]
The compounds were of high enough structural diversity and
included the heavy atoms N, O, S, P, Cl, Br and F.
All structures in the test set were input into the ACD/Structure
Elucidator software.[15] Carbon atoms were associated with both
experimental and QM-calculated 13C chemical shifts according
to the assignment performed in corresponding articles. If the
QM chemical shifts of a structure were computed using several
different protocols, then the best approximation was chosen. In
Structure Elucidator, the structure set under test was included into
a user database (UDB)where all results from the calculations could
be stored. For all structures, 13C chemical shifts were calculated
using ACD/CNMR Predictor[9] employing all available algorithms:
HOSE codes, NN and additive rules (increments, Inc). Before
performing the HOSE-based calculations, the program checked
whether a given structure was present in the ACD/Labs database
(175 000 entries) employed for spectrum prediction. If a structure
was detected in the database, it was excluded from the spectrum
prediction process. For each of the 205 structures, the following
Table 1. Average statistical parameters calculated for the test set of
moleculesa
Method MAE (ppm) SD (ppm) dmax (ppm)
HOSE 1.58 2.55 18.9
NN 1.91 2.79 21.7
Inc 2.15 3.12 22.2
QM 3.29 4.98 28.3
a The total number of chemical shifts was 2531. MAE is calculated by
the summation of absolute errors found for each carbon atom divided
by the total number of shifts.
values were estimated and stored in the user database relative to
the HOSE, NN and QM methods of prediction:
• The experimental and predicted shifts for each individual
carbon atom;
• The differences δexp − δcalc (with their signs) between the
experimental and calculated chemical shifts for each carbon
atom;
• Mean absolute error (MAE);
• Standard error (standard deviation, SD);
• Maximum absolute error (maximum deviation, dmax)
• The regression parameters from linear regression (r, R2, SE,
slope a, intersect b, etc.)
For every structure plot showing the δcalc = δexp line (45
◦
line) and linear regression lines for QM, HOSE and NN shift
predictionswere generated. Utilizing theUDB allows us to access a
routinewhich automatically produces electronic tables containing
comprehensivestatistical anddescriptive information relatedboth
to each structure and to the full structural set. The obtained
statistical data and plots were carefully analyzed. All structures
along with their associated MAE values found by QM, HOSE
and NN shift predictions are presented in Table 1S (Supporting
Information).
Statistical comparison of methods
The quantitative parameters characterizing the accuracy of the
empirical and QM methods of 13C NMR chemical shift prediction
for the set of structures under examination are presented in
Table 1.
The table shows that for the given test set of molecules, the
MAE value obtained for the HOSE-based prediction approach is
less thanhalf thevaluecalculatedwhenQMmethodswereutilized.
MAE(NN) is less than MAE(QM) by a factor of 1.7. An analogous
trend is observed for MAE(Inc) – the fastest method of chemical
shift prediction based on additive rules,[17] while not the most
accurate, also exceeds the QM methods in average precision.
Figures 1 and 2 show a plot of the MAE and maximal deviation
dmax values found by the HOSE, NN and QM methods determined
for every structure.
Visual assessment allows us to conclude that the majority of
MAE values calculated by all three methods are less than 4 ppm,
whereas deviations exceeding 4 ppm were shown mainly for the
QMpredictions. In this case, theQMpredictions also produce large
deviationswith values larger than those delivered by the empirical
methods. The average values of the maximum deviations dmax
are 4.75, 5.15 and 7.40 ppm for HOSE, ANN and QM approaches,
respectively.
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M. Elyashberg et al.
Figure 1. MAEs calculated by the QM, HOSE and ANN methods.
Figure 2. Maximum deviations (dmax) calculated by QM, HOSE and ANN
methods.
Figure 3. A comparison plot of the MAEs established for HOSE, ANN and
QM methods. The last black column means that the MAE(QM) exceeds
8 ppm for 25 structures.
Figure 3 shows a comparison of the errors associated with all
prediction methods.
The histogram shows that 60–70% of the MAE values provided
by the empirical methods are less than 2 ppm and 90% were less
than 3 ppm. The corresponding percentages related to the QM
methods are 45% and 60%, respectively.
Figure 4. A linear regression plot showing the dependence of HOSE-based
predicted chemical shifts versus experimental shifts. The linear regression
equation is δcalc = 0.9991δexp + 0.0199, R2 = 0.9975.
Figure 5. A linear regression plot showing the dependence of NN-based
predicted chemical shifts versus experimental shifts. The linear regression
equation is δcalc = 0.9934δexp + 0.5916, R2 = 0.9970.
Figure 6. A linear regression plot showing the dependence of QM-based
predicted chemical shifts versus experimental shifts. The linear regression
equation is δcalc = 0.9942δexp + 1.0883, R2 = 0.9906.
The results of a linear regression calculation performed for 2531
experimental and predicted 13C chemical shifts are presented in
Figs 4–6.
Comparison of the plots and statistical parameters calculated
for the examined methods shows that all three models are char-
acterized by acceptable quality. However, both visual inspection
and comparison of the linear regression statistical terms shows
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Empirical and DFT GIAO methods of 13C shifts prediction
Table 2. The MAEs corresponding to ring carbon atoms of different
hybridization states
sp3 sp2
CH3 CH2 CH Cq CH CH(ar) C(ar) Cq
Counta 273 459 278 99 59 586 405 188
HOSE 1.51 1.46 1.97 1.34 1.90 1.20 2.05 1.79
NN 1.61 1.79 2.40 1.87 2.61 1.51 2.20 2.46
QM 2.35 1.66 2.61 2.65 2.91 3.64 4.72 5.18
The symbols C(ar) and CH(ar) denote atoms belonging to aromatic
rings.
a Total number of shifts used is 2347 out of 2531.
that the quality gradually decreases in the following order: HOSE
> NN > QM with the QM-based predictions showing the poorest
performance. The HOSE plot practically coincides with the 45◦-
grade line (δcalc = δexp) and is almost coincident with the δcalc
axis zero point, whereas the QM plot is shifted up by 1 ppm,
admittedly a small but notable difference. Larger scattering is
observed in the QM plot in the interval 100–200 ppm indicating
a decrease in the prediction accuracy. As mentioned earlier, Aliev
et al.[47] suggested a universal equation δscalc = 0.95δcalc + 0.3
for scaling the 13C chemical shifts calculated using a GIAO proto-
col B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d) (SHIFTS//GEOMETRY).
The potential application of this equation to the >2500 chemical
shifts calculated by different protocols to improve the average
MAE value was investigated. When scaling was applied, the MAE
increased from 3.29 to 4.77 ppm and the error distribution shifted
to the side of positive axis: the scaled chemical shifts in general
were now underestimated (Supporting Information, Figs 1S–3S)
especially in the region 100–200 ppm. The suggested scaling
equation may thus only be valid when a specific protocol is used.
The results were investigated in more detail specifically
examining the calculated MAE values for various hybridization
states and groups CH3, CH2, CH and quaternary carbons. To
extract statistical significance from the analyzed parameters, atom
types for which there were less than 50 representatives in the
dataset were excluded from consideration. Following this process
produced an atom set belonging only to cyclic structures (Table 2).
This observation is accounted for by the fact that almost all
compounds examined by QM chemical shift predictions were
related to ring systems, mainly to natural products. The atom lists
presented in Table 2 are ordered according to both the number
of attached hydrogen atoms and the type of hybridization (the
ordering also approximately corresponds to increasing chemical
shifts) to ease the investigation of patterns in the values obtained
by QM and empirical methods.
The histogram presented in Fig. 7 allows visual comparison
of the MAE values associated with different atom types. It is
evident that the accuracy associated with the empirical methods
is essentially independent of the carbon atom type. This implies
approximately equal reliability for the calculated shifts across
the full chemical shift scale represented (0–200 ppm). In contrast,
there is adependencebetween theMAEvalues and theatomtypes
observed for QM-calculated points. AmaximumMAE(QM) value of
5.18 ppm is observed for non-aromatic Cq atoms which can be
explained by the influence of substituents attached to quaternary
sp2-hybridized carbons. However, it is also likely that the different
number of shifts for the non-aromatic and aromatic rings [188
for Cq and 405 for C(ar)] leads to the observed difference.
Figure 7. A histogram of the MAEs associated with the corresponding
ring carbon atoms in different hybridization states. The symbols C(ar) and
CH(ar) denote atoms belonging to aromatic rings.
Figure 8. The atom distributions with associated arithmetical differences
between experimental and calculated chemical shifts (δexp − δcalc).
It has been noted[20] that the GIAO approximation of DFT-based
predictions frequently either overestimates or underestimates
the predicted chemical shifts for sp2-hybridized carbon atoms
depending on the calculation protocol used. This observation is
in accord with the data presented here (Fig. 7) for a large number
of shifts (approximately 1240). Figure 7 also clearly shows that
MAE(QM) values increase by a factor of 2 along the chosen plot
order of CH3 to Cq carbon.
It was interesting to learn how the carbon atoms within the
test set are distributed as a function of the differences between
the experimental and calculated chemical shifts (δexp − δcalc). The
correspondingdistributionplots computed for adeviation interval
of ±10 ppm with a summation step of 0.5 ppm are presented in
Fig. 8. The figure shows that the distribution corresponding to
HOSE-based calculations is a near-normal distribution in nature
and characterized by the sharpest peak. The error distribution
for the NN approach is represented by a broad bell-shaped
curve whose maximum is markedly shifted down relative to
the maximum of the HOSE code distribution curve. The shape
associatedwith theQM-distribution appears to be far fromnormal
in nature. It has two additional maxima at ±1 ppm and the
negative wing abates markedly slower than the positive one.
This observation confirms the fact that the QM approach has a
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224
M. Elyashberg et al.
Figure 9. A linear regression plot of HOSE-based predicted 13C chemical
shifts versus experimental shifts for atoms included in the structures listed
in Table 2S.
Figure 10. A linear regression plot of QM-based predicted 13C chemical
shifts versus experiment shifts for atoms in structures listed in Table 2S.
tendency to overestimate calculated chemical shifts when some
frequently employed calculation protocols are used.[20]
Outliers and unusual structures
It was interesting to consider the structures for which the
13C chemical shift prediction by QM and/or empirical methods
produced large MAE values. MAE values of close to 5 ppm
are not rare cases for QM-based calculations (Fig. 3), and the
structures for which MAE >5 ppm obtained at least by one
of the methods were examined. Typical structure-outliers with
their corresponding MAE values and maximum errors dmax are
presented in Table 2S (Supporting Information). Analysis of the
table shows that some large MAE values associated with the QM
predictions relate to the presence of: halogen atoms, heteroatoms
carrying unshared electron pairs and high molecular flexibility.
The contributions from these factors have been discussed inmany
works devoted to QM chemical shift prediction.[20,23,50,51] Figs 9
and 10 show plots of the HOSE- and QM-calculated 13C chemical
shifts versus experimental shifts for all atoms included in the
structures presented in Table 2S, 274 shifts in total.
A comparison of the data presented in Figs 9 and 10 shows
that HOSE-calculated chemical shifts are close to the experimental
values (regression statistics: δcalc = 0.997δexp −0.124,R2 = 0.992),
whereas the QM-calculated shifts are markedly scattered and
the intercept is equal to 5.8 ppm (regression statistics: δcalc =
0.948δexp + 5.804, R2 = 0.931). Among the structures presented
in Table 2S, there are three structures 1–3 (19 S, 22 S and 26 S
in Table 2S) for which MAE(HOSE) >5 ppm. Investigation showed
that the reason was the lack of necessary reference structures in
the database.
It was interesting to learn whether the empirical methods can
be useful even at these conditions [MAE(HOSE) >5 ppm] and how
they act in regard to structures considered in the literature[30] as
unusual.
Structure 1, daphnipaxinin, is a structure suggested by Bagno
et al.[30] to be an example of an unusual molecule which may not
be properly treated using empirical approaches of NMR spectrum
prediction. The assignment for structure 1was performedby Yang
and Yue[52] who were the first who elucidated the structure.
76.00
56.17
N
80.56
17 9.55
52 .90
113.81
147.76
54.7665.01
30.20
111.38
146.70
130.31
207.90 O
41.28
28.97
170.45O
25.95
69.86
O
H3C
H2N
26.08
CH3
34.02
H
H
135.91
134.11
101.04
166.78
132.77
124.00
118.67
138.58
146.61
N+
CH3
53.53
OH
1 2
133.81
147.95
127.25
109.88
HN
165.55
N
H
N
139.78
O
3
This molecule provided an interesting example to test and
challenge empirical methods of 13C chemical shift prediction.
For structure 1, the MAE(HOSE) and MAE(NN) values were
approximately 6.3 ppm and displayed maximum deviations of
dmax(HOSE) = 14.29, dmax(NN) = 17.12 ppm, whereas the QM
calculations predicted the 13C NMR shifts more accurately giving
MAE(QM) = 3.92 ppm. Using the facilities of ACD\CNMR Predictor
to examine the calculation protocol, we determined that the
HOSE code algorithm failed to accurately predict the chemical
shifts for two of the carbon atoms (those resonating at 179.5
and 113.8 ppm) because the data base containing the atoms
with the necessary environments has no reference structures.
Nevertheless, the program offered the chemical shift values of
166.2 and 115 ppm corresponding to those atoms using the NN
algorithms as an approximation.
The main application of chemical shift prediction is to confirm
the correct structural hypothesis during the process of molecular
structure elucidation. Therefore, we investigated whether an
empirical approach can be applicable to the identification of
structure 1 in spite of the low prediction accuracy. The HMQC,
HMBC and COSY data of structure 1 presented in the work[52]
were input into the Structure Elucidator[15] software. The program
automatically detected the presence of non-standard correlations
(NSCs).[53] NSCs are HMBC and COSY correlations whose length
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Empirical and DFT GIAO methods of 13C shifts prediction
Figure 11. The first three structures of the output file ordered in ascending order of dHOSE values. The structure of daphnipaxinin is listed in first position.
exceeds three bonds. Because of the presence of these NSC so-
called ‘fuzzy structure generation’[54] was initialized. Structure
generation options were set which assume the presence of an
unknown number, m, of NSCs having an unknown length in COSY
and HMBC data. The following solution was found at a value
of m = 5: k = 10 456 → 5056 → 2017, tg = 2 m 58 s. In this
representation, k is the number of structures that were generated
(10 456), then stored after the application of some filtering tools
(5056) and finally saved after the removal of duplicates (2017).
The notation tg indicates the CPU time consumed for the process
of structure generation and filtering. According to our general
CASE strategy,[15,55] the final structures were then ranked by dNN
values, the average deviation between the neural net predicted
chemical shifts and the experimental shifts. HOSE code-based
chemical shift predictions were then performed for the first 20
structures of the ranked file and then sorted based on increasing
dHOSE values. Thefirst three structures ranked in ascendingorder of
dHOSE values are shown in Fig. 11. From the figure it is seen that the
suggested structure of daphnipaxinin was distinguished by the
program to be the most probable. At the same time, automated
13C NMR chemical shift assignment agreed with that suggested
by the authors.[30,52] The next two structures have slightly larger
deviations and in addition they contain strained and somewhat
‘exotic’ fragments, which makes them questionable.
The example shows that in spite of the unusual character of the
structure and the large values of the deviations, an ‘engineering
approach’ allows the program to correctly select this challenging
structure from among 2000 candidate structures, though with
very little preference on the closest members of an output file.
Bagnoet al.[30] also testedthemethodofQM-based13Cchemical
shift prediction with other unusual structures which might seem
challenging forempiricalmethods,namelystrychnine,buletunone
(4) and corianlactone ( 5).
H3C H3C
H3CCH3
CH3
OHHO
O
O
O
O
HH
H
H
O
O
O
O
OO
4 5
We found that the empirical 13C NMR prediction for strychnine
gave MAE(HOSE) = 0.61 ppm and MAE(NN) = 1.81 ppm, whereas
the accuracy of the QM-based calculations performed by the
authors[30] was characterized by MAE(QM) = 6 ppm. In respect
to buletunone 4, we have shown earlier[42] that the application
of Structure Elucidator allowed us to confidently identify this
molecule from 2D NMR data with MAE(HOSE) and MAE(NN)
equal to 0.63 and 1.99 ppmcorrespondingly (Bagno et al. reported
MAE(QM) = 5.3 ppm for this structure).
The uncommon nature of the corianlactone structure 5 did not
prevent us from solving this problem using empirical methods
of 13C chemical shift prediction using the StrucEluc system. The
2D NMR data of this compound were taken from the original
publication[56] and input into the Structure Elucidator software.
The following results were obtained: k = 83 → 72 → 65,
tg = 4.7 s. The three best structures in the ordered output file
are shown in Fig. 12.
The structure of corianlactone was confidently identified with
the aid of the StrucEluc software in combination with ACD/CNMR
Predictor. As we demonstrated previously,[43] empirical methods
of 13C chemical shift prediction can also be used for selecting
the preferable configurations from a full set of stereoisomers
associated with a given molecular structure. StrucEluc generated
all 256 stereoisomers of corianlactone, and the most probable
relative configuration, as shown by structure 5, was determined
using HOSE- and NN-based 13C NMR spectrum prediction.
Stereoisomer 5 was ranked as the most likely isomer with
MAE(HOSE) = 2.93 ppm and MAE(NN) = 3.89 ppm while the
MAE(QM) value found for structure 5 using the GIAO approach
was 5.3 ppm.[30]
In a separate study,[51] Bagno et al. carried out QM 13C chemical
shift calculations for structure 6. The MAE(QM) value = 6.83 ppm
and the authors concluded that the QM approach allows 13C NMR
prediction for a polar, flexible molecule in aqueous solution with
a high level of accuracy, comparable to that obtained for less
complex systems.
N
NH
O
O
O
O
P
O
OH
O
O-
6
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M. Elyashberg et al.
Figure 12. The first three structures of the ordered output file resulting from the structure elucidation of the corianlactone molecule (5) using StrucEluc.
Figure 13. Linear regression plots for structure 6 generated from HOSE,
NN and QM methods of 13C chemical shift prediction. The solid line and
black squares are related to QM prediction, the dotted line corresponds to
both HOSE and NN. The HOSE and NN predictions practically coincidewith
the 45◦ line (δcalc = δexp).
The application of empirical methods to structure 6 led to the
following results: MAE(HOSE) = 1.15 ppm, MAE(NN) = 1.75 ppm.
Figure 13 shows the linear regression plots for all three methods,
and the corresponding R2 parameters are: R2(HOSE) = 0.997,
R2(NN) = 0.998, R2(QM) = 0.996.
Analysis of the data shows that the correlation coefficients
are almost the same for all three methods of 13C chemical shift
prediction. The HOSE and NN plots are practically overlapped
with the 45◦ line (δcalc = δexp) while the intercept for the QM-
calculated line is equal to 7.7 ppm [MAE(QM) equal to 6.83 ppm].
A large value of MAE(QM) can frequently arise due to erroneous
calculationof the reference (e.g. TMS) shielding. If, for some reason,
the shieldings of the nuclei within the molecule of interest are
calculated correctly while those of the reference are not, the MAE
valuemaygivean incorrect impression regarding theperformance
of a DFT computational protocol. In this case, a corrected MAE,
CMAE[29] provides a much better description of the performance
of theprotocol. Anerroneous estimationof the reference shielding
is not present in the empirical methods which evaluate directly
the chemical shifts. Therefore, both MAE and R2 are statistically
significant parameters for empirical methods, and the efficiency
of MAE in selecting the most probable structure has been proven
by solving hundreds of problems with the Structure Elucidator
system.
If MAE(QM) (not CMAE) is taken into account (as in the last
example), then the R2 value characterizes only the point scattering
Figure 14. Linear regression plots for structure 2 generated using HOSE,
NN and QM methods of 13C chemical shift prediction. The solid line and
black squares represent the QM prediction. The dotted line corresponds
both to the HOSE and NN predictions. The QM predictions practically
coincide with the 45◦ line (δcalc = δexp).
relative to the regression line but not the real accuracy of the
chemical shift calculation. It is noted[57] that a very high value of R2
can arise even though the relationship between the two variables
is non-linear, so the fit of a model should never simply be judged
from the R2 value.Meanwhile, some researchers qualify the quality
of prediction mainly from the R2 value.
When the capabilities of different methods of chemical
shift prediction are compared, it is desirable to quantify the
difference between the corresponding plots. The better a model
(δcalc = aδexp + b) then the closer the plot should be to the
‘reference’ 45◦ grade line δcalc = δexp. The two parameters
characterizing the proximity of a given linear plot to the reference
line are the intercept b and the angle γ between the reference
line and the regression line. This angle can be calculated using
the equation arc tg(γ ) =(b − 1)/(b + 1). We suggest that the real
difference between the calculated and reference values δcalc and
δexp may be represented more visually if, along with statistical
parameters, the quality of prediction is additionally characterized
by the angle γ .
As an example, the 13C chemical shifts associated with
structure 2 were successfully predicted using the QM approach
accompanied by chemical shift scaling to give MAE(QM) =
2.48 ppm.[58] Empiricalmethodsgave largedeviations:MAE(HOSE)
= 6.11 ppm, MAE(NN) = 5.86 ppm. The linear regression plots
associated with this structure are shown in Fig. 14.
The figure shows that the QM calculations are practically
superimposed on the (δcalc = δexp) line while the HOSE and
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Empirical and DFT GIAO methods of 13C shifts prediction
Figure 15. The first three structures of the ordered output file resulting from the structure elucidation of belizeanolide molecule.
NN plots can be characterized by the angle γ (HOSE) = γ (NN)
= −4◦; both lines project an angle of 41◦ relative to the δexp axis.
It is evident that the signs of the deviations dmodexp = (δexp − δmodel)
will be different at the scale segments situated before and after
the point of line intersection and this may relate to model quality.
For structure 3, shift calculation using both empirical and QM
methods[59] led to large MAE values of 6–8 ppm, which was
associated with significant declinations from the 45◦ degree line.
Synergistic interaction between empirical and non-empirical
methods
Thisworkhasshownthat, inprinciple,bothDFTGIAOandempirical
calculations can be performed with sufficient accuracy to solve
practical problems in organic chemistry. Nevertheless, for the
examined structural set, the average accuracy of QM methods
is 1.5–2 times lower than the accuracy of empirical methods
(Table 1). It isobviousthatempiricalmethodspossess thefollowing
merits: (i) they are fully automatic; (ii) they are fast (prediction
speed is thousandsof shiftsper second); (iii) theyarequite accurate
(MAE = 1.5–1.8 ppm); (iv) there are no limitations imposed by
molecule size. In regards to prediction speed, molecular size and
level of automation QM approaches are inferior to empirical ones
and these limitations, probably, are unlikely to be overcome in
the near future. Accuracy is therefore the main criterion where QM
methods have the potential to complement empirical methods
and, in theory, maybe even surpass them.
Empirical methods are known to suffer from at least one
principal drawback: if the database created for HOSE prediction
or the training set for the neural net algorithm do not contain
specific atoms representing the atom environments existing in
the molecule under investigation, then the empirical methods
can fail to predict the chemical shift of such atoms with sufficient
accuracy. In these situations, QM methods can compensate for
the lack of representative data. However, the problem of accuracy
should be solved to allow QM methods to be considered as a
real analytical tool. We believe that current advances in QM, HOSE
and NN 13C NMR chemical shift prediction allow for the creation
of an efficient strategy for jointly utilizing both empirical and
non-empirical methods to solve actual analytical problems.
The most important task requiring the application of chemical
shift prediction is that of complete structure elucidation, including
stereochemistry. Empirical methods have been successfully used
in this field for many years. Considering the growing capabilities
of non-empirical approaches it is possible to suggest the following
strategy for a combined approach using both methods and, in
theory, deliver a synergistic effect.
Recently,[42] we demonstrated the advantages of a systematic
approach to forming and verifying structural hypotheses. Ac-
cording to this approach, the most efficient strategy consists of
applying theStructure Elucidator expert system for automaticgen-
erationofall (withoutexclusion)conceivablestructuralhypotheses
with their subsequent verification using 13C NMR spectrum pre-
diction. Experience accumulated over the last decade shows[60]
that, in the overwhelming majority of cases, empirical meth-
ods allow the successful sorting of structures using MAE(HOSE)
values and determination of the most probable structure. The
most probable structure is that which satisfies all constraints im-
posed by both the 1D and 2D NMR spectra and has the minimal
MAE(HOSE) value. Generally speaking, this structure fully satis-
fies the partial axiomatic theory formulated regarding the given
spectrum-structural problem.[42] If the MAE(NN) value is also min-
imal for the preferred structure this is considered as additional
support for the selection made. We have observed[60] that if the
difference between the average HOSE deviations  = d(2) − d(1)
found for the second and first structures in the ordered structural
file is >1 ppm then the selected structure is, as a rule, the correct
one. Otherwise, the selected structure should be confirmed with
additional data, both experimental and/or theoretical, including
the application of chemical common sense.
For instance, in the case of daphnipaxinin, the difference in
deviation values between the preferred and second structure is
verymodest: = d(2)−d(1) = 0.13 ppm.The identificationof the
appropriate structure would require additional experimentation
(e.g. NOESY or ROESY data) or alternatively QM-based chemical
shift calculationcouldbehelpful. Thesizeof themoleculecanbean
insurmountable hindrance forQMcalculations. For instance,when
we input into the StrucEluc software the 1D and 2D NMR (HSQC,
HMQC and COSY) data for the recently published[61] molecule,
belizeanolide (C81H32O20), the following solution was obtained:
k = 938 044 → 7845 → 3926, tg = 3 h 9 m.
The three best structures identified by the program from nearly
4000 hypothetical molecules are shown in Fig. 15. The correct
structure was placed in third position. The difference in deviations
d(3) − d(1) is very small −0.08 ppm. Here, the QM 13C chemical
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228
M. Elyashberg et al.
shift calculation is unlikely to be helpful due to the large size of the
molecule. In such a situation only additional experimental data,
chemical knowledge and chemical common sense can help solve
the problem.
If questionable structures ranked first contain some fragment
which seems ‘exotic’ in nature, then it is possible to perform a
preliminary search of this fragment in the database used for 13C
chemical shift prediction. Once it is identified that such a fragment
is not contained within the database then a QM calculation could
be applied to a rationally selected fragment from the molecule
and could be used to deliver reliable chemical shifts which could
then be merged in an appropriate fashion with the shifts which
were calculated by HOSE and NN methods for the rest of the
molecule. Of course, the shifts would be tagged appropriately to
label their underlying prediction algorithm. This approach could
also be used when the calculation protocol facility of the HOSE-
based shift predictor informs the user that it is impossible to
predict the chemical shifts for some atoms due to the absence of
related structures in the database. There are already publications
where fragmental QM chemical shift calculations were utilized to
select or to confirm a structural hypothesis.[35,62]
It should be underlined that the rank-ordered StrucEluc output
file contains structures for which all experimental NMR chemical
shifts are already assigned in accordance with their 2D NMR
correlations. This circumstance significantly simplifies application
of the QM 13C chemical shift prediction for selection of the ‘best’
structure: the first several structures for which the QM calculations
would be employed can be ranked in ascending order ofMAE(QM)
values as is commonly the case when HOSE and NN prediction
approaches are used. An example demonstrating how the fast
NN chemical shift prediction accompanied with bar-graph-based
spectrum comparison allowed avoiding QM calculations was
presented previously.[42] In this case, the correct structure was
easily distinguished visually without utilizing any chemical shift
assignment.
Because the shielding of nuclei resonating in a magnetic field
crucially depends on their 3D coordinates, the calculation of the
mostprobable stereoconfigurationof amolecule followedbyNMR
chemical shiftprediction is a conventionalprocedure formolecular
stereochemistry determination. Nevertheless, empirical methods
of 13C chemical shift calculation have been shown[43] to be useful
for preliminary filtering of the full set of stereoisomers conceivable
for a given chemical structure, as well as for determining the
relative stereochemistry of comparatively rigid molecules by
geometry optimization guided by spatial constraints produced on
the basis of NOESY correlations.[63] Because the time required for
empiricalNMRspectralprediction isnegligibly small incomparison
with that required for QM calculations, it would be useful to
empirically detect a set of the most probable stereoisomers
prior to comprehensive QM-based investigations. A restricted
set of several selected stereoconfigurations could be used as
initial approximations necessary for the purpose of geometry
optimization and theoretically resulting in reduced computational
costs.
We hope that as QM methods for NMR spectrum prediction are
improved and the choice of the appropriate calculation protocol
becomes a user-independent procedure, these methods will be
more readily available for solving different spectrum-structural
problems. A reasonable combination of QM and empirical
approaches should provide a synergistic effect and will make
both approaches more powerful and amenable to be used for
practical purposes.
Computational details
All calculationswere performedusing ACD/NMRpredictor Version
12.00. A personal computer equipped with a 2.8 GHz Intel
processor and 2 GB of RAM and running in the Windows XP
operating systemwas used. All computer programs are an integral
part of the Structure Elucidator expert system. 13C NMR chemical
shift calculations require no intervention from the chemist and are
performed fully automatically.
Conclusions
We have compared the accuracy of 13C chemical shift prediction
achieved by bothQMand empiricalmethods. To achieve this goal,
we extracted from the literature data associated with DFT GIAO
calculations published by different research groups during the
last decade and compared the results with those obtained for the
same structures using HOSE code and NN algorithms developed
within our laboratory. In totally, 2531 chemical shifts associated
with 205 molecules were analyzed. It has been shown that, in
general, QM methods are capable of providing similar but inferior
accuracy to the empirical approaches, but quite frequently they
give largermean average error values. This is accounted formainly
with difficulties in selecting the appropriate calculation protocols
and difficulties arising from molecular flexibility. The data show
that the average accuracy of the QM methods is 1.5–2 times
lower than the accuracy shown by the empirical methods. For
the structural set examined in this work, the following MAEs were
found: MAE(HOSE) = 1.58 ppm, MAE(NN) = 1.91 ppm, MAE(QM)
= 3.29 ppm.
A strategy of combined application of both the empirical
and QM approaches is suggested. The strategy could provide
a synergistic effect if the advantages intrinsic to each method are
exploited. The suggestedstrategy requiresverificationonadiverse
data set and our group welcomes cooperation with theoreticians
interested in such a study. We have >300 problems, all related
to natural products, for which structure elucidation from 1D and
2D NMR spectra has been performed using the StrucEluc system
and using empirical methods for selection of the most probable
structure. These data could provide an interesting dataset for
further informative computational experiments including both
empirical andQM-based methods of 13C chemical shift prediction.
Supporting information
Supporting information may be found in the online version of this
article.
References
[1] J.-T. Clerc, H. A. Sommerauer, Anal. Chim. Acta 1977, 95, 33.
[2] A. Fu¨rst, E. Pretsch, Anal. Chim. Acta 1990, 229, 17.
[3] E. Pretsch, A. Fu¨rst, M. Badertscher, R. Burgin, M. E. Munk, J. Chem.
Inf. Comput. Sci. 1992, 32, 291.
[4] R. B. Schaller, M. E. Munk, E. Pretsch, J. Chem. Inf. Comp. Sci. 1996,
36, 239.
[5] H. Kalchhauser, W. Robien, J. Chem. Inf. Comput. Sci. 1985, 25, 103.
[6] W. Robien, Nachr. Chem. Tech. Lab. 1998, 46, 74.
[7] Modgraph, http://www.Modgraph.Co.Uk/product nmr.Htm.
[8] Upstream Solutions GMBH, http://www.upstream.ch/products/
nmr.html.
[9] Advanced Chemistry Development. ACD/NMR Predictors. Pre-
diction suite includes 1H, 13H, 15N, 19F, 31P NMR prediction.
[10] W. Bremser, Anal. Chim. Acta. Comp. Tech. Optimiz. 1978, 2, 355.
www.interscience.wiley.com/journal/mrc Copyright c© 2010 John Wiley & Sons, Ltd. Magn. Reson. Chem. 2010, 48, 219–229

229
Empirical and DFT GIAO methods of 13C shifts prediction
[11] J. Meiler, R. Meusinger, M. Will, J. Chem. Inf. Comp. Sci. 2000, 40,
1169.
[12] J. Meiler, W. Maier, M. Will, R. Meusinger, J. Magn. Reson. 2002, 157,
242.
[13] M. E. Elyashberg, A. J. Williams, G. E. Martin, Prog. NMR Spectrosc.
2008, 53, 1.
[14] M. E. Munk, J. Chem. Inf. Comput. Sci. 1998, 38, 997.
[15] M. E. Elyashberg, K. A. Blinov, S. G. Molodtsov, A. J. Williams, G. E.
Martin, J. Chem. Inf. Comp. Sci. 2004, 44, 771.
[16] M. E. Elyashberg, K. A. Blinov, S. G. Molodtsov, Y. D. Smurnyy,
A. J. Williams, T. S. Churanova, J. Cheminform. 2009, 1, 3.
DOI:10.1186/1758-2946-1-3.
[17] Y. D. Smurnyy, K. A. Blinov, T. S. Churanova, M. E. Elyashberg, A. J.
Williams, J. Chem. Inf. Model. 2008, 48, 128.
[18] K. A. Blinov, Y. D. Smurnyy, M. E. Elyashberg, T. S. Churanova,
M. Kvasha, C. Steinbeck, B. E. Lefebvre, A. J. Williams, J. Chem. Inf.
Model. 2008, 48, 550.
[19] K. A. Blinov, Y. D. Smurnyy, T. S. Churanova, M. E. Elyashberg, A. J.
Williams, Chemometr. Intell. Lab. Syst. 2009, 97, 91.
[20] P. Cimino, L. Gomez-Paloma, D. Duca, R. Riccio, G. Bifulco, Magn.
Reson. Chem. 2004, 42, S26.
[21] A. Balandina, A. Kalinin, V. Mamedov, B. Figadere, S. Latypov, Magn.
Reson. Chem. 2005, 43, 816.
[22] N. J. R. Eikema Hommes, T. Clark, J. Mol. Model. 2005, 11, 175.
[23] A. R. Katritzky, N. G. Akhmedov, J. Doskocz, C. D. Hall, R. G.
Akhmedova, S. Majumder, Magn. Reson. Chem. 2007, 45, 5.
[24] W. Migda, B. Rys, Magn. Reson. Chem. 2004, 42, 459.
[25] K. W. Wiitala, C. J. Cramer, T. R. Hoye, Magn. Reson. Chem. 2007, 45,
819.
[26] R. Infante-Castillo, S. P. Hernandez-Rivera, J. Mol. Struct. 2009, 917,
158.
[27] M. Karabacak, A. Coruh, M. Kurt, J. Mol. Struct. 2008, 892, 125.
[28] M. Karabacak, M. Cınar, A. Coruh, M. Kurt, J. Mol. Struct. 2009, 919,
26.
[29] G. Barone, L.Gomez-Paloma,D.Duca,A. Silvestri, R. Riccio,G. Bifulco,
Chemistry 2002, 8, 3233.
[30] A. Bagno, F. Rastrelli, G. Saielli, Chemistry 2006, 12, 5514.
[31] A. Balandina,D. Saifina, V. Mamedov, S. Latypov, J.Mol. Struct.2006,
791, 77.
[32] A. A. Balandina, V. A. Mamedov, E. A. Khafizova, S. K. Latypov, Russ.
Chem. Bull. 2006, 55, 2256.
[33] P. Wipf, A. D. Kerekes, J Nat Prod 2003, 66, 716.
[34] K. N.White, T. Amagata,A. G.Oliver, K. Tenney, P. J.Wenzel, P. Crews,
J. Org. Chem. 2008, 73, 8719.
[35] T. A. Johnson, T. Amagata, A. G. Oliver, K. Tenney, F. A. Valeriote,
P. Crews, J. Org. Chem. 2008, 73, 7255.
[36] C. Fattorusso, E. Stendardo,G. Appendino, E. Fattorusso, P. Luciano,
A. Romano, O. Taglialatela-Scafati, Org. Lett. 2007, 9, 2377.
[37] E. Fattorusso, P. Luciano, A. Romano, O. Taglialatela-Scafati,
G. Appendino, M. Borriello, C. Fattorusso, J. Nat. Prod. 2008, 71,
1988.
[38] S. D. Rychnovsky, Org. Lett. 2006, 8, 2895.
[39] A. M. Sarotti, S. C. Pellegrinet, J. Org. Chem. 2009, 74, 7254.
[40] C. A. Franca, R. P. Diez, A. H. Jubert, J. Mol. Struct. THEOCHEM 2008,
856, 1.
[41] V. Barone, P. Cimino, O. Crescenzi, M. Pavone, J. Mol. Struct. 2007,
811, 323.
[42] M. E. Elyashberg,K. Blinov,A. W. Williams,Magn.Reson.Chem.2009,
47, 371.
[43] M. E. Elyashberg,K. Blinov,A. W. Williams,Magn.Reson.Chem.2009,
47, 333.
[44] I. Stappen, G. Buchbauer, W. Robien, P. Wolschann, Magn. Reson.
Chem. 2009, 47, 720.
[45] P. A. M. Dirac, History of Twentieth Century Physics: Proceedings of the
International School of Physics ‘‘Enrico Fermi’’. Course LVII. Academic
Press: London, 1977.
[46] D. B. Chesnut, Chem. Phys. Lett. 2003, 380, 251.
[47] A. E. Aliev, D. Courtier-Murias, S. Zhou,Mol. Struct. THEOCHEM2009,
893, 1.
[48] R. Infante-Castillo, L. A. Rivera-Montalvo, S. P. Hernandez-Rivera,
J. Mol. Struct. 2008, 887, 10.
[49] C. J. Pouchert, J. Behnke,Aldrichlibraryof13Cand1HFT-NMRspectra.
1993.
[50] K. Dybiec, A. Gryff-Keller, Magn. Reson. Chem. 2009, 47, 63.
[51] A. Bagno, F. Rastrelli, G. Saielli, Magn. Reson. Chem. 2008, 46, 518.
[52] S.-P. Yang, J.-M. Yue, Org. Lett. 2004, 6, 1401.
[53] S. G. Molodtsov, M. E. Elyashberg, K. A. Blinov, A. J. Williams, G. M.
Martin, B. Lefebvre, J. Chem. Inf. Comput. Sci. 2004, 44, 1737.
[54] M. E. Elyashberg, K. A. Blinov, S. G. Molodtsov, A. J. Williams, G. E.
Martin, J. Chem. Inf. Model. 2007, 47, 1053.
[55] K. A. Blinov, D. Carlson, M. E. Elyashberg, G. E. Martin, E. R.
Martirosian, S. G. Molodtsov, A. J. Williams, J. Magn Reson. Chem.
2003, 41, 359.
[56] Y.-H. Shen, S.-H. Li, R.-T. Li, Q.-B. Han, Q.-S. Zhao, L. Liang, H.-D. Sun,
Y. Lu, P. Cao, Q.-T. Zheng, Org. Lett. 2004, 6, 1593.
[57] http://www.babylon.com/definition/Multiple regression
correlation coefficient (R2)/English.
[58] M. Szafran, P. Barczynski, A. Komasa, Z. Dega-Szafran, J. Mol. Struc.
2008, 887, 20.
[59] O. Tsikouris, T. Bartl, J. Tousˇek, N. Lougiakis, T. Tite, P. Marakos,
N. Pouli, E. Mikros, R. Marek, Magn. Reson. Chem. 2008, 46, 643.
[60] M. E. Elyashberg, K. A. Blinov, A. J. Williams, S. G. Molodtsov, G. E.
Martin, J. Chem. Inf. Model. 2006, 46, 1643.
[61] J. G.Napolitano,M.Norte, J. M.Padron, J. J. Fernandez,A. H.Daranas,
Angew. Chem. Int. Ed. 2009, 48, 796.
[62] D. Sanz, R. M. Claramunt, A. Saini, V. Kumar, R. Aggarwal, S. P. Singh,
I. Alkorta, J. Elguero, Magn. Reson. Chem. 2007, 45, 513.
[63] Y. D. Smurnyy,M. E. Elyashberg, K. A. Blinov, B. Lefebvre,G. E.Martin,
A. J. Williams, Tetrahedron 2005, 61, 9980.
Magn. Reson. Chem. 2010, 48, 219–229 Copyright c© 2010 John Wiley & Sons, Ltd. www.interscience.wiley.com/journal/mrc