Toward More Reliable 13C and 1H Chemical Shift Prediction: A Systematic Comparison
of Neural-Network and Least-Squares Regression Based Approaches
Yegor D. Smurnyy,† Kirill A. Blinov,† Tatiana S. Churanova,† Mikhail E. Elyashberg,† and
Antony J. Williams*,‡,§
Advanced Chemistry Development, Moscow Department, 6 Akademik Bakulev Street,
Moscow 117513, Russian Federation, and Advanced Chemistry Development, Inc., 110 Yonge Street,
14th Floor, Toronto, Ontario, Canada M5C 1T4
Received July 17, 2007
The efficacy of neural network (NN) and partial least-squares (PLS) methods is compared for the prediction
of NMR chemical shifts for both 1H and 13C nuclei using very large databases containing millions of chemical
shifts. The chemical structure description scheme used in this work is based on individual atoms rather than
functional groups. The performances of each of the methods were optimized in a systematic manner described
in this work. Both of the methods, least-squares and neural network analyses, produce results of a very
similar quality, but the least-squares algorithm is approximately 2-3 times faster.
1. INTRODUCTION
The accurate and robust prediction of NMR chemical shifts
has both practical and theoretical interest. The de noVo
structure elucidation of natural products, the verification of
chemical structures contained within synthetic libraries, and
the potential for enhancing the experience of chemical
education are just a few areas which could derive value from
NMR shift prediction. NMR prediction is now a tool utilized
not only by NMR spectroscopists but also by synthetic
chemists. Contemporary robotic open-access spectrometers
provide convenient access to both 1D and 2D NMR spectra
for chemists to assist in structure verification and elucidation.
1H and 13C 1D spectra are the primary tools utilized by
chemists for structure verification, and the provision of
prediction tools provides reasonable to excellent accuracy
in the quality of NMR prediction (Vide infra) and thereby
provides a means to speed up the analysis of spectra using
a strong basis of prior knowledge. In recent years, the
utilization of NMR chemical shift prediction as an integral
part of an expert system intended for computer-aided
structure elucidation (CASE) has been common. For this
purpose, both 13C and 1H NMR spectral predictions are used
for the identification of the most probable structure (see
review in ref 1 and refs 2 and 3).
Historically, two main classes of algorithms have been
developed: database-based and rules-based prediction algo-
rithms. For the first approach, a large database of chemical
structures with associated chemical shifts is compiled. For
each structure, a descriptor is assigned which reflects its
major structural features. Then, when the database is queried
with the descriptor, similar structures are identified, and the
resulting values are weighted averages of the experimental
data corresponding to these structures. A number of com-
mercial databases and associated prediction software are
currently available including CSEARCH,4,5 ACD/Labs,6 and
SpecInfo7 as well as a publicly available database known as
NMRShiftDB.8 The most popular structure description
algorithm is the Hierarchical Organization of Spherical
Environments (HOSE) code,9 despite its supposed poor
performance with unusual structures and the slow speed of
prediction due to relatively slow database engines.
Another class of algorithm utilizes a database to extract a
set of additivity rules which allow for the rapid calculation
of chemical shift values for atoms of interest. In an ideal
case, these algorithms would perform similarly upon a
diverse set of chemical structures. This approach was
originally suggested in 1964 in the pioneering work of Grant
and Paul10 for the prediction of the 13C chemical shifts of
alkanes. The method was then extended to many different
classes of organic compounds and then also applied to 1H
chemical shift prediction: Reed presented a scheme for the
prediction of chemical shifts in substituted benzenes.11 The
prediction rules published in the literature were later general-
ized in the monograph of Pretsch et al.12 The first computer
program for 13C chemical shift prediction on the basis of
additivity rules was presented by Clerc and Sommerauer.13
Later, Pretsch and co-workers developed programs to provide
fast prediction of both 13C and 1H chemical shifts.14-18
Traditionally, least-squares regression techniques have been
used19,20 to formulate the rules. However, since the 1990s,
there have been increasing efforts by researchers to use neural
networks as an alternative and potentially more flexible and
powerful approach.21-23
Despite decades of intensive research, there are a number
of questions not yet fully addressed in the field of neural
network applications. First, very few research groups (for
example, ref 24) have systematically compared available
approaches such as partial least-squares (PLS) versus neural
networks (NN). Second, many studies23,25-27 focus on a
limited class of compounds. This approach biases the results
due to the lack of structural variability but severely limits
practical applications. Third, we believe that it is necessary
to separate the two parts of an algorithm: (a) encoding a
* Corresponding author e-mail: antony.williams@chemspider.com.
† Advanced Chemistry Development, Moscow Department.
‡ Advanced Chemistry Development, Toronto.
§ Current address: ChemZoo Inc., 904 Tamaras Circle, Wake Forest,
NC-27587.
128 J. Chem. Inf. Model. 2008, 48, 128-134
10.1021/ci700256n CCC: $40.75 © 2008 American Chemical Society
Published on Web 12/05/2007

chemical structure into a numerical input, the number and
nature of the descriptors, the involvement of stereochemistry,
and so forth, and (b) the regression process, either by least-
square methods or neural network methods. These two parts
should be evaluated and compared separately as is discussed
in this work but, to the best of our knowledge, absent in
earlier works.
In this article, we seek to address each of the above-
mentioned issues using 13C chemical shifts as the data for
analysis. We initially optimized the description scheme used
throughout our studies; then, the parameters affecting the
performance of the neural networks were tuned to achieve
optimal performance. We then compared both PLS and
neural networks using one of the largest available databases6
for the purpose of training. Finally, we applied our findings
from our studies for 13C chemical shifts to examine the
performance of 1H chemical shift prediction to demonstrate
the general applicability of our findings.
2. METHODS
2.1. Databases. The carbon and proton chemical shift
databases used in this work are comprised of approximately
2 million 13C and 1.2 million 1H chemical shift values,
respectively. Care was taken to avoid overlap between the
data sets used for NN training and comparison. The training
data set was compiled using experimental data published
from the early 1990s until 2004. Spectral assignments were
taken from articles published in a number of journals,
including J. Org. Chem., Tetrahedron, J. Nat. Prod., and so
forth. During each run, 3% of the data set was randomly
chosen to be used as a test set during training. A comparison
of the algorithms reported in this article was performed using
a completely independent database compiled from data
originally published in 2005 and consisting of approximately
118 000 13C and 116 000 1H chemical shifts.
2.2. Algorithms. The effectiveness of different neural
network configurations was tested using custom scripts
written in the MATLAB programming language (version
6.0.; The MathWorks, Natick, MA) and using the associated
Neural Networks toolbox. The neural network and partial
least-square regression algorithms were then coded using the
Borland Delphi 5.0 environment, Object Pascal, and as-
sembler programming languages. The LAPACK library28 was
used for matrix computations. The detailed mathematical
descriptions of neural network29 and nonlinear regression30
analyses can be found elsewhere. All programs were
executed on Intel PC workstations running under the
Windows XP operating system using CPUs operating with
clock speeds of 1.8-3.2 GHz and 1-4 GB of memory
installed.
All of the neural networks tested in this work include an
input layer, one to four hidden layers, and a single output
neuron. Logistic or hyperbolic tangent activation functions
were used. Networks were trained using the standard back-
propagation algorithm.29 Weights were updated after process-
ing each pattern with both the training speed and the
momentum set to 0.5. Neural network input and output values
were assumed to be within the interval of [0;1]. The tri-
linear function shown in Figure 1 was used to map an
arbitrary interval onto [0;1]. This choice is due to the
simplicity and robustness of the function. Simultaneously,
this tri-linear function allows the algorithm to cover a wider
interval than a simple linear function. Such a tri-linear scaling
scheme allows the prediction of chemical shift values up to
four standard deviations away from the mean value, which,
assuming a Gaussian distribution of values, accounts for
99.9% of the data.
For the network inputs xi, the corresponding values of an
average of aaver ) xaveri, and the associated standard deviations
were calculated using all available training patterns in which
the input has a nonzero value. The values for the chemical
shifts were calculated using all available training patterns
subsequently used for reverse transformation from the [0;1]
output to a chemical shift value in parts per million delivered
to the user.
2.3. Data Encoding. To encode a chemical structure into
a numerical representation, an atom-based scheme was used
as shown in Figure 2.
The environment surrounding an atom is divided into
spheres, each including all atoms and separated from the
center by a definite number of covalent bonds. In our work,
we typically account for the nearest six spheres or less. Every
atom within a sphere is classified into one of the predefined
atomic classes described in Table 1. The scheme was inspired
by earlier works in this field.22,24 We have added extra
features such as a more complete list of nontypical atoms
and the ability to take solvents into account in the prediction
algorithm.
Some additional parameters improve chemical shift pre-
diction for atoms included in conjugated systems. For the
purpose of this work, we define a conjugated system as atoms
forming conjugated double bonds plus all of their immediate
neighbors. If a central atom participates in a system, then
all other atoms in the system are marked with a special flag.
For example, in the molecule shown in Figure 2, the central
atom marked as number 1 is part of a conjugated system.
As a result, atoms 3, 4, 9, and 12 (the diene system) and
their neighbors 1 (the center), 13, and 15 will be marked.
Note that atoms 6, 7, 16, and 17 are not marked since they
Figure 1. Tri-linear function used to map the input values onto
the [0;1] interval utilized by our neural networks. aaver is the mean
value of the a variable, and ó is the standard deviation.
Figure 2. Encoding of the atom environment. The three nearest
spheres are marked as cyan, green, and yellow circles, and the
Roman numerals denoting the number of each sphere are shown.
Atom no. 1 is the central atom. The blue numbers are assigned
arbitrarily and serve as references (see the text for more details).
MORE RELIABLE 13C AND 1H CHEMICAL SHIFT PREDICTION J. Chem. Inf. Model., Vol. 48, No. 1, 2008 129

are separated from the central atom by two ó bonds.
Additional flags were also used to take into account double-
bond stereochemistry. If we use atom 4 as the central atom,
then atoms 13 and 15 both lie in the third sphere and both
have equivalent descriptors. The addition of stereo descriptors
allows these atoms to be distinguished. Atom 15 lies on the
same side as the atom of the double-bond marked by 9-12,
while atom 13 lies on the opposite side. Atom 15 is therefore
marked as the Z atom, while atom 13 is marked as the E
atom.
Stereochemical descriptors are not implemented systemati-
cally throughout the system. However, a separate flag is set
for atoms which are one bond away from a three- to six-
membered aliphatic ring. These atoms are classified as
located on either the same or opposite side of a ring. In the
molecule shown in Figure 2, atom 10 lies on the same side
of the five-membered ring made up of atoms 2, 6, 7, 8, and
5 while atom 11 lies on the opposite side relative to the
central atom 1. This method obviously can only be used for
relatively rigid rings and is inapplicable to the stereochem-
istry of flexible systems such as large rings and chains.
In many cases, so-called “cross-increments” were used.
These refer to pairs of atomssfor each two atoms separated
by a small number of bonds, an independent identifier is
generated and stored. In this study, we considered pairs
separated by one to three bonds, or by one to four bonds in
conjugated systems, with both atoms located within the first
three to four spheres. For example, if we use atom 1 as the
central atom, then the following pairs of atoms, 3-14, 3-2,
and 2-14 (in the first sphere) and 3-4, 2-6, 2-5, 3-6,
3-5, 2-4, 5-6, 4-14, 5-14, and 6-14 in the second
sphere, should be taken into account. Atom pairs 4-5 and
4-6 are ignored since the distance between the atoms is too
long in this casesfour bonds. The distances between atom
and sphere numbers are also used to describe cross-
increments. For example, the atoms in pair 3-4 are both
CH (sp2 hybridized) and lie in the first and second spheres,
correspondingly, and are separated by one bond. The atoms
in pair 3-6 are also both CH (sp2 hybridized), lie in the
first and second spheres, and are separated by three bonds.
3. RESULTS AND DISCUSSION
3.1. Optimization of the Neural Network Performance.
Since the performance of neural network algorithms depends
on a large set of factors, we first performed a set of test
calculations to try and establish an optimal parameter set
using a smaller test data set. For this purpose, we randomly
selected 32 000 structures from the main training database.
We also questioned whether a neural network would benefit
from the inclusion of cross-increments. One could argue that,
since neurons in hidden layers receive inputs from all input
neurons, weights can be adjusted to take into account the
simultaneous occurrence of specific atomic types. For
example, the carbonyl and the hydroxyl groups together
would represent a carboxylic group and would render cross-
increments unnecessary.
Using a MATLAB implementation of the neural network
algorithms, we set up 18 test runs while varying a few
parameters in order to investigate the variation in perfor-
mance as a result of changes in the different parameters.
¥The number of cross-increments varied as (1) none, (2)
pairs of atoms separated only by one bond, or (3) pairs of
atoms separated by up to two bonds.
¥The geometry of the neural networks was (1) 50 hidden
neurons in one layer, (2) 30 hidden neurons in one layer, or
(3) two hidden layers of 20 and 10 neurons.
¥The transfer function was either the logistic function f(x)
) (1 + e-x)-1 or hyperbolic tangent (tanh).
As shown in Table 2, the top configurations 1-4 took
into account the maximum available number of cross-
increments. The best result without cross-increments is shown
for comparison and is only ranked 12th out of the 18 runs.
At the same time, it is clear that arrangement of the neurons
into layers plays a somewhat secondary role since the
difference between the first two networks with the same total
number of neurons but with different geometries is negligible.
These results define a reference point for further studies.
While subsequently scaling up our calculations to ap-
proximately 2 000 000 13C chemical shifts, we mainly utilized
networks with one to three hidden layers and with a logistic
transfer function. We have also tried to provide as many
cross-increments as possible to our networks with only time
and memory restrictions limiting our analyses.
3.2. Choosing the Optimal Number of Subdatabases.
While dealing with a large database is likely to be of value
for analysis purposes, we chose to split it into a number of
smaller subsets. The most popular strategy for splitting a
Table 1. Atomic Classes Used to Classify Atomsa
carbon sp3 (C, CH, CH2, CH3), sp2 (C, CH, CH2),
sp (C, dCd), aromatic (C, CH), carbonyl
heteroatoms (3-)N, (2-)NH, NH2, dNH, N(sp), N(V),
aromatic N, (2-)O, OH, dO, (3-)P, P(V),
(2-)S, dS, S(IV), S(VI), F, Cl, Br, I
exotic elements Si, Ge, Sn, (2-)Se, dSe, (2-)Te, dTe, B, As(III),
As(V), Sb(III)
solvent CHCl3, CH2Cl2, C6H6, (CH3)2SO, dioxane,
CH3OH, CH3NO2, tetrahydrofuran,
cyclohexane, (CH3)2CO, CH3CN,
(CH3)2CONH2, pyridine, CF3COOH,
CH3COOH, C6H5NO2, C6H5CH3, CCl4,
CS2, H2O, other/unknown
other parameters formal positive charge, formal negative charge,
total count of hydrogen atoms, total
count of ring closures, involvement into the
same ð-conjugated system with the central
atom, Z or E double bond, stereochemistry
a The adjective “aromatic” means that the atom is within an aromatic
system. The symbol “(n-)X” designates that n single bonds are attached
to the X atom.
Table 2. Results of Some of the Test Runs Using a MATLAB
Implementation of the Neural Network Algorithma
no.
number of neurons
in hidden layers
transfer
function
cross-
increments
mean error, ppm
(test data set)
1 20-10 logistic two bonds 3.06
2 30 logistic two bonds 3.07
3 50 logistic two bonds 3.12
4 20-10 tanh two bonds 3.15
5 30 logistic one bond 3.23
6 20-10 logistic one bond 3.23
12 20-10 logistic none 3.68
18 50 tanh none 4.58
a The mean error of the test set is shown as a function of the neural
network configuration. The data are sorted by the mean error in
ascending order, with some entries being omitted for clarity.
130 J. Chem. Inf. Model., Vol. 48, No. 1, 2008 SMURNYY ET AL.

large database is based on the nature of the central atom
type. All carbons can be classified according to hybridization,
the number of attached protons, or both. Also, some groups
are so specific and abundant, for example, a carbonyl group,
that they might deserve a separate class. We have utilized
four different strategies:
¥The database was used as a whole.
¥The carbon atoms were classified only according to
hybridization, three aliphatic classes (sp,3 sp,2 and sp) and
one for all carbons within aromatic rings, to give a total of
four different classes.
¥The hybridization and the number of attached protons
were both taken into account. This led to 10 classifications:
four sp3 (C, CH, CH2, and CH3), three sp2 (C, CH, and CH2),
one sp, and two aromatic (C and CH).
The most detailed scheme includes states of hybridization,
the number of protons attached to the carbon atom, and the
presence or absence of a heteroatom within one bond of a
central atom. The 15 resulting classes include aliphatic sp3
(seven classes: C, C(het), CH, CH(het), CH2, CH2(het), and
CH3), aliphatic sp2 (four classes: C, CH, CH2, and CO),
aliphatic sp, and three aromatic classes (C, C(het), and CH).
The symbol (het) denotes a heteroatom, oxygen, or nitrogen,
in this case, nearby. Some classes were merged into one
subclass, for example, aliphatic sp3 CH3 and CH3(het),
because a smaller class was too small or not diverse enough
to reliably teach a network, especially one with a higher
number of neurons.
It appears that more detailed classifications bring more
flexibility. For example, one can introduce specific descrip-
tion schemes for certain atomic typesschemical shifts of the
methyl group might highly depend on stereochemistry, and
it is possible to introduce stereo descriptors specifically for
this atomic type. Smaller databases are also easier to handle
in terms of computer memory requirements. However,
restricting the training set to very similar compounds prevents
a neural network from making generalizations and decreases
the quality of the results.
As seen in Figure 3, the differences between classifications
are more apparent with a smaller number of training pools.
These results suggest that, for a large enough database, about
50 000-100 000 compounds, the results are only slightly
dependent on the classification scheme. For the largest
database utilized here, over 207 000 compounds, the differ-
ence between the best classification, four centers giving an
error of 1.65 ppm, and the worst, one center giving an error
of 1.75 ppm, was only 0.10 ppm. This difference is not
practically important for carbon NMR shifts. We decided to
utilize the scheme with 15 classes for commercial purposes
due to the flexibility discussed earlier.
3.3. Choosing the Optimal Number of Cross-Incre-
ments. Using cross-increments is one of the few ways to
boost the performance of a regression-based scheme. Al-
though the approach is less popular with neural networks, it
was illustrated above that the latter can also benefit from
explicitly specified cross-increments. At the same time,
providing too many increments and cross-increments leads
to an unnecessarily detailed description of a structure and,
consequently, to overtraining. Using a small part of the whole
database, 16 000 compounds with 212 000 chemical shifts,
we systematically changed a few parameters to elucidate an
optimal scheme. Since it is possible to vary the number of
atomic spheres under consideration, we tried values from 3
to 7. Due to limited computational resources, it is impossible
to generate all possible cross-increments between atoms up
to the sixth and seventh spheres. In this study, cross-
increments were created for atoms located no further than
the third sphere. We varied the maximum number of bonds
between the atoms in the cross-increments from zero (no
cross-increments) to four.
For these tests, our main training database was split into
10 subdatabases (see above), and a PLS routine was used.
Figure 4 summarizes our findings. The best result was
obtained from a combination of six spheres and three bonds
to provide a mean error of 2.27 ppm. There is practically no
difference between the two largest sets of increments with
up to three or four bonds between the atoms, and this
suggests that further refinement might not be necessary and
can lead to overfitting. The same applies to the total number
of spheresssix are enough. This makes perfect chemical
sense since there are few electrostatic interactions or
conjugation, inductive, or mesomeric effects in aromatic
systems that span across more than five or six covalent bonds.
3.4. Comparison of 13C Chemical Shift Prediction by
Neural Networks and Partial Least Squares. After opti-
mization of a few key features such as the structure
description algorithm and the NN parameters, we compared
the PLS and NN methods. For the neural networks, we varied
Figure 3. Dependence of the mean error derived from the test set
for a number of subdatabases relative to the size of the training
set. The results were obtained with neural networks containing 30
neurons in one hidden layer. The splitting schemes leading to 1, 4,
10, and 15 different classes are described in the text.
Figure 4. Mean error of a set as a function of the maximum
number of bonds between the atoms in the cross-increments and
the number of spheres used to describe an atom’s neighborhood.
MORE RELIABLE 13C AND 1H CHEMICAL SHIFT PREDICTION J. Chem. Inf. Model., Vol. 48, No. 1, 2008 131

the size of the network, varying the number of hidden layers,
the quantity of neurons, and the number of cross-increments
provided. All other parameters such as the transfer function,
the number of subdatabases, and so forth were taken as
optimized during the previous steps. An independent test set
of 118 000 individual 13C chemical shifts was used for
comparison. Calculations were performed with 15 individual
subdatabases as described above. All cross-increments were
constructed from atoms separated by not more than one
covalent bond and located within one to three spheres from
the central atom.
As shown in Figure 5, the performance of neural networks
gradually increases upon adding more hidden neurons and
cross-increments. Not surprisingly, the best result, providing
a mean error of 1.77 ppm, was achieved with the maximum
number of cross increments and the largest neural network.
It should be noted that, for the various network configurations
compared, the total number of parameters for each network
is not the same and all networks with more than one layer
have more parameters. That said, the only extra parameter,
and therefore additional degree of freedom, is the number
of neurons in the additional hidden layers. This additional
single extra parameter was optimized by comparing the two
configurations of 100-25-5 and 75-40-15, both with the
same total number of neurons. In general, it is concluded
that the total number of neurons matters but not their
arrangement.
The configuration was tuned by adding more cross-
increments up to the third sphere with no more than two
covalent bonds between the atoms and using stereo informa-
tion in the atomic descriptors (see above). With three layers
of 100, 25, and 5 hidden neurons, the network produced a
mean error of 1.59 ppm with a largest error value of 85 ppm
and 0.6% of the chemical shifts predicted with an error of
more than 10 ppm (Table 3).
A similar approach was used to evaluate the performance
of the PLS algorithm. The optimal number of latent variables
was determined using an independent test data set. Calcula-
tions were performed on this control data set using up to
200 latent variables, and the number providing the lowest
average deviation was used for further analysis. The optimal
number of latent variables is different for different types of
carbon environments and varies between 50 and 150. The
same database split of 15 subdatabases was used. For the
cross-increments, we used a configuration of six spheres,
and cross-increments were taken from three first spheres with
atoms separated by not more than three covalent bonds. This
setup was shown to be the most effective in our previous
studies (see above). The results obtained were of a similar
quality. The mean 13C chemical shift error is slightly higher
(1.71 ppm), but other benchmark parameters were close to
those obtained for the neural network (Table 3). The number
of severe outliers is somewhat lower with only 0.7% of the
centers producing errors of greater than 10 ppm. The
maximum error was 56 ppm.
One may request an explanation for why the neural-
network-based 13C chemical shift calculations give the best
accuracy and yet have the largest maximum error. This is
due to the fact that the ability to predict values for the most
representative compounds in a given class while also
providing optimal performance for the most exotic com-
pounds is a significant challenge. Predictions can be opti-
mized either for “typical” or “atypical” members of a data
set, and as a result, we observe good prediction performance
for “average structures” but poor performance for the more
exotic compounds.
Values for the mean error determined using NN and
presented in Figure 6 as a function of the number of
substituents (i.e., CH2 vs CH for the same hybridization state)
suggest that generally the errors are higher for more highly
substituted atoms. This would appear reasonable because the
cross-influence between the different substituents enhances
the nonlinear effects.
The comparison shows that both methods can provide
results of similar quality after being properly optimized. A
Figure 5. Mean 13C chemical shift error as a function of the neural
network geometry and the maximum number of bonds separating
atoms in the cross-increments. See text for details.
Table 3. Best Results for the Prediction of Both 13C and 1H
Chemical Shifts by HOSE6 Codes, PLS, and NN Algorithmsa
type of
spectrum
prediction
method
mean error,
ppm
standard
deviation,
ppm
maximum
error, ppm
percent of
outliers
13C HOSE 1.81 3.05 57.99 2.8%
PLS 1.71 2.61 51.57 0.7%
NN 1.59 2.45 85.82 0.6%
1H HOSE 0.19 0.30 3.94 1.3%
PLS 0.18 0.26 2.72 0.7%
NN 0.18 0.26 3.71 0.8%
a The specific set of parameters for each method is described in the
text. Outliers are defined as those shifts predicted with an error of more
than 10 ppm for 13C predictions and more than 1.0 ppm for 1H
predictions.
Figure 6. Dependence of the mean error (ppm) on the number of
substituents and the hybridization of the central atom. The data
shown are for 13C chemical shift predictions with the most efficient
neural network configurations (see text for details).
132 J. Chem. Inf. Model., Vol. 48, No. 1, 2008 SMURNYY ET AL.

neural network, in general, seems to perform better with
atoms whose chemical shifts are closer to an average value
for the corresponding atomic type. Linear regression can
more easily handle exotic fragments (such as in the com-
pound CI4 with a chemical shift of -292.5 ppm), since even
the most unusual combination of substituents can easily be
assigned with an appropriate incremental value leading to a
more accurate prediction. At the same time, values of weights
for most of the neurons in a network are affected by all of
the structures present during the training process, and the
impact of unusual structures is masked by the majority of
the more regular structures. These differences are highlighted
by the lower value of the mean error for the neural network.
Simultaneously, the maximum error being more sensitive to
a small number of badly predicted structures is better for
the incremental scheme.
Both of these methods perform better than our implemen-
tation6 of the database-based HOSE code approach9 (Table
3). For a given atom, the algorithm6 retrieves few structures
from a database which have chemically similar nuclei. The
predicted value is the weighted average of chemical shifts
contained within the database structures. The approach fails
with structures which are underrepresented in the database,
and this raises the standard deviation and the maximum error.
3.5. Prediction of 1H Chemical Shifts. An attempt was
made to apply the experiences from the 13C-related analyses
to the prediction of proton chemical shifts. Over 1 million
chemical shifts were used as a training set, and the same
test data set was that used for the 13C analysis, with a total
of 114 494 1H chemical shifts.
The whole training database was split into nine sub-
datasets, namely, the aliphatic sp3 (five classes: CH, CH-
(het), CH2, CH2(het), and CH3), aliphatic sp2, aromatic sp2,
aliphatic sp, and protons attached to heteroatoms. The
notation (het) denotes a group attached to a hetereoatom.
The neighborhood of an atom was described in exactly the
same manner as described earlier for the 13C studies. All
additional flags specified in the section above (stereo
configuration, Z/E conjugated system, etc) were included.
The neural network used for the calculation had 100, 25,
and 5 hidden neurons arranged in three layers. The six nearest
spheres were used; cross-increments were constructed from
atoms in the first three layers separated by not more than
one covalent bond. PLS regression was performed within
the same six-sphere vicinity, though with more cross-
increments: within the three nearest spheres with atoms
separated by three covalent bonds or less.
The best results for the 1H chemical shifts predictions are
presented in Table 3. The neural networks and PLS ap-
proaches performed in a remarkably similar manner. The
quality of results is much less dependent on the number of
cross-incrementssmost of the NN and PLS configurations
result in a mean error of approximately 0.2 ppm. In order to
reduce the error to that experienced in experimental deter-
minations, further optimization such as the detailed descrip-
tion of the 3D geometry might be necessary. Table 4
summarizes the separate steps carried out in this work.
3.6. Speed of Chemical Shift Prediction. Modern CASE
expert systems are based on the utilization of 2D NMR data,
and this allows the identification of isolated materials such
as natural products or synthesized organic molecules. These
systems are capable of elucidating large molecules containing
100 or more skeletal atoms.1 Since the initial structural
information extracted from 2D NMR data is fuzzy by nature,1
the number of structures that are consistent with the spectral
data can usually be rather large (up to tens of thousands3).
As a result, the selection of the most probable structure from
a large output file containing many molecules requires an
approach whereby the expert systems can utilize both
accurate and fast approaches for NMR chemical shift
prediction.
Both the 13C and 1H chemical shift calculations compared
in this study were implemented into a software expert system
known as Structure Elucidator.2,3 The prediction speed was
estimated by the spectral prediction of candidate structures
generated by the program. The average speed of the 13C
chemical shift prediction by PLS is about 9000 shifts per
second on a 2.8 GHz computer, while the neural-network-
based algorithm was approximately 2.5-3 times slower. The
combination of this high speed of prediction with an
appropriate accuracy for prediction with an average deviation
of 1.71 ppm makes the PLS approach a powerful tool for
computer-aided structure elucidation. A study regarding the
impact of these new NMR spectrum prediction tools in regard
to the possibility of improving CASE systems is in progress,
and the results will be reported in a future publication.
4. CONCLUSIONS
The results of both 13C and 1H NMR chemical shift
predictions using neural networks and partial least-squares
algorithms have been systematically compared. Two of the
largest databases currently available were utilized in this
work: over 2 million 13C shifts and 1 million 1H shifts. In
Table 4. The General Workflow of the Analysisa
size of the database,
chemical shifts
size of the database,
compounds
step nucleus algorithm training testing training testing
optimization of neural
network parameters
13C NN 422 000 12 660 29 000 3000
optimization of number
of subdatabases
13C PLS 2 000 000 118 000 207 000 11 000
optimization of number of
structure descriptors
13C PLS 212 000 118 000 16 000 11 000
comparison of least-square
regression vs neural
networks
13C PLS, NN 2 000 000 118 000 207 000 11 000
1H PLS, NN 1 150 000 116 000 189 000 14 000
a The sizes of the databases are represented by the number of chemical shifts as well as the number of compounds.
MORE RELIABLE 13C AND 1H CHEMICAL SHIFT PREDICTION J. Chem. Inf. Model., Vol. 48, No. 1, 2008 133

most cases, these two algorithms performed remarkably
similarly. It is concluded that neural networks do not
automatically lead to better results and that a simpler least-
squares approach might still be the method of choice. It was
determined that the way a chemical structure was converted
into a numerical representation provided the most influence
regarding the results obtained. Both methods required rather
detailed descriptions of the structure and included atoms up
to six covalent bonds apart. It has been shown that neural
networks still require cross-increments and are unable to
recognize even the most common functional groups such as
a carbonyl group from a description based solely on the
individual atoms.
The quality of results obtained using our current setup is
probably limited to average errors of 1.5 ppm for carbon
and 0.2 ppm for protons. Our belief is that any further
improvement in the precision of NMR prediction will be due
to the perfection of the structure description algorithms and,
more importantly, the quality of training databases rather than
the method of regression used to extract the prediction
algorithms. An important result from this study is that the
incremental approach now implemented in ACD/CNMR
Predictor provides an average speed for 13C chemical shift
prediction of over 9000 shifts per second with a mean
chemical shift deviation of 1.7 ppm. This is a significant
improvement in both speed and accuracy over previously
available algorithms.
REFERENCES AND NOTES
(1) Elyashberg, M. E.; Williams, A. J.; Martin, G. E. Computer-assisted
structure verification and elucidation tools in NMR-based structure
elucidation. Prog. NMR Spectrosc. 2007, in press.
(2) Elyashberg, M. E.; Blinov, K. A.; Molodtsov, G. S.; Williams, A. J.;
Martin, G. E. Structure Elucidator: A Versatile Expert System for
Molecular Structure Elucidation from 1D and 2D NMR Data and
Molecular Fragments. J. Chem. Inf. Comput. Sci. 2004, 44, 771-792.
(3) Elyashberg, M. E.; Blinov, K. A.; Williams, A. J.; Molodtsov, S. G.;
Martin, G. E. Are deterministic expert systems for computer assisted
structure elucidation obsolete? J. Chem. Inf. Model. 2006, 46, 1643-
1656.
(4) Robien, W. CSEARCH. http://nmrpredict.orc.univie.ac.at/ (accessed
June 25, 2007).
(5) Robien, W. Das CSEARCH-NMR-Datenbanksystem. Nachr. Chem.,
Tech. Lab. 1998, 46, 74-77.
(6) ACD/NMR Predictors; Advanced Chemistry Development: Toronto,
Canada, 2007.
(7) Bremser, W.; Grzonka, M. SpecInfo - A multidimensional spectro-
scopic interpretation system. Microchim. Acta 1991, 104, 1-6.
(8) Steinbeck, C.; Krause, S.; Kuhn, S. NMRShiftDB - Constructing a
Free Chemical Information System with Open-Source Components.
J. Chem. Inf. Comput. Sci. 2003, 43, 1733-1739.
(9) Bremser, W. HOSE - A Novel Substructure Code. Anal. Chim. Acta
1978, 2, 355-365.
(10) Grant, D. M.; Paul, E. G. Carbon-13 Magnetic Resonance. II. Chemical
Shift Data for the Alkanes. J. Am. Chem. Soc. 1964, 86, 2984-2990.
(11) Reed, J. J. R. Structure Determination of Substituted Benzenes by
Proton Magnetic Resonance. Empirical Treatment of Substituent
Effects and Their Utility in Predicting Chemical Shifts. Anal. Chem.
1967, 39, (13), 1586-1593.
(12) Pretsch, E.; Clerc, T. E.; Seibl, J.; Simon, W. Tables of Spectral Data
for Structure Determination of Organic Compounds; Springer-Ver-
lag: Berlin, 1989.
(13) Clerc, J.-T.; Sommerauer, H. A Minicomputer Program Based on
Additivity Rules for the Estimation of Carbon-13 NMR Chemical
Shifts. Anal. Chim. Acta 1977, 95, 33-40.
(14) Fu¨rst, A.; Pretsch, E. A Computer Program for the Prediction of
Carbon-13 NMR Chemical Shifts of Organic Compounds. Anal. Chim.
Acta 1990, 229, 17-25.
(15) Pretsch, E.; Fu¨rst, A.; Badertscher, M.; Burgin, R.; Munk, M. E.
C13shift - a Computer-Program for the Prediction of Carbon-13 NMR-
Spectra Based on an Open Set of Additivity Rules. J. Chem. Inf.
Comput. Sci. 1992, 32, 291-295.
(16) Schaller, R. B.; Arnold, C.; Pretsch, E. New Parameters for Predicting
1H NMR Chemical Shifts of Protons Attached to Carbon Atoms. Anal.
Chim. Acta 1995, 312, 95-105.
(17) Schaller, R. B.; Pretsch, E. A Computer Program for the Automatic
Estimation of 1H NMR Chemical Shifts. Anal. Chim. Acta 1994, 290,
295-302.
(18) Upstream Solutions GMBH, NMR Prediction Products (SpecTool).
http://www.upstream.ch/products/nmr.html (accessed May 28, 2007).
(19) Clouser, D. L.; Jurs, P. C. Simulation of the 13C Nuclear Magnetic
Resonance Spectra of Ribonucleosides Using Multiple Linear Regres-
sion Analysis and Neural Networks. J. Chem. Inf. Comput. Sci. 1996,
36, 168-172.
(20) Lucic, B.; Amic, D.; Trinajstic, N. Nonlinear Multivariate Regression
Outperforms Several Concisely Designed Neural Networks on Three
QSPR Data Sets. J. Chem. Inf. Comput. Sci. 2000, 40, 403-413.
(21) Ivanciuc, O.; Rabine, J. P.; Cabrol-Bass, D.; Panaye, A.; Doucet, J.
P. 13C NMR Chemical Shift Prediction of sp2 Carbon Atoms in Acyclic
Alkenes Using Neural Networks. J. Chem. Inf. Comput. Sci. 1996,
36, 644-653.
(22) Meiler, J.; Meusinger, R.; Will, M. Fast Determination of Carbon-13
NMR Chemical Shifts Using Artificial Neural Networks. J. Chem.
Inf. Comput. Sci. 2000, 40, 1169-1176.
(23) Kaur, J.; Brar, A. S. An Approach to Predict the C-13 NMR Chemical
Shifts of Acrylonitrile Copolymers Using Artificial Neural Network.
Eur. Polym. J. 2007, 43, 156-163.
(24) Meiler, J.; Maier, W.; Will, M.; Meusinger, R. Using Neural Networks
for Carbon-13 NMR Chemical Shift Prediction-Comparison with
Traditional Methods. J. Magn. Reson. 2002, 157, 242-252.
(25) Bosque, R.; Sales, J. A QSPR Study of the 31P NMR Chemical Shifts
of Phosphines. J. Chem. Inf. Comput. Sci. 2001, 41, 225-232.
(26) Da Costa, F. B.; Binev, Y.; Gasteiger, J.; Aires-De-Sousa, J. Structure-
based predictions of H-1 NMR Chemical Shifts of Sesquiterpene
Lactones Using Neural Networks. Tetrahedron Lett. 2004, 45, 6931-
6935.
(27) Beger, R. D.; Harris, S.; Xie, Q. Models of Steroid Binding Based on
the Minimum Deviation of Structurally Assigned 13C NMR Spectra
Analysis (MiDSASA). J. Chem. Inf. Comput. Sci. 2004, 44, 1489-
1496.
(28) Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.;
Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney,
A.; Sorensen, D. LAPACK Users’ Guide, 3rd ed.; Society for Industrial
and Applied Mathematics: Philadelphia, PA, 1999.
(29) Anthony, M.; Bartlett, P. In Neural Network Learning: Theoretical
Foundations; Cambridge University Press: Cambridge, U.K., 1999.
(30) Press, W.; Teukolsky, S.; Vetterling, W.; Flannery, B. In Numerical
Recipes: The Art of Scientific Computing; Cambridge University
Press: Cambridge, U.K., 2007.
CI700256N
134 J. Chem. Inf. Model., Vol. 48, No. 1, 2008 SMURNYY ET AL.