Are Deterministic Expert Systems for Computer-Assisted Structure Elucidation
Obsolete?
Mikhail E. Elyashberg,† Kirill A. Blinov,† Antony J. Williams,*,‡ Sergey G. Molodtsov,§ and
Gary E. Martin|,⊥
Advanced Chemistry Development, Moscow Department, 6 Akademik Bakulev Street,
Moscow 117513, Russian Federation, Advanced Chemistry Development, Inc., 110 Yonge Street, 14th floor,
Toronto, Ontario, Canada M5C 1T4, Novosibirsk Institute of Organic Chemistry, Siberian Branch of Russian
Academy of Science, Lavrentiev Avenue 9, Novosibirsk 630090, Russia, and Michigan Structure Elucidation
Group, Pfizer Global Research and Development, Kalamazoo, Michigan 49001-0199
Received October 24, 2005
Expert systems for spectroscopic molecular structure elucidation have been developed since the mid-1960s.
Algorithms associated with the structure generation process within these systems are deterministic; that is,
they are based on graph theory and combinatorial analysis. A series of expert systems utilizing 2D NMR
spectra have been described in the literature and are capable of determining the molecular structures of
large organic molecules including complex natural products. Recently, an opinion was expressed in the
literature that these systems would fail when elucidating structures containing more than 30 heavy atoms.
A suggestion was put forward that stochastic algorithms for structure generation would be necessary to
overcome this shortcoming. In this article, we describe a comprehensive investigation of the capabilities of
the deterministic expert system Structure Elucidator. The results of performing the structure elucidation of
250 complex natural products with this program were studied and generalized. The conclusion is that 2D
NMR deterministic expert systems are certainly capable of elucidating large structures (up to about 100
heavy atoms) and can deal with the complexities associated with both poor and contradictory spectral data.
1. INTRODUCTION
Expert systems allowing computer-assisted structure elu-
cidation based on spectral data, including multidimensional
NMR data, have proven valuable in the elucidation of
complex organic molecules. Articles published in recent years
have reported on systems capable of elucidating the chemical
structures of even complex natural products.1-9 Some
studies7,10-21 report the application of expert systems to the
elucidation of novel structures of natural compounds. Until
recently, most publications presented examples that showed
the capabilities of the expert systems in terms of solving
tasks that would commonly be dealt with by qualified
spectroscopists. In one of our recent studies,11 an expert
system elucidated the structure of a complex alkaloid
C31H20N4 that could not be identified by a highly experienced
spectroscopist, even after a decade of effort. The success of
this work11 highlights the capabilities of the Structure
Elucidator system, referred to as StrucEluc for the remainder
of this article,7-9 developed as a result of tenacious efforts
to develop algorithms and databases that can be applied to
structure elucidation tasks in a general manner.
The successes of StrucEluc are dependent on the impres-
sive achievements and developments of 2D NMR spectros-
copy that are now both routine and widespread. The variety
and quality of the data inputs available from 2D NMR data
have allowed the development of expert systems that are able
to elucidate structures of very complex organic molecules.
Until recently, systems were deterministic, using discrete
mathematical methods such as logic, combinatorial analysis,
and graph theory combined with heuristic approaches for
the exhaustive generation of all isomeric structures satisfying
a set of structural constraints.
Experience accumulated as a result of the application of
expert systems to many examples has demonstrated that such
systems derive direct value from the huge amount of
chemical structure information contained within spectral data.
Figure 1 displays the structures of a series of small natural
product molecules elucidated from their 2D NMR spectra,
as reported in the literature, and analyzed by our research
group using the StrucEluc expert system.7,8
In Figure 1, N is the number of structural isomers that
were generated using the structure generator within the
StrucEluc system. Even the simplest structures can have
hundreds of millions if not billions of isomers, and a
successful result depends on the screening and rejection of
N - 1 structural formulas that do not comply with the
experimental data and systematic constraints applied. The
number of isomers associated with the structures of medium-
sized complex organic molecules can be estimated at about
1020-1030 isomers. For comparison purposes, the number
of stars in our galaxy is “only” 1011, so it is appropriate to
comment that astronomical numbers and “isomeric” numbers
are comparable.
* Corresponding author phone: 919-341-8375; fax: 425-790-3749;
e-mail: tony@acdlabs.com.
† Advanced Chemistry Development, Moscow Department.
‡ Advanced Chemistry Development, Inc.
§ Siberian Branch of Russian Academy of Science.
| Pfizer Global Research and Development.
⊥ Present address: Schering-Plough Corp., 2000 Galloping Hill Rd,
K-11-3 L5, Kenilworth, NJ 07033.
1643J. Chem. Inf. Model. 2006, 46, 1643-1656
10.1021/ci050469j CCC: $33.50 © 2006 American Chemical Society
Published on Web 05/11/2006

A huge number of isomers corresponding to molecules
containing 30-100 skeletal atoms resulted in some re-
searchers22-24 declaring that, in principle, deterministic
systems would not be able to analyze the entire space of
potential isomers and, therefore, would fail in the elucidation
of structures. As an alternative, they suggested stochastic
algorithms for structure generation, specifically simulated
annealing,22,23 and genetic algorithms.24,25 In a series of
reports,23,24,26 Steinbeck et al. limited the number of skeletal
atoms in a molecule that could be identified by deterministic
systems to 30 or less. Examples of large molecules that were
successfully elucidated and reported, but above the limit of
30 atoms, were considered to be exceptions.23 One would
expect that, in order to support their position, the proponents
of stochastic algorithms would cite successful examples of
stochastic algorithms applied to molecules with more than
30 skeleton atoms. This has not happened to the best of our
knowledge. Steinbeck et al.23,24 have shown that stochastic
methods can elucidate structures containing close to 30
skeletal atoms.
Stochastic methods of structure generation are of interest
because any such algorithms should be comprehensively
studied in terms of their potential advantages in expert
systems. It is not improbable that the use of techniques
peculiar to deterministic systems in combination with
stochastic algorithms could lead to the creation of hybrid
systems that, because of synergistic effects, could success-
fully compete with purely deterministic systems. While this
interest exists, we question the validity of the statement that
deterministic systems are already obsolete and are limited
to the elucidation of structures of molecules containing less
than 30 skeletal atoms. During the past 35 years of
development of deterministic systems, a large number of
methods have been elaborated to overcome the “problem of
dimensionality”.1-9 It will be shown below that molecules
with 40-80 skeletal atoms are fairly typical examples in
computer-assisted structure elucidation using deterministic
systems. With the effective application of the structural
constraints provided by 2D NMR spectra, as well as the use
of sophisticated databases and spectra-structural correlations
accumulated by several generations of spectroscopists, it is
possible to significantly reduce the resulting output set of a
deterministic system. The sum total of all of these innovations
introduces elements of artificial intelligence into expert
systems, thereby supplying many abilities that are absent
from a human expert. The program starts with a huge but
restricted space for all possible isomers containing, of course,
structures complying with the constraints imposed by spectral
data or introduced as additional information. The challenge
is to reveal these selected structures and select the most
probable.
In this work, we investigate the properties, strategies, and
techniques for elucidating the structure of an unknown
compound using the deterministic system StrucEluc7-9,11,27-30
and on the basis of an input data set including 2D NMR
spectra.
The principal scheme illustrating the operation of
StrucEluc is shown in Figure 2.
Conceptually, the system operates in two modessthe so-
called common and fragment modes. The common mode
implies the utilization of 2D NMR data without the applica-
tion of substructural fragments either suggested by the
chemist or identified within the system knowledge base. The
fragment mode is initiated when user-defined fragments are
used or fragments are found as a result of a 13C NMR search
in the fragment library (FL) containing ca. 1.5 million
fragments and their associated 13C NMR subspectra. The final
step in the elucidation is the selection of the most probable
structure and determination of its likely relative stereochem-
istry and 3D geometry.
In this study, the solutions of over 250 complex structure
elucidation problems, specifically, natural products, were
comprehensively analyzed. The reliability of the system’s
knowledge base was examined together with the character-
istics of the structures which were elucidated. Also, the
Figure 1. Structures of a number of natural products including
their associated molecular formulas and the numbers of mathemati-
cally possible isomers.
1644 J. Chem. Inf. Model., Vol. 46, No. 4, 2006 ELYASHBERG ET AL.

properties of the 2D NMR data used as the basis of analysis
were studied to determine what specific features would be
problematic and would limit the successful application of a
computer-assisted structure elucidation system. Attention was
given to the possibility of identifying the most probable
structure in a large results output file and specifically to
solving problems in the presence of either correlation
spectroscopy (COSY) or heteronuclear multiple-bond cor-
relation (HMBC) correlations of “nonstandard”27 length
(nonstandard correlations, NSC), that is, where correlations
are characterized by nJHH and nJCH with n > 3.
Extensive research has resulted in the development of
NMR spectral prediction methods that enable the selection
of the most probable structure from an output set (for
instance, refs 31-36). To the best of our knowledge, no tests
have been performed on a wide range of real-world tasks to
validate the effectiveness of these methods. In this article, a
study of the discriminating ability of the prediction methods
described previously in our other works7-9 has been con-
ducted. The method includes several stages and is based on
the prediction of both 1H and 13C NMR spectra using ACD/
NMR prediction software.32
As a result of our studies, we conclude that deterministic
expert systems are certainly not yet obsolete and, moreover,
it is likely that the near future will see an increasing
application of such software programs to the elucidation of
even more highly complex chemical structures.
2. RESULTS AND DISCUSSIONS
2.1. Analyzing the Relevance of the System Knowledge
Base. It may seem that 2D NMR data allow the elucidation
of a molecular structure as if it is an ab initio approach
(common mode). Structure elucidation is, however, an inverse
problem37,38 by nature. To obtain a unique structure as an
output file, spectral data provided in various forms are
Figure 2. Flow diagram describing StrucEluc.
DETERMINISTIC EXPERT SYSTEMS J. Chem. Inf. Model., Vol. 46, No. 4, 2006 1645

commonly necessary (including MS, NMR, IR, Raman, UV
spectra, databases containing spectrum-structural information,
spectral calculation outputs, etc.), and this problem can
therefore be related to a class of so-called ill-posed prob-
lems.37,38 A consequence is that arbitrarily small changes in
the input experimental data or in the knowledge base of a
system may lead to arbitrarily large changes in the solution.
With this in mind, it can be concluded that automated or
computer-assisted structure elucidation is possible only in
those cases when the data are correct, consistent, and
comprehensive. The accuracy of the input spectral data
should be confirmed by the spectroscopist. If these data are
correct and consistent, the result of computer-aided structure
elucidation will correspondingly depend on the quality and
reliability of the system knowledge base. The following types
of data are used in the knowledge base of StrucEluc:
1. A database of structures and their corresponding
assigned 1H and 13C NMR spectra (>215 000 pairs) is used
as the basis of the search for structures according to their
13C NMR spectra and for the creation of the fragments
database described below.
2. A fragments database generated from the structures
database containing the assigned 13C NMR subspectra
(>1 500 000 fragments) is used to generate structures based
on the 1D 13C NMR spectra and to aid in the solution of
tasks using 2D NMR in those cases when the 2D NMR data
are not definitive enough to resolve the problem (the
molecules may be too large, there may be extensive
resonance overlap in one or both dimensions, or there may
be a dearth of hydrogen atoms resulting in a scarcity of cross-
peaks, etc.7,8).
3. A database of spectra-structure correlations for 1H
NMR, 13C NMR, and IR spectra is used for the spectral
filtering of selected fragments and their generated structures.
4. A set of correlation tables containing atom-centered
fragments and their spectral characteristics in the 1H and 13C
NMR spectra (atom property correlation table, APCT) is
used. These correlation tables are designed to allow auto-
mated determination of the properties of carbon atoms,
specifically the hybridization state and the probability of
certain neighboring heteroatoms. These correlations are used
to create molecular connectivity diagrams (MCD)7,8 and to
reduce the expanse of the search during the process of
structure generation.
5. A set of special databases containing structures and their
assigned 1H and 13C NMR spectra is used to assist in the
prediction of the NMR spectra of structures contained in the
resultant output file. A comparison between the experimental
data and the predicted data is used to help identify the most
probable structure.
The properties of the knowledge base of StrucEluc were
examined and optimized using large files of reference data.
The structure database was produced from literature
encompassing numerous journals publishing the assigned
NMR spectra of synthetic substances and natural products.
The structure database is therefore characterized by a high
level of diversity, and the fragments excised from the
structures will therefore also be diverse and available for
the analysis of a wide range of classes of organic molecules.
To optimize the chemical shift intervals assigned to the
fragments present in the correlation tables and tables used
for setting the atom properties (APCT), all 215 000 structures
contained within the database of assigned 1H and 13C NMR
spectra were used. The database structures were filtered with
the help of the fragment libraries. If any contradictions were
detected between a structure and the characteristic spectral
intervals associated with a fragment, the program provided
a corresponding message. On the basis of these messages,
the intervals were modified to resolve the contradiction.
Some fragments characterized by specific chemical shift
values were placed into a library of exceptions that was
applied as part of the structure filtration process using a
specially derived algorithm.
Analysis of the fragment tables revealed that spectral filter
libraries and correlation tables (APCT) allowed the solution
of tasks with a negligible risk of overlooking the correct
structure. A total of 96% of the structures present in the
system database withstood a verification challenge by both
1H and 13C NMR spectra using both spectral filters and
ACPT. When the high degree of diversity of the structure
library is taken into account, it can be expected that the
spectral filtering of the output file is a procedure that offers
only a small risk of losing the actual structure. To validate
the spectral filters as applied to natural products, we chose
ca. 13 500 natural product compounds from the Full Structure
database. It was found that 99.8% of them withstood spectral
filtering.
As mentioned previously, a database containing ca. 1.5
million fragments was produced from the structures in the
Full Structure database and forms the system fragment
library. The properties of the fragment library were scruti-
nized as a result of challenging the StrucEluc system with a
set of 250 problems. During the period over which the
StrucEluc system has been developed, 155 of the 250 solved
problems (set A) have been subsequently included into the
Full Structure database, and as a result, these structures were
involved in producing the current fragment library. Set B is
identified as the set of remaining 95 problems whose
structures are absent from the database. The full set of solved
problems is referred to as P where P ) A \ B.
For all 250 problems, fragments with 13C NMR spectra
were searched in the fragment database. The sizes of the
identified fragment files were generally 1000 < x < 2000
structures, though in rare cases, they can be significantly
larger (up to 20 000). It is noteworthy that the procedure of
searching the fragments using 13C NMR spectra is rather fast
and generally does not exceed 30 s on a standard desktop
computer (Pentium IV, 2.8 MHz).
The amount of information that can be elucidated from
the system fragment library about an unknown structure is
of interest. All structures included in the set P of “unknown”
structures were filtered using the FL, and the real fragments
(RFs) identified in each molecule were saved. These frag-
ments, if found, offer the possibility of forming “good”
MCDs from which a correct solution can be generated.
The main advantage of using fragments found in the
database is that their carbon atoms are associated with
chemical shifts close or equal to the experimental values
observed in the 13C NMR spectrum of the unknown
substance. StrucEluc includes a procedure7,8 that will auto-
matically assign the experimental chemical shifts to the
carbon atoms of the fragments used to form the MCDs. Each
assignment is then checked by the program for agreement
with the 2D NMR connectivities. Other investigators26,39 have
1646 J. Chem. Inf. Model., Vol. 46, No. 4, 2006 ELYASHBERG ET AL.

reported the application of user-defined fragments for
structure generation from 2D NMR data but gave no
information about the method employed for chemical shift
assignment of the fragment carbon atoms. We suspect that
the authors simply set the chemical bonds between definite
atoms, but we consider this an artificial approach. For
instance, let the 13C NMR spectrum of an unknown contain
the following chemical shifts: 115 (d), 116 (d), 121 (d), 127
(d), 126 (s), 131 (s), 132 (s), 145 (s), and 150 (s) ppm. The
user defined fragment is
A total of 2880 combinations of the chemical shift
assignments should be produced and checked to select the
single correct combination that will lead to the generation
of the correct structure corresponding to all of the 2D NMR
data. Obviously, it is impossible to guess the appropriate shift
assignment without checking all of the combinations.
In reality, not all real fragments present in the database
are selected during the fragment search using the 13C NMR
spectrum of an unknown structure. This is illustrated in
Figure 3 where the numbers of real fragments existing in
the database are measured by tens or even exceed hundreds,
while the numbers of found real fragments (blue triangles)
are always less than the corresponding possible values (violet
circles).
An investigation was performed to reveal how the presence
of an unknown molecule in the Full Structure database
influences the result of a fragment search. The numbers of
RFs ni(A) and nj(B) (i ) 1/155, j ) 1/95) were calculated
for both subsets of P. The corresponding values niF(A) and
njF(B) were determined to show how many RFs were found
as a result of library searching using 13C NMR spectra. In
accord with Figure 3, it was shown that in all cases niF(A)
< ni(A) and njF(B) < nj(B). The average values of ni(A) and
nj(B) are equal to 76 and 49, correspondingly, and for niF(A)
and njF(B), the values are 59 and 34, respectively. This means
that the numbers of real fragments nj(B) and njF(B) are
therefore large enough even in those cases when the unknown
structures are absent from the Full Structure library and,
consequently, when they were not used in the production of
the fragment library. The dependence of njF(B) on nj(B) is
presented in Figure 4, which shows that the relationship
between these values is linear in nature and has a correlation
coefficient of 0.97.
The analysis described here leads us to conclude that
fragments contained within the unknown molecule usually
make up only a small amount of the fragments found as a
result of a database search. To further improve the efficiency
of employing fragments in the structure elucidation process,
it is necessary to raise the selectivity of the fragment search
and perfect methods that position the largest real fragments
at the top of the list of found fragments.
2.2. General Characteristics of Identified Structures.
During the process of developing the StrucEluc system, more
than 250 challenges were undertaken to elucidate the
structures of recently isolated materials; almost all of the
250 compounds were natural products because nature delivers
far more structural diversity than that generally observed via
laboratory-based synthesis. Each of the problems was solved
using spectral data obtained from two sources. The first
source was literature articles spanning the years 2000-2004
extracted from the Journal of Natural Products, the Journal
of Organic Chemistry, and Magnetic Resonance in Chem-
istry. The only criterion that influenced the choice of articles
for the tasks was the presence of tables containing 1H NMR,
13C NMR, or HMQC or HSQC, and, optionally, COSY
spectral data. The second source was raw NMR data acquired
by users of the StrucEluc system whose interests included
the identification of novel natural products. The diversity of
structures identified in the 250 challenges is very likely
representative of the diversity of natural products isolated
and characterized during the identified period. For example,
the selected compounds were identified to be members of
the following classes: steroids, terpenoids, acyclic and cyclic
peptides, glycosides, various alkaloids and heterocyclic
compounds, and so forth.
The problems extracted from the literature were solved
immediately after the corresponding publication appeared,
thereby ensuring the exclusion of the new compounds from
the system databases. If there was a need to solve the task
later for revalidation as the algorithms were improved, the
unknown structure was initially preliminary searched in the
Figure 3. Numbers of real fragments (RFs) existing in the database
(violet circles) compared with the numbers of found RFs (blue
triangles). Not all of the RFs were detected during the fragment
search.
Figure 4. Dependence of njF(B) on nj(B). The correlation coef-
ficient is 0.97.
DETERMINISTIC EXPERT SYSTEMS J. Chem. Inf. Model., Vol. 46, No. 4, 2006 1647

system database in an automated fashion. If it was found in
the system databases, it was temporarily removed from the
library for the process of revalidation. This allowed the
deliberate exclusion of any influence of the presence of the
molecule under study consideration during both the fragment
search process and the prediction of both 1H and 13C NMR
spectra.
The distribution of structures relative to the number of
skeletal atoms is shown in Figure 5.
From the histogram in Figure 5, it is seen that the most
typical structures are those where the number of skeletal
atoms varies from 20 to 30 (typical molecular weights lie in
the range of 300-600 Da). At the same time, more than
100 molecules contain from 30 to 90 skeletal atoms, which
immediately invalidates the limit declared by others for
deterministic expert systems.22,23 Almost all of the com-
pounds contained oxygen or nitrogen atoms, up to a total of
30 such heteroatoms in a single molecule.
For the majority of structures, the double-bond equivalent
(DBE) value varies between 5 and 15 and reached a
maximum value of 25. The number of cycles varies from
two to eight, with the majority of molecules containing three
to four cycles. As expected, the molecules contained mostly
five- and six-membered cycles. There were 35 structures
containing seven-membered cycles. Other researchers sug-
gested that structures containing n-membered cycles with n
> 7 are uncommon.40 However, in the series of structures
under consideration, there were about 60 compounds con-
taining rings of this size. No structures containing four-
membered cycles were detected.
Some examples of structures identified with the aid of
StrucEluc operating in the common mode (i.e., without
fragments found in the knowledge base and user-defined
fragments) are presented in Table 1. The structures are
accompanied by the main parameters, allowing the evaluation
of the system to perform efficiently as a CASE tool.
Listed in the table of elucidated chemical structures is the
following information: a reference to the article from which
the NMR data were extracted; the molecular formula (MF)
and molecular weight; the number of skeletal atoms, n; the
number of connectivities in the COSY and HMBC spectra;
the number of nonstandard correlations in the 2D NMR data;
k, the number of structures in the output file before and after
the removal of duplicates; tg, the time of structure generation;
T, the total time for solving the problem; and rA, rF, rH, and
r“, the position of the correct structure in the output file
ranked by the deviations calculated using different compu-
tational methods (see refs 7 and 8). Calculations were
performed on a Pentium IV, 2.8 MHz PC.
The data allow us to conclude that the molecules used in
the investigation discussed in this article were complex and
characterized by the diversity of both their topology and
chemical composition. The MF, molecular mass (M), and
DBE averaged across all of the problems are represented by
MF ) C25H33O5N1, M ) 427, and DBE ) 10.
A comparison of Figure 5 with the results of statistical
analysis on approximately 3.5 million structures published
by Petitjean and Dubois53 allows us to conclude that, when
the size of structures successfully elucidated by the StrucEluc
system is taken into account, this system can be, in principle,
applied to at least 98% of all organic compounds encountered
in chemical investigations.
2.3. Peculiarities of 2D NMR Spectral Data. Our
experience has shown that the successful elucidation of a
chemical structure by the StrucEluc system depends not only
on the size of the structure but on the information contained
within the experimental 2D NMR spectra and on the number
of observed correlations relative to the theoretically expected
value. The degree of overlap of the signals is, of course, a
major consideration. The key point in the operation of the
system is the generation of structures with the restrictions
arising from both the HMBC and COSY data. The more
correlations that are observed in the 2D NMR spectra, the
correspondingly more restrictions that can be imposed during
the generation process, thereby increasing the likelihood that
the problem can be solved in a reasonable period of time.
The number of observed 2D NMR correlations depends
on a series of complicating factors including not only the
experiment and the parameters used when the experiment is
performed but the dispersion of the proton and carbon NMR
spectra, in addition to spatial effects. The number of
correlations observed experimentally commonly turns out to
be less than the number expected theoretically. This number
is calculated on the basis of the assumption that all
correlations corresponding to the coupling constants ex-
pressed as 2,3JHH and 2,3JCH should be observed in the COSY
and HMBC spectra. In our previous works,7,8,27 we defined
such correlations as “standard”. In those cases where there
are n>3JHH/CH couplings, the number of experimentally
observed peaks can be greater than theoretically possible on
the basis of the defined constraints.
Efforts have been made to determine the connection
between the numbers of observed correlations by analyzing
the results of problems studied to date. For this purpose, both
theoretical COSY and HMBC spectra were generated for
the entire set of problems and the MCDs were created from
the calculated spectra. All problems were then solved in a
batch mode. Under the specified conditions, most of the
problems resulted in only one structure being generated. For
20 of the tasks, two to four structures were generated, and
only 4 out of 250 tasks gave output files containing several
tens of structures. The generation time for most of the tasks
did not exceed 2-3 s (Pentium IV, 2.8 MHz). In an ideal
case, information that can be obtained from 2D NMR spectra
Figure 5. Distribution of structures relative to the number of
skeletal atoms across the 250-example problem set. The bars
correspond to the number of problems in a given range. The first
bar comprised of 37 problems involved molecules with 1-20 atoms.
The second bar with 111 problems involved molecules with 21-
30 atoms, etc.
1648 J. Chem. Inf. Model., Vol. 46, No. 4, 2006 ELYASHBERG ET AL.

is sufficient to elucidate the structure of natural products of
fairly high complexity.
When solving real problems, difficulties occur primarily
due to the sparse numbers of experimentally observed
correlations, the presence of extraneous correlations of
“nonstandard” length (nJHH/CH, n>3), and the overlap of
signals that leads to the appearance of ambiguous correla-
tions.
Parts A and B of Figure 6 show the relationship between
the numbers of observed and theoretically possible correla-
tions in both the HMBC and COSY spectra. When creating
Figure 6B, only those problems with available COSY spectra
were used.
It is generally believed by others in this field that
correlations of nonstandard length are observed only
rarely.23,24,26 In this work, 114 out of 250 tasks (i.e., 45%)
contained nonstandard correlations in the 2D NMR data.
Figure 7 illustrates the distribution of the number of non-
standard correlations present across the 2D NMR data sets.
Obviously, the presence of nonstandard correlations in 2D
NMR data is not as rare of an occurrence as some workers
have suggested. In the examples cited in this work, a
maximum of 15 nonstandard correlations was observed for
a single structure. For the problem data sets as a whole,
nonstandard correlations were observed in the COSY data
in 52 cases and in the HMBC data in 85 cases. Indeed, it is
quite likely with the higher sensitivity afforded by cryogenic
NMR probes that the frequency with which nonstandard
correlations will be observed will increase as access to
spectrometers equipped with cryogenic probe capabilities
broadens.54
Numerous examples of structures whose HMBC spectra
contain nonstandard correlations have been reported.55 From
our work, it is evident that spectral data can not only contain
a large number of nonstandard correlations but also the
deviation from the standard connectivity length can be up
to three bonds to provide a 6JXH coupling constant. It is
evident that the method reported in some works39 to
Table 1. Examples of Solutions to Problems Solved Using the Common Mode
DETERMINISTIC EXPERT SYSTEMS J. Chem. Inf. Model., Vol. 46, No. 4, 2006 1649

overcome contradictions in 2D NMR data by lengthening
all of the correlations by one bond (using couplings 2-4JHH
and 2-4JCH by default) would be insufficient to elucidate
structures in the presence of correlations characterized by
5,6JXH coupling constants. In our work,27 we suggested
approaches for addressing this issue in such situations.
Experience has shown that the application of fuzzy structure
generation27 can deliver great value, and the methodology
and advantages of this approach will be discussed in a
separate publication.
2.4. Some Important Properties of Solutions to Prob-
lems. 2.4.1. Time of Problem Solving. The total time
necessary to solve a problem, Ttot, can be represented as a
sum of the following components:
where tMCD is the time required to create the MCD (when
the problem is solved in the common mode,7,8 this value is
practically zero); tg is the time of structure generation; tflt is
the time consumed in performing spectral filtering on the
generated structural file (a process applied just after structures
are generated in to save free disk space) and the removal of
duplicates; tspr is the time necessary to perform spectrum
prediction on the output file and the ranking of the structures
in ascending order of dA deviation (see below and refs 7
and 8). The histogram presented in Figure 8A shows that
the majority of problems were solved in less than 2 min and
that, as a rule, this time does not exceed 20 min.
Structure generation times are shown as a histogram in
Figure 8B. These data demonstrate that tg comprises only a
small part of the Ttot value. In particular, for 200 out of 250
problems, tg is less than 1 min.
2.4.2. Efficiency of Filtering Generated Structures.
Figure 9A shows a histogram plot illustrating the number
of structures output into the resultant file prior to filtering
and the removal of duplicates.
Analysis of Figure 9A allows us to conclude that, for 75%
of the problems, the output file of generated structures
contains less than 1000 structures and only in 2% of the cases
Figure 6. (A) Ratio of the number of experimental HMBC
correlations vs the number of theoretical correlations across the
250 example problems. The problems are ordered in ascending order
of the ratio. (B) Ratio of the number of COSY correlations vs the
number of theoretical correlations across the 120 example problems
that included COSY data. The problems are ordered in ascending
order of the ratio.
Figure 7. Histogram illustrating the number of nonstandard
connectivities contained within the 114 problems.
Figure 8. (A) Histogram showing the total time required to
elucidate the structures within the problem set. (B) Distribution of
structure generation time across the entire problem set.
Ttot ) tMCD + tg + tflt + tspr
1650 J. Chem. Inf. Model., Vol. 46, No. 4, 2006 ELYASHBERG ET AL.

does the output file grow to around half a million structures.
Recalling that the number of potential isomers for a molec-
ular formula comprising a natural product can be astronomi-
cal (see Figure 1), the results obtained can be considered as
particularly successful. The results again provide evidence
that the statement made by other workers22,23 regarding the
limited possibilities of deterministic expert systems because
of the potential threat of a combinatorial explosion is in fact
unjustified.
Figure 9B illustrates the distribution of the size of the
output file obtained following both spectral and structural
filtering of the initial file of generated structures followed
by the removal of duplicates. A comparison of the distribu-
tions presented in Figure 9A,B illustrates the high efficiency
of the filtering process because the number of generated
structures is reduced dramatically as a result of the applica-
tion of the filtering procedures. The filtering efficiency is
obvious in Figure 9C where the initial and final output files
are shown for problems with output files containing between
5000 and 50 000 structures.
2.4.3. Evaluation of Methods for Selection of the Most
Probable Structure. A three-step method for selection of
the most probable structure contained within the output file
obtained using StrucEluc has been fully described previ-
ously.7,8 The dA values represent the average deviations of
the “accurately” calculated 13C NMR chemical shifts relative
to the experimental shifts. These values play a decisive role
in the process of selecting the correct structure. It is generally
assumed that the first-ranked structure with the minimum
dA value is the most probable structure match. For the prob-
lem sets examined in this report, for 93% of the problems,
dA ranking placed the correct structure in the first position.
The distribution of problems with first-order rankings is
presented in Figure 10, where dA(1) values, the deviations
corresponding to the first-ranked structures, are presented.
In about 60% of the cases, the dA(1) value is less than 2
ppm, and the average value is 2.09 ppm. To reveal the
general trend of dA values within a ranked output file, the
average magnitudes corresponding to the 10 first structures
in the ranked output file were calculated (see Figure 11).
The figure shows that dA deviations increase for the first
four structures by an increment of approximately 1 ppm from
each structure to the next. Average similarity coefficients
were also considered for the 10 structures as represented in
Figure 12. The similarity coefficients were calculated by
comparing all structures with that ranked first. Recall that
the first-ranked structure was correct in 93% of the cases.
Figure 12 shows that the average similarity coefficients drop
Figure 9. (A) Histogram of the number of structures in the output
file prior to filtering and removal of duplicates. (B) Distribution of
structures in the reduced output files resulting from filtering and
removal of duplicates. (C) Reduction in the number of generated
structures after spectral and structural filtering. The data are
provided for a subset of problems with output files containing
between 5000 and 50 000 structures.
Figure 10. Histogram illustrating the distribution of problems with
deviations corresponding to the first-ranked structures, dA(1) values.
Figure 11. Average dA magnitudes corresponding to the first 10
structures of the ranked output file.
DETERMINISTIC EXPERT SYSTEMS J. Chem. Inf. Model., Vol. 46, No. 4, 2006 1651

slowly starting from the second structure, whose average
similarity coefficient is equal to 0.67. The observed depen-
dence confirms that, in general, the main assumption
common to molecular spectroscopy is that similar structures
have similar spectra.
Experience has shown that the probability of coincidence
of the first-ranked structure with the correct one sufficiently
depends on the difference ¢2-1 between dA(2) and dA(1):
the greater the difference, the greater the probability that the
first-ranked structure is the target structure. The distribution
of ¢2-1 values for output files containing more than one
structure across the problem set is presented in Figure 13.
Investigations performed on a large number of problems
confirmed the following empirical fact, which was estab-
lished by us earlier:56 if the value ¢2-1 > 1 ppm, then the
structure ranked first has a significant probability of being
the correct solution to the problem. At the same time, it was
also found that the correct structures were distinguished by
structural ranking in many cases, even when the difference
¢2-1 was very small. It turned out that only in ca. 20
problems was the correct structure not placed in the first
position (see the problem distribution in Figure 14).
Figure 14 illustrates for a series of examples that the
correct structure was ranked as either second or third for
eight problems in each case. Analysis of the improperly
ranked solutions establishes that the cause of the incorrect
structure ranking is most frequently the absence of appropri-
ate structures from the database that allow precise prediction
of the chemical shifts of certain carbon atoms characterized
by unusual environments. In other cases, the carbon atom
environment was not poorly represented per se, but the
chemical shift of the given atom was unusual because of
some particular spatial effects. The following empirical
observation was deduced: for the majority of improperly
ranked structures, the difference ¢2-1 is less than 1. A large
dA(1) value in combination with a small ¢2-1 value is
suggestive of either improper structural ranking or incorrect
13C chemical shift assignment, the latter due to misassign-
ment by the investigator.
Traditionally, the developers of expert systems aspire to
minimize the structure generation time and the size of the
output file. However, the results presented above indicate
that an output file containing many thousands of structures
cannot seriously hamper the selection of the most probable
structure because the methods described push the actual
structure to the top of the rank-ordered file.
2.7. Deterministic versus Stochastic Systems. In his
paper,23 Steinbeck compares the results of structure elucida-
tions performed by the deterministic system LUCY3 and the
“stochastic” system SENECA on the basis of a simulated
annealing (SA) structure generation algorithm. Both systems
were developed by the author.
Steinbeck concluded that “the data in Table 2 are in
agreement with a polynomial behavior, which, in contrast
to the exponential growth of time for the LUCY calculation,
strongly suggests that the SENECA system will be able to
tackle problems too large for deterministic algorithms”.
We argue against this conclusion for the following reasons:
(a) The comparison is not with deterministic systems but
rather for a series of runs for the LUCY system. In the case
of polycarpol, the generation time was 120 times higher than
that of monochaetin, and we believe this reflects a peculiarity
within the system. Our calculations show that, with the
StrucEluc system,7,8 the comparative generation times were
only fractions of a second for tasks 1-3 given in Table 2
when executed on a 500 MHz Pentium III computer in an
automated mode and without the interference of a user. The
data obtained using other deterministic systems1,6,14,46 also
contradict Steinbeck’s conclusion. As demonstrated above
for deterministic systems, the structure generation time not
only depends on the number of heavy atoms in a molecule
but also, and to a higher degree, on the nature of the
information captured within the 2D NMR spectra.
(b) From the examples discussed (with molecular formulas
of C15H28O2, C18H20O5, and C30H48O2), it cannot be concluded
Figure 12. Average similarity coefficients of the first 10 ranked
structures. The first structure was the reference structure for
similarity.
Figure 13. Distribution of problems as a function of the difference
in deviations between the first and second ranked structures, dA(2)
- dA(1) values.
Figure 14. Position of the correct structure in output files for 20
problem sets where the first-ranked structure was not the correct
solution.
1652 J. Chem. Inf. Model., Vol. 46, No. 4, 2006 ELYASHBERG ET AL.

that the “SENECA system will be able to tackle problems
too large for deterministic algorithms”. This conclusion is
purely speculative and has not been proven by any examples
reported to date. The simulated annealing algorithm has not
been successfully applied to the analysis of problems that
could not be solved by deterministic systems.
(c) The comparison of the number of structures generated
by the SENECA simulated annealing program and the
StrucEluc deterministic system shows that, in the case of
monochaetin, StrucEluc produces 18 structures at the first
stage and, in the case of polycarpol, only 6. The first stage
is before spectral filtering is performed and identical
structures are removed. This demonstrates that the exhaustive
search in StrucEluc is performed within a highly restricted
area of the full isomer space, while SENECA searches
through hundreds of thousands of structures.
(d) The underestimation of the performance of determin-
istic expert systems is likely explained by the fact that
skeptics do not take into account that these systems are
intended to mimic an expert’s reasoning. Experienced
spectroscopists can determine the structures of molecules
with formulas capable of generating 1020-1030 isomers. In
doing so, a spectroscopist does not search the full isomer
space but identifies the probable structures by “tunneling”.
The possibility of performing computer-assisted structure
elucidation using such a “tunneling” approach is the most
important capability of a well-designed expert system.
Steinbeck has also expressed an opinion23 that the scoring
function itself makes the simulated annealing algorithm more
flexible by honoring the exceptions to the rules of interpreting
cross signals in 2D NMR spectra. While considering structure
generation in the presence of connectivities of nonstandard
lengths, the author concluded that deterministic algorithms
will fail and CASE systems will not find the correct structure.
As was mentioned above, structure generation tools capable
of coping with nonstandard connectivity lengths can be dealt
with in a deterministic system, and this considerably reduces
the structure space search area and generation time. Steinbeck
rightly notes, however, that the number of structures and the
generation time will grow and suggests that deterministic
algorithms will not honor the rareness of four-bond correla-
tions in HMBC spectra, while “in SENECA, this problem
can be easily overcome by the scoring system.” Steinbeck’s
declaration that four-bond HMBC correlations are a rare
phenomenon is arguable. According to our observations
described above, four-bond or even higher-order correlations
in both HMBC and COSY spectra occur quite regularly and
will likely be encountered even more often as investigators
have increasing access to instruments equipped with cryo-
genic NMR probes.54 The computer-assisted structure elu-
cidation of 250 natural products showed that nonstandard
correlations were observed in 2D NMR spectra in almost
half of the tasks examined (see Figure 7). To the best of our
knowledge, the statement that “in SENECA, this problem
can be easily oVercome by the scoring system” has not yet
been proven.
Faulon elaborated a stochastic structure generator called
SIGNATURE.57 He declared that “for large molecular
compounds, deterministic techniques are not applicable to
resolve the problem of structure elucidation. In such an
instance one has to use a stochastic structure generation.”
This suggestion has also not been confirmed experimentally.
To illustrate the superiority of stochastic generators over
deterministic ones, Faulon compared the efficiency of a very
slow and incorrectly working deterministic structure genera-
tor with that of SIGNATURE.57 For the molecular formula
C8H10, Faulon’s deterministic structure generator produced
4008 isomers in 353 s on an SGI Personal Iris Workstation.
He commented, “For comparison, the stochastic version of
the structure generator estimated the number of isomers to
be 3,399. To calculate this number the stochastic generator
was run for 16.5 s CPU time ...”. By comparison, StrucEluc
has generated 4679 isomers with the C8H10 composition in
0.023 s (Pentium IV, 2.8 MHz). The results described require
little additional commentary.
Despite these results, the potential use of stochastic
algorithms remains of interest. The successful selection of a
scoring function allows the algorithm to effectively direct
the search to an isomer subspace where the structures comply
with the constraints imposed by the 2D NMR data. An
advantage of the approach is that very few assumptions are
made prior to the structure elucidation run. Large fragments
do not need to be deduced from the spectral data in the
preprocessing run, and no particular hybridization states are
assumed. This does not indicate that additional data may not
be necessary in certain situations, for example, when a large
molecule has a structure with a deficit of hydrogen atoms
and a significant number of heteroatoms. Deterministic
systems can successfully solve such tasks as evidenced by
Table 1 and the materials presented in our previous
publications.7-12,27-29
In the examples given by Steinbeck,23 the number of
heteroatoms varies only from two to five nuclei, while the
problems solved with the use of the deterministic StrucEluc7,8
system contain structures where the number of various
heteroatoms can be up to 30 nuclei.
Another report published by Han and Steinbeck24 dem-
onstrates that the SENECA system has markedly expanded
the size of the molecular structures (20 heavy atoms) that
were examined with the genetic algorithms of Meiler and
Will25 using 1D NMR. This was achieved using 2D NMR
spectra and a strategy for structure generation that allows
for the application of a series of control parameters while
simultaneously having a well-selected fitness function. The
authors again did not succeed in demonstrating that the
stochastic algorithms could solve tasks of similar or greater
complexity than those solved by deterministic systems. The
results do suggest that this approach may indeed find
increasing applications in spectroscopic analysis, and the task
remains to validate the performance and reliability of the
approach. Even for small molecules with 15 skeletal atoms
(see Figure 1), the number of possible isomers is immense
(>1012), and the ability of the genetic algorithm to identify
Table 2. Calculation Time and Number of Iterations Required for
Three Example Compoundsa Studied with SENECA
calculation time
name
molecular
formula LUCY SENECA
number of SA
iterations performed
eurabidiol C15H28O2 29 s 5 min 90 000
monochaetin C18H20O5 16 s 9 min 250 000
polycarpol C30H48O2 33 min 12 min 350 000
a The calculation was performed using desktop PCs operating at
processor speeds of 600 MHz.
DETERMINISTIC EXPERT SYSTEMS J. Chem. Inf. Model., Vol. 46, No. 4, 2006 1653

the target structure in a short time is promising. It is quite
possible that future deterministic and stochastic expert
systems will become complementary in the solution of
specific structural problems. It can be expected that, if certain
components of a deterministic system are implemented in a
system utilizing a stochastic algorithm, then overall the
effectiveness of the system may be enhanced.
There is, however, a stage of molecular structure elucida-
tion that has been shown to demand the application of a
genetic algorithm. The relative stereochemistry of the most
probable structure and calculation of its 3D molecular model
has been addressed in this manner. Generally, the final step
in contemporary structure characterization efforts is to define
the relative and, if possible, absolute stereochemistries of
the individual centers. NMR-based determination of relative
stereochemistry is based on the nuclear Overhauser effect
(NOE), which is dependent on the distance separating the
cross-relaxing nuclides.58 Typically, NOESY or ROESY two-
dimensional NMR experiments or their selective 1D ana-
logues are used to provide the data for analysis. In a recent
study, we extended the capabilities of StrucEluc to the
derivation of multiple relative stereocenters in complex
structures such as taxol and brevetoxin. This work has been
described in detail elsewhere.30 An appropriate penalty
function was suggested30 that can be minimized by calcula-
tion for all rigid stereoisomeric structures or by using a
genetic algorithm to limit the number of stereoisomers that
need to be investigated. To improve genetic algorithm
convergence, efficient methods of parameter optimization
were suggested and compared.
To challenge the system, the structure of breVetoxin B (1)
was examined (Chart 1). This remarkable structure includes
11 rings, 23 stereogenic centers, and 3 carbon-carbon double
bonds. The CPU time necessary for running over all 8.4
million stereoisomers corresponding to this structure was
estimated to be about 1 month for a Pentium IV computer.
In Figure 15, the structure of brevetoxin B from X-ray
studies (yellow) and the structure obtained from the best
chromosome in the final pool for our system for stereo-
chemistry determination (blue) are shown as superimposed
structures. In this case, the configurations of all of the
stereocenters in both structures are the same. Even the
conformations of the most “flexible” seven- and eight-
membered rings are similar. This demonstrates the power
of the approach we have described to facilitate the identifica-
tion of relative stereochemistry in a complex molecule
containing multiple stereocenters.
3. CONCLUSIONS
This work was conducted for the purpose of evaluating
the capabilities of deterministic expert systems for elucidating
molecular structures from 2D NMR data. To achieve this
aim, a comprehensive analysis of the databases making up
the advanced expert system StrucEluc was performed. The
structural features of 250 molecules belonging to the class
of natural products that were identified with the aid of the
system under study were investigated. Simultaneously, the
influence of the nature of the correlations contained within
the 2D NMR spectral data used for elucidation was studied.
The program is shown to cope with those problems where
2D NMR data were assumed to contain an unknown number
of nonstandard (corresponding to nJHH,CH, n > 3) correlations
of unknown lengths.
It was conclusively demonstrated that the deterministic
expert system StrucEluc possessed algorithms allowing the
program to elucidate the chemical structures of complex
natural products containing at least 100 skeletal atoms. The
Chart 1
Figure 15. X-ray crystal structure of brevetoxin B (yellow) and the 3D model of the best stereoisomer calculated by StrucEluc. Small
differences in the bond angles of some of the more flexible rings are present, but all stereocenters have been properly oriented.
1654 J. Chem. Inf. Model., Vol. 46, No. 4, 2006 ELYASHBERG ET AL.

deterministic algorithm for structure generation in combina-
tion with an intelligent strategy of the most probable structure
selection provides complete solution of a problem in a short
timesfrom several seconds up to several minutes. This result
alone disproves the beliefs of other workers that molecules
containing 30 skeletal atoms were an upper limit for study
by deterministic expert systems and only stochastic algo-
rithms of molecular structure generationssimulated anneal-
ing and genetic algorithmsswill allow solving real problems
of great dimensionality.
At the same time, it was shown that genetic algorithms
could be efficiently applied within a deterministic expert
system. Recently, we extended our system30 to make it
capable of determining the relative stereochemistry of
complex rigid structures or molecules containing rigid
substructures that contain a large number of stereocenters.
To solve this problem, a genetic algorithm was used.
Including stereochemical assignment capabilities into
StrucEluc allowed the automation of all stages of identifica-
tion, from the spectra representing an unknown compound
to elucidation, stereocenter identification, and 3D model
generation.
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