Structure Elucidation from 2D NMR Spectra Using the StrucEluc Expert System:
Detection and Removal of Contradictions in the Data
Sergey G. Molodtsov,† Mikhail E. Elyashberg,‡ Kirill A. Blinov,‡ Antony J. Williams,*,§
Eduard E. Martirosian,‡ Gary E. Martin,| and Brent Lefebvre§
Novosibirsk Institute of Organic Chemistry, Siberian Branch of Russian Academy of Science,
Lavrentiev Avenue 9, Novosibirsk 630090, Russia, Advanced Chemistry Development, Moscow Department,
6 Akademik Bakulev Street, Moscow 117513, Russian Federation, Advanced Chemistry Development Inc.,
90 Adelaide Street West, Suite 600, Toronto, Ontario M5H 3V9, Canada, and Rapid Structure
Characterization Group, Global Research and Development, Pfizer, Kalamazoo, Michigan 49001-0199
Received January 26, 2004
The elucidation of chemical structures from 2D NMR data commonly utilizes a combination of COSY,
HMQC/HSQC, and HMBC data. Generally COSY connectivities are assumed to mostly describe the
separation of protons that are separated by 1 skeletal bond (3JHH), while HMBC connectivities represent
protons separated from carbon atoms by 1 to 2 skeletal bonds (2JCH and 3JCH). Obviously COSY and HMBC
connectivities of lengths greater than those described have been detected. Though experimental techniques
have recently been described to aid in the identification of the nature of the couplings the detection of
whether a coupling is 2-bond or greater still remains a challenge in most laboratories. In the StrucEluc
software system the common lengths of the connectivities, 1-bond for COSY and 1- or 2-bond for HMBC,
derived from 2D NMR data are set as the default. Therefore, in the presence of any extended connectivities
contradictions can appear in the 2D NMR data. In this article, algorithmic methods for the detection and
removal of contradictions in 2D NMR data that have been developed in support of StrucEluc are described.
The methods are based on the analysis of molecular connectivity diagrams, MCDs. These methods have
been implemented in the StrucEluc system and tested by solving 50 structural problems with 2D NMR
spectral data containing contradictions. The presence of contradictions was detected by the algorithm in
90% of the cases, and the contradictions were automatically removed in 50% of the problems. A method
of “fuzzy” structure generation in the presence of contradictions has been suggested and successfully tested
in this work. This work will demonstrate examples of the application of developed methods to a number of
structural problems.
1. INTRODUCTION
2D NMR spectra are the primary form of spectral data
used today for the elucidation, rather than the confirmation,
of molecular structures. During the past decade, a series of
expert systems based on 2D NMR spectral data have been
reported, for instance.1-5 Previously the ACD/Structure
Elucidator (StrucEluc) expert system was described, and the
results of structure elucidation for ca. 150 natural products
were discussed.6-11 The conclusion from these reports is that
the system is able to solve very complicated problems if the
2D NMR data are free of contradictions. Since the system
is adjusted by default to account for the coupling constants
2,3JHH and 2,3JCH which are common for COSY and HMBC
correlations correspondingly (referred to as “standard” cor-
relations), contradictions will appear when at least one
correlation of >3 bonds results in a response in the 2D NMR
data. Despite recent developments to aid in the identification
of the correlation lengths12,13 there is no presently available
NMR technique capable of distinguishing couplings of
different lengths in a reliable fashion. Therefore, development
of theoretical methods for 2D NMR data analysis that identify
the presence of “nonstandard” correlations is of considerable
importance.
During this work algorithms and programs have been
developed that are able to detect the presence of nonstandard
correlations in 2D NMR data in the majority of cases.
Moreover, algorithms that help to remove contradictions by
lengthening certain connectivities have been delivered. An
algorithm for “fuzzy” structure generation was elaborated,
which allows structure generation to be performed using the
condition that the lengths of several connectivities can be
varied by means of searching a set of connectivities. The
resulting programs were tested on 50 challenging elucidation
problems where the 2D NMR data were known to contain
nonstandard connectivities and the results are detailed in this
report.
2. DETERMINATION AND REMOVAL OF
CONTRADICTORY CONNECTIVITIES
2.1. Basic Terms and Definitions. In the StrucEluc expert
system, a molecular connectivity diagram (MCD) is used as
* Corresponding author phone: (919)570-0217; fax: (425)790-3749;
e-mail: tony@acdlabs.com.
† Siberian Branch of Russian Academy of Science.
‡ Advanced Chemistry Development, Moscow Department.
§ Advanced Chemistry Development Inc.
| Pfizer.
1737J. Chem. Inf. Comput. Sci. 2004, 44, 1737-1751
10.1021/ci049956+ CCC: $27.50 © 2004 American Chemical Society
Published on Web 08/04/2004

a graphical representation of connectivities that are obtained
from processed 2D NMR data (see examples reported in refs
6-11). Connectivities are designated as Ckl(Vi-Vj), to indicate
that vertices Vi and Vj are at a distance of k to l bonds from
each other in the chemical structure, while it is assumed that
Vi and Vj, in the general case, are skeletal atoms. For instance,
the vicinal coupling constant 3JHH observed in COSY implies
a connectivity C11(Vi-Vj) of length one bond and 2,3JCH HMBC
coupling constant is associated with a connectivity C12(Vi-
Vj) whose length varies from one to two bonds. In other
words, C12(Vi-Vj) (or 1,2- connectiVities) are connectivities
whose lengthes may be 1-1, 1-2, or 2-2 bonds.
A molecular connectivity diagram can contain connec-
tivities of two types: fixed and formal. Fixed connectivities
are those of a fixed length that are either specified by the
user on the basis of some prior information or are input on
the basis of certain 2D NMR methods (for example ref 12).
In particular, chemical bonds in a structure can be defined
as fixed connectivities. Examples of fixed connectivities
having length 1, 2, and 3 bonds correspondingly are C11(Vi-
Vj), C22(Vi-Vj), and C33(Vi-Vj).
Formal connectivities are those drawn by the MCD
program itself on the basis of 2D NMR data analysis and
with default correlation lengths assumed for each type of
two-dimensional spectra. In particular, default connectivities
C11(Vi-Vj) are produced from COSY data and C12(Vi-Vj) from
HMBC data. Formal connectivities can be divided into two
categoriessstandard and nonstandard ones. Formal con-
nectivities that correspond to the structure of the analyzed
molecule will be called standard connectivities, and they
allow the program to generate a correct structure.
If a 2D NMR spectrum contains correlations of a nonde-
fault length (exceeding the default upper limits) and their
lengths were not identified explicitly by the chemist, the
corresponding formal connectivities will be called nonstand-
ard. Note that in the case when there is no prior information
about the presence of nondefault correlations all formal
connectivities are considered as standard. Obviously formal
nonstandard connectivities contradict the structure of the
molecule under study.
Examples of nonstandard COSY (two C-C bonds, green
two-sided arrow) and HMBC (three C-C bonds, red one-
sided arrow) connectivities are shown below:
The nonstandard COSY connectivity C22(C3-C4) and
HMBC connectivity C33(C5-C2) will be accepted by the
program as C11(C3-C4) and C12(C5-C2) connectivities
correspondingly, if their true lengths were not specified by
the chemist on the basis of preliminary 2D NMR experi-
ments.
Since the structure generator is adjusted to utilize con-
nectivities of default (standard) lengths, nonstandard con-
nectivities, if present in a diagram, yield either a zero result
since no structure can be generated, or an invalid result where
the results file does not contain a correct structure. This
happens as the algorithm considers the topological distances
between corresponding skeletal atoms (they are specified by
inherent chemical shifts) of a nonstandard connectivity equal
to standard length, while in reality this distance is longer.
Therefore, nonstandard connectivities appear “nonstandard”
to the software algorithms. Nonstandard connectivities may
also appear due to heavy overlap of the NMR resonances or
accidental degeneracy which can lead to permuted pairs of
assignments.
We assume the fixed connectivities, unlike the formal ones,
are standard (correct) in all cases. A set of vertices in the
structure separated by a distance of k bonds from the V vertex
will be denoted as the kth layer of the V vertex environment.
The set of vertices in the structure separated by less than or
equal to k bonds from the V vertex shall be the kth sphere of
the V Vertex enVironment. Generally, an MCD is considered
to be a graphical representation whose vertices are skeletal
atoms of the molecule under study and with the hydrogen
atoms attached.
Assume that an MCD diagram is created on the basis of
a series 2D NMR spectra for an unknown. In other words,
there is a set of fixed and formal connectivities. The task is
to detect the nonstandard connectivities, or, at least, locate
these by detecting small groups of connectivities that contain
nonstandard responses. A correct solution and structure
determination of the compound under study can be achieved
only after the correction or elimination, of all nonstandard
connectivities.
Experience indicates that all nonstandard connectivities
can be partitioned into at least four different types which
are dependent on their position in the MCD and the extent
to which they contradict the rest of the connectivities:
1. Explicit nonstandard connectivities that contradict the
environment of a skeletal atom (vertex) and some fixed
connectivities that refer to this vertex.
2. A group of connectivities containing at least one
nonstandard connectivity. Vertices and vertex pairs with a
set of connectivities that contain nonstandard ones are
detected.
3. A group of connectivities referring to a vertex that
contradict other connectivities that refer to other vertices.
4. Implicit nonstandard connectivities that are not obvi-
ously contradictory but nevertheless prevent the elucidation
of a correct structure.
It is necessary to consider methods that allow the detection
and removal of each type of nonstandard connectivity.
2.2. Explicitly Nonstandard Connectivities. An explicitly
nonstandard connectivity can be detected if a vertex exists
whose fixed connectivities fully determine all Vertices and
all bonds between them in the rth sphere of this vertex
environment. If there are formal connectivities Ckl(Vi-Vj),
where l e r, defined for this V vertex, it is possible to
determine the appropriateness of each of the connectivities.
Furthermore, the validity of a formal connectivity
Ckl(Vi-Vj) may sometimes be determined even if not all the
Vertices and bonds in the first sphere of the V1 vertex are
defined. It is only possible if a set of the allowed environment
spheres is defined for each of the C-vertices. These spheres
are defined using the Atom Property Correlation Table
(APCT)11 and is based on chemical shifts of the appropriate
carbon atoms.
It should be noted that there is a significant difference
between the ambiguity associated with the HMBC or COSY
correlations and that associated with the APCT. For instance,
the HMBC correlations (in particular, the standard ones of
1738 J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 MOLODTSOV ET AL.

2 or 3 bond lengths) are defined by nature and cannot be
overcome without the development of new experimental
techniques for distinguishing correlations of different lengths.
This is true to a greater extent as related to the nonstandard
correlations. At present StrucEluc uses structure generators
to search all possible variants for the different distance
lengths of standard bond length selective NMR correlations
within a reasonable time frame since these bond length
selective NMR experiments do not presently exist. The
ambiguity involved in the elucidation process using APCT
data has a different character and is a consequence of the
fuzziness of knowledge regarding the interrelation between
units used to construct the molecular structure and their
associated spectral features. The diversity of the different
kinds of atom environments means that it is impossible to
enumerate all conceivable atom combinations and their
related spectral features. It is therefore necessary to determine
some typical atom combinations and associate assigned
ranges of spectral features which characterize them. The
boundaries of these spectral ranges are fuzzy since such a
combination could have a spectral feature (for instance, a
13C chemical shift) that is observed slightly out of the limits
of a specific range. While using the Atom Property Cor-
relation Table can be deemed to be a risky procedure, it is
difficult to avoid since it helps overcome the possibility of
a combinatorial explosion and the enormous time associated
with structure generation. Such a situation is inevitable in
the case of big molecules when there are a large number of
atoms and no assumptions can be made about the nearest
neighbors of a given carbon atom having specific chemical
shifts.
Example 1. Assume that the figure below represents a
fragment with the fixed bonds indicated for the Vl vertex
environment (in the figure the vertices are denoted by their
numbers, and the bond with a heteroatom provided for by
the APCT is represented by a dashed line):
Assume there is a formal HMBC connectivity C12(V1-V6) and
the APCT indicates that the V6 Vertex has no bonds with
heteroatoms. In this case, the V6 vertex cannot obviously be
located both in the first and second layers of the V1 Vertex,
and the C12(V1-V6) connectivity is, therefore, nonstandard.
Explicitly nonstandard connectivities can be removed
either by simply deleting them or by increasing the maximum
possible distance between the vertices. Replacing the C12(V1-
V6) connectivity with C13(V1-V6) in the above example ensures
that it is no longer nonstandard. Explicitly nonstandard
connectivities are the primary targets for detection and
removal during the elucidation process.
2.3. Sets Containing Nonstandard Connectivities. Obvi-
ously it is possible to determine the maximum possible
number of vertices in each layer and therefore in each sphere
of a vertex. The CH3 vertex, for example, always has one
vertex in the first layer, and no more than 3 vertices in the
second layer (e.g., CH3-C(C)3). The second sphere of a CH3
vertex therefore has no more than 4 vertices. Thus, if a CH3
vertex has more than 4 different 1,2-connectivities, at least
one of these must be nonstandard. The data regarding the
maximum possible number of vertices in the second sphere
are used as a criterion for detecting nonstandard connectivi-
ties in the vertices and vertex pairs with a relatively large
number of formal 1,2-connectivities.
2.3.1. Vertices with Nonstandard Connectivities. Con-
sider the molecular connectivity diagram of a compound
defined on a set of N vertices, where N is the number of
skeletal atoms in the molecule. The task is to determine if
the set of 1,2-connectivities of a given vertex V contains at
least one nonstandard connectivity.
As defined previously each C-vertex has a set of allowed
enVironment spheres defined on the basis of the correspond-
ing carbon atom chemical shift value and the total set of
vertices. A quaternary carbon atom with a chemical shift of
180 ppm (at the boundary of the chemical shift range
characteristic for esters and ketones) in a compound contain-
ing only C, H, and O atoms, for example, has the following
allowed spheres:
Having analyzed these sets, we can calculate the maximum
possible number of adjacent C-vertices and the maximum
possible number of adjacent vertices for each C-vertex.
Define the maximum possible number of the adjacent
C-vertices for the C-vertex V as DC(V) and the maximum
possible number of the adjacent vertices as D(V). Obviously,
DC(V) e val(V) and D(V) e val(V), where val(V) - is the
valence of the V-vertex. The following equations DC(u) )
val(u) and D(u) ) val(u) are presumed to be true for the
non C-vertex u.
It is assumed that there is a set of 1,2-connectivities for
the V vertex. The term “the admissible bond distribution of
the V Vertex” is introduced here and described as follows.
Take into account that bonds between separate vertices in a
structure can be provided as fixed connectivities and a bond
distribution of the V vertex to other vertices can be
constructed. For this purpose, bonds are drawn from the V
vertex to other vertices so that the sum of bond multiplicities
is equal to the valence of the V vertex and the resulting sphere
of the V vertex is allowable.
Let U ) {uj} be the set of vertices adjacent to the V vertex
and W ) {wk} be the set of vertices adjacent to at least one
vertex of U. The drawing below shows an example fragment
whose real bonds are shown as solid lines and hypothetical
bonds as dotted lines. Undefined vertices that can correspond
to either carbon atoms or to heteroatoms are marked as A.
The figure indicates that DC(u1) ) 1, D(u1) ) 2, DC(u2) )
3, D(u2) ) 3, DC(u3) ) 3, and D(u3) ) 3.
Consider whether the 1,2-connectivities of the V vertex
correspond to the obtained fragment. Obviously, the cor-
respondence for each formal C11(V-Vi) connectivity of the
V vertex can be determined. The C11(V-Vi) connectivity of
the V vertex corresponds to the fragment if Vi 2 U. If at least
STRUCELUC EXPERT SYSTEM J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 1739

one C11 connectivity of the V vertex does not correspond to
the fragment, the distribution of bonds for the V vertex is
inadmissible. Assume that all C11 connectivities of the V
vertex correspond to the fragment. Now check to determine
if any of C12 and C22 connectivities of the V vertex do not
correspond to the fragment. The C12(V-Vi) connectivity of
the V vertex does not correspond to the fragment if the vertex
Vi 2 U [ W and cannot be connected to any of the vertices
uj 2 U regarding the allowable enVironment spheres of the
Vi and uj vertices. If at least one C12 or C22 connectivity of
the V vertex does not correspond to the fragment, then this
bond distribution of the V vertex is inadmissible.
It is noteworthy that both the C12 and C22 connectivities
of the V vertex can be partitioned into three groups:
1. connectivities corresponding to the fragment;
2. connectivities not corresponding to the fragment;
3. connectivities whose correspondence to the fragment
are undefined.
Connectivities corresponding to the fragment contain
information regarding the distances between fragment-
compatible vertices. These distances will still be valid
regardless of the bonds between the vertices uj 2 U (i.e. the
vertices from the first layer of the V vertex) and other vertices.
However, in addition to these, there may be connectivities
that are feasible or infeasible depending on the vertices that
the uj vertex is bound to. The correspondence of the C12(V-
Vi) (or C22(V-Vi)) connectivity to the vertex is regarded as
undefined if the vertex Vi ∉ U [ W and there exists such a
vertex uj 2 U so that the bond between the Vi and uj vertices
is possible.
Assume that there are no C12(V-Vi) and C22(V-Vi) con-
nectivities of group 2 (connectivities not corresponding to
the fragment). For the time being disregard the C12 and C22
connectivities of the V vertex whose correspondences to the
fragment are confirmed. Later the rest of the connectivities
(group 3) whose correspondence to the fragment remains
undefined will be analyzed. Let K2(V) be the number of the
remaining C12 and C22 connectivities of the V vertex. In other
words, K2(V) is the number of vertices that are to be
additionally included in the second layer of the V vertex under
the bond distribution of the V vertex under consideration.
Let dC(uj) and d(uj) be the number of the adjacent
C-vertices and the number of the adjacent vertices of the uj
vertex in the examined fragment, respectively. Denote as
D2
C(V) ) ∑j[DC(uj) - dC(uj)] and D2(V) ) ∑j[D(uj) - d(uj)]
the maximum possible numbers of the additional C-vertices
and vertices in the second layer of the V vertex, respectively.
Thus, the following is true dC(u1) ) 1, d(u1) ) 2, dC(u2) )
1, d(u2) ) 1, dC(u3) ) 1, d(u3) ) 1 and D2C(V) ) 4, D2(V) )
4 for the fragment in the drawing.
Depending on the type of vertices, there may be two
cases: (1) all vertices Vi in the remaining C12(V-Vi) and C22-
(V-Vi) connectivities are C-vertices and (2) there is a non-C
Vi vertex. Consider the first case. Let all vertices Vi in the
remaining C12(V-Vi) and C22(V-Vi) connectivities be C-
vertices. Then, if K2(V) > D2C(V), it is impossible to locate
all vertices Vi from the remaining C12(V-Vi) and C22(V-Vi)
connectivities in the second layer of the V vertex; therefore,
the examined bond distribution of the V vertex is inadmis-
sible.
If, however, there is a non-C Vi vertex (second case), the
examined bond distribution of the V vertex is inadmissible,
when K2(V) > D2(V). The examined bond distribution of the
V vertex is termed admissible, if the fact that it is inadmissible
is not proven.
Let {Vi},i ) 1,...N be the set of vertices in the MCD. To
determine whether the given set of 1,2-connectivities of the
Vi vertex contains at least one nonstandard connectivity, all
possible bond distributions for the Vi vertex are consecutively
generated. Only if all bond distributions of the Vi vertex
appear to be inadmissible, can it be concluded that the set
of its 1,2-connectivities contains at least one nonstandard
connectivity. The algorithm below describes the process for
determining the vertices with nonstandard 1,2-connectivities:
0. i ) 0
1. i ) i + 1
2. Testing feasibility of recurrent bond distribution of the
Vi vertex. If the distribution is not allowable, it is concluded
that the set of 1,2-connectiVities of the Vi vertex contains at
least one nonstandard connectivity, go to 1.
3. The next distribution of bonds made with other vertices
in the Vi vertex is generated.
4. Verification of the bond distribution of the Vi vertex
for being admissible. If the bond distribution is inadmissible,
transfer to 2, otherwise, go to 1.
Example 2
Consider five 1,2-connectivities C11(V1-V2), C12(V1-V3), C12(V1-
V4), C12(V1-V5), and C12(V1-V6) to be specified for the V1(CH)
vertex in the fragment above, where the hypothetical heavy
atoms attached to the free bonds of the fragment are denoted
by A. It is also known that all the given vertices are
C-vertices, and the chemical shift values of the corresponding
C atoms indicate that the V1 atom is in the sp2-hybridization
state and that the V2-V6 atoms are in the sp3-hybridization
state. Presume that it is known that the V2 vertex corresponds
to the -CH2- group. Now, it will be proven that the given
set of 1,2-connectivities of the V1 vertex contains at least
one nonstandard connectivity.
The input data indicates that the V1 vertex can be bound
to two vertices only. Presume that all of the connectivities
associated with the V1 vertex are standard. Then, the V1 vertex
is to be connected to the V2 vertex by an ordinary bond, and
the second bond should have a multiplicity equal to two.
The vertices V3-V6 corresponding to the C-atoms in the sp3-
hybridization state cannot have incident multiple bonds and,
therefore, cannot be connected to the V1 vertex. As a result,
these 4 vertices are to be located in the second environment
layer of the V1 vertex regardless of the distribution of bonds
of the V1, i.e., K2(V1) ) 4. On the other hand, the maximum
possible number of vertices in the second layer of the V1
vertex is 3 (see the figure above). Therefore, all vertices
represented by V3-V6 cannot be simultaneously located in the
second layer of the V1 vertex regardless of its bond distribu-
tion. Hence, the given set of 1,2-connectivities of the V1
vertex contains at least one nonstandard connectivity, as
suggested.
2.3.2. Selection of Vertex Pairs Having Nonstandard
Connectivities. If nonstandard connectivities are not reVealed
1740 J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 MOLODTSOV ET AL.

as a result of an analysis of individual vertices, it does not
necessarily indicate that they are really absent. It may happen
that among the vertices for which the algorithm fails to detect
the presence of nonstandard connectivities it is possible to
find groups of vertices that possess the following property:
the union of connectivities included in the groups must
contain a nonstandard connectivity. At the same time, the
vertices included in the group may not have common
connectivities (see example below).
Currently consideration is given to groups containing only
two vertices and having 1,2-connectivities. This is for the
following reasons: (a) the number of possible groups formed
from more vertices would be rather large, and (b) in those
cases where a group containing many vertices with non-
standard connectivities was selected, the union of connec-
tivities belonging to these vertices would, in turn, contain a
great number of connectivities. This reduces the significance
of selecting a group of vertices. The smaller the set of
connectivities among which nonstandard connectivities exist,
the greater is the probability of removing any contradictions
in the initial connectivity set.
If a MCD contains N vertices, then the number of different
groups consisting of two vertices is obviously equal to Nâ
(N - 1)/2. In reality, only groups where both vertices contain
1,2-connectivities can be considered, while the presence of
nonstandard connectivities is not revealed for these particular
vertices. As an example, assume that two vertices A and B
are examined and at least one of them has an associated
nonstandard connectivity. The algorithm can fail to detect
the presence of the nonstandard connectivity. However, when
these vertices are unified in a group of two vertices, the
algorithm could become capable of detecting the presence
of a nonstandard connectivity in the connectivity set formed
from the connectivities belonging to both vertices.
Let {V1,V2} be a group of two vertices where each contains
1,2-connectivities. Consider all bond distributions at the
vertex î1 one at a time. For each bond distribution of vertex
î1 consider all bond distributions at î2 vertex. This will help
to determine the admissibility of the bond distributions of
both the î1 and î2 vertices. If it is shown that there are no
admissible bond distributions for î1 and î2 vertices, it will
prove that the 1,2-connectivity union of both î1 and î2
vertices contains at least one nonstandard connectivity.
Consider the algorithm describing the connectivity analysis
of the vertex pair.
1. Check whether the next bond distribution of the vertex
î1 is possible. If the distribution is not possible, then end
the analysis at this point. It is concluded that the set of 1,2-
connectiVities of î1 and î2 Vertices contains at least one
nonstandard connectiVity.
2. The next bond distribution of the î1 vertex is then
generated for the rest of the vertices.
3. Check whether the next bond distribution of the vertex
î2 is possible. If the distribution is not possible then go to 1.
4. The next bond distribution of the î2 vertices is then
generated for other vertices.
5. Check whether the bond distribution of the î1 and î2
vertices is admissible. If the bond distribution of least one
of these vertices is not admissible, then go to 3. Otherwise,
end the analysis at this point. The conclusion is that the set
of 1,2-connectiVities of î1 and î2 Vertices is admissible.
Example 3. Let V1(CH3), V2(CH2), V3(C), V4(CH), V5(CH2),
V6(CH), and V7(CH) be vertices, and the NMR chemical shift
of the corresponding C atom indicates that the î2 vertex is
bonded to an oxygen atom (designated as vertex O). In
addition, the following formal connectivities are given for
the î1 vertex: C12(V1-V3), C12(V1-V4), C12(V1-V5), C12(V1-V6)
and for the î2 vertex: C11(V2-V7), C12(V2-V3). It can be shown
that the given 1,2-connectivity set related to the î1 and î2
vertices contains at least one nonstandard connectivity.
Assume all connectivities specified at vertices î1 and î2 are
standard. It is evident from the connectivities of vertex î1
that a unique admissible bond distribution at vertex î1
exists: it must be bonded to the î3 vertex. In reality the CH3
vertex always contains only one vertex in the first layer of
the environment, while no more than 3 vertices can exist in
the second layer (see the figure above). Therefore, the first
and second layers of the CH3 vertex environment may not
contain more than a total of 4 vertices. In this case, exactly
four vertices will be present in the environment only if the
CH3 vertex is connected with a tetravalent C-vertex having
no multiple bonds. Since there are four C12 connectivities at
the î1 vertex, only vertices V3, V4, V5, and V6 located at
opposite ends of the connecting bonds can be present in both
the first and second layers of the î1 vertex environment, and
the î1 vertex has to be connected to the tetravalent C-vertex.
As is shown in the figure among all the vertices V3, V4, V5,
and V6 only the î3 vertex is a quaternary C-vertex. Conse-
quently, the î1 vertex must be connected to the î3 vertex,
while the vertices V4, V5, and V6 are located in the second
layer of the î1 vertex environment as shown in the figure.
Furthermore, taking into account the fact that the î2 vertex
is connected with the O-vertex and considering the con-
nectivity C11(V2-V7), it is obvious that the î2 vertex has a
unique bond distribution: the î2 vertex must be connected
with both the î7 and O vertices. The figure illustrates that
the î7 and O vertices adjacent to the î2 vertex cannot be
connected with the î3 vertex, that is, the unique bond
distribution of the î2 vertex is inadmissible. It follows that
the union of 1,2-connectivities at the î1 and î2 vertices must
contain at least one nonstandard connectivity. It is impossible
to prove the presence of a nonstandard connectivity at the
î1 and î2 vertices if at least one of the mentioned connec-
tivities is removed. This explains why the algorithm is not
always capable of indicating the possibility of a nonstandard
connectivity present in an MCD.
2.3.3. Nonstandard Connectivity Removal When Ver-
tices and Groups of Vertices with Nonstandard Connec-
tivities Are Revealed. To remove problems from a set of
connectivities containing nonstandard connectivities two
methods are suggested:
1. Lengthen the shortest connectivities of the set by one
bond.
2. Lengthen all connectivities of the set by one bond.
The first method is used when it can be supposed that the
presence of nonstandard connectivities C11 is more probable
STRUCELUC EXPERT SYSTEM J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 1741

compared with the probability of the presence of C12
nonstandard connectivities in a given problem. At the same
time all connectivities of equal length are assumed to have
the same probability of being nonstandard. The choice of
method for the removal of a nonstandard connectivity is the
choice of the user. The second method is generally employed
more frequently however. In each specific case, the best
manner to remove contradictions is determined by trial and
error.
The general strategy for contradiction removal in 2D NMR
data consists of two steps: first, all vertices and groups of
vertices having, according to the algorithm, nonstandard
connectivities are determined, and then all connectivities
included in these “suspicious” connectivity sets are length-
ened by one bond. If the contradictions are removed as
soon as vertices with nonstandard connectivities are detected
it is possible that the presence of nonstandard connectiv-
ities at another vertex will become undetectable after the
error is removed from the connectivity set of a given
vertex.
Assume î1 and î2 are two vertices whose connectivity sets
contain nonstandard connectivities. Allow a connectivity
C11(V1-V2). Lengthen the connectivities at the î1 vertex only.
In particular the connectivity C11(V1-V2) will be replaced by
C12(V1-V2). Now two cases are possible:
¥ Repeated analysis shows that the set of connectivities at
the î2 vertex does not contain nonstandard connectivities.
Consequently, lengthening only one connectivity at the î2
vertex removes the “inaccuracy” in the set of connectivities.
It is assumed that all short connectivities are nonstandard
with equal probability.
¥ As before, repeated analysis shows that the connectivity
set at the î2 vertex contains nonstandard connectivities. Then,
lengthening all connectivities at the î2 vertex will lead to
the replacement of the C12(V1-V2) connectivity by C13(V1-V2),
i.e. the length of the initial C11(V1-V2) connectivity will be
extended more than those of any of the other connectivities.
This is undesirable since it will make structural constraints
buried in the 2D NMR data more fuzzy and will, as a result,
increase in more structures being generated. Additional
structures, where î1 and î2 vertices are separated by three
bonds, will be generated in the presence of the C13(V1-V2)
connectivity, which would be impossible in the presence of
the C12(V1-V2) connectivity.
As a result of lengthening the connectivity we obtain a
renewed initial connectivity set. At this stage the search for
nonstandard connectivities begins over in the renewed
connectivity set.
2.4. Nonstandard Connectivities that Prevent Structure
Generation. Assume that explicit nonstandard connectivities
as well as vertices and groups of vertices having nonstandard
connectivities are not found in the initial or renewed set of
connectivities. Nevertheless, when the presence of contradic-
tory data prevents the generation of chemical structures
corresponding to all connectivities, it may be possible to
detect the presence of nonstandard connectivities in the initial
connectivity set. Moreover, it is possible to predict a vertex
containing nonstandard connectivities.
A bond distribution for a vertex î is termed accurate if
the bond distributions of all filled vertices, including the î
vertex, are admissible. If all accurate bond distributions at
the î vertex are analyzed, then it may be possible to
determine the obligatory and forbidden bonds between the
î vertex and other vertices. If all accurate bond distribu-
tionsof the î vertex contain any bonds, then all of these bonds
are defined as obligatory ones. Bonds that are absent in all
the accurate bond distributions are forbidden. Detecting
obligatory and forbidden bonds in a chemical structure is
based on the assumption that all the given connectivities are
standard.
It is necessary to sequentially conduct a bond analysis of
all vertices. If, when analyzing bonds at the î vertex, it is
found that there is no accurate bond distribution of the given
vertex, it means that the connectivities of the î vertex are at
variance with the connectivities of the vertices analyzed
earlier. It follows that the assumption regarding the validity
of all connectivities is incorrect, and as a result the MCD
will therefore contain some nonstandard connectivities. The
bond refinement of any vertex directly influences the bond
analysis of all the other vertices. Hence, after the bond
analysis of the last vertex, it is necessary to start analyzing
the bonds of the first vertex. Bond analysis is only complete
when new obligatory and forbidden bonds are no longer
identified as a result of successive bond analysis of all
vertices.
Let i be the number of the current vertex under examina-
tion, j, be the number of the vertex for which the analysis of
connectivities is completed, and let N be the total number
of vertices in a structure. The algorithm for checking the
MCD for the presence of nonstandard connectivities can be
written in a series of steps as follows:
1. i ) 1, j ) 1.
2. Perform the bond analysis of the îi vertex. If the
accurate bond distributions of the îi vertex are not found by
bond analysis of this vertex, then END the procedure. It can
be concluded that the connectivities belonging to the îi vertex
are in contradiction with all remaining connectivities, and
the initial data set therefore contains nonstandard ex-
amples.
3. Determine new obligatory and forbidden bonds of the
îi vertex with other vertices. If refinement is possible, then
j ) i.
4. i ) i + 1. If i ) N + 1, then i ) 1.
5. If i ) j, then END the procedure. The conclusion will
be that nonstandard connectivities cannot be identified.
6. Return to step 2.
It should be noted that in practice the vertex for which
the contradiction was identified during bond analysis
often contains nonstandard connectivities. This follows from
the fact that the number of vertices having nonstandard
connectivities is usually small. Most frequently, bond anal-
ysis is carried out initially for vertices with standard
connectivities. As a result the correct obligatory and forbid-
den bonds are determined in the structure. When a contradic-
tion is identified during the bond analysis of a recurrent
vertex, it is very probable that the nonstandard connectivities
of a given vertex are in conflict with those belonging to
vertices which have already been analyzed. In any case, the
connectivities of the found vertex are then lengthened to
attempt removal of the contradictions, after which the
check for the presence of nonstandard connectivities is
restarted.
Example 4. Assume that the formal connectivities
C11(V1-V2), C12(V1-V3), C12(V1-V4), C12(V2-V6), C11(V3-V5), and
1742 J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 MOLODTSOV ET AL.

C12(V4-V5) are set as the fragment vertices for V1(CH3),
V2(dC<),V3(dCH-), V4(dCH-), V5(dCH-), and V6(dCH-) as
illustrated in the drawing below:
In a situation where the fragment structure is unknown it
can be shown that the connectivity set given above contains
at least one nonstandard connectivity.
Assume that all the suggested connectivities are standard.
Bond analysis of the V1-V4 vertices provides the following
conclusions:
¥ The î1 vertex with connectivities C11(V1-V2), C12(V1-V3),
and C12(V1-V4) can be connected only with the î2 vertex.
¥ The î2 vertex can be connected with the î1, î3, and î4
vertices only, since only the bond distribution of the î1 vertex
will be admissible in this case. All the connectivities of the
î1 vertex will be standard.
¥ The î3 vertex with the C11(V3-V5) connectivity can only
be connected with the î2 and î5 vertices.
¥ To allow the possibility of the C12(V2-V6) connectivity at
the î2 vertex (see fragment A in the drawing below), the î4
vertex can be connected with the î2 and î6 vertices only.
Analyze the bonds at the î5 vertex. To provide an accurate
description of the bond distribution at the î5 vertex it must
be connected to the î3 and î6 vertices since the C12(V4-V5)
connectivity will not correspond to the obtained fragment
for all the other bond distributions of the î5 vertex. As a
result of vertex bond analysis fragment B is obtained as
illustrated below:
All the vertices of the given fragment already have the
necessary number of adjacent vertices. The fragment vertices
cannot therefore be connected with the remaining vertices
of the structure. Consequently, a contradiction is identified
during the bond analysis of the î5 vertex, i.e., the given set
of connectivities contains nonstandard members.
Consider the operating sequence for the determination and
removal of nonstandard connectivities using an example
for which the 2D NMR data were borrowed from the litera-
ture.14 The solution for this problem will be given
below.
Example 5. Comparison of the experimental data with the
true molecular structure supplied with assigned 13C NMR
chemical shifts showed that there were two nonstandard
connectivities. These are the COSY formal connectivity
C11(2-18) marked with the bold green two-sided arrow and
the HMBC formal connectivity C12(16-22) marked by a bold
red one-sided arrow. From hereon only the vertex numbers
are shown to describe the connectivities.
The following description outlines how the algorithm reveals
the connectivity sets containing nonstandard connectivities.
During the early stage of the analysis a search for explicitly
nonstandard connectivities is carried out. In this case it
showed that nonstandard connectivities were absent. In the
second stage, the check for the presence of vertices and
vertex pairs having nonstandard connectivities is performed.
For this data set, the algorithm revealed that only the î2(CH3)
vertex had nonstandard connectivities. The program arrived
at this observation in the following way.
The starting point is that the following three connectivities
are given at the î2 vertex: C11(2-18), C12(2-23), and
C12(2-24). According to the experimental data the î18(CH)
vertex has äC ) 69.8 ppm and äH ) 5.65 ppm. Comparison
of these values with the data of the Atom Property Correla-
tion Table shows that the î18 vertex cannot be connected
with the three neighboring C-vertices, i.e., DC(V18) ) 2.
Assuming that the C11(2-18) connectivity is standard, the
î2 vertex must be connected with the î18 vertex and,
consequently, dC(V18) ) 1 and D2C(V2) ) DC(V18) - dC(V18)
) 1. On the other hand, K2(V2) ) 2, as two connectivities
C12(2-23) and C12(2-24) remain at the î2 vertex. As a result
K2(V2) > D2C(V2) and consequently, there exists at least one
nonstandard connectivity in the connectivity set at the î2
vertex.
If the user defines that short connectivities, those having
only one bond C11(îi -îj), should first be lengthened, then
the connectivity C11(2-18) will be replaced by C12(2-18).
This corresponds to the real relative positions of the î2 and
î18 vertices in the structure. As a result of connectivity
lengthening a renewed set of connectivities is obtained. The
search for nonstandard connectivities now continues in the
renewed set of connectivities. However, in this example
repeated analysis does not identify nonstandard connectivities
in the first and second stages, so the presence of the
nonstandard connectivity C12(16-22) remains undetected.
In the third stage, the presence of nonstandard connec-
tivities that prevent the building of structures is checked.
Vertices whose connectivities are in contradiction with the
connectivities of other vertices are now searched. The
analysis starts with the î1 vertex, while none of the bonds
implied by the formal C11 connectivities are set.
As a result of bond analysis of the î1(CH3) vertex, with
connectivities C12(1-12), C12(1-16), and C12(1-21), it is
shown that the î1 vertex can be connected only with the î11,
î12, or î13 vertices. From the indicated connectivities
belonging to the î1 vertex it follows that three C-vertices
î12, î16, and î21 are present in first and second layers of the
î1 vertex environment.
STRUCELUC EXPERT SYSTEM J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 1743

Initially consider the possibility of the î1 vertex being
connected to the î12, î16, and î21 C-vertices. To provide for
feasibility of all the connectivities at the î1 vertex, the î1
C-vertex must be connected with one of the mentioned
vertices that, in turn, must be connected with the two
remaining C-vertices. Therefore the î1 vertex can only be
connected to a vertex with bonds to three C-vertices. Only
the î12 vertex possesses this property among the trivalent
vertices î12, î16, and î21, since the î16 and î21 vertices must
be connected with the O-vertex, as follows from the 13C and
1H chemical shifts of the corresponding atoms.
Now suppose that the î1 vertex is not connected with any
of the C-vertices î12, î16, and î21. From this it follows that
the î12, î16, and î21 vertices have to be situated 2 bonds from
the î1 vertex, all of them being C-vertices. Thus the î1 vertex
can be connected only with vertices that, in turn, can be
connected with four C-vertices. As with all structural vertices
only the tetravalent C-centers may have 4 neighbor vertices.
Therefore the î1 vertex can be connected only with tetrava-
lent C-vertices that, in turn, are connected with four
C-vertices.
Among all vertices describing the structure, only two
C-vertices, î11 and î13, can be connected with four C-vertices.
For instance, the tetravalent C-vertex î22 cannot be connected
with four C-vertices because its 13C chemical shift ä(C22) )
78.2 ppm indicates that an oxygen atom is a neighbor of
this carbon atom. Consequently, the î22 vertex cannot be
connected with four C-vertices. Thus, the î1 vertex can be
connected only with one of the î11, î12, and î13 vertices.
To determine which of the possible vertices that V1 is
bound to, we must consider other correlations associated with
each of the possibilities. In doing so, we begin with an
analysis of the bonds emanating from the î7 (CH3) vertex
with connectivities C12(7-10), C12(7-11), C12(7-14), and
C12(7-23) which shows that the î7 vertex can be connected
with only one of the vertices î10, î11, î14, and î23; in addition,
this vertex must be tetravalent. Among the mentioned
vertices, only the î11 vertex possesses this property indi-
cating the î7 vertex must be connected with the î11 ver-
tex.
Next, the î9 (CH2) vertex has connectivities C11(9-16)
and C11(9-17) and is obviously connected with the î16 and
î17 vertices. For the next vertex, î11, which is already
connected with the î7 vertex, it must be connected to the
î10, î14, and î23 vertices to conclude all connectivities
belonging to the î7 vertex. This means that the î11 vertex
cannot be connected with the î1 vertex. As a result, the
following fragment is constructed:
The î12 (CH) vertex has the connectivity C11(12-19). This
vertex cannot be connected with the î1 vertex as this would
require the following fragment
and consequently, both connectivities C12(1-16) and C12(1-
21) cannot be standard. It can be concluded that the î1 vertex
can be connected only with the î13 vertex. Bond analysis of
the î13 vertex leads to the conclusion that this vertex has to
be connected with the î1, î12, î16, and î21 vertices to provide
a set of connectivities at the î1 vertex. Thus, the following
fragment is established:
Continuing, the bonds of the î16(CH) vertex are analyzed.
This vertex has the following 7 connectivities: C11(16-9),
C12(16-1), C12(16-13), C12(16-17), C12(16-21), C12(16-
22), and C12(16-26).
The drawing shows that the first five connectivities
correspond to the assembled fragment. The chemical shifts
measured for the î16 vertex äC ) 68.9 ppm and äH ) 5.59
ppm indicate that, according to the APCT, this vertex cannot
be connected with the three neighboring C-vertices, and
consequently the î16 vertex has to be connected with
O-vertex, as shown in the representation below:
Counting up the maximum number of vertices that can also
be present in the second layer of the î16 vertex environment
only the O-vertex has one free valence bond in the first layer
of the î16 vertices shown in the drawing above. As a result
the second layer of the î16 vertex environment can therefore
contain one additional vertex only, i.e. D2
C(V16) ) 1. At the
same time, from the connectivities C12(16-22) and C12(16-
26) it follows that two vertices, î22 and î26, must also be
present in the second layer of the n16 vertex environment,
i.e., K2(V16) ) 2. As a result K2(V2) > D2C(V2) and conse-
quently the unique bond distribution of the î16 vertices is
inadmissible. The contradiction was identified when the
bonds of the î16 vertices were analyzed. To remove the
contradiction, all connectivities belonging to the î16 vertex,
specifically the nonstandard connectivity C12(16-22), are
lengthened by one bond.
Note that if the vertex numbering started from the vertex
that currently has the number 16, the analysis would also be
started here, and the contradiction would be found during
the analysis of other vertices depending on the vertex
numbering.
2.5. Implicit Nonstandard Connectivities. Thus far, we
have considered only the detection of nonstandard connec-
tivities that prevents final structure generation. However,
there are situations (see the examples in section 3) when
building the structures corresponding to all the defined
connectivities, including the nonstandard ones, is possible.
In these cases it is impossible to identify the nonstandard
connectivities and this leads to inValid solutions. It is
possible, even after successfully checking the data for
contradictions that nonstandard connectivities remain un-
noticed by the algorithm. Their presence can only be
identified in indirect ways, including the following: (a) large
1744 J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 MOLODTSOV ET AL.

value(s) for the 13C NMR spectral deviations11 calculated
for the most probable structure(s); (b) inconsistencies
between the most probable structure and additional experi-
mental data (for instance, NOESY, ROESY, etc.); (c)
comparison of the chemical shifts and multiplicities of the
experimental and calculated data of 1H NMR spectra; and
(d) by checking the structures using infrared correlation tables
(if an IR spectrum is available) and/or interpretation of a
mass spectrum, if available. The nonstandard connectivities
that do not prevent the structure from being built are termed
implicit nonstandard connectivities.
As the identification of implicit nonstandard connectivities
cannot be guaranteed since any of the given connectivities
may be nonstandard, a method of removing nonstandard
connectivities was developed and tested that in some cases
allows the identification of a valid solution even in this
situation.
To remove implicit nonstandard connectivities, the fol-
lowing approach is suggested. Some connectivities are
declared as a series to be suspicious and are lengthened or
eliminated. Each time the structure generation is initiated
with a renewed connectivity set. This process is termed Fuzzy
Structure Generation.
Let n be the total number of connectivities and m be the
number of connectivities that are suggested to be nonstand-
ard. In this case it is necessary to consider (mn ) ) (n!/m!(n -
m)!) different sets from m connectivities that will be declared
as suspicious. The calculation time increases dramatically
as the number of tasks resulting in structure generation
sharply increases with the rise of the m value. At present
we consider those cases when me5. The suspicious con-
nectivity concept has a number of applications. Declaring
members of the connectivity sets to be suspicious is
sometimes useful for search vertices and pairs of vertices
with nonstandard connectivities as well as the direct deter-
mination of the presence of nonstandard connectivities. In
these cases, the program usually lengthens all connectivities
belonging to the vertices selected during data analysis. In
so doing both nonstandard and standard connectivities are
deliberately lengthened, which correspondingly leads to an
increase in the number of structures generated. If only the
definite connectivities (related to vertices at which the
presence of nonstandard connectivities are revealed, termed
found vertices) are lengthened, then the number of generated
structures will be considerably lower. In some cases the total
time of structure generation will decrease despite the repeated
initiation of the generation process. This is explained by the
fact that most connectivity sets that do not contain connec-
tivities emanating from the found vertices are excluded from
consideration. Furthermore, during the vertex bond analysis
process and the lengthening of definite connectivities, a
greater number of obligatory and forbidden bonds can be
established relative to the case when all the connectivities
at the found vertices are lengthened. In this case the structure
generation time with the new connectivity sets can sharply
decrease.
It is worth noting that in the presence of vertices with
nonstandard connectivities, sets of connectivities declared
as suspicious must contain connectivities belonging to all
found vertices. This indicates that the considered number of
suspicious connectivity sets will decrease.
The problem considered in Example 5 with the number
of nonstandard connectivities equal to two (m)2) can be
solved using the Fuzzy Structure Generation. As discussed
in section 3.1 (Example 1), a single correct structure was
generated in 13 s. For this article all calculations were
performed on a PC Celeron operating at 500 MHz, Win-
dows98, RAM 128 Mb.
3. MOLECULAR STRUCTURE ELUCIDATION IN THE
PRESENCE OF CONTRADICTIONS IN 2D NMR DATA
Over 150 separate elucidations using 2D NMR literature
data as well as raw 2D NMR spectra have been performed
in this work. In accordance with the methodology described
in earlier reports6,7,11 spectral data taken from the literature
or other sources were entered into the program, and the
structures were assumed to be unknown. Later, an attempt
was made to elucidate the structures on the assumption that
no information existed regarding the presence of contradic-
tions in the 2D NMR data. For one-third of all problems
analyzed, about 50 tasks, this subset was used to perform
experiments to determine and remove the contradictions. This
was feasible since the 2D NMR data related to these
problems certainly contained COSY and/or HMBC connec-
tivities of nonstandard length. For convenience this term
“connectivities of nonstandard length” is used to denote
spin-spin couplings that are present over distances longer
than those set as defaults in the system options.
In this section the results of this work will be analyzed. It
was shown that the program was capable of determining the
presence of connectivities of nonstandard length in 90% of
all cases using the MCD checking procedure described in
section 2. These results are very encouraging since experi-
mental methods guaranteeing the precise determination of
COSY and HMBC connectivity lengths are not available.
Knowledge of the presence of contradictions in 2D NMR
data can give the investigator valuable information that can
determine the strategy of structure elucidation with these data.
An invalid suggestion regarding the presence of nonstandard
connectivities may appear only if there are contradictions
between the atom properties and the Atom Property Cor-
relation Table (APCT) used during the data analysis. The
validity of the statement can be checked by repeated data
verification with the APCT disabled. Such cases actually aid
in the development and correction of the correlation tables.
A false statement can also appear in rare cases when an
unknown under study contains a pair of bonded hetetroatoms.
The absence of such atomic pairs is set in the program
options as the default. In these cases a message regarding
the “existence” of contradictions can help the chemist to
reveal the presence of bonded heteroatoms. For instance, it
allowed the detection of the O-O group from only the
published shift data, during the elucidation of mycaperoxide
H.15 With this in mind there were no cases of incorrect
detection of nonstandard connectivities when solving ca. 100
tasks where contradictions in 2D NMR data were not present.
For about 50% of cases studied, the program not only
identified the contradictions in the data correctly but also
was able to successfully remove them automatically to allow
determination of the correct structure. Examples were
encountered where the program resolved contradictions
caused by the presence of a large number of nonstandard
connectivities (up to 8).
STRUCELUC EXPERT SYSTEM J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 1745

In six of 50 cases the program was unable to determine
the presence of connectivities of nonstandard length. In five
of those six cases the 2D NMR data contained only one
nonstandard HMBC connectivity. This occurrence can be
explained by the fact that if there are only one or two HMBC
nonstandard connectivities in the data, the atoms in the
structure may be arranged so that their arrangement complies
with the standard length of all connectivities. If the number
of nonstandard connectivities is large, such an arrangement
of atoms is unlikely. The presence of implicit nonstandard
connectivities can become apparent as a result of structure
generation and their subsequent filtration with the use of
spectral libraries: if all the generated structures obviously
contradict the spectral data, the program generates an empty
results file. Indirect evidence of the possibility that contradic-
tions were not detected may be an empty results file or large
values, more than 5.5 ppm, of the chemical shift deviation,
dA, calculated for the first ranked structure.7,11 Investigations
have shown that nonstandard connectivities were detected
by both direct and indirect methods for 95% of the analyzed
tasks containing contradictory data. If there are reasons to
assume that the program did not detect contradictions in the
initial data it would be highly likely that the problem could
be solved with the use of “fuzzy” structure generation as
described in section 2.
Since it is possible that 2D NMR data could contain
implicit nonstandard connectivities, the most probable struc-
ture generally requires additional verification by independent
methods. In particular, if the structure is generated after
automatic contradiction removal, it is still desirable to check
for the presence of nonstandard connectivities. For this
purpose a preview mode in the Structure View window exists
to view the connectivities. If such connectivities are found,
they can be verified with appropriate experimental parameter
optimization to probe the values of the spin couplings.16,17
It has been shown18 that incorrect structures are often rejected
on the basis of predicted chemical shifts and multiplets in
the 1H NMR spectrum (see the examples below).
Experience gained in this work shows it is not always
possible to find nonstandard connectivities and to automati-
cally resolve the contradictions in 2D NMR data sets. These
investigations show that in practice the following difficult
situations may typically arise:
1. The program detects the presence of nonstandard
connectivities and makes an attempt to remove the contradic-
tions in the data but then reports that contradictions cannot
be removed. Sometimes fuzzy structure generation can help
to solve the problem. Generally additional experiments are
required in an effort to detect nonstandard connectivities.
2. The program fails to detect nonstandard connectivities
and displays a message informing the researcher about the
absence of contradictions. In this case, structure generation
is initiated. The following outcomes are possible: (a) no
structure is generated and (b) the wrong structure(s) is
generated.
3. The program detects the presence of nonstandard
connectivities, makes an attempt to remove the contradictions
in the data, and displays a message that the contradictions
were removed, though, in fact, contradictions remain. This
is due to the fact that not all nonstandard connectivities are
lengthened. Possible consequences are similar to those listed
for point 2 above.
It should be obvious that the most dangerous situations,
when incorrect solutions are offered, can occur for points 2
and 3 and will be considered later. Even in the case when
the program is not able to remove detected contradictions,
case 1, the fact that contradictions are identified is still
extremely important.
In this section attention will be focused on examples that
demonstrate how a correct result can be obtained using the
StrucEluc system in those cases where the program does not
remove all contradictions. First we will cite several examples
of the successful automatic removal of contradictions from
2D NMR data.
3.1. Examples of Successful Contradictions Removal.
Example 1. In the work of Shen et al.14 a natural product
(1), related to the class of taxoids, was identified. For this
compound the authors presented 1H and 13C NMR data as
well as COSY and HMBC correlations in the form of peak
tables. These data were used as inputs to the StrucEluc
system. The given molecular formula was C28H42O12 with
MW ) 570 and the number of skeletal atoms being nsk )
40:
The molecular formula and the cross-peaks from the COSY,
HMQC, and HMBC spectra were fed as inputs into the
program. These formed tables containing 22 HMQC direct
correlations, 21 COSY cross-peaks, and 47 HMBC correla-
tions. As mentioned above, the default settings of the
program are such that the COSY and HMBC spectra
distances between intervening spins are within 2-3 bonds.
This means that the default connectivity lengths are one
skeletal bond for COSY correlations and from one to twos
for HMBC experiments (see section 2.1). Comparison of the
cross-peaks with the molecular structure, a process that can
only be performed after the structure of an unknown
compound is determined, showed that one long-range cor-
relation 4JHH (H2-H18) exists in the COSY spectrum and
one exists in the HMBC 4JCH (H16-C22). These long-range
COSY and HMBC connectivities are shown on the structure
1 with the corresponding two-sided green and one-sided red
arrows. These correlations contradict the default options, and
consequently the correct structure will not be generated. If
additional 2D experiments are not performed, it is impossible
to determine in advance which correlations may be non-
standard. Information regarding experiments utilized to check
the correlation lengths was not available in ref 14.
The MCD was automatically created by the program using
the peak tables as a basis. When the Check MCD for
Contradictions command was applied, the program displayed
the appropriate message that some correlations contradicted
the standard values. The algorithms attempted to resolve the
contradictions in an iterative mode. The procedure required
1746 J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 MOLODTSOV ET AL.

two iterations and 28 s to successfully resolve the contradic-
tions. The process for detection and removal of contradictions
was described earlier in section 2.4 (Example 5). An
important feature of an advanced expert system is the ability
to create an audit trail of the actions and decision-making
process. This is particularly useful when a scientist needs to
review, repeat, or “tweak” the elucidation. To support this
function a “contradiction resolution protocol” is generated
by the StrucEluc system. In addition, connectivities that were
edited by the program appear in the MCD marked by colors
corresponding to the new connectivity lengths. For this
example, one C11 connectivity and all 1,2-connectivities
belonging to the carbon 16 as well as one C11 connectivity
at the carbon 2 were lengthened by 1 bond. The protocol
indicates the results of each iterative step of the program
and produces a complete list of the new lengths of connec-
tivities introduced.
Based on the MCD with the corrected connectivity lengths,
the generation and filtration of structures using spectral
libraries and a structural BADLIST (Bredt’s rule, unstable
fragments) were performed. No changes were made to the
default atom properties. The program generated 1 molecule
identical in structure to structure 1 in about 3 s (This is
denoted as k ) 1, tg ) 3 s.). The deviation values (dA )
1.34 ppm, dF ) 3.09 ppm, dH ) 0.21 ppm) are appropropriate
for a correct structure determination. Here the subscripts A
and F are used for denoting different types of 13C NMR
spectral prediction, correspondingly known as the accurate
and fast methods, while H defines 1H NMR spectral
prediction.11 This task was also successfully solved using
the Fuzzy Structure Generation mode. Assuming that the total
number of nonstandard connectivities in both types of
spectra, COSY, and HMBC did not exceed 2, the correct
structure was generated in 13 s.
Example 2. The program was applied to the structure
generation of betulinic acid (2)19 C30H48O3, whose COSY
spectrum contained only one nonstandard connectivity
C22(109.9-19.5). Note that here the COSY connectivity is
represented via the chemical shifts of carbon atoms to which
the intervening hydrogen atoms are attached.
Contradictions in the 2D NMR data were searched and the
one contradiction identified was removed by the program,
and, as a result, only one correct structure was generated in
1 s. A similar result was obtained in the Fuzzy Structure
Generation mode with m equaling 1 and 2.
In the examples described above, the program successfully
overcame contradictions in the presence of one and two
nonstandard connectivities. Note that the number of non-
standard connectivities may be much larger, up to 10 or more.
Example 3
In case of the analysis of horiolide (3),20 whose 2D NMR
spectra contain five nonstandard connectivities C22(17-23),
C22(7-23), C22(7-17), C22(7-5), C33(6-17) in the COSY
data and 1 nonstandard C33(15-13) connectivity in the
HMBC spectrum (remember that they are accepted by the
program as having lengths common for COSY and HMBC)
as indicated with arrows on the structure, the program found
and automatically removed all contradictions. As a result,
the only structure to be generated was the correct structure,
and tg ) 1 s (dA ) 3 ppm).
Example 4. The 2D NMR spectra of triterpene E, C30H48O2
(4), which was isolated and characterized by Reynolds et
al.,21 contained a total of 8 nonstandard connectivities: 7 in
the COSY spectrum and 1 in the HMBC.
All contradictions were resolved automatically in 3 iterations,
and one, correct structure, was generated in 7 s.
3.2. Resolving Contradictions in Complicated Cases.
Example 1. It is possible that the program will not detect
the presence of connectivities of nonstandard length. In these
cases when the program fails, for a data set containing
HMBC and COSY connectivities the COSY data are often
excluded from consideration, and an attempt is made to solve
the problem from the HMBC data only. In so doing, the
HMBC data are analyzed again, as these data may contain
no contradictions or the contradictions may be resolvable
and, consequently, a solution can be found. In the previous
example if the COSY data of triterpene E are excluded from
consideration, only one nonstandard HMBC connectivity
C33(12-26) is left. The new MCD was checked, but the
program did not detect the one remaining contradiction.
An attempt to generate structures, both using and ignoring
the APCT, resulted in empty output files, characteristic of
the presence of contradictions in data. If the contradictions
are not found at the checking stage, but structure generation
indicates they are present as noted above then this may be
STRUCELUC EXPERT SYSTEM J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 1747

indirect evidence that there are a small number (1 or 2) of
nonstandard connectivities.
Fuzzy Structure Generation was attempted without impos-
ing any constraints. The m parameter was set to 1. The result
was k ) 120, tg ) 4 min, dA(1) ) 1.81 ppm, ¢(2-1) ) dA(2)-
dA(1) ) 0.22 ppm, rA ) rH ) 1, rF ) 2. Here ¢(2-1) is the
difference in deviation values between the second and first
structures in the structural output file ranked in ascending
order of dA(i) values (i)1k); rA, rF, and rH are the ranks
assigned to the correct structure by the different methods of
spectral prediction.11 The generation was repeated after
manual correction of the nonstandard connectivity (12-26),
which resulted in k ) 81, tg ) 25 s, rA ) 1. In this case, the
fuzzy mode using m ) 1 was 9 times slower, and the number
of generated structure was 1.5 times greater.
Example 2. When the program is not able to detect
connectivities of nonstandard length, the structure generation
results in either an empty or invalid result file. In the latter
case the large dA(1) deviations usually indicate that the results
are incorrect. When the structure of hermitamide (5) was
elucidated from the published22 HMBC data, the program
did not reveal the presence of the C33(27-23) connectivity,
and as a result, two structures were generated in 12 s.
The deviations dA(1) ) 5.75 ppm, dF(1) ) 5.67 ppm are
large enough that the obtained solution is suspicious. For
this reason, the generation was repeated in the fuzzy mode
with m ) 1. The result was k ) 394f42, tg ) 6 min 30 s,
dA(1) ) 0.90 ppm, dF(1) ) 1.60 ppm, and dH ) 0.09 ppm
(the arrow indicates how the size of the output file is reduced
as a result of removing identical structures). The resulting
preferred structure and the chemical shifts assignment of the
13C NMR spectrum coincided with those given by the
authors.22
Example 3. This example demonstrates the ability of the
program to verify the validity of the 2D NMR data and the
results of structure elucidation reported in the literature.
Horgen et al.23 reported the structure of a novel natural
product (6), isolated and identified as maleVamide-D on the
basis of spectroscopic data:
The high-resolution ESI mass spectrum of (6) gave a
molecular ion m/z 733.5114, suggesting the molecular
formula C40H68N4O8. The 1H, 13C, COSY, HMQC, and
HMBC NMR spectra were recorded and presented in a peak
table without any indication of the presence of correlations
of nonstandard lengths. The information captured in this table
was used to determine the structure using the StrucEluc
program. Checking for contradictions did not reveal the
presence of any connectivities of nonstandard length, and
structure generation was completed in the automated mode
without any limitations imposed. The results were k )
40f10, tg ) 4 s. Ranking the obtained structures suggested
the following structure as the most likely:
This solution does not formally allow us to question the
validity of the generated structure, since the deviations of
the three different types of calculated spectra from the
experimental ones are minimal and the absolute values of
the deviations are well within the statistical limits: dA(1) )
1.452, dF(1) ) 2.725, and dH(1) ) 0.240 ppm. Comparison
of the resultant structure with that obtained by the authors
shows clearly that they differ in the functional groups
highlighted in the central part of the molecule. The differing
fragments are marked with bold lines in structures (6 and
6′). It can be seen that the differences are fairly subtle. The
calculation of the Tanimoto similarity match factor between
the structures gave a value of 0.96. The validity of the
generated structure is doubtful when the difference between
the experimental and calculated 1H NMR spectra is consid-
ered. Using the ACD/HNMR prediction component of the
program, comparison of the spectra indicated differences in
the region 0.5-1.5 ppm. The predicted doublet of the methyl
group (C6) at äH ) 1.4 ppm is absent in the experimental
spectrum. There are two suggestions that will explain this
observation: either the authors elucidated the wrong struc-
ture, or the 2D NMR data contains nonstandard connectivities
that were not revealed by the program.
Comparison of the HMBC correlations with structure 6
identified the presence of the 6JCH correlation C55(7-21) as
indicated with the dotted arrow in structure 6. However, the
search for contradictions in the 2D NMR data produced no
results. This indicates that the program identified an arrange-
ment(s) of atoms under which the corresponding topological
distances between the carbon nuclei, represented by their
chemical shifts, are the same as the default values. In other
words, the program found that it was possible to generate a
chemical structure that meets both the constraints and the
atom properties assigned by the program with the help of
the APCT. As can be seen in structure 6′ atoms 7 and 21
are separated by two C-C bonds that corresponds to the
standard HMBC connectivity.
This observation was communicated to the authors23 with
the result of a misprint in the published tables being
identified. The experimental data actually displayed a HMBC
connectivity C12(6-7) of standard length (see structure 6).
After the initial data were corrected, the generation was
repeated with the following results: k ) 156f44, tg ) 4 s,
dA(1) ) 0.721 ppm, dF(1) ) 2.148 ppm, dH(1) ) 0.170 ppm,
1748 J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 MOLODTSOV ET AL.

rA ) rF ) rH ) 1. The most highly ranked structure that was
generated, coincided with that reported by the authors,
structure 6. The deviation values dA(1), dF(1), and dH(1) were
also less than those calculated initially for the wrong
structure. In fact, the dA(1) value was decreased by a factor
of 2. Note that the HMBC correlation between CH3-6 and
CH3-7 would generally not be possible in the structure 6′,
or, if a correlation were observed, it would be weak.
The conclusion of this study is that if the program is not
able to reveal nonstandard connectivities, it is possible that
the program can generate a structure similar to the correct
one. As noted above it is always desirable to verify the
solutions suggested by the software for their correctness and
stability. It can be very effective to check the structural
validity by comparing the experimental and predicted 1H
NMR spectral patterns visually. The stability of the result
can be verified by lengthening some connectivities to which
the weakest peaks of the 2D NMR spectra correspond, by
loosening the limitations on the atom properties, or by using
the fragments from the knowledge base. It may also be of
value to use the ACD/Structure Elucidator system in the
mode which uses the 1D 13C NMR spectrum only to perform
structure elucidation.11,18 If the first structures of the ranked
result files from several generation processes are different,
the most probable structure is the one with the minimal dA(1)
value.
Example 4. The next example indicates how the combined
usage of different system tools can help in solving challeng-
ing problems. In this case,24 the HMQC, COSY, and
CIGAR-HMBC spectra were used to elucidate cytochalasin
(7), C29H36N2O5. Comparison of the table of 2D NMR peaks
cited in the original publication with the structure suggested
by the authors revealed the presence of one nonstandard
connectivity C33(17.4-57.6) in the HMBC data.
Solution of this problem proceeded using an iterative method
with the use of various system tools.
Iteration 1. Checking the MCD revealed the presence of
contradictions. Repetitive checking with the automated
correction of the connectivities gave a message informing
that the contradictions had been removed. Visual analysis
of the corrected MCD showed that the connectivity (17.4-
57.6) had not been lengthened, but other correct connectivi-
ties (126.4-14.0), (126.4-17.4), (126.4-57.6), (63.7-57.6),
and (63.7-NH) had been lengthened. In reality the program
had not managed to remove the contradictions in the data,
and the user may be oblivious to this fact. The program made
this conclusion because it eventually became possible to
generate structures from the “corrected” MCD. So, with the
assumption that the program correctly adjusted the MCD,
structures were generated with only one limitation, no four-
membered cycles should be present, with the following
results: k ) 3486, tg ) 32 min. To identify the most probable
structure without calculating the 13C NMR spectra of 3500
structures, the system knowledge base was searched for
fragments using the method described previously.8,11 The
program selected 4427 fragments. Searching for functional
groups in the selected fragments showed that around 500
fragments contained a benzene ring. Experience has shown
that in this case, it would be safe to assume that there is a
benzene ring in the molecule under analysis. Filtering the
resulting file using a GOODLIST containing a benzene ring
reduced the file to 48 structures. After rank ordering
following NMR spectral prediction the most preferable one
was structure 7′ characterized by a deviation of dA(1) ) 3.40
ppm. The structure with the assigned experimental chemical
shifts is shown below:
The atom chemical shifts, topological peculiarities of the
structure, and dA(1) values are acceptable, and there was no
basis to reject the structure. The length of the connectivity
17.4-57.6 in this structure, marked with the solid arrow in
the drawing, is also “standard”. Investigation of the structure
in the ConnectiVity Viewing mode showed that it had three
HMBC 4JCH connectivities as indicated with the dashed
arrows. If the experimental spectra were available to the
authors a check for found nonstandard connectivities using
the potential relationship with the intensities of the corre-
sponding peaks of HMBC spectrum would be made or
alternatively additional experimental data would be gener-
ated.
In the absence of such opportunities the 1H NMR spectrum
was calculated and compared with the experimental one. A
considerable difference in the region 1-2 ppm was ob-
served: instead of a singlet äH ) 1.52 ppm (äC ) 17.4 ppm)
for the methyl group observed in the experimental spectrum,
in the calculated spectrum a doublet at äH ) 1 ppm was
assigned to this methyl group. A conclusion was made that
the generated structure was incorrect and Fuzzy Structure
Generation may be an appropriate path forward from the
initial, not corrected, MCD.
Iteration 2. Fuzzy Structure Generation was performed
using m ) 1 and a restriction on the presence of four-
membered ring cycles. The result was k ) 4552, tg ) 36
min. As with the previous iteration, to reduce the size of the
resulting file, the structures were filtered using a GOODLIST
containing a single benzene ring. The result gave k )
4552f112, dA(1) ) 1.94 ppm, dF(1) ) 3.09 ppm, dH(1) )
0.30 ppm, and rA ) rF ) 1 and the most preferable generated
structure corresponded to that reported in the publication.24
Iteration 3. Comparison of the 13C NMR subspectra of
the first fragments from the beginning of the list indicated
that they were quite consistent with the spectrum of the
analyzed molecule. A solution was sought using these found
fragments. The following calculation parameters (see defini-
STRUCELUC EXPERT SYSTEM J. Chem. Inf. Comput. Sci., Vol. 44, No. 5, 2004 1749

tions11) were selected: l ) 100, E ) 2.5 ppm, q ) 0, nf )
1 which resulted in n(MCD) ) 11. Fuzzy structure generation
using m ) 1 gave k ) 16f12, tg ) 8 s, rA ) rF ) 1. Fuzzy
Structure Generation using fragments elucidated the structure
270 times faster.
4. CONCLUSION
This work has analyzed the various situations which may
appear when there are COSY and HMBC connectivities
whose length is greater than the values set as default in the
ACD/Structure Elucidator system (1 skeletal bond for COSY
and from 1 to 2 skeletal bonds for HMBC). From this a series
of classifications has been defined. “Nonstandard” connec-
tivities are classified as those connectivities that resulted in
an incorrect solution or gave no solution resulting in an
empty output file. A series of nonstandard connectivity
classifications has been identified; sets of connectivities
containing nonstandard connectivities at one or several
vertices; sets of connectivities of one vertex contradicting
the connectivities of other vertices; and implicit nonstandard
connectivities that caused no contradictions but caused the
wrong structure generation. Each case has been examined
using practical examples with an analysis of the cor-
respondence between subgraphs built from the vertices
(skeletal atoms) of the considered molecule and the connec-
tivities connected to the vertices of graphs.
The algorithms developed iteratively as a result of this
work have been implemented into the StrucEluc system and
tested on 50 tasks whose 2D NMR data contained correla-
tions with lengths exceeding the default values in the system.
The presence of nonstandard connectivities was automatically
revealed by the program in 90% of the cases studied. In
almost 50% of cases the program removed the contradictions
by lengthening the connectivities at corresponding vertices
or vertex pairs, which led to successful problem solution. It
has been shown that the program is capable of resolving
contradictions and solving problems in cases where the
number of nonstandard connectivities in the data set can be
large, up to 8 connectivities to date.
A series of typically challenging situations has been
identified that may appear during the elucidation of a
molecular structure from 2D NMR data containing contra-
dictions. Complications appear when the presence of con-
tradictions in the initial data is not recognized by the
program. These are the so-called implicit nonstandard
connectivities. Also complications arise when a false message
is generated that suggests that the contradictions have been
removed. Nonstandard connectivities could remain undetec-
ted mainly in those cases where the data contain one or two
nonstandard HMBC connectivities. The probability of detect-
ing the contradictions increases with a concomitant increase
in the number of carbon atoms for which the properties are
strictly set, for example the presence of C-X bonds where
X is explicitly specified as a carbon or a heteroatom eases
the search through the MCD for the presence of contradic-
tions. Methods of structure elucidation depending on the
various situations that can be encountered have been outlined
in this article. In those cases where the number of nonstand-
ard connectivities did not exceed five, a solution could be
found with the help of Fuzzy Structure Generation in a
reasonable time.
The authors are continuing to work on improving the
efficiency of the data analysis processes and specifically on
the removal of contradictions. Experience suggests that this
can be achieved by further analysis of the atomic environ-
ments in the MCDs (Molecular Connectivity Diagram). At
present a publication is in preparation which describes the
results of further development of the Fuzzy Structure
Generation algorithm. This allows the solution of structural
problems even in the presence of 15-20 nonstandard
connectivities (4J or 5J). These results were obtained during
the review period for this manuscript.
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