The general scheme of scientific investigation consists of three
main components: the experimental (observational) part, the construction
of a compilation of the experimental data available in the scientific
literature, and the interpretation of different data sets selected from
this compilation via some systematic way. The more experimental results
are in principle available, the more labour consuming the extraction of
the data sets to be used for the data processing related to some
(theoretical) models becomes. The models with the proved degree of
reliability can be employed for the prognosis of the new data for the
situations not yet studied experimentally . Such prognosis is an
essence of the use of scientific results for different practical
applications. The use of the computerized approach for the automation of
the stages of the process described, enabling the generation of primary
experimental data, is the topic of this communication. This is realized
on the example of the rate and equilibrium constants for the heterolytic
chemical reactions. However, the technique described and the related
software can be applied in other fields as well.
The traditional way of the general representation of existing
quantitative experimental data is reduced to the compilation of the
related information into tables published as a series of books
("hard copies"). For the field stated above, it is a result of
the efforts of the scientific team at the Department of Chemistry of the
University of Tartu during 1970-1990. The set of 16 volumes (10 basic
and 6 supplementary ones) of the Tables of Rate and Equilibrium
Constants of Heterolytic Organic Reactions was created and published [2,
3]. The number of the independent data rows covered reached nearly 500
DATABASE OF RATE AND EQUILIBRIUM CONSTANTS
The extraction of the systematically organized data compilations
from the Tables mentioned is a labour consuming and wearisome business.
Especially, if one takes into consideration that closely related data
are located in the basic as well as in the supplementary volumes. This
is inevitable when new data becoming available are involved.
Therefore, from the very beginning of the use of computers a
project was started for the generation of software for the computerized
systematic storage and retrieval of such information. However, one has
to keep in mind that the computers available at the beginning of the
1970s were hardly applicable for convenient practical use for this
purpose. Only the last generations of powerful PCs enable to obtain an
acceptable solution to this problem for an ordinary user.
The system described was created by combining separate parts as
For the storing of the reactivity information, a special language,
LINCS (Linear Coding of Structures), has been created [4, 5]. This
language represents the chemical structures of reactants via connected
labelled graphs with atoms as the nodes and chemical bonds as arcs. All
additional information about reaction conditions (logarithms of the
values of rate or equilibrium constants, solvents, temperature,
pressure, chemical ingredients added, methods of measurement, and
literature sources) is represented by additional nonconnected labelled
nodes. The possibility of distinguishing of the reaction centre from the
remaining part of the corresponding molecule (for instance, the
substituent) is introduced. The information represented via LINCS codes
is automatically converted into graph tables used for the internal
Secondary coding via introduction of direct codes (DC) for
arbitrary substituents (discrete parts of the molecules) is introduced.
Users can voluntarily define these DC, representing any fragments of
molecules by single nodes. They can be used for a more compact
representation of the LINCS codes, employing the conventional symbols
used by chemists. For each DC a sequence number can be introduced. This
makes possible an alternative numerical coding of (structural)
information, which is the preferred way of the representation of the
information when the sets of initial data for (statistical) processing
have to be created. For instance, the DC denoted as ET (or Et) can be
substituted for the basic LINCS code (<<< C.H > .H >.
<<< C.H > .H > .H >>) for the fragment
(substituent) called ethyl (C[H.sub.3]-C[H.sub.2]-). No limit exists for
the complexity of structural units for which the DC can be introduced
but the maximum amount of the memory reserved for the storage of a
single LINCS code.
For the retrieval of information from the database, two different
versions of software are available. One of them represents a dialogue
version of the selection of a branch of the tree of hierarchically
organized reactant structures, with the possibility of defining the
limiting restrictions for the selection of the solvent, temperature, and
pressure. This version is realized  for the Bronsted
acidity--basicity and equipped with the graphical representation of the
chemical structures. Its use is reduced to the sequence of choices of
the structural types and solvents until the terminating branch is
reached. The results of each session of data retrieval are visualized
graphically on the computer screen and saved for subsequent fast
reproduction, making use of the computer program specially suited for
this purpose. Additionally the results of each session are stored in a
plain text file. This version enables visual observation of the whole
procedure of the ordering of data and the results of their retrieval.
Therefore, it is suitable for the purpose of training students. However,
it is not very convenient for the creation of specifically organized
data sets for their further use for some kind of processing (checking
the degree of their conformity to some mathematical model etc.).
For the last purpose, the other version for the retrieval of data
has been created. This covers all types of the reactions represented in
the database. The more general types of reactions are identified with
basic digital codes (sequence numbers M). Altogether 16 such general
reaction types are covered by the database. More concrete subtypes of
reactions are labelled by the secondary digital codes (N) and the
complete reaction code is represented by their combinations like M/N,
which corresponds to the LINCS code of some definite structure of the
reaction centre and its change in consequence of the respective chemical
process. Special labels are in use for the denotation of the breaking
and forming of bonds and the way (polarity) of the bond breaking and
formation. The set of digital codes is related to "elementary"
substituents (any one can be declared as such if the corresponding DC is
declared). For complex substituents, the bridging fragments or their
sequences can be introduced. These bridges connect some elementary
substituent with the reaction centre. They are defined via corresponding
bivalent structural fragments represented by respective DC and related
digital codes. For instance, DC as 1Ph4 for the p-phenylene bridge with
LINCS code--<:C:CH::C:CH::>[4.1 - (for the DC for CH
is already substituted) can be used. The order for data retrieval
consists of the reaction code M/N or reaction LINCS code with actual or
variable substituents connected to the (indexed) position(s) at the
reaction centre. Additionally, the list of sequence number(s)
(index(es)) of the substituent(s), and of the (components of) solvent
can be specified. Solvents can be represented by the corresponding DC
and sequence number (solvent index), too. It is also possible to specify
the value of molar percentage or other concentration measure stored for
a particular data set for the second component of the binary mixed
solvent, the temperature (range), the pressure (range), and other
restrictions for the experimental method, and different notes and the
literature sources for data rows to be retrieved. If these restrictions
are not specified, all data rows for the reaction ordered are retrieved
and listed in the file with the name specified by the user.
THE DATA TABLE FOR THE OBSERVATION SPACE SPECIFIED
This approach enables automatic composition of the table of data
designed for further treatment. This table consists of data rows and
columns. The latter define the conditions (further the term
"factors" is used) to be specified to grant the
reproducibility of the experimental measurements. Each factor involved
can be represented by some formal (sequence number for the reaction,
substituent, or solvent) or pithy (for instance the value of absolute
temperature) specification. This is possible via specification of a set
of distinguishable variable levels it may occupy (different substituent
in a definite position, different solvents, etc.). Consequently, the
table cited is comprised of rows, each of them representing some
independently measured value called response (in the case under
consideration the logarithm of rate or equilibrium constant) as well as
of a set of corresponding factor levels for all variable factors
involved. The factors stay constant for the entire observation space
(OS) defined, can be specified for the table as a whole, and they can be
omitted from particular data rows. So, the data table is represented by
a set of the columns formed by response values. Each of them represents
a selection of the levels for some given factor in correspondence with
each data row specified. The table described represents actually the OS
formed by the coordinate axes represented by factors and the response as
a dependent value . The latter can be considered a functional from
the coordinates defined by the factor axes.
The retrieval system described enables automatic formation of
differently defined particular experimentally described OS if the
corresponding data are available in the database.
SOFTWARE FOR STATISTICAL TREATMENT OF THE DATA FROM SOME
OBSERVATION SPACE FORMED
For some kind of conceptual quantitative interpretation of the
particular OS the corresponding mathematical model has to be employed.
For this purpose, the formal factor levels do not represent explicitly
the arguments (descriptors) the response value is dependent on.
Therefore, for each factor a single or several descriptor scales have to
be defined and substituted for the corresponding selection of the factor
levels. For some factors, the corresponding scale is independently
available. For instance, the reverse value of the absolute temperature
(1/T) can be substituted for each T value. This procedure is justified
by the fundamental thermodynamic approach, although the empirical data
obtained via the observation of the temperature dependence of the
isobaric volume or the isochoric pressure for the ideal gas are usable
for this purpose as well. The possible descriptor scales for the
practically successful use are defined mostly on the basis of empirical
data. Nevertheless, it is reasonable do distinguish between scales
available independently of the particular OS to be interpreted, or
established proceeding from the results of the (statistical) data
processing applied to the corresponding data set itself. In the case of
success, a new set of descriptors related to the influencing factors is
In the field of reactivity, spectral and several other sets of data
the approach called "Correlation Equations" (CE) has been
widely used through years. As a result, different sets of substituent
and solvent constants are available for the use as the descriptors
related to corresponding factors (variable substituent or solvent). For
these constants, the essential physical or chemical interpretations are
assigned. One can differentiate the substituent polar or steric
properties or the solvent polarity, polarizability, as well as the
hydrogen bonding acidity and basicity, responsible for the existence of
the specific solvation of the solutes.
The CE represent, in general, multiparameter linear functions of
the response values on the sets of constants considered as descriptors.
Each data column involved is characterized by the coefficients of the
(multi)linear regression and characteristics that reflect the quality of
WAYS OF SOLVING THE PROBLEM OF NON-ORTHOGONALITY
The greatest difficulty connected with the multilinear approach is
due to the non-orthogonality (mutual linear interdependence) of the
descriptor scales used . This is a case for both the descriptor
scales defined independently of the data compilation processed and
established as a result of this processing.
The classical way to define the scales of substituent or solvent
constants is to find out a data set presumably related to a single
definite property characteristic for some variable factor. If there
exist a number of data series dependent on a single "pure"
descriptor scale, the response values for all of them are in mutual
(nearly) linear dependence. On the other hand, the observation of such
kind of mutual linearity for a family of the sets of experimental data
related to some common variable factor is considered a proof of the
existence of such single scale. As the logarithms of the rate and
equilibrium constants are linearly related to the free energy changes
for reactions (equilibriums) or activation (rates), the term
"linear free energy relationships" (LFR) has been introduced.
As the spectral frequencies are linearly related to the corresponding
excitation energies, the more general formulation "linear energy
and free energy relationships" (LEFR) is used. It was very soon
realized that these linear dependences are, in the general case, held
roughly or not at all. This was considered as a proof that in the
general case the LEFR do not hold (at least not precisely enough). As a
further development of this approach, it has been assumed that more than
a single property and the corresponding descriptor scale can be related
to the same influencing factor. Therefore, multiparameter relationships
were introduced. If more than a single factor is varied for some
selection of data (e.g. the simultaneous variation of the substituent,
solvent, and temperature), the multi-parameter processing of data
In favourable cases, some descriptor scales may be nearly
orthogonal for a definite selection of the corresponding factor levels.
Nevertheless, even if this is the case for some more numerous set of
data for different (combinations of) factor(s) levels, it is usually not
true for several subsets of these data. If a number of points for the
mutual plot of two independently defined scales related to some
selection of data rows do not represent a corresponding linear
dependence, this does not apply for the different subsets of data rows.
For these this kind of interdependence may be more or less pronounced
just by chance. In the limiting case, a straight line can be drawn
through any two non-coinciding points.
For the case of the data matrixes with all positions filled, the
method called Factor Analysis (FA) can be used to define a set of purely
formal but orthogonal descriptors (called Factors) . Up to now, there
remain two main shortages of FA, which considerably limit its use. One
of them is a lack of a fully distinct criterion for the detection of a
number of significant factors. In addition, as already mentioned, its
use is limited to the completely filled data matrixes, mostly not
available for the sets of existing data. Although there may exist some
ways for overcoming these difficulties, in this paper FA is not
considered. The main reason is that this approach does not directly lead
to the definition of the descriptors with some definite essential
(physical or chemical) meaning.
Sufficiently numerous data compilations are usually incomplete. If
for a large part of the points of the corresponding OS the response or
the descriptor values are lacking (no empirical data are available), the
non-orthogonality of the descriptor values for the sets of data rows for
particular response columns is rather a common case.
Therefore, the quantitative characteristics of the degrees of
orthogonality or non-orthogonality were defined and the procedure was
elaborated for the derivation of the nearly orthogonal sets of the
descriptor scales for the complete set of rows present in the data set
processed. Besides the regression coefficients and their scaled
versions, the contributions into the total variance (dispersion) by the
different significant descriptors are characterized by their weights.
These values differ from the corresponding orthogonal figures
represented by the squares of the correlation coefficients
[R.sup.2.sub.xy]) between the column of the response values and of the
corresponding descriptor column. The difference between this value and
the weight obtained as a result of actual data processing is considered
as a measure of the "mixed" part of the weight value. The
corresponding scaled (by [R.sup.2.sub.xy]) value [W.sub.mixd] represents
the relative measure of the influence of the non-orthogonality on the
contribution of the related descriptor. If the absolute value of
[W.sub.mixd] is larger than 1.0, the observed weight value is mainly
defined by the concerted effect of other descriptors present and has
little to do with the real influence of the descriptor it is nominally
related to. Therefore, if [absolute value of W.sub.mixd] 1.0 W >
(other limiting thresholds can be used), the corresponding term in the
expression for the response value can be considered not to possess an
essential meaning and deserves to be omitted.
A procedure was elaborated for removing (subtracting) from each
subsequent descriptor scale the contributions of the preceding ones to
obtain a set of nearly orthogonal "pure" (residual) descriptor
vectors for the whole set of rows processed.
DATA PROCESSING PROGRAM
The software created for testing multilinear mathematical models
for the description of a set of response columns related to some OS can
be ordered for use [8, 10]. In this case, the main procedures are
executed automatically as follows:
The regression of all response columns present in the table of
initial data, with the selection for each of them of only such
descriptors that are statistically significant on the risk level
assigned, with the mixed component of weight not exceeding the threshold
stated, with the weight exceeding the minimal limit value stated, and
with the over-pumping effect (anomalously large standard deviation of
the scaled regression coefficient at the expense of the mutual
interrelation of descriptors) not exceeding the acceptable maximal value
stated. Various other restrictions may be introduced if desired. The
list of all results is calculated and output for every particular
response column is obtained. The averaged results for the complete data
set are output as well. The general contributions of the particular
descriptors are characterized by their mean weights and degrees of
representation (the parts (total numbers) of response columns that
depend on the particular descriptors).
The whole set of response columns can be divided into two
parts--the more and less precisely (roughly) described ones--via stating
a corresponding criterion (e.g. the critical value of the multiple
correlation coefficient). For these parts, all the averaged results are
additionally output separately.
Several procedures are available for the ordering of the way the
parallel (alternative) response values for a single data row for
particular data columns have to be treated.
Different approaches are available for the elimination of strongly
deviating response values. For the large set of different responses
subjected to concerted processing, the traditional way of the use of the
Student criterion on some risk level stated appears not to be a
reasonable one. This is due to the different scaling and considerably
varying precision of the description for the different response columns.
Therefore, an alternative procedure is for use: for each data column
from their roughly described set, the maximally deviating point is
excluded until the transition of this column into the set of the more
precisely described ones. Additional limiting conditions can be
introduced via stating a maximal value of the excluded points for a
single data column and a specified lower limit of the statistical
degrees of freedom. This procedure opens a limited possibility for
improving the quality of description at the expense of the eliminating
of presumably unreliable data points.
There is a possibility of ordering the calculation of the missing
values of descriptor rows, making use of the response values available
for a corresponding row dependent on the related descriptor.
It is also possible to recalculate the values of the elements for
some of the descriptors or for all of them retaining their scaling. If
the suitable arbitrary initial approximations for these descriptors are
substituted for the values of their elements, the set of them can be
calculated in part or in whole from the very beginning. This is the most
universal way for the (re-)establishing of the set of descriptors
adjusted to some data matrix given. The nearly orthogonal set of
residual descriptors obtained can be used for the calculation of the
missing or unreliable values of the response columns.
Repeating the processing after the inclusion of these values,
nearly orthogonal solutions for all response columns (at least for the
ones from the more precisely described set) can be obtained.
Simultaneously the predicted values are obtained for all respective
positions in the data table for which the experimental values are
missing or unreliable.
The justification of the inclusion of the particular descriptors
into the set used for the description of some data table can be checked
by the F-test of their significance for the whole set of data. This is
possible if the averaged effect of the substitution of different
selections of the (pseudo) random values for the descriptor columns
tested is taken into account. The point is that, for a sufficiently
numerous set of data series, the introduction of an additional
"descriptor" consisting of random values appears to be
formally statistically significant for some subset of response columns
just by chance. For different selections of random values, the number of
response columns for such subset remains nearly constant, but its
concrete list may be a specific one for each new selection of random
For the data sets corresponding to multifactor OS the cross terms
(products of two or more starting descriptor values for each row) can be
automatically added. To avoid the additional over-pumping effect, caused
by the large differences between the mean values and scale origins (zero
points) for the descriptors multiplied in the course of the formation of
cross terms, the possibility of the formation of these terms from the
preliminary centred descriptor scales exists. For instance, a
characteristic case is represented by the scale 1/T, because the ranges
of temperature represented by the experimental data available lie mostly
rather far from the absolute zero. The recalculation of the results to
the ones corresponding to the initial non-centred scales is made
possible, too. The technique of the formation of the cross terms can be
used for the generation of the exponents of descriptors of different
powers as well.
Besides the testing of multiparameter linear models, the testing
and parameterization of nonlinear models is also possible. If the
nonlinear function to be used is not included into the corresponding
list of standard ones supplied, it can be additionally programmed and
added for the additional compiling and linking. Another possibility is
an additional EXE-file prepared by the user and conventionally named to
grant calling of this function by the standard part of the computer
The numerical procedure of the generation of the set of partial
derivatives to be used is executed automatically. If desired, the
procedure of the generation of the analytical ones can be substituted
for the numerical one. Techniques analogous to the one described for the
nonlinear function can be used.
All problems, beginning with the non-orthogonality, that are
encountered in the case of the multiparameter linear approach, arise in
the case of nonlinear models for the set of the partial derivatives used
in the iterative procedure. The corresponding difficulties can be
overcome using the approach applied for the linear models. However, as a
result of the higher complexity of the nonlinear problems, this cannot
always be done completely successfully.
Several procedures are included for establishing reasonable initial
approximations for the parameters of the processed nonlinear function.
If desired, the user can add some additional version making use of the
technique cited for the inclusion of the nonstandard version of the
nonlinear function and analytical procedure for the calculation of
SELECTION OF THE DIFFERENT VERSIONS OF THE CRITERIONS AND
The fully automatic functioning of the whole system described is
possible if all the (limiting) criterions, flags, and switches of the
program are accepted on the default levels. In practice, this is rather
unacceptable, and the corresponding initial data should be input
additionally. Additional check of the results of the automatic formation
of the table of responses and descriptors is rather reasonable, too. The
choice between different data processing versions available and the
criterions to be used is possible just by the assigning of the proper
values to corresponding initial data (flags, switches, and the values of
criterions preferred by the user). Acceptance of the default levels
defined for them may be justified for the majority of them and their
change would be reasonable only for advanced approaches to test some
peculiar versions and ideas. Therefore, the list of the parameters,
recommended not to be "touched", is defined.
The software is created in Fortran .
After statistical processing, the calculation of the values for all
missing positions in the OS is possible. This means that the limit of
the prognosis of new data, proceeding from it, could be achieved.
LIST OF THE MAIN REACTION TYPES
1. Dissociation of hydrogen acids according to the Bronsted scheme
2. Rate constants of proton transfer
3. First-order nucleophilic substitution at nonaromatic centres,
4. Second-order nucleophilic substitution at nonaromatic centres
5. Electrophilic substitution at nonaromatic centres
6. Addition to double and triple bonds
7. Elimination with the formation of a double or triple bond
8. Hydrolysis of carboxylic esters
9. Reactions of carbonyl compounds as electrophiles
10. Aromatic electrophilic substitution
11. Aromatic nucleophilic substitution
12. Tautomeric equilibria
13. Intramolecular rearrangements
14. Formation of complexes from general acids and general bases
A part of this project was carried on using the funds of grants Nos
4590 and 6476 awarded by the Estonian Science Foundation, and the two
year "long-term" grant from the Soros Foundation.
Received 20 September 2005
[1.] Palm, V. A. Foundations of Quantitative Theory of Organic
Reactions. Khimia, Leningrad, 2nd ed., 1977 (in Russian).
[2.] Palm, V. A. (ed.) Tables of Rate and Equilibrium Constants of
Heterolytic Organic Reactions, Vols 1-5. VINITI, Moscow, 1975-1979 (in
[3.] Palm, V. A. (ed.) Tables of Rate and Equilibrium Constants of
Heterolytic Organic Reactions, Vols 1-6. University of Tartu, Tartu,
1984-1990 (in Russian).
[4.] Palm, V. Computer-managed automatic data retrieval and
prognozing system for rate and equilibrium constants of organic
reactions. J. Chem. Inf. Comp. Sci., 1990, 30, 409-412.
[5.] Palm, V., Jalas, A., Kiho, J. & Tenno, T. A computerized
system for storage, processing and prognosis of data with orientation
toward the use of correlation equations. Org. React., 1997, 31, 111-132.
[6.] Jalas, A., Kiho, J., Palm, V. & Tenno, T. Data structure
and menu-based access of the rate and equilibrium constants of
heterolytic organic reactions database. Org. React., 1997, 31, 135-140.
[7.] Palm, V. Some fundamental criteria of the scientific method
and the internal structure of science. In Estonian Studies in the
History and Philosophy of Science (Vihalemm, R., ed.). Kluwer Academic
Publishers, Dordrecht, 2001, 91-110.
[8.] Palm, V. & Palm, N. On the total number and list of
parameter scales significant for general quantitative description of
solvent effects. Org. React., 1993, 28, 125-150.
[9.] Malinowski, E. R. Factor Analysis in Chemistry. J. Wiley &
Sons, Toronto, New York, 1980.
[10.] Palm, V., Palm, N. & Tenno, T. Modification of data
processing and interpretation of results related to the use of
multiparameter correlation analysis. Introduction of additional
characteristics and criterions. I. Application to the treatment of
solvent effects. J. Phys. Org. Chem., 2004, 17, 876-889.
[11.] Microsoft Fortran PowerStation, Version 4.0, 0895 Part No.
Viktor Palm *, Natalia Palm, and Tiina Tenno
Institute of Chemical Physics, University of Tartu, Jakobi 2, 51014
* Corresponding author, email@example.com