Computer-assisted bilateral solution of chemical problems and generation of reaction networks

Analytica Chimica Acta, 210 (1988) 123-134 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

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COMPUTER-ASSISTED BILATERAL SOLUTION OF CHEMICAL PROBLEMS AND GENERATION OF REACTION NETWORKS”

J. BAUER, E. FONTAIN and I. UGI*

Znstitut fcir Organische Chemie der Technischen Universltiit Munchen, Lichtenbergstrasse 4, D-8046 Garching (Federal Republic of Germany)

(Received 10th August 1987)

SUMMARY

The theory of the bond/electron and reaction matrices, a mathematical model of the logical structure of constitutional chemistry, serves as the basis of a new generation of strictly logic- orientated programs for the solution of a variety of chemical problems without the use of any detailed empirical chemical information. These programs are interactive, have comfortable user- menus, and are implemented under the operating system MS-DOS on an IBM-compatible personal computer. The first representatives of the new generation are an improved version of IGOR (interactive generation of organic reactions) which “invents” chemical structures and reactions, and RAIN (reaction and intermediates networks) which generates, in a bilateral approach, pathways of chemical reactions and sequences of reactions from their given starting materials and products.

MOLECULAR LOGIC AND THE THEORY OF THE BOND/ELECTRON AND REACTION

MATRICES

In stable molecules, the covalent bonds and the lone valence electrons at every atom form a pattern that belongs to one of the allowable valence schemes of the corresponding chemical element. Thus, the valence schemes of the chemical elements not only determine the chemical constitution of molecules, but also define for the atoms the spatial arrangement of the covalently bound neighbors [ 1,2]. Accordingly, the essential constitutional and stereochemical features of molecules depend on the valence chemical schemes of their atoms. The interconversions of molecules and ensembles of molecules (EM) by redistribution of valence electrons establish equivalence relations between the EM and comprise transitions from one set of valence schemes to another set of valence schemes. The logical structure of chemistry [ 3-51 is a consequence of the nature of chemical bonds, the conservation of atomic cores and the total number of valence electrons during chemical reactions, and of the valence schemes of the chemical elements. Thus, the particular logic of chemistry,

“This paper is dedicated to the 60th birthday of Prof. George Olah.

0003-2670/&J/$03.50 0 1988 Elsevier Science Publishers B.V.

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briefly molecular logic, a term proposed by F. Ramirez, derives from a few general principles and fundamental results of quantum chemistry. The methods and techniques of numerical quantum chemistry are not needed for for- mulation of a mathematical model of the logical structure of chemistry and its applications.

The constitutional aspect of molecular logic is expressed by the theory of the bond/electron and reaction matrices, a mathematical model of constitutional chemistry [ 3,4] that relies on valence bond theory. The complementary stereochemical aspect of molecular logic is covered by the theory of the chemical identity groups [ 2,4].

The traditional theories of physics and chemistry are useful for the prediction of some observable properties of well-defined single objects and systems. In contrast, the theory of the bond/electron and reaction matrices, as well as the theory of the chemical identity groups, concern the conceivable existence and classification of chemical objects, and their relations to other objects of chemistry. The theory of these matrices is a theory of the conceivable chemistry of a given collection of atoms; the existence of any objects and phenomena is conceivable if it does not violate the principles of physics and chemistry. The above theory indicates that chemistry as a whole is topological in nature, and that relations in chemistry have a topological and even a metric aspect.

The use of this theory for the solution of chemical problems involves imbed- ding the individual systems within the chemistry of a family of isomeric EM (FIEM) of a given collection of atoms A = {A,, A2...A,}. The FIEM of A is the complete set of all EM that contain each atom of A, E A once and only once. Within the theory of the bond/electron and reaction matrices, an EM ofA = {A,, A*...A,} is represented by a symmetric n x n BE matrix B (bonds and electrons matrix); the rows/columns of the matrix are assigned to the n atoms of A, and the positive integer entries b, indicate the placement of the covalent bonds and lone valence electrons within the EM. An EM of n atoms can in fact be represented by up to n! distinct but equivalent BE matrices B’ =P B P-’ that differ by row/column permutations; P is an n x n permutation matrix [ 3,6,7].

A chemical reaction EM (B ) -+EM (E ) of a starting material EM (B ) at the beginning of the reaction to give a product EM(E) at the end of a reaction is represented by the equation B+R=E [ 1-5 1. These matrices, B and E, are the BE matrices of EM (B ) and EM(E), while R is a reaction matrix that describes the redistribution of the valence electrons during the reaction EM(B) -+ EM (E). Its entries rv indicate the covalent bonds that are broken/ made and the lone valence electrons that change position.

COMPUTER ASSISTANCE IN CHEMISTRY AND REACTION GENERATORS

A variety of computer programs for the deductive solution of chemical problems has been developed in the past 16 years [ 1,8,9 1. The three distinct cate-

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gories of solutions of the equation B +R= E comprise the diverse types of computer programs for the solution of chemical problems [ 11. Hitherto, computer assistance in chemistry has mostly involved decision trees that begin with either the starting materials, or the products of chemical reactions, or sequences thereof. Such trees tend to grow rapidly, and may lead to “combinatorial explosions” if no effective pruning procedure is available. A bilateral approach to the solution of chemical problems seems to be an attractive alter- native to the customary decision trees. With our mathematical model, the bilateral approach requires less pruning than a tree.

Computer-assisted bilateral design of synthesis was first proposed in 1979 [lo], and several chemical computer programs that are based on the bilateral concept have been implemented [8,9] or are under development. In this Insti- tute, two types of bilateral approaches to computer assistance in chemistry are pursued. In one type, programs for the bilateral design of synthesis [lo] and the generation of reaction pathways have been implemented and undergo further development, e.g., the program RAIN [9]. In the other type, the generation of the starting materials and products of a chemical reaction from an R matrix representing an electron shift pattern is accomplished by IGOR [ 1,111, a computer program that “invents” new molecules and reactions.

Reaction generators Reaction generators are the main device in chemical computer programs

that answer chemical problems by solving the equation B+R=E. There are two.basic types of reaction generator. A reaction generator of type I(RG-I) produces from a given BE matrix B those pairs (B,E ) that comply with B + R = E under the mathematical fitting conditions and the valence chemical boundary conditions [l-5]. A reaction generator of type II (RG-II) manufac- tures for a given R matrix R all those pairs (B,E ) that satisfy B + R = E under the above conditions. Thus, an RG-I generates all of the conceivable chemical reactions that an EM (B ) can undergo, or also all those reactions by which EM (B ) can be formed under the restrictions specified. In contrast, all reactions that have in common an electron-shift pattern as specified by an R matrix, are obtained from an RG-II. The program RAIN contains an RG-I, whereas IGOR uses an RG-II.

In a retroreactive synthesis design program, an RG-I accomplishes in es- sence what a reaction library with a structure-perception routine does for an information-based synthesis design program [ 12-171, i.e., it leads from the target to its precursors, and then to their precursors. However, because a reaction generator does not know the chemical literature, it invents each reaction ad hoc, often re-inventing the wheel.

The first RG-I was part of the synthesis design program CICLOPS [ 181, a feasibility study. The reaction generator of CICLOPS contained a fixed set of irreducible R matrices [8] from which their equivalent R matrices R’ were

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obtained by row/column permutations according to R’ = P R P-l, with P being a permutation matrix [ 6,7]. These matrices R’ were used to generate from a matrix B those pairs (R’,E) that fit mathematically and comply with the aforementioned boundary conditions. This approach is cumbersome, ineffi- cient and produces too many results. Yet the essential features of this reaction generator of CICLOPS are still used in EROS [ 191, where only a fixed set of three, and optionally up to five, R matrices is used; in EROS, thermochemical as well as charge-affinity estimates serve to find the reactive atoms and bonds in order to prune the tree of synthetic pathways.

A more advanced reaction generator was introduced with the synthesis design program ASSOR [ 201. In ASSOR the additive transformation of B according to B + R = E is achieved by the stepwise action of the basic components of the R matrices. These represent the mechanistic steps of the reactions [ 31. Thus it is possible to take into account the mechanistic aspects of the reactions used.

An heuristic approach to RG-I was chosen by Brandt and co-workers [ 21,221 and Stadler [ 231 through the use of algorithms that are similar to some that had previously been developed for the documentation of chemical reactions [21,22].

In RAIN, a new kind of RG-I is used. This is called a transition table-guided reaction generator of type I (TRG-I). The main advantage of this TRG-I is that it is not restricted to any fixed set of R matrices. Instead, it takes into account all R-matrices under boundary conditions as specified by the user. For a given EM, this TRG-I generates a set of reactions that contains the results of all aforementioned RG-I as subsets.

For each chemical element or chemical entity that a row/column of a BE matrix may represent, either a transition table is defined ad hoc for the particular case to be considered, or a general set of transitions tables is applied. In a transition table, the allowed valence chemical schemes of a given chemical element in the EM are assigned to the rows/columns of a table, the entries in which indicate the interconvertibility of the valence chemical schemes during a chemical reaction, as will be described elsewhere. The transition tables of C, H and N of the prebiotic synthesis of adenine [ 24-311 (see Fig. 1) may serve as an illustration.

The TRG-I operates in two steps. First, the allowable valence schemes of the atoms in EM(E) are established by the action of the transition tables on EM (B ). For each combination of valence schemes, all those EM (E) are then generated which have R matrices R = E - B that agree with the theory of the BE and R matrices and comply with optional selection criteria that are im- posed by the user.

The T matrices provide very powerful devices for this selection of R matrices. The T matrix of a chemical reaction is the difference of the adjacency matrices that describe the products and the starting materials of the reaction.

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Fig. 1. Transition tables for C, H and N ( + indicates allowed, -forbidden transitions).

For example, the following three reactions have in common the same irreducible R matrix

but are represented by three distinct T matrices; in R,TI,T2, and T3 only the rows/columns belonging to the reactive centers are given.

Br’- Br2 -+ “; yr

HzC4 = C3H2 H,C -CH2 Tj -j ;; +; +;]

H,C! = CH, H,C -CH2

F,C = CF2 T2=[ +; +; +; +;I

HC = CH2 HC -CH2 I -+ 11 1

HC = CH2 HC-CH, T3=[ ; +i +; ;]

T, involves four atoms and three bonds, T2 four atoms and two bonds, and T3 affects only two atoms and one bond.

The first reaction generator with transition-table guidance was the TRG-II of IGOR that generates pairs (B,E ) from a given R matrix [ 111. TRG-II served extremely well [8] in the early PL/I mainframe computer implementation of IGOR, and TRG-II is now a quintessential part of the latest PC version of IGOR. The starting point of this TRG-II is an R-matrix and a list of transition tables of the chemical elements to be considered. For each row/column of the prospective pairs (B,E) the user selects a collection of the transition tables from the above list. Row by row and column by column, the program checks whether or not the entries of the respective transition tables are compatible with the given R-matrix. This leads to a reduced collection of transition tables that is used to generate the matrices B row by row and column by column. The rows/columns of B are immediately converted to the rows/columns of E according to R. The resulting row/column pairs of (B,E) are then checked for conformity with the transition tables. As soon as the pair (B,E) is thus fully developed, its distinctness is ensured by a modified version of CANON [32] that establishes a unique representation for pairs of isomers. Finally, the pairs (E,B) are analyzed for substructures that are listed as forbidden or required. The acceptable solutions can immediately be graphically displayed for critical review by the user.

A new generation of chemical computer programs In this Institute, the development of chemical computer programs that are

based on the theory of the BE and R matrices began in 1971 with the feasibility study CICLOPS [ 181 from which EROS [ 191 evolved The main shortcoming of CICLOPS was its lack of a selection procedure as a safeguard against combinatorial explosions. In EROS, this problem is solved by using a limited set of fixed R matrices in its reaction generator, and the synthesis tree is pruned according to a semi-empirical heuristic procedure. Because, in our opinion, this approach, as well as other heuristic selection procedures, can lead to arbitrary decisions, heuristic rules and procedures have not been used since 1983 in new chemical computer programs for PC-type computers and inexpensive work- stations. Thus, it was decided to develop interactive chemical computer programs for “small” machines that make best use of the capabilities of both men and machines, and only formal criteria are used in automated decisions.

The computer programs IGOR and RAIN are the first representatives of an emerging generation of computer programs for the solution of chemical problems. IGOR and RAIN have in common the following features that are characteristic of this recent approach. They are interactive “expert systems” in the sense that they have been implemented to be used by experts, and only by experts. They are not designed to replace an expert, not even partially; they are designed to amplify the working power of an expert. They do not contain any data base of detailed chemical information for supplementing the knowledge and experience of the expert. IGOR and RAIN solve chemical problems

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in a deductive mode, i.e., they derive the solutions to the individual problems from the general principles that have been expressed in the theory of the BE and R matrices, the mathematical basis of these programs.

Here, the computer performs all the logic and combinatorial operations that are needed for solving a given problem, whereas the user makes all decisions on the basis of his intelligence and expertise, knowledge and experience. The programs are designed so that the solutions of the problems are achieved stepwise, by following an hierarchy of purely formalistic rules, and hierarchal classification of the conceivable solutions to a given problem. At each step of the procedure, the intermediate results are graphically represented in suitable terms, so that the user can influence any further progress by his decisions.

IGOR \

The traditional chemical concepts have not led to an adequate classification of chemical reactions. The theory of the BE and R matrices, however, i& well- suited to create hierarchal order in the set of all chemical reactions. This hierarchal classification is not only useful as a basis of documentation systems for chemical reactions [ 21,221, but also serves well in the systematic computer- assisted discovery of new reactions.

Chemical reactions are first classified according to the minimal number of valence electrons that must be redistributed in order to convert the starting materials into the products of a given reaction. The redistribution of valence electrons in the course of a chemical reaction follows a distinct pattern that belongs to the characteristic features of a given chemical reaction. In the cur- rent literature on reaction mechanisms, this is described by a pattern of arrows that indicate the flow of electrons. This pattern can be represented by the non- zero row/columns of an R matrix and it stands for a category of reactions that have in common a characteristic pattern of electron redistribution. The cate- gories of reactions can be further partitioned into their “basic reactions” that often correspond to the socalled “name reactions” of organic chemistry. A basic reaction is specified by its reactive centers and the covalent bonds for which the formal bond orders change in the course of the reaction [ 331. By denoting the chemical elements of the reactive centers and stating their peripheral at- tached substituents, one reaches the individual chemical reactions.

The most important ingredient of IGOR is its TRG-II which is capable of generating chemical reactions from irreducible R matrices. However, here the TRG-II does not create indiscriminately the reactions that would qualify, but follows the afore-mentioned hierarchal classification of chemical reactions, and at each level of the hierarchy the user can participate interactively in the search for new reactions by imposing his decisions on IGOR as it follows the hierarchy. Thus, individual reactions can be systematically singled out from very large numbers of conceivable reactions of a chosen category. The search for reactions is narrowed by numerous options that are available to IGOR by spec-

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ifying the desirable, or undesirable features of the expected results at any stage of the search for molecules or reactions.

When a zero R matrix is used, IGOR generates reactions without electron redistribution, i.e., the zero reactions for which the starting materials and products are identical. In this mode, IGOR can be used to generate molecules as defined by the user, e.g., all 23 valence isomers of cyclooctatetraene [B,ll], or the 278 conceivable five-membered cyclic phosphorylating reagents for oli- gonucleotide synthesis [ 34 1.

When IGOR was used to search for unprecedented reactions with six reactive centers and a cyclic redistribution of six valence electrons, the retro-ene reaction was selected as one of the 13 basic reactions; H, C and 0 were optionally admitted as chemical elements at the reactive centers and CO, was specified as one of the products. The pyrolysis of or-formyloxy ketones to form COz and ketones resulted as the first synthetically useful reaction that was discov- ered with computer assistance [ 8,351, demonstrating the innovative power of purely mathematically-based chemical computer programs. (Brownscombe [ 361 implemented a computer program that permuted the chemical elements on the reactive centers of the retro-ene reaction; to our knowledge this program has not led to the discovery of new reactions.)

Initially, IGOR was implemented in PL/I for a Cyber 175 [ 111. This version of IGOR has been used extensively and studied by Herges et. al [ 83 and Herges [ 351. The experience from this work has led to many improvements of IGOR. Recently, a new PC version with a comfortable user menu has been implemented; it will soon become available to the public.

RAIN The elucidation of reaction mechanisms involves generally the search for

the reaction intermediates that form a mechanistic pathway of a chemical reaction from given starting materials EM (B) to known products EM (E) . The conversion of the starting materials EM(B) of a multistep synthesis to the target compounds of the synthesis proceeds along synthetic pathways that lead from EM(B) to an EM(E). The latter consists of the target T and its coprod- ucts through a sequence of preparative reactions via the diverse precursors of the synthesis. Bilateral design of synthesis comprises the selection of an EM (B ) of starting materials for the target TEEM (E ) from a list of available chemical compounds, and the search of synthetic pathways that connect EM(B) with EM(E).

The computer program RAIN is designed to connect two given EM from the same FIEM by a network of intermediates that belong to reaction pathways. Thus RAIN is usable for the elucidation of reaction mechanisms as well as a part of a bilateral synthesis design system.

The initial plan to generate reaction and intermediate networks through the components of the overall R matrix R = E -B, with B and E correlated by the

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PEMCD [6,7,37,38], was rejected after a careful analysis of this approach. Instead, the network of reaction pathways is simultaneously elaborated by a TRG-I from the starting materials EM (B ) and the products EM(E) of the pathways, by generating trees from both ends of the pathways until the trees meet at intermediates that belong to the “starting material tree” and also to the “product tree”. The development of the trees can be executed in such a manner that the distinct branches of the trees are only pursued if they afford a decrease of the chemical distance from the opposite EM. Because of the topological structure of the FIEM this so-called mixed strategy is most efficient.

The system RAIN can also be used as a retroreactive synthesis design program, or as a reaction predictor, because it can also generate a single tree of reactions and intermediates from any EM. RAIN is an interactive program that has been implemented for any IBM-compatible PC. In order to ensure efficiency and comfort to the user, there are many options available, by which the user can express his preferences. Thus the choice of the entries in the transition tables of the chemical elements enables the user to determine whether the nodes of the network represent mechanistic intermediates, or stable mem- bers of a synthetic pathway. Through the transition tables the user can strongly influence the chemistry that is generated by RAIN. The user can select the

4HCN -> DIAMINOMALEODINITRILE

Fig. 2. Reaction pathways generated by RAIN.

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atoms or bonds that may or may not participate in the reaction steps. Upper and lower bounds for various characteristic properties can be set for the R matrices and the T matrices. For the irreducible R and T matrices, upper bounds can be selected for the rank, the number of off-diagonal entries, the number and value of entries in a row/column, the sum of the entries in a row/column, etc. A list of forbidden substructures can also be applied. Further, minimum bond orders may be required; automerizations and direct retro-reactions of intermediates may be forbidden.

RAIN has been used successfully to generate networks of reaction mechanisms [ 91 and for the prediction of the products that can conceivably be formed from a given EM [ 391; its use in combination with IGOR has proved successful [37,38].

The mechanistic analysis by RAIN of the tetramerization of hydrogen cya- nide (see below) illustrates the use of RAIN. This example is part of a study that concerns the formation of adenine by pentamerization of hydrogen cya- nide; the study will be reported elsewhere. The complete network of all reaction pathways with a maximum length of four steps was developed under the following boundary conditions:

maximum rank of an irreducible R matrix 6 maximum number of involved bonds in an R matrix 6 maximum rank of an irreducible T matrix 4 maximum number of involved bonds in a T matrix 3 maximum value of an offdiagonal entry in an R matrix 1 maximum number of offdiagonal entries in an R matrix 2 maximum number of offdiagonal entries in a T matrix 2 smallest allowed ringsize 5

The transition tables of the chemical elements are shown in Fig. 1. Bonds between N and N were forbidden, and the Bredt rule was applied. Figure 2 shows the resulting network.

Conclusion IGOR and RAIN as well as other chemical computer programs that have

been developed in this Institute demonstrate that the purely mathematically- based interactive systems are very well capable of creating innovative solutions of chemical problems by automated reasoning. They have also demonstrated that the division of duties between man and machine is effective and mean- ingful; the performance of all formal, logical, and combinatorial chores by the computer, and decision making by the expert user has some notable advantages over other approaches that try to minimize the demands on the user by auto- matic application of heuristic rules and reactivity estimates. The more an expert wishes to apply his knowledge and intuition, the more a computer program must be endowed with interactive capabilities.

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Judged by experience of more than 16 years in computer chemistry, the use of data banks of empirical knowledge for problem-solving in chemistry has serious drawbacks. To assemble and maintain a data bank always involves considerable cost and manpower. In general, data banks are also error-prone. Furthermore, the solutions of problems that are obtained by retrieval and manipulation of stored data will always be confined to combinations of the known. The theory-based logic-orientated programs take into account all conceivable solutions of a problem, including unprecedented ones. Their interactive design makes them well-suited for personal computers, and thus easily accessible in a research and teaching environment.

The best use that can be made of documented known chemistry is to com- pare the results that have been developed by logic-orientated interactive computer programs with the data of known chemistry, e.g., by comparing the output of chemical computer programs with CAS-online, in order to classify the computer-generated results into those that are novel, and those that have already been reported. Among the output of chemical computer programs, the already known data may be useful to a chemist, but as a rule, the computer-generated new chemistry is more challenging.

The authors gratefully acknowledge the financial support of this work by Deutsche Forschungsgemeinschaft und Fonds der chemischen Industrie.

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Computer-assisted bilateral solution of chemical problems and generation of reaction networks