Molecular logic and computer assistance in chemistry

Journal of Molecular Structure (Theochem), 165 (1988) 229-242 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

MOLECULAR CHEMISTRY

LOGIC AND COMPUTER ASSISTANCE

IVAR UGI and MICAELA

229

IN

WOCHNER

Organisch Chemisches Institut, Technische Unioersitiit Miinchen, Lichtenbergstrasse 4, D8046 Garching (F.R.G.) (Received

7 September

1987)

ABSTRACT The current status of computer programs for the deductive solution of chemical problems on the basis of the theory of the BE and R matrices is discussed, with special emphasis on the newest generation of interactive problem-solving programs for small computers, i.e. the programs RAIN and a new version of IGOR. A new computer program PEMCD for the exact determination of chemical distance is presented. The essential modules of the logic-oriented computer programs, and their role in these programs is described, in particular the transition tables guided reaction generators TRG I and TRG II.

INTRODUCTION

The topic of this article is a theory, and the current status of its application in chemistry through computer programs. Most theories for chemistry are quantitative theories that originate from physics or physicochemistry, or are computable theories able to predict the properties or behaviour of well-defined chemical objects, generally in chemically meaningful numerical terms. These theories are, as a rule “local” theories, since they concern individual chemical systems and their interconversions. In contrast, the theory of the BE and R matrices presented here, is a “global” qualitative mathematical theory of chemistry as a whole, representing a subset of molecular logic. More precisely, it is a model of the logical structure of constitutional chemistry, and the families of isomeric ensembles of molecules (FIEM) . In his paper on the “incomplete associations of atoms”, Preuss [ 1 ] was the first quantum chemist who recognized the importance of the FIEM. The theory of the BE and R matrices reveals the essentially topological nature of chemistry and chemical equivalence relations. It is aesthetically appealing to visualize chemistry as a high-dimensional Euclidean geometric universe where the molecular systems are clusters of points and their reactions are vectors. This picture introduces new dimensions to chemistry. 0166-1280/88/$03.50

0 1988 Elsevier Science Publishers

B.V.

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The theory of the BE and R matrices serves as the theoretical basis of computer programs for the deductive solution of a great variety of chemical problems, without the primary use of detailed empirical information. Our experience of more than 15 years in the development and implementation of problemsolving computer programs for chemistry has shown that interactive computer programs in a one man/one computer situation are most effective in this field. In this mode, the capabilities of man and machine are best utilized. THE LOGICAL STRUCTURE OF CHEMISTRY AND ITS QUALITATIVE MATHEMATICAL REPRESENTATION

Molecular logic, the inherent logic of chemistry, is given by the valence chemical properties of the chemical elements and some general principles of physics that govern the behaviour of molecular systems. Our knowledge of the logic of chemistry developed hand in hand with growing understanding of the structure of matter. The essential features of molecular logic were recognized more than 150 years ago through the brilliant insights of Berzelius, Liebig, Wiihler, Couper, Gerhard, Frankland, Kekule and many others [ 21. They created the so-called “structural theory of chemistry” that became the official credo of chemists in 1860 at the Congress of Chemistry at Karlsruhe. This theory is an intellectual achievement of the same order of magnitude as the Copernican heliocentric model of the solar system [ 31. The structural theory of 1860 provided the logic for the subsequent era of organic syntheses. With the synthesis of vitamin Bi2 about 100 years later by Eschenmoser and Woodward [ 41, organic synthesis had climbed its Mount Everest. The stereochemical concept that entered chemistry from 1874 onwards [ 51, the development of quantum mechanics and quantum chemistry, and new types of information about molecules obtained by spectroscopic and diffraction methods, have led to our present picture of the logical structure of chemistry. From early times, physics has developed in close symbiosis with mathematics, whereas mathematics has entered chemistry rather late, and most successfully via physics and physicochemistry. Until recently the mathematization of chemistry has been mostly confined to the use of quantitative, computable physicochemical theories that afford the mathematical treatment of individual well-defined molecular systems, or their interconversions. The direct application of mathematics to chemistry and its logic in terms of quantitative mathematical theories began a century ago with Cayley’s graph theoretical representation of molecules [ 61; the direct mathematical treatment of chemical systems attracted great attention through Polya’s enumeration of isomers [ 71 but did not play a major role in chemistry until about two decades ago [ 81. Then the qualitative mathematical approaches to chemistry began to gain impetus. Balaban’s efforts in the chemical applications of graph

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theory [8] led to widespread new interest in qualitative mathematical approaches to chemistry. Since 1965, one of us has been active in the development of computer assisted methods for the solution of chemical problems [ 91, and in 1970 Ugi and the late James Dugundji began to develop computer-oriented qualitative mathematical theories of chemistry*, because they realized that purely informationbased computer assistance to chemistry, e.g. in the design of syntheses without a suitable theoretical foundation, is confined to known chemistry and its close analogies. In 1973 Dugundji and Ugi [ 131 published the theory of the BE and R matrices, a qualitative mathematical model of the logical structure of constitutional chemistry; the mathematical foundations of this theory are eighteen elementary, but then new, algebraic theorems [ 13,141. In the meantime this model has become the theoretical basis of a great variety of computer programs for the deductive solution of chemical problems [ 15,161. None of these programs uses any detailed empirical information, and they generate all solutions of chemical problems de novo, often re-inventing the wheel, but also often generating unprecedented chemistry. The centerpiece of the theory of the BE and R matrices [ 131 is the equation

B+R=E that represents

the chemical

reaction

EM(B)+EM(E) EM (B ) and EM (E ) are isomeric ensembles of molecules (EM) at the beginning and end of the reaction; they are represented by the BE matrices (bond and electron matrices) B and E.The rows/columns of a BE matrix are assigned to the individual atoms. The off-diagonal entries b,= bji are the formal bond orders of the covalent bonds AC-A, between the atoms, and the diagonal entries bii are the numbers of the lone valence electrons at the atoms Ai. The so-called reaction matrix (R matrix) R corresponds to a pattern of electron redistribution, or of bond breaking/making during the reaction. The off-diagonal entries rij=rji of an R matrix indicate the changes in the formal order of the covalent bonds Ai-Aj, and the diagonal entries rii denote changes in the placement of lone valence electrons. We have

(1) Since there are no negative bond orders, or numbers of valence electrons, the negative entries rij < 0 of R must coincide with positive entries bij> 1rij1 of *In 1970 the concept of permutational isomerism was first mentioned [ lo]. From this the theory of chemical identity groups evolved [ 11,121.

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B of at least equal value, in order to ensure eij = b,+ rij > 0 (mathematical fitting condition). (2 ) Each row/column of a BE matrix corresponds to a valence scheme of the chemical element it represents. A BE matrix represents a real molecule, or EM, if all rows/columns are allowable valence schemes of the respective chemical elements (valence chemical boundary condition). The sum over the absolute values of the entries of the R matrix R = E - B

5 Irij I =D(B,E) is twice the number of valence electrons that are involved in the reaction. D (B,E ) is the so-called chemical distance ( CD ) between EM ( B ) and EM ( E ) [ 131,a quantitative measure of chemical similarity [ 17-191. CD has a geometric interpretation. The nx n BE matrices of the EM(B) and EM (E) with n atoms correspond to points P(B) , P(E) in R”‘, an n2dimensional Euclidean representation space, and the R matrices may be interpreted as vectors from P(B) to P (E). The CD, II (B,E) ,is the L1 distance, the so-called city-block distance, between the points P (B ) and P (E ) . Since an EM (B ) of n atoms is representable by up to n! distinct but equivalent BE matrices B’ =PxB XI’-‘, EM (B ) corresponds to a “cluster” of BE points P (P XB x P-l). The structure of these clusters is such that for each point P ( PxB x P-l) there exists a point P (E ) at minimal chemical distance D (B,E) in the cluster of EM(E) , just as on two parallel planes, each point on one plane has a closest point on the other plane. This has been exploited in an approximation method for the determination of the minimum CD between isomeric EM [ 181. The result of a chemical reaction, or a sequence of chemical reactions, is generally achieved by redistribution of the minimum number of valence electrons, i.e. chemical reactions tend to follow pathways of minimum CD, and to proceed without redundancy in bond breaking/making. Thus, during a chemical reaction the maximum set of maximum subgraphs is preserved in the formulae of the reactants. This is the principle of minimum chemical distance (PMCD) [ 17-191, a computer-oriented quantitative version of the classical principle of minimum structure change [ 20,211. The mechanistic steps of a reaction are components of the vectors that represent R matrices; their basis vectors correspond to the elementary steps of chemical reactions [ 13,221. The stereochemical aspect of molecular logic is representable by the theory of the chemical identity groups. The most important mathematical device of this theory is the set-valued mapping [ 12,14,23]. THE THEORY OF THE BE AND R MATRICES AND COMPUTER PROGRAMS FOR THE DEDUCTIVE SOLUTION OF CHEMICAL PROBLEMS

Our mathematical model of the logical structure of constitutional chemistry is the theoretical foundation of a variety of computer programs for chemistry

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[ 15,161. These programs have been designed and implemented since 1971 at our institute. The evolution of our programs has led from the early batch type PL/I programs [ 241 for mainframe computers to our present generation of interactive problem-solving FORTRAN 77 programs for small machines [ 161. We use in our mathematically based computer programs a standard set of building blocks that are also useful as independent computer programs. A typical example is CANON [25-271 ( see below), an algorithm and computer program that recognizes constitutionally equivalent atoms and generates unique representations of molecules; CANON may be used independently, or as a part of a larger problem-solving system. Besides CANON, CORREL [ 28,291, PEMCD [ 191 and the reaction generators TRG I and TRG II [ 161 are computer programs that may serve as subunits of more complex modular systems. Two distinct categories of chemical computer programs have evolved from the theory of the BE and R matrices. The first category comprizes the programs for documentation, retrieval and analysis of chemical data; the programs that solve chemical problems by solving the universal equation B + R = E of our model belong to the second category. The “computable theories” for chemistry, including quantum chemistry, are applicable to well-defined molecular systems, their interactions, and their interconversions. There are, however, many problems in chemistry whose unknown “X” is a molecular system, or a chemical reaction. The majority of such problems can be solved by molecular logic, and its universal equation B + R = E. Once “X” has been found, it may be subjected to the computable theories. The relation between molecular logic and its applications, on the one hand, and the “computable theories” of chemistry, on the other hand, may be compared with the global and the local activities in the oil producing industries. First, the oil-carrying geological formations are located by some global exploration, and then the local work of drilling and pumping can be done. In the first category of programs that belong to the documentation and data analysis systems, we have CANON, CORREL, PEMCD, and a hierarchic documentation system for chemical reactions [ 301. The problem-solving computer programs are the diverse retrosynthetic programs (CICLOPS [ 241, EROS [ 311, ASSOR [ 221)) the bilateral synthesis design programs [ 321, RAIN [ 33,341 and IGOR [ 35,361. All of these systems contain some reaction generator that solves the equation B + R = E [ 161. DOCUMENTATION AND DATA ANALYSIS SYSTEMS

CANON [ 25-271 is an algorithm and a computer program that assigns indices to the atoms in a molecule. CANON takes into account simultaneously,

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recognizes immediately any constitutionally equivalent atoms. CANON can be used, like the Cahn, Ingold, Prelog (CIP) sequence rules [ 381, to establish priorities of the ligands of stereogenic centers. The CANONical indices of the a-atoms of the ligands of an asymmetric carbon atom follow generally the CIP priorities. In CANON the atoms are first indexed in the order of decreasing atomic numbers. For each atom, its atomic index (AI) and the AI of its a-neighbors, i.e. the immediate covalently bound neighbors, yield its atomic descriptor (AD). The atoms are reindexed according to their AD. From the new AI a second set of AD is formed, etc., etc. The iteration is terminated when no new AIs are obtained. CANON, or related auxiliary programs, have been incorporated in almost all of our other chemical computer programs, in order to avoid redundant processing of constitutionally equivalent atoms, and for internal documentation purposes. CANON is also used by the Chemical Abstracts Service ( CAS) for the assignment of equivalence class indices (ECI) to the atoms. CORREL [28, 291 is a substructure analysis and correlation system that was first published in 1980. In the first version of CORREL, the list of all molecules considered is converted into a contiguous, hierarchically ordered network of all substructures that these molecules contain. Since, in general, a given molecular substructure belongs to many parent molecules at the same time, the hierarchic network grows the slower, the larger it is already. Within this network, it is easy to detect directly the substructures that any subset of the original list has in common. The oriented substructure network of CORREL becomes very large, unless this network is reduced or selectively generated in some problem-oriented way. Three new versions of CORREL with selectively generated substructure networks have now been implemented; one for bilateral synthesis design, one for structure activity analysis, and one for the elimination of molecules with undesirable substructures from the output of IGOR and RAIN. Furthermore, an experimental version of CORREL is under development with substructures that correspond to the aI, p, y vicinities of distinguished atoms. In substructure correlation, substructures with three spheres of neighboring atoms have some advantages over substructures with only two spheres of neighboring atoms. Substructures with two spheres of neighboring atoms are used in the documentation systems DARC [ 391 and HTSS [ 401. The advantages of hierarchic classification of substructures, and an oriented substructure network, as used in CORREL, have gained some acceptance. The substructure analysis systems HTSS, KOWIST [ 411, RESY [ 421 and Klopman’s structure-activity system [ 431 utilize the aforementioned concepts. PEMCD is a computer program for applying the PMCD, a program for determining the exact minima of chemical distance. In contrast to the PMCD program [ 17, 181 which relies on an approximate algebraic and a heuristic

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branch-and-bound approach [ 441, the PEMCD has a graph theoretical conceptual basis. Whenever the PEMCD finds a minimum of chemical distance (MCD ) , it is a true MCD. The PEMCD finds its results through four algorithms, a CANON-like relaxation algorithm that recognizes constitutional equivalence classes of atoms, algorithms for elaborating the so-called hyperatoms and residues, and an algorithm for determining CD by exhaustive trial-and-error treatment of preselected substructures that contain potential reactive centers. In contrast to CANON that works with individual molecules, the CANONlike relaxation algorithm acts on the unions of the considered EM. This relaxation algorithm detects isomorphic subgraphs in the participating EM of the reactions. This problem has already been studied by Sussenguth [ 451 and Figueras [ 461 with a modified MORGAN algorithm. The hyperatoms are univalent polyatomic groups at the periphery of molecules. When m univalent atoms or hyperatoms are represented as a single mvalent unit, this unit is called a residue. The final exhaustive trial-and-error procedure is applied to settle all problems that have not yet been solved by the action of the three aforementioned procedures. The PEMCD is used to detect the reactive cores that consist of the reactive centers in the educts and products of chemical reactions, and the invariant parts that do not directly participate in the reaction. Also, the PEMCD finds the atom-by-atom mappings of the educts of chemical reactions onto their products, together with the bonds that must at least be broken/made during the conversion of the educts into the products. In synthesis design, the PEMCD provides guidance in the search for optimum synthetic routes. When networks of chemical reactions, or reaction mechanisms, are generated bilaterally by a so-called mixed strategy, the growth of the trees from the educts and the products towards each other is controlled by the PMCD [ 33,341. The PEMCD is indispensable in the systematic documentation of chemical reactions. Without an atom-by-atom mapping of the educts onto the products, and identification of the reactive centers as well as the bonds that are broken/ made, by PEMCD, or an equivalent device, no adequate representation of chemical reactions beyond a statement of the educts and products is possible. This has been overlooked in the design of some recently proposed documentation systems for chemical reactions [ 47,481. These essentially graph theory based systems are isomorphic to parts of the documentation system for the chemical reactions of Brandt et al. [ 301 (see below). Chemical reactions may be classified according to a hierarchy of criteria that are implied by the theory of the BE and R matrices. A corresponding hierarchic documentation system for chemical reactions has been implemented by Brandt et al. [ 301. With this documentation system an unambiguous corre-

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lation of the educts and products is established by PEMCD, and the redistribution of the valence electrons is represented by canonical R matrices. THE SOLUTION OF CHEMICAL PROBLEMS WHOSE UNKNOWN “x” IS A MOLECULAR SYSTEM, OR A CHEMICAL REACTION

There exist many chemical problems whose solution is a molecular system, or a chemical reaction. The unknown X of most such problems can be found by solving the equation B + R = E, either from a given BE matrix B, or from a given R matrix R. The solutions of this equation are obtained by the so-called reaction generators ( RG) . An RG of type I (RG I) manufactures from the BE matrix B all pairs (R, E ) that follow B + R = E under (1) the mathematical fitting condition and (2) the valence chemical boundary conditions, and an RG of type II ( RG II) generates from an R matrix R all pairs (B, E ) under (1) and (2). The search for all pairs ( R, E ) that fulfil B + R = E under the conditions (1) and (2) corresponds to predicting all conceivable chemical reactions that a given EM (B ) can undergo, and all reactions by which it can be formed. In general this is a formidable combinatorial task for our RG I. It is, however, facilited by the fact that all solutions (R, E) are found within the same family of isomeric EM (FIEM ) to which EM(B) and EM(E) belong. In contrast, the pairs (B, E ) of isomeric EM that the solutions of B + R = E from R requires, do not all belong to the same FIEM. Accordingly, here an RG II first finds a collection of atoms A= {Ai...A,} that is compatible with R, and subsequently RG II must determine those isomeric EM (B ) and EM (E ) of A that fit R under the conditions (1) and ( 2 ) . In information based retrosynthetic synthesis design, the target molecule T is converted into its direct precursors by the action of so-called transforms, i.e. the retroreactions of known reactions that are on file in the reaction library of the program, while in mathematics-based synthesis design, the target EM (T,C ) i.e. the union of the target T and its coproducts C, is converted into precursor EM by an RG I. In the feasibility study CICLOPS [ 241, and the synthesis design program EROS [ 311 that evolved from CICLOPS, the RG I consists of a fixed set of R matrices whose rows/columns are permuted to yield R’ = PX R x P-l. The R’ are checked whether or not they (1) fitted mathematically B (T, C) and (2) whether or not they lead to EM (E) that comply with a list of allowable valence schemes of the considered chemical elements. The misfits are discarded. In the retrosynthetic program ASSOR [ 221 and the most recent versions of EROS, an RG I is used that builds the chemical reactions from the basis elements of their R matrices [ 131. By this approach the complete set of qualifying R matrices can be generated, and the mechanistic aspect of the reactions can be accounted for.

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Stadler [ 491 used a heuristic approach to RG I, using algorithms that had previously been developed for the documentation of chemical reactions [ 301. In the latest generation of our problem solving chemical computer programs, we use 100% efficient RG I and RG II, i.e. these RG directly generate only (R,E ) and (B,E) that comply with conditions (1) and (2)) and any conditions that are specified by the user for the given case. In the new RG condition (2) is executed by so-called transition tables [ 16,33, 341 that guide the RG. For each considered chemical element a transition table is defined. A transition table contains the valence schemes that are allowed in the educts and in the products and the allowed transitions of valence schemes during chemical reactions are also fixed. The following transition tables may serve as examples. They have been used for generating the network of the conceivable reaction mechanisms of the prebiotic formation of adenine from hydrogen cyanide [ 501 by RAIN [ 511.

5x

HCN

__C

In such a transition table, the allowed valence chemical schemes of a given chemical element in the EM are assigned to the rows/columns of the table whose entries indicate the interconvertibility of the valence chemical schemes during the considered reaction. In the program RAIN a new kind of RG I was introduced, the so-called transition table guided reaction generator of type I (TRG I). TRG I is not restricted to any fixed set of R matrices. It operates with all R matrices under conditions (1) and ( 2 ) , or conditions that are specified by the user. For each chemical element, or entity that a row/column of B represents, either a standard transition table is used, or a transition table is defined by the user ad hoc for the given case. The action of TRG I on EM(B) involves two stages. First, the allowable valence schemes of the atoms in EM(E) are established by the transition tables. For each combination of valence schemes, all those EM (E) are then gen-

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erated whose R matrices R= E - B agree with the theory of the BE and R matrices, and comply with any optional selection criteria that are imposed by the user, It is advantageous to classify, and to select the R matrices according to the T matrices of the reaction. The T matrix of a chemical reaction is the difference of the adjacent matrices that describe the products and the educts, There are many reactions that have in common the same irreducible R matrix, but are represented by distinct T matrices [ 16 ] . The first RG with transition table guidance was the TRG II of IGOR that generates pairs (B,E) from a given R matrix; TRG II has served extremely well in an early mainframe computer implementation of IGOR [ 351, and TRG II is now the centerpiece of the latest PC version of IGOR [ 361, This TRG II begins with an R matrix, and a list of transition tables of 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/ column by column the program now checks whether or not the entries of the respective transition tables are compatible with the given R matrix. Thus a reduced collection of transition tables is obtained that is used to generate row by row/column by column the matrices B. The rows/columns of B are immediately converted into the rows/columns of E according to R. The resulting row/column pairs of ( B,E ) are now checked for compliance with the transition tables. Our new generation of problem solving computer programs for chemistry is characterized by interactive programs. They are built around TRG I and TRG II, and are endowed with user-friendly graphic menus in color. RAIN [ 33,341 (reaction and intermediate network) and a new version of IGOR [ 361 (interactive generation of organic reactions) are the first members of this new generation. RAIN generates from the given educts and products of a reaction a network of the conceivable reaction pathways. RAIN has been successfully used in the elucidation of reaction mechanisms [ 33,341, and it will be used as a module in bilateral synthesis design. IGOR generates unprecedented molecules and chemical reactions. For example IGOR has been used to predict the 278 conceivable &membered cyclic phosphorylating reagents for oligonucleotide synthesis [ 531. IGOR has also been successful in proposing the first computer-generated new reactions [ 36, 541 that have been verified in the laboratory. CONCLUSION

The concept “artificial intelligence” was introduced in the 1960s at Stanford in the context of DENDRAL [ 551. The DENDRAL project aimed at automated elucidation of molecular structures from spectroscopic data. At about the same time, the development of the artificial intelligence type computer

programs for retrosynthetic analysis and synthesis design began. These retrosynthetic programs are based on known chemistry in the form of reaction libraries. Until recently the chemical community expected the fully automated solution of complex chemical problems by artificial intelligence. Some even feared that chemists would be reduced to technicians who followed instructions from the artificially intelligent computers. More recently, a more realistic attitude towards computer assistance in chemistry has been prevalent; there has even been some disenchantment. No artificially intelligent batch programs are available that will automatically generate complex molecular structures from spectra, nor will they be available in the foreseeable future, and the development of the retrosynthetic synthesis design programs has reached a plateau that is below the early high hopes. Yet there is no reason to be pessimistic about the future of computer assistance in chemistry. The evolution of this discipline does just not agree with the hopes and prognoses of the past; it has taken its own path. Three approaches to computer assistance in solving chemical problems have evolved: one that we may call the anthropomorphic approach, the exhaustive approach, and the most recent structured interactive approach. In the so-called anthropomorphic approach, an attempt is made to simulate human chemical reasoning, and its strategies, together with empirical knowledge that has been stored in data bases; this: is combined with heuristic rules that express prior experience. Heuristic selection procedures may lead to arbitrary decisions. Since 1983 we have preferred not to use any heuristic rules and procedures in our new chemical computer programs for PC type computers and inexpensive workstations. Instead, all automated decisions and selection procedures rely on formalisms and hierarchic classifications. In the exhaustive approach, formalized combinatorial routines are used to generate in an exhaustive manner the conceivable solutions to a given problem, and to select from these the most plausible solutions according to procedures that rely on heuristics and estimates of physicochemical data. The structured interactive approach exploits as many aspects of the logical structure of chemistry as possible in the solution of chemical problems, and hierarchic representation systems of molecules and chemical reactions follow whenever this is advantageous. The interactive operating mode leaves the logic and combinatorial operations to the computer, and assigns all decisions that require chemical knowledge, experience, and intuition to the expert user. Thus there is neither need to gather and maintain large data bases of detailed chemical information, nor is it necessary to execute selection procedures that involve large amounts of data. Accordingly, the structured interactive approach is particularly well-suited for small computers and inexpensive workstations. The structured interactive approach has therefore very good chances

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of widespread proliferation in the future; we shall have expert systems that have been implemented to be used by experts, and only experts. They are not designed to replace an expert, not even partially; they are just made to amplify an expert’s working power. They do not contain any data base of detailed information for supplementing the experts’ knowledge and experience.

REFERENCES

5 6 7 8 9 10 11

12 13 14

15 16 17 18 19 20 21 22 23

H. Preuss, Int. J. Quant. Chem., 3 (1963) 123,131. E. Hjelt, Geschichte der Organischen Chemie, Vieweg und Sohn, Braunschweig, 1916. I. Ugi, Giessener Universititsblatter, 2 (1978) 68. (a) R.B. Woodward, Pure Appl. Chem., 17 (1968) 519. (b) A. Eschenmoser, Angew. Chem., 81 (1969) 301; Angew. Chem. Int. Ed. Engl., 9 (1969) 301. (a) J. Weyer, Angew. Chem., 86 (1974) 604; Angew. Chem. Int. Ed. Engl., 12 (1974) 591. (b) J. Gasteiger, P.D. Gillespie, D. Marquarding and I. Ugi, Top. Curr. Chem., 48 (1974) 1. J. Clayley, Mathematical Papers, Cambridge, (1891) 242. G. Polyi, C.R. Acad. Sci., 201 (1935) 1176; 202 (1936) 1554; Vierteljahresschr. Naturforsch. Ges. Ziirich, 81 (1936) 243; Z. KristaIlogr. A, 93 (1936) 414; Acta Math., 68 (1937) 145. A.T. BaIaban (Ed.), Chemical Applications of Graph Theory, Academic Press, London, 1976. (a) I. Ugi and G. Kaufhold, Justus Liebigs Ann. Chem., 709 (1967) 11. (b) I. Ugi, Rec. Chem. Progr., 30 (1969) 389. I. Ugi, D. Marquarding, H. Klusacek, G. Gokel and P. Gillespie, Angew. Chem., 82 (1970) 741; Angew. Chem. Int. Ed. Engl., 9 (1970) 703. (a) P. Gillespie, P. Hoffmann, H. Klusacek, D. Marquarding, S. Pfohl, F. Ramirez, E.A. Tsolis and I. Ugi, Angew. Chem., 83 (1971) 691; Angew. Chem. Int. Ed. Engl., 10 (1971) 687. (b) I. Ugi, D. Marquarding, H. Klusacek, P. Gillespie and F. Ramirez, Act. Chem. Res., 4 (1971) 288. I. Ugi, J. Dugundji, R. Kopp and D. Marquarding, Perspectives in Theoretical Stereochemistry, Lect. Note Ser., No. 36, Springer, Heidelberg, 1984. J. Dugundji and I. Ugi, Top. Curr. Chem., 39 (1973) 19. (a) I. Ugi, in J. Brandt and I. Ugi (Eds.), Proc. of 7th ICCCRE, Elsevier, New York, 1988, in press. (b) I. Ugi, J. Ind. Chem. Sot., 62 (1985) 761. (c) V. Balb, J. Koca, V. Kvasnicka and M. Sekanina, Caposis pro pestovani matematiky, rot 111 (1986). I. Ugi, J. Bauer, J. Brandt, J. Friedrich, J. Gasteiger, C. Jochum, W. Schubert and J. Dug-undji,Inf. Comm. Math. Chem., 6 (1979) 201. E. Fontain, J. Bauer and I. Ugi, Anal, Chim. Acta, 1988, in press. C. Jochum, J. Gasteiger and I. Ugi, Angew. Chem., 92 (1980) 503; Angew. Chem. Int. Ed. Engl., 19 (1980) 495. C. Jochum, J. Gasteiger, I. Ugi and J. Dugundji, Z. Naturforsch. Teil B, 37 (1982) 1205. (a) M. Wochner, Dissertation, Technische UniversitLitMiinchen, 1985. (b) M. Wochner, J. Brandt, A. v. Scholley and I. Ugi, Chimia, in press. H. Kolbe, Justus Liebigs Ann. Chem., 75 (1850) 211; 76 (1850) 1. W. Hiickel, Theoretische GrundIagen der organischen Chemie I., Akademie Verlagsgesells&aft, Leipzig, 1956. W. Schubert, Dissertation, Technische Universitiit, Mtinchen, 1981; MATCH, 6 (1979) 213. I. Ugi, Chimia, 40 (1986) 340.

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30 41 42 43 44 45 46 47 48 49 50

51

J. Blair, J. Gasteiger, C. Gillespie, P.D. Gillespie and I. Ugi, CICLOPS - A computer program for the design of syntheses on the basis of a mathematical model, in W.T. Wipke, S.R. Heller, R.J. Feldmann and E. Hyde (Eds.) , Computer Representation and Manipulation of Chemical Information, Wiley, New York, 1974. W. Schubert and I. Ugi, J. Am. Chem. Sot., 100 (1978) 37. W. Schubert and I. Ugi, Chimia, 33 (1979) 183. Ref. 12, Chap. 8. J. Friedrich and I. Ugi, J. Chem. Res., S (1980) 70; M (1980) 1301; M(1980) 1401; M (1980) 1501. M. Wochner and I. Ugi, J. Chem. Inf. Comput. Sci., in press. (a) J. Brandt, J. Bauer, R.M. Frank and A. v. Scholley, Chem. Ser., 18 (1981) 53. (b) J. Brandt and A. v. Scholley, Comput. Chem., 7 (1983) 51. (a) J. Gasteiger and C. Jochum, Top. Curr. Chem., 74 (1978) 93. (b) J. Gasteiger, C. Jochum, M. Marsili and J. Thoma, MATCH, 6 (1979) 177. (c) J. Gasteiger, M.G. Hutchings, B. Christoph, L. Gann, C. Hiller, P. Low, M. Marsili, H. Saller and K. Yuki, Top. Curr. Chem., 137 (1987) 19. I. Ugi, J. Bauer, J. Brandt, J. Friedrich, C. Jochum, W. Schubert and J. Dugundji, Computer programs for the deductive solution of chemical problems on the basis of a mathematical model - a systematic bilateral approach to reaction pathways, in J. Bargon (Ed.), Computational Methods in Chemistry, Plenum Press, New York, 1980, p. 275. E. Fontain, J. Bauer and I. Ugi, Chem. Lett., (1987) 37. E. Fontain, J. Bauer and I. Ugi, Z. Naturforsch., Teil B, 42 (1987) 889. J. Bauer and I. Ugi, J. Chem. Res., S (1982) 298; M (1982) 3101; M (1982) 3201. J. Bauer, R. Herges, E. Fontain and I. Ugi, Chimia, 39 (1985) 43. (a) H.L. Morgan, J. Chem. Dot., 5 (1965) 107. (b) W.C. Herndon and J.E. Leonard, Inorg. Chem., 22 (1983) 554. (a) R.S. Cahn and C.K. Ingold, J. Chem. Sot., (1951) 612. (b) R.S. Cahn, C.K. Ingold and V. Prelog, Experientia, 12 (1956) 81; Angew. Chem., 78 (1966) 413. (c) V. Prelog and G. Helmchen, Angew. Chem., 94 (1982) 614; Angew. Chem. Int. Ed. Engl., 21 (1982) 567. (d) E.F. Meyer, J. Comput. Chem., 1 (1980) 229. J.E. Dubois, DARC system in chemistry, in W.T. Wipke, S.R. Heller, R.J. Feldmann and E.Hyde (Eds.) , Computer Representation and Manipulation of Chemical Structure Information, Wiley, New York, 1974, p. 239; 8th ICCCRE, Anal. Chim. Acta, in press. P. Bruck, in ARCH, Anal. Chim. Acta, in press. E. Meyer, in 8th ICCCRE, Anal. Chim. Acta, in press. W. Donner, GdCH-Conf. on Computer im Labor, 13.-17 October 1986, Frankfurt. M.R. Frierson, G. Klopman and H.S. Rosenkranz, Environ. Mutagen., 8 (1986) 283. R.E. Burckard and U. Derigs, Assignment and Matching Problems: Solution Methods with FORTRAN Programs, Spinger Verlag, Heidelberg, 1980. E.H. Sussenguth Jr., J. Chem. Dot., 5 (1965) 36. J. Figueras, J. Chem. Dot., 12 (1972) 237. S. Fujita, J. Chem. Inf. Comput. Sci., 26 (1986) 205,212,. 224,231,238. (a) N.S. Zefirov, S.S. Trach and G.A. Gamziani, J. Org. Chem. USSR, 222 (1986) 1209. (b) N.S. Zefirov, Act. Chem. Res., 20 (1987) 237. K. Stadler, Dissertation, Technische Universitit Mtinchen, 1986. (a) J. Ore, A.P. Kimball, R. Fritz and F. Master, Arch. Biochem. Biophys., 85 (1959) 115. (b) J. Ore and S.S. Kamat, Nature (London), 190 (1961) 442. (c) J. Or6 and A.P. Kimball, Arch. Biochem. Biophys., 94 (1961) 217. E. Fontain, Dissertation, Technische Universitit Miinchen, 1987.

242 52 53

54 55

J. Bauer, Dissertation, Technische Universitit, Mtinchen, 1981. I. Ugi, J. Bauer, E. Fontain, J. Gijtz, G. Hering, P. Jakob, B. Landgraf, R. Karl, P. Lemmen, R. Schneiderwind-Wcklein, R. Schwarz, P. Sluka, N. Balgobin, J. Chattopadhyaya, T. Pathak and X.-X. Zhou, Chem. Ser., 26 (1986) 205. (a) D. Forstmeyer, A. Gieren, J. Bauer and I. Ugi, in preparation. (b) S. Lohberger, J. Bauer and I. Ugi, in preparation. R. Lindsay, B.G. Buchanan, E.A. Feigenbaum and J. Lederberg, Applications of Artificial Intelligence for Organic Chemistry: The DENDRAL Project, New York, McGraw-Hill, 1980.