Abstract:
A method selects a best case set of factors of a chemical reaction by defining a chemical experimental space by (i) identifying relationships between factors of a candidate chemical reaction space; and. (ii) detemininig a chemical experimental space comprising a table of test cases for each of the factors based oil the identified relationships between the factors with the identified relationships based oil researcher specified n-tuple combinations between identities of the relationships. A combinatorial high throughput screening (CHTS) method is effected on1 the chemical experimental space to select the best case set of factors. A system for selecting a best case set of factors of a chemical reaction, comprises a processor, reactor and an evaluator. The processor defines a chemical experimental space by (i) identifying relationships between factors of a candidate chemical reaction space; and (ii) determining the chemical experimental space comprising a table of test cases for each of the factors based o01 the identified relationships between the factors with the identified relationships based on researcher specified n-tuple combinations between identities of the relationships. The reactor and evaluator select a best case set of factors from the chemical experimental space by a combinatorial high throughput screening (CHTS) method to select a best case set of factors.

Description:
[0001]    This application claims the priority of Provisional Application Serial No. 60/177,325, filed Jan. 21, 2000. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    The present invention relates to a method and system for selecting best case set of factors for a chemical reaction. Particularly, the invention is directed to a method and system for defining an experimental space and conducting a combinatorial high throughput screening (CHTS) of the experimental space to determine a best case set of reaction factors.  
           [0003]    In experimental reaction systems, each potential combination of reactant, catalyst and condition must be evaluated in a manner that provides correlation to performance in a production scale reactor. Combinatorial organic synthesis (COS) is a high throughput screening (HTS) methodology that was, developed for pharmaceuticals. COS uses systematic and repetitive synthesis to produce diverse molecular entities formed from sets of chemical “building blocks.” As with traditional research, COS relies on experimental synthesis methodology. However instead of synthesizing a single compound, COS exploits automation and miniaturization to produce large libraries of compounds through successive stages, each of which produces a chemical modification of an existing molecule of a preceding stage. A library is a physical, trackable collection of samples resulting from a definable set of processes or reaction steps. The libraries comprise compounds that can be screened for various activities.  
           [0004]    The technique used to prepare such libraries involves a stepwise or sequential coupling of building blocks to form the compounds of interest. For example, Pirrung et al., U.S. Pat. No. 5,143,854 discloses a technique for generating arrays of peptides and other molecules using, for example, light-directed, spatially-addressable synthesis techniques. Pirrung et al. synthesizes polypeptide arrays on a substrate by attaching photoremovable groups to the surface of the substrate, exposing selected regions of the substrate to light to activate those regions, attaching an amino acid monomer with a photoremovable group to the activated region, and repeating the steps of activation and attachment until polypeptides of desired lengths and sequences are synthesized.  
           [0005]    The methodology of COS has been slow in application to screening to develop chemical production scale reactions because of the difficulty in emulating such reactions on the combinatorial micro-scale. For example, catalyst testing is typically accomplished in bench scale or larger pilot plants by contacting a feed to a continuous flow reactor with a catalyst under near steady state reaction conditions. Rapid combinatorial screening of reactants, catalysts, and associated process conditions requires that a large number of reaction and/or catalytic systems be tested simultaneously. The large number of systems are parameters that can define a very large, multidimensional experimental space.  
           [0006]    For example, even a simple commercial process may have five or six critical factors, each of which can have 2 to 20 levels. These factors can include reactants, catalysts and processing conditions. As shown in FIG. 1, the number of possible combinations of factors can become very large, depending on the number of levels. In addition, little may be known about the reaction kinetics and the role of a catalyst. Accordingly, it may be necessary to search hundreds or thousands of combinations to find a handful of “leads” (i.e., combinations that may lead to commercially valuable applications).  
           [0007]    T. E. Mallouk et al. in Science, 1998, 1735 showed that effective ternary combinations can exist in a system in which none of the binary combinations are effective. As shown in FIG. 2, investigating binary combinations alone can result in completely ineffective exploration of an experimental space. However, as seen in FIG. 1, the number of tertiary, 4-way, 5-way, and 6-way combinations rapidly becomes extremely large. It is extremely difficult to examine all possibilities of such a complex space even with a very productive high throughput screening (HTS) system. There is a need for improved methods for rapidly, yet effectively investigating a complex experimental space relating to these process combinations.  
         BRIEF SUMMARY OF THE INVENTION  
         [0008]    Accordingly, the invention is directed to a method and system for sampling an experimental space for combinatorial high throughput screening (CHTS). CHTS is an HTS methodology that incorporates characteristics of COS. The definition of the experimental space permits a CHTS investigation of highly complex systems. The method selects a best case set of factors of a chemical reaction. The method comprises defining a chemical experimental space by (i) identifying relationships between factors of a candidate chemical reaction space; and (ii) determining a chemical experimental space comprising a table of test cases for each of the factors based on the identified relationships between the factors with the identified relationships based on researcher specified n-tuple combinations between identities of the relationships. A CHTS method is effected on the chemical experimental space to select a best case set of factors.  
           [0009]    In another embodiment, a system for selecting a best case set of factors of a chemical reaction, comprises a processor, reactor and an evaluator. The processor defines a chemical experimental space by (i) identifying relationships between factors of a candidate chemical reaction space and (ii) determining the chemical experimental space comprising a table of test cases for each of the factors based on the identified relationships between the factors with the identified relationships based on researcher specified n-tuple combinations between identities of the relationships. The reactor and evaluator select a best case set of factors from the chemical experimental space by a CHTS method to select a best case set of factors. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]    [0010]FIG. 1 is a graph of six factor combinations;  
         [0011]    [0011]FIG. 2 is a schematic representation of a ternary catalyst bounded by low activity binaries;  
         [0012]    [0012]FIG. 3 is a schematic representation of a method and system for defining an experimental space for CHTS;  
         [0013]    [0013]FIGS. 4 and 5 are TABLES of experimental runs for individual relationships of an experimental space;  
         [0014]    [0014]FIG. 6 is a schematic representation of a method and system for selecting a best case set of factors for a chemical reaction; and  
         [0015]    [0015]FIG. 7 is ahistograph of TON results. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0016]    According to the invention, an algorithm can be applied to determine a minimal number of experimental runs necessary to effectively explore an experimental space by CHTS. The algorithm can be embodied in a computer software program. The software program can be maintained on a server for use by end researchers over a network.  
         [0017]    In a preferred embodiment, a researcher provides factors that may impact the reaction or process of interest as well as identities for those factors. In this context, the term “factors” can include reactants, solvents, carriers, catalysts and chemically inert substances that are present to affect a physical property of one or more components of the reactant system. In various embodiments, the term “factor” can further include reaction or process conditions, such as temperature, flow rate, pressure, or reaction atmosphere. The term “identity” refers to a factor&#39;s value or makeup—whether in kind or amount. The use of a metric “identity” will necessarily vary depending on a given factor. For example, identity of a reactant may refer to chemical identity or concentration, while identity of a factor such as pressure will be a value or ratio.  
         [0018]    The researcher can then provide instructions regarding whether given factors interact with each other. The algorithm then determines a minimal number of necessary experimental runs embodied in a table. In this application, a table is a list of relationships between fields (factors) generated by deterministic procedures as hereinafter described. The factors of one table can be merged with other tables to produce a single table. The merged table is used as a template for parallel chemical reactions and/or high-throughput screening to determine the efficacy of the various combinations of factor identities in the reaction or process of interest.  
         [0019]    An example of an acceptable software program for determining the minimal number of experimental runs is the AETG SM  System available from Telcordia™ Technologies, Inc., Morristown, N.J. The AETG™ System is and has always been lauded and marketed as a software development program and has heretofore not been utilized as part of a combinatorial chemistry effort.  
         [0020]    These and other features will become apparent from the drawings and following detailed discussion, which by way of example without limitation describe preferred embodiments of the present invention.  
         [0021]    An illustrative embodiment of the present method is shown in FIG. 3, which includes a terminal  10 . A researcher enters identities for factors into the terminal  10  (a plurality of terminals may also be employed) and defines the relationships between these factors (hereinafter called a relation), which establishes validation rules for groups of the factors. The researcher may also enter constraints and a parameter specifying the degree of factor interaction for each relation. Display controller  12  stores the factor relations and validation rules in a relation database  18 . Tables of experimental runs for each relation are generated in a process  14  and then stored also in database  18 . After all data are entered, the factor relationships defined and individual tables of experimental runs generated, the researcher requests generation of a consolidated table of experimental runs. The experimental run script merger process  20  then generates a single table of runs combining the tables of runs generated by process  16 . The resulting table of experimental runs is stored in database  22  for subsequent use by the researcher.  
         [0022]    The system described above implements a method for enumerating a minimal number of experimental runs. The method comprises two general sets of procedures—one for generating a table of experimental runs for each individual relation as embodied in process  14  and another for combining the individual tables into a single table as embodied in process  20 . The building blocks used in each set of procedures are the factors, factor identities, relations and degree of factor interactions entered by the researcher.  
         [0023]    To create a relation, the researcher specifies the factors in the relation, a set of identities for each factor and constraints. The factors specified can come from one screen or from a plurality of screens. Once the researcher specifies the relationships among factors and identities, the researcher also specifies the degree of interaction between factors to test the interactions as an n-combination (e.g. pair-wise, triples, exhaustive, etc.). As an example, pair wise combinations mean that for any two factors f 1  and f 2  and any valid identities, v 1  for f 1  and v 2  for f 2 , there is some experimental run in which f 1  has the value v 1  and f 2  has the value v 2 .  
         [0024]    The invention can use a set of procedures based on deterministic algorithms in combination with a set of procedures based on a random algorithm. A deterministic algorithm is a process in which a correct next step is determined only by a current state. If a deterministic process is repeated from a fixed initial state it will yield the same outcome. A standard mathematical process such as a sequence of addition and multiplication is an example of a deterministic process. A random algorithm is a process that is at least partially governed by chance. Repetition of a random process from a fixed initial state will not yield the same outcome. A statistical process such as roulette is an example of a random process.  
         [0025]    In an exemplary embodiment of generation process  14 , deterministic procedures are used first to attempt to produce a table. If deterministic procedures cannot directly be used because the number of factors and interactions are not conducive to a deterministic approach, then the relation is decomposed into sub-parts for which experimental runs can be generated using deterministic procedures. Process  14  uses the generated experimental runs for the sub-parts as seed experimental runs for a random procedure that generates a table of experimental runs for that relation.  
         [0026]    The first step in the deterministic process is to examine a relation and determine the group of factors with the largest number of factor identities or the largest group of factors with the same number of factor identities. The next step is to examine the group of factors to determine if a table of experimental runs can be generated using a deterministic algorithm.  
         [0027]    In this embodiment, the deterministic algorithm can be a projective plane procedure, application of the general product rule procedure or just an exhaustive enumeration of all combinations of factor identities. If only one factor exists with the largest number of factor identities, the deterministic procedure simply generates all n-way combinations (where n is the degree of interaction) for a selected subset of factors with the highest number of factor identities using art-recognized techniques of exhaustive enumeration. In an exhaustive enumeration, all possible outcomes are generated from a mathematical algorithm. This is typically done by various applications of well known techniques of permutation and combination to lists of input variables. For example, suppose a baseball manager wishes to try all possible batting orders for a team of 9 men in successive games. How many games are required to try all orders? An exhaustive enumeration uses all permutations of 9 members taken 9 at a time, or 9P9=9! (9factorial)=9×8×7×6×5×4×3×2×1=363,880 ball games.  
         [0028]    Experimental runs nominated by the deterministic procedure can be compared with experimental runs nominated from a projective plane or product rule procedure from a subset [a part of the whole set as defined by a rule] of the relation with the largest number of factors having common identities. The resulting subset of factors can be used to seed (enter the initial values in the table for the algorithm) the random algorithm that is used for completing the table by filling in identities for the remaining factors.  
         [0029]    A generalized projective plane procedure can be used when the number of identities is a fixed prime power q and the number of factors is q+1. A projective plane is defined as an array of points and lines with the following geometric properties:  
         [0030]    Any two distinct points are incident with exactly one line.  
         [0031]    Any two distinct lines are incident with exactly one point  
         [0032]    There exist four points with not three on a single line.  
         [0033]    See A. Beutelspacher, in The CRC Handbook of Combinatorial Designs, C. J. Colbourn and J. H. Dinitz, eds, CRC Press, New York, 1996, p 694.  
         [0034]    A projective plane is equivalent to the common experimental design known as “Mutually Orthogonal Latin Squares” (ibid, p 113). The generalized projective plane construction gives a table of q n  experimental runs where q is the number of factor identities and n is the degree of interaction and n#q+1. An example where q=3 is given in the following merged RELATION TABLES exemplifying a chemical system.  
       Relation Tables  
       [0035]    [0035]                                                 TABLE 1                                       Factors (q + 1 = 4)                    Metal   Halide   Solvent   Complexing Agent               Identities   Cr   Cl   DMA   Diglyme       (q = 3)   Cu   Br   DEA   Triglyme           Co   I   DBA   Tetraglyme                    
         [0036]    [0036]                                     TABLE 2                           PROJECTIVE PLANE (LATIN SQUARE) DESIGN            Run   Metal   Halide   Solvent   Complexing Agent               1   Cr   Cl   DMA   Diglyme       2   Cr   Br   DEA   Triglyme       3   Cr   I   DBA   Tetraglyme       4   Cu   Cl   DEA   Tetraglyme       5   Cu   Br   DBA   Diglyme       6   Cu   I   DMA   Triglyme       7   Co   Cl   DBA   Triglyme       8   Co   Br   DMA   Tetraglyme       9   Co   I   DEA   Diglyme                            
         [0037]    The generalized projective plane procedures develop n-way coverage as follows. The number of experimental runs necessary to cover n-way interactions of q number of factor identities is q n . The procedure then lists the number of n-way combinations as (α 1 , . . . , α n ) with (0, . . . , 0) being the first and (n−1, . . . ,n−1) being the last. The process then determines experimental runs of the form (a 1 , . . . a f ), with f being the number of factors. For λ from 0 to q, the value (modulus q) is the value at factor λ for an experimental run labeled (α 1 , . . . , α n ). If f=q +1 , then the value for a f  is α n . The factor q +1   is called the “line at infinity.” For the situation when q is a prime power but not a prime number, identification needs to be made between numbers 1 to q and the finite factor with q elements.  
         [0038]    As an example of applying the procedure to a relation, assume the chemical relation shown in the RELATION TABLE with four factors each with three identities. This chemical relation is equivalent to the mathematical relation  30  as shown in FIG. 4. Further, assume that the researcher wishes to generate experimental runs for pair-wise combinations of the factors. The process numbers the experimental runs according to the number of pair wise combinations that can be generated. With three levels of identities for each factor, the number of pair wise combinations (n=2) that can be generated is nine (3 2 ). Therefore, the following formula is used to generate the first of nine experimental runs of the form (a 1 , a 2 , a 3 , a 4 ) for pair-wise interactions:  
         [0039]    Here a 1  is the first value of the first pair  36  and λ is a number representing the factor position  37  from the vector (1, . . . ,q) representing the number of factors. Therefore, the value for a 1  is α 1  times λ 1−1  plus α 2  times λ 2−1  at factor 1 (λ=0), which equals 0 shown at  38 . The value for a 2  is α 1  times λ 1−1  plus a 2  times λ 2−1  at factor 2 (λ=1), which is also 0 shown at  39 . This process is repeated for each a i  for each of the nine experimental runs.  
         [0040]    The resultant table  34  in FIG. 4 shows nine experimental runs as shown in FIG. 4. In the table  34 , each of the columns  33  represents a factor and each number in each cell within each column represents a factor identity. For example, in the fourth experimental run labeled (0,1) 40, the 0 under the column a, indicates the first factor value for factor 1 and the 2 under column a 3  indicates the third value for factor 3. Accordingly, the fourth experimental run shown in table  34  for relation  30  is (v 1 ′, v 2 ′, v 3 , v 2 ′). The equivalent chemical result is shown in Table 2 of the RELATION TABLES.  
         [0041]    A projective plane algorithm is only directly applicable when the number of factor identities is q (a prime or power of prime) and the number of factors is less than or equal to q+1. Although the algorithm is also effective when the number of identities is close to a prime power, for example 10 is close to 11. Often a relation does not easily fit the projective plane construct. Under these circumstances, the experimental run enumeration process breaks the relation into subrelations to determine if experimental runs for a sub-relation can be generated deterministically, either using the projective plane procedure or, if the sub-relation is small enough, through exhaustive enumeration. If so, the subrelations (subsets) are then merged using product rules.  
         [0042]    A product rule is defined as a process in which two tables of experimental runs are merged by repetition of each of the elements in the first table by the number of the factors in the second table and then each of the sequence of elements for the factors in the second table is repeated by the number of factors in the first table. Duplicate rows in the resultant table are then eliminated. The product rules are only directly applicable whenever each factor has the same number of factor identities and the degree of factor interaction is pair-wise.  
         [0043]    As an example, consider a relation  43  shown in FIG. 5 having 9 factors each with two factor identities. In the process, a subset of the relation  44  is taken for which the projective plane algorithm can be applied. Experimental runs are generated for the subset. In this example, experimental runs  45  were generated for relation  44  for pair wise coverage of three factors each with two factor identities. The product rules produce a table of 8 experimental runs for nine factors  46 . These experimental runs  46  are the products of experimental runs  45  combined with themselves. The process for doing so is to repeat each of the elements in the first table by the number of factors in the second table and then repeat each of the sequence of elements for the factors in the second table by the number of factors in the first table. The process then examines the resulting table of experimental runs to eliminate duplicates. In the example above, the fifth experimental run  42  is a duplicate of the first experimental run  41  and is removed.  
         [0044]    Implementation of the product rules can be generalized as follows. Let S and T be two sets of experimental runs with the same number of identities for each factor. The number of factors may vary. As an example, let S have m factors and T have r factors. A typical experimental run in S would be written as (s 1 , . . . ,s m ). A typical experimental run for T would be written as (t 1 , . . . , t r ). The product of experimental runs for m*r factors would be of the form (s 1 , . . . , s 1 ,s 2 , . . . , s 2 , . . . , s m , . . . s m ) repeated r times for each s i  and (t 1 , . . . ,t r , . . . , t 1 , . . . , T r ,) where each experimental run (t 1 , . . . ,t r ) is repeated m times.  
         [0045]    A random procedure can be used to complete the generation of a table of experimental runs when the deterministic procedures cannot be used to generate a complete table of experimental runs for a relation. For each new experimental run, the random procedure begins by generating a set of candidate experimental runs using the locally greedy algorithm described below. Given this set of candidate experimental runs, the algorithm picks the next experimental run using an evaluation function, which assigns a score to each candidate experimental run. The experimental run added to the table is the candidate experimental run with the highest score. The two basic evaluation functions are the “edge-greedy” evaluation function and the “balanced greedy” evaluation function.  
         [0046]    The basic steps that comprise the locally greedy algorithm are as follows:  
         [0047]    1. Select a (n−1) set (n=the degree of interaction) that has the highest priority. Use random selection in the case of ties. For example, in the case of pair-wise coverage, the set would be a factor and value combination that has the greatest number of uncovered pairs (pair-wise combinations of identities which are not included in one of the experimental runs generated by the deterministic procedure).  
         [0048]    2. Select at random an order for the remaining factors. Working in that order, for each factor, find the factor identities that give the highest score with respect to the evaluation function selected by the researcher for the run. The evaluation function, may for example, score by counting the number of additional uncovered pairs which would be covered if that identity was selected. Choose the highest scored identity (at random if ties occur) and proceed to the next factor.  
         [0049]    3. After an identity has been chosen for each factor, check that the set of factor identities contains none of the combinations of experimental runs, which the experimenter does not want to examine (constraints). If the resulting set of factor identities violates a constraint, then permute (interchange) the factor labels (e.g. f 1 ,f 2 ,f 3 ,f 4  in FIG. 4) as they are associated with the specified identities and see if the resultant experimental run violates the constraint. If this does not work, discard the set of factor identities and generate another. If none of the generated experimental runs satisfies the constraints, the locally greedy algorithm uses an exhaustive search to find an experimental run. If a constraint does not rule out a large percentage of the experimental runs, one of the generated sets of factor identities is likely to satisfy it.  
         [0050]    The balanced greedy algorithm is another method of generating a table. For pair-wise coverage defined above the balanced greedy algorithm uses the following:  
         [0051]    If (f,i), where f is a field and i is an identity, is defined as a point in space, a space of a table can be defined as the set of uncovered pairs (connections between all points (f,i) and (f′,i′) where that pair has not already been covered in an experimental run).  
         [0052]    A potential function can be assigned to each point in the space as follows:  
         [0053]    Assign each point a tuple (n a , . . . , n v ) where v is the number of factors and n a  is the number of uncovered pairs {(f,i), (a,i′)} in the space  
         [0054]    Calculate the sum of squares of the entries in the tuple.  
         [0055]    A steepest descent method can then be used to find the greatest decrease in the potential function from point to point, to determine a minimal set of runs. In this method, starting from an initial point (f,I), the value of the potential function is determined at all the points connected to that point (as defined above). The point (f′,i′) with the largest value of the potential function is selected and a run containing the pair of identities (i,i′) for fields (f,f′) is added to the table. The process is then reiterated from the point (f′,i′) and continued until no uncovered pairs remain.  
         [0056]    A researcher can then specify constraints that are used by the method as unallowed experimental runs. A set of unallowed experimental runs can be specified using explicit identities (the exact identity for each factor in a run is specified) or “wild cards,” (exact identities are not specified but values vary freely). Other runs may be specified by the experimenter as unallowed even though they would be valid by all the rules heretofore specified. For example, if a researcher specifies an experimental run that should not happen, that experimental run is removed from the test set.  
         [0057]    In another embodiment, the relations defined above are used in an experimental run merging process  20  that merges individual tables of experimental runs generated for each relation in accordance with the rules that follow:  
         [0058]    1. If two or more relations have factors in common, the merged test set for them is the union of the test sets for the individual relations; and  
         [0059]    2. For those relations that do not have factors in common, a merged test set is created by folding the smaller test set into the larger. In the folding process the smaller test set is replicated until it is equal in number of rows of the larger test set (truncating the last replication if necessary) and columns of the resulting test set are added next to columns of the larger test set.  
         [0060]    Also, a researcher can specify seed experimental runs for each relation. Seed experimental runs can be either required or unallowable. Required seed cases will be guaranteed to be in the final set, while unallowable seed experimental runs are guaranteed not to appear in a final test set. Unallowed seed experimental runs are treated as constraints, while required seed experimental runs are used to seed the random greedy algorithm. Since some of the n-way combinations are already covered in the seed required cases, the system produces fewer additional experimental runs.  
         [0061]    In another aspect of the invention, a group of factors can be selected and that group defined as virtual factors (hereinafter called complexes). These complexes are used with other factors to defined a relation to be processed by the method. In processing, a complex is treated like a singular factor. These relations including complexes can be stored in database  18  and used by the system as a singular factor to be built into relations for the process.  
         [0062]    Many important chemical reactions are based on numerous factors of reactants, catalysts and conditions. The present invention can be used to select a best case set of factors of such reactions or as part of a synthesis procedure to carry out such reactions. In one embodiment, the invention comprises generating varying sets of chemical reaction factors and testing the sets by a high throughput screening process such as CHTS. FIG. 6 is a schematic representation illustrating a method and system for a selecting best case set of factors for a chemical reaction.  
         [0063]    Referring to FIG. 6, an appropriate set of reactant variables and their identities  71 ; a set of process variables and their identities  72  and a degree of interaction or combination (e.g. 2-way, 3-way)  73  are selected. A minimal set of reaction runs is generated  74  and the runs are performed  75  by a CHTS method. The resulting data are analyzed  76  with graphical and statistical tools to determine a set of factors and identities, which provide the best result from the reaction. A determination is made as to whether the determined set of factors and identities is actually a minimal set. If not, the process is reiterated using a reduced set of factors as determined in the first iteration.  
         [0064]    In an embodiment, the invention is directed to a sampling protocol for a CHTS method and system. The method and system of the present invention can be useful for parallel high-throughput screening of chemical reactants, catalysts, and related process conditions. The method and system allows researchers to investigate a complex experimental space defined by two or more factors having multiple possible identities.  
         [0065]    Typically, a CHTS method is characterized by parallel reactions at a micro scale. In one aspect, CHTS can be described as a method comprising (A) an iteration of steps of (i) selecting a set of reactants; (ii) reacting the set and (iii) evaluating a set of products of the reacting step and (B) repeating the iteration of steps (i), (ii) and (iii) wherein a successive set of reactants selected for a step (i) is chosen as a result of an evaluating step (iii) of a preceding iteration.  
         [0066]    In another typical CHTS method, a multiplicity of tagged reactants is subjected to an iteration of steps of (A) (i) simultaneously reacting the reactants, (ii) identifying a multiplicity of tagged products of the reaction and (B) evaluating the identified products after completion of a single or repeated iteration (A).  
         [0067]    A typical CHTS can utilize advanced automated, robotic, computerized and controlled loading, reacting and evaluating procedures.  
         [0068]    In one embodiment, the invention is applied to study a process for preparing diaryl carbonates. Diaryl carbonates such as diphenyl carbonate can be prepared by reaction of hydroxyaromatic compounds such as phenol with oxygen and carbon monoxide in the presence of a catalyst composition comprising a Group VIIIB metal such as palladium or a compound thereof, a bromide source such as a quaternary ammonium or hexaalkylguanidinium bromide and a polyaniline in partially oxidized and partially reduced form. The invention can be applied to screen for a catalyst to prepare a diaryl carbonate by carbonylation.  
         [0069]    Various methods for the preparation of diaryl carbonates by a carbonylation reaction of hydroxyaromatic compounds with carbon monoxide and oxygen have been disclosed. The carbonylation reaction requires a rather complex catalyst. Reference is made, for example, to Chaudhari et al., U.S. Pat. No. 5,917,077. The catalyst compositions described therein comprise a Group VIIIB metal (i.e., a metal selected from the group consisting of ruthenium, rhodium, palladium, osmium, iridium and platinum) or a complex thereof.  
         [0070]    The catalyst material also includes a bromide source. This may be a quaternary ammonium or quaternary phosphonium bromide or a hexaalkylguanidinium bromide. The guanidinium salts are often preferred; they include the ∀, T-bis(pentaalkylguanidinium)alkane salts. Salts in which the alkyl groups contain 2-6 carbon atoms and especially tetra-n-butylammonium bromide and hexaethylguanidinium bromide are particularly preferred.  
         [0071]    Other catalytic constituents are necessary in accordance with Chaudhari et al. The constituents include inorganic cocatalysts, typically complexes of cobalt(II) salts with organic compounds capable of forming complexes, especially pentadentate complexes. Illustrative organic compounds of this type are nitrogen-heterocyclic compounds including pyridines, bipyridines, terpyridines, quinolines, isoquinolines and biquinolines; aliphatic polyamines such as ethylenediamine and tetraalkylethylenediamines; crown ethers; aromatic or aliphatic amine ethers such as cryptanes; and Schiff bases. The especially preferred inorganic cocatalyst in many instances is a cobalt(II) complex with bis-3-(salicylalamino)propylmethylamine.  
         [0072]    Organic cocatalysts may be present. These cocatalysts include various terpyridine, phenanthroline, quinoline and isoquinoline compounds including 2,2′:6′,2″-terpyridine, 4-methylthio-2,2′:6′,2″-terpyridine and 2,2′:6′,2″-terpyridine N-oxide, 1,10-phenanthroline, 2,4,7,8-tetramethyl- 1,10-phenanthroline, 4,7-diphenyl-1,10, phenanthroline and 3,4,7,8-tetramethy-1,10-phenanthroline. The terpyridines and especially 2,2′:6′,2″-terpyridine are preferred.  
         [0073]    Another catalyst constituent is a polyaniline in partially oxidized and partially reduced form.  
         [0074]    Any hydroxyaromatic compound may be employed. Monohydroxyaromatic compounds, such as phenol, the cresols, the xylenols and p-cumylphenol are preferred with phenol being most preferred. The method may be employed with dihydroxyaromatic compounds such as resorcinol, hydroquinone and 2,2-bis(4-hydroxyphenyl)propane or “bisphenol A,” whereupon the products are polycarbonates.  
         [0075]    Other reagents in the carbonylation process are oxygen and carbon monoxide, which react with the phenol to form the desired diaryl carbonate.  
         [0076]    These and other features will become apparent from the following detailed discussion, which by way of example without limitation describes a preferred embodiment of the present invention.  
       EXAMPLE  
       [0077]    This example illustrates an identification of an active and selective catalyst for the production of aromatic carbonates. The Example identifies the best catalyst from a complex chemical space, where the chemical space is defined as an assemblage of all possible experimental conditions defined by a set of variable parameters such as formulation ingredient identity or amount or a process parameter such as reaction time, temperature or pressure. The chemical space consists of the following chemical components and process parameters from TABLE 3 and TABLE 4:  
                       TABLE 3                       Factor   Possible Identities   Possible Identities                   Primary Catalyst   Ru(acac) 3     All at 25 ppm           Pt(acac) 2             Rh(acac) 3             Ir(acac) 3         Metal Cocatalyst   Mn(acac) 2     150 and 1500 ppm           Fe(acac) 3             Co(acac) 2             Ce(acac) 3         Cosolvent   Dimethylformamide (DMFA),   All at 10%           Dimethylacetamide (DMAA),           Tetrahydrofuran (THF),           Diglyme (DiGly)       Anion Cocatalyst   Cl, Br, I, Cn (as    500 and 5000 ppm           hexamethylguanadinium salts)                  
 
         [0078]    [0078]                   TABLE 4                       Factor   Possible Identities                   Pressure   1000 psi, 1500 psi (8% Oxygen in Carbon Monoxide)       Temperature   100 C., 120 C.       Reaction time   120 min, 180 min                    
         [0079]    The next step in the Example is to determine if unusually good results could occur in the system as a result of three-way combinations. The system has four factors with four identities each (Primary catalyst, Metal Cocatalyst, Cosolvent and Anion Cocatalyst) and five factors with two identities each (Metal Cocatalyst amount, Anion Cocatalyst amount, Pressure, Temperature, and Reaction Time). There are 4 4 ×2 5 =8192 possible combinations of these factors. All three-way combinations of the factors are examined in 128 runs, as shown in the following TABLE 5  
                                                                                                                     TABLE 5                                                       Anion       Tem-   Reaction               Primary   Amount   Metal   Amount       Amount   Anion   Cocatalyst   Pressure   perature   Time       Run   Catalyst   (ppm)   Cocatalyst   (ppm)   Solvent   (%)   Cocatalyst   Amount   (psi)   (C.)   (min)   TON                                1   Ru(acac)3   25   Mn(acac)2   1500   DMFA   10   Cl-   5000   1000   100   180   118.2       2   Ru(acac)3   25   Mn(acac)2   150   DMAA   10   Br-   5000   1000   120   180   134.6       3   Ru(acac)3   25   Mn(acac)2   1500   THF   10   I-   5000   1500   120   180   124.1       4   Ru(acac)3   25   Mn(acac)2   1500   Digly   10   CN-   5000   1000   120   120   134.8       5   Ru(acac)3   25   Fe(acac)3   150   DMFA   10   Br-   500   1500   120   180   185.1       6   Ru(acac)3   25   Fe(acac)3   1500   DMAA   10   I-   500   1000   100   120   31.9       7   Ru(acac)3   25   Fe(acac)3   1500   THF   10   CN-   500   1500   120   120   311.8       8   Ru(acac)3   25   Fe(acac)3   1500   Digly   10   Cl-   500   1500   100   180   328.3       9   Ru(acac)3   25   Co(acac)2   1500   DMFA   10   I-   500   1000   120   180   1138.2       10   Ru(acac)3   25   Co(acac)2   150   DMAA   10   CN-   5000   1500   120   120   275.1       11   Ru(acac)3   25   Co(acac)2   150   THF   10   Cl-   5000   1500   100   180   241.1       12   Ru(acac)3   25   Co(acac)2   150   Digly   10   Br-   500   1000   100   180   392.0       13   Ru(acac)3   25   Ce(acac)3   150   DMFA   10   CN-   500   1000   120   120   80.3       14   Ru(acac)3   25   Ce(acac)3   150   DMAA   10   Cl-   500   1500   100   120   98.0       15   Ru(acac)3   25   Ce(acac)3   1500   THF   10   Br-   5000   1500   100   120   347.0       16   Ru(acac)3   25   Ce(acac)3   150   Digly   10   I-   5000   1000   100   120   400.7       17   Pt(acac)2   25   Mn(acac)2   1500   DMFA   10   Br-   5000   1000   100   180   228.6       18   Pt(acac)2   25   Mn(acac)2   150   DMAA   10   I-   5000   1000   120   180   345.2       19   Pt(acac)2   25   Mn(acac)2   1500   THF   10   CN-   5000   1500   120   180   216.1       20   Pt(acac)2   25   Mn(acac)2   1500   Digly   10   Cl-   5000   1000   120   120   419.8       21   Pt(acac)2   25   Fe(acac)3   150   DMFA   10   I-   500   1500   120   180   218.3       22   Pt(acac)2   25   Fe(acac)3   1500   DMAA   10   CN-   500   1000   100   120   205.2       23   Pt(acac)2   25   Fe(acac)3   1500   THF   10   Cl-   500   1500   120   120   347.1       24   Pt(acac)2   25   Fe(acac)3   1500   Digly   10   Br-   500   1500   100   180   311.0       25   Pt(acac)2   25   Co(acac)2   1500   DMFA   10   CN-   500   1000   120   180   231.9       26   Pt(acac)2   25   Co(acac)2   150   DMAA   10   Cl-   5000   1500   120   120   226.8       27   Pt(acac)2   25   Co(acac)2   150   THF   10   Br-   5000   1500   100   180   200.2       28   Pt(acac)2   25   Co(acac)2   150   Digly   10   I-   500   1000   100   180   332.2       29   Pt(acac)2   25   Ce(acac)3   150   DMFA   10   Cl-   500   1000   120   120   195.1       30   Pt(acac)2   25   Ce(acac)3   150   DMAA   10   Br-   500   1500   100   120   313.9       31   Pt(acac)2   25   Ce(acac)3   1500   THF   10   I-   5000   1500   100   120   403.6       32   Pt(acac)2   25   Ce(acac)3   150   Digly   10   CN-   5000   1000   100   120   362.1       33   Rh(acac)3   25   Mn(acac)2   1500   DMFA   10   I-   5000   1000   100   180   244.9       34   Rh(acac)3   25   Mn(acac)2   150   DMAA   10   CN-   5000   1000   120   180   224.3       35   Rh(acac)3   25   Mn(acac)2   1500   THF   10   Cl-   5000   1500   120   180   274.2       36   Rh(acac)3   25   Mn(acac)2   1500   Digly   10   Br-   5000   1000   120   120   387.7       37   Rh(acac)3   25   Fe(acac)3   150   DMFA   10   CN-   500   1500   120   180   226.5       38   Rh(acac)3   25   Fe(acac)3   1500   DMAA   10   Cl-   500   1000   100   120   237.7       39   Rh(acac)3   25   Fe(acac)3   1500   THF   10   Br-   500   1500   120   120   290.4       40   Rh(acac)3   25   Fe(acac)3   1500   Digly   10   I-   500   1500   100   180   622.4       41   Rh(acac)3   25   Co(acac)2   1500   DMFA   10   Cl-   500   1000   120   180   386.0       42   Rh(acac)3   25   Co(acac)2   150   DMAA   10   Br-   5000   1500   120   120   382.0       43   Rh(acac)3   25   Co(acac)2   150   THF   10   I-   5000   1500   100   180   325.1       44   Rh(acac)3   25   Co(acac)2   150   Digly   10   CN-   500   1000   100   180   379.1       45   Rh(acac)3   25   Ce(acac)3   150   DMFA   10   Br-   500   1000   120   120   271.7       46   Rh(acac)3   25   Ce(acac)3   150   DMAA   10   I-   500   1500   100   120   382.4       47   Rh(acac)3   25   Ce(acac)3   1500   THF   10   CN-   5000   1500   100   120   391.5       48   Rh(acac)3   25   Ce(acac)3   150   Digly   10   Cl-   5000   1000   100   120   562.3       49   Ir(acac)3   25   Mn(acac)2   1500   DMFA   10   CN-   5000   1000   100   180   218.7       50   Ir(acac)3   25   Mn(acac)2   150   DMAA   10   Cl-   5000   1000   120   180   207.6       51   Ir(acac)3   25   Mn(acac)2   1500   THF   10   Br-   5000   1500   120   180   271.0       52   Ir(acac)3   25   Mn(acac)2   1500   Digly   10   I-   5000   1000   120   120   198.2       53   Ir(acac)3   25   Fe(acac)3   150   DMFA   10   Cl-   500   1500   120   180   151.2       54   Ir(acac)3   25   Fe(acac)3   1500   DMAA   10   Br-   500   1000   100   120   228.8       55   Ir(acac)3   25   Fe(acac)3   1500   THF   10   I-   500   1500   120   120   232.8       56   Ir(acac)3   25   Fe(acac)3   1500   Digly   10   CN-   500   1500   100   180   578.9       57   Ir(acac)3   25   Co(acac)2   1500   DMFA   10   Br-   500   1000   120   180   185.1       58   Ir(acac)3   25   Co(acac)2   150   DMAA   10   I-   5000   1500   120   120   424.9       59   Ir(acac)3   25   Co(acac)2   150   THF   10   CN-   5000   1500   100   180   471.1       60   Ir(acac)3   25   Co(acac)2   150   Digly   10   Cl-   500   1000   100   180   445.7       61   Ir(acac)3   25   Ce(acac)3   150   DMFA   10   I-   500   1000   120   120   260.9       62   Ir(acac)3   25   Ce(acac)3   150   DMAA   10   CN-   500   1500   100   120   284.9       63   Ir(acac)3   25   Ce(acac)3   1500   THF   10   Cl-   5000   1500   100   120   241.0       64   Ir(acac)3   25   Ce(acac)3   150   Digly   10   Br-   5000   1000   100   120   322.6       65   Ru(acac)3   25   Mn(acac)2   150   DMFA   10   Cl-   500   1500   120   120   128.3       66   Ru(acac)3   25   Mn(acac)2   1500   DMAA   10   Br-   500   1500   100   120   94.4       67   Ru(acac)3   25   Mn(acac)2   150   THF   10   I-   500   1000   100   120   193.6       68   Ru(acac)3   25   Mn(acac)2   150   Digly   10   CN-   500   1500   100   180   352.2       69   Ru(acac)3   25   Fe(acac)3   1500   DMFA   10   Br-   5000   1000   100   120   102.1       70   Ru(acac)3   25   Fe(acac)3   150   DMAA   10   I-   5000   1500   120   180   176.6       71   Ru(acac)3   25   Fe(acac)3   150   THF   10   CN-   5000   1000   100   180   239.6       72   Ru(acac)3   25   Fe(acac)3   150   Digly   10   Cl-   5000   1000   120   120   151.4       73   Ru(acac)3   25   Co(acac)2   150   DMFA   10   I-   5000   1500   100   120   1112.8       74   Ru(acac)3   25   Co(acac)2   1500   DMAA   10   CN-   500   1000   100   180   218.3       75   Ru(acac)3   25   Co(acac)2   1500   THF   10   Cl-   500   1000   120   120   211.5       76   Ru(acac)3   25   Co(acac)2   1500   Digly   10   Br-   5000   1500   120   120   173.6       77   Ru(acac)3   25   Ce(acac)3   1500   DMFA   10   CN-   5000   1500   100   180   125.6       78   Ru(acac)3   25   Ce(acac)3   1500   DMAA   10   Cl-   5000   1000   120   180   295.6       79   Ru(acac)3   25   Ce(acac)3   150   THF   10   Br-   500   1000   120   180   178.9       80   Ru(acac)3   25   Ce(acac)3   1500   Digly   10   I-   500   1500   120   180   520.1       81   Pt(acac)2   25   Mn(acac)2   150   DMFA   10   Br-   500   1500   120   120   97.4       82   Pt(acac)2   25   Mn(acac)2   1500   DMAA   10   I-   500   1500   100   120   220.4       83   Pt(acac)2   25   Mn(acac)2   150   THF   10   CN-   500   1000   100   120   325.5       84   Pt(acac)2   25   Mn(acac)2   150   Digly   10   Cl-   500   1500   100   180   428.7       85   Pt(acac)2   25   Fe(acac)3   1500   DMFA   10   I-   5000   1000   100   120   180.1       86   Pt(acac)2   25   Fe(acac)3   150   DMAA   10   CN-   5000   1500   120   180   310.5       87   Pt(acac)2   25   Fe(acac)3   150   THF   10   Cl-   5000   1000   100   180   300.3       88   Pt(acac)2   25   Fe(acac)3   150   Digly   10   Br-   5000   1000   120   120   251.4       89   Pt(acac)2   25   Co(acac)2   150   DMFA   10   CN-   5000   1500   100   120   244.9       90   Pt(acac)2   25   Co(acac)2   1500   DMAA   10   Cl-   500   1000   100   180   235.3       91   Pt(acac)2   25   Co(acac)2   1500   THF   10   Br-   500   1000   120   120   256.3       92   Pt(acac)2   25   Co(acac)2   1500   Digly   10   I-   5000   1500   120   120   335.7       93   Pt(acac)2   25   Ce(acac)3   1500   DMFA   10   Cl-   5000   1500   100   180   262.3       94   Pt(acac)2   25   Ce(acac)3   1500   DMAA   10   Br-   5000   1000   120   180   187.7       95   Pt(acac)2   25   Ce(acac)3   150   THF   10   I-   500   1000   120   180   517.8       96   Pt(acac)2   25   Ce(acac)3   1500   Digly   10   CN-   500   1500   120   180   505.8       97   Rh(acac)3   25   Mn(acac)2   150   DMFA   10   I-   500   1500   120   120   153.0       98   Rh(acac)3   25   Mn(acac)2   1500   DMAA   10   CN-   500   1500   100   120   82.3       99   Rh(acac)3   25   Mn(acac)2   150   THF   10   Cl-   500   1000   100   120   194.1       100   Rh(acac)3   25   Mn(acac)2   150   Digly   10   Br-   500   1500   100   180   249.2       101   Rh(acac)3   25   Fe(acac)3   1500   DMFA   10   CN-   5000   1000   100   120   201.8       102   Rh(acac)3   25   Fe(acac)3   150   DMAA   10   Cl-   5000   1500   120   180   373.9       103   Rh(acac)3   25   Fe(acac)3   150   THF   10   Br-   5000   1000   100   180   337.1       104   Rh(acac)3   25   Fe(acac)3   150   Digly   10   I-   5000   1000   120   120   330.8       105   Rh(acac)3   25   Co(acac)2   150   DMFA   10   Cl-   5000   1500   100   120   95.7       106   Rh(acac)3   25   Co(acac)2   1500   DMAA   10   Br-   500   1000   100   180   480.9       107   Rh(acac)3   25   Co(acac)2   1500   THF   10   I-   500   1000   120   120   389.6       108   Rh(acac)3   25   Co(acac)2   1500   Digly   10   CN-   5000   1500   120   120   303.0       109   Rh(acac)3   25   Ce(acac)3   1500   DMFA   10   Br-   5000   1500   100   180   180.9       110   Rh(acac)3   25   Ce(acac)3   1500   DMAA   10   I-   5000   1000   120   180   255.3       111   Rh(acac)3   25   Ce(acac)3   150   THF   10   CN-   500   1000   120   180   413.9       112   Rh(acac)3   25   Ce(acac)3   1500   Digly   10   Cl-   500   1500   120   180   497.7       113   Ir(acac)3   25   Mn(acac)2   150   DMFA   10   CN-   500   1500   120   120   171.3       114   Ir(acac)3   25   Mn(acac)2   1500   DMAA   10   Cl-   500   1500   100   120   130.3       115   Ir(acac)3   25   Mn(acac)2   150   THF   10   Br-   500   1000   100   120   374.4       116   Ir(acac)3   25   Mn(acac)2   150   Digly   10   I-   500   1500   100   180   339.4       117   Ir(acac)3   25   Fe(acac)3   1500   DMFA   10   Cl-   5000   1000   100   120   132.4       118   Ir(acac)3   25   Fe(acac)3   150   DMAA   10   Br-   5000   1500   120   180   366.0       119   Ir(acac)3   25   Fe(acac)3   150   THF   10   I-   5000   1000   100   180   561.2       120   Ir(acac)3   25   Fe(acac)3   150   Digly   10   CN-   5000   1000   120   120   192.6       121   Ir(acac)3   25   Co(acac)2   150   DMFA   10   Br-   5000   1500   100   120   260.0       122   Ir(acac)3   25   Co(acac)2   1500   DMAA   10   I-   500   1000   100   180   296.0       123   Ir(acac)3   25   Co(acac)2   1500   THF   10   CN-   500   1000   120   120   162.8       124   Ir(acac)3   25   Co(acac)2   1500   Digly   10   Cl-   5000   1500   120   120   356.6       125   Ir(acac)3   25   Ce(acac)3   1500   DMFA   10   I-   5000   1500   100   180   545.8       126   Ir(acac)3   25   Ce(acac)3   1500   DMAA   10   CN-   5000   1000   120   180   514.9       127   Ir(acac)3   25   Ce(acac)3   150   THF   10   Cl-   500   1000   120   180   264.0       128   Ir(acac)3   25   Ce(acac)3   1500   Digly   10   Br-   500   1500   120   180   564.7                  
 
         [0080]    Catalyst mixtures are made up in phenol solvent using the concentrations of each component as given in the rows of the TABLE 5. The total volume of each catalyst mixture is 1.0 ml. From each mixture, a 25 microliter aliquot is dispensed into a 2 ml reaction vial, forming a film on the bottom. The vials are grouped on an array plate by process conditions (as specified in the Pressure, Temperature, and Reaction Time columns in TABLE 5) and each group is loaded into a high pressure autoclave and subjected to the reaction conditions specified. Thus one group, exemplified by rows number 6, 16, 22, 32, 38, 48, 54, 64, 67, 69, 83, 85, 99, 101, 115, 117, are all subjected to 1000 psi pressure at 100 C for 120 min. At the end of the reaction time, the system is cooled and depressurized and the contents of each vial are analyzed for diphenyl carbonate product using conventional gas chromatographic methods. The turnover number (TON) for each reaction is calculated as (mols of diphenylcarbonate/mols of primary catalyst). The results are given in the TON column of TABLE 4.  
         [0081]    [0081]FIG. 7 is a histogram of the Turnover number (TON) results. FIG. 7 shows that there are two unusually high values that are associated with runs  9  and  73 . Comparison of these two runs shows that they contain the combination of ingredients Ru(acac)3, Co(acac)2, DMFA, and I − . Further reiterations show that DMFA is not part of the combination and that the advantageous three way combination is Ru(acac)3, Co(acac)2, and I − .  
         [0082]    It will be understood that each of the elements described above, or two or more together, may also find utility in applications differing from the types described herein. While the invention has been illustrated and described as experimental designs for combinatorial chemistry, it is not intended to be limited to the details shown, since various modifications and substitutions can be made without departing in any way from the spirit of the present invention. For example, various detection techniques may be coordinated with the reactions to provide data at accelerated rates. As such, further modifications and equivalents of the invention herein disclosed may occur to persons skilled in the art using no more than routine experimentation, and all such modifications and equivalents are believed to be within the spirit and scope of the invention as defined by the following claims.