Abstract:
In a method, factors are selected for an experiment and interactions among levels of the factors are estimated. A probability value of positive interactions is then assigned for each of the estimated interactions. A combinatorial high throughput screening (CHTS) method is effected on an experimental space representing the levels and the probabilities for each interaction are adjusted according to results of the CHTS method. A system for conducting an experiment includes a reactor for effecting a CHTS method on an experimental space to produce results and a programmed controller that stores an assigned probability value for estimated positive interactions between levels of factors of the experimental space and adjusts the probabilities for each interaction according to results of the CHTS method.

Description:
FEDERAL RESEARCH STATEMENT  
       [0001] This invention was made with government support under Contract No. 70NAN89H3038 awarded by NIST. The government may have certain rights to the invention. 
     
    
     
       BACKGROUND OF INVENTION  
         [0002]    The present invention relates to a method and system to conduct a combinatorial high throughput screening (CHTS) experiment.  
           [0003]    Combinatorial organic synthesis (COS) is a high throughput screening (HTS) method 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. Libraries are physical, trackable collections of samples resulting from a definable set of the COS process or reaction steps. The libraries comprise compounds that can be screened for various activities.  
           [0004]    Combinatorial high throughput screening (CHTS) is an HTS method that incorporates characteristics of COS. The CHTS methodology is marked by the search for high order synergies and effects of complex combinations of experimental variables through the use of large arrays in which multiple factors can be varied through multiple levels. Factors of an experiment can be varied within an array (typically formulation variables) and between an array and a condition (both formulation and processing variables). Results from the CHTS experiment can be used to compare properties of the products in order to discover “leads” formulations and/or processing conditions that indicate commercial potential.  
           [0005]    The steps of a CHTS methodology can be broken down into generic operations including selecting chemicals to be used in an experiment, introducing the chemicals into a formulation system (typically by weighing and dissolving to form stock solutions), combining aliquots of the solutions into formulations or mixtures in a geometrical array (typically by the use of a pipetting robot), processing the array of chemical combinations into products and evaluating the products to produce results.  
           [0006]    Typically, CHTS methodology 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.  
           [0007]    The study of catalyzed chemical reactions by CHTS involves the investigation of a complex experimental space characterized by multiple qualitative and quantitative factor levels. Typically, the interactions of a catalyzed chemical reaction such as a carbonylation reaction can involve interactions of an order of 6 or 9 or greater. An investigator must carefully set up a CHTS experiment in order to effectively examine such a complex space. Reactant identities and variables, process identities and variables and levels of combinations of factors, must be chosen to define a space that will provide meaningful results.  
           [0008]    In most instances, an investigator conducts the CHTS experiment for the benefit of a client, who for example, may be a customer from outside the investigator”s company or co-worker from another department within the company. In any case, the client attempts to clearly articulate its expectations for the experiment to the investigator while at the same time, the investigator articulates capabilities and limitations of the CHTS methodology. It is difficult but critical to translate the articulations of the client and investigator into an experiment definition for the CHTS method. The complexity of a catalyzed chemical experimental space makes translation of needs and capabilities into an experiment definition even more difficult. There is a need for a method and system to conduct an experiment according to specific needs of a client and capabilities of the CHTS method.  
         SUMMARY OF INVENTION  
         [0009]    The invention meets this need by a providing a method and system to develop an experiment definition for a CHTS experiment. In the method, factors are selected for the experiment and interactions among levels of the factors are estimated. A probability value of positive interactions is then assigned for each of the estimated interactions. A CHTS method is effected on an experimental space representing the levels and the probabilities for each interaction are adjusted according to results of the CHTS method.  
           [0010]    The invention also relates to a system for conducting an experiment. The system comprises a reactor for effecting a CHTS method on an experimental space to produce results and a programmed controller that stores an assigned probability value for estimated positive interactions between levels of factors of the experimental space and adjusts the probabilities for each interaction according to results of the CHTS method. 
       
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0011]    [0011]FIG. 1 is a schematic representation of a system and method for conducting a CHTS experiment. 
     
    
     DETAILED DESCRIPTION  
       [0012]    In one embodiment, the invention provides a method and system to permit a client and an investigator to confer to develop an experiment definition for a CHTS experiment. The method and system can utilize a knowledge matrix as a visual and organizational aid to serve as an adjustable definitional model. The matrix model can include the factors of the experimental space to be investigated. Determination of these factors can require selection of reactant identities and levels and selection of process identities and levels and selection of the degrees of combination. For example, the experimental factors of the catalyst of a carbonylation reaction can be two different metals and a solvent. Levels of one metal may be Fe, Cu, Ni, Pb, and Re, of another metal may be V, W, Ce, La and Sn and of the solvent may be dimethylformamide (DMFA), dimethylacetamide (DMAA), tetrahydrofuran (THF), diglyme (DiGly) or diethylacetamide (DEAA). The model can be set up originally to represent an estimation of factor level interactions. The estimation can take the form of a probability. The experiment can be conducted and a value of the matrix can be adjusted between each iteration of the experiment to represent a probability change dictated by the experiment results.  
         [0013]    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.  
         [0014]    [0014]FIG. 1 is a schematic representation of a system  10  and method for conducting a CHTS experiment. FIG. 1 shows system  10  including dispensing assembly  12 , reactor  14 , detector  16  and controller  18 . Further shown, is X-Y-Z robotic positioning stage  20 , which supports array plate  22  with wells  24 . The dispensing assembly  12  includes a battery of pipettes  26  that are controlled by controller  18 . X-Y-Z robotic positioning stage  20  is controlled by controller  18  to position wells  24  of the array plate  22  beneath displacement pipettes  26  for delivery of test solutions from reservoirs  28 .  
         [0015]    Controller  18  can include a data base repository for storing interaction identifications and probability values input by a client or investigator. The controller  18  also controls aspiration of precursor solution into the battery of pipettes  26  and sequential positioning of the wells  24  of array plate  22  so that a prescribed stoichiometry and/or composition of reactant and/or catalyst can be delivered to the wells  24 . By coordinating activation of the pipettes  26  and movement of plate  22  on the robotic X-Y-Z stage  20 , a library of materials can be generated in a two-dimensional array for use in the CHTS method. Also, the controller  18  can be used to control sequence of charging of sample to reactor  14  and to control operation of the reactor  14  and the detector  16 . Controller  18  can be a computer, processor, microprocessor or the like.  
         [0016]    An experimental space is defined according to a design that is embodied as a program resident in controller  18 . The design uses input from a client and/or an investigator to define interactions and to assign weights that represent probabilities that the interactions will be positive. Controller  18  translates the defined space into a loading specification for array plate  32 . Then controller  18  controls the operation of pipettes  26  and stage  20  according to the specification to deliver reactant and/or catalyst to the wells  34  of plate  22 .  
         [0017]    Additionally, the controller  18  controls the sequence of charging array plate  22  into the reactor  14 , which is synchronized with operation of detector  16 . Detector  16  detects products of reaction in the wells  24  of array plate  22  after reaction in reactor  14 . Detector  16  can utilize chromatography, infra red spectroscopy, mass spectroscopy, laser mass spectroscopy, microspectroscopy, NMR or the like to determine the constituency of each reaction product. The controller  18  uses data on the sample charged by the pipettes  26  and on the constituency of reaction product for each sample from detector  16  to correlate a detected product with at least one varying parameter of reaction.  
         [0018]    As an example, if the method and system of FIG. 1 is applied to study a carbonylation catalyst and/or to determine optimum carbonylation reaction conditions, the detector  16  analyzes the contents of the well for carbonylated product. In this case, the detector  16  can use Raman spectroscopy. The Raman peak is integrated using the analyzer electronics and the resulting data can be stored in the controller  18 . Other analytical methods may be used—for example, Infrared spectrometry, mass spectrometry, headspace gas-liquid chromatography and fluorescence detection.  
         [0019]    A method of screening complex catalyzed chemical reactions can be conducted in the FIG. 1 system  10 . According to the method, a client and an investigator confer to discuss expectations of the experiment to be conducted in the system  10  and the capability of the system to achieve the expectations. The conference can produce a knowledge matrix comprising the experimental space interactions and an assigned weighting to each interaction that represent a first estimate of a probability that the interaction will be a statistically positive interaction, i.e., that the interaction will be a lead. For example, the probabilities can be high, medium and low probabilities. represented respectively by numerical weighting values. “High, medium and low” mean probabilities that are higher, a medium or lower with respect to one another. When three weighting value probabilities are assigned, the values can be in respective ranges of about 0.6 to about 0.99 for high, about 0.2 to about 0.59 for medium and about 0.01 to about 0.19 for low. Desirably, the respective ranges can be about 0.7 to about 0.9, about 0.2 to about 0.5 and about 0.05 to about 0.15. The knowledge matrix is an adjustable definitional model that represents the estimated interactions and assigned or adjusted probabilities. The model can be a visual organizational aid or the model can be a virtual construct resident in a computer database.  
         [0020]    Formulations and conditions that represent the interactions are then organized according to an experimental design such as a Latin square design or a full factorial design. Formulations are prepared according to the design. For example, a Latin square design can specify a combination of reactants, catalysts and conditions as a multiphase reactant system. In this procedure, a formulation is prepared that represents a first reactant system that is at least partially embodied in a liquid. Each formulation is loaded as a thin film to a respective well  24  of the array plate  22  and the plate  22  is charged into reactor  14 . During the subsequent reaction, the liquid of the first reactant system embodied is contacted with a second reactant system at least partially embodied in a gas. The liquid forms a film having a thickness sufficient to allow the reaction rate of the reaction to be essentially independent of the mass transfer rate of the second reactant system into the liquid.  
         [0021]    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.  
         [0022]    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.  
         [0023]    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.  
         [0024]    Other catalytic constituents are necessary in accordance with Chaudhari et al.  
         [0025]    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.  
         [0026]    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.  
         [0027]    Another catalyst constituent is a polyaniline in partially oxidized and partially reduced form.  
         [0028]    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.  
         [0029]    Other reagents in the carbonylation process are oxygen and carbon monoxide, which react with the phenol to form the desired diaryl carbonate.  
         [0030]    The following Example is illustrative and should not be construed as a limitation on the scope of the claims unless a limitation is specifically recited.  
       EXAMPLE  
       [0031]    This example illustrates an identification of an active and selective catalyst for the production of aromatic carbonates. The procedure includes a combination of a experimental team weighting procedure and a CHTS method to identify a best catalyst from a complex chemical space, where the chemical space is defined as an assemblage of possible experimental conditions defined by a set of variable parameters such as formulation ingredient identity or amount or process parameter such as reaction time, temperature, or pressure.  
         [0032]    The chemical space consists of the following TABLE 1 chemical factor levels and TABLE 2 processing factor levels:  
                                         TABLE 1                                   Formulation Type Parameter   Formulation Amount           Variation   Parameter Variation                                    Precious metal catalyst   Held Constant   Held Constant       Primary Transition   Fe, Cu, Ni, Pb, Re (as their   5,10,20,40 (as molar ratios       Metal Cocatalyst (TM)   acetylacetonates)   to precious metal catalyst)       Secondary Metal   V, W, Ce, La, Sn (as their   5,10,20,40 (as molar ratios       Cocatalyst (LM)   acetylacetonates)   to precious metal catalyst)       Cosolvent (CS)   Dimethylformamide (DMFA),   50,100,200,400 (as molar           Dimethylacetamide (DMAA),   ratios to precious metal           Diethyl acetamide (DEAA),   catalyst)           Tetrahydrofuran (THF),           Diglyme (DiGly)       Hydroxyaromatic   Held constant   Sufficient added to achieve       compound       constant sample volume                  
 
         [0033]    Process parameters are shown in TABLE 2:  
                           TABLE 2                                   Process Parameter   Parameter Variation                           Temperature   Constant at 100° C.           Pressure   Constant at 1500 psig                      
 
         [0034]    Pre-test estimates of interactions among factor levels are postulated at a meeting between a customer and investigators. The estimates are assigned probability values, which are expressed in the following knowledge matrix TABLE 3. The probabilities are constrained to three possible values, 0.8, 0.3 and 0.1, which express high, medium, and low probabilities. Probabilities of 0.0 and 1.0 are excluded from off-diagonal cells since these probabilities imply complete knowledge. The matrix is symmetrical around the main diagonal, since the probability of A interacting with B is the same as the probability of B interacting with A.  
                                                                         TABLE 3                                   TM   TM   LM   LM   CS   CS           Type   Amount   Type   Amount   Type   Amount                                    TM Type   1   0.8   0.3   0.3   0.3   0.3       TM Amount   0.8   1   0.3   0.1   0.3   0.1       LM Type   0.3   0.3   1   0.8   0.3   0.1       LM Amount   0.3   0.1   0.8   1   0.1   0.1       CS Type   0.3   0.3   0.3   0.1   1   0.8       CS Amount   0.3   0.1   0.1   0.1   0.8   1                  
 
         [0035]    The matrix information is loaded into a computer database. The computer defines a full factorial experiment according to two factor interactions between levels as shown in TABLE 4. The computer also controls a dispensing assembly and loading robot to load experimental array trays and a reactor to conduct a CHTS experiment. In the experiment, catalyzed mixtures are made up in phenol solvent using the concentrations of each component as given in the rows of TABLE 4. The total volume of each catalyzed 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 in array plates by process conditions (as specified in the TABLE 2 Pressure and Temperature columns) and each array plate is loaded into a high pressure autoclave and subjected to the reaction conditions specified. At the end of the reaction time, the reactor is cooled and depressurized and the contents of each vial are analyzed for diphenyl carbonate product using a gas chromatographic method. Performance is expressed numerically as a catalyst turnover number or TON. TON is defined as the number of moles of aromatic carbonate produced per mole of Palladium catalyst charged. This is shown in column TON of TABLE 4.  
                                                                     TABLE 4                       TMType   LMType   CSType   TMAmt   LMAmt   CSAmt   TON                                Ni   V   DiGly   10   5   200   1084       Re   Ce   DEAA   10   10   200   1394       Ni   La   DMFA   10   40   400   1221       Ni   Sn   DEAA   40   5   50   1697       Fe   La   DMAA   10   20   200   949       Pb   Sn   DEAA   40   10   50   2317       Fe   Ce   THF   40   20   100   792       Cu   V   THF   10   10   200   1054       Cu   Sn   DEAA   20   10   100   1058       Cu   La   DMAA   10   40   50   1081       Re   Ce   DMFA   5   40   100   1058       Re   V   THF   5   5   400   1074       Cu   W   DMAA   5   40   400   1125       Cu   Ce   THF   5   10   200   1111       Ni   La   DMFA   20   5   50   1358       Fe   Ce   DMFA   10   20   50   955       Pb   V   DEAA   10   5   100   1040       Cu   V   DMFA   20   40   50   1092       Re   V   DMAA   10   10   100   1080       Re   V   DEAA   10   10   50   1049       Pb   V   DEAA   20   10   400   1043       Pb   Ce   THF   10   10   100   1248       Fe   W   DMAA   40   40   50   914       Ni   La   DMAA   5   20   50   1069       Fe   La   DEAA   5   20   400   1069       Cu   Sn   DiGly   20   40   200   1114       Cu   W   DMFA   40   10   200   1105       Pb   Sn   DMAA   10   40   50   1511       Fe   V   THF   40   10   400   1067       Re   W   DiGly   5   10   400   1034       Cu   W   THF   20   10   400   1041       Pb   La   THF   10   5   50   1371       Pb   V   DMFA   20   10   100   1056       Ni   W   THF   20   5   200   1136       Pb   Sn   DiGly   10   10   200   1499       Re   W   DMFA   40   5   50   1535       Ni   Ce   DEAA   10   20   200   1164       Re   Ce   DEAA   40   20   50   1959       Re   La   DiGly   5   40   200   1077       Pb   La   DEAA   5   40   50   1108       Re   Sn   DiGly   10   40   400   1660       Ni   V   DMFA   5   5   100   1083       Re   La   THF   40   5   200   2396       Re   Sn   DiGly   20   10   100   2291       Fe   Ce   DMFA   5   40   200   1029       Re   W   DMAA   40   5   400   1538       Re   Ce   DiGly   10   20   100   1417       Ni   Ce   DEAA   20   10   400   1251       Re   W   DiGly   20   5   100   1376       Pb   W   THF   5   20   50   1058       Ni   Ce   THF   10   5   100   1236       Cu   V   THF   20   40   100   1078       Fe   Sn   DEAA   10   10   400   837       Fe   La   DMAA   20   20   50   805       Re   V   THF   40   20   50   1076       Pb   W   DiGly   10   20   100   1194       Fe   W   DEAA   10   40   200   1017       Fe   Sn   DiGly   10   5   50   857       Ni   V   DiGly   20   20   100   1065       Ni   Sn   DMAA   40   40   400   1645       Re   Sn   THF   40   10   100   2878       Ni   W   DiGly   40   40   100   1173       Pb   Sn   DEAA   5   5   400   1080       Cu   Ce   THF   40   5   50   1038       Ni   W   DiGly   20   10   200   1215       Ni   Ce   DEAA   20   5   200   1275       Re   V   DiGly   20   5   50   1085       Cu   V   DiGly   10   20   400   1046       Cu   Sn   DMFA   10   5   400   1093       Ni   Ce   DiGly   5   5   50   1069       Pb   V   DiGly   5   40   400   1039       Fe   W   DEAA   40   5   400   936       Fe   W   THF   10   10   100   1043       Re   Ce   DMAA   20   5   100   1705       Ni   W   DMFA   20   20   100   1187       Cu   La   DiGly   5   10   50   1098       Pb   Ce   DMFA   20   40   50   1458       Pb   V   DMAA   5   10   200   1113       Pb   V   DMAA   40   20   50   1072       Ni   Sn   DMAA   5   5   100   1089       Ni   V   THF   20   40   50   1092       Re   La   DMFA   10   20   200   1531       Pb   Ce   DiGly   5   10   50   1067       Cu   Sn   DMAA   5   20   200   1034       Fe   Ce   THF   5   40   400   1105       Pb   V   DMFA   10   40   200   1110       Re   Sn   DMFA   5   10   50   1078       Pb   V   THF   5   20   200   1136       Ni   La   DEAA   10   5   100   1256       Fe   Sn   THF   5   5   200   1056       Pb   La   DMAA   5   40   100   1069       Cu   Ce   DiGly   20   5   400   1110       Ni   W   DEAA   5   40   400   1082       Pb   La   DiGly   5   5   100   1068       Pb   Sn   THF   20   40   400   1851       Cu   La   DMFA   10   10   100   1078       Re   Sn   DiGly   5   20   50   1118       Re   W   THF   10   40   50   1252       Pb   W   DEAA   5   10   200   1040       Cu   V   DEAA   10   5   50   1088       Cu   La   DMFA   40   20   50   1086       Fe   Sn   DMFA   5   40   100   1073       Pb   La   DMFA   40   20   400   1926       Cu   W   THF   5   5   100   1085       Fe   V   DMFA   40   40   400   1106       Ni   Ce   THF   10   10   50   1201       Pb   Ce   DMAA   20   40   200   1460       Fe   Sn   DEAA   20   5   50   711       Ni   Sn   THF   10   40   200   1272       Cu   Ce   DiGly   10   40   50   1059       Pb   Ce   DMAA   40   5   50   1718       Fe   V   DiGly   5   10   100   1060       Pb   W   DMAA   20   10   50   1292       Re   Ce   DMAA   5   40   50   1047       Fe   La   DMAA   20   10   200   792       Re   V   DMFA   5   40   50   1057       Fe   Sn   THF   5   20   400   1045       Ni   V   DiGly   40   10   50   1074       Ni   V   DMAA   20   5   400   1070       Fe   La   DiGly   20   40   100   758       Cu   La   DEAA   5   5   200   1047       Re   La   DiGly   20   20   400   2009       Pb   Ce   DEAA   40   5   100   1695       Re   Sn   DMAA   20   20   400   2255       Pb   La   THF   20   10   200   1701       Pb   W   DMAA   40   20   200   1366       Cu   Sn   THF   5   40   50   1073       Re   Sn   DEAA   5   40   200   1090       Pb   La   DEAA   20   20   100   1677       Pb   W   DiGly   40   5   50   1421       Fe   La   THF   10   40   50   945       Fe   Sn   DiGly   40   40   400   453       Pb   Ce   DEAA   10   40   400   1303       Cu   Sn   DEAA   40   20   400   1102       Ni   La   DEAA   10   5   100   1256       Fe   Sn   THF   5   5   200   1056       Pb   La   DMAA   5   40   100   1069       Cu   Ce   DiGly   20   5   400   1110       Ni   W   DEAA   5   40   400   1082       Pb   La   DiGly   5   5   100   1068       Pb   Sn   THF   20   40   400   1851       Cu   La   DMFA   10   10   100   1078       Re   Sn   DiGly   5   20   50   1118       Re   W   THF   10   40   50   1252       Pb   W   DEAA   5   10   200   1040       Cu   V   DEAA   10   5   50   1088       Cu   La   DMFA   40   20   50   1086       Fe   Sn   DMFA   5   40   100   1073       Pb   La   DMFA   40   20   400   1926       Cu   W   THF   5   5   100   1085       Fe   V   DMFA   40   40   400   1106       Ni   Ce   THF   10   10   50   1201       Pb   Ce   DMAA   20   40   200   1460       Fe   Sn   DEAA   20   5   50   711       Ni   Sn   THF   10   40   200   1272       Cu   Ce   DiGly   10   40   50   1059       Pb   Ce   DMAA   40   5   50   1718       Fe   V   DiGly   5   10   100   1060       Pb   W   DMAA   20   10   50   1292       Re   Ce   DMAA   5   40   50   1047       Fe   La   DMAA   20   10   200   792       Re   V   DMFA   5   40   50   1057       Fe   Sn   THF   5   20   400   1045       Ni   V   DiGly   40   10   50   1074       Ni   V   DMAA   20   5   400   1070       Fe   La   DiGly   20   40   100   758       Cu   La   DEAA   5   5   200   1047       Re   La   DiGly   20   20   400   2009       Pb   Ce   DEAA   40   5   100   1695       Re   Sn   DMAA   20   20   400   2255       Pb   La   THF   20   10   200   1701       Pb   W   DMAA   40   20   200   1366       Cu   Sn   THF   5   40   50   1073       Re   Sn   DEAA   5   40   200   1090       Pb   La   DEAA   20   20   100   1677       Pb   W   DiGly   40   5   50   1421       Fe   La   THF   10   40   50   945       Fe   Sn   DiGly   40   40   400   453       Pb   Ce   DEAA   10   40   400   1303       Cu   Sn   DEAA   40   20   400   1102       Fe   W   DMFA   20   5   400   963       Cu   Sn   DiGly   5   5   100   1089       Cu   La   THF   40   40   50   1059       Fe   La   DiGly   10   5   400   902       Re   Sn   DMFA   40   40   400   2853       Re   Sn   DiGly   40   40   50   2870       Pb   W   THF   40   40   100   1352       Fe   V   DMAA   5   5   50   1085       Cu   V   DEAA   5   40   100   1060       Re   Sn   DiGly   40   5   400   2917       Pb   Sn   DiGly   40   20   100   2301       Fe   Ce   THF   20   10   50   868       Fe   Ce   DEAA   5   10   100   1071       Re   Ce   DiGly   40   40   400   1987       Re   W   DMFA   20   40   200   1403       Fe   V   DMAA   10   40   100   1102       Cu   W   THF   40   20   200   1059       Re   La   DMFA   20   10   400   1991       Ni   W   DEAA   40   10   100   1225       Ni   W   DiGly   40   20   400   1219       Re   La   THF   20   40   100   1989       Re   La   DEAA   40   10   400   2390       Ni   Sn   DMFA   5   40   200   1096       Re   V   DiGly   40   20   200   1075       Cu   V   DMFA   5   10   400   1112       Ni   Sn   DMAA   20   10   200   1470       Ni   Ce   DMFA   40   40   50   1411       Re   La   DEAA   5   5   50   1102       Fe   W   DMAA   5   5   100   1031       Ni   La   THF   40   5   400   1545       Fe   Sn   DMFA   40   10   200   432       Pb   La   DMAA   10   10   400   1324       Re   Sn   DMAA   10   5   200   1676       Ni   La   DEAA   20   40   200   1341       Fe   Ce   DiGly   10   10   400   995       Re   W   DMAA   5   20   100   1081       Re   Ce   DMFA   10   5   400   1379       Ni   W   DMFA   10   10   400   1075       Cu   W   DEAA   20   40   50   1037       Ni   La   DMAA   40   10   100   1522       Pb   Ce   DMFA   5   20   400   1061       Ni   W   DMAA   10   40   200   1126       Ni   V   DEAA   5   20   400   1107       Re   Ce   DMAA   40   10   200   1919       Ni   Sn   DMFA   20   20   400   1490                  
 
         [0036]    The results in TABLE 4 are then subjected to an Analysis of Variance (ANOVA) analysis that includes the main effects and all the two-way interactions of the six factors (TM Type, TM Amount, LM type, LM amount, CS Amount, and CS Type). Results of the ANOVA are shown in TABLE 5.  
                                                                             TABLE 5                       Source   DF   Seq SS   Adj SS   Adj MS   F   P                                TMType   4   12344279   5926470   1481617   119.24   0.000           LMType   4   3400185   1381835   345459   27.8   0.000       TMType*LMType   16   5223338   2724490   170281   13.7   0.000   **       CSType   4   171937   76127   19032   1.53   0.231       TMType*CSType   16   788408   436537   27284   2.2   0.049       TMAmount   3   3283677   1543785   514625   41.42   0.000       TMType*TMAmount   12   6432183   2597860   216488   17.42   0.000   **       LMAmount   3   77667   6773   2258   018   0.908       TMType*LMAmount   12   331369   195394   16283   1.31   0.287       CSAmount   3   98658   3220   1073   0.03   0.967       TMType*CSAmount   12   468170   284193   23683   1.91   0.098       LMType*CSType   16   216050   364113   22757   1.83   0.100       LMType*TMAmount   12   1325612   966688   80557   6.48   0.000   **       LMType*LMAmount   12   193246   375448   31287   2.52   0.033       LMType*CSAmount   12   144330   211215   17601   1.42   0.237       CSType*TMAmount   12   143455   162020   13502   1.09   0.420       CSType*LMAmount   12   531604   242598   20217   1.63   0.162       CSType*CSAmount   12   144681   174047   14504   1.17   0.367       TMAmount*LMAmount   9   136750   151726   16858   1.36   0.271       TMAmount*CSAmount   9   140146   109713   12190   0.98   0.484       LMAmount*CSAmount   9   387333   387333   43037   3.46   0.010   *       Error   20   248520   248520   12426       Total   224   36231597                  
 
         [0037]    The client and the investigator observe the rows of TABLE 5 that contain interactions. In the TABLE 5, only three of the interactions, marked **, show very strong evidence of statistical significance (P&lt;0.001), and one, marked *, shows moderately strong evidence (P&lt;0.02). Two show weak evidence (P˜0.05). The rest show no evidence of interaction. The client and the investigator then adjust the weighted probabilities in the computer matrix according to the observed statistically significant results. The probabilities are increased for all the strong interactions and decreased for weak interactions. The following algorithm is used as illustrated in TABLE 6: (1) Very strong interaction: increase the matrix amount by half a distance to 1.0. (2) Moderately strong interaction: increase by 0.25 the distance to 1.0. (3) Weak evidence: no change. (4) No evidence: decrease by half the distance to zero.  
                                                                         TABLE 6                                       TM       LM       CS           TM type   Amount   LM type   Amount   CS Type   Amount                                    TM type   1   0.8 + .1   0.3 + .35   0.3 − .15   0.3   0.3 − .15       TM Amount   0.8 + .1   1   0.3 + .35   0.1 − .05   0.3 − .15   0.1 − .05       LM type   0.3 + .35   0.3 + .35   1   0.8   0.3 − .15   0.1 − .05       LM Amount   0.3 − .15   0.1 − .05   0.8   1   0.1 − .05   0.1 + .225       CS Type   0.3   0.3 − .15   0.3 − .15   0.1 − .05   1   0.8 − 0.4       CS Amount   0.3 − .15   0.1 − .05   0.1 − .05   0.1 + .225   0.8 − 0.4   1                  
 
         [0038]    The revisions shown to TABLE 6, result in TABLE 7.  
                                                                         TABLE 7                                       TM       LM       CS           TM type   Amount   LM type   Amount   CS Type   Amount                                    TM type   1   .9   .65   .15   0.3   .15       TM Amount   .9   1   .65   .05   .15   .05       LM type   .65   .65   1   .8   .15   .05       LM Amount   .15   .05   .8   1   .05   .325       CS Type   0.3   .16   .15   .05   1   .4       CS Amount   .15   .05   .05   .325   .4   1                  
 
         [0039]    A full factorial experiment is organized and run according to the strongest interactions on the TM Type/TM Amount/LM Type variables (5×4×5=100 runs, fully replicated to 200 runs). Results are shown in TABLE 8.  
                                                                     TABLE 8                                   TM   LM               TMType   LMType   CSType   Amount   Amount   CS Amount   TON                                Fe   V   DMAA   5   10   100   1138       Fe   W   DMAA   5   10   100   1137       Fe   Ce   DMAA   5   10   100   1357       Fe   La   DMAA   5   10   100   1424       Fe   Sn   DMAA   5   10   100   1605       Cu   V   DMAA   5   10   100   1000       Cu   W   DMAA   5   10   100   1040       Cu   Ce   DMAA   5   10   100   1159       Cu   La   DMAA   5   10   100   1176       Cu   Sn   DMAA   5   10   100   1048       Ni   V   DMAA   5   10   100   884       Ni   W   DMAA   5   10   100   896       Ni   Ce   DMAA   5   10   100   905       Ni   La   DMAA   5   10   100   848       Ni   Sn   DMAA   5   10   100   972       Pb   V   DMAA   5   10   100   743       Pb   W   DMAA   5   10   100   965       Pb   Ce   DMAA   5   10   100   585       Pb   La   DMAA   5   10   100   709       Pb   Sn   DMAA   5   10   100   129       Re   V   DMAA   5   10   100   549       Re   W   DMAA   5   10   100   767       Re   Ce   DMAA   5   10   100   491       Re   La   DMAA   5   10   100   726       Re   Sn   DMAA   5   10   100   511       Fe   V   DMAA   10   10   100   1002       Fe   W   DMAA   10   10   100   1038       Fe   Ce   DMAA   10   10   100   1124       Fe   La   DMAA   10   10   100   1211       Fe   Sn   DMAA   10   10   100   1388       Cu   V   DMAA   10   10   100   1000       Cu   W   DMAA   10   10   100   1069       Cu   Ce   DMAA   10   10   100   1064       Cu   La   DMAA   10   10   100   1278       Cu   Sn   DMAA   10   10   100   1269       Ni   V   DMAA   10   10   100   1061       Ni   W   DMAA   10   10   100   1136       Ni   Ce   DMAA   10   10   100   977       Ni   La   DMAA   10   10   100   1001       Ni   Sn   DMAA   10   10   100   1487       Pb   V   DMAA   10   10   100   1048       Pb   W   DMAA   10   10   100   1188       Pb   Ce   DMAA   10   10   100   1333       Pb   La   DMAA   10   10   100   907       Pb   Sn   DMAA   10   10   100   1155       Re   V   DMAA   10   10   100   1028       Re   W   DMAA   10   10   100   839       Re   Ce   DMAA   10   10   100   834       Re   La   DMAA   10   10   100   1308       Re   Sn   DMAA   10   10   100   1203       Fe   V   DMAA   20   10   100   879       Fe   W   DMAA   20   10   100   877       Fe   Ce   DMAA   20   10   100   888       Fe   La   DMAA   20   10   100   983       Fe   Sn   DMAA   20   10   100   759       Cu   V   DMAA   20   10   100   1000       Cu   W   DMAA   20   10   100   1016       Cu   Ce   DMAA   20   10   100   1146       Cu   La   DMAA   20   10   100   1236       Cu   Sn   DMAA   20   10   100   1205       Ni   V   DMAA   20   10   100   1149       Ni   W   DMAA   20   10   100   1062       Ni   Ce   DMAA   20   10   100   1289       Ni   La   DMAA   20   10   100   1374       Ni   Sn   DMAA   20   10   100   1668       Pb   V   DMAA   20   10   100   1126       Pb   W   DMAA   20   10   100   1449       Pb   Ce   DMAA   20   10   100   1476       Pb   La   DMAA   20   10   100   1592       Pb   Sn   DMAA   20   10   100   1828       Re   V   DMAA   20   10   100   1136       Re   W   DMAA   20   10   100   1728       Re   Ce   DMAA   20   10   100   1481       Re   La   DMAA   20   10   100   2336       Re   Sn   DMAA   20   10   100   1928       Fe   V   DMAA   40   10   100   765       Fe   W   DMAA   40   10   100   741       Fe   Ce   DMAA   40   10   100   715       Fe   La   DMAA   40   10   100   475       Fe   Sn   DMAA   40   10   100   590       Cu   V   DMAA   40   10   100   1000       Cu   W   DMAA   40   10   100   1061       Cu   Ce   DMAA   40   10   100   1085       Cu   La   DMAA   40   10   100   1181       Cu   Sn   DMAA   40   10   100   1153       Ni   V   DMAA   40   10   100   1198       Ni   W   DMAA   40   10   100   1367       Ni   Ce   DMAA   40   10   100   1514       Ni   La   DMAA   40   10   100   1754       Ni   Sn   DMAA   40   10   100   1913       Pb   V   DMAA   40   10   100   1477       Pb   W   DMAA   40   10   100   1593       Pb   Ce   DMAA   40   10   100   1980       Pb   La   DMAA   40   10   100   2059       Pb   Sn   DMAA   40   10   100   2252       Re   V   DMAA   40   10   100   1745       Re   W   DMAA   40   10   100   1906       Re   Ce   DMAA   40   10   100   2697       Re   La   DMAA   40   10   100   2606       Re   Sn   DMAA   40   10   100   3245       Fe   V   DMAA   5   10   100   1149       Fe   W   DMAA   5   10   100   1257       Fe   Ce   DMAA   5   10   100   1311       Fe   La   DMAA   5   10   100   1435       Fe   Sn   DMAA   5   10   100   1524       Cu   V   DMAA   5   10   100   1000       Cu   W   DMAA   5   10   100   1032       Cu   Ce   DMAA   5   10   100   1109       Cu   La   DMAA   5   10   100   1077       Cu   Sn   DMAA   5   10   100   1301       Ni   V   DMAA   5   10   100   853       Ni   W   DMAA   5   10   100   910       Ni   Ce   DMAA   5   10   100   863       Ni   La   DMAA   5   10   100   971       Ni   Sn   DMAA   5   10   100   799       Pb   V   DMAA   5   10   100   802       Pb   W   DMAA   5   10   100   828       Pb   Ce   DMAA   5   10   100   913       Pb   La   DMAA   5   10   100   529       Pb   Sn   DMAA   5   10   100   496       Re   V   DMAA   5   10   100   691       Re   W   DMAA   5   10   100   395       Re   Ce   DMAA   5   10   100   372       Re   La   DMAA   5   10   100   455       Re   Sn   DMAA   5   10   100   226       Fe   V   DMAA   10   10   100   912       Fe   W   DMAA   10   10   100   1060       Fe   Ce   DMAA   10   10   100   1104       Fe   La   DMAA   10   10   100   1009       Fe   Sn   DMAA   10   10   100   1091       Cu   V   DMAA   10   10   100   1000       Cu   W   DMAA   10   10   100   1084       Cu   Ce   DMAA   10   10   100   1087       Cu   La   DMAA   10   10   100   1246       Cu   Sn   DMAA   10   10   100   1261       Ni   V   DMAA   10   10   100   983       Ni   W   DMAA   10   10   100   1035       Ni   Ce   DMAA   10   10   100   1238       Ni   La   DMAA   10   10   100   1119       Ni   Sn   DMAA   10   10   100   1188       Pb   V   DMAA   10   10   100   1210       Pb   W   DMAA   10   10   100   965       Pb   Ce   DMAA   10   10   100   1480       Pb   La   DMAA   10   10   100   1038       Pb   Sn   DMAA   10   10   100   1182       Re   V   DMAA   10   10   100   1016       Re   W   DMAA   10   10   100   979       Re   Ce   DMAA   10   10   100   828       Re   La   DMAA   10   10   100   1204       Re   Sn   DMAA   10   10   100   1313       Fe   V   DMAA   20   10   100   874       Fe   W   DMAA   20   10   100   923       Fe   Ce   DMAA   20   10   100   840       Fe   La   DMAA   20   10   100   1017       Fe   Sn   DMAA   20   10   100   700       Cu   V   DMAA   20   10   100   1000       Cu   W   DMAA   20   10   100   1046       Cu   Ce   DMAA   20   10   100   1097       Cu   La   DMAA   20   10   100   1172       Cu   Sn   DMAA   20   10   100   1226       Ni   V   DMAA   20   10   100   1106       Ni   W   DMAA   20   10   100   1249       Ni   Ce   DMAA   20   10   100   1201       Ni   La   DMAA   20   10   100   1331       Ni   Sn   DMAA   20   10   100   1302       Pb   V   DMAA   20   10   100   1362       Pb   W   DMAA   20   10   100   1308       Pb   Ce   DMAA   20   10   100   1665       Pb   La   DMAA   20   10   100   1558       Pb   Sn   DMAA   20   10   100   1942       Re   V   DMAA   20   10   100   1390       Re   W   DMAA   20   10   100   1629       Re   Ce   DMAA   20   10   100   1731       Re   La   DMAA   20   10   100   2401       Re   Sn   DMAA   20   10   100   2327       Fe   V   DMAA   40   10   100   748       Fe   W   DMAA   40   10   100   674       Fe   Ce   DMAA   40   10   100   714       Fe   La   DMAA   40   10   100   691       Fe   Sn   DMAA   40   10   100   610       Cu   V   DMAA   40   10   100   1000       Cu   W   DMAA   40   10   100   1028       Cu   Ce   DMAA   40   10   100   1012       Cu   La   DMAA   40   10   100   1227       Cu   Sn   DMAA   40   10   100   1251       Ni   V   DMAA   40   10   100   1258       Ni   W   DMAA   40   10   100   1351       Ni   Ce   DMAA   40   10   100   1568       Ni   La   DMAA   40   10   100   1576       Ni   Sn   DMAA   40   10   100   1663       Pb   V   DMAA   40   10   100   1437       Pb   W   DMAA   40   10   100   1786       Pb   Ce   DMAA   40   10   100   1933       Pb   La   DMAA   40   10   100   2476       Pb   Sn   DMAA   40   10   100   2126       Re   V   DMAA   40   10   100   1447       Re   W   DMAA   40   10   100   1709       Re   Ce   DMAA   40   10   100   2329       Re   La   DMAA   40   10   100   3067       Re   Sn   DMAA   40   10   100   2904                  
 
         [0040]    An ANOVA analysis of variance of the TABLE 8 data is illustrated in TABLE 9.  
                                                                     TABLE 9                       Source   DF   Seq SS   Adj SS   Adj MS   F   P                                TMType   4   4777245   4777246   1194311    83.10   0       LMType   4   2432949   2432949   608237   42.32   0       TMAmount   3   10451748    10451748    3483916    242.42   0       TMType*LMType   16   1330652   1330642    83166   5.79   0       TMType*TMAmount   12   22425009    22425009    1868751    130.03   0       LMType*TMAmount   12   1489975   1489975   124186   8.64   0       TMType*LMType*TMAmount   48   3450829   3450829    71892   5.00   0       Error   100   1437139   1437139    14371       Total   199   47795548                   
 
         [0041]    The ANOVA analysis detects a statistically significant 3-way interaction, which is a lead to high value formulations with high levels (TMA=40) of Re in the presence of La or Sn.  
         [0042]    While preferred embodiments of the invention have been described, the present invention is capable of variation and modification and therefore should not be limited to the precise details of the Examples. The invention includes changes and alterations that fall within the purview of the following claims.