Experimental Design In Organic Synthesis - Chemistry.msu.edu
Statistical Design ofExperiments Applied toOrganic SynthesisLuis SanchezMichigan State UniversityOctober 11th, 2006
Statistical Design of Experiments Methodology developed in 1958 by theBritish statistician Ronald FisherDoE Strategy Appropriate statistical analysis before anyexperimental data are obtained Objective To get as much information as possiblefrom a minimum number of experimentsBayne, C. K.; Rubin, I. B., Practical experimental designs and optimization methods for chemists. VCHPublishers, USA, 1986.Tranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000.
Experimentation in Organic synthesis In any synthetical procedure there are factorstemperature, time, pressure, reagents, rate ofaddition, catalyst, solvent, concentration, pHthat will have an influence on the resultyield, purity, selectivityCarlson, R., Design and optimization in organic synthesis. Elsevier: Amsterdam ; New York, 1992.
Conventional approach to optimizationT CZX Yt minutes Analysis of the reaction conditions that affect the yield:Yield vs. Reaction time (T 125 C)80807575Yield (%)Yield (%)Yield vs. Temperature (t 130 min)7065706560605510555115125135Temperature ( C)1451554070100130160190Time (min) The maximum yield would be obtained at 125 C in 130 min ?Are these really the optimum conditions?Tranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000.
How yield actually behavesTemperature ( C)actualmaximum155Yield vs (Time and 5706011510555“response surface”80105130155180Time (min)Carlson, R., Design and optimization in organic synthesis. Elsevier: Amsterdam ; New York, 1992.Tranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000.
The conventional approach Analysis of the effect of one particular reaction conditionby keeping all the other ones constantcatalystCA BAmount ofCatalystT Ct minutesTemperatureConcentrationof substrateThe problem: The optimum conditions obtained depend on the starting pointOwen, M. R.; Luscombe, C.; Lai, L. W.; Godbert, S.; Crookes, D. L.; Emiabata-Smith, D.Org. Proc. Res. Dev. 2001, 5, 308-323.
The DoE approach To rationally choose points throughout the cube to fullyrepresent the entire space.catalystCA BAmount ofCatalystT Ct minutesTemperatureOwen, M. R.; Luscombe, C.; Lai, L. W.; Godbert, S.; Crookes, D. L.; Emiabata-Smith, D.Org. Proc. Res. Dev. 2001, 5, 308-323.Concentrationof substrate
Outline Determining important reaction conditions Fractional factorial design Analysis of reaction condition effects Factorial design Estimation of the optimum conditions Response surface analysis
Factorial designs Two types of reaction conditions: Numerictemperature, pH, rate of addition, concentration Categoricsolvent, inert atmosphere, presence of molecularsieves, use of a particular reagent Each reaction condition will be screened over a definedset of values (numeric) or options (categoric) Experiments are run using all the possible combinations
mn Factorial designsnumber of valuesfor each reactionconditionnmnumber ofreactionconditions If we analyze 2 values (or options) for 3 reactionconditions, 23 8 experiments need to be run A mn factorial design requires mn experiments The most used method is 2n design
23 factorial designROOCCOOROHCOORCOORT CROOCH 2OCOORacid catalyst(H 2SO 4/H3 PO4 )number ofconditionsnumber ofvalues23 2 values (or options) for 3 reaction conditions:CTTemperature( C)CConcentration(M)1201601.52.5-1 1-1 1KCatalystK(-1,1,1)(-1,1,-1)H3PO4 H2SO4-1 -1)Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
23 factorial designROOCCOOROHCOORT CROOCH 2OCOORCOORacid catalyst(H 2SO 4/H3 PO4 ) 8 experimental runs:runTCKlabelyield (%)1---1602 --t723- -c544 -tc685-- k526 - tk837- ck458 tck80Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
runTCKlabelyield (%)1---1602 --t723- -c544 -tc685-- k526 - tk837- ck458 tck80Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Measuring the effect: TemperaturerunTCKlabelyield (%)1---1602 --t723- -c544 -tc685-- k526 - tk837- ck458 tck80Effect of ,1,-1)(1,-1,1)(1,-1,-1)3135One half of the average ofthe differences of each pair ( t 1) ( tc c ) ( tk k ) ( tck ck ) 12 14 31 35 44 11.5 22Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Measuring the effect: ConcentrationrunTCKlabelyield (%)1---1602 --t723- -c544 -tc685-- k526 - tk837- ck458 tck80Effect of C-6-4-7-3One half of the average ofthe differences of each pair (c 1) ( tc t ) (ck k ) ( tck tk ) ( 6) ( 4) ( 7) ( 3) 44 2.5 22Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Measuring the effect: CatalystrunTCKlabelyield (%)1---1602 --t723- -c544 -tc685-- k526 - tk837- ck458 tck80Effect of K-811-912One half of the average ofthe differences of each pair (k 1) ( tk t ) (ck c ) ( tck tc ) ( 8) 11 ( 9) 12 44 0.75 22Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Concentration-temperature interactionrunTCKlabelyield (%)1---1602 --t723- -c544 -tc685-- k526 - tk837- ck458 tck80on12Effect of C on theeffect of T611473115.53517.5 ( tc c ) ( t 1) ( tck ck ) ( tk k ) 22222 22 One half of the averageof the differences ofeach pair of effects 14 12 35 31 22 2 2 2 0.752Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Temperature-concentration interactiononrunTCKlabelyield (%)1---1602 --t723- -c544 -tc685-- k526 - tk837- ck458 tck80-6Effect of T on theeffect of C-31-4-2-7-3.5-3 ( tc t ) (c 1) ( tck tk ) (ck k ) 22 22 2 2-1.52 One half of the averageof the differences ofeach pair of effects ( 4) ( 6) ( 3) ( 7) 22 22 2 0.752Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Concentration-temperature interactionrunTCKlabelyield (%)1---1602 --t723- -c544 -tc685-- k526 - tk837- ck458 tck80on12Effect of C on theeffect of T611473115.53517.5 ( tc c ) ( t 1) ( tck ck ) ( tk k ) 22222 22 One half of the averageof the differences ofeach pair of effects 14 12 35 31 22 22 2 0.752Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Temperature-catalyst interactionrunTCKlabelyield (%)1---1602 --t723- -c544 -tc685-- k526 - tk837- ck458 tck80on1269.51473115.53517.5 ( tk k ) ( t 1) ( tck ck ) ( tc c ) 22 22 2 210.5One half of the averageof the differences ofeach pair of effects 31 12 35 14 22 22 2 52Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
TCK interactionrunTCKlabelyield (%)1---1602 --t723- -c544 -tc685-- k526 - tk837- ck458 tck80on1269.51473115.53517.5 ( tck ck ) ( tc c ) ( tk k ) ( t 1) 222 22 24.750.510.55.25 35 14 31 12 22 22 2 0.252Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Measuring the effect and interactions Yates’s algorithm: works for any 2n factorial designrunTCKlabelyield (%)(1)(2)(3)divresult1---160132254514864.25 average2 --t7212226092811.5T3- -c5413526-208-2.5C4 -tc6812566680.75TC5-- k5212-10680.75K6 - tk8314-104085.0TK7- ck45312080CK8 tck80354280.25TCKBox, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
What do those numbers mean? First we need to evaluate if they are significantFactor effect plot14123xEffect1086420-23x(when there isno central point)-4TCTCKTKCKFactor If the effect of a factor is lower than the standarddeviation, it’s likely to be due to experimental errorTCK
What do those numbers mean? The effects can be used to calculate a function thatrepresents all the experimental 0TCK0.25yield 64.25 11.5T 2.5C 5TK runTCKlabelyield (%)calculated1---16060.25 22 --t7273.25 23- -c5455.25 24 -tc6868.25 25-- k5250.25 26 - tk8383.25 27- ck4545.25 28 tck8078.25 2
The meaning of those numbersyield 64.25 11.5T 2.5C 5TK TTemperature( C)CConcentration(M)1201601.52.5-1 1-1 1KCatalystH3PO4 H2SO4-1 1 Categorical reaction conditions can be optimizedROOCOHCOORCOORCOORH 2SO 4(aq)heatROOCCOORyield 64.25 16.5T 2.5C
Something important It was possible to choose one catalyst because theinteraction TK was identifiedyield 64.25 11.5T 2.5C 5TK runTCKyield (%)1---602 --723- -544 -685-- 526 - 837- 458 80H3PO4H2SO4In order to get themaximum yield(maximize the function),the catalyst has to beH2SO4
The meaning of those numbersROOCCOOROHCOORH 2SO 4(aq)heatCOORROOCCOORyield 64.25 16.5T 2.5C yield83.2545.25CT To find the optimumconditions, we need to makesure that this functionrepresents the entire space
Other factorial designs Full factorial designCentral compositeBox-BenhkenTye, H. Drug Discovery Today 2004, 9, 485-491.
Outline Determining important reaction conditions Fractional factorial design Analysis of reaction condition effects Factorial design Estimation of the optimum conditions Response surface analysis
Fractional Factorial designs Factorial designs work perfectly for determiningimportant factors if you have 3 reaction conditions, as in the exampleROOCOHCOORCOORCOORT CH 2OROOCCOORacid catalyst(H 2SO 4/H3 PO4 ) If you had to analyze 7 reaction conditions at 2 valueseach, you would need to run 27 128 experiments! By virtue of statistics, it is possible to lower that numberand get the same information
mn-p Fractional Factorial designsnumber of valuesfor each reactionconditionn-pmactual numberof reactionconditionsnumber of “ignored”reaction conditions A mn-p fractional factorial design requires mn-p experiments If we analyze 2 values or options for 4 reaction conditions(as if they were only 3), 24-1 8 experiments need to be runTranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000.
Effects vs. interactions This is what wegot 0CK0TCK0.25Important?main effectsVery often2-factor interactionsOften3-factor interactionsSometimes4-factor interactionsVery rarelymore-than-5-factorinteractionsIf you get to here youhave something veryunusual!Tranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000
24-1 Fractional factorial design Yates’s algorithm:runABCDyield (%)(1)(2)(3)divresult1----####8#av ABCD2 -- ####8#A BCD3- - ####8#B ACD4 --####8#AB CD5-- ####8#C ABD6 - -####8#AC BD7- -####8#BC AD8 ####8#ABC DBox, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Number of experimental runs Fractional factorial designsNumber of reaction conditionsDesign Expert 7.0.3 (Stat-Ease Inc.) (http://www.statease.com)
How to compare the effects? In the case of 3 reaction conditions, a “Factor effect plot”is enoughFactor effect plot1412Effect1086420-2-4TCTCKTKCKTCKFactor For a high number of reactions, a normal plot is needed
Normal plots Let’s assume that the experimental error follows anormal distribution% error In a normal plot, reaction conditioneffects that are due to experimental errorwill appear forming a straight lineNormal plotBox, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Application exampleOOOPivONO2HOBrOPivOPiv2HNNN1CF3Ag 2Omol.sieves18h(Koenigs-Knorrglucuronidation)NO 2OOOPivOOHNNOPivOPivNCF333% Chelation was identified as the reason for the bad yield Addition of TMEDA (10 equiv.), increased the yield to 27%NTMEDA NStazi, F.; Palmisano, G.; Turconi, M.; Clini, S.; Santagostino, M. J. Org. Chem. 2004, 69, 1097-1103.
Application exampleOOOPivONO2HOBrOPivOPiv2HNNN1CF3Ag 2O10 equiv. TMEDAmol.sieves18hNO 2OOOPivOOHNNNOPivOPiv327 % DoE methods (32 factorial design) were applied to screen amineadditives and silver sources giving: HMTTA and Ag2CO3 as bestcombinationNHMTTA NNNCF3
Application exampleOOOPivONO2HOBrOPivHNONNCF31Ag2 CO3NO 2OOPiv2PivO10 equiv. HMTTAHNOONNOPivOPiv342 %mol.sieves18h A 27-4 fractional factorial (8 experiments) design was used:Reaction condition-1 1Apre-complex time (min)060Breaction time (h)26CAg2CO3 (equiv)1.53.8DHMTTA (equiv)1.512.6Esugar derivative (equiv)1.53F4 Å mol sieves (mg)0100Gsolvent (mL)0.51.5CF3
Application example27-4 factorial design results:runABCDEFG yield (%)1--- -14.72 ---- 19.53- -- - 24.44 - ---11.25-- -- 34.26 - - --83.27- -- -56.58 55.4Apre-complex time (min)Breaction time (h)CAg2CO3 (equiv)DHMTTA (equiv)Esugar derivative (equiv)F4 Å mol sieves (mg)Gsolvent (mL)Stazi, F.; Palmisano, G.; Turconi, M.; Clini, S.; Santagostino, M. J. Org. Chem. 2004, 69, 1097-1103.
Application exampleOONO2HOHNOBrPivOOPiv(2.4 eq.) OPivNNCF3Ag 2CO3 (3.7 eq)HMTTA (0.7 eq)30 minNO2OOOPivOOHNNNOPivOPiv86% Finally, a 23 factorial design andresponse surface analysis gavethe optimum conditionsStazi, F.; Palmisano, G.; Turconi, M.; Clini, S.; Santagostino, M. J. Org. Chem. 2004, 69, 1097-1103.CF3
Outline Determining important reaction conditions Fractional factorial design Analysis of reaction condition effects Factorial design Estimation of the optimum conditions Response surface analysis
Response surface analysis The problem of optimizing a synthetic reaction corresponds tolocate the maximum value of a function from a mathematicalpoint of viewyieldyieldCarlson, R., Design and optimization in organic synthesis. Elsevier: Amsterdam; New York, 1992.
Response surface analysisOHCOORROOCCOORH2 SO4(aq) 1.0MCOORttime(min)ROOCT Ct minCOORruntTTTemperature( C)1--2 -3- 7080127.5132.54-1 1-1 1500600700Central point:three times tocalculate theexperimental errorBox, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Response surface analysisROOCOHCOORCOORH2 SO4(aq) 1.0MCOORROOCT Ct minCOORyield 62.01 2.35 t 4.5T tT yield (%)1--54.32 -60.33- 64.64 68.050060.360064.380062.3Yield vs. (Time and Temperature)1353 central pointse 2Temperature ( C)run13364.668.062.31311291271256554.3707580time (min)60.385Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Response surface analysisYield vs. (Time and Temperature)16058.2Temperature ( C)15087.414069.113012060708090100110time (min)Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Response surface analysisYield vs. (Time and Temperature)155yield 82 . 09 2 . 69 t 6 . 97 T 91.1Temperature ( C)85.991.915087.4145 Equation for the 22 factorialdesign:86.879.3 Calculated equation for thesurface:yield 87 . 36 2 . 69 t 6 . 97 T 2 .15 t 2 3 .12 T 2 0 . 58 Tt 14077.273.0171.2135708090100110time (min)Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Response surface analysis22yield 87 . 36 2 . 69 t 6 . 97 T 2 . 15 t 3 .12 T 0 . 58 Tt Yield vs. (Time and Temperature)160Optimum conditions:T 157 Ct 73 minyield: 93%Temperature ( C)15593901508588145140708090100110time (min)Box, G. E. P.; Hunter, W. G.; Hunter, J. S., Statistics for experimenters : an introduction to design, data analysis,and model building. Wiley: New York, 1978.
Sequential nature of experimentationHypercube designin n dimensionsDesign in 2,3,4dimensionsPlanFractionalfactorialdesignFull factorialdesignCentralcompositeResponsesurface analysisTranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000.
Application of response surface analysisTBSOHRHONO1R''TEA 3HFNMPOOHOHRHONR'R''R2ONOR'O3 24 central compositereaction conditionrangeH OOHunitstemperature1030 Ctime1931hoursvolume of NMP37mL/g of substrateequivalents of TEA.3HF11.67Equivalents Monitored results: % yield of alcohol % lactone % remaining silyl etherOwen, M. R.; Luscombe, C.; Lai, L. W.; Godbert, S.; Crookes, D. L.; Emiabata-Smith, D.Org. Proc. Res. Dev. 2001, 5, 308-323.OOR'
Application of response surface analysisTBSOHRHONO1R''NMPOOTEA 3HFR'HOHRHONR''2OHH NOOORR'Owen, M. R.; Luscombe, C.; Lai, L. W.; Godbert, S.; Crookes, D. L.; Emiabata-Smith, D.Org. Proc. Res. Dev. 2001, 5, 308-323.O3OOR'
ApplicationTBSOHRHONO1R''HHRNMPOOHOTEA 3HFR'ONR''O2OHH NOOR'OO3Predicted conditionstarget/constraintsRproduct yield (%)OR'impurity (%)T ( C)Time ax yield19313.61.4295.395.83.33.3lactone 2%17314.81.5094.294.01.91.7lactone 1.1%16295.31.6892.493.11.11.1lactone 2%, solvent 3.5 mL/g14313.451.5893.994.21.82.0lactone 2% Et3N.3HF 1.18eq.2819.571.1793.793.41.92.0lactone 2%, time 23 h24236.31.4194.294.22.01.9Owen, M. R.; Luscombe, C.; Lai, L. W.; Godbert, S.; Crookes, D. L.; Emiabata-Smith, D.Org. Proc. Res. Dev. 2001, 5, 308-323.
When DoE “fails”NONOHO1) AcBr, Ac 2 O, CH 2Cl2HOH2) KOH, MeOH3) HCl, CH 2Cl2HHO21entryOHAcBrAc2O(equiv) (equiv)T ( C)yield (%)(20 g)yield(%)(20 kg)comments133.823-2777.3 70original conditions231.5142.513-1721-2475.882.7–74optimum of DoEnew conditionsConditions: t 4-5h; yield of 2 after crystallizationLarkin, J. P.; Wehrey, C.; Boffelli, P.; Lagraulet, H.; Lemaitre, G.; Nedelec, A.Org. Proc. Res. Dev. 2002, 6, 20-27.
Outline Determining important reaction conditions Fractional factorial design Analysis of reaction condition effects Factorial design Estimation of the optimum conditions Response surface analysis Recent advances Software Automation
“DoE involves a lot of math, it’s rathercomplicated” People tend not to utilize DoE because of thetedious mathematical manipulations.Lendrem, D.; Owen, M.; Godbert, S. Org. Proc. Res. Dev. 2001, 5, 324-327.
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