Experimental Design in organic synthesis · PDF fileStatistical Design of Experiments Applied...
Transcript of Experimental Design in organic synthesis · PDF fileStatistical Design of Experiments Applied...
Statistical Design of Experiments Applied to
Organic Synthesis
Statistical Design of Experiments Applied to
Organic Synthesis
Luis SanchezMichigan State University
October 11th, 2006
Luis SanchezMichigan State University
October 11th, 2006
• Statistical Design of Experiments• Statistical Design of Experiments
Methodology developed in 1958 by the British statistician Ronald Fisher
Strategy• Appropriate statistical analysis before any
experimental data are obtained
Objective• To get as much information as possible
from a minimum number of experiments
Methodology developed in 1958 by the British statistician Ronald Fisher
Strategy• Appropriate statistical analysis before any
experimental data are obtained
Objective• To get as much information as possible
from a minimum number of experiments
Bayne, C. K.; Rubin, I. B., Practical experimental designs and optimization methods for chemists. VCH Publishers, USA, 1986.Tranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000.
DoEDoE
• Experimentation in Organic synthesis• Experimentation in Organic synthesis
In any synthetical procedure there are factorstemperature, time, pressure, reagents, rate of addition, catalyst, solvent, concentration, pH
that will have an influence on the resultyield, purity, selectivity
In any synthetical procedure there are factorstemperature, time, pressure, reagents, rate of addition, catalyst, solvent, concentration, pH
that will have an influence on the resultyield, purity, selectivity
Carlson, R., Design and optimization in organic synthesis. Elsevier: Amsterdam ; New York, 1992.
• Conventional approach to optimization• Conventional approach to optimization
• Analysis of the reaction conditions that affect the yield:• Analysis of the reaction conditions that affect the yield:
Tranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000.
Yield vs. Temperature (t=130 min)Yield vs. Temperature (t=130 min)
55
60
65
70
75
80
105 115 125 135 145 155
Temperature (°C)
Yiel
d (%
)
Yield vs. Reaction time (T=125°C)Yield vs. Reaction time (T=125°C)
55
60
65
70
75
80
40 70 100 130 160 190
Time (min)Yi
eld
(%)
T °C
t minutesZX + Y
• The maximum yield would be obtained at 125 °C in 130 min• The maximum yield would be obtained at 125 °C in 130 min?Are these really the optimum conditions?
?Are these really the optimum conditions?
Yield vs (Time and Temperature)Yield vs (Time and Temperature)
105
115
125
135
145
155
55 80 105 130 155 180Time (min)Time (min)
Tem
pera
ture
(°C
)Te
mpe
ratu
re (°
C)
• How yield actually behaves• How yield actually behaves
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.
maximumyield
70
8090
94
60
actual maximum
“response surface”
localmaximum
• The conventional approach• The conventional approach
Owen, M. R.; Luscombe, C.; Lai, L. W.; Godbert, S.; Crookes, D. L.; Emiabata-Smith, D.Org. Proc. Res. Dev. 2001, 5, 308-323.
• Analysis of the effect of one particular reaction condition by keeping all the other ones constant
• Analysis of the effect of one particular reaction condition by keeping all the other ones constant
The problem:• The optimum conditions obtained depend on the starting pointThe problem:• The optimum conditions obtained depend on the starting point
Concentration of substrate
Concentration of substrate
Amount ofCatalyst
Amount ofCatalyst
TemperatureTemperature
catalyst
T °Ct minutes
CA + B
• The DoE approach• The DoE approach• To rationally choose points throughout the cube to fully
represent the entire space. • To rationally choose points throughout the cube to fully
represent the entire space.
Concentration of substrate
Concentration of substrate
Amount ofCatalyst
Amount ofCatalyst
TemperatureTemperature
catalyst
T °Ct minutes
CA + B
Owen, M. R.; Luscombe, C.; Lai, L. W.; Godbert, S.; Crookes, D. L.; Emiabata-Smith, D.Org. Proc. Res. Dev. 2001, 5, 308-323.
• Outline• Outline
Determining important reaction conditions• Fractional factorial design
Analysis of reaction condition effects• Factorial design
Estimation of the optimum conditions• Response surface analysis
Determining important reaction conditions• Fractional factorial design
Analysis of reaction condition effects• Factorial design
Estimation of the optimum conditions• Response surface analysis
• Factorial designs• Factorial designs• Two types of reaction conditions:
Numerictemperature, pH, rate of addition, concentrationCategoricsolvent, inert atmosphere, presence of molecular sieves, use of a particular reagent
• Each reaction condition will be screened over a defined set of values (numeric) or options (categoric)
• Experiments are run using all the possible combinations
• Two types of reaction conditions:Numerictemperature, pH, rate of addition, concentrationCategoricsolvent, inert atmosphere, presence of molecular sieves, use of a particular reagent
• Each reaction condition will be screened over a defined set of values (numeric) or options (categoric)
• Experiments are run using all the possible combinations
• mn Factorial designs• mn Factorial designs
• If we analyze 2 values (or options) for 3 reaction conditions, 23=8 experiments need to be run
• A mn factorial design requires mn experiments• The most used method is 2n design
• If we analyze 2 values (or options) for 3 reaction conditions, 23=8 experiments need to be run
• A mn factorial design requires mn experiments• The most used method is 2n design
mnmn
number of reaction
conditionsnumber of values for each reaction
condition
• 23 factorial design• 23 factorial design
• 2 values (or options) for 3 reaction conditions:• 2 values (or options) for 3 reaction conditions:
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.
TTemperature
(°C)
CConcentration
(M)
KCatalyst
120 160 1.5 2.5 H3 PO4 H2 SO4
-1 +1 -1 +1 -1 +1
(1,1,1)(1,1,-1)
(-1,1,1)
(-1,1,-1)
(1,-1,1)
(1,-1,-1)
(-1,-1,1)
(-1,-1,-1)
acid catalyst(H2SO4/H3PO4)
OH
COOR
ROOCCOOR
COOR
ROOCCOOR
H2O
T °C
TT
CCKK
2323
number of conditionsnumber of
values
• 23 factorial design• 23 factorial design
• 8 experimental runs:• 8 experimental runs:
acid catalyst(H2SO4/H3PO4)
OH
COOR
ROOCCOOR
COOR
ROOCCOOR
H2O
T °C
run T C K label
1 - - - 12 + - - t3 - + - c4 + + - tc5 - - + k6 + - + tk7 - + + ck8 + + + tck
yield (%)
6072546852834580
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.
k+--5tc-++4c-+-3t--+2
ck++-7tk+-+6
tck+++8
1---1
labelKCTrun
52685472
4583
80
60
yield (%)
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.
• Measuring the effect: Temperature• Measuring the effect: Temperature
12
31
14
35
Effect of Trun T C K label
1 - - - 12 + - - t3 - + - c4 + + - tc5 - - + k6 + - + tk7 - + + ck8 + + + tck
One half of the average of the differences of each pair
5.1124
35311412
24
)cktck()ktk()ctc()1t(
=⎥⎦⎤
⎢⎣⎡ +++
=⎥⎦⎤
⎢⎣⎡ −+−+−+−
=
(1,1,1)(1,1,-1)
(-1,1,1)
(-1,1,-1)
(1,-1,1)
(1,-1,-1)
(-1,-1,1)
(-1,-1,-1)
yield (%)
6072546852834580
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.
• Measuring the effect: Concentration• Measuring the effect: ConcentrationEffect of C
5.224
)3()7()4()6(
24
)tktck()kck()ttc()1c(
−=⎥⎦⎤
⎢⎣⎡ −+−+−+−
=⎥⎦⎤
⎢⎣⎡ −+−+−+−
=
One half of the average of the differences of each pair
-6
-4
-7
-3
run T C K label
1 - - - 12 + - - t3 - + - c4 + + - tc5 - - + k6 + - + tk7 - + + ck8 + + + tck
yield (%)
6072546852834580
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.
• Measuring the effect: Catalyst• Measuring the effect: CatalystEffect of K
75.024
12)9(11)8(
24
)tctck()cck()ttk()1k(
=⎥⎦⎤
⎢⎣⎡ +−++−
=⎥⎦⎤
⎢⎣⎡ −+−+−+−
=
One half of the average of the differences of each pair
-8
11
-9
12
run T C K label
1 - - - 12 + - - t3 - + - c4 + + - tc5 - - + k6 + - + tk7 - + + ck8 + + + tck
yield (%)
6072546852834580
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.
• Concentration-temperature interaction• Concentration-temperature interactionEffect of C on the
effect of T
75.02
2231
235
212
214
2
22
)ktk(2
)cktck(2
)1t(2
)ctc(
on =⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −+⎥⎦
⎤⎢⎣⎡ −
=⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −
−−
+⎥⎦⎤
⎢⎣⎡ −
−−
=
12
31
14
35
1
2
6
15.5
7
17.5
run T C K label
1 - - - 12 + - - t3 - + - c4 + + - tc5 - - + k6 + - + tk7 - + + ck8 + + + tck
yield (%)
6072546852834580
One half of the average of the differences of each pair of effects
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.
1
2
-3
-3.5
-2
-1.5
-6
-7
-4
-3
• Temperature-concentration interaction• Temperature-concentration interactionrun T C K label
1 - - - 12 + - - t3 - + - c4 + + - tc5 - - + k6 + - + tk7 - + + ck8 + + + tck
yield (%)
6072546852834580
Effect of T on the effect of C
One half of the average of the differences of each pair of effects
75.02
22
)7(2
)3(2
)6(2
)4(
2
22
)kck(2
)tktck(2
)1c(2
)ttc(
on =⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −
−−
+⎥⎦⎤
⎢⎣⎡ −
−−
=⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −
−−
+⎥⎦⎤
⎢⎣⎡ −
−−
=
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.
• Concentration-temperature interaction• Concentration-temperature interactionEffect of C on the
effect of T
75.02
2231
235
212
214
2
22
)ktk(2
)cktck(2
)1t(2
)ctc(
on =⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −+⎥⎦
⎤⎢⎣⎡ −
=⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −
−−
+⎥⎦⎤
⎢⎣⎡ −
−−
=
12
31
14
35
1
2
6
15.5
7
17.5
run T C K label
1 - - - 12 + - - t3 - + - c4 + + - tc5 - - + k6 + - + tk7 - + + ck8 + + + tck
yield (%)
6072546852834580
One half of the average of the differences of each pair of effects
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.
• Temperature-catalyst interaction• Temperature-catalyst interaction
9.5
10.5
run T C K label
1 - - - 12 + - - t3 - + - c4 + + - tc5 - - + k6 + - + tk7 - + + ck8 + + + tck
yield (%)
6072546852834580
12
14
31
35
6
7
15.5
17.5One half of the average
of the differences of each pair of effects
52
22
142
352
12231
2
22
)ctc(2
)cktck(2
)1t(2
)ktk(
on =⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −+⎥⎦
⎤⎢⎣⎡ −
=⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −
−−
+⎥⎦⎤
⎢⎣⎡ −
−−
=
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.
• TCK interaction• TCK interaction
9.5
10.5
run T C K label
1 - - - 12 + - - t3 - + - c4 + + - tc5 - - + k6 + - + tk7 - + + ck8 + + + tck
yield (%)
6072546852834580
12
14
31
35
6
7
15.5
17.5
4.75
5.25
0.5
25.02
22
12231
214
235
2
22
)1t(2
)ktk(2
)ctc(2
)cktck(
on =⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −−⎥⎦
⎤⎢⎣⎡ −
=⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −
−−
−⎥⎦⎤
⎢⎣⎡ −
−−
=
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.
• Measuring the effect and interactions• Measuring the effect and interactions
(1)
132122
135
12512
1431
35
(2)
254260
2666-10
-10
2
4
(3)
51492
-2066
40
0
2
div
88
888
8
8
8
result
64.2511.5
-2.50.750.75
5.0
0
0.25
average
T
C
TCK
TK
CK
TCK
run T C K label
1 - - - 1
2 + - - t3 - + - c
4 + + - tc5 - - + k
6 + - + tk7 - + + ck
8 + + + tck
Yates’s algorithm: works for any 2n factorial designYates’s algorithm: works for any 2n factorial design
yield (%)
6072
5468
5283
4580
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.
Factor effect plotFactor effect plot
-4-202468
101214
T C TC K TK CK TCK
FactorFactor
Effe
ctEf
fect
• What do those numbers mean?• What do those numbers mean?• First we need to evaluate if they are significant• First we need to evaluate if they are significant
3x
3x(when there is
no central point)
• If the effect of a factor is lower than the standard deviation, it’s likely to be due to experimental error
• If the effect of a factor is lower than the standard deviation, it’s likely to be due to experimental error
• What do those numbers mean?• What do those numbers mean?
±+−+= TK5C5.2T5.1125.64yieldresult
64.25
11.5
-2.5
0.75
0.75
5.0
0
0.25
average
T
C
TC
K
TK
CK
TCK
run T C K label
1 - - - 12 + - - t3 - + - c4 + + - tc5 - - + k6 + - + tk7 - + + ck8 + + + tck
yield (%)
6072546852834580
calculated
60.25 ± 273.25 ± 255.25 ± 268.25 ± 250.25 ± 283.25 ± 245.25 ± 278.25 ± 2
• The effects can be used to calculate a function that represents all the experimental runs
• The effects can be used to calculate a function that represents all the experimental runs
• The meaning of those numbers• The meaning of those numbers±+−+= TK5C5.2T5.1125.64yield
±−+= C5.2T5.1625.64yield
TTemperature
(°C)
CConcentration
(M)
KCatalyst
120 160 1.5 2.5 H3 PO4 H2 SO4
-1 +1 -1 +1 -1 +1
H2SO4(aq)OH
COOR
ROOCCOOR
COOR
ROOCCOOR
heat
• Categorical reaction conditions can be optimized• Categorical reaction conditions can be optimized
• It was possible to choose one catalyst because the interaction TK was identified
• Something important• Something important
yield (%)
6072546852834580
±+−+= TK5C5.2T5.1125.64yield
H3 PO4
H2 SO4
run T C K
1 - - -2 + - -3 - + -4 + + -5 - - +6 + - +7 - + +8 + + +
In order to get the maximum yield
(maximize the function), the catalyst has to be
H2 SO4
• The meaning of those numbers• The meaning of those numbers
• To find the optimum conditions, we need to make sure that this function represents the entire space
• To find the optimum conditions, we need to make sure that this function represents the entire space
±−+= C5.2T5.1625.64yield
H2SO4(aq)OH
COOR
ROOCCOOR
COOR
ROOCCOOR
heat
yield
TC
45.2583.25
• Other factorial designs• Other factorial designs
• Full factorial design• Central composite• Box-Benhken
• Full factorial design• Central composite• Box-Benhken
Tye, H. Drug Discovery Today 2004, 9, 485-491.
• Outline• Outline
Determining important reaction conditions• Fractional factorial design
Analysis of reaction condition effects• Factorial design
Estimation of the optimum conditions• Response surface analysis
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• Fractional Factorial designs
• Factorial designs work perfectly for determining important factors …if you have 3 reaction conditions, as in the example
• If you had to analyze 7 reaction conditions at 2 values each, you would need to run 27=128 experiments!
• By virtue of statistics, it is possible to lower that number and get the same information
• Factorial designs work perfectly for determining important factors…if you have 3 reaction conditions, as in the example
• If you had to analyze 7 reaction conditions at 2 values each, you would need to run 27=128 experiments!
• By virtue of statistics, it is possible to lower that number and get the same information
acid catalyst(H2SO4/H3PO4)
OH
COOR
ROOCCOOR
COOR
ROOCCOOR
H2O
T °C
• mn-p Fractional Factorial designs• mn-p Fractional Factorial designs
mn-pmn-pactual number
of reaction conditions
number of values for each reaction
condition
number 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 run
• 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 run
Tranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000.
• Effects vs. interactions• Effects vs. interactions
Tranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000
result
64.25
11.5
-2.5
0.75
0.75
5.0
0
0.25
average
T
C
TC
K
TK
CK
TCK
• This is what we got before:
• This is what we got before: Important?
Very rarely4-factor interactions
If you get to here you have something very
unusual!
more-than-5-factor interactions
Sometimes3-factor interactions
Often2-factor interactions
Very oftenmain effects
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.
(1)
##
#
##
##
#
(2)
##
###
#
#
#
(3)
##
###
#
#
#
div
88
888
8
8
8
result
##
###
#
#
#
run A B C D
1 - - - -
2 + - - +3 - + - +
4 + + - -5 - - + +
6 + - + -7 - + + -
8 + + + +
Yates’s algorithm:Yates’s algorithm:
yield (%)
##
##
##
##
• 24-1 Fractional factorial design• 24-1 Fractional factorial design
av + ABCD
A + BCD
B + ACDAB + CDC + ABDAC + BD
BC + AD
ABC + D
• Fractional factorial designs• Fractional factorial designs
Design Expert 7.0.3 (Stat-Ease Inc.) (http://www.statease.com)
Number of reaction conditionsNumber of reaction conditions
Num
ber o
f exp
erim
enta
l run
sN
umbe
r of e
xper
imen
tal r
uns
• How to compare the effects?• How to compare the effects?
Factor effect plotFactor effect plot
-4-202468
101214
T C TC K TK CK TCK
FactorFactor
Effe
ctEf
fect
In the case of 3 reaction conditions, a “Factor effect plot”is enoughIn the case of 3 reaction conditions, a “Factor effect plot”is enough
For a high number of reactions, a normal plot is neededFor a high number of reactions, a normal plot is needed
• Normal plots• Normal plots
Let’s assume that the experimental error follows a normal distributionLet’s assume that the experimental error follows a normal distribution
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.
In a normal plot, reaction condition effects that are due to experimental error will appear forming a straight line
In a normal plot, reaction condition effects that are due to experimental error will appear forming a straight line
Normal plotNormal plot
% error
• Application example• Application example
Stazi, F.; Palmisano, G.; Turconi, M.; Clini, S.; Santagostino, M. J. Org. Chem. 2004, 69, 1097-1103.
HONO2 H
NN
N CF3
ONO2 H
NN
N CF3
O
OPivPivO OPiv
BrO
O
O
OPivPivO OPiv
O
O
Ag2Omol.sieves
18h
3%
1
2
3
(Koenigs-Knorrglucuronidation)
Chelation was identified as the reason for the bad yieldAddition of TMEDA (10 equiv.), increased the yield to 27%Chelation was identified as the reason for the bad yieldAddition of TMEDA (10 equiv.), increased the yield to 27%
N
NTMEDA =
• Application example• Application example
DoE methods (32 factorial design) were applied to screen amine additives and silver sources giving: HMTTA and Ag2CO3 as best combination
DoE methods (32 factorial design) were applied to screen amine additives and silver sources giving: HMTTA and Ag2CO3 as best combination
HONO2 H
NN
N CF3
ONO2 H
NN
N CF3
O
OPivPivO OPiv
BrO
O
O
OPivPivO OPiv
O
O
Ag2O
mol.sieves18h
27 %
1
2
310 equiv. TMEDA
N
N
HMTTA = N
N
• Application example• Application example
HONO2 H
NN
N CF3
ONO2 H
NN
N CF3
O
OPivPivO OPiv
BrO
O
O
OPivPivO OPiv
O
O
Ag2CO3
mol.sieves18h
42 %
1
2
310 equiv. HMTTA
A 27-4 fractional factorial (8 experiments) design was used:A 27-4 fractional factorial (8 experiments) design was used:
Reaction condition -1 +1A pre-complex time (min) 0 60 B reaction time (h) 2 6 C Ag2 CO3 (equiv) 1.5 3.8 D HMTTA (equiv) 1.5 12.6 E sugar derivative (equiv) 1.5 3 F 4 Å mol sieves (mg) 0 100 G solvent (mL) 0.5 1.5
• Application example• Application example
run A B C D E F G yield (%)
1 - - - + + + - 14.7 2 + - - - - + + 19.5 3 - + - - + - + 24.4 4 + + - + - - - 11.2 5 - - + + - - + 34.2 6 + - + - + - - 83.2 7 - + + - - + - 56.5 8 + + + + + + + 55.4
• 27-4 factorial design results:• 27-4 factorial design results:A pre-complex time (min)
B reaction time (h)
C Ag2 CO3 (equiv)
D HMTTA (equiv)
E sugar derivative (equiv)
F 4 Å mol sieves (mg)
G solvent (mL)
Stazi, F.; Palmisano, G.; Turconi, M.; Clini, S.; Santagostino, M. J. Org. Chem. 2004, 69, 1097-1103.
• Application example• Application example
HONO2 H
NN
N CF3
ONO2 H
NN
N CF3
O
OPivPivO OPiv
BrO
O
O
OPivPivO OPiv
O
O
Ag2CO3 (3.7 eq)HMTTA (0.7 eq)
30 min86%
(2.4 eq.)
• Finally, a 23 factorial design and response surface analysis gave the optimum conditions
• Finally, a 23 factorial design and response surface analysis gave the optimum conditions
Stazi, F.; Palmisano, G.; Turconi, M.; Clini, S.; Santagostino, M. J. Org. Chem. 2004, 69, 1097-1103.
• Outline• Outline
Determining important reaction conditions• Fractional factorial design
Analysis of reaction condition effects• Factorial design
Estimation of the optimum conditions• Response surface analysis
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• Response surface analysis
Carlson, R., Design and optimization in organic synthesis. Elsevier: Amsterdam; New York, 1992.
• The problem of optimizing a synthetic reaction corresponds to locate the maximum value of a function from a mathematical point of view
• The problem of optimizing a synthetic reaction corresponds to locate the maximum value of a function from a mathematical point of view
yield yield
• Response surface analysis• Response surface analysisH2SO4(aq) 1.0M
OH
COOR
ROOCCOOR
COOR
ROOCCOOR
T °Ct min
ttime(min)
TTemperature
(°C)
70 80 127.5 132.5
-1 +1 -1 +1
run t T
1 - -2 + -3 - + 4 + + 5 0 06 0 0 7 0 0
Central point: three times to calculate the
experimental error
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 analysis• Response surface analysis
run t T yield (%)
1 - - 54.32 + - 60.3 3 - + 64.6 4 + + 68.0 5 0 0 60.3 6 0 0 64.3 8 0 0 62.3
3 central points
Yield vs. (Time and Temperature)Yield vs. (Time and Temperature)
125
127
129
131
133
135
65 70 75 80 85time (min)time (min)
Tem
pera
ture
(°C
)Te
mpe
ratu
re (°
C)
62.3
68.0 64.6
60.3 54.3e = 2
±++= T5.4t35.201.62yield
H2SO4(aq) 1.0MOH
COOR
ROOCCOOR
COOR
ROOCCOOR
T °Ct 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 analysis• Response surface analysis
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.
Yield vs. (Time and Temperature)Yield vs. (Time and Temperature)
120
130
140
150
160
11060 70 80 90 100
time (min)time (min)
Tem
pera
ture
(°C
)Te
mpe
ratu
re (°
C)
69.1
58.2
87.4
Yield vs. (Time and Temperature)Yield vs. (Time and Temperature)
135
140
145
150
155
70 80 90 100
time (min)time (min)
Tem
pera
ture
(°C
)Te
mpe
ratu
re (°
C)
110
• Response surface analysis• Response surface analysis
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.
87.4
±+−= T97.6t69.209.82yield
77.2 73.01
85.991.9
71.2
91.1
86.8 79.3
• Equation for the 22 factorial design:
• Equation for the 22 factorial design:
• Calculated equation for the surface:
• Calculated equation for the surface:
T97.6t69.236.87yield +−=
±−−− Tt58.0T12.3t15.2 22
Yield vs. (Time and Temperature)Yield vs. (Time and Temperature)
140
145
150
155
160
70 80 90 100
time (min)time (min)
Tem
pera
ture
(°C
)Te
mpe
ratu
re (°
C)
110
• Response surface analysis• Response surface analysis
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.
T97.6t69.236.87yield +−= ±−−− Tt58.0T12.3t15.2 22
88
8590
93
Optimum conditions:T = 157 °Ct = 73 minyield: 93%
Optimum conditions:T = 157 °Ct = 73 minyield: 93%
• Sequential nature of experimentation• Sequential nature of experimentation
PlanPlan
Fractional factorial design
Fractional factorial design
Hypercube design in n dimensions
Hypercube design in n dimensions
Design in 2,3,4 dimensions
Design in 2,3,4 dimensions
Full factorial design
Full factorial design
Tranter, R., Design and analysis in chemical research. Sheffield Academic; CRC Press: Sheffield, England, 2000.
Central composite
Central composite
Response surface analysis
Response surface analysis
• Application of response surface analysis• Application of response surface analysis
Owen, M. R.; Luscombe, C.; Lai, L. W.; Godbert, S.; Crookes, D. L.; Emiabata-Smith, D.Org. Proc. Res. Dev. 2001, 5, 308-323.
N
O
HTBSO
R
HO
R''
O
OR'
N
O
HHO
R
HO
R''
O
OR'
N
O
H
O
R H
O
OR'
+TEA•3HF
NMP
1 2 3
reaction condition range units
temperature 10 30 °C
time 19 31 hours
volume of NMP 3 7 mL/g of substrate
equivalents of TEA.3HF 1 1.67 Equivalents
24 central composite
Monitored results:• % yield of alcohol• % lactone• % remaining silyl ether
24 central composite
Monitored results:• % yield of alcohol• % lactone• % remaining silyl ether
• Application of response surface analysis• Application of response surface analysis
Owen, M. R.; Luscombe, C.; Lai, L. W.; Godbert, S.; Crookes, D. L.; Emiabata-Smith, D.Org. Proc. Res. Dev. 2001, 5, 308-323.
N
O
HTBSO
R
HO
R''
O
OR'
N
O
HHO
R
HO
R''
O
OR'
N
O
H
O
R H
O
OR'
+TEA•3HF
NMP
1 2 3
• Application• Application
Owen, M. R.; Luscombe, C.; Lai, L. W.; Godbert, S.; Crookes, D. L.; Emiabata-Smith, D.Org. Proc. Res. Dev. 2001, 5, 308-323.
Predicted conditions product yield (%) impurity (%)
target/constraints T (°C) Time (h) solvent Et3N·3HF predicted actual predicted actual
max yield 19 31 3.6 1.42 95.3 95.8 3.3 3.3
lactone < 2% 17 31 4.8 1.50 94.2 94.0 1.9 1.7
lactone < 1.1% 16 29 5.3 1.68 92.4 93.1 1.1 1.1
lactone < 2%, solvent < 3.5 mL/g 14 31 3.45 1.58 93.9 94.2 1.8 2.0
lactone < 2% Et3 N.3HF < 1.18eq. 28 19.5 7 1.17 93.7 93.4 1.9 2.0
lactone < 2%, time < 23 h 24 23 6.3 1.41 94.2 94.2 2.0 1.9
N
O
HTBSO
R
HO
R''
O
OR'
N
O
HHO
R
HO
R''
O
OR'
N
O
H
O
R H
O
OR'
+TEA•3HF
NMP
1 2 3
• When DoE “fails”• When DoE “fails”
Larkin, J. P.; Wehrey, C.; Boffelli, P.; Lagraulet, H.; Lemaitre, G.; Nedelec, A.Org. Proc. Res. Dev. 2002, 6, 20-27.
entry Ac2 O (equiv)
AcBr (equiv) T (°C)
yield (%)(20 g)
yield(%)(20 kg)
comments
1 3 3.8 23-27 77.3 < 70 original conditions23
1.51
42.5
13-1721-24
75.882.7
–74
optimum of DoEnew conditions
Conditions: t = 4-5h; yield of 2 after crystallization
O
O
ONH
H
O
HO
ONH
H
H1) AcBr, Ac2O, CH2Cl2
2) KOH, MeOH3) HCl, CH2Cl2
1 2
• Outline• 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
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 rather complicated”
• “DoE involves a lot of math, it’s rather complicated”
• People tend not to utilize DoE because of the tedious mathematical manipulations.
• People tend not to utilize DoE because of the tedious mathematical manipulations.
Lendrem, D.; Owen, M.; Godbert, S. Org. Proc. Res. Dev. 2001, 5, 324-327.
• Software• Software
Most commonly used:
• Stat-Ease Design Expert ®
(http://www.statease.com)
• Umetrics MODDE ®
(http://www.umetrics.com)
• S-matrix Fusion Pro ®
(http://www.smatrix.com)
Most commonly used:
• Stat-Ease Design Expert ®
(http://www.statease.com)
• Umetrics MODDE ®
(http://www.umetrics.com)
• S-matrix Fusion Pro ®
(http://www.smatrix.com)
• What if I need to run >24 experiments?• What if I need to run >24 experiments?
Harre, M.; Tilstam, U.; Weinmann, H. Org. Proc. Res. Dev. 1999, 3, 304-318.
The answer is to use automation
• Some features of automated systems, commercially available:Up to 100 simultaneous reactionsAutomated liquid handler
Vessel volume: 100 μL 250 mLTemperatures: -100 °C 350 °C
Reflux, N2 blanketing, automated N2/vacuum manifold
On-line HPLC
The answer is to use automation
• Some features of automated systems, commercially available:Up to 100 simultaneous reactionsAutomated liquid handler
Vessel volume: 100 μL 250 mLTemperatures: -100 °C 350 °C
Reflux, N2 blanketing, automated N2/vacuum manifold
On-line HPLC
• Example of the use of automation• Example of the use of automationAr
OH
HO
R
O
R
ArPPh3, DIAD
toluene50 - 70 %
Important factors: ratio DIAD/alcohol, alcohol, temperature Important factors: ratio DIAD/alcohol, alcohol, temperature
• System:Automated liquid handlerOn-line HPLC
• Reaction conditions:A equivalents of alcoholB equivalents of DIADC volume of tolueneD temperatureE addition rate of DIAD
• 20 experimental runs• Total research time: 5 days
• System:Automated liquid handlerOn-line HPLC
• Reaction conditions:A equivalents of alcoholB equivalents of DIADC volume of tolueneD temperatureE addition rate of DIAD
• 20 experimental runs• Total research time: 5 days
Emiabata-Smith, D. F.; Crookes, D. L.; Owen, M. R. Org. Proc. Res. Dev. 1999, 3, 281-288.
• Why DoE methods are ideal for us• Why DoE methods are ideal for us
Further exploration would lead us to obtain > 94% yield
Further exploration would lead us to obtain > 94% yield
1.1 equivalents of DIAD and 1.1 equivalents of alcohol89% yield, almost pure product after workup
1.1 equivalents of DIAD and 1.1 equivalents of alcohol89% yield, almost pure product after workup
Emiabata-Smith, D. F.; Crookes, D. L.; Owen, M. R. Org. Proc. Res. Dev. 1999, 3, 281-288.
• Some final comments• Some final comments
• DoE offers powerful mathematical models that are applicable to the behavior of organic reactions
• DoE methods are a daily practice in industrial chemistry. Current applications and results are not being published
• DoE is not a substitute for creative chemistry, but it can be a great supplement
• DoE offers powerful mathematical models that are applicable to the behavior of organic reactions
• DoE methods are a daily practice in industrial chemistry. Current applications and results are not being published
• DoE is not a substitute for creative chemistry, but it can be a great supplement
• DoE is a tool• DoE is a tool
• A tool… like a hammer
• The only way to know how it works is to use it
• If you don’t try it, you will never know that it actually works
• When you get used to the hammer, you wouldn’t use a rock again
• A tool… like a hammer
• The only way to know how it works is to use it
• If you don’t try it, you will never know that it actually works
• When you get used to the hammer, you wouldn’t use a rock again
Lendrem, D.; Owen, M.; Godbert, S. Org. Proc. Res. Dev. 2001, 5, 324-327.
• Acknowledgements• Acknowledgements
Prof. Maleczka
Prof. Walker
The Maleczka groupNicki, Jill, Monica, Feng, Soong-Hyun (Kim),
Il Hwan, Bani, and Kyoungsoo
Aman, Aman, Toyin, Calvin
Prof. Maleczka
Prof. Walker
The Maleczka groupNicki, Jill, Monica, Feng, Soong-Hyun (Kim),
Il Hwan, Bani, and Kyoungsoo
Aman, Aman, Toyin, Calvin