This discussion pertains to the most efficient method to discover higher yield/lower cost procedures for a chemical transformation; this is the individual reaction step optimization aspect of process development. For those to whom optimization strategies are a new subject, this article is not a good place to start. The discussion is geared towards chemists who have applied, or tried to apply such optimization methods as factorial designs, fractional factorial designs, D-optimal designs, the technique of steepest ascent, or simplex optimization. Although using optimization methods I have had some spectacular successes by comparison with one-variable-at-a-time or the intuitive approaches, I have been partially dissatisfied for two reasons:
- The reagent choice, solvent choice and catalyst or other excipient (acid/base etc) variables are discrete and not continuous.
- The randomness required to make good statistics seems to throw away most of the chemist’s book learning.
With respect to the first point; once I had by some means settled upon the reagent and general protocol for the reaction, optimizing the yield by adjusting continuous variables proceeded well but I felt that getting to the particular reagent and its methodology of use was by happenstance and I had not given other choices a fair shake.
With respect to the second point; because statistics asks one to consider at the outset a large reaction space it takes quite a few experiments to get back, quite often to where one intuitively would have begun.
When a chemical synthesis route is selected, the responsible chemists have a certain confidence that after some experimentation each chemical transformation can be made to proceed in an acceptable yield and the intermediates all recovered in an acceptable purity. Those chemists that chose a particular route (sequence of reaction steps) from among all other possibilities, have this confidence in each of the required chemical steps because, based on their experience, inference, intuition and analogies, they expect that the combination of the particular starting material, particular reagent, particular solvent(s) and particular reaction conditions will deliver a satisfactory result.
What needs to be worked out is the research program; the menu of experiments that will lead expeditiously to validating this anticipated outcome.
I propose that a pragmatic and rational development program should start with the information, which gave the creators of the route confidence that the chemical step being studied was do-able. As process chemists, the first thing we would like to know is, if we test the most preferred combinations of reagent/solvent/auxiliary chemicals using typical reaction parameters, whether we are likely to achieve a satisfactory result or whether we need to find or devise, and test other combinations in order to achieve the minimum acceptable yield and purity. I think there is a statistically sound method to answer this question and that is what is discussed below.
Dr. Charles Hendrix, in Chemtech, August 488-496, 1980, published an article, Through the response surface with test tube and pipe wrench which taught that in the beginning of a study completely random experimentation within a defined reaction space can actually quantify how likely it will be to achieve a yield matching or exceeding a target yield set by the chemist. This article is the most useful I have found in my career for chemical process optimization.
Hendrix makes the point that the problem with statistical optimization is that too many of the experiments are performed far away from the higher yield region and too few close to it.
The beauty of the Hendrix approach is that the initially defined reaction space can, it seems, be the sum of several smaller reaction spaces, which allow these smaller reaction spaces to be dedicated to non-continuous variables. Taking a simple example, if I am studying an acetylation, one part of the acetylation reaction space could be using acetic anhydride and one part of the reaction space should be done with acetyl chloride. After 13 randomly selected conditions selected from the whole reaction space, I would be able to express as a percent the likelihood of reaching a specific yield target by looking within the reaction space- either of acetyl chloride or acetic anhydride used within a particular range of stoichiometry, temperature, and other continuous variable conditions.
If I am happy with the odds of achieving my target yield, I can continue experimentation within the reaction space defined, using any of the standard optimization methods and usually starting at my best random result. If I am unhappy with the odds of achieving my target yield, I can change the reaction space by adding new discrete variables, such as, for example, 4-dimethylaminopyridine catalysis, and repeat 13 random experiments in the new reaction space and get a new estimate of success.
Hendrix’s approach, as particularly applied to include discontinuous variables, addresses my two dissatisfactions. First, the chemist’s knowledge of reagent choices that will work, used in the initial route election, is now used to choose the sub-domains for the random search. Second, one gets an early estimate of the likelihood of success so that one can quickly start optimizing in the correct reaction sub-domain starting with the best result up to that point.
This may made clearer by working through a simple example showing how a process research chemist would experiment to test whether one of a number of reagent/solvent choices would be likely to achieve a yield of 80% or higher in a particular case.
The specific question that I will use in the test is: Can we expect to be able to selectively oxidize 7-methyl-2,6-octanediol, to 6-hydroxy-7-methyloctan-2-one in greater than 80% yield using one of the following literature methods (A B C D or E):
A.
Douglas F. Taber, John C. Amedio, Jr. and Kang-Yeoun Jung. J. Org. Chem. 52, 5621 (1987). P2O5 / DMSO / Triethylamine (PDT): A Convenient Procedure for Oxidation of Alcohols to Ketones and Aldehydes.
The method is applicable on a large scale, is selective and uses neither cryogenic methods nor heavy metals.
B.
E. J. Corey and C.U. Kim. Tet. Lett. 12, 919 (1973). Oxidation of Primary and Secondary Alcohols to Carbonyl Compounds using Dimethyl Sulfoxide-Chlorine Complex as Reagent.
The complex reacts with primary and secondary alcohols followed by a tertiary amine to give a ketone. Double bonds are chlorinated. The reaction occurs at –45 C.
C.
E.J. Corey, Ernie-Paul Barrette and Plato A. Magriotis, Tet. Lett. 26(48), 5855 (1985). A New Cr(VI) Reagent for the Catalytic Oxidation of Secondary Alcohols to Ketones.
A new process is described for the oxidation of secondary alcohols to ketones using peroxyacetic acid in the presence of a catalytic amount of 2,4-dimethylpentane-2,4-diol cyclic chromate. As little as 2 mole percent of catalyst is often needed. the reaction proceeds in methylene chloride/carbon tetrachloride mixtures. the catalyst is produced in carbon tetrachloride solution. The peracid used was in ethylacetate solution. For isolation the mixture was diluted with 9:1 hexane / ether and filtered through silica gel to remove the chromium species. The reaction occurs at near zero Centigrade. The simplicity and economy of the method recommend it for large scale work. The method is likely to be sensitive to steric conditions around the alcohol group.
D and E.
Michael P. Doyle, Robert L. Dow, Vahid Bagheri, and William J. Patrie, Tet. Lett. 21 2795 (1980). Selectivity in Oxidation of Diols.
Oxidation of 2,2-disubstituted –1,4-butanediols by the combination of nickel(II) bromide and benzoyl peroxide or by trityl tetrafluoroborate produce ββ-disubstituted-γ-butyrolactones with exceptional selectivity. The less sterically hindered alcohol is preferentially oxidized by these reagents.
All of the reagents are known from literature precedent to be able to oxidize secondary alcohols to ketone. In the example the particular problem is whether we can expect to selectively oxidize a less hindered secondary alcohol is the presence of another more hindered secondary alcohol. We want to know how likely it is that if we explore the reaction space which includes all five of the above literature methods (D and E are in the same paper), we will find a set of conditions which will give a yield of the product (or the equivalent cyclized hemiketal) greater or equal to 80%.
In order to answer this question using Monte-Carlo methods, Hendrix teaches that we must first very precisely specify the reaction space to be explored. For simplicity in these cases we could, for example, say that wherever a tertiary amine is used in any of the methods, it will be triethylamine.
Specifying the limits for each particular sub-domain reaction space we could specify:
Condition A reaction space comprises (0.9-2.7 equivalents of phosphorus pentoxide); (1.—3.0 equivalents of DMSO); methylene chloride solvent and 1.75-5.25 equivalents of triethylamine at 0-30˚C.
Condition B would encompass 1-4 mol. equivalents of chlorine combined with 5 mol equivalents of DMSO based on the chlorine and 1-4 equivalents of triethylamine compared to the chlorine equivalents. The solvent is to be methylene chloride and the reaction temperature –45˚C with quenching at –45 to 25 C˚ with immediate neutralization of the excess oxidant.
Using method C, the chromium catalyst complex should be between 1-4 mol %; the peracetic acid oxidant between 1.5- 3.0 mol. equivalents; the temperature between –20 to +10 C˚; with mixtures of methylene chloride and carbon tetrachloride as solvent. The time should be up to 12 hours.
Using Method D, the reagent combination Ni(II)bromide (1.25- 3.5 mol. equivalents) / benzoyl peroxide (1-4 mol.equivalents), the solvent will be acetonitrile and the temperature will be 40-80˚C and the time up to 48 hours.
Using the reagent trityl tetrafluoroborate, condition E, (1.5-3.5 mol. equivalents), the solvent will be acetonitrile and the temperature range from 40-80˚C. with a time up to 48 hours.
It is important to realize that the reaction condition choices made for the statistical test are not the only ones possible. They are the conditions most optimistic from the perspective of the process chemist. By now performing 13 reactions under conditions randomized within that space, we can predict from the results how likely it will be to obtain the minimum required yield for the step. If the likelihood is excellent, the optimization can be continued within this constrained reaction space using some such process as a directed simplex, starting from the best result and moving in the sub-reaction space of the particular reagent selected. If the probability of reaching the target yield is estimated to be unacceptably low, then the process chemist needs to explore a larger reaction space or a different reaction space that will predict the desired result with a higher likelihood.
To continue working this example I will choose, at random, 13 experiments within the five-reagent reaction space I have defined.
First, I randomly selected how many experiments will be performed in each sub domain. My random selection was that I should perform 3 of the Condition A phosphorus pentoxide/DMSO; two of Condition B which is chlorine/DMSO; five of Condition C which is the chromium catalyst complex; one of Condition D which is the benzoyl peroxide/nickel(II)bromide oxidation and two of Condition E which uses the trityl tetrafluoroborate reagent.
Now I choose using random numbers the actual values of the continuous variables for each sub-domain. In this example:
For Condition A:
Experiment #1
2.7 equivalents of phosphorus pentoxide; 2.0 equivalents of DMSO; 3.5 equivalents of triethylamine at a temperature of 0 C
Experiment #2
0.9 equivalents of phosphorus pentoxide; 2.0 equivalents of DMSO; 1.75 equivalents of triethylamine at a temperature of 15 C
Experiment #3
1.9 equivalents of phosphorus pentoxide; 3.0 equivalents of DMSO; 3.5 equivalents of triethylamine ar a temperature of 15 C
For Condition B:
Experiment #4
1 molar equivalent of chloride and 1 molar equivalent of DMSO and 2 molar equivalents of triethylamine in methylene chloride forming the reagent and doing the initial reaction at –45 C with warming to 0 C and quenching the residual oxidant.
Experiment #5
2 molar equivalent of chloride and 2 molar equivalent of DMSO and 4 molar equivalents of triethylamine in methylene chloride forming the reagent and doing the initial reaction at –45 C with warming to 20 C and quenching the residual oxidant.
For Condition C
Experiment #6
1-4 mol % complex; 1.5-3.0 equiv. peracetic acid; -20 to +10 C; ratio methylene chloride/CCl4 1:1 to 5:1
Experiment #7
4 mol % complex; 2.0 equiv. peracetic acid; -10 C; ratio methylene chloride/CCl4 4:1
Experiment #8
3 mol % complex; 1.5 equiv. peracetic acid; -10 C; ratio methylene chloride/CCl4 3:1
Experiment #9
1 mol % complex; 2.5 equiv. peracetic acid; 0 C; ratio methylene chloride/CCl4 5:1
Experiment #10
2 mol % complex; 3.0 equiv. peracetic acid; +10 C; ratio methylene chloride/CCl4 3:1
For Condition D:
Experiment #11
Ni(II) bromide(2.0 mol. equivalents)/benzoyl peroxide (3 mol. equivalents) the solvent will be acetonitrile and the temperature will be 80 C and the time up to 48 hours.
Condition E :
Experiment #12
(2.0 mol. equivalents), the solvent will be acetonitrile and the temperature will be 60 C. with a time of up to 48 hours.
Experiment #13
(1.5 mol. equivalents), the solvent will be acetonitrile and the temperature 80 C. with a time of up to 48 hours.
I will now consider three different scenarios for the results of the thirteen experiments.
Suppose the results were as shown below designated as Results A. {Alternative possible results will be considered afterward. }
Results A
|
Experiment #
|
Yield
|
Rank Yield
|
Rank
|
(100-Rank)/(N+1)
|
|
1
|
41
|
11
|
1
|
7.1
|
|
2
|
50
|
14
|
2
|
14.3
|
|
3
|
11
|
25
|
3
|
21.4
|
|
4
|
14
|
34
|
4
|
28.6
|
|
5
|
80
|
41
|
5
|
35.7
|
|
6
|
34
|
59
|
6
|
42.9
|
|
7
|
84
|
61
|
7
|
50.0
|
|
8
|
25
|
70
|
8
|
57.1
|
|
9
|
85
|
73
|
9
|
64.3
|
|
10
|
73
|
80
|
10
|
71.5
|
|
11
|
70
|
84
|
11
|
78.5
|
|
12
|
61
|
85
|
12
|
86.7
|
|
13
|
88
|
88
|
13
|
92.8
|
Results B
|
Experiment #
|
Yield
|
Rank Yield
|
Rank
|
(100-Rank)/(N+1)
|
|
1
|
30
|
15
|
1
|
7.1
|
|
2
|
63
|
23
|
2
|
14.3
|
|
3
|
65
|
26
|
3
|
21.4
|
|
4
|
26
|
30
|
4
|
28.6
|
|
5
|
37
|
37
|
5
|
35.7
|
|
6
|
15
|
42
|
6
|
42.9
|
|
7
|
50
|
50
|
7
|
50.0
|
|
8
|
23
|
63
|
8
|
57.1
|
|
9
|
75
|
65
|
9
|
64.3
|
|
10
|
94
|
75
|
10
|
71.5
|
|
11
|
42
|
76
|
11
|
78.5
|
|
12
|
91
|
91
|
12
|
86.7
|
|
13
|
78
|
94
|
13
|
92.8
|
Results C
|
Experiment #
|
Yield
|
Rank Yield
|
Rank
|
(100-Rank)/(N+1)
|
|
1
|
0
|
0
|
1
|
7.1
|
|
2
|
45
|
0
|
2
|
14.3
|
|
3
|
0
|
11
|
3
|
21.4
|
|
4
|
11
|
15
|
4
|
28.6
|
|
5
|
15
|
23
|
5
|
35.7
|
|
6
|
32
|
24
|
6
|
42.9
|
|
7
|
53
|
32
|
7
|
50.0
|
|
8
|
33
|
33
|
8
|
57.1
|
|
9
|
44
|
42
|
9
|
64.3
|
|
10
|
24
|
44
|
10
|
71.5
|
|
11
|
60
|
45
|
11
|
78.5
|
|
12
|
42
|
53
|
12
|
86.7
|
|
13
|
23
|
60
|
13
|
92.8
|
Following the teaching of Hendrix in the article noted above if one makes 13 random observations and then ranks them there is a 7.2% chance (100-92.8) of finding a yield greater than the 13th measurement (which is the highest yield obtained) Here, for the A results set, that is 88% within the reaction space defined for these five reagent/condition combinations taken together. So long as the data is reproducible (and the 88% example should be repeated immediately) we know immediately that at least an 88% yield can be obtained using the conditions of experiment #13. Experiment #13 in our example was (1.5 mol. equivalents) of trityl fluoroborate, the solvent acetonitrile and the temperature 80 C with a time up to 48 hours.
Using different numbers, suppose the results were as designated in Results B. Here there is an 7.2% chance (100-92.8) of finding a yield greater than 94% within the reaction space defined for these five reagent/condition combinations taken together. So long as the data is reproducible (and the 94% example should be repeated immediately) we know immediately that at least a 94% yield can be obtained using the conditions of Experiment #10. Experiment #10 was 2 mol % chromium diol complex; 3.0 equiv. peracetic acid; +10 C; methylene chloride/CCl4 ratio 3:1.
But these results may all be more optimistic than might be obtained. Using a different set of random numbers suppose the results were as shown in designated Results C above. These results predict that there is only a 7% probability of finding a yield greater than 60% in the reaction space made up of conditions A, B, C, D or E. The most promising result is that only a single experiment was conducted with discrete variables of Condition D; that is Ni(II) bromide(2.0 mol. equivalents)/benzoyl peroxide (3 mol. equivalents), solvent acetonitrile and the temperature 80 C and the time up to 48 hours, yet it was the highest of the yields. If the reaction space was now restricted to the D reagent and new random conditions were selected within that subspace a higher yield might be obtained. Another indication from these thirteen experiments in Result Set C is that Condition A where three experiments were conducted (0%, 0%, and 11%) is not promising. Condition C, using the cyclic chromate catalyst, was the sub-domain where five experiments were performed and all of these were less than 43%. This limited data suggests that further variation within the selected ranges of these parameters will not be so promising.
The random yield numbers for these model outcomes were selected from a universe of yield numbers chosen to represent different yield distributions. The number of experiments to be performed in each sub-domain comprising a particular reagent was selected by choosing four random numbers from the numbers 1-5. The number of experiments in the fifth sub-domain was 13 – (the total of the first four numbers chosen). In the event, the numbers were 3,2,5,1, (13-11=2). That is there were three experiments with Condition A; two with condition B; five with condition C; one with Condition D; and two with Condition E.
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