CHAPTER 1: INTRODUCTION: STRATEGIES ON DIFFERENT LEVELS IN ORGANIC
SYNTHESIS 1
1.1 The target ................ ............... .... 2
1.2 The synthetic path .............................. 3
1.3 The synthetic reaction ................... ......... 4
1.4 Strategies for elaborating synthetic reactions . ............... 7
1.5 Theme and variations ... ........ .................. 8
CHAPTER 2: EXPERIMENTAL STUDY OF REACTION
CONDITIONS. INITIAL REMARKS 15
2.1 Organic synthesis and experimental design . ................ 15
2.2 How to approach the problem ................... .. . . 16
2.3 Concretisation of the problem . ................... ... 18
2.4 Screening and optimisation ........ .......... ........ 20
2.5 When to use multivariate designs? . .................. ... 23
CHAPTER 3: MODELS AS TOOLS 27
3.1 Synthetic chemistry and quantitative models . ............... 28
3.2 Local models by Taylor expansions of the response function ....... . 29
3.3 Initial aspects on modelling ................... ...... 39
3.4 Modelling ................................... 43
3.5 Significance of estimated model parameters ..... ........... . . . 54
3A Least squares fit of response surface models . ............... 65
CHAPTER 4: GENERAL OUTLINE OF SCREENING EXPERIMENTS 67
4.1 Some initial questions and comments ................... . 67
4.2 Steps to be taken in a screening experiment . ............... 68
4.3 Example: Synthesis of 1,4-dibromobenzene .......... ..... .. 81
CHAPTER 5: TWO-LEVEL FACTORIAL DESIGNS 87
5.1 Introductory remarks ................... ... .... .. 87
5.2 Different representations of factorial designs . ............... 89
5.3 Generalisation to any number of factors ............. . ..... 94
5.4 Examples of two-level factorial designs . .................. 101
5.5 Quality of model parameters ................... ...... 110
5.6 Suggestions for further reading .. . . .... ...... . ..... . . 114
CHAPTER 6: TWO-LEVEL FRACTIONAL FACTORIAL DESIGNS 119
6.1 Introductory remarks ............................. 119
6.2 How to construct a fractional factorial design . ............... 120
6.3 What is lost by using fractional factorial designs . ............. 123
6.4 Example: Synthesis of a semicarbazone . .................. 129
6.5 How to separate confounded effects ................... .. 135
6.6 Normal probability plots ................. .......... 142
6.7 Other uses of normal probability plots . .................. 155
6.8 Running experiments in blocks. ................... .... 159
6.9 All runs in a fractional factorial design are useful . ............ 164
CHAPTER 7: OTHER DESIGNS FOR SCREENING EXPERIMENTS 169
7.1 Redundancy can be expensive ................... .. ... 169
7.2 Plackett-Burman designs ................... ........ 169
7.3 Screening by D-optimal designs ................... .... 172
7.4 Suggestions for further reading ................... ..... 179
7A Confounding pattern in Plackett-Burman designs . ............ 183
7B Algorithms for the construction of D-optimal designs . .......... 186
7C Some comments on the "optimality" of a design . ............. 190
CHAPTER 8: SUMMARY OF SCREENING EXPERIMENTS 195
8.1 Objectives ....... ............................ 195
8.2 Steps to be taken in a screening experiment . ............... 196
CHAPTER 9: OPTIMISATION 201
9.1 The problem ................... ......... ...... 201
9.2 The methods ......... . . ... ........ ............ 202
9.3 The requisites ............. .................... 203
CHAPTER 10: STEEPEST ASCENT 207
10.1 Principles ................... ............. ..207
10.2 Advantages and disadvantages of steepest ascent . ............. 216
CHAPTER 11: SIMPLEX METHODS 219
11.1 A sequential technique ....... ................. ... 219
11.2 How to use a simplex for optimisation. . ................... 221
11.3 The Basic simplex method ................... .... ... 227
11.4 Modified simplex methods ... ................... .... 232
11.5 A few comments on the choice of simplex method . ........... . 238
11.6 Suggestions for further reading .... ................... . 239
CHAPTER 12: RESPONSE SURFACE METHODS 243
12.1 Preliminaries .............. ................... 243
12.2 Step-wise strategy by composite designs .......... ........ 246
12.3 Validation of the model ................... ...... ... 252
12.4 Optimum conditions ..... ................... ..... 256
12.5 Canonical analysis .............. ................ 259
12.6 Visualisation by projections . ................... ..... 277
12.7 Other designs for quadratic models ................... .. 280
12.8 More than one response ................... ........ 289
12.9 Links between theory and experiments .......... ....... . 300
12A Obtaining a diagonal dispersion matrix . .................. 311
12B Transformation of response variables ................... . . . 314
CHAPTER 13: REACTION KINETICS BY SEQUENTIAL RESPONSE
SURFACE MODELLING 321
13.1 Yield evolution and rates ....... ............. ... ... 321
13.2 Outline of the principles . ..... ................. .. . 322
13.3 Example: A rate model ................... ..... ... 325
13.4 A real experiment: Williamson ether synthesis ....... .. ... ... 329
13.5 A note on statistics ....... ............. .......... 334
13.6 Comments ................... ............. ..335
CHAPTER 14: SUMMARY OF STRATEGIES FOR EXPLORING THE
EXPERIMENTAL SPACE 339
14.1 Benefits of a step-wise strategy ......... .............. 339
14.2 Flow sheet to define a strategy ................... .. . .. 340
CHAPTER 15: THE REACTION SPACE 343
15.1 What is the reaction space? ................... ...... 343
15.2 A design which varies more than one factor is necessary . ......... 345
15.3 Interdependencies ............. .................. 345
CHAPTER 16: PRINCIPAL PROPERTIES 351
16.1 Molecular properties ..... ................. ....... 351
16.2 Geometrical description of PCA ................ ....... 355
16.3 Mathematical description of PCA and FA . ................ 365
16.4 Some general aspects on the use of PCA ........... ....... 379
16.5 Some examples of principal properties in organic synthesis . ....... 383
16.6 Summary .................. ............. ..391
16.7 Suggestions for further reading ................... ..... 392
16A On factoring of matrices ................... ..... .. . 397
16B The NIPALS algorithm ........................... 400
CHAPTER 17: STRATEGIES FOR THE SELECTION OF TEST SYSTEMS 403
17.1 Selection of solvents by their principal properties ... ....... ... 404
17.2 Selection according to the principles of factorial design .. .. .... .. 412
17.3 Example of experimental design in principal properties ....... .. . 413
17.4 Conclusions .. ................. ................ 421
CHAPTER 18: QUANTITATIVE RELATIONS: OBSERVED RESPONSES AND
EXPERIMENTAL VARIATIONS 425
18.1 The problem . .............. . .. ............... ..425
18.2 Multiple regression cannot always be used ........ ......... 426
18.3 PLS .... ... . . . . . .......... ............... 435
18.4 Cross validation of the PLS model ......... ... . ......... 439
18.5 Plots from the PLS model ....... ............ ....... 441
18.6 Examples on the use of PLS modelling in organic synthesis . ....... 442
18.7 Inverse PLS ................ .......... .... ... . . 448
18.8 Conclusions ................ .................. 460
18.9 Suggestions for further reading ......... ... . ......... 460
18A Reaction systems ............. .................. 465
CHAPTER 19: EXPLORING DISCRETE VARIATIONS: NEAR-ORTHOGONAL
EXPERIMENTS BY SINGULAR VALUE DECOMPOSITION 471
19.1 Introduction ..... . . ........ ................. .... 471
19.2 Method .............. .. ................. 474
19.3 An example: The Fischer indole synthesis .... ............. 478
19.4 Sequential experimentation ................... ....... 479
19.5 Some comments ................. ........ ...... 480
19.6 A note on D-optimal designs ................. ........ 482
19.7 Summary of the strategy .......... ........... ...... 482
19A Minimising E {TXtTXtEI} .. . . ....................... 487
CHAPTER 20: OPTIMIZATION WHEN THERE ARE SEVERAL RESPONSES VARIABLES 489
20.1 Introduction ................. ............. ..489
20.2 Response matrix ........ .......... ............. 490
20.3 Connecting the response space to the experimental space . ....... 493
20.4 Types of problems ....... ........ ............. 503
20.5 Summary and some advice . . . ......... ......... ... .. 505
CHAPTER 21: A METHOD FOR DETERMINING SUITABLE ORDER OF
INTRODUCING REAGENTS IN "ONE-POT" PROCEDURES 509
21.1 The problem .............. ......... ..... ...... 509
21.2 Strategy ........ ............................ 510
21.3 Example: Self-condensation of 3,3-dimethyl-
2-butanone ................... ............... 512
21.4 A note on "ad hoc" explanations .............. ........ 513
CHAPTER 22: BOOKS, JOURNALS, AND COMPUTER PROGRAMS 517
22.1 Books ................... .............. .. 517
22.2 Journals ........... ......................... 519
22.3 Computer programs ................... ......... . 519
CHAPTER 23: CONCLUDING REMARKS 527
23.1 Comments on statistics and chemistry ............. .. .... 527
23.2 Strategies for analysing synthetic reactions .......... .. .. .. . 529
EPILOGUE 535
APPENDIX A: MATRIX ALGEBRA 537
A.1 Definitions ............ ................... .... 537
A.2 Matrix operations .............. ................. 540
APPENDIX B: STATISTICAL TABLES 551
B.1 Table B1, t-distribution ................... ........ 551
B.2 Tables B2-B4, F-distribution ............. ........... 552
B.3 Sources . ............ ......................... 553