Multidimensional free energy relationships in asymmetric catalysis

Asymmetric catalysis is a powerful method for synthesizing enantiomerically enriched chiral building blocks. Detailed understanding of how catalysts impart facial bias on prochiral substrates has the potential to enable improved catalyst design and increase catalyst applicability. To this end, linear free energy relationships have been used to relate catalyst properties to enantioselectivity, enabling greater understanding of key catalyst-substrate interactions. Linear free energy relationships also can allow prediction of catalyst performance prior to their preparation. In this dissertation, several linear free energy relationships are described with a focus on developing predictive power and understanding the mechanism of asymmetric induction. In asymmetric catalysis, steric effects are often implicated as key components in imparting enantioselectivity; however, they are typically treated empirically. In Chapter 2, steric parameters, particularly Charton parameters, are used to quantify ligand steric effects in the Nozaki-Hiyama-Kishi allylation of aryl aldehydes and ketones. Multidimensional linear free energy relationships, which simultaneously quantified the steric effects at both positions, are determined and used to predict ligand performance. The multivariate linear free energy relationships have guided the design of a new ligand scaffold capable of enantioselective propargylation of ketones, which is discussed in Chapter 3. The multivariate relationships were expanded to include nonsteric terms, which enabled the development of an electronically and sterically optimized catalytic system for the enantioselective propargylation of ketones, yielding enantioenriched homopropargyl alcohols. The multivariate approach to describing substituent effects in asymmetric catalysis led to the evaluation of Sterimol parameters. Chapter 4 gives five examples of data sets where Sterimol values led to better correlation and predictive power than the previously used Charton parameters. The computational basis of the Sterimol parameters allows for greater interpretation of the models in which they are utilized. Quantifying the factors that lead to enantioselective outcomes is a key challenge in asymmetric catalysis. Combining steric parameters, multidimensional analysis, and the principles of experimental design can lead to increased predictive power in asymmetric catalysis.

MULTIDIMENSIONAL FREE ENERGY RELATIONSHIPS IN ASYMMETRIC CATALYSIS by Kaid Clifton Harper A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Chemistry The University of Utah May 2013 Copyright © Kaid Clifton Harper 2012 All Rights Reserved The Unive r si t y of Utah Graduat e School STATEMENT OF DISSERTATION APPROVAL The dissertation of Kaid Clifton Harper has been approved by the following supervisory committee members: Matthew S. Sigman Chair 11-27-2012 Date Approved Gary Keck Member 11-27-2012 Date Approved Ryan Looper Member 11-27-2012 Date Approved Joel Harris Member 11-27-2012 Date Approved Eric Schmidt Member 11-27-2012 Date Approved and by Henry White the Department of Chemistry Chair of and by Donna M. White, Interim Dean of The Graduate School. ABSTRACT Asymmetric catalysis is a powerful method for synthesizing enantiomerically enriched chiral building blocks. Detailed understanding of how catalysts impart facial bias on prochiral substrates has the potential to enable improved catalyst design and increase catalyst applicability. To this end, linear free energy relationships have been used to relate catalyst properties to enantioselectivity, enabling greater understanding of key catalyst-substrate interactions. Linear free energy relationships also can allow prediction of catalyst performance prior to their preparation. In this dissertation, several linear free energy relationships are described with a focus on developing predictive power and understanding the mechanism of asymmetric induction. In asymmetric catalysis, steric effects are often implicated as key components in imparting enantioselectivity; however, they are typically treated empirically. In Chapter 2, steric parameters, particularly Charton parameters, are used to quantify ligand steric effects in the Nozaki-Hiyama-Kishi allylation of aryl aldehydes and ketones. Multidimensional linear free energy relationships, which simultaneously quantified the steric effects at both positions, are determined and used to predict ligand performance. The multivariate linear free energy relationships have guided the design of a new ligand scaffold capable of enantioselective propargylation of ketones, which is discussed in Chapter 3. The multivariate relationships were expanded to include nonsteric terms, which enabled the development of an electronically and sterically optimized catalytic system for the enantioselective propargylation of ketones, yielding enantioenriched homopropargyl alcohols. The multivariate approach to describing substituent effects in asymmetric catalysis led to the evaluation of Sterimol parameters. Chapter 4 gives five examples of data sets where Sterimol values led to better correlation and predictive power than the previously used Charton parameters. The computational basis of the Sterimol parameters allows for greater interpretation of the models in which they are utilized. Quantifying the factors that lead to enantioselective outcomes is a key challenge in asymmetric catalysis. Combining steric parameters, multidimensional analysis, and the principles of experimental design can lead to increased predictive power in asymmetric catalysis. iv For my wife and parents. TABLE OF CONTENTS ABSTRACT.....................................................................................................................................................................................iii LIST OF ABBREVIATIONS.....................................................................................................................................................viii ACKNOWLEDGMENTS.........................................................................................................................................................xiv Chapter 1. LINEAR FREE ENERGY RELATIONSHIPS IN ASYMMETRIC CATALYSIS.......................................1 Introduction...............................................................................................................................................1 The Curtin-Hammett Principle...................................................................................................... 10 Ligand Electronic Effects in the Mn-catalyzed Epoxidation of c/s-Alkenes............13 Catalyst Acidity in the Organocatalytic Hetero Diels-Alder Reaction.......................20 Polarizability in Thiourea Catalyzed Polyene Cyclization.................................................25 Computed H-bond Length in the Asymmetric Strecker Reaction...............................29 Charton Steric Parameters in Asymmetric Nozaki-Hiyama-Kishi Allylation of Carbonyls ..................................................................................................................................................35 Conclusion ...............................................................................................................................................39 References...............................................................................................................................................41 2. DEVELOPMENT OF STERIC-BASED THREE DIMENSIONAL LINEAR FREE ENERGY IN NOZAKI-HIYAMA-KISHI ALLYLATION REACTIONS.............................................................................46 Introduction............................................................................................................................................ 46 Library Design and Synthesis.......................................................................................................... 47 Developing a Model ............................................................................................................................53 The Principles of Experimental Design Applied to Asymmetric Catalysis...............70 Reevaluation of the Data.................................................................................................................. 75 Conclusion...............................................................................................................................................81 Experimental..........................................................................................................................................83 References ............................................................................................................................................ 111 3. 3D FREE ENERGY RELATIONSHIPS AND THE PROPARGYLATION OF KETONES..............114 Introduction..........................................................................................................................................114 Library Evaluation of the NHK Propargylation of Ketones........................................... 117 Ligand Redesign ..................................................................................................................................119 Synthesis of the Quinoline-Proline Ligand Library........................................................... 123 Model Determination for the Quinoline-Proline Library..............................................129 Conclusion............................................................................................................................................ 137 Experimental.......................................................................................................................................138 References............................................................................................................................................ 165 4. MULTIDIMENSIONAL STERIC PARAMETERS IN THE ANALYSIS OF ASYMMETRIC CATALYTIC REACTIONS.................................................................................................................................... 170 Introduction..........................................................................................................................................170 Comparison of Steric Parameters.............................................................................................171 Sterimol Parameters........................................................................................................................ 175 Application of the Charton Parameter to Asymmetric Catalysis..............................177 Analysis of the NHK Allylation Reactions Using Sterimol Parameters...................183 Evaluation of Substrate Steric Effects for the Desymmetrization of Bisphenols................................................................................................187 Sterimol Analysis of the NHK Propargylation Reaction..................................................194 Conclusion ............................................................................................................................................ 199 Experimental.......................................................................................................................................200 References ............................................................................................................................................ 220 v ii LIST OF ABBREVIATIONS 1-Ad 1-adamantyl 3D three dimensional Ac acetyl AcCl acetyl chloride Ac2O acetic anhydride AcOH acetic acid AIBN azobisisobutyronitrile aq. aqueous Ar aryl atm atmosphere BINAP 2,2'-bis(diphenylphosphino)-1,1'-binaphthyl BINOL 1,1'-Bi-2-naphthol Boc tert-butoxycarbonyl Bn benzyl bs broad singlet BTM benzotetramisole Bu butyl iBu iso-butyl IBCF iso-butyl chloroformate tBu tert-butyl C coefficient value matrix °C degrees Celsius calcd calculated Cbz carbobenzyloxy CHCl3 chloroform cm centimeter CoMFA comparative molecular filed analysis Cr chromium Cy cyclohexyl d doublet A heat DAST diethylaminosulfurtrifluoride DCC N,N'-dicyclohexylcarbodiimide DCE 1,2-dichloroethane DCM dichloromethane dd doublet of doublets ddd doublet of doublet of doublets DMAP 4-dimethylaminopyridine DMf dimethylformamide DMS( dimethyl sulfoxide dr diastereomeric ratio EDCI 1-Ethyl-3-(3-dimethylaminopropyl)carbodiimide ee enantiomeric excess equiv. equivalents ix er enantiomeric ratio ESI electrospray ionization Et ethyl Et2O diethyl ether EtOAc ethyl acetate EtOH ethanol FTIR fourier transform infrared spectroscopy g gram GC gas chromatography h hour H-bond hydrogen bond hv ultraviolet light HDA hetero-Diels-Alder Hep 4-heptyl HPLC high pressure liquid chromatography HRMS high resolution mass spectrometry Hz Hertz IBCF /so-butylchloroformate IR infrared spectroscopy K equilibrium constant k rate constant L liter LAH lithium aluminum hydride LFER linear free energy relationship x LOO leave-one-out ln natural logarithm m multiplet M molar m meta Me methyl MeCN acetonitrile MEK methyl ethyl ketone MeOH methanol mg milligram MHz megaHertz min minute mL milliliter ^L microliter mmol millimole ^mol micromole mol mole MM molecular mechanics Mn manganese MP melting point MS mass spectrometry NBS N-bromosuccinimide NHK Nozaki-Hiyama-Kishi NMM N-methylmorpholine Xi NMR nuclear magnetic resonance Nu nucleophile o ortho obsvd. observed OTf trifluoromethylsulfonate p para Pd/C palladium on carbon Ph phenyl PG undefined protecting group PMA phosphomolybdic acid stain ppm parts per million iPr iso-propyl iPrOH iso-propyl alcohol q quartet QM quantum mechanical quinox quinoline oxazoline QuinPro quinoline-proline QSAR quantitative structure-activity relationship R universal gas constant RDS rate determining step Rf retention factor RT room temperature s singlet or second SFC supercritical fluid chromatography x ii STD DEV standard deviation sub substrate T temperature t triplet TBAF tetrabutylammonium fluoride TBS ferf-butyldimethylsilyl TEA triethylamine THF tetrahydrofuran TLC thin layer chromatography TMSCl trimethylsilylchloride tol toluene TsCl poro-toluenesulfonyl chloride UV ultraviolet V variance-covariance matrix vs. versus X design matrix Y response matrix x iii ACKNOWLEDGMENTS Writing this dissertation has made me reflect on my entire education; in doing so, I have realized that all my achievements have been made possible by the help and sacrifice of many. First, I acknowledge and thank my advisor Matt Sigman for his mentorship and friendship. Over the past four years, he has taught me a great deal about many subjects ranging from organic chemistry to mentoring, and I appreciate his patience with me as I developed my abilities. I also appreciate the effort he puts forward in creating a group learning environment and high scientific standards. I am thankful to past and present members of the Sigman group for their support and friendship. Specifically, I would like to thank Katrina Jensen for her kindness and also for her musings, which eventually turned into my initial project. I would like to thank Laura Steffens for her friendship from my first day of graduate school. I would most like to thank Ryan Deluca, Rachel Vaden and Benjamin Stokes, whose friendship over the years has made the lab one of the most enjoyable work experiences, even when facing difficulties. I am grateful to Elizabeth Bess for both her insight and collaboration on this project. I would also thank Katie Schafer, whose contributions as an undergraduate helped to define this work, and whose eventual friendship has eased the next transition in my life. After 25 nearly continuous years of formal education, I have been the beneficiary of wonderful and dedicated teachers, and I thank all of them. From elementary to high school, I was continually challenged by these dedicated individuals who are too numerous to mention specifically. From my undergraduate experience, I thank Professor Merritt Andrus and Mike Christiansen, who mentored me and helped develop my love of physical organic chemistry. From my graduate experience, I would also thank my committee members, each of which is a wonderful teacher. Specifically, I am grateful to Professor Joel Harris without whose help this project would not have taken shape. Finally, I thank my family for their constant support and love. For my parents Kelly and Carilee, who are the greatest teachers I have ever known. All that I have that is good in me is from them. Most especially, I thank my wife, Jenny, whose constant love and support has allowed me to endure the difficult moments and rejoice in the happy moments. I am grateful for her sacrifices to allow me to pursue my education. I dedicate all of my work, past and future, to her. x v CHAPTER 1 LINEAR FREE ENERGY RELATIONSHIPS IN ASYMMETRIC CATALYSIS Introduction Nobel Laureate William Knowles once wrote, "Since achieving 95% [enantiomeric excess] only involves energy differences of about 2 kcal [per mol], which is no more than the barrier encountered in a simple rotation of ethane, it is unlikely that before the fact one can predict what kind of ligand structures will be effective."1 True to this statement, the field of asymmetric catalysis has relied on empiricism to develop catalysts. The challenge and the inherent interest in asymmetric catalysis is controlling the finite energies associated with asymmetric induction. This challenge is juxtaposed to the considerable potential that the enantioenriched products possess in synthetic chemistry. Even as the number of reported asymmetric catalytic methodologies expands at a rapid rate, the number of tools available to probe the origin of enantioselectivity in reactions remains relatively stagnant. However, if new reactions are to be applied broadly in organic synthesis, often additional studies must be performed beyond the initial report to ensure applicability to a desired substrate. Therefore, in general, synthetic chemists are not as willing to explore recently reported reactions where effort is required to generate the catalyst and the results are not certain or predictable. A modern goal in asymmetric catalysis is to provide a degree of predictability to these reaction outcomes and in so doing increase their implementation and acceptance in mainstream organic synthesis. Prediction of enantioselective outcomes not only holds considerable potential in applying asymmetric reactions in synthetic chemistry but also presents a powerful tool in designing and optimizing catalysts within the field itself. Development of asymmetric catalysts is often a time consuming and difficult process. Two primary paths towards catalyst optimization have been reported in the literature. The first is using a combinatorial chemistry approach by evaluating a large number of catalysts. This approach is often multigenerational with the highest performing catalysts becoming "parents" of further generations. A requirement in this approach is a modular ligand scaffold compatible with high throughput synthetic methods. The second path utilizes single catalyst probes designed to elucidate key elements responsible for enantioselectivity. This step-by- step approach is more hypothesis oriented but often requires a significant synthetic effort to create each meaningful catalyst probe. If the goal of developing new asymmetric catalytic reactions is simply generating high enantiomeric excess, at present there is no clear advantage in either path when more often than not the two paths converge. In attempts to streamline and quantify catalyst performance, several techniques capable of predicting or correlating enantioselectivity have emerged. A purely computational approach has been applied to several systems, often with positive results.2-9 A recent example from Houk and coworkers demonstrates how state-of-the-art computation techniques can be applied in organocatalysis.10 They examined the benzotetramisole-catalyzed dynamic kinetic resolution of azlactones first reported by Birman and Li shown in Figure 1.1.11,12 The resolution of azlactones is interesting synthetically because it provides direct access to enriched amino acid derivatives from racemic starting materials. Using a simplified system, B3LYP/6-31-G(d) calculations of the (R) and (S) transition states predicted only low enantioselectivity (AAG* = -0.2 kcal/mol) and opposite facial selectivity to that observed. To overcome the underestimated 2 3 M , Ph (S)-BTM BzOH Ri o eOBz BTM NHBz R 2Q H R1 o O-Ro NHBz Figure 1.1. The benzotetramisole-catalyzed dynamic kinetic resolution of azlactones. energy, Houk and coworkers turned to specialized functionals and hybrid basis sets shown in Table 1.1. The M06-2X/6-31G(d) geometry optimization gave the best results overall. M06-2X functional has been shown to model nonbonding interactions such as cation-n interactions, n-n interactions and hydrogen bonding with a higher degree of accuracy in several systems (v/da /nfra).13-15 With a reliable calculation of the transitions state structure, the key elements that imparted enantioselectivity became apparent. The cation-n interaction between catalyst and the alcohol nucleophile shown in Figure 1.2 rigidifies both diastereomeric transition states. The rate amplification responsible for resolution lies in the stabilization of the acyl anion by the benzoyl group in the transition state that leads to the major enantiomer (Figure 1.2). This type of carbonyl-carbonyl interaction is also found in crystal structures of proteins.16-18 In the transition state leading to the minor enantiomer, the benzamide is orientated on the opposite side of the molecule and cannot stabilize the approach of the anion-nucleophile adduct. The above example demonstrates that the B3LYP functional has limitations in estimating some types of key interactions present in catalytically relevant transition states.2,3 In transition metal-mediated asymmetric catalysis, a greater challenge exists beyond selecting the correct functional. Molecular mechanics (MM) methods are often used to determine transition state structure where ground-state intermediates on either side of the transition state structure are well-defined energetically. MM methods require specific parameters, which are well-established for organic frameworks but do not exist for many transition metals. Thus, transition states involving metals are calculated using slower quantum mechanical (QM) methods. It is impractical to apply QM methods generally because they are time-consuming even for simple systems. Norrby and coworkers successfully hybridized the two types of calculation into a computational technique, which utilizes the speed of MM and the accuracy of QM in transition metal-mediated catalysis.4,19,20 Essentially, they employ QM calculations of a simplified system 4 5 Table 1.1. Methods of calculation used to predict the enantioselectivity (AAG*) in the kinetic resolution of azlactones. [Data from 10] AAG* Method_________ (kcal/mol) Experimental Data 1.2 B3LYP/6-31G(d) -0.2 M06-2X/6-311+G (d,p)// 1.9 B3LYP/6-31G(d) B3LYP-D3/6-31G (d)// 2.6 B3LYP/6-31G(d) MP2/6-311+G (d)// 2.1 B3LYP/6-31G(d) M06-2X/6-31 G(d) 1.8 M06-2X/6-311 +G(d,p)// 1.2 M06-2X/6-31 G(d) MP2/6-31g(d)// 1.3 M06-2X/6-31 G(d) Fast Reacting Enantiomer Figure 1.2. Calculated transitions states in kinetic resolution of azlactones showing the presence of a proposed stabilizing carbonyl-carbonyl interaction leading to high enantiomeric excess. to develop a set of reaction specific parameters employed in a transition state force field. This force field can then be manipulated using faster MM methods and applied, evaluated, and optimized for enantioselectivity. Initially, Norrby and coworkers developed this model with the Os-catalyzed dihydroxylation reaction.19,21-25 After benchmarking their techniques against this reaction, they have since applied it to rationalize the diastereoselectivity of dialkylzinc additions to aldehydes, Ag-catalyzed hydroamination of alkenes and the enantioselectivity of Rh-catalyzed hydrogenations successfully.5,26,27 In the report of asymmetric hydrogenation, they were able to predict the enantioselectivities for a variety of ligand scaffolds and ligand/substrate pairings shown in Figure 1.3. This example highlights the advantages and potentially the future of in silico design of asymmetric catalysts. These examples reveal that the viability of a completely in silico approach to asymmetric catalyst design depends on the ability to correctly determine the structure of the transition states. The key to accurately predicting enantioselectivity lies in the ability to precisely model the key interactions in not one but at least two diastereomeric transitions states. As basis sets advance their ability to accurately model complex interactions, the prediction of enantioselectivity completely in silico will become more of a reality. At the present time, a degree of uncertainty remains in transition state calculation and these calculations are usually verified by one of the few physical organic techniques available to probe transition state structure. Efforts to boost the viability of computational techniques have coupled physical data with computation.28-36 An interesting technique was reported by Denmark and coworkers where they applied the principles of quantitative structure activity relationships (QSAR), a widely applied method in drug design.35 They investigated an asymmetric alkylation reaction using chiral ammonium ions developed in their lab and shown in Figure 1.4. Examining the 6 7 A) ig YCOOH NHAc 2 2-4 Rh1 Catalyst Chiral Ligand^ Hb * r ' ^ Y NHAc COOR Ligands Evaluated PPh, 1a: R = H 1b: R = 0/'Pr 2 1c: R = OMe pph2 1d: R = OCOfBu 1e: R = OBn R Y / Substrates Evaluated „COOMe Ph NHAc 3 1i: R = fBu 1j: R = CEt3 1k:R = C5H9 11: R = Cy COOMe NHAc Experimental AAG* (kcal/mol) Figure 1.3. Predication and evaluation of several ligand and substrate pairings. A) The ligands and substrates explored experimentally and through calculation in the Rh-catalyzed asymmetric hydrogenation reaction. B) Plot of calculated enantioselectivity and experimentally observed enantioselectivity for the ligand substrate pairings shown in A. Deviation of the slope from unity represents calculated error. [Data from 27] 8 RCH2Br O | 10 mol% catalyst O i J< -- "!£!!?--_ ">yvV< Y ° 50% KOH (aq.) T h Ph R Figure 1.4. The asymmetric alkylation of glycine derivatives under phase-transfer conditions using a modular tetraalkylammonium salt. enantioselectivity of the reaction, they employed comparative molecular field analysis (CoMFA).37 CoMFA is considered a molecular interaction field technique where a molecule is described in steric and electronic elements. This is accomplished by encasing the molecule in a fine grid and interrogating it at each gridpoint with a point charge and an atom. The point charge interrogation provides information about the electronic nature of the molecule while the atomic interrogation provides steric information. CoMFA specifically refers to this gridpoint analysis when performed on a series of molecules that are related through a common factor. Prior to analysis, each catalyst's low energy conformation is determined through MM calculation and then aligned to a common element or framework. Denmark and coworkers used partial least squares regression to correlate the steric and electronic components in CoMFA with enantioselectivity, and identified regions where catalyst variation leads to greater enantioselectivity. Superimposing a proposed catalyst-substrate binding motif onto a visualization of these effects led them to formulate hypotheses about the source of enantioselectivity, which included several steric interactions as well as a proposed n-n stacking electronic interaction. This technique, as well as others related to it, can provide powerful insight into the source of enantioselectivity and lead to improved design and understanding. The drawback of such an approach is that the synthetic effort required to generate libraries capable of interrogating simple systems is significant. Also, the active catalyst structure is assumed to be related to the ground state structure, which may not be a good assumption in asymmetric catalysis. Denmark and coworkers' system benefitted from a high degree of structural rigidity, which limited the number of potential conformers; nevertheless, it was challenging to accurately assess conformational effects on the model. In systems with a larger number of potential conformers, this problem could be compounded. 9 The computational methods outlined above represent a few select examples of the state-of-the-art in predicting and understanding the origins of asymmetric induction in catalytic reactions. The Sigman lab has pursued an alternative approach to attempt to predict and understand catalytic enantioselective reactions. Our and others' approaches have utilized linear free energy relationships (LFERs) to correlate substituent effects of the catalyst and substrate to enantioselectivity. Our interest in developing LFERs in enantioselective catalytic systems is based on the fundamental curiosity of how these reactions operate. Application of LFERs in asymmetric catalysis has closely paralleled quantitative structure activity relationship (QSAR) methodology, which has revolutionized medicinal chemistry.38 In the process of our studies, we have become keenly aware of the techniques employed in the QSAR field and have endeavored to utilize this technology for developing our own studies. Whether or not LFERs possess the same potential to elucidate and manipulate key features in asymmetric catalysis remains to be seen and is the subject of this thesis. This chapter will examine several different reported LFERs, which correlate various catalyst properties to enantioselectivity. These studies have been instrumental in evolving the current design-based approach used for developing asymmetric catalysts in the Sigman laboratory. The Curtin-Hammett Principle LFERs have been used in physical organic chemistry for many years to probe reaction mechanism. The basis for all LFERs is found in the relation of the relative rate constant (krel) to the difference in the free energy of the transition state shown in Equation 1.1.39 AG* = -RT/n(krel) (1.1) Traditional LFER analysis used in physical organic chemistry has focused on defining and examining the rate-determining step of a reaction. Identifying and understanding the transition 10 state structure in the rate-determining step has led to countless catalyst improvements. In order to apply Equation 1.1 to asymmetric catalysis or any stereoselective reaction, the Curtin- Hammett principle must be applied. The simplest interpretation of the Curtin-Hammett principle dictates that in reactions where there are multiple interconverting reaction isomers, conformers, or intermediates leading to a distribution of products, the distribution of products is principally determined by the largest energy barrier along the reaction coordinate, not necessarily the energy of interconversion between isomers, conformers or intermediates (Figure 1.5).40,41 This principle applied to asymmetric catalysis relates to catalyst-substrate interactions through the enantiodetermining step and their effects on enantioselectivity. A simple example is a substrate binding to an asymmetric catalyst. The substrate can bind to the catalyst through a considerable number of conformers. Assuming substrate-catalyst binding is reversible and the barrier to intercoversion is low with regards to the enantiodetermining step, the product ratio or enantioselectivity observed is attributed solely to the difference in energy of the diastereomeric transition states and not the populated conformational states (Figure 1.5). Halpern and coworkers pioneered the application of the Curtin-Hammett principle in asymmetric catalysis, and they observed that the nature of catalyst-substrate interactions is normally assumed to be much weaker than the bond formation or cleavage occurring in reactions, indicating that the Curtin-Hammett principle should be applied with caution.42 The application of the Curtin- Hammett principle allows the enantiomeric ratio (er), as determined typically by chiral separation, to be treated as a relative rate of formation of the two enantiomers. Using er as a relative rate also requires that the thermodynamic quantity be modified to reflect the relative difference in Gibb's free energy of the transition state or AAG* (Figure 1.5). 11 Energy 12 Figure 1.5. A catalytic asymmetric reaction coordinate that demonstrates the key features of the Curtin-Hammett principle. AAG* is only a curiosity when considered as a single measured enantioselectivity, but examining AAG* as function of catalyst perturbation provides a glimpse into the key features of the transition state structure. The assumption in observing LFERs using a series of catalysts or substrates is that the mechanism of asymmetric induction is perturbed but not fundamentally changed. If the mechanism of asymmetric induction changes with variation of the catalyst, the comparability is lost. If a relationship can be drawn, it implies that the mechanism of asymmetric induction is robust to changes in the system. The discussion so far has largely ignored one other key aspect of developing LFERs: identifying appropriate catalyst elements that can be systematically modified and quantified by parameterization. To accommodate systematic changes, a modular catalyst is ideal, as modularity increases the ability to explore a variety of potential effects. Furthermore, these potential effects must be accurately parameterized to encapsulate the properties of interest. The selected case studies in this chapter each represent novel application of different parameters in asymmetric catalysis and evaluate the information gained through correlative outcomes. Ligand Electronic Effects in the Mn-catalyzed Epoxidation of c/s-Alkenes Although Halpern and coworkers first recognized the Curtin-Hammett principle in interpreting product enantiomeric ratio (er) in asymmetric catalysis, they did not report a LFER using this principle. The first and seminal report of a LFER in asymmetric catalysis was described by Jacobsen and coworkers in the context of the Mn-salen-catalyzed asymmetric epoxidation of c/s-alkenes, a key method to access unfuctionalized chiral epoxides.43 Mn-salen-catalyzed epoxidation is proposed to proceed via oxidation of Mn(III) to Mn(V), for which a number of suitable terminal oxidants have been reported (Figure 1.6). The resulting Mn(V)-oxo species 13 14 r Cat. Mn r J) -----Qxidant - > o R K ' Ph Ph M R Figure 1.6. The manganese mediated epoxidation of alkenes. readily reacts with various olefins, likely via a radical process, although debate still exists. For the reaction detailed below, aqueous bleach was used as the terminal oxidant, and Jacobsen and coworkers observed that the phase-transfer dynamics of Mn-oxidation were rate-limiting.44 The Jacobsen epoxidation was uniquely qualified for LFER anaylsis as the salen ligand template is modularly synthesized from readily available salicylaldehyde derivatives and a chiral diamine backbone (Figure 1.7A).45 Catalyst assessment revealed a correlation between ligand electronic variation and enantioselectivity.46 To quantify this electronic effect, o-Hammett parameters, derived from the acidities of benzoic acid derivatives, were employed.47 C/s-2,2-dimethylchromene, c/s-P-methylstyrene, and c/s-2,2-dimethyl-3-hexene (Figure 1.7B-C) were all separately evaluated and each revealed a LFER with catalyst electronic nature as shown in Figure 1.8. The same general trend was observed for each substrate with electron-donating salens yielding the highest enantioselectivity. The sensitivities toward the electronic nature of the catalyst varied by substrate with c/s-2,2-dimethylchromene displaying the greatest sensitivity and c/s-2,2-dimethyl-3-hexene being the least sensitive. To explain these observations, Jacobsen and coworkers invoked the Hammond postulate and hypothesized that the nature of the electronic effect was through bias for a more product-like transition state. The best evidence of this hypothesis is found in the slope of the Hammett plots. For each substrate, electron-donating ligands positively impact enantioselectivity, which is thought to originate by forming a more stabilized Mn(V)-oxo species, effectively making it a weaker oxidant and decreasing the rate of epoxidation. However, the weaker oxidant requires greater proximity of the alkene substrate in order for the epoxidation to occur. The increased proximity can in turn lead to greater substrate catalyst interaction, particularly, steric interactions between the chiral backbone of the salen ligand and the sterically dominate element of the alkene shown in Figure 1.9. These hypotheses were further 15 16 B) C) Ph Ph M + Catalyst Substrate 2 er Substrate 3 er Substrate 4 er 1a: R = OMe 98:2 91.5:8.5 68.5:31.5 1b: R = Me 97:3 90.5:9.5 68.5:31.5 1c: R = H 94.5:5.5 89:11 67:33 1d: R = Cl 93:7 84:16 66:34 1e: R = N02 61:39 74.5:25.5 63:37 Figure 1.7. Electronic effects in the Jacobsen epoxidation. A) Synthesis of salen-type ligands. B) Substrates and conditions used to develop the ligand-based electronic LFER. C) Enantiomeric Ration (er) for multiple ligands and substrates. [45,46] 17 0 . 0-1------------1----------- 1------------■------------1------------■------------1-------------------------1------------■------------1------------■------------1- -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 Figure 1.8. Plot of the enantioselectivities of substrates 2-4 with the Hammett o values for catalysts 1a-1e. [Data from 45,46] Increased Substrate Catalyst Ordering Tighter Transition State ,R' X Looser Transition State Figure 1.9. The hypothesized electronic effect on transition state structure results in varying degrees of tightness in the transition state and corresponding levels of enantioselectivity. substantiated through kinetic isotope effects, Eyring analysis, and computational studies, all of which indicated that the electronic effect created a more product-like transition state.48 Also supporting this hypothesis was a more recent study reported by Pericas and coworkers in which they examined the role of substrate electronics under modified epoxidation conditions using the commercial Jacobsen catalyst 5.49 They found a strong correlation between substrate electronics and enantioselectivity using trisubstituted olefins (Figure 1.10). They found the same trend originally observed by Jacobsen and coworkers for the electronic nature of the catalyst was mirrored in the substrate. Electron-rich alkenes, which are more reactive towards oxidation by the Mn(V)-oxo species, gave lower enantioselectivities, while electron-poor alkenes gave higher enantioselectivities. Comparison of the p values between the catalyst LFER and the substrate LFER reveals that the reaction is less sensitive to substrate electronics; however, this comparison may not be direct. The effect measured by Pericas and coworkers is for a highly conjugated system wherein the electronic perturbations would be delocalized over the alkene and the adjacent aryl rings, which would mitigate the electronic variation. Jacobsen and coworkers' report introduced the field to the potential that LFERs have in asymmetric catalysis. The application of LFER analysis in this example elucidated a key nonintuitive interaction. Prior to this report, enantioselective outcomes had been primarily rationalized through steric effects. Jacobsen and coworkers' study and follow-up studies revealed electronic effects as important considerations in asymmetric catalysis. The information provided by the LFER about transition state structure led to a model for asymmetric induction, which has withstood multiple probes over a span of 20 years. 18 19 Ph Ar Ph 5 mol% 5 6 mol% 4-PPNO 0 °C, DCM, NaCIO (aq) Ph^ A r Ph Figure 1.10. The experimental model reported by Pericas and coworkers evaluating the asymmetric epoxidation of trisubstituted alkenes with Jacobsen's catalyst. Plot of enantioselectivity as a function of substrate electronics in the same reaction. [Data from 49] Catalyst Acidity in the Organocatalytic Hetero Diels-Alder Reaction Jensen and Sigman employed the power of LFER analysis in asymmetric catalysis to a variant of the enantioselective hetero-Diels-Alder (HDA) reaction first reported by Rawal and coworkers.50 After Rawal and coworkers initial report, they subsequently reported the rate enhancement and ultimately asymmetric catalysis by chiral a,a,a',a'-tetra-2-napthyl-1,3- dioxolan-4,5-dimethanol.51-54 The reaction was developed in a synthetic context, as the pyrone products generated through HDA are a common motif in natural products and active pharmaceuticals. Sigman and Jensen became interested in the reaction to showcase a modular catalyst scaffold designed to be capable of H-bond catalysis.55,56 The catalyst contains an oxazoline core to which is appended a serine derived tertiary alcohol and another amino acid derived amine (Figure 1.11). The modular nature of the catalyst allowed a wide variety of catalysts to be evaluated from readily available building blocks. Evaluation of a number of catalysts revealed the camphorsulfonamide derived catalyst 6 generated the highest enantioselectivity (Figure 1.12). Substitution of the camphorsulfonamide for a variety of amides revealed a surprising trend. Having initially assumed the high enantioselectivity exhibited by 6 was due to the bulky nature of the camphor appendage, the authors were surprised to observe a pronounced effect on enantioselectivity by simple amide groups.57 Catalyst series 7a-e revealed that more acidic catalysts yielded higher enantioselectivities for the HDA reaction (Figure 1.13). To develop the linear free energy relationship, the pKa's of the corresponding acetic acids as measured in H20 were employed (Figure 1.14). Br0nsted acid-based LFERs have used acid pKa's to correlate rate and acid catalysis in tradition physical organic chemistry for years.39 The authors' use of pKa's by analogy assumes that the substituent effects would scale similarly between acids and amides. The resulting LFER verifies this assumption, but because the inherent differences in H-bonding 20 21 ^NH? Protecting Group [I H0 -------------------------"* 'OH * H O ^ ^ R 1. Amide Bond Formation 2. Cyclization nh2 R'MgBr ^ R.^ _OH RS " ' o R cN NHPG OH R' OH Figure 1.11. Modular synthesis of the H-bond catalyst framework. TBSO 1. 20 mol% 6 tol., - 40 °C, 48hr b l l 2. AcCI, DCM, -78 0C* o ^ ^ ^ 'A r 7 examples 48 -80% Yield 85:15-96:4 er Figure 1.12. HDA reaction of Rawal's diene and aromatic aldehydes catalyzed by 6. [57] TBSO Ph Ph' 1. 20 mol% 7 tol., - 40 °C, 48hr O 2. AcCI, DCM, -78 °C o ^ ^ ^ ^Ar Catalyst er 7a R = CF3 95.5 : 4.5 \ ^ 7b R = CCI3 90.5 : 9.5 7c R = CHCI2 87.5:12.5 > f N HN^ r 7d R = CH2F 81 :19 ' OH _ K 7e R = CH2CI 7 6 :24 Figure 1.13. Evaluation of catalysts with different acidities in the asymmetric HDA reaction. [58] 22 Figure 1.14. Plot of enantioselectivity as a function of catalyst acidity for the HDA reaction. [Data from 58] and traditional acid catalysis, it remains to be seen if comparisons of the slope are relevant. This correlation implicates the strength of the H-bond formed between the substrate carbonyl, and the catalyst N-H bond is directly impacting enantioselectivity. To fully explore the effect of amide N-H bond acidity on the system, a full kinetic study was undertaken.58 The rate-determining step was shown to be the cycloaddition and not catalyst binding of the substrate. Kinetic data also suggested that the acidity of the catalyst affects the rate of substrate binding as well as the rate of reaction with diene. Similarly, the rate of formation of the major enantiomer was more sensitive to catalyst acidity. To further examine the system, the authors exploited another modular aspect of the catalyst system, the substrate. Using a series of para-substituted benzaldehydes, a Hammett relationship was developed, which was predicted to mirror the effect of catalyst acidity (Figure 1.15). Evaluation of these substrates yielded no sensitivity between their electronic nature and the enantioselectivity of the reaction. However, a Hammett plot correlating substrate electronics and rate was observed at both low aldehyde and high aldehyde concentrations, which is consistent with the rate-determining step. At first glance, the strong correlation between catalyst acidity and enantioselectivity and the lack of correlation between substrate electronics and enantioselectivity is perplexing. If stronger H-bonding occurs as a result of effectively pairing pKa's of the donor and acceptor, a relationship between substrate electronics and enantioselectivity would be expected.59,60 Another hypothesis was formulated that explains the lack of substrate electronic effects via application of the Hammond postulate. Stronger catalyst acidity stabilizes the buildup of negative charge on the carbonyl oxygen creating a transition state where the substrate more closely resembles a product-like benzyl alcohol (Figure 1.16). The electronic substituent effects of benzyl alcohols have much less variation than the corresponding benzoic acids. The range of pKa's of para-substituted benzyl alcohols is 23 24 Figure 1.15. Plot of enantioselectivity as a function of substrate o values for the HDA reaction. [Data from 58] OH R K a oe + H pKa range ~0.6 K a R N + H@ p/^a range ~5 © Figure 1.16. Proposed transition state for the HDA reaction which reflects more benzyl alcohol charater. The relative acidities of benzyl alcohol derivatives and amide derivatives. roughly 0.6 pKa units whereas the pKa range of the substituted benzoic acids is 3.2; thus any lack of trend by the substrate could be easily attributed to experimental error. In this case, the coupling of two LFER studies together with kinetic data provided the basis for a reasonable hypothesis of transition state interactions. The Br0nsted-like correlation in an H-bond catalyzed system might find broader application as the number of enantioselective organocatalytic reactions that implicate H-bonding as a key element for enantioselection grows. Polarizability in Thiourea Catalyzed Polyene Cyclization Hydrogen bonding is a common motif for transition state stabilization in enzymes. Another common motif, which has come to light recently in understanding polyene cyclization, is cation-n interactions.61,62 Cation-n interactions refer to the stabilization of cationic intermediates via electrostatic interaction with a n-system, typically an arene as demonstrated in Figure 1.17. This stabilization is facilitated by the polarizability of a molecule or its ability to disseminate charge. Inspired by reports of these cation-n interactions in nature, Jacobsen and Knowles set out to design a catalyst capable of highly enantioselective polyene cyclizations.63,64 The designed catalyst would combine the anion binding capabilities of thioureas as well as a moiety capable of stabilizing a cation via cation-n interaction (Figure 1.17). The result would be a catalyst capable of ionizing a substrate and providing a chiral environment for further reaction. The model reaction they studied was the bicyclization of hydroxyl lactams, which are known to ionize under acidic conditions (Figure 1.18). The N-acyliminum ion formed by ionization can be attacked by the nucleophilic alkene generating a carbocation, which can undergo another intramolecular addition by the arene. 25 26 Cation-71 Interactions Proposed Catalyzed Ionic Disproportionation X - Y S y N N' H H S X N ^ N ' i i H\ H/ v 0 / 'X' Figure 1.17. A cation-n interaction. Design elements of a catalyst capable of stabilizing ionic elements. Aryl = er 8a Phenyl 62.5 : 7.5 8b 2-Napthyl 80.5 : 19.5 8c 9-Phenanthryl 93.5 : 6.5 8d 4-Pyrenyl 97.5 : 2.5 Figure 1.18. The enantioselective cyclization of hydroxyl-lactams. The catalyst designed made use of the well-characterized bistrifluoromethylphenyl thiourea employed by many in this field, connected by an amide linker to a chiral aryl pyrolidene. Proof of their design concept was exhibited by catalyst 8 in the model system, although in low yield and low enantioselectivity. Expanding the size of the aryl ring led to better yields and improved enantioselectivities. It should be noted that the reaction forms three new contiguous stereocenters through separate bond-forming events, and the reported enantioselectivities are for the single diastereomer formed in the reaction. To determine the role of the arene, Jacobsen and Knowles correlated enantioselectivity with arene polarizability for catalysts 8a-8d (Figure 1.19).65 The measure of an arene's polarizability is its capability to delocalize charge through distortion. The correlation between polarizability and enantioselectivity implies that the catalysts were stabilizing the cationic intermediates by delocalizing positive charge.66 The correlation indicates even larger aryl rings would generate higher selectivity; however, extrapolation of this LFER as a design principle was not explored. This might be due to the fact that polarizability values for larger substituents are not available, and the corresponding aryl bromides are not commercially available. The LFER implicates the ability of the extended n-systems to stabilize cationic charge but did not rule out the argument that the aryl ring's effect is steric and not electronic in nature. To delineate the role of the arene, they evaluated the effect of temperature on enantioselectivity with each catalyst (Figure 1.20). The resultant Eyring analysis showed that varying the aryl ring had a primarily enthalpic effect. This is consistent with energetic stabilization of the cation intermediates, as such stabilization would be primarily enthalpic with a negligible entropic element.67 Conversely, if the role of the aryl ring was primarily a steric effect, the Eyring analysis would have revealed an entropic effect relating to substrate ordering. 27 28 Figure 1.19. Plot of enantioselectivity as a function of arene polarizability in the asymmetric bicyclization of hydroxyl lactams. [Data from 63,64] Figure 1.20. Eyring analysis comparing the roles of aryl substituents in the bicylcization of hydroxyl lactams. [Data from 63,64] The mechanism of asymmetric induction in the polycyclization reaction is less clear. The reaction presumably proceeds through a closed six-membered transition state, which results in high diastereoselectivity. The catalyst might be capable of stabilizing each of three separate cations formed in the reaction pathway. The LFER indicates that the catalyst is interacting with the initial N-acylimminium ion to form the first chiral center, whether or not the catalyst remains in contact with the substrate after the initial enantioselective bond forming event is not clear. It seems reasonable that given the strong enthalpic contribution generated by the cation-n stabilization that the subsequent cations would remain in contact with the catalyst. However, the remaining bonds could be formed through favorable diastereoselective pathways. This correlation between catalyst polarizability and enantioselectivity not only constitutes an important novel LFER with a noncovalent attractive interaction but quantifies an important design element in asymmetric catalysis. Although cation-n interactions might play significant roles in other reactions they had never been so directly implicated and quantified. This will be an important consideration in the future for reactions where cationic intermediates are accessible. Computed H-bond Length in the Asymmetric Strecker Reaction Among organocatalytic reactions, few have received as much attention as the enantioselective Strecker reaction.68 In the Strecker reaction, nucleophilic cyanide is added to a an imine via 1,2-addition (Figure 1.21). The products of asymmetric Strecker reactions are synthetic precursors to many unnatural amino acids. Jacobsen and Sigman first reported an enantioselective variant of the Strecker reaction in the late 1990's.69-71 The culmination of this work was reported in 2009 with a simplified highly enantioselective Strecker catalyst compatible with a wide range of substrates (Figure 1.21).72 The reaction also used nonvolatile cyanide 29 30 Amino Acid Stecker ReBdion Derivatives ° NH2R' r N'R' CN -, HN'R H> , _ X ^ O H * H „ X H R ^'N Ph NA Ph 0.5 mol% 8 2 equiv KCN 1.2 equiv AcOH 4 equiv. H20 tol., 0 °C Figure 1.21. The Strecker reaction and hydrolysis to form amino acid derivatives. The asymmetric Strecker reaction for tertiary imines. sources and moderate temperatures as compared to previous iterations. In an effort to understand the subtleties of this powerful reaction, Jacobsen and Zeund undertook a kinetic, physical organic, and computational study of their system.14 As a part of their kinetic and optimization studies, they generated a small library of thiourea based catalysts (Figure 1.22). Upon first inspection, these catalysts possess different properties and do not contain a complementary set of variations, as would be required to develop a traditional LFER. Using this set of catalysts, they computed the energy differences between the major and minor enantiomeric pathways at three different levels of theory, B3LYP/6-31G(d), M05-2X/6-31+G(d,p) and MP2/6-31G(d). In each case, correlation was found between the calculated AAE* and the observed AAG*. Interestingly, B3LYP/6-31G(d) was shown to be the most accurate level of theory for the system, despite its propensity to underestimate the energies associated with noncovalent attractive interactions. Although the calculations consistently overestimate the AAE* values, the correlation to observed enantioselectivity suggests that the error is systematic. Also, the computation correctly predicted the growing energetic preference for the R enantiomer across the catalyst set. Considering the amount of variation within the catalyst library, the correlation verifies the viability of computation for examining the system. Exploring the computed structure for each catalyst revealed no obvious steric interaction that could explain increased enantioselectivity. The spatial arrangement of atoms was either static through the series or deemed inconsequential to the enantioselective outcome. This observation raised the question of how the variation in enantioselectivity is achieved for the different catalysts. In fact, the calculations revealed no significant difference in the H-bond lengths between the (R) or (S) product forming pathways for highly or poorly enantioselective catalysts. However, their computational work had revealed that the computed 31 32 Me tBu S 'Y V ^ N N PIh. OII H H 8a Me tBu O P fu .N . r m Ph O 8b Me Me S V rV S Ph O 8c tBu S n^ n H H Me P h ^ N y Me Me Me^Ny 8d Me Ph. Y ? Me 8e 8g Me P h y N y Ph 8h Me Me^ A T V Me 8f Figure 1.22. Library of catalysts used to evaluate the Strecker reaction computationally and experimentally. rate-determining step of the reaction was rearrangement of the ion pair through a carbonyl stabilized H-bonding network (Figure 1.23A). They examined the role of this H-bond network through this step and identified no strong correlation between the cumulative H-bond distances in the R selective pathway. However, in the 5-selective pathway they observed a LFER between cumulative H-bond distance and enantioselectivity (Figure 1.23B). This LFER provides compelling evidence that the source of enantioselectivity is due to weaker stabilization of the imminium ion in the 5-pathway. For the more enantioselective catalysts, the amide carbonyl becomes less accessible in the preferred transition state geometry inherent to the 5-pathway which leads to its destabilization relative to the R-pathway. This highlights another feature of H-bonding not discussed previously: the directionality of the bond matters. In this system, there are no direct steric interactions that explain destabilization of a specific pathway. Instead, the steric effect arises from the catalyst itself, where its low energy conformation presumably leads to subtle differences in the amide carbonyl direction relative to the thiourea. This, in turn, leads to increased differences in the H-bonding network responsible for stabilization of the key intermediate. This study presents another case where LFER analysis provided evidence for a nonintuitive catalyst-substrate interaction and implied transition state structure. Not only does it present LFER analysis in the development of an extremely powerful synthetic reaction, but it represents the melding of LFERs with computational chemistry. While evaluation and prediction of catalysts in silico has not yet fully arrived, this work presents an effective application of computational chemistry to develop a set of specialized parameters (cumulative H-bond length) and correlate them to experimentally derived results. Specifically, the use of such parameters in LFER analysis to evaluate or support specific mechanistic hypothesis has potential application in asymmetric catalysis. 33 34 A) B) R-enantiomer X € o> cC D -J ■Q Co 00 (D ■C ■2 3 E3O (0 O 5.4-, ▲ (R)-TS (d+d2) 5.2- • ▲ (S)-TS (d1+d2) (R)-TS (d3+d4) 5.0- • (S)-TS (d3+d4) 4.8- • ___^ 4.6- --" ▲ - A------- 1 4.4- t r 4.2- r ------- £ - 00 8b - ^ . 4.0- h- 8g ------- i --------- 8c ----------------------- 8e 8h - r "--- --------±f 3 8 J 0.0 0.5 1.0 1.5 Experimental a aG* (kcal/mol) 2.0 Figure 1.23. Prediction of enantioselectivities using H-bond length. A) Calculation of the proposed enantiodetermining transitions states leading to the R and S enantiomers (B3LYP-/6- 31G(d)) The key bonding interactions are plotted and labeled. B) Plot of calculated bond lengths as function of experimentally observed enantioselectivity. [Data from 14] Charton Steric Parameters in Asymmetric Nozaki-Hiyama-Kishi Allylation of Carbonyls The previous example demonstrates how a subtle steric effect can have a profound influence on enantioselectivity. As previously stated, steric effects are widely implicated in asymmetric catalysis. Although several sets of experimentally based steric parameters have existed for years, no real effort to correlate steric effects to enantioselectivity existed until our group became interested in correlating a pronounced steric effect discovered in our investigations of the Cr-mediated Nozaki-Hiyama-Kishi (NHK) additions of allyl fragments to carbonyls.73 The NHK reaction mechanism is outlined in Figure 1.24 and involves addition of Cr(II) into an allylic bromide bond.74 The subsequent Cr(III) allyl species is Lewis acidic and will activate a carbonyl to undergo nucleophilic addition from the pendant alkene. This nucleophilic addition occurs, presumably, through a closed, six-membered transition state. Initially reported as a reaction requiring super-stoichiometric amounts of Cr, it was rendered catalytic in Cr by addition of a terminal reductant for Cr(II), typically manganese, and a species capable of sequestering the Cr-alkoxide (TMSCl).74 The reaction is just one of many 1,2-allylations of carbonyls, the synthetic utility of which is well-documented. Sigman and Lee became interested in these reactions as a platform for the same amino acid-oxazoline ligand template as previously described.75,76 Their initial entry was the report of ligand 9 imparting high degrees of enantioselectivity in the allylation of aryl aldehydes (Figure 1.25A). After catalyst modification, Sigman and Miller reported the expansion of the substrate scope to aryl ketones, for which no previous NHK asymmetric methodology had been reported (Figure 1.25B).76 In many empirical iterations of the modular catalyst, a significant steric effect was observed through manipulation of the carbamoyl group. This observation, in combination 35 36 2 CrCI2 co o3 ■Q d> o: MnX2 Mnu Oxidative Addition Brv ^ CrCI2Br 2 CrCI2X ^ ^ ^ C rC I2 O R^ , Y CI2Crv OTMS TMSCI R' 2: co_ CD ■3§; o' i . •-K 03 £■ Proposed Closed Transition State Silylation Figure 1.24. Proposed catalytic cycle for the Cr-mediated NHK allylation reaction with the proposed cyclic transition state shown. A) B) O Ar H + Ar OX 5 mol% CrCI3 10 mol% Ligand 10 mol% TEA 2 equiv. TMSCI 2 equiv. Mn(0) THF, RT, 20h 10 mol% CrCI3*(THF)3 10 mol% Ligand 10 mol% TEA 4 equiv. TMSCI 2 equiv. Mn(0) THF, 0 °C, 20h OH 73 - 95% Yield 25:75 - 3:97 er 7:93 - 3:97 er Figure 1.25. Previously reported reaction conditions for the NHK allylation of aldehydes and ketones. [72,73] with the modular nature of the ligand template, provoked further investigation into the role of the carbamate. In contrast to all of the previously discussed studies, this study of steric effects in the NHK reaction was not accompanied by a detailed examination of mechanism. Preliminary investigations into the reaction suggested that the rate-limiting step was silylation of the Cr-alkoxide and prior steps are relatively fast, a conclusion that is generally supported in the NHK literature. This suggests mechanistic and structural information cannot be obtained using kinetic analysis. In addition, the ground state catalyst has resisted any attempts to crystalize, providing the impetus to study the system using LFER analysis. Regardless of this lack of general information, a model system was selected using catalyst framework 10 to examine two model reactions: the allylation of benzaldehyde and acetophenone (Figure 1.26).73 Although ligand 10 was not an optimal ligand for ketone allylation, it had proven a competent ligand for the reaction. Variation of the carbamoyl group gave a series of ligands 10a-e, which were evaluated in the model reactions. The results showed significant sensitivity to the presumed steric effects at this position. The difficulty in quantifying and correlating this steric effect lies with the parameter choice. A significant portion of Chapter 4 will explore various steric parameters in depth and is beyond the scope of this introductory chapter. In short, Charton parameters were selected largely due to their larger number of reported values.77-80 The nature of the Charton parameter is based on Taft's classical experiments to delineate steric effects from electronic effects (Figure 1.27).81-83 Charton evaluated Taft's experimental data and found correlation between it and the calculated Van Der Waals radii of the substituent. The correlation allowed Charton to extrapolate Taft's data set, and generate parameters for a large number of substituents. 37 38 + xO P lr^ H (M e ) 10 mol% CrCI3*(THF)3 10 mol% Ligand 10 mol% TEA 4 equiv. TMSCI 2 equiv. Mn(0) THF, RT, 20h HO, ,H(Me) Ph" -N Ph- R 10 Benzaldehyde Acetophenone ^ o er er A - 10a R = Me 60:40 25:75 t o 10b R = Et 65.5:34.5 25:75 10c R = iPr 78:22 38:62 : ° T fo 10d R = tBu 95.8:4.2 69:31 10e R = 1 -Adamantyl 95.8:4.2 72:28 Figure 1.26. The exploration of steric effects in the NHK allylation. [Data from 73] Taft-based Steric Parameters O h30® O r A 0 ,CH3 - _ Figure 1.27. The experimental model used to derive Taft's steric parameters. AOH Applying Charton's parameters to the NHK allylation reaction led to a strong correlation between the substituents size and the enantioselectivity (Figure 1.28). The slopes also indicated that the reaction was very sensitive to steric bulk at the carbamate position. It was this sensitivity that was explored as a catalyst design element in extrapolation of the LFER. Using the available Charton parameters, three larger substituents were selected for incorporation into the ligand and subsequent evaluation in the NHK reaction. Using the LFER, the enantioselectivities for these substituents was predicted to be beyond the previously reported optimized system. However, evaluation of these catalysts manifested a break in the correlation and rendered the LFER ineffective as a predictive tool (Figure 1.29).84 The resolution of this perceived break in linearity will be the focus of much of this dissertation. The observation of this type of steric effect was not unique in asymmetric catalysis. Evaluation of published data revealed that Charton steric parameters could correlate steric effects in numerous systems.84 In contrast to the above cases, the LFER was used as a design element more than a tool to derive the mechanism of asymmetric induction for the NHK allylation reactions. This study does represent the first successful attempt to correlate steric effects in asymmetric catalysis and reveals Charton parameters as potential tools to examine such effects. The application of steric parameters to asymmetric catalysis provided the impetus for what will be described in the remainder of this dissertation. Conclusion These examples showcase the power of LFERs in asymmetric catalysis. The use of LFERs can provide key insight into transition state structure and contribute to the analysis of the reaction. It is insight into these transition state structures that will prove vital to applying these reactions generally in organic synthesis. These examples are only a sampling of the various 39 Enantioselectivity aaGt (kcal/mol) 40 - 0 .6-1--------------------------------------------1--------------------------------------------1--------------------------------------------1--------------------------------------------1 0.3 0.6 0.9 1.2 1.5 Charton Value ( v) Figure 1.28. Plot of enantioselectivity of the NHK allylation reaction as a function of Charton's steric parameters. [Data from 73] O CH(Pr)2 : 2 4 CH(Et)3 : CH(/Pr)2 : Charton Value (v) Figure 1.29. Plot of the enantioselectivity of the NHK allylation as a function of Charton steric parameters showing the nonlinear nature for larger substituents. [Data from 73] substituent effects that can be explored through LFER analysis. The requirements of LFER analysis are that the system be robust to changes in the overall mechanism of asymmetric induction, the system must possess some degree of modularity, and parameters must exist that encapsulate the systematic changes and their effect. Development of LFERs requires synthetic effort to arrive at catalyst libraries. In this regard, LFERs are no different than many of the other tools available to probe asymmetric reactions. The element that sets LFERs apart is the wealth and character of information available should the analysis prove fruitful. LFER development can be complementary to computational-based designs, and the combination of the two is a powerful approach where computation can be used to arrive at unique parameters and correlated to enantioselectivity. This chapter has focused on a handful of examples, in which a wide variety of parameters have been used to develop these LFERs. 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Chem. 5oc. 1994, 116, 2812. 45 CHAPTER 2 DEVELOPMENT OF STERIC-BASED THREE DIMENSIONAL LINEAR FREE ENERGY RELATIONSHIPS IN NOZAKI-HIYAMA-KISHI ALLYLATION REACTIONS Introduction The ubiquitous implication of steric effects in asymmetric catalysis makes quantifying these effects a desirable goal.1-4 The correlation found between the carbamoyl substituent and enantioselectivity shown in Figure 1.28 demonstrated that Charton values could be used to quantify steric elements in a system.5 The breaks in the LFERs (Figure 1.29) led to several hypotheses, which included a proposed global shift in catalyst conformation, overcrowding of the most selective site on the chromium center funneling reactivity through less selective pathways, and flawed application of the Charton parameters. To fully explore these hypotheses, we embarked on a more sophisticated study of the ligand-catalyst system. The study we designed was a simultaneous study of substituents X and Y shown in Figure 2.1. In prior studies, we had observed a subtle effect of position X on enantioselectivity. The nature of this effect was not intuitive because in the limited computation and hand modeling we had performed it appeared that substituent X was positioned away from the reactive center. This position had been dubbed the backbone position because of this presumed orientation. We thought probing the X position simultaneously with the Y position's more pronounced steric effects might provide information about how these two groups are interacting. Similarly, we thought by adding another dimension to our analysis we could develop a model with greater predictive power than exhibited by the previous steric-based LFERs. With these goals, we set out to synthesize a ligand library where positions X and Y were systematically varied, evaluate these ligands in prototypical reactions, and collectively model the data as a complete set.6 Library Design and Synthesis The initial ligand library was designed around the modular ligand scaffold described in our report of the Nozaki-Hiyama-Kishi allylation of ketones (Figure 2.1).7 This truncated ligand scaffold was selected rather than the scaffold with which we had reported the steric-based LFERs (Figure 1.26).5 This ligand scaffold presents two advantages over the previously reported scaffold. The first is that the truncated scaffold has only two diastereomers, one of which is not effective in the reaction in terms of enantioselectivity, which allows for more direct conclusions to be made about the nature of the steric effects. The second advantage is that the two steric effects we would be examining would be associated with the two chiral centers again potentially simplifying the analysis. The truncated ligand synthesis is compatible with an efficient route to the ligand library.8 To assay the ligand library, we chose the allylations of benzaldehyde and acetophenone as model reactions. These reactions were selected primarily because of the wealth of data we had compiled over years of study that would allow us to benchmark the library approach. Also, the appropriate assays for enantioselectivity were already in place. The substituents chosen for both the X and Y position were selected to reflect those commonly examined in an empirical examination of steric effects. Only carbon-based substituents were selected to avoid potential interaction between heteroatoms and the Cr-center, which might result in a mechanistic change. At the X position, the substituents depicted in Figure 2.2 were chosen primarily due to their availability from commercial amino acids. At 47 48 X o 1 Figure 2.1. The oxazoline-proline modular ligand scaffold. the Y position, the substituents shown in Figure 2.2 were selected to mirror those of the X position with exclusion of hydrogen because of the instability of such a molecule. The 4-heptyl (Hep) substituent was included because it was one of the substituents that "broke" from linearity in the previous LFERs. The underlying purpose for including this substituent was to generate some predictive power around this break in linearity and explore if the break was present across the ligand series. Synthesis of the ligands began by installing the various carbamoyl substituents onto L-proline. Boc-L-proline is commercially available so synthesis of the YtBu ligand series forgoes the first step. The mild condensation of chloroformates onto L-proline is a straightforward way to generate the methyl-, ethyl-, and isopropyl-protected prolines (Scheme 2.1). The 4-heptyl chloroformate is not commercially available so an alternate path was pursued. To synthesize the desired proline analog (Hep), 4-heptanol is condensed with 4-nitrophenylchloroformate to prepare the carbonate 2 (Scheme 2.2). To avoid formation of the mixed anhydride, the benzyl ester-protected proline is used. The condensation of carbonate 2 with benzyl protected proline proceeds cleanly under the same conditions used with chloroformates. Finally, hydrogenolysis of the benzyl ester generates the acid, which can be carried on according to Scheme 2.1. Anderson's conditions for peptide bond formation gave good results for each of the differentially-protected prolines with the appropriate amino acid salts.9,10 The final peptide bond can be formed under thermal conditions with aminoethanol in refluxing THF/toluene (1:1) mixture. Several reaction conditions were employed for oxazoline cyclization but conditions reported by Wipf and coworkers, using diethylaminosulphurtriflouride (DAST), were synthetically favorable.11 The high cost of D-tert-leucine prompted us to synthesize the opposite enantiomer of the ligand for each of the XtBu series. The same reactions outlined above were 49 50 ox Ph r ^H (Me) + 10 mol% CrCI3*(THF)3, 11 mol% Ligand X, _ 20 mol% TEA, 2 equiv. 4 equiv. TMSCI, 2 equiv. Mn(0), THF, 0 °C Oxazoline-Proline Ligand Library P N "H V N>-/ .0 X H Me Et /Pr fBu H(D H (Me) Ph' Y Me Et /'Pr tBu Hep Figure 2.2. The allylation of benzaldehyde and acetophenone under standard conditions using the oxazoline-proline ligand library. 51 Scheme 2.1. Ligand library synthesis. O O Y X /? 1) 1.2 equiv. IBCF, * 9 J ^CT^CI 1.5 equiv. NMM, H0 V \ 2 equiv- a n > 0.2 M PCM, 0 °Ct O h ' / H N ^ y 0.4 M NaHCCK ° ^ r /' 2) 1.2 e2q) u1iv.2. NeqMuMiv. NMM ° 0 ^ N L-Proline n0./4i MM TTHHFF 10 0°C, 2vh , RT, \P 24 h, RT Y q X HC| Y Y = Me, Et, /Pr ^ ^ [ ^ N H 2 75-92% 60-89% O X = H, Me, Et, /Pr, fBu 1.5 equiv. Y = Me, Et, /Pr, fBu, Hep H X O X O ' " O ) 1.2 equiv. DAST ( " O ) O Z N -/ ____ ____ » '- N Z N-/ ho^ - NH2 / 5 equiv. HO Toluene/THF (1:1) ~ K2C03, DCM, ^ O c ^ ' reflux, 0.5 M O ° ^ ' o 1-5 d Y 1 h Y 80-98% 50-81% o o - I & ^ N-SF3 J IBCF NMM DAST 52 Scheme 2.2. Synthesis of the 4-heptyl substituted ligands. o 2n . O 1.5 equiv OA Cl 2 equiv. pyridine 0.5 M DCM RT, 18 h O 2 85% N02 BnO OX » o 10% wt Pd/C (5 mol% Pd) H2 balloon EtOAc, RT 0.25 M,12 h HO O A £ > O B n O ^ ' ' ' ^ \ HN-V 1.1 equiv. 0.4M NaHC03 0.4 M THF RT, 24 h 91% 98% performed with the appropriate D-proline derivatives. Therefore, the absolute value of er was used for the purposes described below. With the 25 ligands synthesized, evaluation of the allylation of benzaldehyde was conducted under the conditions shown in Figure 2.2. Each allylation was repeated and the reported values represent the average of at least two replicates. The measured enantioselectivities are given in Table 2.1. To initially quantify the steric effects, Charton values were investigated.12-15 This choice was based on our previous LFERs as well as our desire to extrapolate the model making use of the extensive library of reported Charton values to facilitate this extrapolation.5,16 A scatterplot of the Charton values of X, Y and enantioselectivities is shown in Figure 2.3. Although our intention was to model the data collectively, we initially modeled the data in 2D slices in order to understand the overall character. Excitingly, a new LFER was discovered for the XMe ligand series (Figure 2.4). Notably, this LFER included the XMe YHep ligand in the correlation, a Y substituent, which had not been correlated in previous LFERs. This result suggested that extrapolation of this XMe ligand series might not suffer from the same breaks in linearity as previously observed. Developing a Model As previously stated, our desire was to mathematically model the data as a complete set. In order to develop such a model, key assumptions required consideration. The first assumption is that linear free energy relationships refer to "linear" in the mathematical sense.17 In order for a function to be linear in a mathematical sense it must possess two characteristics; the first is additivity and the second is homogeneity. Additivity can be defined such that the sum of functions is the same as each function added to the other as shown in Equation 2.1. f(x+y) = f(x) +f(y) (2.1) 53 54 Table 2.1. Results of the ligand library screen in the allylation of benzaldehyde. Substituent er AAG* x H ^Me 50:50 0.00 XH YEt 36.5:63.5 0.30 XH Y;Pr 38.5:61.5 0.25 XH YfBu 15:85 0.94 XH YHep 26.3:73.7 0.56 X|\/|e YMe 44:56 0.13 XMe Y a 39:61 0.24 XMe Y/Pr 35.5:64.5 0.32 XMe YfBu 17:83 0.86 XMe Y|Hep 12:88 1.08 XEt YMe 39:61 0.24 XEt YEt 25.5:74.5 0.58 XEt Y/pr 16.5:83.5 0.88 XEt YfBu 18:82 0.82 XEt Y|Hep 11:89 1.13 X/Pr YMe 37.5:62.5 0.28 X/Pr YEt 16.5:83.5 0.88 X/Pr Y/Pr 14.5:85.5 0.96 X/Pr YfBu 8.5:91.5 1.29 X/Pr Y|Hep 24.3:75.7 0.62 XfBu YMe 39.6:60.4 0.23 XfBu YEt 41:59 0.20 XfBu Y/Pr 35.3:64.7 0.33 XfBu YfBu 35:65 0.34 XfBu YHep 31.5:68.5 0.42 55 o A. + Ph H 10 mol% CrCI3*(THF)3 11 mol% Ligand X 20 mol% TEA, * 4 equiv. TMSCI, 2 equiv. Mn(0), THF, 0 °C, 18 h Figure 2.3. Three-dimensional scatterplot of the measured enantioselectivities in the allylation of benzaldehyde. 56 Charton Value Figure 2.4. LFER between the Y substituent and enantioselectivity which includes the 4-Heptyl (Hep) derived ligand. Homogeneity implies that for each discreet input into the function there is a single output as demonstrated in Equation 2.2. f(ax) = af(x) (2.2) Simply, a linear function is any function where one value in X corresponds to one value in Y. Using LFERs in asymmetric catalysis assumes homogeneity and additivity for the mechanism of asymmetric induction for the reaction but also the source of the parameters used to develop the LFER. These assumptions must be made with caution if causality is going to be implied. Equation 2.3, upon which all LFERs are based, is a linear function. AAG* = -RTln(krei) (2.3) A linear free energy relationship does not have to exhibit a first order (straight line) relationship, i.e. polynomials and other mathematical operations can produce a linear function. First order relationships have prevailed in the literature because interpretation and development is simplified. For this reason, the term "linear" is often interpreted to mean only first order character. For the remainder of this thesis, the term "linear" will reference the mathematical definition and not the colloquial interpretation. Justification for including not first order terms is found in examining the Lennard-Jones potential, a model for steric repulsion. Steric effects, by definition, are the electrostatic repulsive forces exhibited by two atoms or molecules as they approach one another beyond their Van der Waals distances, as modeled by the Lennard-Jones potential (Figure 2.5).18-20 Thus, any comprehensively modeled steric interaction would not likely possess straight line character but rather a curved exponential character. However, this does not discount the first order relationships previously described. The complexity of steric interactions can be modeled in many different ways, but should not be limited to first order relationships with steric parameters (Figure 1.27). 57 58 Distance Figure 2.5. The Lennard-Jones potential for steric interactions indicating the region where straight line character might be approximated for a repulsive interaction. Our empirical inspection of the data in Figure 2.3 led us to propose a full third order polynomial as the base model, upon which we could regress the data (Equation 2.4).21 AAG*= z0 + aX + bY + cX2 + dY2 + fXY + gX3 + hY3 + iYX2 + jXY2 (2.4) The data from the ligand library would possess 25 individual points gathered from the 25 individual ligands. A base model with higher order terms would mean a larger number of terms to fit to the data and could lead to over fitting the model to the data. The number of data points less the number of terms used to model the data is defines the number of degrees of freedom. The higher the degrees of freedom, the more ability a model possesses to accommodate experimental error. Thus, a balance between the terms included and the size of the data set must be achieved. The fear of over fitting a model and losing predictive power led to limiting the base model as a full third order polynomial. We chose a full 3rd order polynomial to balance an apparent need of higher order terms to model the curvature evident in the data, and maximizing the degrees of freedom. Equation 2.4 includes crossterms which relate variables X and Y under a single coefficient. Crossterms of this variety are typically included in models where the variables are presumed to be interacting. Hence, crossterms were included into the model as a test of the hypothesis that the two steric elements were synergistically influencing enantioselectivity. This hypothesis would be tested through regression of the data onto Equation 2.4; if the crossterms were deemed statistically significant to a predictive model, then the hypothesis would be supported. To fit the polynomial model to the data, a backward stepwise regression technique was used. Applying regression techniques to polynomial models requires that the Charton values (u) be translated to center around zero. This translation is required to eliminate a potential source of error. When only positive values are used, second and third order polynomial character is 59 difficult to distinguish using standard regression techniques and the true character of the relationship can be obscured. The translation was accomplished according to Equation 2.5 for values in each dimension and Figure 2.6 lists the adjusted values. ^adjusted _ ^original - (umax - umin)/2 (2.5) Because Charton values are relative values, which were arbitrarily set with hydrogen equal to zero, the translation has no effect on their interpretation. To perform the regression, the data was assembled into a design matrix X and a response matrix Y shown in Figure 2.7.21 The columns of the design matrix correspond to the terms within a 3rd order polynomial base model, where the first column is an offset (z0) and subsequent columns correspond to X, Y, X2, Y2, XY, etc. In this case, the response matrix is only a single column of the measured enantioselectivity converted to AAG* values. The rows in the design matrix correspond to each different ligand with adjusted Charton values for the X and Y substituent inserted into the columns in the appropriate order. For an example, for the ligand XMe YMe, the adjusted value for Me along the x axis is -0.1 which is placed in the X column, and that value squared (0.01) is placed in the X2 column. Similarly, the adjusted Charton value for Me along the Y axis is -0.51, so that value is placed in the Y column and similarly that value squared (0.26) is placed in the Y2 column. A unique feature of translating the data along two separate axes is that two different values for each group emerge. Because the two data sets were designed with different substituents, the separate values are required. However, the key principle is that the values remain relative along a single axis in order to maintain comparability and not bias the model's development. Examining the data in matrices can be instructive as to how multivariate regression is performed. The base 3rd order polynomial has ten unknown parameter coefficients (z0-j). These coefficients can be considered in the same manner that slope is considered in a first order 60 61 Adj. Charton Values Substituent X Y X Substituent Charton Values x H YMe -0.62 -0.51 XH Ya -0.62 -0.47 •*- 1----------- 1---------1------------ 1-------------1- - XH Y/Pr -0.62 -0.27 0 .52 .56 .76 1.24 XH YfBu -0.62 0.21 (H) (Me) (Et) (/Pr) (fBu) XH YHep -0.62 0.51 Xiwe YMe -0.1 -0.51 X Substituent Adjusted Charton Values X|\/ie YEt -0.1 -0.47 X|\/|e Y/'Pr -0.1 -0.27 •*- I----------- 1---------1------------ 1-------------1- - XMe YfBu -0.1 0.21 -.62 -.1 -.06 .14 .62 X|\/|e YHep -0.1 0.51 (H) (Me) (Et) (/Pr) (fBu) XEt YMe -0.06 -0.51 XEt Y a -0.06 -0.47 Y Substituent Charton Values XEt Y/'Pr -0.06 -0.27 XEt YfBu -0.06 0.21 - H--------1-----------1---------------1----------- 1- ► XEt Y|Hep -0.06 0.51 .52 .56 .76 1.24 1.54 X/Pr YMe 0.14 -0.51 (Me) (Et) (/Pr) (tBu) (Hep) X/Pr Y a 0.14 -0.47 X/Pr Y/Pr 0.14 -0.27 Y Substituent Adjusted Charton Values X/Pr YfBu 0.14 0.21 X/Pr YHep 0.14 0.51 ■*- I--------1-----------1---------------1----------- 1- ► XfBu YMe 0.62 -0.51 -.51 -.47 -.27 .21 .51 XfBu Y a 0.62 -0.47 (Me) (Et) (/Pr) (fBu) (Hep) XfBu Y/pr 0.62 -0.27 XfBu YfBu 0.62 0.21 XfBu YHep 0.62 0.51 Figure 2.6. A) Original Charton values and their translation according to Equation 5 along both axes. B) Tabulation of translated values for the ligand library. 62 Ligand zO ‘H YMe ‘H Yh ‘H Y,pr ‘H YfBu ‘H Y|Hep ‘Me YMe ‘Me Yh ‘Me Y/Pr ‘Me YfBu ‘Me Y|Hep ‘Et YMe ■Et Yh ■Et Y/Pr ■Et YfBu ■Et Y|Hep ‘/'Pr YMe ‘/'Pr YEt ‘/'Pr Y/Pr ‘/'Pr YfBu ‘/'Pr Y|Hep ■fBuYMe 'fBuYh ‘fBu Y/Pr ‘fBuYfBu ‘fBuY|Hep X Y Design Matrix X X2 Y2 XY X3 X3 YX2 Respons Matrix XY2 AAG% -0.62 -0.51 0.3844 0.2601 0.3162 -0.2383 -0.1327 -0.1960 -0.1613 0.00 -0.62 -0.47 0.3844 0.2209 0.2914 -0.2383 -0.1038 -0.1807 -0.1370 0.30 -0.62 -0.27 0.3844 0.0729 0.1674 -0.2383 -0.0197 -0.1038 -0.0452 0.25 -0.62 0.21 0.3844 0.0441 -0.1302 -0.2383 0.0093 0.0807 -0.0273 0.94 -0.62 0.51 0.3844 0.2601 -0.3162 -0.2383 0.1327 0.1960 -0.1613 0.56 -0.1 -0.51 0.01 0.2601 0.051 -0.0010 -0.1327 -0.0051 -0.0260 0.13 -0.1 -0.47 0.01 0.2209 0.047 -0.0010 -0.1038 -0.0047 -0.0221 0.24 -0.1 -0.27 0.01 0.0729 0.027 -0.0010 -0.0197 -0.0027 -0.0073 0.32 -0.1 0.21 0.01 0.0441 -0.021 -0.0010 0.0093 0.0021 -0.0044 0.86 -0.1 0.51 0.01 0.2601 -0.051 -0.0010 0.1327 0.0051 -0.0260 1.08 -0.06 -0.51 0.0036 0.2601 0.0306 -0.0002 -0.1327 -0.0018 -0.0156 0.24 -0.06 -0.47 0.0036 0.2209 0.0282 -0.0002 -0.1038 -0.0017 -0.0133 0.58 -0.06 -0.27 0.0036 0.0729 0.0162 -0.0002 -0.0197 -0.0010 -0.0044 0.88 -0.06 0.21 0.0036 0.0441 -0.0126 -0.0002 0.0093 0.0008 -0.0026 0.82 -0.06 0.51 0.0036 0.2601 -0.0306 -0.0002 0.1327 0.0018 -0.0156 1.13 0.14 -0.51 0.0196 0.2601 -0.0714 0.0027 -0.1327 -0.0100 0.0364 0.28 0.14 -0.47 0.0196 0.2209 -0.0658 0.0027 -0.1038 -0.0092 0.0309 0.88 0.14 -0.27 0.0196 0.0729 -0.0378 0.0027 -0.0197 -0.0053 0.0102 0.96 0.14 0.21 0.0196 0.0441 0.0294 0.0027 0.0093 0.0041 0.0062 1.29 0.14 0.51 0.0196 0.2601 0.0714 0.0027 0.1327 0.0100 0.0364 0.62 0.62 -0.51 0.3844 0.2601 -0.3162 0.2383 -0.1327 -0.1960 0.1613 0.23 0.62 -0.47 0.3844 0.2209 -0.2914 0.2383 -0.1038 -0.1807 0.1370 0.20 0.62 -0.27 0.3844 0.0729 -0.1674 0.2383 -0.0197 -0.1038 0.0452 0.33 0.62 0.21 0.3844 0.0441 0.1302 0.2383 0.0093 0.0807 0.0273 0.34 0.62 0.51 0.3844 0.2601 0.3162 0.2383 0.1327 0.1960 0.1613 0.42 Figure 2.7. The design matrix used in the initial iteration of model development for the allylation of benzaldehyde. model, the value of the coefficient reflects the sensitivity of the model to the term. The data can be considered a series of equations (rows) with solutions (AAG* values) that can be used to solve for the ten unknown parameter coefficients. As long as there are fewer unknowns than equations, linear least squares regression can be performed. Accordingly, regression was performed using the linear algebra definition of regression given in Equation 2.6, where C is the output matrix of coefficients z0-j. C = (XtX)-1(XtY) (2.6) To analyze the regression model, the variance-covariance matrix V was also calculated according to Equation 2.7 where s2 is the variance of the AAG* values. V = s2(XtX)'1 (2.7) The variance-covariance matrix estimates the variance or error associated with each coefficient value along the diagonal. The off diagonal terms relate the covariance between terms in the model. Covariance between terms implies two terms depend on each other linearly. Linear dependence between terms is a major source of error in predictive models because it obscures the true relationships within a model. Ideally, no covariance between terms would lead to the most predictive model. Hence, interpretation of the variance-covariance matrix was an essential component of model development. To demonstrate how the model was developed the first iteration will be given in detail, and the remaining iterations can be examined in the supplemental information. The original data is given in Figure 2.7 as matrices X and Y. Regression according to Equation 2.6 was performed and the resulting coefficient estimates are given in Equation 2.8. AAG*= 0.93 - 0.0001X + 0.58Y - 0.91X2 - 1.01Y2 - 0.50XY - 0.41X3- 0.0002Y3- 0.48YX2 + 0.00XY2 63 (2.8) This model was used to predict AAG* values for all 25 data points, which were plotted against the experimentally measured AAG* values as shown in Figure 2.8. The slope of the linear correlation between predicted and measured values is the R2 value for the model and is 0.75. This value was used as a measure for the statistical goodness of fit. To avoid over fitting the data, an analysis of variance (ANOVA) was performed and the Fischer statistic (f-value) for the model was calculated to be 46. These two statistical measures provide the criteria, we used to development the initial model. In order to maximize each of these statistical criteria the variance-covariance matrix was calculated and used as rational for elimination of terms (Figure 2.9). Examining the highlighted values along the diagonal reveals that jXY2, which has a value of zero, also has the highest error relative to the coefficient value. As a result, the column corresponding to this term in the design matrix X is removed giving a revised design matrix X1 shown in Figure 2.10. This design matrix is used to evaluate new coefficient terms given in Equation 2.9. AAG*= 0.93 - 0.0001X + 0.58Y - 0.91X2 - 1.01Y2 - 0.50XY - 0.41X3 - 0.0002Y3 - 0.48YX2 (2.9) Elimination of this zero term did not have any significant effect on the terms of the model but does increase the f-value to 58. The new variance-covariance matrix shown in Figure 2.11 reveals the term with the highest relative error is the hY3 term, which would be eliminated in subsequent rounds. This process was repeated until the elimination of a term led to an insignificant or detrimental effect on the statistical criteria R2 and f-value. It should also be noted that in cases where omission of a term led to a detrimental effect on statistical criteria, elimination of the terms that showed covariance with the initial term was also performed. Once a minimum number of terms were reached, each individual term was added again to the model one by one and their statistical significance reassessed to ensure no term was eliminated due to high covariance unnecessarily. The final derived model is given in Equation 2.10. Equation 2.10 64 65 Measured aaGt (kcal/mol) Figure 2.8. Plot comparing the predicted enantioselectivities from Equation 8 to experimentally measured enantioselectivities. zO X Y 0.21 0.07 0.00 0.07 7.41 0.00 0.00 0.00 3.13 -0.21 -0.21 -0.13 -0.78 -0.02 0.37 0.00 0.02 0.01 -0.17 17.13 0.00 0.13 0.00 -11.96 -0.13 0.00 -1.20 -0.02 -4.84 0.00 X2 Y2 XY X3 X3 YX2 XY2 -0.21 -0.78 0.00 -0.17 0.13 -0.13 -0.02 ■0.21 -0.02 0.02 -17.13 0.00 0.00 -4.84 ■0.13 0.37 0.01 0.00 -11.96 -1.20 0.00 1.29 0.00 0.00 0.54 0.00 0.79 0.00 0.00 4.63 0.00 0.00 -1.04 0.00 0.12 0.00 0.00 1.58 0.00 0.00 -0.04 0.83 0.54 0.00 0.00 46.40 0.00 0.00 0.00 0.00 -1.04 0.00 0.00 53.33 0.00 0.01 0.79 0.00 -0.04 0.00 0.00 7.45 0.00 0.00 0.12 0.83 0.00 0.01 0.00 28.70 Figure 2.9. The variance-covariance matrix associated with coefficients of Equation 8. 66 Response Ligand Revised Design Matrix X 1 Matrix Y zO X Y X2 Y2 XY X3 Y3 YX2 AAG* XH ^Me 1 -0.62 -0.51 0.3844 0.2601 0.3162 -0.2383 -0.1327 -0.1960 0.00 XH YEt 1 -0.62 -0.47 0.3844 0.2209 0.2914 -0.2383 -0.1038 -0.1807 0.30 XH Y;Pr 1 -0.62 -0.27 0.3844 0.0729 0.1674 -0.2383 -0.0197 -0.1038 0.25 XH Y,bu 1 -0.62 0.21 0.3844 0.0441 -0.1302 -0.2383 0.0093 0.0807 0.94 Xh YHep 1 -0.62 0.51 0.3844 0.2601 -0.3162 -0.2383 0.1327 0.1960 0.56 XMe YMe 1 -0.1 -0.51 0.01 0.2601 0.051 -0.0010 -0.1327 -0.0051 0.13 XMe YEt 1 -0.1 -0.47 0.01 0.2209 0.047 -0.0010 -0.1038 -0.0047 0.24 XMe Y/pr 1 -0.1 -0.27 0.01 0.0729 0.027 -0.0010 -0.0197 -0.0027 0.32 XMe YfBu 1 -0.1 0.21 0.01 0.0441 -0.021 -0.0010 0.0093 0.0021 0.86 XMe YHep 1 -0.1 0.51 0.01 0.2601 -0.051 -0.0010 0.1327 0.0051 1.08 XEt YMe 1 -0.06 -0.51 0.0036 0.2601 0.0306 -0.0002 -0.1327 -0.0018 0.24 XEt YEt 1 -0.06 -0.47 0.0036 0.2209 0.0282 -0.0002 -0.1038 -0.0017 0.58 XEt Y/Pr 1 -0.06 -0.27 0.0036 0.0729 0.0162 -0.0002 -0.0197 -0.0010 0.88 XEt YfBu 1 -0.06 0.21 0.0036 0.0441 -0.0126 -0.0002 0.0093 0.0008 0.82 XEt YHep 1 -0.06 0.51 0.0036 0.2601 -0.0306 -0.0002 0.1327 0.0018 1.13 X/Pr YMe 1 0.14 -0.51 0.0196 0.2601 -0.0714 0.0027 -0.1327 -0.0100 0.28 X/Pr YEt 1 0.14 -0.47 0.0196 0.2209 -0.0658 0.0027 -0.1038 -0.0092 0.88 X/Pr Y/Pr 1 0.14 -0.27 0.0196 0.0729 -0.0378 0.0027 -0.0197 -0.0053 0.96 X/Pr YfBu 1 0.14 0.21 0.0196 0.0441 0.0294 0.0027 0.0093 0.0041 1.29 X/Pr YHeD 1 0.14 0.51 0.0196 0.2601 0.0714 0.0027 0.1327 0.0100 0.62 XfRn Ymq 1 0.62 -0.51 0.3844 0.2601 -0.3162 0.2383 -0.1327 -0.1960 0.23 XfBu YEt 1 0.62 -0.47 0.3844 0.2209 -0.2914 0.2383 -0.1038 -0.1807 0.20 XfBu Y/pr 1 0.62 -0.27 0.3844 0.0729 -0.1674 0.2383 -0.0197 -0.1038 0.33 XfBu YfBu 1 0.62 0.21 0.3844 0.0441 0.1302 0.2383 0.0093 0.0807 0.34 XfBu Y|Hep 1 0.62 0.51 0.3844 0.2601 0.3162 0.2383 0.1327 0.1960 0.42 Figure 2.10. The first iteration of the design matrix after elimination of the hXY2 term. zO X Y X2 Y2 XY X3 Y3 YX2 0.21 0.06 0.00 -0.21 -0.78 0.00 -0.17 0.13 -0.13 0.06 6.59 0.00 -0.21 0.00 0.16 -17.13 0.00 0.00 0.00 0.00 3.13 -0.13 0.37 0.01 0.00 -11.96 -1.20 -0.21 -0.21 -0.13 1.29 0.00 0.00 0.54 0.00 0.79 -0.78 0.00 0.37 0.00 4.63 0.00 0.00 -1.04 0.00 0.00 0.16 0.01 0.00 0.00 1.56 0.00 0.00 -0.04 -0.17 - 17.13 0.00 0.54 0.00 0.00 46.40 0.00 0.00 0.13 0.00 11.96 0.00 -1.04 0.00 0.00 53.33 0.00 -0.13 0.00 -1.20 0.79 0.00 -0.04 0.00 0.00 7.45 Figure 2.11. The variance-covariance matrix associated with the coefficients in Equation 9. represents the achievement of our goal and models the entire data set. The final statistical measures for the model are an R2 value of 0.75 and an f-value of 125. Equation 2.10 possesses three dimensions (adjusted Charton value of X, adjusted Charton value of Y, and experimentally determined AAG*) so it can be visualized as a surface as shown in Figure 2.12. AAG*= 0.93 + 0.58Y - 0.91X2 - 1.01Y2 - 0.50XY - 0.41X3 - 0.48YX2 (2.10) The development of the model was based on statistical significance of the terms incorporated into the model. The result of this treatment of the data is that each term's has statistical significance in the final model. The inclusion of two statistically significant crossterms in the final model suggests that X and Y substituents are in fact interacting and influencing enantioselectivity. The spectroscopically elusive nature of the ligand-catalyst complex has deflected our attempts to probe structure directly but hand models and limited computation have suggested that the groups are on opposite sides of the catalyst. While the exact meaning of this relationship is still unclear, the crossterms have provided considerable insight into the catalyst system. The purpose of the 3D free energy relationship was not only to examine the proposed synergistic effect but to overcome the observed breaks in linearity. The 3D model shown in Figure 2.12, and the 2D LFER shown in Figure 2.4 presented a situation to compare the predictive power of the two models. The two models exhibit different trends with increasing size in the Y dimension. The 3D model demonstrates downward curvature and the 2D model exhibits a positive trend. Our desire to extrapolate the two models as well as externally validate the 3D model led us to synthesize ligands 3a-3c because of their large Y value would be a maximum extrapolation of the linear model. Ligand 3b provides direct comparison between models and ligands 3a and 3c were also used to validate Equation 2.10. The synthesis paralleled the previously described syntheses and the results for these ligands are given in Figure 2.13. For 67 68 A) U | TO o e> > 0.6 Measured aa(j (kcal/mol) Figure 2.12. A) Three-dimensional surface model described by Equation 10 overlaid onto the original data. B) Plot of the predicted enantioselectivities given by Equation 10 with their experimentally measured values. 69 X o D Predicted er Measured _______X Linear 3D_______Error______ar 3a H NA 40.8:59.2 ±4 42.5:57.5 3b Me 3:97 46.7:53.3 ±4 36:64 3c /Pr NA 38.6:61.3 ±4 40:60 Figure 2.13. Comparison of predictions made by the 2D LFER and the 3D LFER for a several ligands bearing a bulky carbamoyl group. ligand 3b, the 3D LFER was able to predict the enantioselectivity with much greater accuracy than the 2D LFER. The 2D LFER relationship exhibits another break in linearity for a large substituent. Prediction of enantioselectivity for ligands 3a and 3c, is accurate to within error and prediction of ligand 3b is within reason. The accuracy of these predictions is remarkable given the magnitude of the extrapolation and the limitations imposed on the model discussed below. In critique of this effort to develop 3D LFERs, development of the library and data evaluation was time consuming and led to only 3 predictions of poor ligand performance. The model itself did not give a high degree of correlation to the source data. The method would be more compelling if it were capable of predicting higher performing ligands, whereas from a practical stand point most chemists would not invest this much effort for such predictions. The analysis did reveal the presence of crossterms relating X and Y. The use of crossterms in models such as this is an intriguing technique, which might be capable of probing relationships for which there is no direct measure. Similar to the examination of benzaldehyde, a separate evaluation was performed on data gathered from the allylation of acetophenone but weaker correlation and no predictive power was exhibited by several derived models. In order to refine the 3D-LFER approach, it became apparent that the principles of experimental design would need to be applied to the system. The Principles of Experimental Design Applied to Asymmetric Catalysis Experimental design has existed since the 1870s and has become a field unto itself.21 The application of statistical inference in chemical problems has taken the name chemometrics or chemoinformatics. The fundamental concept is that if statistical inferences are going to be made about a body of data with variance, then statistical design of the experiment will lead to 70 greater predictive power. In order to develop better 3D-LFERs, two key principles were applied from the principles of experimental design namely the even distribution of data and interpolation of result rather than extrapolation.21 Due to some inherent complications, the principles of experimental design cannot be applied to steric effects and asymmetric catalysis in their purest forms. The conflict in this application primarily arises from the discreet nature of the substituents employed. Charton's steric parameters do not present a continuous spectrum of values but rather a series of discreet values limited by synthetic constraints. Essentially, there is no substituent between a methyl group and an ethyl group. While not quite correct, this statement exemplifies the problem inherent in applying experimental design principles to steric parameters. Experimental design in its purest form is applied to variables that are continuous such as temperature or pressure. This limitation not only complicates the application of the principles but also the interpretation of the results. The first principle of experimental design applied to the ligand library dealt with the distribution of data points along the X and Y axes. Figure 2.14 shows how the data points were aligned according to our initial attempt. The data is not evenly spread across either axis. This uneven distribution results in biasing the model with greater predictive power in quadrant III and weaker predictive power in quadrant I. The bias in the model can complicate and cause inaccuracy in extrapolation. Experimental design dictates that a data set designed with an even spread of data points can have as much or greater predictive power than one with more points that is unevenly spread. One of the critiques of the previous model was that 25 (5x5) ligands required a large synthetic effort to generate moderate predictions. Revising the ligand library to include only 9 (3x3) ligands, which have substituents that are evenly spaced along both the X 71 72 X o V V V > Figure 2.14. Quadrant array of data points for the 5x5 ligand library showing a bias of data in quadrant III. and Y axes, appeared to be an ideal reconciliation of minimum synthetic effort with potential prediction of better performing catalysts. The second principle states that extrapolation outside the range of a data spread is far less accurate than interpolation. In order to accommodate this second principle of experimental design, the types of ligands used in the library had to be rethought. To expand our model to make it interpolative instead of extrapolative, we designed a new nearly evenly spread library of 9 ligands, which also employed the previously synthesized ligand 3a-c (Figure 2.15). The bulky CEt3 substituent has one of the largest Charton values reported. Although synthesis of larger substituents at the Y position is theoretically possible, such substituents could not be quantified because they lack Charton values. Thus, the CEt3 substituent constitutes the upper bound along the Y axis and the Me substituent the lower bound. On the X axis the largest readily available substituent was the tBu group, which represents the upper bound and hydrogen the lower bound. One result of using the YCEt3 ligands is that the data had to be readjusted using Equation 2.5. Table 2.2 lists the adjusted Charton values for the 3x3 ligand library. The center points chosen were Me and £Bu in the X and Y axes respectively. The spread of data points in the X and Y axes is given in Figure 2.15. These center points do not lie perfectly on the center of the spread but, because of the discreet nature of the substituents, are reasonable approximations. The new design encapsulates the available synthetic space with a minimal number of ligands. Of note, the XtBu YCEt3 ligand proved synthetically difficult to prepare and was substituted in the data array for the X,Pr YCEt3 ligand. The effect of this is the indicated region where the predictive power of the model becomes poor. 73 74 Quandrant II • • ' H,CEt3 Me,CEf3 Y Quandrant 1 /Pr,CEt, \ % o 0.5 'O <5- n n -0.5 oo a 0.5 • • • H, fBu Me,fBu -0.5 fBu, fBu • • -1.0 • H,Me Me,Me‘ fBu, Me Quandrant III Quandrant IV Figure 2.15. Quadrant array of the revised 3x3 ligand library. Table 2.2. Adjusted Charton values for the 3x3 ligand library. Adj. Charton Values Substituent X Y xH ^Me -0.62 -0.93 xH YfBu -0.62 -0.21 XH YcEt3 -0.62 0.93 XMe YMe -0.1 -0.93 XMe YfBu -0.1 -0.21 XMe Y CEt3 -0.1 0.93 XfBu YMe 0.62 -0.93 XfBu YfBu 0.62 -0.21 XfBu YcEt3 0.62 0.93 Reevaluation of the Data Reevaluation of the data for allylation of benzaldehyde also incorporated a new technique for regression. Using the above method to regress the data for benzaldehyde revealed a model described by Equation 2.11 and depicted in Figure 2.16A. AAG*= 0.92 - 0.53X - 0.89X2 - 0.89Y2 - 0.69XY - 0.97XY2 (2.11) Because the nine-member ligand library was employed to generate the model, the remaining data of the original 25-membered library could be used to externally validate the model. The validation plot of predicted and measured enantioselectivities is given in Fig 2.16B. Q2 is a common statistical measure for predictive validation, where Q2 is the slope of a predicted versus measured plot. The model gives a Q2 value of 0.6 where values > 0.5 are generally considered predictive in the QSAR literature.22 The surface model possesses a clear maximum point within the synthetic space. Again because of the discreet nature of Charton values, the model can only be treated in a semi-empirical fashion. The model maximum falls between the values for ligand 4a and 4b shown in Figure 2.17. These two ligands were the best performing ligands evaluated with the truncated scaffold in this allylation reaction. In our 3x3 ligand library, both of these ligands were not included in the training set. The model developed from only 9 ligands was able to accurately predict a priori the optimal ligand structure. Prediction of the performance of these ligands is lower than experimentally observed, which might be attributed to the small and unavoidable biases in the data set. Comparison of Equations 2.10 and 2.11 show the presence of the same crossterms in both models with roughly the same direction and magnitude. The preservation of the crossterms across models derived using different data further validates the proposed synergistic relationship of the X and Y substituents. 75 76 A) P h ^ H + 10 mol% CrCI3*(THF)3 11 mol% Ligand X 20 mol% TEA, * 4 equiv. TMSCI, 2 equiv. Mn(0), THF, 0 °C, 18 h B) 1.0 o 0.8 |TO 0 1 0.6^ ■O 0 .4 So3 | 0.2 0.0 Q = 0.60 0.0 -i- 0.2 " o T 0'6 "oT -i- 1.0 -I- 1.2 -i- 1.4 Measured aaG* (kcal/mol) Figure 2.16. A) Surface model given by Equation 11 for the allylation of benzaldehyde under standard conditions. B) Validation plot for 19 other ligands not included in the training data. 77 X O . . KA Nr > Predicted Measured _______X________ er Error er 4a Et 16:84 ±5 9.5:90.5 4l» /Pr 17:83 ±5 8:92 Figure 2.17. Predictions of the optimal ligand from Equation 11. The allylation of acetophenone was reevaluated using the revised 3x3 ligand library and data analysis techniques. The revised model is given in Equation 2.12 and the surface is given in Figure 2.18A. AAG*= 1.31 + 0.046X - 0.69X2- 1.1Y2 - 0.069XY + 0.92Y3 (2.12) Again, independent validation was performed using ligands not contained in the training set. The Q2 value shown in Figure 2.18B again indicates the model is reasonably predictive. The surface described by Equation 2.12 predicts a maximum enantioselectivity achievable for this ligand scaffold. Similar to the above example, this maximum was determined to lie closest to ligand 5 (Figure 2.19). Evaluating all of the data gathered for this reaction and ligand scaffold holds that this ligand is the highest performing of any ligand in the enantioselective ketone allylation reaction. The data for this ligand was not incorporated into the training set again, demonstrating the ability of 3D QSAR to predict optimal structure a priori. The predicted enantioselectivity for 5 was lower than experimentally observed as was the case in the 3x3 allylation of benzaldehyde model. Both of these examples demonstrate the ability of 3D free energy surfaces in interpolating the optimal ligand structure. However, the models developed were based on systems, which we had studied and reported optimized reaction conditions. Our desire was to use this system on challenging reactions to quickly identify optimal ligand structure for high enantioselectivity. To explore the potential of the system on a challenging reaction, we explored the NHK allylation of methyl ethyl ketone (MEK). Our previous reports of enantioselective NHK reactions had focused on aryl substrates primarily because observed enantioselectivity was poor for aliphatic substrates. We hoped that the development of a 3D free energy surface for the allylation of the simplest aliphatic substrate, MEK, would direct us to an optimized ligand structure for the allylation of aliphatic ketones. 78 79 A) u + Pt r^Me Br 2 equiv. 10 mol% CrCI3*(THF)3 11 mol% Ligand X ^ 20 mol% TEA, * 4 equiv. TMSCI, 2 equiv. Mn(0), THF, 0 °C, 18 h Measured AAG* (kcal/mol) Figure 2.18. A) Surface model given by Equation 12 for that allylation of acetophenone under standard conditions. B) Validation plot for 19 other ligands not included in the training data. 80 Predicted Measured er Error er /Pr tBu 8:92 ±2 4.5:95.5 Figure 2.19. Predictions of the optimal ligand allylation of acetophenone. To probe the allylation of MEK, we utilized the same reaction conditions that had been previously used in our allylation reactions. Evaluation of the nine-member ligand library and analysis of the subsequent data yielded Equation 2.13 which is shown in Figure 2.20. AAG*= -0.87 - 0.94X - 0.29Y + 0.11X2 + 0.20Y2 + 0.11XY + 2.17X3+ 0.44XY2 (2.13) Disappointingly, the model revealed a rather featureless relationship between enantioselectivity and positions X and Y. Interestingly, the optimal ligand observed in the screen was XMe, YMe indicating that smaller catalyst features were desirable. However, the conclusion that must be drawn from the model is that modification of the ligand scaffold will not lead to the desired levels of enantioselectivity. The surface indicates major modification to the reaction must be explored to achieve higher enantioselectivity either through condition modification or ligand restructuring. In this case, the entire 25-membered library was not explored in the reaction before this conclusion was drawn. Hence, full validation of the model was not pursued. Although disappointing, the analysis of the allylation of MEK presents another desirable aspect of this type of analysis. After evaluating only nine ligands, we were able to determine that satisfactory enantioselectivity was not likely to be achieved using the current ligand and conditions. The result was that we could change course if our goal is to obtain a highly enantioselective reaction. Not including synthesis of the ligands, evaluation of the reaction took less than a week. Frequently in asymmetric reaction development, a greater investment of time and ligand synthesis is required before similar conclusions can be drawn. Conclusion Through the use of 3D free energy surfaces, we were able to make accurate predictions about catalyst performance and design. After some initial crude attempts led to some predictive power, we were able to apply the principles of experimental design to develop a nine- 81 82 Br ^ 2 equiv. 10 mol% CrCI3*(THF)3 11 mol% Ligand X ^ 20 mol% TEA, * 4 equiv. TMSCI, 2 equiv. Mn(0), THF, 0 °C, 18 h HO Me Figure 2.20. Surface model given by Equation 13 for that allylation of MEK under standard conditions. membered library, which was used to develop models able to correctly predict the optimal ligand structure for the allylation of benzaldehyde as well as acetophenone. Only a handful of examples exist where accuracy of this level was achieved in predicting enantioselective outcomes in asymmetric catalysis.23-26 Through the use of Charton's steric parameters, evidence was found via statistically significant crossterms that both the X and Y positions were interacting synergistically. This hypothesis would have been difficult to examine via other techniques. The overall approach does not require kinetic or structural data beyond the substituents examined. This study demonstrates the power of experimental design applied to catalysis or reaction optimization. Although this study focused on steric-steric-enantioselective relationships, the techniques are not limited to such relationships or dimensionality. Any quantifiable, variable catalyst characteristic could be employed as the dependent variables and several measurable quantities could be used in place of enantioselectivity. As we continue to explore the application of these predictive techniques, we hope to expand the scope of independent as well as dependent variables used in them. Experimental General Considerations Unless otherwise noted, all reactions were performed under a nitrogen atmosphere with stirring. Toluene, dichloromethane, dichloroethane and THF were dried before use by passing through a column of activated alumina. Methanol was distilled from magnesium methoxide. Triethylamine was distilled from CaH2. Benzaldehyde was purified by aqueous base wash, drying with sodium sulfate, and followed by fractional distillation. Acetophenone was purified by drying over Na2SO4 then fractional distillation. Methyl Ethyl Ketone was purified by two sequential fractional distillations. Allyl bromide was purified by drying over magnesium 83 sulfate, filtration and fractional distillation. CrCl3(THF)3 was prepared by soxhlet extraction of anhydrous CrCl3 with anhydrous THF. All other reagents were purchased from commercial sources and used without further purification. Yields were calculated for material judged homogeneous by thin-layer chromatography and NMR. Thin-layer chromatography was performed with EMD silica gel 60 F254 plates eluting with the solvents indicated, visualized by a 254 nm UV lamp, and stained either with potassium permanganate, phosphomolybdic acid, or ninhydrin. Flash column chromatography was performed with EcoChrom MP Silitech 32-63D 60A silica gel, slurry packed with solvents indicated in glass columns. Nuclear magnetic resonance spectra were acquired at 300, 400, or 500 MHz for 1H, and 75, 100, or 125 MHz for 13C and 50°C. Chemical shifts for proton nuclear magnetic resonance (1H NMR) spectra are reported in parts per million downfield relative to the line of CHCl3 singlet at 7.24 ppm. Chemical shifts for carbon nuclear magnetic resonance (13C NMR) spectra are reported in parts per million downfield relative to the center-line of the CDCl3 triplet at 77.23 ppm. The abbreviations s, d, t, p, sep, dd, td, bs, and m stand for the resonance multiplicities singlet, doublet, triplet, pentet, septet, doublet of doublets, triplet of doublets, broad singlet, and multiplet, respectively. Optical rotations were obtained (Na D line) using a Perkin Elmer Model 343 Polarimeter fitted with a micro cell with a 1 dm path length. Concentrations are reported in g/100 mL. SFC (super critical fluid chromatography) analysis was performed at 25 °C or 40 °C, using a Thar instrument fitted with chiral stationary phase (as indicated). Melting points were obtained on an electrothermal melting point apparatus and are uncorrected. Unless otherwise noted, glassware for all reactions was oven-dried at 110 oC and cooled in a dry atmosphere prior to use. 84 Ligand Synthesis and Characterization 5,7,8,27 Anderson Coupling with Proline (Figure 2.21) To a flame-dried round bottom flask flushed with N2 containing a stirbar and fitted with a septum was added the differentially protected proline (1 equiv.) as a solid or as a standard solution in DCM. The flask is fitted with a septum and attached to a positive pressure of N2. The starting material was then diluted with solvent (0.2M). NMM (1.2 equiv.) was added dropwise and the solution cooled to ~ 0 °C in an ice/water bath. After cooling for 10 min, the IBCF is added slowly dropwise (1 mL/min) and formation of a colorless precipitate is observed. The reaction is allowed to stir 30 min at ~ 0 °C under nitrogen, after which a second portion of NMM (1.1 equiv.) is added. Immediately following the second addition of NMM, the septum is removed and the amino acid methylester hydrochloride salt is added (1.2 equiv.) in one-third portions over 1-2 min. Once the addition of the amino acid methyl ester is complete the ice/water bath is removed and the reaction allowed to stir until starting material is no longer observed by TLC (5% MeOH/DCM, PMA with charring). Upon completion the reaction is diluted in DCM (0.01M) and washed with aqueous sodium bicarbonate. The aqueous layer is then extracted with DCM (3 x 20 mL) and the organic extracts combined and dried with Na2SO4 and concentrated and purified by column chromatography. Thermal Amide Bond Formation (Figure 2.22) To a flame-dried round bottom flask with stir bar, flushed with N2 was added to the methyl ester starting material (1 equiv.) as a solid. The starting material was diluted with THF (1M) and toluene (1M). Then 2-aminoethanol (5 equiv.) was added through the septum and fitted with a condenser. The septum was replaced at the top of the condenser and the mixture was stirred in a sand bath in excess of 100 °C for 1-5 days until complete by TLC (50% 85 86 X o JX A. . . . * o h o A ^ - r " H 2 ^ J r > hci o H r > 0 ^ - N- ~ / |BCF NMM O ^ I W }o DCM ,6 Y Y Figure 2.21. Peptide bond formation using Anderson's conditions. A X \\ HO^\^NvA T Y v > h2N^ o h , O n ° Y N^ THF/Tol. _ A ,0 Y Y Figure 2.22. Thermal amide-bond formation. Acetone / Hexanes). Upon completion the reaction was diluted in DCM (0.05M) and washed with an equal volume of water. The aqueous layer was then extracted with DCM (3x20 mL) and the organic extracts combined and dried with Na2SO4 and concentrated and purified by column chromatography. Oxazoline Cyclization (Figure 2.23) To a flame-dried round bottom flask with stir bar, flushed with N2 and fitted with a septum was added the amide-alcohol starting material (1 equiv.). The starting material was then diluted in DCM (0.125M) and cooled to ~ -78 °C in an isopropyl/dry ice bath. After 10 min of cooling, the DAST is added dropwise. The reaction is allowed to stir at -78 °C for 1 h and then solid K2CO3 is added all at once. The reaction is allowed to warm to ambient temperature and then concentrated. The crude mixture is purified by column chromatography to furnish the ligand products. (S)-methyl-2-((4,5-dihydrooxazol-2-yl)methylcarbamoyl)pyrrolidine-1-carboxylate. The product of the DAST cyclization, was purified by flash silica-gel column chromatography with 5-10% MeOH/DCM as eluent to give 0.301 g. Rf = 0.3 w / 10% MeOH/DCM, yellow oil, [a]20D = - 69.5° (c = 0.965, CHCl3). 1H-NMR (400 MHz, CDCl3) 5 = 6.99 (bs, 1 H), 4.16 (s, 1 H), 4.12 (s, 1H), 3.855 (d, J = 4, 2 H), 3.65 (td, J = 9.6, 1.6; 2 H), 3.53 (s, 3 H), 3.34 (bs, 2 H), 2.1-1.65 (m, 4 H). 13C-NMR {1H} (100 MHz, CDCl3) 5 = 171.9, 164.5, 67.9, 60.5, 54.0, 52.5, 46.9, 36.7, 28.9, 24.0. HRMS CnH17N3O4 (M+H)+ calcd. 256.1297, obsvd. 256.1300. (S)-ethyl-2-((4,5-dihydrooxazol-2-yl)methylcarbamoyl)pyrrolidine-1-carboxylate. The product of the DAST cyclization was purified by flash silica-gel column chromatography with 5­10% MeOH/DCM as eluent to give 0.150 g of L2. Rf = 0.4 w/ 10% MeOH/DCM, yellow oil, [a]20D = -69.7° (c = 1.095, CHCl3). 1H-NMR (400 MHz, CDCl3) 5 = 7.02 (bs, 1H), 4.16 (s, 1H), 4.11 (t, J = 9.6, 87 88 H * O H0^ - Nyn ^ NN A' . o h r > ro o ^ n V k2c o 3 o ^ N^ / Y Figure 2.23. Oxazoline cyclization. 2H), 3.96 (m, 2H), 3.85 (s, 2H), 3.65 (dt, J = 9.6,1.6; 2H), 3.33 (bs, 2H), 2.1-1.65 (m, 4H), 1.071 (t, J = 7.2, 3H). 13C-NMR {1H} (100 MHz, CDCl3) 5 = 172.0, 164.5, 67.9, 61.3, 60.4, 54.0, 46.9, 36.7, 28.9, 24.0, 14.3. HRMS C12H19N3O4 (M+H)+ calcd. 270.1454, obsvd. 270.1451. (S)-isopropyl-2-((4,5-dihydrooxazol-2-yl)methylcarbamoyl)pyrrolidine-1-carboxylate. The product of the DAST cyclization was purified by flash silica-gel column chromatography with 5-10% MeOH/DCM as eluent to give 0.190 g. Rf = 0.4 w / 10% MeOH/DCM, yellow oil, [a]20D = - 0.4° (c = 0.055, CHCl3). 1H-NMR (400 MHz, CDCl3) 5 = 7.08 (bs, 1H), 4.81 (sep, J = 6.4, 1H), 4.17 (m, 3H), 3.92 (d, J = 4.8, 2H), 3.71 (dt, J = 9.6, 1.6; 2H), 3.37 (bs, 2H), 2.2-1.7 (m, 4H), 1.13 (m, 6H), 13C-NMR {1H} (100 MHz, CDCl3) 5 = 172.1, 164.6, 69.0, 68.1, 60.5, 54.1, 47.0, 36.9, 28.5, 24.1, 22.1. HRMS C13H21N3O4 (M+H)+ calcd. 284.1610, obsvd. 284.1606. (S)-tert-butyl-2-((4,5-dihydrooxazol-2-yl)methylcarbamoyl)pyrrolidine-1-carboxylate. The product of the DAST cyclization was purified by flash silica-gel column chromatography with 5-10% MeOH/DCM as eluent to give 0.167 g. Rf = 0.4 w / 10% MeOH/DCM, yellow oil, [a]20D = - 11.8° (c = 0.195, CHCl3). 1H-NMR (400 MHz, CDCl3) 5 = 6.63 (bs, 1H), 4.23 (m, 1H), 4.23 (t, J = 9.2, 2H), 3.99 (m, 2H), 3.77 (t, J = 9.6, 2H), 3.40 (bs, 2H), 2.29-1.75 (bs, 4H), 1.41 (s, 9H). 13C-NMR {1H} (100 MHz, CDCl3) 5 = 172.5, 164.8, 80.6, 68.3, 60.7, 54.3, 47.2, 37.1, 28.5, 24.3. HRMS C14H23N3O4 (M+H)+ calcd. 298.1767, obsvd. 298.1765. (S)-heptan-4-yl 2-((4,5-dihydrooxazol-2-yl)methylcarbamoyl)pyrrolidine-1-carboxylate. The product of the DAST cyclization was purified by flash silica-gel column chromatograp