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Despite the signficant advances in asymmetric hydrogenation, the development of novel and efficient chiral phosphorus ligands to solve new synthetic challenges continues to an important goal. [1] C 2 -Symmetric chiral bisphosphorus ligands such BINAP, [2] DuPhos, [3] and TangPhos [4] are among the most versatile and important ligands for asymmetric hydrogenation, yet they are not universal. To expand their synthetic utilities, one common strategy is to develop structurally similar ligands, such as Tol-BINAP, Xyl-BINAP, Et-DuPhos, or iPr-DuPhos by increasing the size of the substituents on the phosphorus centers (Figure 1 a). Such modifications lead to the design of ligands with deeper chiral pockets mainly owing to the increased bulk of the R groups, which protrude slightly forward to the substrate coordination. In this study we adopt a new strategy to design a ligand with a deep chiral pocket by installing R groups that protrude directly forward to the substrate coordination site. There are two advantages of this strategy: 1) The R groups that protrude directly forward to the substrate coordination site can lead to a dramatic conformational variation of the chiral pocket; 2) the R groups are in close proximity to the metal center and the substrate, thereby providing a well-defined and deep chiral pocket. We herein report the development of WingPhos (L5) by using this strategy.Chiral b-arylamines exist in numerous biologically interesting natural products and therapeutic agents. For examples, such moieties commonly exist in a series of naphthylisoquinoline alkaloids such as michellamine B and korupensamine A (Scheme 1). [5] They also serve as pivotal structural units for many active pharmaceutical ingredients such as 3,4-methylenedioxyamphetamine (MDA), [6a] tamsulosin, [6b] selegiline, [6c] arformoterol, [6d] rotigotine, [6e] and silodosin. [6f] Development of efficient asymmetric synthetic methods of chiral b-arylamines has thus become a subject of significant interest. [7] However, the asymmetric hydrogenation of b-aryl enamides to prepare chiral b-arylamines remains underdeveloped. Zhang, Lei, and co-workers reported high enantioselectivities on the asymmetric hydrogenation of (Z)-b-aryl enamides by using a Rh-TangPhos catalyst. [8] Nevertheless, low ee values were observed with thermodynamically more stable sub-Figure 1. Design of novel chiral bisphosphorus ligand L5 (WingPhos) with a deep chiral pocket (9-An = 9-anthracenyl). Scheme 1. Selected natural products and therapeutic agents containing chiral b-arylamines.

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The perturbation analysis of singular value decomposition (SVD) has been well documented in the literature within the context of subspace decomposition. The contribution of the signal subspace to the perturbation of the singular vectors that span the signal subspace is often ignored as it is treated as second and higher order terms, and thus the first-order perturbation is typically given as the column span of the noise subspace. In this paper, we show that not only the noise subspace, but also the signal subspace, contribute to the first-order perturbation of the singular vectors. We further show that the contribution of the signal subspace does not impact on the performance analysis of algorithms that rely on the signal subspace for parameter estimation, but it affects the analysis of algorithms that depends on the individual basis vectors. For the latter, we also give a condition under which the contribution of the signal subspace to the perturbation of singular vectors may be ignored in the statistical sense.

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