New Catalytic Properties of Chiral-at-Metal Complexes and a Cyclometalated Ru Complex

Asymmetric transition-metal catalysis constitutes one of the most powerful strategies to construct non-racemic chiral molecules. This thesis deals with enantioselective catalysis of chiral-at-metal iridium and ruthenium complexes as well as a chiral mono-cyclometalated ruthenium complex. 1) Kinetic resolution of racemic epoxides with CO2 catalyzed by a chiral-at-metal bis-cyclometalated iridium complex was accomplished, and s-factors between 6.4 and 16.6 were obtained for overall 21 monosubstituted epoxides containing diverse functional side chains. Notably, all reactions were performed at room temperature, and no copolymerization side reaction which occurred often in other catalytic systems was observed (Chapter 3.1). 2) Enantioselective intramolecular benzylic C-H amination of primary aliphatic azides was achieved by using a chiral-at-metal bis(pyridyl-NHC) ruthenium complex in combination with tris(p-fluorophenyl)phosphine (both 1 mol%) to provide a variety of chiral -aryl pyrrolidines with enantioselectivities of up to 99% ee. In this unique case, the phosphine serves as a crucial nitrene transfer co-catalyst and activates the organic azide through the formation of an intermediate iminophosphorane. This methodology offers direct access to non-racemic -aryl pyrrolidines which are very important structural motifs in many bioactive compounds. (Chapter 3.2). 3) A chiral cyclometalated ruthenium catalyst enabled direct enantioselective and highly diastereoselective oxidative homocoupling of 2-acyl imidazoles in the presence of one equivalent BrCCl3 to provide chiral symmetric 1,4-dicarbonyl compounds in 38-75% yield with 57-95% ee. Only one diastereomer was obtained for all the investigated substrates. Mechanistic experiments support a unique ruthenium catalyzed two-steps mechanism. The first step is a ruthenium catalyzed bromination of 2-acyl imidazole generating a brominated intermediate, followed by a ruthenium catalyzed stereo-controlled radical-enolate reaction providing the final product (Chapter 3.3)

The Brown-Halmos theorems on the Fock space

In this paper, we extend the Brown-Halmos theorems to the Fock space and investigate the range of the Berezin transform. We observe that there are many non-pluriharmonic functions $u$ that can be written as a finite sum $B(u)=\sum_lf_l\overline{g_l}$, where $f_l,g_l$ are holomorphic functions belonging to the class $\mathrm{Sym}(\mathbb{C}^n)$. In addition, we answer an open question about zero products of Toeplitz operators. Our results reveal that the Brown-Halmos theorems on the Fock space are more complicated than that on the classical Bergman space.Comment: 18 page

Semi-commutants of Toeplitz Operators on Fock-Sobolev space of Negative orders

We make a progress towards describing the semi-commutants of Toeplitz operators on Fock-Sobolev spaces of negative orders. We generalize the results in \cite{Bauer1,Qin}. For the certain symbol spaces, we obtain two Toeplitz operators can semi-commute only in the trivial cases, which is different from what is known for the classical Fock spaces. As an application, we consider the conjecture which was shown to be false for Fock space in \cite{MA}. The main results of this paper say that there is the fundamental difference between the geometries of Fock and Fock-Sobolev space.Comment: 25page

Bounded Hankel products on Fock-Sobolev spaces

Let $F^{2,m}(\mathbb{C})$ denote the Fock-Sobolev space of complex plane. The purpose of this paper is to study the conjecture which was shown to be false for Fock space by Ma-Yan-Zheng-Zhu in 2019. For a certain symbol spaces, the main result of the paper says that the conjecture is actually true in $F^{2,m}(\mathbb{C})(m>0)$.Comment: 19 page