Synthesis and small molecule chemistry of the niobaziridine-hydride functional group

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2005.Vita.Includes bibliographical references.Chapter 1. Synthesis and Divergent Reactivity of the Niobaziridine-Hydride Functional Group The synthesis, characterization and reactivity of the niobaziridine-hydride complex Nb(H)([eta]²-t- ]Bu(H)C=NAr)(N[Np]Ar)₂ (la-H; Np = neopentyl, Ar = 3,5-Me₂C₆H₃) is discussed. The niobaziridine-hydride functional group in complex la-H serves as a protecting group for the reactive three-coordinate d² species, Nb(N[Np]Ar)₃ (2a), via reversible C-H activation of the 3- ]H-containing N[Np]Ar ligand. At elevated temperatures, complex la-H rapidly converts to the neopentylimido complex, Nb(NNp)(Ar)(N[Np]Ar)₃ (3a), which is the product of N[Np]Ar ligand C'-N oxidative addition by putative three-coordinate 2a. Although not observed directly, the evidence for the intermediacy of 2a in N[Np]Ar ligand C-H and C-N activation processes has been obtained through isotopic labeling (H/D) studies. To further ascertain the propensity of la- H to serve as a masked form of 2a, its reactivity with small-molecule substrates was surveyed. Treatment of la-H with nitrous oxide (N₂0) or triphenylphosphine oxide (OPPh₃), readily generated the oxo Nb(V) complex, ONb(N[Np]Ar)₃, thus establishing la-H as a source of the potent two-electron reductant 2a. Complex la-H was also found to effect the two-electron reduction of a host of other inorganic substrates. However, when treated with certain unsaturated organic molecules, insertion into the Nb-H moiety of complex la-H is observed in which the niobaziridine ring is left intact. Based on synthetic studies, a coordinatively induced, C-H bond reductive elimination mechanism is proposed for reactions between la-H and small molecules.(cont.) This mechanistic proposal accounts for both the observed insertion and two-electron reduction behavior exhibited by niobaziridine-hydride la-H. To extend the generality of niobaziridine- hydride functional group as a protecting group for three-coordinate Nb(NR₂)₃ species, the complexes Nb(H)([eta]²-Me₂C=NAr)(N[i-Pr]Ar)₂ (lb-H) and Nb(H)([eta]²-Ad(H)C=NAr)(N[CH₂- Ad]Ar)₂ (1c-H) were synthesized. The thermal behavior of niobaziridine-hydrides lb-H and lc- 1-I is compared and contrasted to that of the N-neopentyl variant la-H. Chapter 2. Activation of Elemental Phosphorus: Synthesis of an Anionic Terminal Phosphide of Niobium The niobazinidine-hydride complex Nb(H)( [eta]²-t-Bu(H)C=NAr)(N[Np]Ar)₂ (la-H; Np neopentyl, Ar = 3,5-Me₂C₆H₃) was found to react quantitatively with elemental phosphorus (P₄) to provide the bridging diphosphide complex ([mu]₂:[eta]²,[eta]²-P₂)[Nb(N[Np]Ar)₃]₂ ([mu]-P₂)[2a]₂. Reductive cleavage of ([mu]-P₂)[2a]₂ with sodium amalgam afforded the sodium salt of the terminal niobium phosphide anion, [PNb(N[Np]Ar)₃)]⁻ ([2a-P]⁻), which is best formulated as containing a Nb-P triple bond. The phosphorus atom of [2a-P]⁻ has proven to be nucleophilic and is readily functionalized upon addition of an electrophile. Treatment of [2a-P]⁻ with trimethylstannyl chloride provided the terminal phosphinidene complex Me₃SnP=Nb(N[Np]Ar)₃ which contains a P-Sn single bond. However, treatment of [2a-P]⁻ with ClP(t-Bu)₂ or ClP(Ph)₂ provided niobium- complexed [eta]²-phosphinophosphinidene complexes, which contain considerable P-P multiple bonding character. Thus, substantial electronic reorganization of the Nb [equal] P moiety in [2a-P]⁻ is induced upon functionalization.(cont.) The tendency for the Nb[equal]P unit in [2a-P]- to undergo electronic reorganization has been exploited, resulting in the synthesis of a complexed [eta]²-P,P- diphosphaorganoazide (PPNR) species, which eliminates a 'P2' unit when heated. Furthermore, treatment of the phosphido anion [2a-P]⁻ with divalent group 14 salts affords complexes of the formulation ([mu]₂:[eta]₃,[eta]₃ -cyclo-EP₂)[Nb(N[Np]Ar)₃]₂ (E = Ge, Sn, Pb). The bridging cyclo-EP₂ units in these complexes can be considered as neutral 2[pi]-electron, three-membered rings isolobal to the cyclopropenium ion. The molecular and electronic structure of anion [2a-P]⁻ and several of its derivatives are discussed. Chapter 3. Isovalent Pnictogen for O(Cl) Exchange Mediated by Terminal Pnictide Anions of Niobium Reported herein is a new, metathetical P for O(Cl) exchange mediated by an anionic niobium phosphide complex which furnished phosphaalkynes (RC [equal] P) from acyl chlorides (RC(O)Cl) under mild conditions. The niobaziridine hydride complex, Nb(H)(t-Bu(H)C=NAr)(N[Np]Ar)₂ (la-H, Np = neopentyl, Ar = 3,5-Me₂C₆H₃), has been shown in chapter 2 to react with elemental phosphorus (P₄) affording the [mu]-diphosphide complex, ([mu]²:[eta]²,[eta]²-P₂)[Nb(N[Np]Ar)₃]₂ (([mu]- P)[2a]₂), which can be subsequently reduced by sodium amalgam to the anionic, terminal phosphide complex, [Na][PNb(N[Np]Ar)₃] (Na[2a-P]).(cont.) Treatment of Na[2a-P] with either ]pivaloyl (t-BuC(O)Cl) or 1-adamantoyl (1-AdC(O)Cl) chloride provides the thermally unstable, niobacycles, (t-BuC(O)P)Nb(N[Np]Ar)₃ (2-t-Bu) and (1-AdC(O)P)Nb(N[Np]Ar)₂ (2-1-Ad) which are intermediates along the pathway to ejection of the known phosphaalkynes t-BuC-P (3- t-Bu) and 1-AdC [equal] P (3-1-Ad). Phosphaalkyne ejection from 2-t-Bu and 2-1-Ad proceeds with formation of the niobium(V) oxo complex ONb(N[Np]Ar)₃ (2a-0) as a stable byproduct. Preliminary kinetic measurements for fragmentation of 2-t-Bu to 3-t-Bu and 2a-0 in C₆D₆ solution are consistent with a first order process. Separation of volatile 3-t-Bu from 2a-0 after thermolysis has been readily achieved by vacuum transfer in yields of 90%. Pure 2a-0 is recovered after vacuum transfer and can be treated with 1.0 equivalent of triflic anhydride (Tf₂O, Tf = SO₂CF₃) to afford the bistriflate complex, Nb(OTf)₂(N[Np]Ar)₃ (2a-(OTf)₂), in high yield. Complex 2a-(OT'f)₂ provides direct access to la-H upon reduction with magnesium anthracene, thus completing a cycle of element activation, small-molecule generation via metathetical P-atom transfer and deoxygenative recycling of the final niobium(V) oxo product. Extension of this metathetical P for O(C1) exchange to the synthesis of novel phosphaalkynes is discussed. In addition, the analogous N for O(C1) exchange reaction for the synthesis of organonitriles from the niobium nitrido anion, [NNb(N[Np]Ar)₃]⁻ ([2a-N]⁻) has been developed. Nitrido anion [2a- N]⁻ is obtained in a heterodinuclear N₂ scission reaction which employs the molybdenum trisamide system as a reaction partner.(cont.) Treatment of [2a-N]⁻ with acyl chloride substrates rapidly furnishes organonitriles concomitant with the formation of niobium oxo 2a-0. Deoxgenative recycling of 2a-0 to a niobium complex appropriate for heterodinuclear N2 scission has been developed as well. Utilization of ¹⁵N-labeled ¹⁵N₂ gas in this chemistry has afforded a series of ¹⁵N-labeled organonitriles which have been characterized by solution ¹⁵N NMR. While, no intermediate complexes are observed during the organonitrile formation process, synthetic and computational studies on model systems provide strong evidence for the intermediacy of niobacyclic species.by Joshua S. Figueroa.Ph.D

Forensic identification: the Island Problem and its generalisations

In forensics it is a classical problem to determine, when a suspect $S$ shares a property $\Gamma$ with a criminal $C$, the probability that $S=C$. In this paper we give a detailed account of this problem in various degrees of generality. We start with the classical case where the probability of having $\Gamma$, as well as the a priori probability of being the criminal, is the same for all individuals. We then generalize the solution to deal with heterogeneous populations, biased search procedures for the suspect, $\Gamma$-correlations, uncertainty about the subpopulation of the criminal and the suspect, and uncertainty about the $\Gamma$-frequencies. We also consider the effect of the way the search for $S$ is conducted, in particular when this is done by a database search. A returning theme is that we show that conditioning is of importance when one wants to quantify the "weight" of the evidence by a likelihood ratio. Apart from these mathematical issues, we also discuss the practical problems in applying these issues to the legal process. The posterior probabilities of $C=S$ are typically the same for all reasonable choices of the hypotheses, but this is not the whole story. The legal process might force one to dismiss certain hypotheses, for instance when the relevant likelihood ratio depends on prior probabilities. We discuss this and related issues as well. As such, the paper is relevant both from a theoretical and from an applied point of view

U-Spin Tests of the Standard Model and New Physics

Within the standard model, a relation involving branching ratios and direct CP asymmetries holds for the B-decay pairs that are related by U-spin. The violation of this relation indicates new physics (NP). In this paper, we assume that the NP affects only the Delta S = 1 decays, and show that the NP operators are generally the same as those appearing in B -> pi K decays. The fit to the latest B -> pi K data shows that only one NP operator is sizeable. As a consequence, the relation is expected to be violated for only one decay pair: Bd -> K0 pi0 and Bs -> Kbar0 pi0.Comment: 12 pages, latex, no figures. References changed to follow MPL guidelines; info added about U-spin breaking and small NP strong phases; discussion added about final-state pi-K rescattering; analysis and conclusions unaltere

Measurements of New Physics in B -> pi pi Decays

If new physics (NP) is present in B -> pi pi decays, it can affect the isospin I=2 or I=0 channels. In this paper, we discuss various methods for detecting and measuring this NP. The techniques have increasing amounts of theoretical hadronic input. If NP is eventually detected in B -> pi pi -- there is no evidence for it at present -- one will be able to distinguish I=2 and I=0, and measure its parameters, using these methods.Comment: 24 pages, no figures, revte

Overview of Neutron-Proton Pairing

The role of neutron-proton pairing correlations on the structure of nuclei along the $N=Z$ line is reviewed. Particular emphasis is placed on the competition between isovector ($T=1$) and isoscalar $(T=0$) pair fields. The expected properties of these systems, in terms of pairing collective motion, are assessed by different theoretical frameworks including schematic models, realistic Shell Model and mean field approaches. The results are contrasted with experimental data with the goal of establishing clear signals for the existence of neutron-proton ($np$) condensates. We will show that there is clear evidence for an isovector $np$ condensate as expected from isospin invariance. However, and contrary to early expectations, a condensate of deuteron-like pairs appears quite elusive and pairing collectivity in the $T=0$ channel may only show in the form of a phonon. Arguments are presented for the use of direct reactions, adding or removing an $np$ pair, as the most promising tool to provide a definite answer to this intriguing question.Comment: 89 pages, 59 figures. Accepted for publication in Progress in Particle and Nuclear Physics (ELSEVIER

Computation Environments, An Interactive Semantics for Turing Machines (which P is not equal to NP considering it)

To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a universal processor and ii) a computist who uses the computability power of the universal processor to perform effective procedures. The notion of computation finds it meaning, for the computist, through his \underline{interaction} with the universal processor. We are interested in those computation environments which can be considered as alternative for the real computation environment that the human being is its computist. These computation environments must have two properties: 1- being physically plausible, and 2- being enough powerful. Based on Copeland' criteria for effective procedures, we define what a \emph{physically plausible} computation environment is. We construct two \emph{physically plausible} and \emph{enough powerful} computation environments: 1- the Turing computation environment, denoted by $E_T$, and 2- a persistently evolutionary computation environment, denoted by $E_e$, which persistently evolve in the course of executing the computations. We prove that the equality of complexity classes $\mathrm{P}$ and $\mathrm{NP}$ in the computation environment $E_e$ conflicts with the \underline{free will} of the computist. We provide an axiomatic system $\mathcal{T}$ for Turing computability and prove that ignoring just one of the axiom of $\mathcal{T}$, it would not be possible to derive $\mathrm{P=NP}$ from the rest of axioms. We prove that the computist who lives inside the environment $E_T$, can never be confident that whether he lives in a static environment or a persistently evolutionary one.Comment: 33 pages, interactive computation, P vs N

Computing quantum discord is NP-complete

We study the computational complexity of quantum discord (a measure of quantum correlation beyond entanglement), and prove that computing quantum discord is NP-complete. Therefore, quantum discord is computationally intractable: the running time of any algorithm for computing quantum discord is believed to grow exponentially with the dimension of the Hilbert space so that computing quantum discord in a quantum system of moderate size is not possible in practice. As by-products, some entanglement measures (namely entanglement cost, entanglement of formation, relative entropy of entanglement, squashed entanglement, classical squashed entanglement, conditional entanglement of mutual information, and broadcast regularization of mutual information) and constrained Holevo capacity are NP-hard/NP-complete to compute. These complexity-theoretic results are directly applicable in common randomness distillation, quantum state merging, entanglement distillation, superdense coding, and quantum teleportation; they may offer significant insights into quantum information processing. Moreover, we prove the NP-completeness of two typical problems: linear optimization over classical states and detecting classical states in a convex set, providing evidence that working with classical states is generically computationally intractable.Comment: The (published) journal version http://iopscience.iop.org/1367-2630/16/3/033027/article is more updated than the arXiv versions, and is accompanied with a general scientific summary for non-specialists in computational complexit