Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians

We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our analysis to finite dimensional Hilbert spaces. In particular, we propose some experiments which could discriminate between the various possibilities considered in the paper. An example taken from the literature is discussed in detail.     

Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m$m$ fermions (or bosons) in N$N$ single particle states and interacting via k$k$-body interactions, we have EGUE(k$k$) [embedded GUE of k$k$-body interactions] with GUE embedding and the embedding algebra is U(N)$U\left(N\right)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k$k$) representation for a Hamiltonian that is k$k$-body and an independent EGUE(t$t$) representation for a transition operator that is t$t$-body and employing the embedding U(N)$U\left(N\right)$ algebra, finite-N$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀$k_0$ number of particles from a system of m$m$ spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2$k=2$) Hamiltonians (in some examples for k=3$k=3$ and 4$4$) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.     

POLYMERIZATION OF 1-BUTYL-2-TRIMETHYLSILYLACETYLENE BY TRANSITION METAL CATALYSTS

New silicon-containing disubstituted polyacetylene was prepared by the polymerization of BTMSA having two bulky substituents (n-butyl and trimethylsilyl) using transition metal catalysts. The polymerization proceeded in a mild manner and the final polymer yield was generally lower than those of silicon-containing monosubstituted acetylenes by the similar catalyst system. The characterization on the polymer structure revealed that the resulting poly(BTMSA) have a conjugated backbone system, but the polymers have peculiar copolymer composition of poly-(BTMSA) and poly(1-hexyne) due to the spontaneous desilylation during the polymerization. The fluoride-ion induced desilylation of poly(BTMSA) using n-Bu₄N⁺F^? in THF yielded a completely desilylated product, pure poly(1-hexyne).     

MONOMETALLIC SOLVENT STABILIZED TRANSITION METAL CATIONS AS INITIATORS FOR CYCLOPENTADIENE POLYMERIZATION

Several mononuclear transition metal cations stabilized by acetonitrile molecules act as initiators for the polymerization of cyclopentadiene. The highest yield is reached with Cr, Mn, Fe, and Zn complexes, all of them in the oxidation state +II. The analogous V and Ni complexes, however, are completely or nearly inactive. In general, the observed activity of the examined monomeric complexes correlates well with the ligand field stabilization energy as a function of the number of d electrons for octahedrally coordinated transition metals in the oxidation state +II. The counter ions have a pronounced influence on the catalytic activity: the less coordinating they are, the higher is the activity of the cations. The reaction temperature also has a significant influence: above 50°C the complex activity is on decline, possibly due to initiator decomposition or com-petitive inhibition by dicyclopentadiene.     

SYNTHESIS AND PROPERTIES OF COPOLYMERS FROM 1-[3,5-BIS(TRIMETHYLSILYL)PHENYL]-2-PHENYLACETYLENE

Copolymerization of 1-[3,5-bis(trimethylsilyl)phenyl]-2-phenylacetylene (m,m-(Me₃Si)₂DPA) with other diphenylacetylene derivatives and their copolymer properties were investigated. Homopolymerization of m,m-(Me₃Si)₂DPA by TaCl₅─n-Bu₄Sn (1:2) did not give the polymer due to steric hindrance. However, m,m-(Me₃Si)2DPA copolymerized with diphenylacetylene (DPA), 1-phenyl-2-[p-(trimethylsilyl)phenyl]acetylene (p-Me₃Si DPA), and 1-phenyl-2-[m-(trimethylsilyl)phenyl]acety-lene (m-Me₃SiDPA) in the presence of TaCl₅─n-Bu₄Sn at various feed ratios to give copolymers in moderate yields. The formed copolymers were yellow to orange solids, which were soluble in common organic solvents such as toluene and CHCl₃. The highest weight-average molecular weights (M_w) of these copolymers reached ca. 6 × 105 and tough films could be obtained by solution casting. Their onset temperatures of weight loss in air were observed around 400°C, indicating high thermal stability. The oxygen permeability coefficients at 25°C of copoly(m,m-(Me₃Si)₂ DPA/DPA) (feed ratio 1:1) and copoly(m,m-(Me₃Si)₂DPA/p-Me₃SiDPA) (feed ratio 1:2) were 21 and 100 barrers, respectively, medium in magnitude among polymers from substituted acetylenes.     

Synthesis of L-Lysine and L-Glutamic Acid Derivatives with Long Alkyl Chains and Polycondensation of Langmuir-Blodgett Films

Two esters of L-lysine and L-glutamic acid containing long alkyl groups were synthesized and their polycondensation in monolayers and multilayers was investigated. The pressure-area isotherms of the ester of L-lysine depend markedly on the time of residence at the air-water interface. The change of FT-IR spectra of the deposited film, which can be lifted as a Z-type film, indicates that polycondensation can occur in the monolayer at 10°C without any treatment. The spectrum of the film cast from chloroform hardly changed with time. These results lead to the conclusion that a regular arrangement of monomer molecules in the monolayer, where the amino and ester carbonyl groups are concentrated, is more suitable for the polycondensation. The ester of L-glutamic acid can also form stable monolayers which can be easily deposited on a hydrophobic plate as a Y-type film by the Blodgett technique. The polycondensation of multilayers under an atmosphere of triethylamine was investigated by IR spectroscopy. It indicates that the condensation in multilayers proceeds via intermolecular and intramolecular reactions, by which poly(L-glutamate) derivatives and 2-pyrrolidone derivatives are formed, respectively. The condensation in the bulk crystalline powder gives exclusively the 2-pyrrolidone derivative by intramolecular reaction. These results suggest that the monomer molecules in the multilayers are favorably aligned for the intermolecular reaction, in contrast to the situation in the bulk crystalline powder.     

Oxidative addition transition states of Pd(0) complexes in polar solvent—a DFT study involving implicit and explicit solvation

Previous reports in the literature have suggested that concerted transition states for oxidative addition would not exist in solution. By contrast, this report describes the successful location of transition states for the oxidative addition of monoligated Pd(P^tBu₃), bisligated Pd(P^tBu₃)(MeCN), and anionic Pd(P^tBu₃)F^? complexes to C–Cl and C–OTf of an aryl chloro triflate in polar solvent (MeCN). Optimizations were done with implicit solvation and a combined implicit/explicit solvation approach in which six acetonitrile molecules were additionally involved in the optimization. The geometries obtained from optimizations employing an implicit solvation model are structurally largely analogous to those found using a combination of implicit and explicit solvation.     

Synthesis,characterization and metal ion complexation and extraction capabilities of calix[4]arene Schiff base compounds

The syntheses, characterization and metal ion complexation and extraction capabilities of six new calix[4]arene Schiff base compounds, 5–10, are reported. The preparation of the compounds was achieved by the condensation of 5,17-diamino-11,23-di-tert-butyl-25,27-di-n-butoxy-26,28-dihydroxycalix[4]arene with the appropriate aldehyde (5-bromosalicylaldehyde for 5, 4-anisaldehyde for 6, 4-(dimethylamino)benzaldehyde for 7, 9-anthracenecarboxaldehyde for 8, 1-pyrenecarboxaldehyde for 9, and 9-fluorenecarboxaldehyde for 10) in refluxing ethanol. The compounds were characterized by ¹H and ¹³C NMR spectroscopy, IR spectroscopy, high-resolution mass spectrometry and elemental analysis. The X-ray crystal structures of 7, 8 and 9 (as dichloromethane solvates) revealed that the calixarene molecules adopt H-bond stabilized, distorted-cone conformations and form centrosymmetric dimers in the solid state. Compounds 5–10 did not form host–guest complexes with NEt₄[(bdt)MoO₂(OSiPh₃)] (bdt^2–=benzene-1,2-dithiolate), a potential precursor for biologically relevant oxosulfido-Mo(VI/V) enzyme models; such host–guest complexes have the potential to stabilize these sought-after but highly reactive model compounds. In addition, the capabilities of 5–10 to extract selected metal ions (Ni²⁺, Co²⁺, Cu²⁺, Zn²⁺, Ag⁺, Pb²⁺, Cd²⁺ and Hg²⁺) from an aqueous into an organic phase have been assessed by picrate extraction experiments. Compound 5 displayed exceptional selectivity towards Ni²⁺, compound 7 exhibited enhanced extraction towards all of the metal ions tested and compounds 6, 9 and 10 showed very high selectivity towards Hg²⁺. On the other hand, compound 8 exhibited negligible capacity to extract any of the metal ions tested.     

Structure and Polymorphism of M(thd)3 (M = Al,Cr, Mn,Fe, Co,Ga, and In)

Formation, crystal structure, polymorphism, and transition between polymorphs are reported for M(thd)₃, (M = Al, Cr, Mn, Fe, Co, Ga, and In) [(thd)^– = anion of H(thd) = C₁₁H₂₀O₂ = 2, 2, 6, 6‐tetramethylheptane‐3, 5‐dione]. Fresh crystal‐structure data are provided for monoclinic polymorphs of Al(thd)₃, Ga(thd)₃, and In(thd)₃. Apart from adjustment of the M–O_k bond length, the structural characteristics of M(thd)₃ complexes remain essentially unaffected by change of M. Analysis of the M–O_k, O_k–C_k, and C_k–C_k distances support the notion that the M–O_k–C_k–C_k–C_k–O_k– ring forms a heterocyclic unit with σ and π contributions to the bonds. Tentative assessments according to the bond‐valence or bond‐order scheme suggest that the strengths of the σ bonds are approximately equal for the M–O_k, O_k–C_k, and C_k–C_k bonds, whereas the π component of the M–O_k bonds is small compared with those for the O_k–C_k, and C_k–C_k bonds. The contours of a pattern for the occurrence of M(thd)₃ polymorphs suggest that polymorphs with structures of orthorhombic or higher symmetry are favored on crystallization from the vapor phase (viz. sublimation). Monoclinic polymorphs prefer crystallization from solution at temperatures closer to ambient. Each of the M(thd)₃ complexes subject to this study exhibits three or more polymorphs (further variants are likely to emerge consequent on systematic exploration of the crystallization conditions). High‐temperature powder X‐ray diffraction shows that the monoclinic polymorphs convert irreversibly to the corresponding rotational disordered orthorhombic variant above some 100–150 °C (depending on M). The orthorhombic variant is in turn transformed into polymorphs of tetragonal and cubic symmetry before entering the molten state. These findings are discussed in light of the current conceptions of rotational disorder in molecular crystals.     

Synthesis,Crystal Structures,and Magnetic Properties of Two Copper(II) Radical Heterospin Complexes

Two heterospin complexes [Cu(NIT3Py)(cda)H₂O] · H₂O ( 1 ) and [Cu(NIT2Py)(cda)H₂O] · H₂O · CH₃OH ( 2 ) with Cu^II ions and pyridyl‐substituted nitronyl nitroxide radicals (NITxPy = 2‐(x′‐pyridyl)‐4,4,5,5‐tetramethyl‐imidazoline‐1‐oxyl‐3‐oxide, x = 3, 2; H₂cda = 4‐hydroxy‐pyridine‐2,6‐dicarboxylic acid) were synthesized and characterized structurally and magnetically. The single crystal structures show that the two complexes are both two‐spin complexes, in which the different radicals make the two complexes have different hydrogen bonding interactions to form 2D and 1D supramolecular network for complexes 1 and 2 , respectively. The magnetic measurements indicate that complexes 1 and 2 both exhibit antiferromagnetic interactions between Cu^II and radicals.