The structure of projection-valued states: A generalization of Wigner's theorem

A projection-valued state is defined to be a completely orthoadditive map from the projections on one Hilbert space into the projections on another Hilbert space, which preserves the unit. Any such mapping is shown to have the formP U ₁(P 1₁)U ₁ ^–1 U ₂(P 1₂)U ₂ ^–1 , whereU ₁ is unitary andU ₂ is antiunitary, generalizing Wigner's theorem on symmetry transformations. A physical interpretation is given and the relation to quantum logic is discussed.The contents of this paper are a portion of the author's dissertation at the University of Massachusetts at Amherst.     

Heavier alkali-metal monosulfides (KS, RbS, CsS, and FrS) and their cations

The heavier alkali-metal monosulfides (KS, RbS, CsS, and FrS) have been studied by high-level ab initio calculations. The RCCSD(T) method has been employed, combined with large flexible valence basis sets. All-electron basis sets are used for potassium and sulfur, with effective core potentials being used for the other metals, describing the core electrons. Potential-energy curves are calculated for the lowest two neutral and cationic states: all neutral monosulfide species have a (2)Pi ground state, in contrast with the alkali-metal monoxide species, which undergo a change in the electronic ground state from (2)Pi to (2)Sigma(+) as the group is descended. In the cases of KS, RbS, and CsS, spin-orbit curves are also calculated. We also calculate potential-energy curves for the lowest (3)Sigma(-) and (3)Pi states of the cations. From the potential-energy curves, spectroscopic constants are derived, and for KS the spectroscopic results are compared to experimental spectroscopic values. Ionization energies, dissociation energies, and heats of formation are also calculated; for KS, we explore the effects of relativity and basis set extrapolation on these values.     

The effect of bond functions on molecular dissociation energies

Multi-reference Cl calculations are reported for the ground states of HCl and N₂ at their equilibrium distances, and for their separated atoms. Basis sets of double-zeta and double-zeta plus polarization quality are systematically augmented by additional sets of functions located at the bond centers. It is shown that use of bond functions can lead to either an underestimate or an overestimate of the the bond energy. Optimum basis sets for each molecule were obtained, giving D_e values of 4.59 eV for HCl (expt. 4.62 eV) and 9.96 eV for N₂ (expt. 9.905 eV) at the estimated full Cl level. The quality of the potential curves obtained with these basis sets is discussed.     

New Monoterpene-Substituted Dihydrochalcones from Piper aduncum

Five New unusual monoterpene-substituted dihydrochalcones, the adunctins A–E (1″S)-1-{2′-hydroxy-4′-methoxy-6′-[4″-methyl-1″-(1?-methylethyl)cyclohex-3″ -en-1″ -yloxy]phenyl}-3-phenylpropan-1-one ( 1 ), (5aR*,8R*,9aR*)-3-phenyl-1-[5′,8′,9′,9′a-tetrahydro-3′-hydroxy-1′-methoxy-8′-(1″-methylethyl)-5′-a-methyldibenzo-[b,d]furan-4′-yl]propan-1-one ( 2 ), (2′R*,4″S*)-1-{6′-hydroxy-4′-methoxy-4″-(1?-methylethyl)spiro[benzo[b]-furan-2′(3′H),1″ -cyclohex-2″ -en]-7′-yl}-3-phenylpropan-1-one ( 3 ), (2′R*,4″R*)-1-{6′-hydroxy-4′-methylethyl-4″-(1?-methylethyl)spiro[benzo[b]furan-2′(3′H),1″-cyclohex-2″-en]-7′-yl}-3-phenypropan-1-one ( 4 ), and (5′aR*,6′S*, 9′R*,9′aS*)-1-[5′a,6′,7′,8′,9′a-hexahydro-3′,6′-methoxy-6′-methyl-9′-(1″-methylethyl)dibenzo[b,d]-furan-4′-yl]-3-phenylpropan-1-one ( 5 ) were isolated from the leaves of Piper aduncum (Piperaceae) by preparative liquid chromatography. In addition, (?)-methyllindaretin ( 6 ), trans-phytol, and α-tocopherol ( = vitamin E) were also isolated and identified. The structures were elucidated by spectroscopic methods, including 1D- and 2D-NMR spectroscopy as well as single-crystal X-ray diffraction analysis. The antibacterial and cytotoxic potentials of the isolates were also investigated.     

Selection of the cis and trans phosph(III)azane macrocycles [{P(mu-NtBu)}2(1-Y-2-NH-C6H4)]2(Y=O, S)

The 1 : 1 reactions of [ClP(mu-NtBu)]2 with the difunctional aromatic amines 1,2-1-YH-2-NH2-C6H4 in the presence of Et3N give the dimeric phosph(III)azane macrocycles [{P(mu-NtBu)2(1-Y-2-HN-C6H4)]2, predominantly as the cis isomer in the case of Y=O (1.cis) and as the trans isomer for Y=S (2.trans). Model M.O. calculations suggest that the selection of the cis and trans isomers is not thermodynamically controlled. The alternative isomers 1.trans and 2.cis are generated exclusively by the deprotonation of the model intermediates [(1-Y-2-NH2-C6H4)P(mu-NtBu)]2[Y=O (3), S (4)] with nBuLi followed by cyclisation with [ClP(mu-NtBu)]2. The solid-state structures of 1.cis/trans(50 : 50), 2.cis, 3 and 4 are reported.     

Exo-metal coordination by a tricyclic [(P(mu-N-2-NC5H4))2(mu-O)]2 dimer in [(P(mu-N-2-NC5H4))2(mu-O)]2(CuCl x (C5H5N)2)4 (2-NC5H4 = 2-pyridyl, C5H5N = pyridine)

The in situ reaction of the phosphazane dimer [CIP(mu-N-2-NC5H4)]2 (2) with CuCl in the presence of CsH5N/H2O gives the title complex [(P(mu-N-2-NC5H4))2(mu-O)]2(CuCl x (C5H5N)2)4 (1), containing a tricyclic [(P(mu-N-2-NC5H4))2(mu-O)]2 ligand which is isoelectronic with species of the type [(P(mu-NR))2NR]2.     

New halogenated furanones from the marine alga delisea pulchra (cf. fimbriata)

An investigation of the natural products chemistry of the red alga Delisea pulchra, collected from the Cape Banks, New South Wales, Australia, yielded eight new polyhalogenated furanones (1–7) and the previously reported metabolites 8–24). The structures of 1–8 were determined from the interpretation of their 1D and 2D NMR, UV, IR and mass spectral data. For the first time, complete ¹H and ¹³C NMR data for compounds 14, 18, and 20-23 are reported.     

Steric control in the oligomerisation of phosphazane dimers; towards new phosphorus-nitrogen macrocycles

The reaction of [ClP(mu-NtBu)]2 (1) with H2O (1 : 2 equivalents) in the presence of excess Et3N gives the new chain compound [(mu-O)[P(mu-NtBu)2P(H)=O]2] (3), consisting of two P2N2 rings linked by a mu-O atom and terminating in P(V)(H)=O groups. A similar chain species is obtained from the reaction of the lithiate of [(tBuNH)P(mu-NtBu)2P(H)=O] (5) with [ClP(mu-NtBu)2P(NHtBu)] (2), the product being [(mu-O)[P(mu-NtBu)2P(NHtBu)]2] (6). Compounds 3 and 6 are the first examples of O-bridged chain phosphazanes and potential precursors to new phosphorus-nitrogen macrocycles. The syntheses and X-ray structures of 3, 5 and 6 are reported.     

The reaction intermediate spectrum. A new type of experiment in tandem mass spectrometry

A new scan is described which responds to ions that are intermediates in the dissociation of a mass-selected parent ion (m_p) to give a mass-selected daughter ion (m_d). The scan gives a simple mass v. abundance output for ions which satisfy this condition. It is implemented here on a BEQQ hybrid mass spectrometer using, in sequence, collision-induced dissociation occurring at high energy in the first reaction region, and low-energy collisional activation in the collision quadrupole. The experiment provides information on reaction sequences not available from single scans of other types. In the several cases examined, it is demonstrated that, among many conceivable fragmentation routes connecting a parent ion with a particular fragment ion, only a few are significant. Examination of reaction intermediate spectra also appears to be a fruitful new approach to mechanistic questions, as illustrated by consideration of the behavior of several isomeric octanones. These new spectra also have analytical value: they show good signal-to-noise ratios and allow ready distinction between isobaric and isomeric ions. A comparison of the reaction intermediate spectrum with a daughter spectrum obtained by the B/E linked-scanning technique reveals the contributions of artifact peaks which result from poor parent ion mass resolution in the latter. Reaction intermediate spectra combine information from the daughter spectra of m_p and the parent spectra of m_d and, as a specified portion of this data domain, have unique characteristics.     

Synthesis and structure of the calixarene-like phosph(III)azane macrocycle [{P(mu-N(t)Bu)}2{1,5-(NH)2C10H6}]3

The reaction of [ClP(mu-NtBu)]2 with 1,5-diamino-naphthalene [1,5-(NH2)2C10H6] in Et3N-thf gives the trimeric macrocycle [{P(mu-NtBu)}2{1,5-(NH)2C10H6}]3(1); the X-ray structure of the toluene solvate 1.3toluene reveals a cone-shaped (calixarene-like) arrangement in which toluene guest molecules are trapped within the cavity.