Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems

Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the periodic orbit sum and the uncertainty principle of the usual Fourier analysis, thus yielding results of high resolution and high precision. Based on the close analogy between periodic orbit trace formulae for regular and chaotic systems the technique is generalized in this paper for the semiclassical quantization of integrable systems. Thus, harmonic inversion is shown to be a universal tool which can be applied to a wide range of physical systems. The method is further generalized in two directions: Firstly, the periodic orbit quantization will be extended to include higher order hbar corrections to the periodic orbit sum. Secondly, the use of cross-correlated periodic orbit sums allows us to significantly reduce the required number of orbits for semiclassical quantization, i.e., to improve the efficiency of the semiclassical method. As a representative of regular systems, we choose the circle billiard, whose periodic orbits and quantum eigenvalues can easily be obtained.Comment: 21 pages, 9 figures, submitted to Eur. Phys. J.

Reactions of cyclomanganated complexes with carbon disulfide: routes to η²-aryldithiocarboxylate-Mn(CO)₄ complexes and to the trithiocarbonate complex (μ₃-CS₃)₂Mn₄(CO)₁₆

Reaction of cyclomanganated aryl ketones with CS₂ proceeds with insertion into the Mn–C bond to give η²-dithiocarboxylato–Mn(CO)₄ compounds. With other cyclomanganated substrates such as that from Ph₃P=S and also with Mn₂(CO)₁₀, CS₂ gives (μ₃-CS₃)₂Mn₄(CO)₁₆ with bridging trithiocarbonate ligands

Manganese carbonyl-mediated reactions of azabutadienes with phenylacetylene, methyl acrylate and other unsaturated molecules

Reaction of PhCH₂Mn(CO)₅ with l,4-di-aryl-1-aza-1,3-butadienes gave substituted pyrrolinonyl rings which were η⁴-coordinated to a Mn(CO)₃ group. These are formed by intramolecular CO insertion into a (non-isolated) cyclomanganated intermediate, followed by cyclisation. Other unsaturated reagents (PhC≡CH, CH2=CHCOOMe, PhNCO) gave products arising from insertion of these, including a structurally characterised tri-aryl-η⁵-azacyclohexadienyl-Mn(CO)₃ complex from the reaction with the alkyne. PhCH₂Mn(CO)₅ reacts with l,4-di-aryl-1-aza-1,3-butadienes in the presence of unsaturated substrates to give products based on a cyclomanganated intermediate

2-(1,4-Dioxo-1,4-dihydro-2-naphthyl)-2-methylpropanoic acid

The sterically crowded title compound, C₁₄H₁₂O₄, crystallizes as centrosymmetric hydrogen-bonded dimers involving the carboxyl groups. The naphthoquinone ring system is folded by 11.5 (1)° about a vector joining the 1,4-C atoms, and the quinone O atoms are displaced from the ring plane, presumably because of steric interactions with the bulky substituent