On the direct calculation of the time evolution of excited molecular states in the presence of nonadiabatic interactions

The possibility is explored of calculating the time evolution of a given initial molecular state, in the presence of sufficiently strong nonadiabatic interactions, with a fully quantum-mechanical approach. Two methods are presented. The first one is based on the determination of the molecular eigenstates, with expansion of the nuclear wavefunctions on a Hermite basis. The second method is based on the Padé 1,1 approximation of the time evolution operator and on a finite difference representation of the time-dependent nuclear wavefunctions. Both methods are applied to simple models of a diatomic molecule.     

Configuration-interaction calculations for the ground state of OF2, NO 2 − , CN−: Canonical orbitals and exclusive orbitals

The C.I. method is applied to already published double- SCF wave functions for OF₂, NO ₂ ^– and CN^–. All doubly excited configurations are considered. The second order approximation values presented for those cases are compared with the exact energy values in some minor cases. An attempt has been made to improve the rate of convergency of the process by transforming the canonical SCF occupied orbitals into localized ones and the virtual canonical orbitals into a particular type of localized orbitals. These latter show also an intuitively acceptable spatial conformation.

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Zusammenfassung Die CI Methode wird auf bereits bekannte Doppel-Zeta-SCF-Wellenfuntionen für die Systeme OF₂, NO ₂ ^– und CN^– angewandt. Dabei werden alle doppelt angeregten Konfigurationen berücksichtigt. Um die Konvergenz zu verbessern, werden versuchsweise die kanonischen und besetzten SCF-Orbitale in lokalisierte Orbitale und die virtuellen kanonischen Orbitale in einen besonderen Typ von lokalisierten Orbitalen transformiert. Die letzteren zeigen eine besonders geeignete räumliche Anpassung.

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Résumé Pour un calcul de intéraction de configurations, comprenant toutes le configurations à double excitation, on a employé des fonctions d'onde SCF sur une base doublée. Pour le calcul complet on a essayé des formules d'approximation, qu'on a pu vérifier avec le calcul exact sur des cas réduits.Pour améliorer la vélocité de convergence du procés on a transformé les orbitales canoniques SCF en orbitales localisées et aprés on a construit, selon un procedé particulier, des orbitales virtuelles localisées qui montrent une conformation dans l'espace qui est intuitivement satisfaisante.

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Work supported by the Consiglio Nazionale delie Ricerche.     

Thermally Induced Synthesis of Anthracene-, Pyrene- and Naphthalene-Fused Porphyrins

The synthesis of π-extended porphyrins containing anthracenyl moieties still represents an important challenge. Here, we report on the synthesis of a series of unsubstituted naphthyl-, pyrenyl- and anthracenyl-fused zinc porphyrin derivatives. To this aim, meso-substitued porphyrins are synthesized and the fusion of the PAHs (Polycyclic Aromatic Hydrocarbon) on the β-positions are performed through thermally induced dehydro-aromatization. The fused zinc-porphyrin derivatives are fully characterized and their optical absorption and photoluminescence properties are reported. We also demonstrate that zinc can be removed from the porphyrin core, giving rise to pure C, H, N materials. This work constitutes the first step towards the synthesis of the fully-fused tetra-anthracenylporphyrin.     

Monitoring of the Pre-Equilibrium Step in the Alkyne Hydration Reaction Catalyzed by Au(III) Complexes: A Computational Study Based on Experimental Evidences

The coordination ability of the [(ppy)Au(IPr)]²⁺ fragment [ppy = 2-phenylpyridine, IPr = 1,3-bis(2,6-di-isopropylphenyl)-imidazol-2-ylidene] towards different anionic and neutral X ligands (X = Cl⁻, BF₄⁻, OTf⁻, H₂O, 2-butyne, 3-hexyne) commonly involved in the crucial pre-equilibrium step of the alkyne hydration reaction is computationally investigated to shed light on unexpected experimental observations on its catalytic activity. Experiment reveals that BF₄⁻ and OTf⁻ have very similar coordination ability towards [(ppy)Au(IPr)]²⁺ and slightly less than water, whereas the alkyne complex could not be observed in solution at least at the NMR sensitivity. Due to the steric hindrance/dispersion interaction balance between X and IPr, the [(ppy)Au(IPr)]²⁺ fragment is computationally found to be much less selective than a model [(ppy)Au(NHC)]²⁺ (NHC = 1,3-dimethylimidazol-2-ylidene) fragment towards the different ligands, in particular OTf⁻ and BF₄⁻, in agreement with experiment. Effect of the ancillary ligand substitution demonstrates that the coordination ability of Au(III) is quantitatively strongly affected by the nature of the ligands (even more than the net charge of the complex) and that all the investigated gold fragments coordinate to alkynes more strongly than H₂O. Remarkably, a stabilization of the water-coordinating species with respect to the alkyne-coordinating one can only be achieved within a microsolvation model, which reconciles theory with experiment. All the results reported here suggest that both the Au(III) fragment coordination ability and its proper computational modelling in the experimental conditions are fundamental issues for the design of efficient catalysts.     

Mean-field versus microconvection effects in nanofluid thermal conduction

Transient hot-wire data on thermal conductivity of suspensions of silica and perfluorinated particles show agreement with the mean-field theory of Maxwell but not with the recently postulated microconvection mechanism. The influence of interfacial thermal resistance, convective effects at microscales, and the possibility of thermal conductivity enhancements beyond the Maxwell limit are discussed.     

K-stability of constant scalar curvature Kähler manifolds

We show that a polarised manifold with a constant scalar curvature Kähler metric and discrete automorphisms is K-stable. This refines the K-semistability proved by S.K. Donaldson.     

Phase separation and pattern formation in a binary Bose-Einstein condensate

The miscibility-immiscibility phase transition in binary Bose-Einstein condensates (BECs) can be controlled by a coupling between the two components. Here we propose a new scheme that uses coupling-induced pattern formation to test the Kibble-Zurek mechanism (KZM) of topological-defect formation in a quantum phase transition. For a binary BEC in a ring trap we find that the number of domains forming the pattern scales as a function of the coupling quench rate with an exponent as predicted by the KZM. For a binary BEC in an elongated harmonic trap we find a different scaling law due to the transition being spatially inhomogeneous. We perform a "quantum simulation" of the harmonically trapped system in a ring trap to verify the scaling exponent.