"Divide and Conquer" Semiclassical Molecular Dynamics: A practical method for Spectroscopic calculations of High Dimensional Molecular Systems

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits to perform spectroscopic calculations of high dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Liouville's theorem. Comparisons of calculated vibrational frequencies to exact quantum ones for a set of molecules including benzene show that the new implementation performs better than the original one and that, on average, the loss in accuracy with respect to full-dimensional semiclassical calculations is reduced to only 10 wavenumbers. Furthermore, by investigating the challenging Zundel cation, we also demonstrate that the "divide-and-conquer" approach allows to deal with complex strongly anharmonic molecular systems. Overall the method very much helps the assignment and physical interpretation of experimental IR spectra by providing accurate vibrational fundamentals and overtones decomposed into reduced dimensionality spectra

Semiclassical "Divide-and-Conquer" Method for Spectroscopic Calculations of High Dimensional Molecular Systems

A new semiclassical "divide-and-conquer" method is presented with the aim of demonstrating that quantum dynamics simulations of high dimensional molecular systems are doable. The method is first tested by calculating the quantum vibrational power spectra of water, methane, and benzene - three molecules of increasing dimensionality for which benchmark quantum results are available - and then applied to C60, a system characterized by 174 vibrational degrees of freedom. Results show that the approach can accurately account for quantum anharmonicities, purely quantum features like overtones, and the removal of degeneracy when the molecular symmetry is broken

Anharmonic Vibrational Eigenfunctions and Infrared Spectra from Semiclassical Molecular Dynamics

We describe a new approach based on semiclassical molecular dynamics that allows to simulate infrared absorption or emission spectra of molecular systems with inclusion of anharmonic intensities. This is achieved from semiclassical power spectra by computing first the vibrational eigenfunctions as a linear combination of harmonic states, and then the oscillator strengths associated to the vibrational transitions. We test the approach against a 1D Morse potential and apply it to the water molecule with results in excellent agreement with discrete variable representation quantum benchmarks. The method does not require any grid calculations and it is directly extendable to high dimensional systems. The usual exponential scaling of the basis set size with the dimensionality of the system can be avoided by means of an appropriate truncation scheme. Furthermore, the approach has the advantage to provide IR spectra beyond the harmonic approximation without losing the possibility of an intuitive assignment of absorption peaks in terms of normal modes of vibration

An Effective Semiclassical Approach to IR Spectroscopy

We present a novel approach to calculate molecular IR spectra based on semiclassical molecular dynamics. The main advance from a previous semiclassical method [M. Micciarelli, R. Conte, J. Suarez, M. Ceotto J. Chem. Phys. 149, 064115 (2018)] consists in the possibility to avoid state-to-state calculations making applications to systems characterized by sizable densities of vibrational states feasible. Furthermore, this new method accounts not only for positions and intensities of the several absorption bands which make up the IR spectrum, but also for their shapes. We show that accurate semiclassical IR spectra including quantum effects and anharmonicities for both frequencies and intensities can be obtained starting from semiclassical power spectra. The approach is first tested against the water molecule, and then applied to the 10-atom glycine aminoacid

Istituzioni e Governance Cooperativa

Nella distribuzione delle forme organizzative di impresa quelle in società per azioni prevalgono su quelle cooperative. Si ritiene ciò sia dovuto alla maggiore efficienza del regime di proprietà individuale rispetto a quello di proprietà comune. Partendo da questo assunto, il paper si propone di rispondere alle domande seguenti. Se quest’ultima affermazione è vera, perché la forma di impresa cooperativa non scompare? E’ possibile ritenere che il codice civile e la costituzione offrano tutela ed incentivi ad una forma organizzativa inefficiente? Portando l’attenzione sui nessi tra proprietà e controllo dell’impresa, il paper evidenzia come sia in questi - più che nel regime proprietario - che l’impresa cooperativa trovi sia la ragion d’essere, sia la capacità di confronto competitivo con le altre forme di impresa. In particolare, sottolinea come istituzioni e governance cooperativa formino un insieme di complementarietà istituzionale in grado di generare oltre ai beni prodotti, anche un modo di produrli: la reciprocità condizionale, che in quanto assimilabile a un bene pubblico è in grado, sotto la corretta struttura di incentivi, di ridurre i costi di transazione e consentire la continuità dell’impresa nel tempo.

Atti volontari ed atti involontari in Aristotele. Una lettura in chiave giuridica contemporanea

L’autore rilegge alcune pagine dell’Etica Nicomachea evidenziando come alcuni concetti aristotelici sono tuttora a fondamento di nozioni giuridiche contemporanee, con particolare riferimento alle categorie del diritto penale

Segmenti di un profilo introduttivo del principio d’eguaglianza

Premessi brevi cenni storici sulla formulazione del principio d’eguaglianza, con particolare riferimento alle Costituzioni della Rivoluzione francese, l’A. esamina alcune questioni affrontate dalla Corte costituzionale italiana in relazione all’art. 3 Cost.: dalla parità di trattamento tra uomo e donna, all’eguaglianza delle religioni rispetto alla legge, all’illegittimità di alcuni privilegi per categorie di persone (es.: immunità per parlamentari e ministri). Si sofferma, inoltre, su alcuni nuovi profili (es.: il riconoscimento delle relazioni omosessuali), anche alla luce del cosiddetto principio d’eguaglianza sostanziale, sancito dal secondo comma dell’art. 3 Cost., e della centralità della persona, sancito dall’art. 2 Cost

Reproducing Deep Tunneling Splittings, Resonances, and Quantum Frequencies in Vibrational Spectra From a Handful of Direct Ab Initio Semiclassical Trajectories

A time-dependent semiclassical approach for vibrational spectra calculations is shown to describe deep tunneling splittings, resonances, and quantum frequencies in multidimensional multiwell systems, by propagating a very limited number of classical trajectories. The approach is tested on ammonia by evolving eight trajectories on a full-dimensional PES. Quantum effects are reproduced, and results are in good agreement with time-independent quantum calculations. All the features are maintained when ab initio “on-the-fly” dynamics is adopted, thus demonstrating that precomputation of the PES can be avoided. The approach overcomes the typical scaling issues of quantum mechanical techniques without introducing any simplifications nor reductions of dimensionality of the problem. The proposed methodology is promising for further applications to systems of major complexity.Chemistry and Chemical Biolog