arXiv subjects

Vincenzo Aquilanti

Publications and source records attributed to Vincenzo Aquilanti.

18 recordsLinked to original sources

arXiv2026

Vectorial Imaging of the Photodissociation of 2-Bromobutane Oriented via Hexapolar State Selection

Molecular orientation techniques are becoming available in the study of elementary chemical processes, in order to highlight those structural and dynamical properties that would be concealed by random rotational motions. Recently successful orientation was achieved for asymmetric-top and chiral molecules of much larger complexity than hitherto. In this work, we report and discuss the correlation between the vectors photofragment recoil velocity v, transition dipole moment μ, and permanent dipole moment d in a dissociation experiment on hexapole oriented 2-bromobutane, photoinitiated by a linearly polarized laser. The sliced ion images of the Br* (2P1/2) and Br (2P3/2) photofragment were acquired at 234.0 and 254.1 nm, respectively, by (2+1) resonance-enhanced multiphoton ionization technique. A detailed analysis of the sliced ion images obtained at a tilting angle 45o of the laser polarization provides the information on correlation of the three vectors, which are confined by two polar angles α, \c{hi} and one azimuthal angle ϕμd in the recoil frame. The sliced ion images of Br fragments eliminated individually from the enantiomers at 254.1 nm yield the asymmetric factor close to zero; for this reason the photofragment angular distributions do not show significant differences. The elimination of Br* fragment at 234.0 nm is mainly correlated with a parallel transition, giving rise to a large anisotropy parameter of 1.85, and thus can be considered as a single state excitation. The resulting recoil frame angles are optimized to 163.8° and 164.1° for α and \c{hi}, respectively, whereas ϕμd approaches close to 0o for the best fit. Since in the present case, the three vectors have an only slight spatial arrangement, the photofragment angular distributions of the two enantiomers do not show appreciable differences...

physics.chem-ph↗

arXiv2021

Quadrilaterals on the square screen of their diagonals: Regge symmetries of quantum-mechanical spin-networks and Grashof classical mechanisms of four-bar linkages

The four-bar linkage is a basic arrangement of mechanical engineering and represents the simplest movable system formed by a closed sequence of bar-shaped bodies. Although the mechanism can have in general a spatial arrangement, we focus here on the prototypical planar case, starting however from a spatial viewpoint. The classification of the mechanism relies on the angular range spanned by the rotational motion of the bars allowed by the ratios among their lengths and is established by conditions for the existence of either one or more bars allowed to move as cranks, namely to be permitted to rotate the full 360 degrees range (Grashof cases), or as rockers with limited angular ranges (non-Grashof cases). In this paper, we provide a view on the connections between the "classic" four-bar problem and the theory of 6j symbols of quantum mechanical angular momentum theory, occurring in a variety of contexts in pure and applied quantum mechanics. The general case and a series of symmetric configurations are illustrated, by representing the range of existence of the related quadrilaterals on a square "screen" (namely as a function of their diagonals) and by discussing their behavior according both to the Grashof conditions and to the Regge symmetries, concertedly considering the classification of the two mechanisms and that of the corresponding objects of the quantum mechanical theory of angular momentum. An interesting topological difference is demonstrated between mechanisms belonging to the two Regge symmetric configurations: the movements in the Grashof cases span chirality preserving configurations with a 2 pi-cycle of a rotating bar, while by contrast the non-Grashof cases span both enantiomeric configurations with a 4 pi-cycle.

quant-ph↗

arXiv2021

Stereodynamics Imaging of Bromine Atomic Photofragments Eliminated from 1-Bromo-2-methylbutane Oriented via Hexapole State Selector

Both single-laser and two-laser experiments were conducted to look into the ion-imaging of Br*(2P1/2) and Br(2P3/2) photo-fragmented from 1-bromo-2-methylbutane in the range 232-240 nm via a detection scheme of (2+1) resonance-enhanced multiphoton ionization. The angular analysis of these photofragment distributions yields the anisotropy parameter beta = 1.88 +/- 0.06 for the Br* excited state which arises from a parallel transition, while beta = 0.63 +/- 0.09 for the Br ground state indicates the contribution from both a perpendicular transition and a non-adiabatic transition. When a hexapole coupled with an orienting field was implemented, the parent molecules are spatially oriented to yield an orientation efficiency | | of 0.15. Besides the chi angle between the recoil velocity v and the transition dipole moment mu, orienting molecules allows for the evaluation of the angle alpha between v and the permanent molecular dipole moment d. The angular analysis of Br* photofragment distribution yields chi to be 11.5 degrees and alpha in the range from 160 degrees to 180 degrees with weak dependency. In the two-laser experiments, the angular anisotropy of Br photofragment distribution was found to be smaller (0.38 +/- 0.10) when the photolysis wavelength was red-shifted to 240 nm, suggesting the increasing contributions from perpendicular transitions.

physics.atom-ph↗

arXiv2020

Spherical and hyperspherical harmonics representation of van der Waals aggregates

The representation of the potential energy surfaces of atom molecule or molecular dimers interactions should account faithfully for the symmetry properties of the systems, preserving at the same time a compact analytical form. To this aim, the choice of a proper set of coordinates is a necessary precondition. Here we illustrate a description in terms of hyperspherical coordinates and the expansion of the intermolecular interaction energy in terms of hypersherical harmonics, as a general method for building potential energy surfaces suitable for molecular dynamics simulations of van der Waals aggregates. Examples for the prototypical case diatomic molecule diatomic molecule interactions are shown.

physics.chem-ph↗

arXiv2020

Double photoionization of propylene oxide: a coincidence study of the ejection of a pair of valence-shell electrons

Propylene oxide, a favorite target of experimental and theoretical studies of circular dichroism, was recently discovered in interstellar space, further amplifying the attention to its role in the current debate on protobiological homochirality. In the present work, a photoelectron-photoion-photoion coincidence technique, using an ion-imaging detector and tunable synchrotron radiation in the 18.0-37.0 eV energy range, permits: (i)-to observe six double-ionization fragmentation channels, their relative yields being accounted for about two-thirds by the couple (C2H4+, CH2O+), one-fifth by (C2H3+, CH3O+); (ii)-to measure thresholds for their openings as a function of photon energy; (iii)-to unravel a pronounced bimodality for a kinetic-energy-released distribution, fingerprint of competitive non-adiabatic mechanisms.

physics.atom-ph↗

arXiv2018

Projective Ponzano-Regge spin networks and their symmetries

We present a novel hierarchical construction of projective spin networks of the Ponzano-Regge type from an assembling of five quadrangles up to the combinatorial 4-simplex compatible with a geometrical realization in Euclidean 4-space. The key ingrendients are the projective Desargues configuration and the incidence structure given by its space-dual, on the one hand, and the Biedenharn--Elliott identity for the 6j symbol of SU(2), on the other. The interplay between projective-combinatorial and algebraic features relies on the recoupling theory of angular momenta, an approach to discrete quantum gravity models carried out successfully over the last few decades. The role of Regge symmetry --an intriguing discrete symmetry of the $6j$ which goes beyond the standard tetrahedral symmetry of this symbol-- will be also discussed in brief to highlight its role in providing a natural regularization of projective spin networks that somehow mimics the standard regularization through a q-deformation of SU(2).

math-ph↗

arXiv2017

The spherical-harmonics representation for the interaction between diatomic molecules: the general case and applications to CO-CO and CO-HF

The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties, specifically in van der Waals clusters, with applications also to classical and quantum molecular dynamics simulations. The technique consists in the construction (by ab initio or semiempirical methods) of the expanded potential interaction up to terms that provide the generation of a number of leading configurations sufficient to account for faithful geometrical representations. This paper reports the full general description of the method of the spherical-harmonics expansion as applied to diatomic-molecule-diatomic-molecule systems of increasing complexity: the presentation of the mathematical background is given for providing both the application to the prototypical cases considered previously (O2-O2, N2-N2, and N2-O2 systems) and the generalization to: (i) the CO-CO system, where a characteristic feature is the lower symmetry order with respect to the cases studied before, requiring a larger number of expansion terms necessary to adequately represent the potential energy surface; and (ii) the CO-HF system, which exhibits the lowest order of symmetry among this class of aggregates and therefore the highest number of leading configurations.

physics.chem-ph↗

arXiv2017

Interactions of Hydrogen Molecules with Halogen-Containing Diatomics from Ab Initio Calculations: Spherical-Harmonics Representation and Characterization of the Intermolecular Potentials

For the prototypical diatomic-molecule - diatomic molecule interactions H2-HX and H2-X2, where X = F, Cl, Br, quantum-chemical ab initio calculations are carried out on grids of the configuration space, which permit a spherical-harmonics representation of the potential energy surfaces (PESs). Dimer geometries are considered for sets of representative leading configurations, and the PESs are analyzed in terms of isotropic and anisotropic contributions. The leading configurations are individuated by selecting a minimal set of mutual orientations of molecules needed to build the spherical-harmonic expansion on geometrical and symmetry grounds. The terms of the PESs corresponding to repulsive and bonding dimer geometries and the averaged isotropic term, for each pair of interacting molecules, are compared with representations in terms of a potential function proposed by Pirani et al. (see Chem. Phys. Lett. 2004, 394, 37-44 and references therein). Connections of the involved parameters with molecular properties provide insight into the nature of the interactions.

physics.chem-ph↗

arXiv2017

Hexapole-Oriented Asymmetric-Top Molecules and Their Stereodirectional Photodissociation Dynamics

Molecular orientation is a fundamental requisite in the study of stereodirected dynamics of collisional and photoinitiated processes. In this last decade, variable hexapolar electric filters have been developed and employed for the rotational-state selection and the alignment of molecules of increasing complexity, for which main difficulties are their mass, their low symmetry and the very dense rotational manifold. In this work, for the first time, a complex molecule such as 2-bromobutane, an asymmetric-top containing a heavy atom (the bromine), has been successfully oriented by a weak homogeneous field placed downstream the hexapolar filter. Efficiency of the orientation has been characterized experimentally, by combining time-of-flight measurements and a slice-ion-imaging detection technique. The application is described to the photodissociation dynamics of the oriented 2-bromobutane, which was carried out at a laser wavelength of 234 nm, corresponding to the breaking of the C Br bond. The Br photofragment is produced in both the ground Br (2P3/2) and the excited Br (2P1/2) electronic states and both channels are studied by the slice imaging technique, revealing new features in the velocity and angular distributions with respect to previous investigations on non-oriented molecules.

physics.chem-ph↗

arXiv2014

Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective

A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.

quant-ph↗

arXiv2014

The screen representation of vector coupling coefficients or Wigner 3j symbols: exact computation and illustration of the asymptotic behavior

The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in discretization approximations. We point out the important role of the Regge symmetries for defining the screen where images of the coefficients are projected, and for discussing their asymptotic properties and semiclassical behavior. Recursion relationships are formulated as eigenvalue equations, and exploited both for computational purposes and for physical interpretations.

quant-ph↗

arXiv2014

The Screen representation of spin networks. Images of 6j symbols and semiclassical features

This article presents and discusses in detail the results of extensive exact calculations of the most basic ingredients of spin networks, the Racah coefficients (or Wigner 6j symbols), exhibiting their salient features when considered as a function of two variables - a natural choice due to their origin as elements of a square orthogonal matrix - and illustrated by use of a projection on a square "screen" introduced recently. On these screens, shown are images which provide a systematic classification of features previously introduced to represent the caustic and ridge curves (which delimit the boundaries between oscillatory and evanescent behaviour according to the asymptotic analysis of semiclassical approaches). Particular relevance is given to the surprising role of the intriguing symmetries discovered long ago by Regge and recently revisited; from their use, together with other newly discovered properties and in conjunction with the traditional combinatorial ones, a picture emerges of the amplitudes and phases of these discrete wavefunctions, of interest in wide areas as building blocks of basic and applied quantum mechanics.

quant-ph↗

arXiv2014

The Screen representation of spin networks: 2D recurrence, eigenvalue equation for 6j symbols, geometric interpretation and Hamiltonian dynamics

This paper treats 6j symbols or their orthonormal forms as a function of two variables spanning a square manifold which we call the "screen". We show that this approach gives important and interesting insight. This two dimensional perspective provides the most natural extension to exhibit the role of these discrete functions as matrix elements that appear at the very foundation of the modern theory of classical discrete orthogonal polynomials. Here we present 2D and 1D recursion relations that are useful for the direct computation of the orthonormal 6j, which we name U. We present a convention for the order of the arguments of the 6j that is based on their classical and Regge symmetries, and a detailed investigation of new geometrical aspects of the 6j symbols. Specifically we compare the geometric recursion analysis of Schulten and Gordon with the methods of this paper. The 1D recursion relation, written as a matrix diagonalization problem, permits an interpretation as a discrete Schrödinger-like equations and an asymptotic analysis illustrates semiclassical and classical limits in terms of Hamiltonian evolution.

quant-ph↗

arXiv2013

Statistics of energy partitions for many-particle systems in arbitrary dimension

In some previous articles, we defined several partitions of the total kinetic energy T of a system of N classical particles in the d-dimensional Euclidean space into components corresponding to various modes of motion. In the present paper, we propose formulas for the mean values of these components in the normalization T=1 (for any d and N) under the assumption that the masses of all the particles are equal. These formulas are proven at the "physical level" of rigor and numerically confirmed for planar systems (d=2) at N from 3 through 100. The case where the masses of the particles are chosen at random is also considered. The paper complements our article of 2008 [Russian J Phys Chem B, 2(6), 947-963] where similar numerical experiments were carried out for spatial systems (d=3) at N from 3 through 100.

math-ph↗

arXiv2013

Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials

The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given as a second order difference equation which, by a complex phase change, we turn into a discrete Schrödinger-like equation. The introduction of discrete potential-like functions reveals the surprising crucial role here of hidden symmetries, first discovered by Regge for the quantum mechanical 6j symbols; insight is provided into the underlying geometric features. The spectrum and wavefunctions of the volume operator are discussed from the viewpoint of the Hamiltonian evolution of an elementary "quantum of space", and a transparent asymptotic picture emerges of the semiclassical and classical regimes. The definition of coordinates adapted to Regge symmetry is exploited for the construction of a novel set of discrete orthogonal polynomials, characterizing the oscillatory components of torsion-like modes.

quant-ph↗

arXiv2011

Semiclassical Mechanics of the Wigner 6j-Symbol

The semiclassical mechanics of the Wigner 6j-symbol is examined from the standpoint of WKB theory for multidimensional, integrable systems, to explore the geometrical issues surrounding the Ponzano-Regge formula. The relations among the methods of Roberts and others for deriving the Ponzano-Regge formula are discussed, and a new approach, based on the recoupling of four angular momenta, is presented. A generalization of the Yutsis-type of spin network is developed for this purpose. Special attention is devoted to symplectic reduction, the reduced phase space of the 6j-symbol (the 2-sphere of Kapovich and Millson), and the reduction of Poisson bracket expressions for semiclassical amplitudes. General principles for the semiclassical study of arbitrary spin networks are laid down; some of these were used in our recent derivation of the asymptotic formula for the Wigner 9j-symbol.

math-ph↗

arXiv2010

3nj Morphogenesis and Semiclassical Disentangling

Recoupling coefficients (3nj symbols) are unitary transformations between binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum operators. They have been used in a variety of applications in spectroscopy, quantum chemistry and nuclear physics and quite recently also in quantum gravity and quantum computing. These coefficients, naturally associated to cubic Yutsis graphs, share a number of intriguing combinatorial, algebraic, and analytical features that make them fashinating objects to be studied on their own. In this paper we develop a bottom--up, systematic procedure for the generation of 3nj from 3(n-1)j diagrams by resorting to diagrammatical and algebraic methods. We provide also a novel approach to the problem of classifying various regimes of semiclassical expansions of 3nj coefficients (asymptotic disentangling of 3nj diagrams) for n > 2 by means of combinatorial, analytical and numerical tools.

quant-ph↗

arXiv2007

Semiclassical analysis of Wigner $3j$-symbol

We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's oscillators. A novel element is the appearance of compact Lagrangian manifolds that are not tori, due to the fact that the observables defining the quantum states are noncommuting. These manifolds can be quantized by generalized Bohr-Sommerfeld rules and yield all the correct quantum numbers. The geometry of the classical angular momentum vectors emerges in a clear manner. Efficient methods for computing amplitude determinants in terms of Poisson brackets are developed and illustrated.

quant-ph↗