Alessandro Ferretti

Quantum dynamics of a model system with a conical intersection

We study the quantum dynamics of a two-electronic state model system with a conical intersection involving two vibrational degrees of freedom, x and y. The two diabatic surfaces are displaced only along x, while the interstate coupling is linear in y and contains Gaussian damping factors along x and y. The role of the initial momentum and of the difference of the slopes at the conical intersection is discussed. In particular, the analysis of the numerical results shows that the diabatic transition at the conical intersection is accompanied mainly by a massive flow of vibrational quanta from the x to the y oscillator of the same electronic state. Furthermore, we propose a simplified time-dependent monodimensional model in which the x oscillator is assumed to move as an independent classical oscillator, while the y oscillator is described quantum-mechanically. Despite the crude approximations involved, this simplified model reproduces quite well the exact results for the transition probabilities at the firs...

A study of coupled logistic map and its applications in chemical physics

Abstract The results of a detailed study of the coupled logistic map are reported in view of its application to processes of interest in chemical physics. The nature of the fixed points is considered analytically. Extensive numerical computation has been performed to obtain bifurcation sequences, correlation of the two variables, largest Lyapunov exponent, spacing distribution and power spectra, resulting in pinpointing regions of chaotic, periodic and quasiperiodic behaviour of this map. New zones of chaos as well as windows of quasiperiodicity have been found. Possible applications of this map that would be useful in chemical physics, such as chemical reactions and absorption of infrared photons from two distinct external electromagnetic fields by polyatomic molecules, are discussed.

Solvent effect on the optical properties of [(NH3)5Ru–pyrazine]+m (m=2,3) complexes by ab initio calculations

We have carried out a study, by ab initio methods, of the solvent effect on [(NH3)5Ru–pyrazine]m+ (m=2 and 3) complexes, which are of interest as basic units of metallic chains with potential application in molecular electronics and photonics. We have performed multireference configuration interaction (CI) calculations in which solvent effects are included by the Polarizable Continuum Model. A new method for the estimate of the size of the cavities in this approach, which has proven to be suitable for the specific case under study, is also proposed. Our calculations account for the red shift of the metal-to-ligand charge transfer band, observed experimentally for the Ru(II) compound as the solvent donor number increases, and furnish an explanation with a solid theoretical foundation. For the Ru(III) compound we find that the ground state configuration is different in vacuum and in electron donor solvents.

Control of the yield of photophysical/photochemical processes by excitation with properly delayed ultrashort phase-locked light pulses: a model study on the pyrazine S2 → S 1 internal conversion

We study the internal conversion S2[1B2u(ππ∗)] → S1[1B3u(nπ∗)] due to the conical intersection between potential energy surfaces in the pyrazine molecule by numerically solving (by the Lanczos method) the diabatic model proposed by Stock and Domcke. The model involves three normal modes, one promoting and two accepting. After optical excitation of the S2 state with a single δ-pulse, the total (i.e., summed over the vibrational manifold) population of S2 decays very rapidly but incompletely. It is shown that the fraction of the population trapped in S2 can be significantly reduced if two phase-locked ultrashort light pulses are used, provided the time delay as well as the phase relation between them are properly chosen.

Effect of the increase of molecular complexity on statistical properties of vibrational spectra

Abstract We present for the first time a study on the influence of the increase in the number of molecular vibrational degrees of freedom on level statistics. A model of three Morse oscillators coupled by Wilson terms has been considered for tetratomic molecules and the level statistics of its spectra have been studied in comparison with that of an analogous two-oscillator model for triatomics. The nearest-neighbor level spacing distribution for three oscillators is essentially a Wigner distribution, while for two oscillators it is a Brody distribution, which is intermediate between a Poisson and a Wigner distribution.

Transition probability due to a conical intersection: On the role of the initial conditions and of the geometric setup of the crossing surfaces

We have carried out a study of the dynamics in a two-state, two-mode conical intersection with the aim of understanding the role played by the initial position of the wave packet and the slope of potential energy surfaces at the conical intersection point on the transition probability between the two diabatic states. Studying the dynamics for a single period of the tuning oscillator, we find two distinct rules that can be used for a qualitative prediction of the behavior of the transition probability after the first passage through the conical intersection and after a period (two passages). The first quantity is relevant for systems undergoing a rapid, irreversible decay and the second one for understanding in what kinds of conditions one has to expect a periodic fluorescence spectrum.

Quantum dynamics at a conical intersection: The role of the variation of oscillator frequencies in the diabatic transition

The role of frequency variation in the transition between two crossing diabatic electronic states originating in a conical intersection is studied. We have considered a minimal model with two vibrational degrees of freedom, a coupling mode, and a tuning mode, and performed computations varying the frequency of both in the initially unoccupied diabatic state. It is shown that neglecting this effect may result in a wrong estimate of the transition probability. Two simple rules for evaluating qualitatively such an effect are proposed.

Dynamics around a multidimensional conical intersection: A mixed quantum-classical model

We investigate the dynamics around a two-state conical intersection in a polyatomic molecule. The simplified model considered is an extension of that proposed and tested previously for the case of one active (coupling) mode and one passive mode. Here we study a multidimensional conical intersection built adding many other passive modes, which globally share a small fraction (up to 20%) of the total vibrational energy. The model simply consists in treating the coupling mode quantum mechanically, while the others are described as classical oscillators running unperturbed trajectories on the initial diabatic surface. The computed adiabatic transition probabilities show, in some conditions, a marked effect of the extra passive modes, which can be explained in terms of the time spent by the classical trajectories in the region where the diabatic coupling is at its maximum.

Optical properties of linear mixed valence coordination compounds by two-band Hubbard Hamiltonian

Abstract We have investigated the optical conductivity spectra of M(LM) n linear complexes, as well as their periodic (ring) counterparts, whose constituent elements are transition metal ions (M), bridged by ligand species (L), through a two-band Hubbard Hamiltonian modified to include the effect of orbital expansion/contraction upon electron/hole occupation. It is shown that interesting conductive properties appear by doping, i.e. by varying the oxidation state of a fraction of the Ms. In the specific case of the Creutz-Taube ions ((Ru-L-Ru) m + ; m =4, 5, 6) we were able to reproduce the low-frequency behaviour observed experimentally.

Optical properties of pyrazine-bridged ruthenium chains by the two-band Hubbard Hamiltonian

We have investigated the optical conductivity spectra of [Ru(pzRu)4]m+ (pz=pyrazine), as representative of the whole class of linear mixed valence complexes of ruthenium, through a two-band Hubbard Hamiltonian. It is shown that the main features of absorption spectra, observed experimentally for various degrees of oxidation (m), are well reproduced within this simple model.