Antiadiabatic View of Fast Environmental Effects on Optical Spectra

An antiadiabatic approach is proposed to model how the refractive index of the surrounding medium affects optical spectra of molecular systems in condensed phases. The approach solves some of the issues affecting current implementations of continuum solvation models and more generally of effective models where a classical description is adopted for the molecular environment

Études quantiques et quantiques-classiques des processus ultrarapides photo-induits

L'interprétation des processus photo-induits repose aujourd'hui fortement sur les simulations numériques. Un aspect important à prendre en compte est le caractère quantique de la dynamique, conséquence de l'interaction entre la dynamique nucléaire et la dynamique électronique, impliquant plusieurs états électroniques. De nombreuses théories et algorithmes de la dynamique moléculaire de l'état excité ont été développés au fil des ans, mais sont encore en développement continu. Les méthodes les plus utilisées, car les plus pratiques numériquement, sont les algorithmes mixtes quantiques-classiques, qui introduisent une description de la dynamique nucléaire basée sur des trajectoires classiques couplée à une description quantique de la dynamique électronique. Cependant, en raison d'une telle approximation classique, certains effets peuvent être perdus ou mal décrits. L'effet de décohérence quantique en est le principal exemple, ainsi que les effets d'interférence. À cet égard, l'approche numérique quantique-classique basée sur la exact factorization, appelée coupled-trajectory mixed quantumclassica algorithme (CT-MQC), semble montrer une amélioration dans la description de la décohérence quantique, par rapport, par exemple, à la méthode connue sous le nom de trajectory surface hopping. Le principal obstacle à une large application de la exact factorization est son coût numérique, car l'algorithme quantique-classique nécessite de propager un grand nombre de trajectoires en parallèle, contrairement au trajectory surface hopping, pour lequel les trajectoires peuvent être propagées indépendamment. Ce coût numérique empêche également l'utilisation de la exact factorization avec les techniques ab initio de structure électronique de haut niveau. En conséquence, le but ultime de cette thèse est d'interfacer les méthodes de exact factorization développées à l'Institut de Chimie Physique de l'Université Paris-Saclay, avec la méthode de structure électronique semi-empirique FOMO-CI, développée au Département de Chimie de l'Université de Pise. La grande efficacité de calcul de l'utilisation d'une méthode semi-empirique permettra de calculer facilement de nombreuses trajectoires pour de longues échelles de temps, de l'ordre de la picoseconde, pour des systèmes moléculaires de taille moyenne à grande. Dans la suite, au chapitre 2, le problème général de la dynamique électronique et nucléaire couplée est formulé en partant de l'équation de Schrödinger dépendant du temps et de sa forme de "exact factorization". Ensuite, dans le chapitre 3, les schémas quantiques classiques sont revisités, en présentant quelques nouveaux développements proposés dans le cadre de cette thèse. Dans le chapitre 4, des applications numériques de ces schémas sont proposées en se concentrant sur diverses situations physiques survenant typiquement dans des conditions non-adiabatiques. Les conclusions et les perspectives sont d'abord présentées au chapitre 4. Ensuite, dans le chapitre 7, ces schémas sont proposés en se concentrant sur deux processus moléculaires intéressants: la photoisomérisation de l'azobenzène et la photo-fragmentation de l'azométhane. Ce dernier a été pris comme cas d'essai pour un autre problème affectant toutes les méthodes de trajectoire, y compris celles basées sur la exact factorization: l'échantillonnage des conditions initiales (chapitre 6). Nous nous sommes concentrés sur les conséquences des différentes distributions d'énergie qui sont obtenues avec plusieurs procédures d'échantillonnage, et sur l'effet dit de "ZPE leaking". L'utilisation de la méthode FOMO-CI a permis de réaliser un grand nombre de tests, chacun consistant en une simulation de 10 ps. Dans ce but, nous avons dû reparamétrer l'hamiltonien semi-empirique pour les deux premiers états singlets de l'azométhane, afin d'obtenir une description précise des réactions d'isomérisation et de fragmentation (chapitre 5).The interpretation of photo-induced processes relies nowadays strongly on numerical simulations. An important aspect to be taken into account is undoubtedly the quantum character of the dynamics, consequence of the interaction between the nuclear and the electronic dynamics, involving several electronic states, i.e. the ground state and - possibly many - excited states. Many theories and algorithms of excited state molecular dynamics have been developed over the years, but are still in continuous development. The most used methods, as they are the most practical numerically, are the mixed quantum-classical algorithms, which introduce a description of nuclear dynamics based on classical trajectories coupled to a quantum description of electronic dynamics. However, as a consequence of such a classical approximation, some effects can be lost or improperly described. The quantum decoherence effect is the main example. In this respect, the quantum-classical numerical approach based on exact factorization, dubbed coupled-trajectory mixed quantumclassical (CT-MQC) algorithm, seems to show an improvement in the description of quantum decoherence, compared to, for example, the method that goes by the name of trajectory surface hopping (to date, probably the most widely used quantum-classical method in the community). The main obstacle to the wide application of exact factorization is its numerical cost, because the quantum-classical algorithm requires to propagate a large number of trajectories in parallel, contrary to trajectory surface hopping, for which the trajectories can be propagated independently. This numerical cost also prevents the use of exact factorization with ab initio techniques of high-level electronic structure. As a consequence, the ultimate goal of this thesis is to interface the exact factorization methods developed at the Institut de Chimie Physique of the University Paris-Saclay, with the FOMO-CI semi-empirical electronic structure method, developed at the Department of Chemistry of the University of Pisa. The high computational efficiency of using a semi-empirical method will make it possible to easily compute many trajectories for long timescales, on the order of picoseconds, for medium to large molecular systems. In the following, in Chapter 2, the general problem of coupled electronic and nuclear dynamics is formulated starting with the time-dependent Schrödinger equation and its “exact factorization” form. Afterwards, in Chapter 3, the quantum-classical schemes are revisited, presenting some new developments proposed in the framework of this thesis. In Chapter 4, numerical applications of those schemes are proposed by focusing on various physical situations typically arising in non-adiabatic conditions. First conclusions and perspectives are presented in Chapter 4. Then, in Chapter 7 those schemes are proposed by focusing on two interesting molecular processes: the photoisomerization of azobenzene and the photo-fragmentation of azomethane. The latter has been taken as a test case also for another problem affecting all trajectory methods, including those based on the exact factorization: the sampling of the initial conditions (see Chapter 6). We have focussed on the consequences of the different energy distributions that are obtained with several sampling procedures, and on the so called “ZPE leaking” effect. Running a large number of tests, each consisting a 10 ps simulation, was possible by the use of the FOMO-CI method. To this aim, we had to reparameterize the semiempirical hamiltonian for the first two singlet states of azomethane, to obtain an accurate description of the isomerization and fragmentation reactions (Chapter 5)

Quantum and quantum-classical studies of photo-induced ultrafast processes

The interpretation of photo-induced processes relies nowadays strongly on numerical simulations. An important aspect to be taken into account is the quantum character of the dynamics, consequence of the interaction between the nuclear and the electronic dynamics, involving several electronic states. Many theories and algorithms of excited state molecular dynamics have been developed over the years, but are still in continuous development. The most used methods are the mixed quantum-classical algorithms, which introduce a description of nuclear dynamics based on classical trajectories coupled to a quantum description of electronic dynamics. As a consequence of such a classical approximation, some effects can be lost (as the quantum decoherence effect). In this respect, the quantum-classical numerical approach based on exact factorization seems to show an improvement in the description of quantum decoherence, compared to trajectory surface hopping method. The main obstacle to the wide application of exact factorization is its numerical cost, because the quantum-classical algorithm requires to propagate a large number of trajectories in parallel, contrary to trajectory surface hopping, for which the trajectories can be propagated independently. This numerical cost also prevents the use of exact factorization with ab initio techniques of high-level electronic structure. The ultimate goal of this thesis is to interface the exact factorization methods, with the FOMO-CI semi-empirical electronic structure method. The high computational efficiency of using a semiempirical method will make it possible to easily compute many trajectories for long timescales for medium to large molecular systems

Relaxation dynamics through a conical intersection: Quantum and quantum–classical studies

International audienc

Effect of Initial Conditions Sampling on Surface Hopping Simulations in the Ultrashort and Picosecond Time Range. Azomethane Photodissociation as a Case Study

: We tested the effect of different ways of sampling the initial conditions in surface hopping simulations, with a focus on the initial energy distributions and on the treatment of the zero point energy (ZPE). As a test case, we chose the gas phase photodynamics of azomethane, which features different processes occurring in overlapping time scales: geometry relaxation in the excited state, internal conversion, photoisomerization, and fast and slow dissociation. The simulations, based on a semiempirical method, had a sufficiently long duration (10 ps) to encompass all of the above processes. We tested several variants of methods based on the quantum mechanical (QM) distributions of the nuclear coordinates q and momenta p, which yield, at least on the average over a large sampling set, the correct QM energy, namely the ZPE when starting from the ground vibrational state. We compared the QM samplings with the classical Boltzmann (CB) distribution obtained by a thermostated trajectory, whereby thermal effects are taken into account, but the ZPE is utterly ignored. We found that most QM and CB approaches yield similar results as to short time dynamics and decay lifetimes, whereas the rate of the ground state dissociation reaction CH3NNCH3 → CH3NN + CH3 is sharply affected by the sampling method. With QM samplings a large fraction of trajectories dissociate promply (<1 ps) after decay to the ground state and with rates of the order of 10-1 ps-1 after the first ps. Instead, the CB samplings yield a much smaller fraction of prompt dissociations and much lower rates at long times. We provided evidence that the ZPE "leaks" from high frequency modes to the reactive ones (N-C bond elongations), therefore unphysically increasing the dissociation rates with QM samplings. We show that an effective way to take into account the ZPE and to avoid the "leaking" problem is to add the ZPE to the potential energy surfaces as a function of the most relevant internal coordinates. Then, Boltzmann sampling can be done as usual, so this approach is suitable also for condensed state dynamics. In the tests we present here, the ZPE correction method yields dissociation rates intermediate between QM and uncorrected Boltzmann samplings

Exact Factorization of the Electron-Nuclear Wavefunction:Fundamentals and Algorithms

This Chapter provides an overview on the exact factorization of the electron-nuclear wavefunction, from the presentation of the fundamental theory to its application in the domain of photochemistry. The exact factorization is presented in relation to the more standard Born-Oppenheimer picture, often employed to interpret and simulate excited-state processes that are at the heart of photochemistry. Numerical studies on a two-mode two-state model system are reported focusing on the photo-excitation process by an ultrashort laser pulse and on the subsequent relaxation dynamics through a conical intersection. The aim here is to analyze the time-dependent potentials of the theory and to introduce the concept of nuclear trajectories in the context of the exact factorization. Various applications in photochemistry are then presented, namely the cis-trans photo-isomerization of 2-cis-penta-2,4-dieniminium cation, the photo-dissociation of IBr with the inclusion of spin-orbit coupling, different examples of proton-coupled electron transfer. Those studies are performed by applying the nonadiabatic coupled-trajectory algorithms derived from the exact factorization.</p

Investigating the photodynamics of trans-azobenzene with coupled trajectories

In this work, we present the first implementation of the coupled-trajectory Tully surface hopping (CT-TSH) suitable for applications to molecular systems. We combine CT-TSH with the semiempirical Floating Occupation Molecular Orbitals-Configuration Interaction (FOMO-CI) electronic structure method to investigate the photoisomerization dynamics of trans-azobenzene. Our study shows that CT-TSH can capture correctly decoherence effects in this system, yielding consistent electronic and nuclear dynamics in agreement with (standard) decoherence-corrected TSH. Specifically, CT-TSH is derived from the exact factorization and the electronic coefficients’ evolution is directly influenced by the coupling of trajectories, resulting in the improvement of internal consistency if compared to standard TSH

Investigating the Photodynamics of trans-Azobenzene with Coupled Trajectories

In this work, we present the first implementation of coupled-trajectory Tully surface hopping (CT-TSH) suitable for applications to molecular systems. We combine CT-TSH with the semiempirical floating occupation molecular orbital-configuration interaction electronic structure method to investigate the photoisomerization dynamics of trans-azobenzene. Our study shows that CT-TSH can capture correctly decoherence effects in this system, yielding consistent electronic and nuclear dynamics in agreement with (standard) decoherence-corrected TSH. Specifically, CT-TSH is derived from the exact factorization and the electronic coefficients' evolution is directly influenced by the coupling of trajectories, resulting in the improvement of internal consistency if compared to standard TSH

Effect of Initial Conditions Sampling on Surface Hopping Simulations in the Ultrashort and Picosecond Time Range. Azomethane Photodissociation as a Case Study

We tested the effect of different ways of sampling the initial conditions in surface hopping simulations, with a focus on the initial energy distributions and on the treatment of the zero point energy (ZPE). As a test case, we chose the gas phase photodynamics of azomethane, which features different processes occurring in overlapping time scales: geometry relaxation in the excited state, internal conversion, photoisomerization, and fast and slow dissociation. The simulations, based on a semiempirical method, had a sufficiently long duration (10 ps) to encompass all of the above processes. We tested several variants of methods based on the quantum mechanical (QM) distributions of the nuclear coordinates q and momenta p, which yield, at least on the average over a large sampling set, the correct QM energy, namely the ZPE when starting from the ground vibrational state. We compared the QM samplings with the classical Boltzmann (CB) distribution obtained by a thermostated trajectory, whereby thermal effects are taken into account, but the ZPE is utterly ignored. We found that most QM and CB approaches yield similar results as to short time dynamics and decay lifetimes, whereas the rate of the ground state dissociation reaction CH3NNCH3 → CH3NN + CH3 is sharply affected by the sampling method. With QM samplings a large fraction of trajectories dissociate promply (<1 ps) after decay to the ground state and with rates of the order of 10–1 ps–1 after the first ps. Instead, the CB samplings yield a much smaller fraction of prompt dissociations and much lower rates at long times. We provided evidence that the ZPE “leaks” from high frequency modes to the reactive ones (N–C bond elongations), therefore unphysically increasing the dissociation rates with QM samplings. We show that an effective way to take into account the ZPE and to avoid the “leaking” problem is to add the ZPE to the potential energy surfaces as a function of the most relevant internal coordinates. Then, Boltzmann sampling can be done as usual, so this approach is suitable also for condensed state dynamics. In the tests we present here, the ZPE correction method yields dissociation rates intermediate between QM and uncorrected Boltzmann samplings

Prevalence of transthyretin-related amyloidosis in Tuscany: Data from the regional population-based registry

: The limited available data regarding the prevalence of transthyretin amyloidosis, both for wild-type (ATTRwt) and hereditary form (ATTRv), is inferred from highly selected patients and subsequent extrapolations that limit the comprehension of the clinical disease impact. The Tuscan healthcare system in 2006 developed a web-based rare disease registry, to monitor and profile patients affected by rare diseases. Clinicians belonging to regional validated healthcare data centres can register patients at the diagnosis, with a rigorous approach and distinguishing the types of amyloidosis, i.e., ATTRwt versus ATTRv. Thanks to this data collection method, available from July 2006 and extended with electronic therapy plans related to a diagnosis since May 2017, we analysed prevalence and incidence of ATTR and its subtypes. On November 30th 2022, ATTRwt prevalence in Tuscany is 90.3 per 1,000,000 persons and ATTRv prevalence is 9.5 per 1,000,000 persons, whereas the annual incidence ranges from 14.4 to 26.7 per 1,000,000 persons and from 0.8 to 2.7 per 1,000,000 persons, respectively. The male gender is predominant in both forms. All except one patient showed evidence of cardiomyopathy. This epidemiological data requires attention, not only to increase the effort for the clinical management and earlier diagnosis, but also to underline the need for the disease-specific treatments