arXiv subjects

Federica Agostini

Publications and source records attributed to Federica Agostini.

At least 19 recordsLinked to original sources

arXiv2026

On the interpretation of molecular photoexcitation with long and ultrashort laser pulses

Photoexcitation is an inherent part of any photochemical or spectroscopic experiment, yet its impact on the excited-state dynamics is often overlooked. However, it is the excited molecular state, built upon photoexcitation and shaped by the characteristics of the light source, that determines the fate of the excited molecule and its subsequent photochemical reactions. In this work, we investigate how excited molecular states are built by different laser pulses, leveraging two representations of the molecular wave function: the Born-Huang expansion and the exact factorization. We explore the generation of two limiting cases: a stationary molecular state generated with a long laser pulse and an electronic wave packet created by an ultrashort (attosecond) laser pulse. The standard concepts of population transfer between electronic states, the resonance condition, or sudden vertical excitation, inherent to the Born-Huang representation and used by chemists to approximate the impact of photoexcitation on molecular systems, are brought to a new light by the exact factorization.

physics.chem-ph↗

arXiv2026

Perspective on a challenge: predicting the photochemistry of cyclobutanone

This Perspective is part of a Special Topic that explored the maturity of nonadiabatic molecular dynamics for predicting photochemical processes. In 2023, a prediction challenge was issued to the community of computational photochemists to simulate the photochemistry of cyclobutanone, photoexcited at 200 nm, and the resulting time-resolved MeV-UED signal. The challenge attracted 15 theoretical predictions from more than 70 researchers, employing a wide range of strategies for electronic structure and nonadiabatic molecular dynamics to predict the time-resolved MeV-UED signal before the experiment had been conducted at SLAC (Stanford, USA). The MeV-UED instrument at Shanghai Jiao Tong University was also used to provide a second independent time-resolved MeV-UED signal for the photochemistry of cyclobutanone. This Perspective discusses the various approaches and strategies used by the participants to predict the photochemistry of cyclobutanone. This work also summarizes the strengths and weaknesses of various methods used for photoexcitation, electronic structure, nonadiabatic dynamics, and calculation of observables, as agreed by the participants during a CECAM workshop dedicated to the results of the challenge and organized in Lausanne in April 2025. This Perspective also collects all the predicted time-resolved MeV-UED signals into a single figure, together with the experimental signal. This challenge (i) demonstrated the qualitative predictive power of nonadiabatic molecular dynamics and (ii) underscore the impact of electronic-structure theory on the outcome of the excited-state dynamics and the need for its careful benchmarking. This effort allowed the community to share practical strategies to perform nonadiabatic dynamics (discussed in the present Perspective) and constitutes a 'calibration' exercise for computational photochemistry.

physics.chem-ph↗

arXiv2026

Different perspectives on the exact factorization for photon-electron-nuclear systems

We employ the exact factorization of a multi-component wavefunction to analyze the dynamics of interacting photons, electrons and nuclei. We consider physical situations emerging in the regime of strong coupling between light excitations and molecular - electronic excitations, giving rise to the so-called molecular polaritons. Nonadiabatic molecular dynamics techniques, routinely used in the field of chemical physics, have been often employed to simulate photophysical and photochemical phenomena in the presence of molecular polaritons. In this work, we analyze the foundations of these techniques in the eye of the exact factorization and we assess their performance on illustrative model studies.

physics.chem-ph↗

arXiv2026

Exact factorization of a many-body wavefunction beyond the electron-nuclear problem

This Review is devoted to the presentation of the exact factorization as a framework employed to study a variety of quantum-mechanical many-body problems. Since its original formulation in the 70s, the main applications of the exact factorization were directed towards understanding the properties of multi-component systems, e.g. electron-nuclear systems. Especially in the electron-nuclear case, the exact factorization is viewed as an exactification of the Born-Oppenheimer approximation, thus it was, and still is, largely employed in nonadiabatic dynamics. Nonetheless, as early as the 80s, the formalism was employed to study many-electron interacting systems and, quite recently, i.e. less than a decade ago, it was extended to study the behavior of molecules in the context in cavity quantum electrodynamics. These formulations, perhaps less popular than the electron-nuclear formulation, have attracted a lot of attention over the years. Therefore, we review here the exact electron-only factorization and the exact photon-electron-nuclear factorization.

physics.chem-ph↗

arXiv2025

Best practices for nonadiabatic molecular dynamics simulations

Nonadiabatic molecular dynamics simulations aim to describe the coupled electron-nuclear dynamics of molecules in excited electronic states. These simulations have been applied to understand a plethora of photochemical and photophysical processes, and, as a result, the number of nonadiabatic dynamics simulations has been growing significantly over the past decade. Yet, the field remains in its infancy, and a potential user may find it difficult to approach this type of simulation, given their complexity and the number of elements that should be considered for a (hopefully) successful nonadiabatic dynamics simulation. Nonadiabatic molecular dynamics relies on several key steps: finding a level of electronic-structure theory to describe the molecule in its Franck-Condon region and beyond, describing the photoexcitation process, selecting a method to perform the nonadiabatic dynamics, and analyzing the final results before calculating observables for a more direct comparison with experiment. This Best Practices guide aims to provide a general guide for the user of nonadiabatic molecular dynamics by (i) discussing the fundamentals of nonadiabatic molecular dynamics and the various trajectory-based methods developed for molecular systems, (ii) introducing the different electronic-structure methods and concepts - adiabatic/diabatic representation, conical intersections - that can be used with nonadiabatic molecular dynamics (or for benchmarking), (iii) providing details on the various steps required to perform a nonadiabatic dynamics simulation and their practical use, as well as guided examples and a discussion on the calculation of observables, (iv) proposing a FAQ with the typical questions a user may have when performing nonadiabatic dynamics, and (v) sketching a checklist for the key practical steps when performing a (trajectory-based) nonadiabatic molecular dynamics.

physics.chem-ph↗

arXiv2025

A coupled-trajectory approach for decoherence, frustrated hops and internal consistency in surface hopping

We address the issues of decoherence, frustrated hops and internal consistency in surface hopping. We demonstrate that moving away from an independent-trajectory picture is the strategy which allows us to propose a robust surface hopping scheme overcoming all these issues at once. Based on the exact factorization and on the idea of coupled trajectories, we consider the swarm of trajectories, that mimics the nuclear dynamics in nonadiabatic processes, as a unique entity. In this way, imposing energy conservation of the swarm and allowing the trajectories to share energy when hops occur clearly indicates the route towards a new surface hopping scheme. Encouraging results are reported, in terms of electronic and vibrational time-dependent properties on the photodynamics of fulvene and 4-(dimethyloamino)benzonitrile, modeled with a full-dimensional linear vibronic coupling Hamiltonian.

physics.chem-ph↗

arXiv2025

Roadmap for Molecular Benchmarks in Nonadiabatic Dynamics

Simulating the coupled electronic and nuclear response of a molecule to light excitation requires the application of nonadiabatic molecular dynamics. However, when faced with a specific photophysical or photochemical problem, selecting the most suitable theoretical approach from the wide array of available techniques is not a trivial task. The challenge is further complicated by the lack of systematic method comparisons and rigorous testing on realistic molecular systems. This absence of comprehensive molecular benchmarks remains a major obstacle to advances within the field of nonadiabatic molecular dynamics. A CECAM workshop, Standardizing Nonadiabatic Dynamics: Towards Common Benchmarks, was held in May 2024 to address this issue. This Perspective highlights the key challenges identified during the workshop in defining molecular benchmarks for nonadiabatic dynamics. Specifically, this work outlines some preliminary observations on essential components needed for simulations and proposes a roadmap aiming to establish, as an ultimate goal, a community-driven, standardized molecular benchmark set.

physics.chem-ph↗

arXiv2025

Quantum Dynamics Predicts Coherent Oscillatory Behavior in the Early-times of a Photoisomerization Reaction

In this work, we study the quantum dynamics of a photoisomerization reaction employing a two-electronic-state three-vibrational-mode model of the 2-cis-penta-2,4-dieniminium cation (cis-PSB3). In particular, we address two main issues: the challenges encountered in properly converging quantum dynamics calculations, even when a reduced-dimensionality molecular model is used; the emergence of a coherent oscillatory behavior in the formation of the trans isomer upon photoexcitation of cis-PSB3. The two issues are strictly related, since only upon reliable convergence, the simulated dynamics is able to capture the large amplitude motion associated to the torsion around the reactive bond, typical of photoisomerizations, which is due to the large amount of kinetic energy acquired by the vibrational modes after light excitation.

physics.chem-ph↗

arXiv2024

Modelling the Kohn-Sham potential for molecular dissociation with orbital-independent functionals: a proof of principle

We model the Hartree-exchange-correlation potential of Kohn-Sham density-functional theory adopting a novel strategy inspired by the strictly-correlated-electrons limit and relying on the exact decomposition of the potential based on the exact factorization formalism. Starting with accurate density and conditional potential for a one-dimensional model of a stretched heteronuclear molecule, we provide a proof-of-principle example of an approximation that accurately reproduces the step of the exact Kohn-Sham potential without resorting to the Kohn-Sham orbitals, virtual or occupied. We also test our strategy using the approximate conditional potentials corresponding to the strictly-correlated-electron and the exact-exchange functionals. The results are encouraging in that the initial approximations are modified in the qualitatively correct way: decreasing correlation in the former and increasing it in the latter.

physics.chem-ph↗

arXiv2024

Exploring exact-factorization-based trajectories for low-energy dynamics near a conical intersection

We study low-energy dynamics generated by a two-dimensional two-state Jahn-Teller Hamiltonian in the vicinity of a conical intersection using quantum wavepacket and trajectories dynamics. Recently, these dynamics were studied by comparing the adiabatic representation and the exact factorization, with the purpose to highlight the different nature of topological- and geometric-phase effects arising in the two theoretical representation of the same problem. Here, we employ the exact factorization to understand how to model accurately low-energy dynamics in the vicinity of a conical intersection using an approximate description of the nuclear motion that uses trajectories. We find that, since nonadiabatic effects are weak but non-negligible, the trajectory-based description that invokes the classical approximation struggles to capture the correct behavior.

physics.chem-ph↗

arXiv2022

Exact Factorization Adventures: A Promising Approach for Non-bound States

Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.

physics.chem-ph↗

arXiv2021

Ultrafast dynamics with the exact factorization

The exact factorization of the time-dependent electron-nuclear wavefunction has been employed successfully in the field of quantum molecular dynamics simulations for interpreting and simulating light-induced ultrafast processes. In this work, we summarize the major developments leading to the formulation of a trajectory-based approach, derived from the exact factorization equations, capable of dealing with nonadiabatic electronic processes, and including spin-orbit coupling and the non-perturbative effect of an external time-dependent field. This trajectory-based quantum-classical approach has been dubbed coupled-trajectory mixed quantum-classical (CT-MQC) algorithm, whose performance is tested here to study the photo-dissociation dynamics of IBr.

physics.chem-ph↗

arXiv2021

Quantum-classical nonadiabatic dynamics of Floquet driven systems

We develop a trajectory-based approach for excited-state molecular dynamics simulations of systems subject to an external periodic drive. We combine the exact-factorization formalism, allowing to treat electron-nuclear systems in nonadiabatic regimes, with the Floquet formalism for time-periodic processes. The theory is developed starting with the molecular time-dependent Schroedinger equation with inclusion of an external periodic drive that couples to the system dipole moment. With the support of the Floquet formalism, quantum dynamics is approximated by combining classical-like, trajectory-based, nuclear evolution with electronic dynamics represented in the Floquet basis. The resulting algorithm, which is an extension of the coupled-trajectory mixed quantum-classical scheme for periodically driven systems, is applied to a model study, exactly solvable, with different field intensities.

physics.chem-ph↗

arXiv2018

The Coupled-Trajectory Mixed Quantum-Classical Algorithm: A Deconstruction

We analyze a mixed quantum-classical algorithm recently derived from the exact factorization equations [Min, Agostini, Gross, PRL {\bf 115}, 073001 (2015)] to show the role of the different terms in the algorithm in bringing about decoherence and wavepacket branching. The algorithm has the structure of Ehrenfest equations plus a "coupled-trajectory" term for both the electronic and nuclear equations, and we analyze the relative roles played by the different non-adiabatic terms in these equations, including how they are computed in practise. In particular, we show that while the coupled-trajectory term in the electronic equation is essential in yielding accurate dynamics, that in the nuclear equation has a much smaller effect. A decoherence time is extracted from the electronic equations and compared with that of augmented fewest-switches surface-hopping. We revisit a series of non-adiabatic Tully model systems to illustrate our analysis.

physics.chem-ph↗

arXiv2016

The adiabatic limit of the exact factorization of the electron-nuclear wave function

We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model proton- coupled electron transfer in different non-adiabatic regimes.

physics.chem-ph↗

arXiv2016

On the mass of atoms in molecules: Beyond the Born-Oppenheimer approximation

Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons and only bare nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires to include the participation of electrons in the internal motion of the molecule. More than 80 years after the original work of Born and Oppenheimer, this issue still is not solved in general. Here, we present a theoretical and numerical framework to address this problem in a general and rigorous way. Starting from the exact factorization of the electron-nuclear wave function, we include electronic effects beyond the Born-Oppenheimer regime in a perturbative way via position-dependent corrections to the bare nuclear masses. This maintains an adiabatic-like point of view: the nuclear degrees of freedom feel the presence of the electrons via a single potential energy surface, whereas the inertia of electrons is accounted for and the total mass of the system is recovered. This constitutes a general framework for describing the mass acquired by slow degrees of freedom due to the inertia of light, bounded particles. We illustrate it with a model of proton transfer, where the light particle is the proton, and with corrections to the vibrational spectra of molecules. Inclusion of the light particle inertia allows to gain orders of magnitude in accuracy.

physics.chem-ph↗

arXiv2016

An Exact Factorization Perspective on Quantum Interferences in Nonadiabatic Dynamics

Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface - the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly-solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrast to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics the one of the exact nuclear probability density.

physics.chem-ph↗

arXiv2016

Quantum-Classical Non-Adiabatic Dynamics: Coupled- vs. Independent-Trajectory Methods

Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic non-adiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron-nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories, and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods.

quant-ph↗