Quantum Trajectories for the Dynamics in the Exact Factorization Framework: A Proof-of-Principle Test

In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation. Those characteristics are referred to as quantum trajectories, since they are generated via ordinary differential equations similar to Hamilton's equations, but including the so-called quantum potential, and they can be used to reconstruct exactly the quantum-mechanical nuclear wave function, provided infinite initial conditions are propagated in time.

Internal Conversion and Intersystem Crossing with the Exact Factorization

We present a detailed derivation of the generalized coupled-trajectory mixed quantum-classical (G-CT-MQC) algorithm based on the exact-factorization equations. The ultimate goal is to propose an algorithm that can be employed for molecular dynamics simulations of nonradiative phenomena, as the spin-allowed internal conversions and the spin-forbidden intersystem crossings. Internal conversions are nonadiabatic processes driven by the kinetic coupling between electronic states, whereas intersystem crossings are mediated by the spin-orbit coupling. In this paper, we discuss computational issues related to the suitable representation for electronic dynamics and the different natures of kinetic and spin-orbit coupling. Numerical studies on model systems allow us to test the performance of the G-CT-MQC algorithm in different situations.

On the Theoretical Determination of Photolysis Properties for Atmospheric Volatile Organic Compounds

Volatile organic compounds (VOCs) are ubiquitous atmospheric molecules that generate a complex network of chemical reactions in the troposphere, often triggered by the absorption of sunlight. Understanding the VOC composition of the atmosphere relies on our ability to characterize all of their possible reaction pathways. When considering reactions of (transient) VOCs with sunlight, the availability of photolysis rate constants, utilized in general atmospheric models, is often out of experimental reach due to the unstable nature of these molecules. Here, we show how recent advances in computational photochemistry allow us to calculate in silico the different ingredients of a photolysis rate constant, namely, the photoabsorption cross-section and wavelength-dependent quantum yields. The rich photochemistry of tert-butyl hydroperoxide, for which experimental data are available, is employed to test our protocol and highlight the strengths and weaknesses of different levels of electronic structure and nonadiabatic molecular dynamics to study the photochemistry of (transient) VOCs.

Embedding via the Exact Factorization Approach

We present a quantum electronic embedding method derived from the exact factorization approach to calculate static properties of a many-electron system. The method is exact in principle but the practical power lies in utilizing input from a low-level calculation on the entire system in a high-level method computed on a small fragment, as in other embedding methods. Here, the exact factorization approach defines an embedding Hamiltonian on the fragment. Various Hubbard models demonstrate that remarkably accurate ground-state energies are obtained over the full range of weak to strongly correlated systems.

Conservation of Angular Momentum in Direct Nonadiabatic Dynamics

Direct nonadiabatic dynamics is used to study processes involving multiple electronic states from small molecules to materials. Compared with dynamics with fitted analytical potential energy surfaces, direct dynamics is more user-friendly in that it obtains all needed energies, gradients, and nonadiabatic couplings (NACs) by electronic structure calculations. However, the NAC that is usually used does not conserve angular momentum or the center of mass in widely used mixed quantum-classical nonadiabatic dynamics algorithms, in particular, trajectory surface hopping, semiclassical Ehrenfest, and coherent switching with decay of mixing. We show that by using a projection operator to remove the translational and rotational components of the originally computed NAC, one can restore the conservation.

Spin-Orbit Interactions in Ultrafast Molecular Processes

We investigate spin-orbit interactions in ultrafast molecular processes employing the exact factorization of the electron-nuclear wave function. We revisit the original derivation by including spin-orbit coupling, and show how the dynamics driven by the time-dependent potential energy surface alleviates inconsistencies arising from different electronic representations. We propose a novel trajectory-based scheme to simulate spin-forbidden non-radiative processes, and we show its performance in the treatment of excited-state dynamics where spin-orbit effects couple different spin multiplets.

A molecular perspective on Tully models for nonadiabatic dynamics

We present a series of standardized molecular tests for nonadiabatic dynamics, reminiscent of the one-dimensional Tully models proposed in 1990.

Competition between charge migration and charge transfer induced by nuclear motion following core ionization: Model systems and application to Li2. J Chem Phys 2019;151:124108. [PMID: 31575213 DOI: 10.1063/1.5117246]

Attosecond and femtosecond spectroscopies present opportunities for the control of chemical reaction dynamics and products, as well as for quantum information processing; we address the somewhat unique situation of core-ionization spectroscopy which, for dimeric chromophores, leads to strong valence charge localization and hence tightly paired potential-energy surfaces of very similar shape. Application is made to the quantum dynamics of core-ionized Li₂ ⁺. This system is chosen as Li₂ is the simplest stable molecule facilitating both core ionization and valence ionization. First, the quantum dynamics of some model surfaces are considered, with the surprising result that subtle differences in shape between core-ionization paired surfaces can lead to dramatic differences in the interplay between electronic charge migration and charge transfer induced by nuclear motion. Then, equation-of-motion coupled-cluster calculations are applied to determine potential-energy surfaces for 8 core-excited state pairs, calculations believed to be the first of their type for other than the lowest-energy core-ionized molecular pair. While known results for the lowest-energy pair suggest that Li₂ ⁺ is unsuitable for studying charge migration, higher-energy pairs are predicted to yield results showing competition between charge migration and charge transfer. Central is a focus on the application of Hush's 1975 theory for core-ionized X-ray photoelectron spectroscopy to understand the shapes of the potential-energy surfaces and hence predict key features of charge migration.

Exact Potential Energy Surface for Molecules in Cavities

We find and analyze the exact time-dependent potential energy surface driving the proton motion for a model of cavity-induced suppression of proton-coupled electron transfer. We show how, in contrast to the polaritonic surfaces, its features directly correlate to the proton dynamics and we discuss cavity modifications of its structure responsible for the suppression. The results highlight the interplay between nonadiabatic effects from coupling to photons and coupling to electrons and suggest caution is needed when applying traditional dynamics methods based on polaritonic surfaces.