@phdthesis{Bouakline2023,
  author    = {Bouakline, Foudhil},
  title     = {Manifestations of Quantum-Mechanical Effects in Molecular Reaction Dynamics},
  school      = {Universit{\"a}t Potsdam},
  pages     = {316},
  year      = {2023},
  abstract  = {This habilitation thesis summarises the research work performed by the author during the last quindecennial period. The dissertation reflects his main research interests, which revolve around quantum dynamics of small-sized molecular systems, including their interactions with electromagnetic radiation or dissipative environments. This covers various dynamical processes that involve bound-bound, bound-free, and free-free molecular transitions. The latter encompass light-triggered rovibrational or rovibronic dynamics in bound molecules, molecular photodissociation induced by weak or strong laser fields, state-to-state reactive and/or inelastic molecular collisions, and phonon-driven vibrational relaxation of adsorbates at solid surfaces. Although the dissertation covers different topics of molecular reaction dynamics, most of these studies focus on nuclear quantum effects and their manifestations in experimental measures. The latter are assessed through comparison between quantum and classical predictions, and/or direct confrontation of theory and experiment. Most well known quantum concepts and effects will be encountered in this work. Yet, almost all these quantum notions find their roots in the central pillar of quantum theory, namely, the quantum superposition principle. Indeed, quantum coherence is the main source of most quantum effects, including interference, entanglement, and even tunneling. Thus, the common and predominant theme of all the investigations of this thesis is quantum coherence, and the survival or quenching of subsequent interference effects in various molecular processes. The lion's share of the dissertation is devoted to two associated quantum concepts, which are usually overlooked in computational molecular dynamics, viz. the Berry phase and identical nuclei symmetry. The importance of the latter in dynamical molecular processes and their direct fingerprints in experimental observables also rely very much on quantum coherence and entanglement. All these quantum phenomena are thoroughly discussed within the four main topics that form the core of this thesis. Each topic is described in a separate chapter, where it is briefly summarised and then illustrated with three peer-reviewed publications. The first topic deals with the relevance of quantum coherence/interference in molecular collisions, with a focus on the hydrogen-exchange reaction, H+H2 --> H2+H, and its isotopologues. For these collision processes, the significance of interference of probability amplitudes arises because of the existence of two main scattering pathways. The latter could be inelastic and reactive scattering, direct and time-delayed scattering, or two encircling reaction paths that loop in opposite senses around a conical intersection (CI) of the H3 molecular system. Our joint theoretical-experimental investigations of these processes reveal strong interference and geometric phase (GP) effects in state-to-state reaction probabilities and differential cross sections. However, these coherent effects completely cancel in integral cross sections and reaction rate constants, due to efficient dephasing of interference between the different scattering amplitudes. As byproducts of these studies, we highlight the discovery of two novel scattering mechanisms, which contradict conventional textbook pictures of molecular reaction dynamics. The second topic concerns the effect of the Berry phase on molecular photodynamics at conical intersections. To understand this effect, we developed a topological approach that separates the total molecular wavefunction of an unbound molecular system into two components, which wind in opposite senses around the conical intersection. This separation reveals that the only effect of the geometric phase is to change the sign of the relative phase of these two components. This in turn leads to a shift in the interference pattern of the molecular system---a phase shift that is reminiscient of the celebrated Aharonov-Bohm effect. This procedure is numerically illustrated with photodynamics at model standard CIs, as well as strong-field dissociation of diatomics at light-induced conical intersections (LICIs). Besides the fundamental aspect of these studies, their findings allow to interpret and predict the effect of the GP on the state-resolved or angle-resolved spectra of pump-probe experimental schemes, particularly the distributions of photofragments in molecular photodissociation experiments. The third topic pertains to the role of the indistinguishability of identical nuclei in molecular reaction dynamics, with an emphasis on dynamical localization in highly symmetric molecules. The main object of these studies is whether nuclear-spin statistics allow dynamical localization of the electronic, vibrational, or even rotational density on a specific molecular substructure or configuration rather than on another one which is identical (indistinguishable). Group-theoretic analysis of the symmetrized molecular wavefunctions of these systems shows that nuclear permutation symmetry engenders quantum entanglement between the eigenstates of the different molecular degrees of freedom. This subsequently leads to complete quenching of dynamical localization over indistinguishable molecular substructures---an observation that is in sharp contradiction with well known textbook views of iconic molecular processes. This is illustrated with various examples of quantum dynamics in symmetric double-well achiral molecules, such as the prototypical umbrella inversion motion of ammonia, electronic Kekul{\´e} dynamics in the benzene molecule, and coupled electron-nuclear dynamics in laser-induced indirect photodissociation of the dihydrogen molecular cation. The last part of the thesis is devoted to the development of approximate wavefunction approaches for phonon-induced vibrational relaxation of adsorbates (system) at surfaces (bath). Due to the so-called 'curse of dimensionality', these system-bath complexes cannot be handled with standard wavefunction methods. To alleviate the exponential scaling of the latter, we developed approximate yet quite accurate numerical schemes that have a polynomial scaling with respect to the bath dimensionality. The corresponding algorithms combine symmetry-based reductions of the full vibrational Hilbert space and iterative Krylov techniques. These approximate wavefunction approaches resemble the 'Bixon-Jortner model' and the more general 'quantum tier model'. This is illustrated with the decay of H-Si (D-Si) vibrations on a fully H(D)-covered silicon surface, which is modelled with a phonon-bath of more than two thousand oscillators. These approximate methods allow reliable estimation of the adsorbate vibrational lifetimes, and provide some insight into vibration-phonon couplings at solid surfaces. Although this topic is mainly computational, the developed wavefunction approaches permit to describe quantum entanglement between the system and bath states, and to embody some coherent effects in the time-evolution of the (sub-)system, which cannot be accounted for with the widely used 'reduced density matrix formalism'.},
  language  = {en}
}