TY - JOUR A1 - Witzorky, Christoph A1 - Paramonov, Guennaddi A1 - Bouakline, Foudhil A1 - Jaquet, Ralph A1 - Saalfrank, Peter A1 - Klamroth, Tillmann T1 - Gaussian-type orbital calculations for high harmonic generation in vibrating molecules BT - Benchmarks for H-2(+) JF - Journal of chemical theory and computation N2 - The response of the hydrogen molecular ion, H-2(+), to few-cycle laser pulses of different intensities is simulated. To treat the coupled electron-nuclear motion, we use adiabatic potentials computed with Gaussian-type basis sets together with a heuristic ionization model for the electron and a grid representation for the nuclei. Using this mixed-basis approach, the time-dependent Schrodinger equation is solved, either within the Born-Oppenheimer approximation or with nonadiabatic couplings included. The dipole response spectra are compared to all-grid-based solutions for the three-body problem, which we take as a reference to benchmark the Gaussian-type basis set approaches. Also, calculations employing the fixed-nuclei approximation are performed, to quantify effects due to nuclear motion. For low intensities and small ionization probabilities, we get excellent agreement of the dynamics using Gaussian-type basis sets with the all-grid solutions. Our investigations suggest that high harmonic generation (HHG) and high-frequency response, in general, can be reliably modeled using Gaussian-type basis sets for the electrons for not too high harmonics. Further, nuclear motion destroys electronic coherences in the response spectra even on the time scale of about 30 fs and affects HHG intensities, which reflect the electron dynamics occurring on the attosecond time scale. For the present system, non-Born-Oppenheimer effects are small. The Gaussian-based, nonadiabatically coupled, time-dependent multisurface approach to treat quantum electron-nuclear motion beyond the non-Born-Oppenheimer approximation can be easily extended to approximate wavefunction methods, such as time-dependent configuration interaction singles (TD-CIS), for systems where no benchmarks are available. KW - Basis sets KW - Chemical calculations KW - Ionization KW - Lasers KW - Quantum mechanics Y1 - 2021 U6 - https://doi.org/10.1021/acs.jctc.1c00837 SN - 1549-9618 SN - 1549-9626 VL - 17 IS - 12 SP - 7353 EP - 7365 PB - American Chemical Society CY - Washington ER - TY - JOUR A1 - Bouakline, Foudhil A1 - Tremblay, Jean Christophe T1 - Is it really possible to control aromaticity of benzene with light? JF - Physical chemistry, chemical physics : PCCP N2 - Recent theoretical investigations claim that tailored laser pulses may selectively steer benzene's aromatic ground state to localized non-aromatic excited states. For instance, it has been shown that electronic wavepackets, involving the two lowest electronic eigenstates, exhibit subfemtosecond charge oscillation between equivalent Kekule resonance structures. In this contribution, we show that such dynamical electron-localization in the molecule-fixed frame contravenes the principle of the indistinguishability of identical particles. This breach stems from a total omission of the nuclear degrees of freedom, giving rise to nonsymmetric electronic wavepackets under nuclear permutations. Enforcement of the latter leads to entanglement between the electronic and nuclear states. To obey quantum statistics, the entangled molecular states should involve compensating nuclear-permutation symmetries. This in turn engenders complete quenching of dynamical electron-localization in the molecule-fixed frame. Indeed, for the (six-fold) equilibrium geometry of benzene, group-theoretic analysis reveals that any electronic wavepacket exhibits a (D-6h) totally symmetric electronic density, at all times. Thus, our results clearly show that the six carbon atoms, and the six C-C bonds, always have equal Mulliken charges, and equal bond orders, respectively. However, electronic wavepackets may display dynamical localization of the electronic density in the space-fixed frame, whenever they involve both even and odd space-inversion (parity) or permutation-inversion symmetry. Dynamical spatial-localization can be probed experimentally in the laboratory frame, but it should not be deemed equivalent to charge oscillation between benzene's identical electronic substructures, such as Kekule resonance structures. Y1 - 2020 U6 - https://doi.org/10.1039/c9cp06794a SN - 1463-9076 SN - 1463-9084 VL - 22 IS - 27 SP - 15401 EP - 15412 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Bouakline, Foudhil T1 - Unambiguous signature of the berry phase in intense laser dissociation of diatomic molecules JF - The journal of physical chemistry letters N2 - We report strong evidence of Berry phase effects in intense laser dissociation of D-2(+) molecules, manifested as Aharonov-Bohm-like oscillations in the photofragment angular distribution (PAD). Our calculations show that this interference pattern strongly depends on the parity of the diatom initial rotational state, (-1)(j). Indeed, the PAD local maxima (minima) observed in one case (j odd) correspond to local minima (maxima) in the other case (j even). Using simple topological arguments, we clearly show that such interference conversion is a direct signature of the Berry phase. The sole effect of the latter on the rovibrational wave function is a sign change of the relative phase between two interfering components, which wind in opposite senses around a light-induced conical intersection (LICI). Therefore, encirclement of the LICI leads to constructive (j odd) or destructive (j even) self-interference of the initial nuclear wavepacket in the dissociative limit. To corroborate our theoretical findings, we suggest an experiment of strong-field indirect dissociation of D-2(+) molecules, comparing the PAD of the ortho and para molecular species in directions nearly perpendicular to the laser polarization axis. Y1 - 2018 U6 - https://doi.org/10.1021/acs.jpclett.8b00607 SN - 1948-7185 VL - 9 IS - 9 SP - 2271 EP - 2277 PB - American Chemical Society CY - Washington ER - TY - THES A1 - Bouakline, Foudhil T1 - Manifestations of Quantum-Mechanical Effects in Molecular Reaction Dynamics N2 - 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 Kekulé 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'. N2 - Diese Habilitationsschrift fasst die Forschungsarbeiten des Autors während der letzten 15 Jahre zusammen. Die wissenschaftliche Abhandlung spiegelt seine hauptsächlichen Forschungsinteressen wider, die sich um die Quantendynamik kleiner molekularer Systeme drehen, einschließlich ihrer Wechselwirkung mit elektromagnetischer Strahlung oder dissipativer Umgebungen. Dies umfasst verschiedene dynamische Prozesse, die Übergänge zwischen molekulare Zuständen (gebunden-gebunden, gebunden-frei und frei-frei) beinhalten. Dazu zählen lichtgesteuerte rovibronische Dynamik in gebundenen Molekülen, molekulare Photodissoziation durch schwache oder starke Laserfelder, reaktive und/oder inelastische molekulare Kollisionen und phononengesteuerte Schwingungsrelaxation von Adsorbaten auf Festkörperoberflächen. Obwohl die Habilitationsschrift verschiedene Themengebiete molekularer Reaktionsdynamik abdeckt, konzentrieren sich die meisten Arbeiten auf nukleare Quanteneffekte und wie sich diese in experimentellen Messgrößen äußern.. Dies wird durch den Vergleich von quantenphysikalischen und klassischen Vorhersagen und/oder eine direkte Gegenüberstellung von Theorie und Experiment beurteilt. Die meisten wohlbekannten quantenphysikalischen Konzepte und Effekte kommen in dieser Arbeit vor. Fast alle davon beruhen auf der zentralen Säule der Quantentheorie, dem Quanten-Superpositionsprinzip. Tatsächlich ist Quantenkohärenz die Hauptquelle der meisten Quanteneffekte, einschließlich Interferenz, Verschränkung und sogar Tunneln. Daher ist das gemeinsame und vorherrschende Thema aller Untersuchungen in dieser Arbeit die Quantenkoheränz und das Fortbestehen oder die Auslöschung der daraus folgenden Interferenzauswirkungen in verschiedenen molekularen Prozessen. Der Hauptanteil dieser Habilitationsschrift behandelt zwei verwandte Quantenkonzepte, die in Molekulardynamik-Rechnungen meist keine Beachtung finden, nämlich der Berry-Phase und der Symmetrie identischer Kerne. Deren Bedeutung in dynamischen molekularen Prozessen und ihre Anzeichen in experimentellen Messgrößen beruhen auch zu großen Teilen auf Quantenkohärenz und Verschränkung. Alle diese Quantenphänomene werden in den vier Hauptthemen, die den Kern dieser Arbeit bilden, umfassend behandelt. Jedes Themengebiet wird in einem separaten Kapitel beschrieben, in dem es kurz zusammengefasst und durch drei extern begutachtete Veröffentlichungen dargestellt wird. Das erste Themengebiet behandelt die Relevanz von Interferenz bei molekularen Kollisionen, wobei der Fokus auf der Wasserstoff-Austauschreaktion, H+H2 --> H2+H, und ihren Isotopologen liegt. Die Bedeutsamkeit der Interferenz der Wahrscheinlichkeits-Amplituden für solche Kollisionsprozesse erwächst aus der Existenz zweier Haupt-Streupfade. Dabei kann es sich um inelastische und reaktive Streuung, direkte und zeitverzögerte Streuung oder zwei gegenläufige Reaktionspfade um eine konische Durchschneidung (conical intersection, CI) im H3-Molekülsystem handeln. Unsere gemeinsamen theoretische und experimentelle Untersuchungen dieser Prozesse offenbaren einen starken Einfluss von Interferenz und der geometrischen Phase (GP) auf “state-to-state” Reaktionswahrscheinlichkeiten und differentielle Querschnitte. Allerdings heben sich diese kohärenten Effekte bei integralen Querschnitten und Reaktionsgeschwindigkeitskonstanten durch effiziente Dephasierung der Interferenz zwischen verschiedenen Streuamplituden komplett auf. Als Nebenprodukte dieser Studien heben wir die Entdeckung zweier neuartiger Streumechanismen hervor, die herkömmlichen Lehrbuchmeinungen widersprechen. Das zweite Thema dreht sich um die Auswirkungen der Berry-Phase auf molekulare Photodynamik an konischen Durchschneidungen. Um diesen Effekt zu verstehen, haben wir einen topologischen Ansatz entwickelt, der die gesamte molekulare Wellenfunktion eines ungebundenen molekularen Systems in zwei Komponenten trennt, die sich in unterschiedlichen Richtungen um die CI winden. Diese Unterteilung zeigt, dass die einzige Auswirkung der geometrischen Phase ein Vorzeichenwechsel der relativen Phase der beiden Komponenten ist. Dieser führt seinerseits zu einer Verschiebung im Interferenzmuster des molekularen Systems---eine Phasenverschiebung, die an den berühmten Aharonov–Bohm-Effekt erinnert. Dieses Verfahren wird numerisch anhand der Photodynamik von üblichen CI-Modellen sowie der Dissoziation von zweiatomigen Molekülen an lichtinduzierten konischen Durchschneidungen (light-induced conical intersections, LICIs) in starken Feldern dargestellt. Neben den fundamentellen Aspekten dieser Arbeiten erlauben die Ergebnisse auch, den Einfluss der geometrischen Phase auf zustandsaufgelöste oder winkelaufgelöste Spektren in “Pump-Probe”-Experimenten zu interpretieren und vorherzusagen, insbesondere die Verteilungen von Photofragmenten in Photodissoziationsexperimenten. Das dritte Themengebiet betrifft die Rolle der Ununterscheidbarkeit identischer Kerne in der molekularen Reaktionsdynamik, wobei der Schwerpunkt auf der dynamischen Lokalisierung hochsymmetrischer Moleküle liegt. Zentraler Gegenstand dieser Arbeiten ist die Frage, ob Kernspin-Statistiken eine dynamische Lokalisierung der Elektronen-, Vibrations- oder sogar Rotations-Dichte auf eine spezifische molekulare Unterstruktur oder Konfiguration anstelle einer anderen identischen (ununterscheidbaren) Teilstruktur erlauben. Gruppentheoretische Betrachtungen der symmetrisierten molekularen Wellenfunktionen dieser Systeme zeigen, dass die nukleare Permutationssymmetrie eine Quantenverschränkung zwischen den Eigenzuständen der verschiedenen molekularen Freiheitsgrade verursacht. Dies führt zu einer kompletten Löschung der dynamischen Lokalisierung auf ununterscheidbare molekulare Teilstrukturen---ein Ergebnis, das in krassem Widerspruch zu weitverbreiteten Lehrbuchansichten ikonischer molekularer Prozesse steht. Dies wird anhand verschiedener Beispiele für die Quantendynamik in achiralen Molekülen mit symmetrischem Doppelminimumspotential illustriert, wie etwa der prototypische pyramidale Inversion von Ammoniak, der elektronischen Kekulé-Dynamik im Benzol-Molekül und der gekoppelte Elektron-Kern-Dynamik bei der laser-induzierten indirekten Photodissoziation des Diwasserstoff-Kations. Der letzte Teil der Habilitationsschrift widmet sich der Entwicklung genäherter Wellenfunktions-Ansätze für die phononengesteuerte Schwingungsrelaxation von Adsorbaten (System) auf Oberflächen (Bad). Aufgrund des sogenannten “Fluchs der Dimensionalität” können diese System-Bad-Komplexe nicht mit üblichen Wellenfunktionsmethoden behandelt werden. Um deren exponentielle Skalierung zu vermindern, haben wir genäherte, aber recht genaue, numerische Verfahren mit polynomialer Skalierung in Bezug auf die Bad-Dimensionen entwickelt.. Die entsprechenden Algorithmen vereinen eine symmetriebasierte Verringerung des vollen Vibrations-Hilbertraums und iterative Krylov-Verfahren. Diese genäherten Wellenfunktionsansätze ähneln dem “Bixon-Jortner Modell” und dem allgemeineren “Quanten-Stufenmodell”. Sie werden auf den Zerfall der H(D)-Si-Schwingungen auf einer komplett mit H (D) bedeckten Siliziumoberfläche angewandt, die durch ein Phononenbad mit mehr als zweitausend Oszillatoren dargestellt wird. Diese Näherungsverfahren erlauben eine zuverlässige Abschätzung der Schwingungslebensdauern der Adsorbate und gewähren Einsicht in die Vibrations-Phonon-Kopplungen an Festkörperoberflächen. Obwohl dieses Thema hauptsächlich rechenbetont ist, ermöglichen die entwickelten Wellenfunktionsmethoden eine Beschreibung der Quantenverschränkung zwischen System- und Bad-Zuständen und die Illustration einiger kohärenter Effekte in der zeitlichen Entwicklung des (Teil-)Systems, die nicht mit dem häufig verwendeten reduzierten Dichtematrix-Formalismus erfasst werden können. KW - Molecular Collisions KW - Conical Intersections KW - Berry Phase KW - Nuclear-Spin-Statistics KW - Dissipation-Decoherence KW - Molekulare Kollisionen KW - Konischen Durchschneidungen KW - Berry-Phase KW - Kernspin-Statistiken KW - Dissipation-Dekohärenz Y1 - 2023 ER - TY - JOUR A1 - Bouakline, Foudhil A1 - Saalfrank, Peter T1 - Seemingly asymmetric atom-localized electronic densities following laser-dissociation of homonuclear diatomics JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistry N2 - Recent experiments on laser-dissociation of aligned homonuclear diatomic molecules show an asymmetric forward-backward (spatial) electron-localization along the laser polarization axis. Most theoretical models attribute this asymmetry to interference effects between gerade and ungerade vibronic states. Presumably due to alignment, these models neglect molecular rotations and hence infer an asymmetric (post-dissociation) charge distribution over the two identical nuclei. In this paper, we question the equivalence that is made between spatial electron-localization, observed in experiments, and atomic electron-localization, alluded by these theoretical models. We show that (seeming) agreement between these models and experiments is due to an unfortunate omission of nuclear permutation symmetry, i.e., quantum statistics. Enforcement of the latter requires mandatory inclusion of the molecular rotational degree of freedom, even for perfectly aligned molecules. Unlike previous interpretations, we ascribe spatial electron-localization to the laser creation of a rovibronic wavepacket that involves field-free molecular eigenstates with opposite space-inversion symmetry i.e., even and odd parity. Space-inversion symmetry breaking would then lead to an asymmetric distribution of the (space-fixed) electronic density over the forward and backward hemisphere. However, owing to the simultaneous coexistence of two indistinguishable molecular orientational isomers, our analytical and computational results show that the post-dissociation electronic density along a specified space-fixed axis is equally shared between the two identical nuclei-a result that is in perfect accordance with the principle of the indistinguishability of identical particles. Published under an exclusive license by AIP Publishing. Y1 - 2021 U6 - https://doi.org/10.1063/5.0049710 SN - 0021-9606 SN - 1089-7690 VL - 154 IS - 23 PB - American Institute of Physics CY - Melville ER -