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 - Fischer, Eric Wolfgang A1 - Werther, Michael A1 - Bouakline, Foudhil A1 - Grossmann, Frank A1 - Saalfrank, Peter T1 - Non-Markovian vibrational relaxation dynamics at surfaces JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr N2 - Vibrational dynamics of adsorbates near surfaces plays both an important role for applied surface science and as a model lab for studying fundamental problems of open quantum systems. We employ a previously developed model for the relaxation of a D-Si-Si bending mode at a D:Si(100)-(2 x 1) surface, induced by a "bath " of more than 2000 phonon modes [Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], to extend previous work along various directions. First, we use a Hierarchical Effective Mode (HEM) model [Fischer et al., J. Chem. Phys. 153, 064704 (2020)] to study relaxation of higher excited vibrational states than hitherto done by solving a high-dimensional system-bath time-dependent Schrodinger equation (TDSE). In the HEM approach, (many) real bath modes are replaced by (much less) effective bath modes. Accordingly, we are able to examine scaling laws for vibrational relaxation lifetimes for a realistic surface science problem. Second, we compare the performance of the multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) approach with that of the recently developed coherent-state-based multi-Davydov-D2 Ansatz [Zhou et al., J. Chem. Phys. 143, 014113 (2015)]. Both approaches work well, with some computational advantages for the latter in the presented context. Third, we apply open-system density matrix theory in comparison with basically "exact " solutions of the multi-mode TDSEs. Specifically, we use an open-system Liouville-von Neumann (LvN) equation treating vibration-phonon coupling as Markovian dissipation in Lindblad form to quantify effects beyond the Born-Markov approximation. Published under an exclusive license by AIP Publishing. KW - phonons KW - Vibrational states KW - Chemical dynamics KW - Adsorption KW - Surface science KW - Open quantum systems KW - Density-matrix KW - Coherent states KW - Markov processes Y1 - 2022 U6 - https://doi.org/10.1063/5.0092836 SN - 0021-9606 SN - 1089-7690 SN - 1520-9032 VL - 156 IS - 21 PB - AIP Publishing CY - Melville 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 - TY - JOUR A1 - Bouakline, Foudhil T1 - Umbrella inversion of ammonia redux JF - Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies N2 - Umbrella inversion of ammonia is a prototypical example of large-amplitude vibrational motion, described with a symmetric double-well potential. The transition state of the latter corresponds to a planar (D-3h) molecular geometry, whereas the two equilibrium configurations are equivalent (C-3v) pyramidal structures, with the nitrogen atom being either 'above' or 'below' the plane of the hydrogen atoms. As commonly understood, inversion motion of ammonia corresponds to the coherent, anharmonic, vibrational motion of the molecule, which shuttles back and forth between the two potential wells; that is, oscillation of the nitrogen atom from one side of the H-3 plane to the other, via coherent tunneling. However, this intuitively appealing view of umbrella inversion results from a reduced description of the dynamics, which includes only the inversion vibrational coordinate and fully neglects all the other molecular degrees of freedom. As such, this textbook picture of inversion motion ignores the fact that the two equilibrium structures of ammonia are superimposable, and can only be distinguished by labelling the identical hydrogen nuclei. A correct description of umbrella inversion, which incorporates nuclear permutations, requires the inclusion of other molecular modes. Indeed, it is well known that the quantum symmetrization postulate engenders entanglement between ammonia's nuclear-spin, inversion, and rotation. Using the explicit expressions of the corresponding zeroth-order eigenstates, we clearly show that the inversion density of any multilevel wavepacket of ammonia, including the case of perfectly aligned molecules, is symmetrically distributed between the two potential wells, at all times. This follows from a rigorous demonstration based on the evaluation of the expectation values of the inversion coordinate or equivalent projection operators. However, provided that these wavepackets involve inversion-rotation levels with opposite parity, the inversion density may exhibit dynamical spatial localization. In the latter case, the space-fixed inversion density or, equivalently, the expectation values of the projections of the inversion coordinate on the space-fixed axes, may oscillate between opposite directions in the space-fixed frame. Nevertheless, in all cases, localization of ammonia in a single potential well is impossible, even partially or transiently. This is equivalent to saying that the nitrogen atom has the same probability (one-half) to be on either side of the H-3 plane, for any wavepacket of the molecule and at all times-a conclusion which is in perfect accord with the principle of the indistinguishability of identical particles (nuclei). Y1 - 2021 U6 - https://doi.org/10.1039/d1cp01991k SN - 1463-9076 SN - 1463-9084 VL - 23 IS - 36 SP - 20509 EP - 20523 PB - Royal Society of Chemistry CY - Cambridge ER - 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 - Fischer, Eric W. A1 - Werther, Michael A1 - Bouakline, Foudhil A1 - Saalfrank, Peter T1 - A hierarchical effective mode approach to phonon-driven multilevel vibrational relaxation dynamics at surfaces JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistry N2 - We discuss an efficient Hierarchical Effective Mode (HEM) representation of a high-dimensional harmonic oscillator bath, which describes phonon-driven vibrational relaxation of an adsorbate-surface system, namely, deuterium adsorbed on Si(100). Starting from the original Hamiltonian of the adsorbate-surface system, the HEM representation is constructed via iterative orthogonal transformations, which are efficiently implemented with Householder matrices. The detailed description of the HEM representation and its construction are given in the second quantization representation. The hierarchical nature of this representation allows access to the exact quantum dynamics of the adsorbate-surface system over finite time intervals, controllable via the truncation order of the hierarchy. To study the convergence properties of the effective mode representation, we solve the time-dependent Schrodinger equation of the truncated system-bath HEM Hamiltonian, with the help of the multilayer extension of the Multiconfigurational Time-Dependent Hartree (ML-MCTDH) method. The results of the HEM representation are compared with those obtained with a quantum-mechanical tier-model. The convergence of the HEM representation with respect to the truncation order of the hierarchy is discussed for different initial conditions of the adsorbate-surface system. The combination of the HEM representation with the ML-MCTDH method provides information on the time evolution of the system (adsorbate) and multiple effective modes of the bath (surface). This permits insight into mechanisms of vibration-phonon coupling of the adsorbate-surface system, as well as inter-mode couplings of the effective bath. Y1 - 2020 U6 - https://doi.org/10.1063/5.0017716 SN - 0021-9606 SN - 1089-7690 VL - 153 IS - 6 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Bouakline, Foudhil T1 - Does nuclear permutation symmetry allow dynamical localization in symmetric double-well achiral molecules? JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr N2 - We discuss the effect of molecular symmetry on coherent tunneling in symmetric double-well potentials whose two molecular equilibrium configurations are interconverted by nuclear permutations. This is illustrated with vibrational tunneling in ammonia molecules, electronic tunneling in the dihydrogen cation, and laser-induced rotational tunneling of homonuclear diatomics. In this contribution, we reexamine the textbook picture of coherent tunneling in such potentials, which is depicted with a wavepacket shuttling back and forth between the two potential-wells. We show that the common application of this picture to the aforementioned molecules contravenes the principle of the indistinguishability of identical particles. This conflict originates from the sole consideration of the dynamics of the tunneling-mode, connecting the double-well energy minima, and complete omission of all the remaining molecular degrees of freedom. This gives rise to double-well wavepackets that are nonsymmetric under nuclear permutations. To obey quantum statistics, we show that the double-well eigenstates composing these wavepackets must be entangled with the wavefunctions that describe all the omitted molecular modes. These wavefunctions have compensating and opposite nuclear permutation symmetry. This in turn leads to complete quenching of interference effects behind localization in one potential-well or another. Indeed, we demonstrate that the reduced density of probability of the symmetrized molecular wavefunction, where all the molecular coordinates but the tunneling-mode are integrated out, is symmetrically distributed over the two potential-wells, at all times. This applies to any multilevel wavepacket of isotropic or fully aligned symmetric double-well achiral molecules. However, in the case of coherent electronic or vibrational tunneling, fully aligned molecules may exhibit dynamical localization in the space-fixed frame, where the tunneling-mode density shuttles between the opposite directions of the alignment axis. This dynamical spatial-localization results from linear combinations of molecular states that have opposite parity. In summary, this study shows that dynamical localization of the tunneling-mode density on either of the two indistinguishable molecular equilibrium configurations of symmetric double-well achiral molecules is forbidden by quantum statistics, whereas its dynamical localization in the space-fixed frame is allowed by parity. The subtle distinction between these two types of localization has far-reaching implications in the interpretation of many ultrafast molecular dynamics experiments. Y1 - 2020 U6 - https://doi.org/10.1063/1.5141746 SN - 0021-9606 SN - 1089-7690 VL - 152 IS - 24 PB - American Institute of Physics CY - Melville 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 A1 - Fischer, E. W. A1 - Saalfrank, Peter T1 - A quantum-mechanical tier model for phonon-driven vibrational relaxation dynamics of adsorbates at surfaces JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr N2 - We present a quantum-mechanical tier model for vibrational relaxation of low-lying excited states of an adsorbate vibrational mode (system), coupled to surface phonons (bath), at zero temperature. The tier model, widely used in studies of intramolecular vibrational energy redistribution in polyatomics, is adapted here to adsorbate-surface systems with the help of an embedded cluster approach, using orthogonal coordinates for the system and bath modes, and a phononic expansion of their interaction. The key idea of the model is to organize the system-bath zeroth-order vibrational space into a hierarchical structure of vibrational tiers and keep therein only vibrational states that are sequentially generated from the system-bath initial vibrational state. Each tier is generated from the previous one by means of a successor operator, derived from the system-bath interaction Hamiltonian. This sequential procedure leads to a drastic reduction of the dimension of the system-bath vibrational space. We notably show that for harmonic vibrational motion of the system and linear system-bath couplings in the system coordinate, the dimension of the tier-model vibrational basis scales as similar to N-lxv. Here, N is the number of bath modes, l is the highest-order of the phononic expansion, and l is the size of the system vibrational basis. This polynomial scaling is computationally far superior to the exponential scaling of the original zeroth-order vibrational basis, similar to M-N, with M being the number of basis functions per bath mode. In addition, since each tier is coupled only to its adjacent neighbors, the matrix representation of the system-bath Hamiltonian in this new vibrational basis has a symmetric block-tridiagonal form, with each block being very sparse. This favors the combination of the tier-model with iterative Krylov techniques, such as the Lanczos algorithm, to solve the time-dependent Schrodinger equation for the full Hamiltonian. To illustrate the method, we study vibrational relaxation of a D-Si bending mode, coupled via two-and (mainly) one-phonon interactions to a fully D-covered Si(100)-(2 x 1) surface, using a recent first-principles system-bath Hamiltonian. The results of the tier model are compared with those obtained by the Lindblad formalism of the reduced density matrix. We find that the tier model provides much more information and insight into mechanisms of vibration-phonon couplings at surfaces, and gives more reliable estimates of the adsorbate vibrational lifetimes. Moreover, the tier model might also serve as a benchmark for other approximate quantum-dynamics methods, such as multiconfiguration wavefunction approaches. Published under license by AIP Publishing. Y1 - 2019 U6 - https://doi.org/10.1063/1.5099902 SN - 0021-9606 SN - 1089-7690 VL - 150 IS - 24 PB - American Institute of Physics CY - Melville 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 - JOUR A1 - Bouakline, Foudhil A1 - Lorenz, Ulrich J. A1 - Melani, Giacomo A1 - Paramonov, Guennaddi K. A1 - Saalfrank, Peter T1 - Isotopic effects in vibrational relaxation dynamics of H on a Si(100) surface JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr N2 - In a recent paper [U. Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], we proposed a robust scheme to set up a system-bath model Hamiltonian, describing the coupling of adsorbate vibrations (system) to surface phonons (bath), from first principles. The method is based on an embedded cluster approach, using orthogonal coordinates for system and bath modes, and an anharmonic phononic expansion of the system-bath interaction up to second order. In this contribution, we use this model Hamiltonian to calculate vibrational relaxation rates of H–Si and D–Si bending modes, coupled to a fully H(D)-covered Si(100)-(2×1) surface, at zero temperature. The D–Si bending mode has an anharmonic frequency lying inside the bath frequency spectrum, whereas the H–Si bending mode frequency is outside the bath Debye band. Therefore, in the present calculations, we only take into account one-phonon system-bath couplings for the D–Si system and both one- and two-phonon interaction terms in the case of H–Si. The computation of vibrational lifetimes is performed with two different approaches, namely, Fermi’s golden rule, and a generalized Bixon-Jortner model built in a restricted vibrational space of the adsorbate-surface zeroth-order Hamiltonian. For D–Si, the Bixon-Jortner Hamiltonian can be solved by exact diagonalization, serving as a benchmark, whereas for H–Si, an iterative scheme based on the recursive residue generation method is applied, with excellent convergence properties. We found that the lifetimes obtained with perturbation theory, albeit having almost the same order of magnitude—a few hundred fs for D–Si and a couple of ps for H–Si—, are strongly dependent on the discretized numerical representation of the bath spectral density. On the other hand, the Bixon-Jortner model is free of such numerical deficiencies, therefore providing better estimates of vibrational relaxation rates, at a very low computational cost. The results obtained with this model clearly show a net exponential decay of the time-dependent survival probability for the H–Si initial vibrational state, allowing an easy extraction of the bending mode “lifetime.” This is in contrast with the D–Si system, whose survival probability exhibits a non-monotonic decay, making it difficult to define such a lifetime. This different behavior of the vibrational decay is rationalized in terms of the power spectrum of the adsorbate-surface system. In the case of D–Si, it consists of several, non-uniformly distributed peaks around the bending mode frequency, whereas the H–Si spectrum exhibits a single Lorentzian lineshape, whose width corresponds to the calculated lifetime. The present work gives some insight into mechanisms of vibration-phonon coupling at surfaces. It also serves as a benchmark for multidimensional system-bath quantum dynamics, for comparison with approximate schemes such as reduced, open-system density matrix theory (where the bath is traced out and a Liouville-von Neumann equation is solved) or approximate wavefunction methods to solve the combined system-bath Schrödinger equation. Y1 - 2017 U6 - https://doi.org/10.1063/1.4994635 SN - 0021-9606 SN - 1089-7690 VL - 147 IS - 14 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Bouakline, Foudhil A1 - Lüder, Franziska A1 - Martinazzo, Rocco A1 - Saalfrank, Peter T1 - Reduced and exact quantum dynamics of the vibrational relaxation of a molecular system interacting with a finite-dimensional bath JF - The journal of physical chemistry : A, Molecules, spectroscopy, kinetics, environment & general theory N2 - We investigate the vibrational relaxation of a Morse oscillator, nonlinearly coupled to a finite-dimensional bath of harmonic oscillators at zero temperature, using two different approaches: Reduced dynamics with the help of the Lindblad formalism of reduced density matrix theory in combination with Fermi's Golden Rule, and exact dynamics (within the chosen model). with the multiconfiguration time-dependent Hartree (MCTDH) method. Two different models have been constructed, the situation where the bath spectrum is exactly resonant with the anharmonic oscillator transition frequencies, and the case for which the subsystem is slightly off-resonant with the environment. At short times, reduced dynamics calculations describe the relaxation process qualitatively well but fail to reproduce recurrences observed with MCTDH for longer times. Lifetimes of all the vibrational levels of the Morse oscillator have been calculated, and both Lindblad and MCTDH. results show the same dependence of the lifetimes on the initial vibrational state quantum number. A prediction, which should be generic for adsorbate systems is a striking, sharp increase of lifetimes of the subsystem vibrational levels close to the dissociation This is contradictory with harmonic/linear extrapolation laws, which predict a monotonic decrease of the lifetime with initial vibrational quantum number. Y1 - 2012 U6 - https://doi.org/10.1021/jp304466u SN - 1089-5639 VL - 116 IS - 46 SP - 11118 EP - 11127 PB - American Chemical Society CY - Washington ER - TY - JOUR A1 - Jankunas, Justin A1 - Zare, Richard N. A1 - Bouakline, Foudhil A1 - Althorpe, Stuart C. A1 - Herraez-Aguilar, Diego A1 - Aoiz, F. Javier T1 - Seemingly anomalous angular distributions in H+D-2 reactive scattering JF - Science N2 - When a hydrogen (H) atom approaches a deuterium (D-2) molecule, the minimum-energy path is for the three nuclei to line up. Consequently, nearly collinear collisions cause HD reaction products to be backscattered with low rotational excitation, whereas more glancing collisions yield sideways-scattered HD products with higher rotational excitation. Here we report that measured cross sections for the H + D-2 -> HD(v' = 4, j') + D reaction at a collision energy of 1.97 electron volts contradict this behavior. The anomalous angular distributions match closely fully quantum mechanical calculations, and for the most part quasiclassical trajectory calculations. As the energy available in product recoil is reduced, a rotational barrier to reaction cuts off contributions from glancing collisions, causing high-j' HD products to become backward scattered. Y1 - 2012 U6 - https://doi.org/10.1126/science.1221329 SN - 0036-8075 VL - 336 IS - 6089 SP - 1687 EP - 1690 PB - American Assoc. for the Advancement of Science CY - Washington ER - TY - JOUR A1 - Bartlett, Nate C. -M. A1 - Jankunas, Justin A1 - Goswami, Tapas A1 - Zare, Richard N. A1 - Bouakline, Foudhil A1 - Althorpe, Stuart C. T1 - Differential cross sections for H + D-2 -> HD(v '=2, j '=0,3,6,9) + D at center-of-mass collision energies of 1.25, 1.61, and 1.97 eV JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - We have measured differential cross sections (DCSs) for the reaction H + D-2 -> HD- (v' = 2, j' = 0,3,6,9) + D at center-of-mass collision energies E-coll of 1.25, 1.61, and 1.97 eV using the photoloc technique. The DCSs show a strong dependence on the product rotational quantum number. For the HD(v' = 2, j' = 0) product, the DCS is bimodal but becomes oscillatory as the collision energy is increased. For the other product states, they are dominated by a single peak, which shifts from back to sideward scattering as j' increases, and they are in general less sensitive to changes in the collision energy. The experimental results are compared to quantum mechanical calculations and show good, but not fully quantitative agreement. Y1 - 2011 U6 - https://doi.org/10.1039/c0cp02460k SN - 1463-9076 VL - 13 IS - 18 SP - 8175 EP - 8179 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Bouakline, Foudhil A1 - Althorpe, Stuart C. A1 - Larregaray, Pascal A1 - Bonnet, Laurent T1 - Strong geometric-phase effects in the hydrogen-exchange reaction at high collision energies : II. quasiclassical trajectory analysis N2 - Recent calculations on the hydrogen-exchange reaction [Bouakline et al., J. Chem. Phys. 128, 124322 (2008)], have found strong geometric phase (GP) effects in the state-to-state differential cross-sections (DCS), at energies above the energetic minimum of the conical intersection (CI) seam, which cancel out in the integral cross-sections (ICS). In this article, we explain the origin of this cancellation and make other predictions about the nature of the reaction mechanisms at these high energies by carrying out quasiclassical trajectory (QCT) calculations. Detailed comparisons are made with the quantum results by splitting the quantum and the QCT cross-sections into contributions from reaction paths that wind in different senses around the CI and that scatter the products in the nearside and farside directions. Reaction paths that traverse one transition state (1-TS) scatter their products in just the nearside direction, whereas paths that traverse two transition states (2-TS) scatter in both the nearside and farside directions. However, the nearside 2-TS products scatter into a different region of angular phase-space than the 1-TS products, which explains why the GP effects cancel out in the ICS. Analysis of the QCT results also suggests that two separate reaction mechanisms may be responsible for the 2-TS scattering at high energies. Y1 - 2010 UR - http://www.informaworld.com/openurl?genre=journal&issn=0026-8976 U6 - https://doi.org/10.1080/00268971003610218 SN - 0026-8976 ER -