@article{FischerWertherBouaklineetal.2022, author = {Fischer, Eric Wolfgang and Werther, Michael and Bouakline, Foudhil and Grossmann, Frank and Saalfrank, Peter}, title = {Non-Markovian vibrational relaxation dynamics at surfaces}, series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, volume = {156}, journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, number = {21}, publisher = {AIP Publishing}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/5.0092836}, pages = {16}, year = {2022}, abstract = {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.}, language = {en} } @article{BouaklineSaalfrank2021, author = {Bouakline, Foudhil and Saalfrank, Peter}, title = {Seemingly asymmetric atom-localized electronic densities following laser-dissociation of homonuclear diatomics}, series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistry}, volume = {154}, journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistry}, number = {23}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/5.0049710}, pages = {10}, year = {2021}, abstract = {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.}, language = {en} } @article{FischerWertherBouaklineetal.2020, author = {Fischer, Eric W. and Werther, Michael and Bouakline, Foudhil and Saalfrank, Peter}, title = {A hierarchical effective mode approach to phonon-driven multilevel vibrational relaxation dynamics at surfaces}, series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistry}, volume = {153}, journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistry}, number = {6}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/5.0017716}, pages = {15}, year = {2020}, abstract = {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.}, language = {en} } @article{BouaklineLuederMartinazzoetal.2012, author = {Bouakline, Foudhil and L{\"u}der, Franziska and Martinazzo, Rocco and Saalfrank, Peter}, title = {Reduced and exact quantum dynamics of the vibrational relaxation of a molecular system interacting with a finite-dimensional bath}, series = {The journal of physical chemistry : A, Molecules, spectroscopy, kinetics, environment \& general theory}, volume = {116}, journal = {The journal of physical chemistry : A, Molecules, spectroscopy, kinetics, environment \& general theory}, number = {46}, publisher = {American Chemical Society}, address = {Washington}, issn = {1089-5639}, doi = {10.1021/jp304466u}, pages = {11118 -- 11127}, year = {2012}, abstract = {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.}, language = {en} } @article{BouaklineAlthorpeLarregarayetal.2010, author = {Bouakline, Foudhil and Althorpe, Stuart C. and Larregaray, Pascal and Bonnet, Laurent}, title = {Strong geometric-phase effects in the hydrogen-exchange reaction at high collision energies : II. quasiclassical trajectory analysis}, issn = {0026-8976}, doi = {10.1080/00268971003610218}, year = {2010}, abstract = {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.}, language = {en} } @article{JankunasZareBouaklineetal.2012, author = {Jankunas, Justin and Zare, Richard N. and Bouakline, Foudhil and Althorpe, Stuart C. and Herraez-Aguilar, Diego and Aoiz, F. Javier}, title = {Seemingly anomalous angular distributions in H+D-2 reactive scattering}, series = {Science}, volume = {336}, journal = {Science}, number = {6089}, publisher = {American Assoc. for the Advancement of Science}, address = {Washington}, issn = {0036-8075}, doi = {10.1126/science.1221329}, pages = {1687 -- 1690}, year = {2012}, abstract = {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.}, language = {en} } @article{BartlettJankunasGoswamietal.2011, author = {Bartlett, Nate C. -M. and Jankunas, Justin and Goswami, Tapas and Zare, Richard N. and Bouakline, Foudhil and Althorpe, Stuart C.}, title = {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}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {13}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {18}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c0cp02460k}, pages = {8175 -- 8179}, year = {2011}, abstract = {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.}, language = {en} } @article{BouaklineLorenzMelanietal.2017, author = {Bouakline, Foudhil and Lorenz, Ulrich J. and Melani, Giacomo and Paramonov, Guennaddi K. and Saalfrank, Peter}, title = {Isotopic effects in vibrational relaxation dynamics of H on a Si(100) surface}, series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, volume = {147}, journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, number = {14}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/1.4994635}, pages = {11}, year = {2017}, abstract = {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 Schr{\"o}dinger equation.}, language = {en} } @article{BouaklineFischerSaalfrank2019, author = {Bouakline, Foudhil and Fischer, E. W. and Saalfrank, Peter}, title = {A quantum-mechanical tier model for phonon-driven vibrational relaxation dynamics of adsorbates at surfaces}, series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, volume = {150}, journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, number = {24}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/1.5099902}, pages = {14}, year = {2019}, abstract = {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.}, language = {en} } @article{Bouakline2021, author = {Bouakline, Foudhil}, title = {Umbrella inversion of ammonia redux}, series = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies}, volume = {23}, journal = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies}, number = {36}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/d1cp01991k}, pages = {20509 -- 20523}, year = {2021}, abstract = {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).}, language = {en} }