@article{AndrianovKlamrothSaalfranketal.2005, author = {Andrianov, Igor V. and Klamroth, Tillmann and Saalfrank, Peter and Bovensiepen, U. and Gahl, Cornelius and Wolf, M. M.}, title = {Quantum theoretical study of electron solvation dynamics in ice layers on a Cu(111) surface}, issn = {0021-9606}, year = {2005}, abstract = {Recent experiments using time- and angle-resolved two-photon photoemission (2PPE) spectroscopy at metal/polar adsorbate interfaces succeeded in time-dependent analysis of the process of electron solvation. A fully quantum mechanical, two-dimensional simulation of this process, which explicitly includes laser excitation, is presented here, confirming the origin of characteristic features, such as the experimental observation of an apparently negative dispersion. The inference of the spatial extent of the localized electron states from the angular dependence of the 2PPE spectra has been found to be non-trivial and system-dependent. (C) 2005 American Institute of Physics}, language = {en} } @article{AndrianovSaalfrank2006, author = {Andrianov, Ivan and Saalfrank, Peter}, title = {Free vibrational relaxation of H adsorbed on a Si(100) surface investigated with the multi-configurational time-dependent Hartree method}, series = {Chemical physics letters}, volume = {433}, journal = {Chemical physics letters}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0009-2614}, doi = {10.1016/j.cplett.2006.11.067}, pages = {91 -- 96}, year = {2006}, abstract = {The results of a quantum-mechanical study of vibrational relaxation of hydrogen adsorbed on a Si(100) surface with the multi-configurational time-dependent Hartree (MCTDH) method are presented. A two-dimensional subsystem is coupled non-linearly to a bath of harmonic oscillators (phonons of the Si bulk), and the relaxation of subsystem vibrations proceeds primarily via a two-phonon process. Characteristic times of the system evolution agree well with our previous perturbation theory study. The vibrational population decay is non-exponential, exhibiting pronounced recurrences due to finite bath size. The dependence of the lifetimes of the vibrational levels on the bath size and on the coupling details is investigated.}, language = {en} } @article{AndrianovSaalfrank2006, author = {Andrianov, Ivan and Saalfrank, Peter}, title = {Theoretical study of vibration-phonon coupling of H adsorbed on a Si(100) surface}, issn = {0021-9606}, doi = {10.1063/1.2161191}, year = {2006}, abstract = {In this paper a perturbation-theory study of vibrational lifetimes for the bending and stretching modes of hydrogen adsorbed on a Si(100) surface is presented. The hydrogen-silicon interaction is treated with a semiempirical bond-order potential. Calculations are performed for H-Si clusters of different sizes. The finite lifetime is due to vibration-phonon coupling, which is assumed to be linear or bilinear in the phonon and nonlinear in the H-Si stretching and bending modes. Lifetimes and vibrational transition rates are evaluated with one- and two-phonon processes taken into account. Temperature effects are also discussed. In agreement with the experiment and previous theoretical treatment it is found that the H-Si (upsilon(s)=1) stretching vibration decays on a nanosecond timescale, whereas for the H-Si (upsilon(b)=1) bending mode a picosecond decay is predicted. For higher-excited vibrations, simple scaling laws are found if the excitation energies are not too large. The relaxation mechanisms for the excited H-Si stretching and the H-Si bending modes are analyzed in detail.}, language = {en} } @article{BanerjeeKroenerSaalfrank2012, author = {Banerjee, Shiladitya and Kr{\"o}ner, Dominik and Saalfrank, Peter}, title = {Resonance Raman and vibronic absorption spectra with Duschinsky rotation from a time-dependent perspective application to beta-carotene}, series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, volume = {137}, journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, number = {22}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/1.4748147}, pages = {9}, year = {2012}, abstract = {The time-dependent approach to electronic spectroscopy, as popularized by Heller and co-workers in the 1980s, is applied here in conjunction with linear-response, time-dependent density functional theory to study vibronic absorption and resonance Raman spectra of beta-carotene, with and without a solvent. Two-state models, the harmonic and the Condon approximations are used in order to do so. A new code has been developed which includes excited state displacements, vibrational frequency shifts, and Duschinsky rotation, i.e., mode mixing, for both non-adiabatic spectroscopies. It is shown that Duschinsky rotation has a pronounced effect on the resonance Raman spectra of beta-carotene. In particular, it can explain a recently found anomalous behaviour of the so-called nu(1) peak in resonance Raman spectra [N. Tschirner, M. Schenderlein, K. Brose, E. Schlodder, M. A. Mroginski, C. Thomsen, and P. Hildebrandt, Phys. Chem. Chem. Phys. 11, 11471 (2009)], which shifts with the change in excitation wavelength.}, language = {en} } @article{BanerjeeSaalfrank2014, author = {Banerjee, Shiladitya and Saalfrank, Peter}, title = {Vibrationally resolved absorption, emission and resonance Raman spectra of diamondoids: a study based on time-dependent correlation functions}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {16}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {1}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c3cp53535e}, pages = {144 -- 158}, year = {2014}, language = {en} } @article{BanerjeeSaalfrank2014, author = {Banerjee, Shiladitya and Saalfrank, Peter}, title = {Vibrationally resolved absorption, emission and resonance Raman spectra of diamondoids : a study based on time- dependent correlation functions}, doi = {10.1039/C3CP53535E}, year = {2014}, language = {en} } @misc{BanerjeeSaalfrank2013, author = {Banerjee, Shiladitya and Saalfrank, Peter}, title = {Vibrationally resolved absorption, emission and resonance Raman spectra of diamondoids}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-94542}, pages = {144 -- 158}, year = {2013}, abstract = {The time-dependent approach to electronic spectroscopy, as popularized by Heller and coworkers in the 1980's, is applied here in conjunction with linear-response, time-dependent density functional theory to study vibronic absorption, emission and resonance Raman spectra of several diamondoids. Two-state models, the harmonic and the Condon approximations, are used for the calculations, making them easily applicable to larger molecules. The method is applied to nine pristine lower and higher diamondoids: adamantane, diamantane, triamantane, and three isomers each of tetramantane and pentamantane. We also consider a hybrid species "Dia = Dia" - a shorthand notation for a recently synthesized molecule comprising two diamantane units connected by a C[double bond, length as m-dash]C double bond. We resolve and interpret trends in optical and vibrational properties of these molecules as a function of their size, shape, and symmetry, as well as effects of "blending" with sp2-hybridized C-atoms. Time-dependent correlation functions facilitate the computations and shed light on the vibrational dynamics following electronic transitions.}, language = {en} } @article{BanerjeeStuekerSaalfrank2015, author = {Banerjee, Shiladitya and Stueker, Tony and Saalfrank, Peter}, title = {Vibrationally resolved optical spectra of modified diamondoids obtained from time-dependent correlation function methods}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {17}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {29}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c5cp02615f}, pages = {19656 -- 19669}, year = {2015}, abstract = {Optical properties of modified diamondoids have been studied theoretically using vibrationally resolved electronic absorption, emission and resonance Raman spectra. A time-dependent correlation function approach has been used for electronic two-state models, comprising a ground state (g) and a bright, excited state (e), the latter determined from linear-response, time-dependent density functional theory (TD-DFT). The harmonic and Condon approximations were adopted. In most cases origin shifts, frequency alteration and Duschinsky rotation in excited states were considered. For other cases where no excited state geometry optimization and normal mode analysis were possible or desired, a short-time approximation was used. The optical properties and spectra have been computed for (i) a set of recently synthesized sp(2)/sp(3) hybrid species with CQC double-bond connected saturated diamondoid subunits, (ii) functionalized (mostly by thiol or thione groups) diamondoids and (iii) urotropine and other C-substituted diamondoids. The ultimate goal is to tailor optical and electronic features of diamondoids by electronic blending, functionalization and substitution, based on a molecular-level understanding of the ongoing photophysics.}, language = {en} } @misc{BanerjeeStuekerSaalfrank2015, author = {Banerjee, Shiladitya and St{\"u}ker, Tony and Saalfrank, Peter}, title = {Vibrationally resolved optical spectra of modified diamondoids obtained from time-dependent correlation function methods}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86826}, year = {2015}, abstract = {Optical properties of modified diamondoids have been studied theoretically using vibrationally resolved electronic absorption, emission and resonance Raman spectra. A time-dependent correlation function approach has been used for electronic two-state models, comprising a ground state (g) and a bright, excited state (e), the latter determined from linear-response, time-dependent density functional theory (TD-DFT). The harmonic and Condon approximations were adopted. In most cases origin shifts, frequency alteration and Duschinsky rotation in excited states were considered. For other cases where no excited state geometry optimization and normal mode analysis were possible or desired, a short-time approximation was used. The optical properties and spectra have been computed for (i) a set of recently synthesized sp2/sp3 hybrid species with C[double bond, length as m-dash]C double-bond connected saturated diamondoid subunits, (ii) functionalized (mostly by thiol or thione groups) diamondoids and (iii) urotropine and other C-substituted diamondoids. The ultimate goal is to tailor optical and electronic features of diamondoids by electronic blending, functionalization and substitution, based on a molecular-level understanding of the ongoing photophysics.}, language = {en} } @article{BanerjeeStuekerSaalfrank2015, author = {Banerjee, Shiladitya and St{\"u}ker, Tony and Saalfrank, Peter}, title = {Vibrationally resolved optical spectra of modified diamondoids obtained from time-dependent correlation function methods}, series = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies}, volume = {17}, journal = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies}, number = {29}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9084}, doi = {10.1039/C5CP02615F}, pages = {19656 -- 19669}, year = {2015}, abstract = {Optical properties of modified diamondoids have been studied theoretically using vibrationally resolved electronic absorption, emission and resonance Raman spectra. A time-dependent correlation function approach has been used for electronic two-state models, comprising a ground state (g) and a bright, excited state (e), the latter determined from linear-response, time-dependent density functional theory (TD-DFT). The harmonic and Condon approximations were adopted. In most cases origin shifts, frequency alteration and Duschinsky rotation in excited states were considered. For other cases where no excited state geometry optimization and normal mode analysis were possible or desired, a short-time approximation was used. The optical properties and spectra have been computed for (i) a set of recently synthesized sp2/sp3 hybrid species with C[double bond, length as m-dash]C double-bond connected saturated diamondoid subunits, (ii) functionalized (mostly by thiol or thione groups) diamondoids and (iii) urotropine and other C-substituted diamondoids. The ultimate goal is to tailor optical and electronic features of diamondoids by electronic blending, functionalization and substitution, based on a molecular-level understanding of the ongoing photophysics.}, language = {en} } @article{BedurkeKlamrothKrauseetal.2019, author = {Bedurke, Florian and Klamroth, Tillmann and Krause, Pascal and Saalfrank, Peter}, title = {Discriminating organic isomers by high harmonic generation}, 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 = {23}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/1.5096473}, pages = {10}, year = {2019}, abstract = {High Harmonic Generation (HHG) is a nonlinear optical process that provides a tunable source for high-energy photons and ultrashort laser pulses. Recent experiments demonstrated that HHG spectroscopy may also be used as an analytical tool to discriminate between randomly oriented configurational isomers of polyatomic organic molecules, namely, between the cis- and trans-forms of 1,2-dichloroethene (DCE) [M. C. H. Wong et al., Phys. Rev. A 84, 051403 (2011)]. Here, we suggest as an economic and at the same time a reasonably accurate method to compute HHG spectra for polyatomic species, Time-Dependent Configuration Interaction Singles (TD-CIS) theory in combination with extended atomic orbital bases and different models to account for ionization losses. The HHG spectra are computed for aligned and unaligned cis- and trans-DCE. For the unaligned case, a coherent averaging over possible rotational orientations is introduced. Furthermore, using TD-CIS, possible differences between the HHG spectra of cis- and trans-DCE are studied. For aligned molecules, spectral differences between cis and trans emerge, which can be related to their different point group symmetries. For unaligned, randomly oriented molecules, we also find distinct HHG spectra in partial agreement with experiment. In addition to HHG response in the frequency space, we compute time-frequency HHG spectra to gain insight into which harmonics are emitted at which time. Further differences between the two isomers emerge, suggesting time-frequency HHG as another tool to discriminate configurational isomers.}, language = {en} } @article{BedurkeKlamrothSaalfrank2021, author = {Bedurke, Florian and Klamroth, Tillmann and Saalfrank, Peter}, title = {Many-electron dynamics in laser-driven molecules}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {23}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {24}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/d1cp01100f}, pages = {13544 -- 13560}, year = {2021}, abstract = {With recent experimental advances in laser-driven electron dynamics in polyatomic molecules, the need arises for their reliable theoretical modelling. Among efficient, yet fairly accurate methods for many-electron dynamics are Time-Dependent Configuration Interaction Singles (TD-CIS) (a Wave Function Theory (WFT) method), and Real-Time Time-Dependent Density Functional Theory (RT-TD-DFT), respectively. Here we compare TD-CIS combined with extended Atomic Orbital (AO) bases, TD-CIS/AO, with RT-TD-DFT in a grid representation of the Kohn-Sham orbitals, RT-TD-DFT/Grid. Possible ionization losses are treated by complex absorbing potentials in energy space (for TD-CIS/AO) or real space (for RT-TD-DFT), respectively. The comparison is made for two test cases: (i) state-to-state transitions using resonant lasers (pi-pulses), i.e., bound electron motion, and (ii) large-amplitude electron motion leading to High Harmonic Generation (HHG). Test systems are a H-2 molecule and cis- and trans-1,2-dichlorethene, C2H2Cl2, (DCE). From time-dependent electronic energies, dipole moments and from HHG spectra, the following observations are made: first, for bound state-to-state transitions enforced by pi-pulses, TD-CIS nicely accounts for the expected population inversion in contrast to RT-TD-DFT, in agreement with earlier findings. Secondly, when using laser pulses under non-resonant conditions, dipole moments and lower harmonics in HHG spectra are obtained by TD-CIS/AO which are in good agreement with those obtained with RT-TD-DFT/Grid. Deviations become larger for higher harmonics and at low laser intensities, i.e., for low-intensity HHG signals. We also carefully test effects of basis sets for TD-CIS/AO and grid size for RT-TD-DFT/Grid, different exchange-correlation functionals in RT-TD-DFT, and absorbing boundaries. Finally, for the present examples, TD-CIS/AO is observed to be at least an order of magnitude more computationally efficient than RT-TD-DFT/Grid.}, language = {en} } @article{BeyversOhtsukiSaalfrank2006, author = {Beyvers, Stephanie and Ohtsuki, Y and Saalfrank, Peter}, title = {Optimal control in a dissipative system : vibrational excitation of CO/Cu(100) by IR pulses}, issn = {0021-9606}, doi = {10.1063/1.2206593}, year = {2006}, abstract = {The question as to whether state-selective population of molecular vibrational levels by shaped infrared laser pulses is possible in a condensed phase environment is of central importance for such diverse fields as time-resolved spectroscopy, quantum computing, or "vibrationally mediated chemistry." This question is addressed here for a model system, representing carbon monoxide adsorbed on a Cu(100) surface. Three of the six vibrational modes are considered explicitly, namely, the CO stretch vibration, the CO-surface vibration, and a frustrated translation. Optimized infrared pulses for state-selective excitation of "bright" and "dark" vibrational levels are designed by optimal control theory in the framework of a Markovian open-system density matrix approach, with energy flow to substrate electrons and phonons, phase relaxation, and finite temperature accounted for. The pulses are analyzed by their Husimi "quasiprobability" distribution in time-energy space.}, language = {en} } @article{BlegerDokicPetersetal.2011, author = {Bleger, David and Dokic, Jadranka and Peters, Maike V. and Grubert, Lutz and Saalfrank, Peter and Hecht, Stefan}, title = {Electronic decoupling approach to quantitative photoswitching in linear multiazobenzene architectures}, series = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry}, volume = {115}, journal = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry}, number = {33}, publisher = {American Chemical Society}, address = {Washington}, issn = {1520-6106}, doi = {10.1021/jp2044114}, pages = {9930 -- 9940}, year = {2011}, abstract = {A strategy to optimize the photoswitching efficiency of rigid, linear multiazobenzene constructs is presented. It consists of introducing large dihedral angles between azobenzene moieties linked via aryl-aryl connections in their para positions. Four bisazobenzenes exhibiting different dihedral angles as well as three single azobenzene reference compounds have been synthesized, and their switching behavior has been studied as well as experimentally and theoretically analyzed. As the dihedral angle between the two azobenzene units increases and consequently the electronic conjugation decreases, the photochromic characteristics improve, finally leading to individual azobenzene switches operating independently in the case of the perpendicular ortho,ortho,ortho',ortho'-tetramethyl biphenyl linker. The electronic decoupling leads to efficient separation of the absorption spectra of the involved switching states and hence by choosing the appropriate irradiation wavelength, an almost quantitative E -> Z photoisomerization up to 97\% overall Z-content can be achieved. In addition, thermal Z -> E isomerization processes become independent of each other with increasing decoupling. The electronic decoupling could furthermore be proven by electrochemistry. The experimental data are supported by theory, and calculations additionally provide mechanistic insight into the preferred pathway for the thermal Z,Z -> Z,E -> E,E isomerization via inversion on the inner N-atoms. Our decoupling approach outlined herein provides the basis for constructing rigid rod architectures composed of multiple azobenzene photochromes, which display practically quantitative photoswitching properties, a necessary prerequisite to achieve highly efficient transduction of light energy directly into motion.}, language = {en} } @article{BoeseSaalfrank2016, author = {Boese, Adrian Daniel and Saalfrank, Peter}, title = {CO Molecules on a NaCl(100) Surface: Structures, Energetics, and Vibrational Davydov Splittings at Various Coverages}, series = {The journal of physical chemistry : C, Nanomaterials and interfaces}, volume = {120}, journal = {The journal of physical chemistry : C, Nanomaterials and interfaces}, publisher = {American Chemical Society}, address = {Washington}, issn = {1932-7447}, doi = {10.1021/acs.jpcc.6b03726}, pages = {12637 -- 12653}, year = {2016}, abstract = {In this work, we study the adsorption of CO from low to high coverage at a defect-free NaCl(100) surface by means of duster and periodic models, using highly accurate wave function-based QM:QM embedding as well as density functional theory. At low coverages, the most accurate methods predict a zero-point-corrected adsorption energy of around 13 kJ/mol, and the CO molecules are found to be oriented perpendicular to the surface. At higher coverages, lower-energy phases with nonparallel/upright, tilted orientations emerge. Besides the well-known p(2 x 1)/antiparallel phase (T/A), we find other tilted phases (tilted/irregular, T/I; tilted/spiral, T/S) as local minima. Vibrational frequencies for CO adsorbed on NaCl(100) and Davydov splittings of the C-O stretch vibration are also determined. The IR spectra are characteristic fingerprints for the relative orientation of CO molecules and may therefore be used as sensitive probes to distinguish parallel/upright from various tilted adsorption phases.}, 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{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{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{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{BronnerLeyssnerStremlauetal.2012, author = {Bronner, C. and Leyssner, F. and Stremlau, S. and Utecht, Manuel Martin and Saalfrank, Peter and Klamroth, Tillmann and Tegeder, P.}, title = {Electronic structure of a subnanometer wide bottom-up fabricated graphene nanoribbon: End states, band gap, and dispersion}, series = {Physical review : B, Condensed matter and materials physics}, volume = {86}, journal = {Physical review : B, Condensed matter and materials physics}, number = {8}, publisher = {American Physical Society}, address = {College Park}, issn = {1098-0121}, doi = {10.1103/PhysRevB.86.085444}, pages = {5}, year = {2012}, abstract = {Angle-resolved two-photon photoemission and high-resolution electron energy loss spectroscopy are employed to derive the electronic structure of a subnanometer atomically precise quasi-one-dimensional graphene nanoribbon (GNR) on Au(111). We resolved occupied and unoccupied electronic bands including their dispersion and determined the band gap, which possesses an unexpectedly large value of 5.1 eV. Supported by density functional theory calculations for the idealized infinite polymer and finite size oligomers, an unoccupied nondispersive electronic state with an energetic position in the middle of the band gap of the GNR could be identified. This state resides at both ends of the ribbon (end state) and is only found in the finite sized systems, i.e., the oligomers.}, language = {en} }