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CO oxidation on Ru(0001) is a long-standing example of a reaction that, being thermally forbidden in ultrahigh vacuum, can be activated by femtosecond laser pulses. In spite of its relevance, the precise dynamics of the photoinduced oxidation process as well as the reasons behind the dominant role of the competing CO photodesorption remain unclear. Here we use ab initio molecular dynamics with electronic friction that account for the highly excited and nonequilibrated system created by the laser to investigate both reactions. Our simulations successfully reproduce the main experimental findings: the existence of photoinduced oxidation and desorption, the large desorption to oxidation branching ratio, and the changes in the O K-edge X-ray absorption spectra attributed to the initial stage of the oxidation process. Now, we are able to monitor in detail the ultrafast CO desorption and CO oxidation occurring in the highly excited system and to disentangle what causes the unexpected inertness to the otherwise energetically favored oxidation.
Porous, layered materials containing sp(2)-hybridized carbon and nitrogen atoms, offer through their tunable properties, a versatile route towards tailormade catalysts for electrochemistry and photochemistry. A key molecule interacting with these quasi two-dimensional materials (2DM) is water, and a photo(electro)chemical key reaction catalyzed by them, is water splitting into H-2 and O-2, with the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) as half reactions. The complexity of some C/N-based 2DM in contact with water raises special needs for their theoretical modelling, which in turn is needed for rational design of C/N-based catalysts. In this work, three classes of C/N-containing porous 2DM with varying pore sizes and C/N ratios, namely graphitic carbon nitride (g-C3N4), C2N, and poly(heptazine imides) (PHI), are studied with various computational methods. We elucidate the performance of different models and model chemistries (the combination of electronic structure method and basis set) for water and water fragment adsorption in the low-coverage regime. Further, properties related to the photo(electro)chemical activity like electrochemical overpotentials, band gaps, and optical excitation energies are in our focus. Specifically, periodic models will be tested vs. cluster models, and density functional theory (DFT) vs. wavefunction theory (WFT). This work serves as a basis for a systematic study of trends for the photo(electro)chemical activity of C/N-containing layered materials as a function of water content, pore size and density.
Recent molecular beam experiments have shown that water may adsorb molecularly or dissociatively on an α-Al2O3(0001) surface, with enhanced dissociation probability compared to “pinhole dosing”, i.e., adsorption under thermal equilibrium conditions. However, precise information on the ongoing reactions and their relative probabilities is missing. In order to shed light on molecular beam scattering for this system, we perform ab initio molecular dynamics calculations to simulate water colliding with α-Al2O3(0001). We find that single water molecules hitting a cold, clean surface from the gas phase are either reflected, molecularly adsorbed, or dissociated (so-called 1–2 dissociation only). A certain minimum translational energy (above 0.1 eV) seems to be required to enforce dissociation, which may explain the higher dissociation probability in molecular beam experiments. When the surface is heated and/or when refined surface and beam models are applied (preadsorption with water or water fragments, clustering and internal preexcitation in the beam), additional channels open, among them physisorption, water clustering on the surface, and so-called 1–4 and 1–4′ dissociation.
α-Al2O3 surfaces are common in a wide variety of applications and useful models of more complicated, environmentally abundant, alumino-silicate surfaces. While decades of work have clarified that all properties of these surfaces depend sensitively on the crystal face and the presence of even small amounts of water, quantitative insight into this dependence has proven challenging. Overcoming this challenge requires systematic study of the mechanism by which water interacts with various α-Al2O3 surfaces. Such insight is most easily gained for the interaction of small amounts of water with surfaces in ultra high vacuum. In this study, we continue our combined theoretical and experimental approach to this problem, previously applied to water interaction with the α-Al2O3 (0001) and (11̅02) surfaces, now to water interaction with the third most stable surface, that is, the (112̅0). Because we characterize all three surfaces using similar tools, it is straightforward to conclude that the (112̅0) is most reactive with water. The most important factor explaining its increased reactivity is that the high density of undercoordinated surface Al atoms on the (112̅0) surface allows the bidentate adsorption of OH fragments originating from dissociatively adsorbed water, while only monodentate adsorption is possible on the (0001) and (11̅02) surfaces: the reactivity of α-Al2O3 surfaces with water depends strongly, and nonlinearly, on the density of undercoordinated surface Al atoms.
In the light of recent intensity-voltage low energy electron diffraction (LEED-IV) experiments [Surf. Sci. 316, 92 (1994); Surf. Rev. Lett. 10, 487 (2003)], the electronic and geometric structure of a water bilayer adsorbed at the Ru(0001) surface are investigated through first-principles total energy calculations, using periodic slab geometries and gradient-corrected density functional theory (DFT). We consider five possible bilayer structures, all roughly consistent with the LEED-IV analysis (three intact structures and two half-dissociated), and a water single layer at Ru(0001). Adsorption energies and substrate-adsorbate geometry parameters are given and discussed in the light of the experiments. We also give a comparative analysis of the electron density redistribution (Delta rho) and of the dipole moment change (Delta mu) induced by water adsorption on the Ru(0001) surface. In agreement with Feibelman [Science 295, 99 (2002)], the half-dissociated structures are found to be more stable than the intact ones, and their adsorption geometries in better agreement with the LEED-IV data. However, the Delta rho analysis shows that a half-dissociated structure induces a Delta mu>0, which would be incompatible with the experimentally measured decrease of the work function following bilayer adsorption; the latter would be consistent, instead, with the Delta mu < 0 induced by the intact structures. It is the aim of this paper to compare various possible adsorption structures, most of them already considered previously, with one and the same method. For this purpose, thick slabs and restrictive computational parameters are chosen to generally address the accuracy and the limits of DFT in reproducing adsorption energies and bond lengths of water-metal interacting systems
Vibrationally resolved lowest-energy bands of the photoelectron spectra (PES) of adamantane, diamantane, and urotropine were simulated by a time-dependent correlation function approach within the harmonic approximation. Geometries and normal modes for neutral and cationic molecules were obtained from B3LYP hybrid density functional theory (DFT). It is shown that the simulated spectra reproduce the experimentally observed vibrational finestructure (or its absence) quite well. Origins of the finestructure are discussed and related to recurrences of autocorrelation functions and dominant vibrations. Remaining quantitative and qualitative errors of the DFT-derived PES spectra refer to (i) an overall redshift by ∼0.5 eV and (ii) the absence of satellites in the high-energy region of the spectra. The former error is shown to be due to the neglect of many-body corrections to ordinary Kohn-Sham methods, while the latter has been argued to be due to electron-nuclear couplings beyond the Born-Oppenheimer approximation [Gali et al., Nat. Commun. 7, 11327 (2016)].
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.
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.
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.
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.
Vibrationally resolved absorption and emission (fluorescence) spectra of perylene and its N-derivatives in gas phase and in solution (acetonitrile) were simulated using a time-dependent approach based on correlation functions determined by density functional theory. By systematically varying the number and position of N atoms, it is shown that the presence of nitrogen heteroatoms has a negligible effect on the molecular structure and geometric distortions upon electronic transitions, while spectral properties change: in particular the number of N atoms is important while their position is less decisive. Thus, the N-substitution can be used to fine-tune the optical properties of perylene-based molecules.
Diamondoids are hydrogen-saturated molecular motifs cut out of diamond, forming a class of materials with tunable optoelectronic properties. In this work, we extend previous work on neutral, closed-shell diamondoids by computing with hybrid density functional theory and time-dependent correlation functions vibrationally broadened absorption spectra of cations and radicals derived from the simplest diamondoid, adamantane, namely, the neutral 1- and 2-adamantyl radicals (C10H15), the 1- and 2-adamantyl cations (C10H15+), and the adamantane radical cation (C10H16+). For selected cases, we also report vibrationally broadened emission, photoelectron, and resonance Raman spectra. Furthermore, the effect of the damping factor on the vibrational fine-structure is studied. The following trends are found: (1) Low-energy absorptions of the adamantyl radicals and cations, and of the adamantane cation, are all strongly red-shifted with respect to adamantane; (2) also, emission spectra are strongly red-shifted, whereas photoelectron spectra are less affected for the cases studied; (3) vibrational fine-structures are reduced compared to those of adamantane; (4) the spectroscopic signals of 1- and 2-adamantyl species are significantly different from each other; and (5) reducing the damping factor has only a limited effect on the vibrational fine-structure in most cases. This suggests that removing hydrogen atoms and/or electrons from adamantane leads to new optoelectronic properties, which should be detectable by vibronic spectroscopy.
Using gradient- and dispersion-corrected density functional theory in connection with ab initio molecular dynamics and efficient, parametrized Velocity-Velocity Autocorrelation Function (VVAF) methodology, we study the vibrational spectra (Vibrational Sum Frequency, VSF, and infrared, IR) of hydroxylated alpha-Al2O3(0001) surfaces with and without additional water. Specifically, by considering a naked hydroxylated surface and the same surface with a particularly stable, "ice-like" hexagonal water later allows us to identify and disentangle main spectroscopic bands of OH bonds, their orientation and dynamics, and the role of water adsorption. In particular, we assign spectroscopic signals around 3700 cm(-1) as being dominated by perpendicularly oriented non-hydrogen bonded aluminol groups, with and without additional water. Furthermore, the thin water layer gives spectroscopic signals which are already comparable to previous theoretical and experimental findings for the solid/(bulk) liquid interface, showing that water molecules closest to the surface play a decisive role in the vibrational response of these systems. From a methodological point of view, the effects of temperature, anharmonicity, hydrogen-bonding, and structural dynamics are taken into account and analyzed, allowing us to compare the calculated IR and VSF spectra with the ones based on normal mode analysis and vibrational density of states. The VVAF approach employed in this work appears to be a computationally accurate yet feasible method to address the vibrational fingerprints and dynamical properties of water/metal oxide interfaces. Published by AIP Publishing.
Water can adsorb molecularly or dissociatively onto different sites of metal oxide surfaces. These adsorption sites can be disentangled using surface-sensitive vibrational spectroscopy. Here, we model Vibrational Sum Frequency (VSF) spectra for various forms of dissociated, deuterated water on a reconstructed, Al-terminated α-Al2O3(0001) surface at submonolayer coverages (the so-called 1-2, 1-4, and 1-4′ modes). Using an efficient scheme based on velocity-velocity autocorrelation functions, we go beyond previous normal mode analyses by including anharmonicity, mode coupling, and thermal surface motion in the framework of ab initio molecular dynamics. In this way, we calculate vibrational density of states curves, infrared, and VSF spectra. Comparing computed VSF spectra with measured ones, we find that relative frequencies of resonances are in quite good agreement and linewidths are reasonably well represented, while VSF intensities coincide not well. We argue that intensities are sensitively affected by local interactions and thermal fluctuations, even at such low coverage, while absolute peak positions strongly depend on the choice of the electronic structure method and on the appropriate inclusion of anharmonicity.
Carbon monoxide on copper surfaces continues to be a fascinating, rich microlab for many questions evolving in surface science. Recently, hot-electron mediated, femtosecond-laser pulse induced dynamics of CO molecules on Cu(100) were the focus of experiments [Inoue et al., Phys. Rev. Lett. 117, 186101 (2016)] and theory [Novko et al., Phys. Rev. Lett. 122, 016806 (2019)], unraveling details of the vibrational nonequilibrium dynamics on ultrashort (subpicoseconds) timescales. In the present work, full-dimensional time-resolved hot-electron driven dynamics are studied by molecular dynamics with electronic friction (MDEF). Dissipation is included by a friction term in a Langevin equation which describes the coupling of molecular degrees of freedom to electron-hole pairs in the copper surface, calculated from gradient-corrected density functional theory (DFT) via a local density friction approximation (LDFA). Relaxation due to surface phonons is included by a generalized Langevin oscillator model. The hot-electron induced excitation is described via a time-dependent electronic temperature, the latter derived from an improved two-temperature model. Our parameter-free simulations on a precomputed potential energy surface allow for excellent statistics, and the observed trends are confirmed by on-the-fly ab initio molecular dynamics with electronic friction (AIMDEF) calculations. By computing time-resolved frequency maps for selected molecular vibrations, instantaneous frequencies, probability distributions, and correlation functions, we gain microscopic insight into hot-electron driven dynamics and we can relate the time evolution of vibrational internal CO stretch-mode frequencies to measured data, notably an observed redshift. Quantitatively, the latter is found to be larger in MDEF than in experiment and possible reasons are discussed for this observation. In our model, in addition we observe the excitation and time evolution of large-amplitude low-frequency modes, lateral CO surface diffusion, and molecular desorption. Effects of surface atom motion and of the laser fluence are also discussed.
Using density functional theory and Ab Initio Molecular Dynamics with Electronic Friction (AIMDEF), we study the adsorption and dissipative vibrational dynamics of hydrogen atoms chemisorbed on free-standing lead films of increasing thickness. Lead films are known for their oscillatory behaviour of certain properties with increasing thickness, e.g., energy and electron spill-out change in discontinuous manner, due to quantum size effects [G. Materzanini, P. Saalfrank, and P.J.D. Lindan, Phys. Rev. B 63, 235405 (2001)]. Here, we demonstrate that oscillatory features arise also for hydrogen when chemisorbed on lead films. Besides stationary properties of the adsorbate, we concentrate on finite vibrational lifetimes of H-surface vibrations. As shown by AIMDEF, the damping via vibration-electron hole pair coupling dominates clearly over the vibration-phonon channel, in particular for high-frequency modes. Vibrational relaxation times are a characteristic function of layer thickness due to the oscillating behaviour of the embedding surface electronic density. Implications derived from AIMDEF for frictional many-atom dynamics, and physisorbed species will also be given. (C) 2014 AIP Publishing LLC.
Vibrational relaxation of adsorbates is a sensitive tool to probe energy transfer at gas/solid and liquid/solid interfaces. The most direct way to study relaxation dynamics uses time-resolved spectroscopy. Here we report on a non-equilibrium ab initio molecular dynamics (NE-AIMD) methodology to model vibrational relaxation of OH vibrations on a hydroxylated, water-covered alpha-Al2O3(0001) surface. In our NE-AIMD approach, after exciting selected O-H bonds their coupling to surface phonons and to the water adlayer is analyzed in detail, by following both the energy flow in time, as well as the time-evolution of Vibrational Density of States (VDOS) curves. The latter are obtained from Time-dependent Correlation Functions (TCFs) and serve as prototypical, generic representatives of time-resolved vibrational spectra. As most important results, (i) we find a few-picosecond lifetime of the excited modes and (ii) identify both hydrogen-bonded aluminols and water molecules in the adsorbed water layer as main dissipative channels, while the direct coupling to Al2O3 surface phonons is of minor importance on the timescales of interest. Our NE-AIMD/TCF methodology is powerful for complex adsorbate systems, in principle even reacting ones, and opens a way towards time-resolved vibrational spectroscopy.
Combining photochromism and nonlinear optical (NLO) properties of molecular switches-functionalized self-assembled monolayers (SAMs) represents a promising concept toward novel photonic and optoelectronic devices. Using second harmonic generation, density functional theory, and correlated wave function methods, we studied the switching abilities as well as the NLO contrasts between different molecular states of various fulgimide-containing SAMs on Si(111). Controlled variations of the linker systems as well as of the fulgimides enabled us to demonstrate very efficient reversible photoinduced ring-opening/closure reactions between the open and closed forms of the fulgimides. Thus, effective cross sections on the order of 10(-18) cm(-2) are observed. Moreover, the reversible switching is accompanied by pronounced NLO contrasts up to 32%. Further molecular engineering of the photochromic switches and the linker systems may even increase the NLO contrast upon switching.
Thermally stable photoswitches that are driven with low-energy light are rare, yet crucial for extending the applicability of photoresponsive molecules and materials towards, e.g., living systems. Combined ortho-fluorination and -amination couples high visible light absorptivity of o-aminoazobenzenes with the extraordinary bistability of o-fluoroazobenzenes. Herein, we report a library of easily accessible o-aminofluoroazobenzenes and establish structure-property relationships regarding spectral qualities, visible light isomerization efficiency and thermal stability of the cis-isomer with respect to the degree of o-substitution and choice of amino substituent. We rationalize the experimental results with quantum chemical calculations, revealing the nature of low-lying excited states and providing insight into thermal isomerization. The synthesized azobenzenes absorb at up to 600 nm and their thermal cis-lifetimes range from milliseconds to months. The most unique example can be driven from trans to cis with any wavelength from UV up to 595 nm, while still exhibiting a thermal cis-lifetime of 81 days. <br /> [GRAPHICS] <br /> .
An efficient method for the numerical solution of a non-Markovian, open-system density matrix equation of motion in coordinate representation is developed. We apply the scheme to model simulations of the laser-assisted O+H -> OH association reaction in an environment. The suggested approach is based on the application of the time-evolution operator to the "closed-system" part of the overall Hamiltonian and transformation of the open-system equation of motion to the Heisenberg picture suitable for numerical propagation. A dual role of the system-environment coupling with respect to the infrared (ir) laser-driven association of OH is demonstrated: the association probability is increased due to the coupling at relatively weak laser fields, but decreased at strong laser fields. Moreover, at a certain strength of the ir laser field, the association probability does not depend on the strength of the system-bath coupling at all.
We present a systematic study of the influence of energy and phase relaxation on dynamic polarizability simulations in the linear response regime. The nonperturbative approach is based on explicit electron dynamics using short laser pulses of low intensities. To include environmental effects on the property calculation, we use the time- dependent configuration-interaction method in its reduced density matrix formulation. Both energy dissipation and nonlocal pure dephasing are included. The explicit treatment of time-resolved electron dynamics gives access to the phase shift between the electric field and the induced dipole moment, which can be used to define a useful uncertainty measure for the dynamic polarizability. The nonperturbative treatment is compared to perturbation theory expressions, as applied to a simple model system, the rigid H-2 molecule. It is shown that both approaches are equivalent for low field intensities, but the time-dependent treatment provides complementary information on the phase of the induced dipole moment, which allows for the definition of an uncertainty associated with the computation of the dynamic polarizability in the linear response regime.
We report simulations of laser-driven many-electron dynamics by means of the time-dependent configuration interaction singles (doubles) approach. The method accounts for the correlation of ground and excited states, is capable of describing explicitly time-dependent, nonlinear phenomena, and is systematically improvable. Lithium cyanide serves as a molecular test system in which the charge distribution and hence the dipole moment are shown to be switchable, in a controlled fashion, by (a series of) laser pulses which induce selective, state-to-state electronic transitions. One focus of our time-dependent calculations is the question of how fast the transition from the ionic ground state to a specific excited state that is embedded in a multitude of other states can be made, without creating an electronic wave packet. (c) 2005 American Institute of Physics
The thermal Z -> E (back-) isomerization of azobenzenes is a prototypical reaction occurring in molecular switches. It has been studied for decades, yet its kinetics is not fully understood. In this paper, quantum chemical calculations are performed to model the kinetics of an experimental benchmark system, where a modified azobenzene (AzoBiPyB) is embedded in a metal-organic framework (MOF). The molecule can be switched thermally from cis to trans, under solvent-free conditions. We critically test the validity of Eyring transition state theory for this reaction. As previously found for other azobenzenes (albeit in solution), good agreement between theory and experiment emerges for activation energies and activation free energies, already at a comparatively simple level of theory, B3LYP/6-31G* including dispersion corrections. However, theoretical Arrhenius prefactors and activation entropies are in qualitiative disagreement with experiment. Several factors are discussed that may have an influence on activation entropies, among them dynamical and geometric constraints (imposed by the MOF). For a simpler model-Z -> E isomerization in azobenzene-a systematic test of quantum chemical methods from both density functional theory and wavefunction theory is carried out in the context of Eyring theory. Also, the effect of anharmonicities on activation entropies is discussed for this model system. Our work highlights capabilities and shortcomings of Eyring transition state theory and quantum chemical methods, when applied for the Z -> E (back-) isomerization of azobenzenes under solvent-free conditions.
We report on the experimental and theoretical investigation of a considerable increase in the rate for thermal cis -> trans isomerization of azobenzene-containing molecules in the presence of gold nanopartides. Experimentally, by means of UV vis spectroscopy, we studied a series of azobenzene-containing surfactants and 4-nitroazobenzene. We found that in the presence of gold,nanoparticles the thermal lifetime of the cis isomer of the azobenzenecontaining molecules was decreased by up to 3 orders of magnitude in comparison to the lifetime in solution without nanoparticles. The electron transfer between azobenzene-containing molecules and a surface of gold nanopartides is a possible reason to promote the thermal cis trans switching. To investigate the effect of electron attachment to, and withdrawal from, the azobenzene-containing molecules on the isomerization rate, we performed density functional theory calculations of activation energy barriers of the reaction together with Eyring's transition state theory calculations of the rates for azobenzene derivatives with donor and acceptor groups in para position of one of the phenyl rings, as well as for one of the azobenzene-containing surfactants. We found that activation barriers are greatly lowered for azobenzene-containing molecules, both upon electron attachment and withdrawal, which leads, in turn, to a dramatic increase in the thermal isomerization rate.
In this contribution, recent advances in the theory of laser and, to a lesser extent, of scanning tunneling microscope (STM) induced cleavage of bonds between an adsorbate and a solid surface, will be reviewed. Special emphasis will be given to the quantum dynamics of electronically non-adiabatic reactions. (c) 2005 Elsevier Ltd. All rights reserved
The quantum chemical description of the adsorption, vibrations, and reactions of molecules at periodic solid surfaces is frequently based on a methodological "standard model": density functional theory (DFT) in the generalized gradient approximation (GGA), using plane wave bases and three-dimensional supercells. Although the computationally efficient GGA functionals can be very successful, cases are known where they do not perform so well. Most importantly, activation energies for chemical reactions are typically underestimated, with the consequence of computed reaction rates being too large. In this work, we consider a well-studied model system: water or water fragments adsorbed on an Al-terminated alpha-Al2O3(0001) surface as a test bed for studying the performance of electronic structure methods, both from DFT and wave function theory. On the DFT side, we employ two GGA exchange correlation functionals: PW91 and PBE with and without dispersion corrections, whose results are then compared to those of hybrid functionals B3LYP and HSE06. Further, we follow a periodic wave function approach in the form of local second-order Moller-Plesset perturbation theory, LMP2, on a Hartree-Fock reference. En route, we address issues arising from the choice of the basis set. The key findings of our study are as follows: (i) DFT-GGA adsorption energies are in reasonable agreement with both hybrid-DFT and LMP2 values. In particular, the deviations between the relative energies, corresponding to different adsorption structures, are in the range of the error due to missing dispersion corrections or the basis set error. (ii) Harmonic DFT-GGA vibrational frequencies for oxygen hydrogen stretch modes are by several tens of wavenumbers red-shifted compared to corresponding hybrid-DFT values. The latter are in much better agreement with recent experimental data. (iii) The activation energy for a hydrogen diffusion reaction is grossly underestimated by GGA compared to hybrid-DFT or LMP2, which in turn are quite comparable.
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.
The Photoinduced E -> Z Isomerization of Bisazobenzenes: A Surface Hopping Molecular Dynamics Study
(2015)
The photoinduced E -> Z isomerization of azobenzene is a prototypical example of molecular switching. On the way toward rigid molecular rods such as those for opto-mechanical applications, multiazobenzene structures have been suggested in which several switching units are linked together within the same molecule (Bleger et al., J. Phys. Chem. B 2011, 115, 9930-9940). Large differences in the switching efficiency of multiazobenzenes have been observed, depending on whether the switching units are electronically decoupled or not. In this paper we study, on a time-resolved molecular level, the E -> Z isomerization of the simplest multiazobenzene, bisazobenzene (BAB). Two isomers (ortho- and para-BAB), differing only in the connectivity of two azo groups on a shared phenyl ring will be considered.To do so, nonadiabatic semiclassical dynamics after photo-excitation of the isomers are studied by employing an "on-the-fly", fewest switches surface hopping approach. States and couplings are calculated by Configuration Interaction (CI) based on a semiempirical (AM1) Hamiltonian (Persico and co-workers, Chem. Eur. J. 2004, 10, 2327-2341). In the case of para-BAB, computed quantum yields for photoswitching are drastically reduced compared to pristine azobenzene, due to electronic coupling of both switching units. A reason for this (apart from altered absorption spectra and reduced photochromicity) is the drastically reduced lifetimes of electronically excited states which are transiently populated. In contrast for meta-connected species, electronic subsystems are largely decoupled, and computed quantum yields are slightly higher than that for pristine azobenzene because of new isomerization channels. In this case we can also distinguish between single- and double-switch events and we find a cooperative effect: The isomerization of a single azo group is facilitated if the other azo group is already in the Z-configuration.
We apply the multiconfiguration time-dependent Hartree-Fock method to electronic structure calculations and show that quantum chemical information can be obtained with this explicitly time-dependent approach. Different equations of motion are discussed, as well as the numerical cost. The two-electron integrals are calculated using a natural potential expansion, of which we describe the convergence behavior in detail
The electronic structure of the metal-organic interface of isolated ligand coated gold nanoparticles
(2022)
Light induced electron transfer reactions of molecules on the surface of noble metal nanoparticles (NPs) depend significantly on the electronic properties of the metal-organic interface. Hybridized metal-molecule states and dipoles at the interface alter the work function and facilitate or hinder electron transfer between the NPs and ligand. X-ray photoelectron spectroscopy (XPS) measurements of isolated AuNPs coated with thiolated ligands in a vacuum have been performed as a function of photon energy, and the depth dependent information of the metal-organic interface has been obtained. The role of surface dipoles in the XPS measurements of isolated ligand coated NPs is discussed and the binding energy of the Au 4f states is shifted by around 0.8 eV in the outer atomic layers of 4-nitrothiophenol coated AuNPs, facilitating electron transport towards the molecules. Moreover, the influence of the interface dipole depends significantly on the adsorbed ligand molecules. The present study paves the way towards the engineering of the electronic properties of the nanoparticle surface, which is of utmost importance for the application of plasmonic nanoparticles in the fields of heterogeneous catalysis and solar energy conversion.
In this work, we present theoretical simulations of laser-driven vibrational control of NO adsorbed on a gold surface. Our goal is to tailor laser pulses to selectively excite specific modes and vibrational eigenstates, as well as to favor photodesorption of the adsorbed molecule. To this end, various control schemes and algorithms are applied. For adsorbates at metallic surfaces, the creation of electron hole pairs in the substrate is known to play a dominant role in the transfer of energy from the system to the surroundings. These nonadiabatic couplings are included perturbatively in our reduced density matrix simulations using a generalization of the state-resolved position-dependent anharmonic rate model we recently introduced. An extension of the reduced density matrix is also proposed to provide a sound model for photodesorption in dissipative systems.
The chemistry of water on alpha-alumina kinetics and nuclear quantum effects from first principles
(2012)
Water adsorption on an alumina (alpha-Al2O3) surface is studied here from first principles using periodic density functional theory in the generalized gradient approximation. Two different coverage regimes, low and high, are considered. For the low-coverage regime (with a coverage of 1/4 with respect to the number of coordinatively unsaturated Al sites), possible reactions at the surface such as dissociation, rotation, and diffusion of water and its fragments are investigated, using first principles thermodynamics and kinetics. A microkinetic model is set up with rates calculated from Eyring's transition state theory in order to cover a wide range of time scales. Special emphasis of this study is on the magnitude of quantum effects and on anharmonic corrections, particularly for reactions and dynamics. These have often been neglected in the past for water/alumina systems but can influence the system. This is particularly true for processes involving hydrogen atoms, where, for example, tunneling corrections to reaction rates are found to be important even at room temperature. For a higher-coverage regime (with a coverage of 2 ML), hydrogen dynamics becomes even more complex and is characterized, e.g., by concerted atom motion, strong anharmonicity, and delocalization. In this regime, classical molecular dynamics becomes questionable as well as quantum mechanical treatments based on the harmonic approximation.
Fluoroionophores of fluorophore-spacer-receptor format were prepared for detection of PdCl2 by fluorescence enhancement. The fluorophore probes 1-13 consist of a fluorophore group, in alkyl spacer and a dithiomaleonitrile PdCl2 receptor. First, varying the length of the alkylene spacer (compounds 1-3) revealed, dominant through-space pathway for oxidative photoinduced electron transfer (PET) in CH2-bridged dithiomaleonitrile fluoroionophores. Second. fluorescent probes 4-9 containing two anthracene or pyrene fragments connected through CH2 bridges to the dithiomaleonitrile unit were synthesized. Modulation of the oxidation potential (E-Ox) through electron-withdrawing or -donating groups on the anthracene moiety regulates file thermodynamic driving force for oxidative PET (Delta G(PET)) in bis(anthrylmethylthio)maleonitriles and therefore the fluorescence quantum yields (Phi(f)), too. The new concept was confirmed and transferred to pyrenyl ligands, and fluorescence enhancements (FE) greater than 3.2 in the presence of PdCl2 were achieved by 7 and 8 (FE=5.4 and 5.2). Finally, for comparison, monofluorophore ligands 10-13 were synthesized.
Fluoroionophores of fluorophore-spacer-receptor format were prepared for detection of PdCl2 by fluorescence enhancement. The fluorescent probes 1-13 consist of a fluorophore group, an alkyl spacer and a dithiomaleonitrile PdCl2 receptor. First, varying the length of the alkylene spacer (compounds 1-3) revealed a dominant through-space pathway for oxidative photoinduced electron transfer (PET) in CH2-bridged dithiomaleonitrile fluoroionophores. Second, fluorescent probes 4-9 containing two anthracene or pyrene fragments connected through CH2 bridges to the dithiomaleonitrile unit were synthesized. Modulation of the oxidation potential (EOx) through electron-withdrawing or -donating groups on the anthracene moiety regulates the thermodynamic driving force for oxidative PET (GPET) in bis(anthrylmethylthio)maleonitriles and therefore the fluorescence quantum yields (f), too. The new concept was confirmed and transferred to pyrenyl ligands, and fluorescence enhancements (FE) greater than 3.2 in the presence of PdCl2 were achieved by 7 and 8 (FE=5.4 and 5.2). Finally, for comparison, monofluorophore ligands 10-13 were synthesized.
The photochemistry as well as electrochemistry of novel donor-acceptor bis(morpholinothiazolyl)maleimides has been investigated. Proper substitution of these diarylethene-type molecular switches leads to the unique situation in which their ring-closure can only be accomplished electrochemically, while ring-opening can only be achieved photochemically. Hence, these switches operate with orthogonal stimuli, i.e. redox potential and light, respectively. The switch system could be optimized by introducing trifluoromethyl groups at the reactive carbon atoms in order to avoid by-product formation during oxidative ring closure. Both photochemical and electrochemical pathways were investigated for methylated, trifluoromethylated, and nonsymmetrical bis(morpholinothiazolyl) maleimides as well as the bis(morpholinothiazolyl) cyclopentene reference compound. With the aid of the nonsymmetrical "mixed" derivative, the mechanism of electrochemically driven ring closure could be elucidated and seems to proceed via a dicationic intermediate generated by two-fold oxidation. All experimental work has been complemented by density functional theory that provides detailed insights into the thermodynamics of the ring-open and closed forms, the nature of their excited states, and the reactivity of their neutral as well as ionized species in different electronic configurations. The particular diarylethene systems described herein could serve in multifunctional (logic) devices operated by different stimuli (inputs) and may pave the way to converting light into electrical energy via photoinduced "pumping" of redox-active meta-stable states.
With ongoing miniaturization of electronic devices, the need for individually addressable, switchable molecules arises. An example are azobenzenes on surfaces which have been shown to be switchable between trans and cis forms. Here, we examine the "direct" (rather than substrate-mediated) channel of the trans -> cis photoisomerization after pi pi* excitation of tetra-tert-butyl-azobenzene physisorbed on surfaces mimicking Au(111) and Bi(111), respectively. In spirit of the direct channel, the electronic structure of the surface is neglected, the latter merely acting as a rigid platform which weakly interacts with the molecule via Van-der-Waals forces. Starting from thermal ensembles which represent the trans-form, sudden excitations promote the molecules to pi pi*-excited states which are non-adiabatically coupled among themselves and to a n pi*-excited and the ground state, respectively. After excitation, relaxation to the ground state by internal conversion takes place, possibly accompanied by isomerization. The process is described here by "on the fly" semiclassical surface hopping dynamics in conjunction with a semiempirical Hamiltonian (AM1) and configuration-interaction type methods. It is found that steric constraints imposed by the substrate lead to reduced but non-vanishing, trans -> cis reaction yields and longer internal conversion times than for the isolated molecule. Implications for recent experiments for azobenzenes on surfaces are discussed.
Azobenzenes easily photoswitch in solution, while their photoisomerization at surfaces is often hindered. In recent work, it was demonstrated by nonadiabatic molecular dynamics with trajectory surface hopping [Titov et al., J. Phys. Chem. Lett. 2016, 7, 3591-3596] that the experimentally observed suppression of trans -> cis isomerization yields in azobenzenes in a densely packed SAM (self-assembled monolayer) [Gahl et al., J. Am. Chem. Soc. 2010, 132, 1831-1838] is dominated by steric hindrance. In the present work, we systematically study by ground-state Langevin and nonadiabatic surface hopping dynamics, the effects of decreasing packing density on (i) UV/vis absorption spectra, (ii) trans -> cis isomerization yields, and (iii) excited-state lifetimes of photoexcited azobenzene. Within the quantum mechanics/ molecular mechanics models adopted here, we find that above a packing density of similar to 3 molecules/nm(2), switching yields are strongly reduced, while at smaller packing densities, the "monomer limit" is quickly approached. The UV/vis absorption spectra, on the other hand, depend on packing density over a larger range (down to at least similar to 1 molecule/nm(2)). Trends for excited-state lifetimes are less obvious, but it is found that lifetimes of pi pi* excited states decay monotonically with decreasing coverage. Effects of fluorination of the switches are also discussed for single, free molecules. Fluorination leads to comparatively large trans -> cis yields, in combination with long pi pi* lifetimes. Furthermore, for selected systems, also the effects of n pi* excitation at longer excitation wavelengths have been studied, which is found to enhance trans -> cis yields for free molecules but can lead to an opposite behavior in densely packed SAMs.
The alpha-Al2O3(0001) surface has been extensively studied because of its significance in both fundamental research and application. Prior work suggests that in ultra-high-vacuum (UHV), in the absence of water, the so-called Al-I termination is thermodynamically favored, while in ambient, in contact with liquid water, a Gibbsite-like layer is created. While the view of the alpha- Al2O3(0001)/H2O(l) interface appears relatively clear in theory, experimental characterization of this system has resulted in estimates of surface acidity, i.e., isoelectric points, that differ by 4 pH units and surface structure that in some reports has non-hydrogen-bonded surface aluminol (Al-OH) groups and in others does not. In this study, we employed vibrational sum frequency spectroscopy (VSFS) and density functional theory (DFT) simulation to study the surface phonon modes of the differently terminated alpha-Al2O3(0001) surfaces in both UHV and ambient. We find that, on either water dosing of the Al-I in UHV or heat-induced dehydroxylation of the Gibbsite-like in ambient, the surfaces do not interconvert. This observation offers a new explanation for disagreements in prior work on the alpha-Al2O3(0001)/liquid water interface -different preparation methods may create surfaces that do not interconvert-and shows that the surface phonon spectral response offers a novel probe of interfacial hydrogen bonding structure.
Complete sticking at low incidence energies and broad angular scattering distributions at higher energies are often observed in molecular beam experiments on gas-surface systems which feature a deep chemisorption well and lack early reaction barriers. Although CO binds strongly on Ru(0001), scattering is characterized by rather narrow angular distributions and sticking is incomplete even at low incidence energies. We perform molecular dynamics simulations, accounting for phononic (and electronic) energy loss channels, on a potential energy surface based on first-principles electronic structure calculations that reproduce the molecular beam experiments. We demonstrate that the mentioned unusual behavior is a consequence of a very strong rotational anisotropy in the molecule-surface interaction potential. Beyond the interpretation of scattering phenomena, we also discuss implications of our results for the recently proposed role of a precursor state for the desorption and scattering of CO from ruthenium.
Stochastic approach to laser-induced ultrafast dynamics : the desorption of H-2/D-2 from Ru(0001)
(2010)
The desorption of molecular hydrogen and deuterium induced by femtosecond-laser pulses is studied theoretically for the so-called DIMET (Desorption Induced by Multiple Electronic Transitions) process. These investigations are based on nonadiabatic classical Monte Carlo trajectory (CMCT) simulations on a ground and an excited state potential energy surface, including up to all six adsorbate degrees of freedom. The focus is on the hot-electron mediated energy transfer from the surface to the molecule and back, and the energy partitioning between the different degrees of freedom of the desorbing molecules. We first validate for a two-mode model comprising the desorption mode and the internal vibrational coordinate, the classical Monte Carlo trajectory method by comparing with Monte Carlo wavepacket (MCWP) calculations arising from a fully quantum mechanical open-system density matrix treatment. We then proceed by extending the CMCT calculations to include all six nuclear degrees of freedom of the desorbing molecule. This allows for a detailed comparison between theory and experiment concerning isotope effects, energy partitioning (translational, vibrational, and rotational energies and their distributions), and the dependence of these properties on the laser fluence. The most important findings are as follows. (i) CMCT agrees qualitative with the MCWP scheme. (ii) The basic experimental features such as the large isotope effect, the non-linear increase of yield with laser fluence, translationally hot products (in the order of several 1000 K) and non-equipartitioning of translational and internal energies (E-trans > E- vib > E-rot) are well reproduced. (iii) Predictions concerning a strong angular dependence of translational energies at large observation angles are also made.
The scanning tunnelling microscope (STM)-induced switching of a single cyclooctadiene molecule between two stable conformations chemisorbed on a Si(100) surface is investigated using an above threshold model including a neutral ground state and an ionic excited state potential. Switching was recently achieved experimentally with an STM operated at cryogenic temperatures (Nacci et al 2008 Phys. Rev. B 77 121405(R)) and rationalized by a below threshold model using just a single potential energy surface (Nacci et al 2009 Nano Lett. 9 2997).
In the present paper, we show that experimental key findings on the inelastic electron tunnelling (IET) switching can also be rationalized using an above threshold density matrix model, which includes, in addition to the neutral ground state potential, an anionic or cationic excited potential. We use one and two-dimensional potential energy surfaces. Furthermore, the influence of two key parameters of the density matrix description, namely the electronic lifetime of the ionic resonance and the vibrational lifetimes, on the ground state potential are discussed.
The BLUF (blue-light sensing using flavine) domain of the AppA photoreceptor protein from Rhodobacter sphaeroides was modelled by using quantum chemical chromophore plus amino acid models at the (TD-)B3LYP/6-31G* level of theory. The models were based on NMR structures, and further refined by CHARM force field molecular dynamics simulations. The goal is to explain the total redshift by about 10 nm in the UV/Vis spectra of BLUF domains after illumination, and to relate it to structural changes. For this purpose UV/Vis spectra of the available NMR structures were calculated and related to geometrical features. In particular, the hydrogen network embedding the central chromophore is discussed. Specifically, the position of a conserved glutamine, Q63, is found to be important in agreement with findings from previous works. Additionally, however, we find a systematic dependence also on the geometry of a conserved serine, S41. Based on a series of calculations with known structures and with artificial structural models, we argue that indeed the light-induced switching of both Q63 and S41 is necessary to explain the full similar to 10 nm redshift in the light (signalling) state of serine containing BLUF domains. Following or accompanying the double switching, two structurally highly important residues W104 and M106 exchange places, but do not affect the overall UV/ Vis properties of the chromophore.
Femtosecond-laser pulse driven non-adiabatic spectroscopy and dynamics in molecular and condensed phase systems continue to be a challenge for theoretical modelling. One of the main obstacles is the "curse of dimensionality" encountered in non-adiabatic, exact wavepacket propagation. A possible route towards treating complex molecular systems is via semiclassical surface-hopping schemes, in particular if they account not only for non-adiabatic post-excitation dynamics but also for the initial optical excitation. One such approach, based on initial condition filtering, will be put forward in what follows. As a simple test case which can be compared with exact wavepacket dynamics, we investigate the influence of the different parameters determining the shape of a laser pulse (e.g., its finite width and a possible chirp) on the predissociation dynamics of a NaI molecule, upon photoexcitation of the A(0(+)) state. The finite-pulse effects are mapped into the initial conditions for semiclassical surface-hopping simulations. The simulated surface-hopping diabatic populations are in qualitative agreement with the quantum mechanical results, especially concerning the subpicosend photoinduced dynamics, the main deviations being the relative delay of the non-adiabatic transitions in the semiclassical picture. Likewise, these differences in the time-dependent electronic populations calculated via the semiclassical and the quantum methods are found to have a mild influence on the overall probability density distribution. As a result, the branching ratios between the bound and the dissociative reaction channels and the time-evolution of the molecular wavepacket predicted by the semiclassical method agree with those computed using quantum wavepacket propagation. Implications for more challenging molecular systems are given. (C) 2015 AIP Publishing LLC.
A theoretical model for the selective subsurface absorption of atomic hydrogen in a Pd(111) surface by infrared (IR) laser pulses is presented. The dynamics of the adsorbate is studied within the reduced density matrix approach. Energy and phase relaxation of the hydrogen atom are treated using the semigroup formalism. The vibrational excitation leading to subsurface absorption is performed using rationally designed pulses as well as IR laser pulses optimized on- the-fly. It is shown that dissipation can be used as a tool to transfer population to an otherwise inaccessible state via a mechanism known as "laser distillation." We demonstrate that when the reaction path is generalized from a reduced one-dimensional to full three-dimensional treatment of the system, the laser control strategy can prove very different.
Selective excitation of molecule-surface vibrations in H2 and D2 dissociatively adsorbed on Ru(0001)
(2012)
In this contribution we report about the selective vibrational excitation of H2 and D2 on Ru(0001) as an example for nonadiabatic coupling of an open quantum system to a dissipative environment. We investigate the possibility of achieving state-selective vibrational excitations of H2 and D2 adsorbed on a Ru(0001) surface using picosecond infrared laser pulses. The systems behavior is explored using pulses that are rationally designed and others that are optimized using a time-local variant of Optimal Control Theory. The effects of dissipation on the laser-driven dynamics are studied using the reduced-density matrix formalism. The non-adiabatic couplings between adsorbate and surface are computed perturbatively, for which our recently introduced state-resolved anharmonic rate model is used. It is shown that mode- and state-selective excitation can be achieved in the absence of dissipation when using optimized laser pulses. The inclusion of dissipation in the model reduces the state selectivity and the population transfer yield to highly excited states. In this case, mode activation is most effectively realized by a rational pulse of carefully chosen duration rather than by a locally optimized pulse.
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.
Incorporating photochromic molecules into organic/inorganic hybrid materials may lead to photoresponsive systems. In such systems, the second-order nonlinear properties can be controlled via external stimulation with light at an appropriate wavelength. By creating photochromic molecular switches containing self-assembled monolayers on Si(111), we can demonstrate efficient reversible switching, which is accompanied by a pronounced modulation of the nonlinear optical (NLO) response of the system. The concept of utilizing functionalized photoswitchable Si surfaces could be a way for the generation of two-dimensional NLO switching materials, which are promising for applications in photonic and optoelectronic devices.
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.