Shaping the laser control landscape of a hydrogen transfer reaction by vibrational strong coupling. A direct optimal control approach.

Controlling molecular reactivity by shaped laser pulses is a long-standing goal in chemistry. Here, we suggest a direct optimal control approach that combines external pulse optimization with other control parameters arising in the upcoming field of vibro-polaritonic chemistry for enhanced controllability. The direct optimal control approach is characterized by a simultaneous simulation and optimization paradigm, meaning that the equations of motion are discretized and converted into a set of holonomic constraints for a nonlinear optimization problem given by the control functional. Compared with indirect optimal control, this procedure offers great flexibility, such as final time or Hamiltonian parameter optimization. A simultaneous direct optimal control theory will be applied to a model system describing H-atom transfer in a lossy Fabry-Pérot cavity under vibrational strong coupling conditions. Specifically, optimization of the cavity coupling strength and, thus, of the control landscape will be demonstrated.

A quantum-mechanical tier model for phonon-driven vibrational relaxation dynamics of adsorbates at surfaces.

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 ∼Nl×υ. Here, N is the number of bath modes, l is the highest-order of the phononic expansion, and υ 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, ∼MN, 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 Schrödinger 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 × 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.

Isotopic effects in vibrational relaxation dynamics of H on a Si(100) surface.

In a recent paper [U. Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], we proposed a robust scheme to set up a system-bath model Hamiltonian, describing the coupling of adsorbate vibrations (system) to surface phonons (bath), from first principles. The method is based on an embedded cluster approach, using orthogonal coordinates for system and bath modes, and an anharmonic phononic expansion of the system-bath interaction up to second order. In this contribution, we use this model Hamiltonian to calculate vibrational relaxation rates of H-Si and D-Si bending modes, coupled to a fully H(D)-covered Si(100)-(2×1) surface, at zero temperature. The D-Si bending mode has an anharmonic frequency lying inside the bath frequency spectrum, whereas the H-Si bending mode frequency is outside the bath Debye band. Therefore, in the present calculations, we only take into account one-phonon system-bath couplings for the D-Si system and both one- and two-phonon interaction terms in the case of H-Si. The computation of vibrational lifetimes is performed with two different approaches, namely, Fermi's golden rule, and a generalized Bixon-Jortner model built in a restricted vibrational space of the adsorbate-surface zeroth-order Hamiltonian. For D-Si, the Bixon-Jortner Hamiltonian can be solved by exact diagonalization, serving as a benchmark, whereas for H-Si, an iterative scheme based on the recursive residue generation method is applied, with excellent convergence properties. We found that the lifetimes obtained with perturbation theory, albeit having almost the same order of magnitude-a few hundred fs for D-Si and a couple of ps for H-Si-, are strongly dependent on the discretized numerical representation of the bath spectral density. On the other hand, the Bixon-Jortner model is free of such numerical deficiencies, therefore providing better estimates of vibrational relaxation rates, at a very low computational cost. The results obtained with this model clearly show a net exponential decay of the time-dependent survival probability for the H-Si initial vibrational state, allowing an easy extraction of the bending mode "lifetime." This is in contrast with the D-Si system, whose survival probability exhibits a non-monotonic decay, making it difficult to define such a lifetime. This different behavior of the vibrational decay is rationalized in terms of the power spectrum of the adsorbate-surface system. In the case of D-Si, it consists of several, non-uniformly distributed peaks around the bending mode frequency, whereas the H-Si spectrum exhibits a single Lorentzian lineshape, whose width corresponds to the calculated lifetime. The present work gives some insight into mechanisms of vibration-phonon coupling at surfaces. It also serves as a benchmark for multidimensional system-bath quantum dynamics, for comparison with approximate schemes such as reduced, open-system density matrix theory (where the bath is traced out and a Liouville-von Neumann equation is solved) or approximate wavefunction methods to solve the combined system-bath Schrödinger equation.

Comparing thermal wave function methods for multi-configuration time-dependent Hartree simulations.

We compare two methods for creating stochastic temperature wave functions that can be used for Multi-Configuration Time-Dependent Hartree (MCTDH) simulations. In the first method, the MCTDH coefficients are chosen randomly, while the other method uses a single Hartree product of random single-particle functions (SPFs). We find that using random SPFs dramatically improves convergence for a model system for surface sticking.

Electron correlation dynamics in atoms and molecules.

In this paper, we present quantum dynamical calculations on electron correlation dynamics in atoms and molecules using explicitly time-dependent ab initio configuration interaction theory. The goals are (i) to show that in which cases it is possible to switch off the electronic correlation by ultrashort laser pulses, and (ii) to understand the temporal evolution and the time scale on which it reappears. We characterize the appearance of correlation through electron-electron scattering when starting from an uncorrelated state, and we identify pathways for the preparation of a Hartree-Fock state from the correlated, true ground state. Exemplary results for noble gases, alkaline earth elements, and selected molecules are provided. For Mg we show that the uncorrelated state can be prepared using a shaped ultrashort laser pulse.

Concept of a single temperature for highly nonequilibrium laser-induced hydrogen desorption from a ruthenium surface.

Laser-induced condensed phase reactions are often interpreted as nonequilibrium phenomena that go beyond conventional thermodynamics. Here, we show by Langevin dynamics and for the example of femtosecond-laser desorption of hydrogen from a ruthenium surface that light adsorbates thermalize rapidly due to ultrafast energy redistribution after laser excitation. Despite the complex reaction mechanism involving hot electrons in the surface region, all desorption product properties are characterized by equilibrium distributions associated with a single, unique temperature. This represents an example of ultrahot chemistry on the subpicosecond time scale.

Following excited-state chemical shifts in molecular ultrafast x-ray photoelectron spectroscopy.

The conversion of photon energy into other energetic forms in molecules is accompanied by charge moving on ultrafast timescales. We directly observe the charge motion at a specific site in an electronically excited molecule using time-resolved x-ray photoelectron spectroscopy (TR-XPS). We extend the concept of static chemical shift from conventional XPS by the excited-state chemical shift (ESCS), which is connected to the charge in the framework of a potential model. This allows us to invert TR-XPS spectra to the dynamic charge at a specific atom. We demonstrate the power of TR-XPS by using sulphur 2p-core-electron-emission probing to study the UV-excited dynamics of 2-thiouracil. The method allows us to discover that a major part of the population relaxes to the molecular ground state within 220-250 fs. In addition, a 250-fs oscillation, visible in the kinetic energy of the TR-XPS, reveals a coherent exchange of population among electronic states.

Microscopic model of the optical absorption of carbon nanotubes functionalized with molecular spiropyran photoswitches.

The adsorption of molecules to the surface of carbon nanostructures opens a new field of hybrid systems with distinct and controllable properties. We present a microscopic study of the optical absorption in carbon nanotubes functionalized with molecular spiropyran photoswitches. The switching process induces a change in the dipole moment leading to a significant coupling to the charge carriers in the nanotube. As a result, the absorption spectra of functionalized tubes reveal a considerable redshift of transition energies depending on the switching state of the spiropyran molecule. Our results suggest that carbon nanotubes are excellent substrates for the optical readout of spiropyran-based molecular switches. The gained insights can be applied to other noncovalently functionalized one-dimensional nanostructures in an externally induced dipole field.

STM-switching of organic molecules on semiconductor surfaces: an above threshold density matrix model for 1,5 cyclooctadiene on Si(100).

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.

Femtosecond stimulated Raman spectroscopy of flavin after optical excitation.

In blue-light photoreceptors using flavin (BLUF), the signaling state is formed already within several 100 ps after illumination, with only small changes of the absorption spectrum. The accompanying structural evolution can, in principle, be monitored by femtosecond stimulated Raman spectroscopy (FSRS). The method is used here to characterize the excited-state properties of riboflavin and flavin adenine dinucleotide in polar solvents. Raman modes are observed in the range 90-1800 cm(-1) for the electronic ground state S(0) and upon excitation to the S(1) state, and modes >1000 cm(-1) of both states are assigned with the help of quantum-chemical calculations. Line shapes are shown to depend sensitively on resonance conditions. They are affected by wavepacket motion in any of the participating electronic states, resulting in complex amplitude modulation of the stimulated Raman spectra. Wavepackets in S(1) can be marked, and thus isolated, by stimulated-emission pumping with the picosecond Raman pulses. Excited-state absorption spectra are obtained from a quantitative comparison of broadband transient fluorescence and absorption. In this way, the resonance conditions for FSRS are determined. Early differences of the emission spectrum depend on excess vibrational energy, and solvation is seen as dynamic Stokes shift of the emission band. The nπ* state is evidenced only through changes of emission oscillator strength during solvation. S(1) quenching by adenine is seen with all methods in terms of dynamics, not by spectral intermediates.

Time-dependent approach to electronically excited states of molecules with the multiconfiguration time-dependent Hartree-Fock method.

In this paper the authors show how the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method can be used for the calculation of electronic properties of molecules associated with the population of excited states. In contrast to other methods for correlated electron dynamics, such as configuration interaction, MCTDHF does not rely on a solution of the electronic Schrodinger equation prior to the propagation. The authors apply this approach to the calculation of vertical excitation energies, transition dipole moments, and oscillator strengths for two test molecules, lithium hydride and methane.

The multiconfiguration time-dependent Hartree-Fock method for quantum chemical calculations.

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.

Quantum theoretical study of electron solvation dynamics in ice layers on a Cu(111) surface.

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.

Direct and indirect DIET and DIMET from semiconductor and metal surfaces: what can we learn from 'toy models'?

Desorption induced by electronic transitions (DIET) and its variant DIMET (M = 'Multiple'), are among the simplest possible "reactions" of ad-species involving ultra-short lived electronically excited states at surfaces. The non-adiabatic bond-cleavage can be enforced, for example, with laser irradiation or with electrons or holes emitted from the tip of a scanning tunnelling microscope (STM). The transient creation of excited intermediates can proceed directly (localised to the adsorbate-substrate complex), or indirectly (i.e., through the substrate). To understand the basic processes, simple one-mode two-state "toy models" such as the Menzel-Gomer-Redhead (MGR) or the Antoniewicz scenarios have proven very useful in the past. We adopt and extend MGR- and Antoniewicz-type models together with numerically exact open-system density matrix theory to address a few actual problems/experiments in DI(M)ET: (1) Direct, laser-induced desorption of H(D) from Si(100) surfaces which has been realised in the continuous-wave DIET regime only recently [T. Vondrak and X.-Y. Zhu, Phys. Rev. Lett., 1999, 82, 1967], is studied and compared to so-far hypothetical femtosecond laser desorption. The possibility of controlling the reaction by shaping the laser pulses is addressed. (2) For the same system, temperature effects are studied for electron- or hole-stimulated desorption with an STM [T. C. Shen, C. Wang, G. C. Abeln, T. R. Tucker, J. W. Lyding, Ph. Avouris and R. E. Walkup, Science, 1995, 268, 1590; C. Thirstrup, M. Sakurai, T. Nakayama and K. Stokbro, Surf. Sci., 1999, 424, L329]. A modified version of Gadzuk's "sudden transition and averaging" approach is adopted which accounts for temperature dependent excited state lifetimes. (3) For photodesorption of NO from Pt(111), based on quantum dynamical simulations possible experimental tests involving static electric fields are suggested to address the relevance of the recently challenged [F. M. Zimmermann, Surf. Sci., 1997. 390, 174], "negative ion resonance" model of the Antoniewicz type.