Surface Hopping Dynamics on Vibronic Coupling Models.

The simulation of photoinduced non-adiabatic dynamics is of great relevance in many scientific disciplines, ranging from physics and materials science to chemistry and biology. Upon light irradiation, different relaxation processes take place in which electronic and nuclear motion are intimately coupled. These are best described by the time-dependent molecular Schrödinger equation, but its solution poses fundamental practical challenges to contemporary theoretical chemistry. Two widely used and complementary approaches to this problem are multiconfigurational time-dependent Hartree (MCTDH) and trajectory surface hopping (SH). MCTDH is an accurate fully quantum-mechanical technique but often is feasible only in reduced dimensionality, in combination with approximate vibronic coupling (VC) Hamiltonians, or both (i.e., reduced-dimensional VC potentials). In contrast, SH is a quantum-classical technique that neglects most nuclear quantum effects but allows nuclear dynamics in full dimensionality by calculating potential energy surfaces on the fly. If nuclear quantum effects do not play a central role and a linear VC (LVC) Hamiltonian is appropriate-e.g., for stiff molecules that generally keep their conformation in the excited state-then it seems advantageous to combine the efficient LVC and SH techniques. In this Account, we describe how surface hopping based on an LVC Hamiltonian (SH/LVC)-as recently implemented in the SHARC surface hopping package-can provide an economical and automated approach to simulate non-adiabatic dynamics. First, we illustrate the potential of SH/LVC in a number of showcases, including intersystem crossing in SO2, intra-Rydberg dynamics in acetone, and several photophysical studies on large transition-metal complexes, which would be much more demanding or impossible to perform with other methods. While all of the applications provide very useful insights into light-induced phenomena, they also hint at difficulties faced by the SH/LVC methodology that need to be addressed in the future. Second, we contend that the SH/LVC approach can be useful to benchmark SH itself. By the use of the same (LVC) potentials as MCTDH calculations have employed for decades and by relying on the efficiency of SH/LVC, it is possible to directly compare multiple SH test calculations with a MCTDH reference and ponder the accuracy of various correction algorithms behind the SH methodology, such as decoherence corrections or momentum rescaling schemes. Third, we demonstrate how the efficiency of SH/LVC can also be exploited to identify essential nuclear and electronic degrees of freedom to be employed in more accurate MCTDH calculations. Lastly, we show that SH/LVC is able to advance the development of SH protocols that can describe nuclear dynamics including explicit laser fields-a very challenging endeavor for trajectory-based schemes. To end, this Account compiles the typical costs of contemporary SH simulations, evidencing the great advantages of using parametrized potentials. The LVC model is a sleeping beauty that, kissed by SH, is fueling the field of excited-state molecular dynamics. We hope that this Account will stimulate future research in this direction, leveraging the advantages of the SH/VC schemes to larger extents and extending their applicability to uncharted territories.

Excited-State Dynamics of [Ru(S-Sbpy)(bpy)2]2+ to Form Long-Lived Localized Triplet States.

The novel photosensitizer [Ru(S-Sbpy)(bpy)2]2+ harbors two distinct sets of excited states in the UV/Vis region of the absorption spectrum located on either bpy or S-Sbpy ligands. Here, we address the question of whether following excitation into these two types of states could lead to the formation of different long-lived excited states from where energy transfer to a reactive species could occur. Femtosecond transient absorption spectroscopy identifies the formation of the final state within 80 fs for both excitation wavelengths. The recorded spectra hint at very similar dynamics following excitation toward either the parent or sulfur-decorated bpy ligands, indicating ultrafast interconversion into a unique excited-state species regardless of the initial state. Non-adiabatic surface hopping dynamics simulations show that ultrafast spin-orbit-mediated mixing of the states within less than 50 fs strongly increases the localization of the excited electron at the S-Sbpy ligand. Extensive structural relaxation within this sulfurated ligand is possible, via S-S bond cleavage that results in triplet state energies that are lower than those in the analogue [Ru(bpy)3]2+. This structural relaxation upon localization of the charge on S-Sbpy is found to be the reason for the formation of a single long-lived species independent of the excitation wavelength.

Validating fewest-switches surface hopping in the presence of laser fields.

The capability of fewest-switches surface hopping (FSSH) to describe non-adiabatic dynamics under explicit excitation with external fields is evaluated. Different FSSH parameters are benchmarked against multi-configurational time dependent Hartree (MCTDH) reference calculations using SO2 and 2-thiocytosine as model, yet realistic, molecular systems. Qualitatively, FSSH is able to reproduce the trends in the MCTDH dynamics with (also without) an explicit external field; however, no set of FSSH parameters is ideal. The adequate treatment of the overcoherence in FSSH is revealed as the driving factor to improve the description of the excitation process with respect to the MCTDH reference. Here, two corrections were tested: the augmented-FSSH (AFSSH) correction and the energy-based decoherence correction. A dependence on the employed basis is detected in AFSSH, performing better when spin-orbit and external laser field couplings are treated as off-diagonal elements instead of projecting them onto the diagonal of the Hamilton operator. In the presence of an electric field, the excited state dynamics was found to depend strongly on the vector used to rescale the kinetic energy along after a transition between surfaces. For SO2, recurrence of the excited wave packet throughout the duration of the applied laser pulse is observed for laser pulses (>100 fs), resulting in additional interferences missed by FSSH and only visible in variational multi-configurational Gaussian when utilizing a large number of Gaussian basis functions. This feature vanishes when going toward larger molecules, such as 2-thiocytosine, where this effect is barely visible in a laser pulse 200 fs long.

Electrochemical and Photophysical Properties of Ruthenium(II) Complexes Equipped with Sulfurated Bipyridine Ligands.

The development of new solar-to-fuel scenarios is of great importance, but the construction of molecular systems that convert sunlight into chemical energy represents a challenge. One specific issue is that the molecular systems have to be able to accumulate redox equivalents to mediate the photodriven transformation of relevant small molecules, which mostly involves the orchestrated transfer of multiple electrons and protons. Disulfide/dithiol interconversions are prominent 2e-/2H+ couples and can play an important role for redox control and charge storage. With this background in mind, a new photosensitizer [Ru(S-Sbpy)(bpy)2]2+ (12+) equipped with a disulfide functionalized bpy ligand (S-Sbpy, bpy = 2,2'-bipyridine) was synthesized and has been comprehensively studied, including structural characterization by X-ray diffraction. In-depth electrochemical studies show that the S-Sbpy ligand in 12+ can be reduced twice at moderate potentials (around -1.1 V vs Fc+/0), and simulation of the cyclic voltammetry (CV) traces revealed potential inversion (E2 > E1) and allowed to derive kinetic parameters for the sequential electron-transfer processes. However, reduction at room temperature also triggers the ejection of one sulfur atom from 12+, leading to the formation of [Ru(Sbpy)(bpy)2]2+(22+). This chemical reaction can be suppressed by decreasing the temperature from 298 to 248 K. Compared to the archetypical photosensitizer [Ru(bpy)3]2+, 12+ features an additional low energy optical excitation in the MLCT region, originating from charge transfer from the metal center to the S-Sbpy ligand (aka MSCT) according to time-dependent density functional theory (TD-DFT) calculations. Analysis of the excited states of 12+ on the basis of ground-state Wigner sampling and using charge-transfer descriptors has shown that bpy modification with a peripheral disulfide moiety leads to an energy splitting between charge-transfer excitations to the S-Sbpy and the bpy ligands, offering the possibility of selective charge transfer from the metal to either type of ligands. Compound 12+ is photostable and shows an emission from a 3MLCT state in deoxygenated acetonitrile with a lifetime of 109 ns. This work demonstrates a rationally designed system that enables future studies of photoinduced multielectron, multiproton PCET chemistry.

From Surface Hopping to Quantum Dynamics and Back. Finding Essential Electronic and Nuclear Degrees of Freedom and Optimal Surface Hopping Parameters.

We report an efficient iterative procedure that exploits surface-hopping trajectory methods and quantum dynamics to achieve two complementary purposes: to identify the minimum dimensionality of a molecular Hamiltonian in terms of electronic and nuclear degrees of freedom to study radiationless relaxation mechanisms as well as to provide a reference quantum dynamical calculation that allows assessing of the validity of surface-hopping parameters. This double goal is achieved by a feedback loop between surface hopping and MCTDH calculations based on potential energy surfaces parametrized with a linear vibronic coupling method. Initially, a surface hopping calculation in full dimensionality with a chosen set of parameters is performed, and it is repeated, gradually reducing its dimensionality until divergence with the initial calculation is observed or the system is small enough to be treated quantum dynamically. A comparison between the quantum dynamics and surface hopping simulations dictates the validity of the surface hopping parameters. Using these new parameters, the reduction loop is started again, until convergence. As an example, this strategy is applied to simulate the ultrafast intersystem crossing dynamics of [PtBr6]2- in solution. The 15-dimensional space initially including 200 electronic states is reduced to a 9-dimensional problem with 76 electronic states, without a considerable loss of accuracy.

Additive polarizabilities of halides in ionic liquids and organic solvents.

The design of room-temperature ionic liquids featuring high refractive indices is desirable for a number of applications. Introducing strongly polarizable (poly)halides as anions is a promising route to increase the polarizability of an ionic liquid and thus the refractive index. Based on the experimental refractive indices and mass densities of imidazolium ionic liquids, additive atomic polarizabilities and volumes for chlorine, bromine, and iodine are determined. In addition, atomic polarizabilities and volumes for halide atoms in organic solvents are calculated and compared to ionic liquids. We find that especially iodine behaves differently in anions than in neutral or cationic species. A quantum-mechanical calculation of molecular and atomic polarizabilities complements and enhances the designed regression analysis. The gained insights into halide polarizability and volume are deployed to predict the refractive index of arbitrary ionic liquids.

Taming Disulfide Bonds with Laser Fields. Nonadiabatic Surface-Hopping Simulations in a Ruthenium Complex.

Laser control of chemical reactions is a challenging field of research. In particular, the theoretical description of coupled electronic and nuclear motion in the presence of laser fields is not a trivial task and simulations are mostly restricted to small systems or molecules treated within reduced dimensionality. Here, we demonstrate how the excited state dynamics of [Ru(S-Sbpy)(bpy)2]2+ can be controlled using explicit laser fields in the context of fewest-switches surface hopping. In particular, the transient properties along the excited state dynamics leading to population of the T1 minimum energy structure are exploited to define simple laser fields capable of slowing and even completely stopping the onset of S-S bond dissociation. The use of a linear vibronic coupling model to parametrize the potential energy surfaces showcases the strength of the surface-hopping methodology to study systems including explicit laser fields using many nuclear degrees of freedom and a large amount of close-lying electronic excited states.

Ultrafast imaging of terahertz electric waveforms using quantum dots.

Microscopic electric fields govern the majority of elementary excitations in condensed matter and drive electronics at frequencies approaching the Terahertz (THz) regime. However, only few imaging schemes are able to resolve sub-wavelength fields in the THz range, such as scanning-probe techniques, electro-optic sampling, and ultrafast electron microscopy. Still, intrinsic constraints on sample geometry, acquisition speed and field strength limit their applicability. Here, we harness the quantum-confined Stark-effect to encode ultrafast electric near-fields into colloidal quantum dot luminescence. Our approach, termed Quantum-probe Field Microscopy (QFIM), combines far-field imaging of visible photons with phase-resolved sampling of electric waveforms. By capturing ultrafast movies, we spatio-temporally resolve a Terahertz resonance inside a bowtie antenna and unveil the propagation of a Terahertz waveguide excitation deeply in the sub-wavelength regime. The demonstrated QFIM approach is compatible with strong-field excitation and sub-micrometer resolution-introducing a direct route towards ultrafast field imaging of complex nanodevices in-operando.

Vibrational Sampling and Solvent Effects on the Electronic Structure of the Absorption Spectrum of 2-Nitronaphthalene.

The influence of vibrational motion on electronic excited state properties is investigated for the organic chromophore 2-nitronaphtalene in methanol. Specifically, the performance of two vibrational sampling techniques - Wigner sampling and sampling from an ab initio molecular dynamics trajectory- is assessed, in combination with implicit and explicit solvent models. The effects of the different sampling/solvent combinations on the energy and electronic character of the absorption bands are analyzed in terms of charge transfer and exciton size, computed from the electronic transition density. The absorption spectra obtained using sampling techniques and its underlying properties are compared to those of the electronic excited states calculated at the Franck-Condon equilibrium geometry. It is found that the absorption bands of the vibrational ensembles are red-shifted compared to the Franck-Condon bright states, and this red-shift scales with the displacement from the equilibrium geometry. Such displacements are found larger and better described when using ensembles from the harmonic Wigner distribution than snapshots from the molecular dynamics trajectory. Particularly relevant is the torsional motion of the nitro group that quenches the charge transfer character of some of the absorption bands. This motion, however, is better described in the molecular dynamics trajectory. Thus, none of the vibrational sampling approaches can satisfactorily capture all important aspects of the nuclear motion. The inclusion of solvent also red-shifts the absorption bands with respect to the gas phase. This red-shift scales with the charge-transfer character of the bands and is found larger for the implicit than for the explicit solvent model. The advantages and drawbacks of the different sampling and solvent models are discussed to guide future research on the calculation of UV-vis spectra of nitroaromatic compounds.