Etienne Gindensperger

Short-time dynamics through conical intersections in macrosystems. II. Applications

We present several numerical applications based upon the effective-mode formulation for the short-time dynamics through conical intersections in macrosystems, as detailed in the preceding paper and first proposed by Cederbaum et al. [Phys. Rev. Lett. 94, 113003 (2005)]. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective environmental modes are needed-together with the systems modes-to accurately calculate the low resolution spectra and the short-time dynamics of the entire macrosystem. For the systems discussed here, results are compared to those of a full quantum wave-packet propagation. Some rules are extracted to provide general tendencies; these rules allow one to understand and predict the dynamical properties in more general situations where the exact quantum dynamics of the macrosystem is out of reach.

Mechanism of visible-light photoisomerization of a rhenium(I) carbonyl-diimine complex

The mechanism of photoisomerization of a Re(I) carbonyl-diimine complex under visible-light irradiation is deciphered by means of ab initio calculations. By highlighting the key role of triplet states as well as spin-orbit and vibronic couplings, we provide a clear picture of this complicated multi-step process.

Hierarchy of effective modes for the dynamics through conical intersections in macrosystems

An extension of the effective-mode theory for the short-time dynamics through conical intersections in macrosystems [L. S. Cederbaum et al., Phys. Rev. Lett. 94, 113003 (2005)] is proposed. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective modes are needed-together with the systems modes-to accurately calculate low resolution spectra and the short-time dynamics of the entire macrosystem. Here, the authors propose an iterative scheme to construct a hierarchy of additional triplets of effective modes. This naturally extends the effective-mode formulation. By taking into account more and more triplets, the dynamics are accurately predicted for longer and longer times, and more resolved spectra can be calculated. Numerical examples are presented, computed using various numbers of additional effective modes.

Directionality of Double-Bond Photoisomerization Dynamics Induced by a Single Stereogenic Center

In light-driven single-molecule rotary motors, the photoisomerization of a double bond converts light energy into the rotation of a moiety (the rotor) with respect to another (the stator). However, at the level of a molecular population, an effective rotary motion can only be achieved if a large majority of the rotors rotate in the same, specific direction. Here we present a quantitative investigation of the directionality (clockwise vs counterclockwise) induced by a single stereogenic center placed in allylic position with respect to the reactive double bond of a model of the biomimetic indanylidene-pyrrolinium framework. By computing ensembles of nonadiabatic trajectories at 300 K, we predict that the photoisomerization is >70% unidirectional for the Z → E and E → Z conversions. Most importantly, we show that such directionality, resulting from the asymmetry of the excited state force field, can still be observed in the presence of a small (ca. 2°) pretwist or helicity of the reactive double bond. This questions the validity of the conjecture that a significant double-bond pretwist (e.g., >10°) in the ground state equilibrium structure of synthetic or natural rotary motors would be required for unidirectional motion.

An effective Hamiltonian for the short-time dynamics at a conical intersection

The construction of an effective Hamiltonian which accurately accounts for the short-time dynamics at a conical intersection in high-dimensional systems [Phys. Rev. Lett. 94, 113003 (2005)] is discussed and extended to include topological considerations. A set of three topology-adapted, orthogonal coordinates is introduced, two of which span the branching space at the conical intersection. The new coordinates are at the same time characteristic dynamical and topological coordinates. This description is compared with the characteristic (g,h,s) vectors of the adiabatic representation. The dynamics induced by the effective Hamiltonian is discussed for a 22-dimensional model system related to the D1–D0 conical intersection in the butatriene cation.

Exploring the Mechanism of Ultrafast Intersystem Crossing in Rhenium(I) Carbonyl Bipyridine Halide Complexes: Key Vibrational Modes and Spin–Vibronic Quantum Dynamics

The mechanism of ultrafast intersystem crossing in rhenium(I) carbonyl bipyridine halide complexes Re(X)(CO)3(bpy) (X = Cl, Br, I) is studied by exploring the structural deformations when going from Franck-Condon (FC) to critical geometries in the low-lying singlet and triplet excited states and by selecting the key vibrational modes. The luminescent decay observed in [Re(Br)(CO)3(bpy)] is investigated by means of wavepacket propagations based on the multiconfiguration time-dependent Hartree (MCTDH) method. The dominant coordinates underlying the nonradiative decay process are extracted from minima, minimum energy seam of crossing (MESX) and minimum energy conical intersection (MECI) geometries obtained by the seam model function (SMF)/single-component artificial force induced reaction (SC-AFIR) approach. By choosing the normal modes used in MCTDH from the MECI and MESX geometries, not only the degenerate energy points but also the low-energy-gap regions are included. For this purpose a careful vibrational analysis is performed at each critical geometry and analyzed under the light of the pertinent nonadiabatic coupling terms obtained from the linear vibronic coupling (LVC) model augmented by spin-orbit coupling (SOC) in the electronic diabatic representation.

Quantum dynamics in macrosystems with several coupled electronic states : Hierarchy of effective hamiltonians

We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multistate conical intersections. The general situation of an arbitrary number of states and arbitrary number of nuclear degrees of freedom (modes) is considered. The macrosystem is decomposed into a system part carrying a few, strongly coupled modes and an environment, comprising the vast number of remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment is constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. By considering the systems Hamiltonian along with a few members of the hierarchy, it is shown mathematically by a moment analysis that the quantum dynamics of the entire macrosystem can be numerically exactly computed on a given time scale. The time scale wanted defines the number of effective Hamiltonians to be included. The contribution of the environment to the quantum dynamics of the macrosystem translates into a sequential coupling of effective modes. The wave function of the macrosystem is known in the full space of modes, allowing for the evaluation of observables such as the time-dependent individual excitation along modes of interest as well as spectra and electronic-population dynamics.

Ultrafast excited-state dynamics at a conical intersection: the role of environmental effects

We review some of the concepts which we have recently developed in order to describe the influence of an environment on the ultrafast dynamical events at a conical intersection (CI). In particular, we propose a description in terms of effective environmental modes, which accurately account for the short-time dynamics at the conical intersection. We address the construction of these modes (i) for intramolecular situations, where the modes in question result from an orthogonal coordinate transformation for the overall N-mode system, and (ii) for solute–solvent interactions in polar solvents, where a description in terms of a Marcus-like solvent coordinate is obtained. In both cases, the dynamical process is determined by the combined evolution of the internal molecular modes and the environmental coordinates, on an ultrafast timescale. We discuss examples related to an intramolecular multi-mode situation in pyrazine, and the polar solvation dynamics for protonated Schiff bases.

Ultrafast Excited-State Decays in [Re(CO)3(N,N)(L)]n+: Nonadiabatic Quantum Dynamics

The ultrafast luminescent decay of [Re(CO)3(phen)(im)]+, representative of Re(I) carbonyl α-diimine photosensitizers, is investigated by means of wavepacket propagations based on the multiconfiguration time-dependent Hartree (MCTDH) method. On the basis of electronic structure data obtained at the time-dependent density functional theory (TD-DFT) level, the luminescence decay is simulated by solving a 14 electronic states multimode problem including both vibronic and spin-orbit coupling (SOC) up to 15 vibrational modes. A careful analysis of the results provides the key features of the mechanism of the intersystem crossing (ISC) in this complex. The intermediate state, detected by means of fs - ps time-resolved spectroscopies, is assigned to the T3 state corresponding to the triplet intraligand (3IL) transition localized on the phen ligand. By switching off/on SOC and vibronic coupling in the model it is shown that efficient population transfer occurs from the optically active metal-to-ligand-charge-transfer1,3MLCT states to T3 and to the lowest long-lived phosphorescent 3MLCT (T1) state. The early ultrafast SOC-driven decay followed by a T3/T1 equilibration controlled by vibronic coupling underlies the photoluminescent properties of [Re(CO)3(phen)(im)]+. The impact of the axial and N,N ligands on the photophysics of this class of Re(I) complexes is further rationalized on the basis of their calculated optical properties. The relative position of the 3IL and upper 3MLCT states with respect to the optically active singlet state is influenced by the N,N ligand and affects the relaxation dynamics.

Spin-Vibronic Mechanism for Intersystem Crossing

Intersystem crossing (ISC), formally forbidden within nonrelativistic quantum theory, is the mechanism by which a molecule changes its spin state. It plays an important role in the excited state decay dynamics of many molecular systems and not just those containing heavy elements. In the simplest case, ISC is driven by direct spin-orbit coupling between two states of different multiplicities. This coupling is usually assumed to remain unchanged by vibrational motion. It is also often presumed that spin-allowed radiationless transitions, i.e. internal conversion, and the nonadiabatic coupling that drives them, can be considered separately from ISC and spin-orbit coupling owing to the vastly different time scales upon which these processes are assumed to occur. However, these assumptions are too restrictive. Indeed, the strong mixing brought about by the simultaneous presence of nonadiabatic and spin-orbit coupling means that often the spin, electronic, and vibrational dynamics cannot be described independently. Instead of considering a simple ladder of states, as depicted in a Jablonski diagram, one must consider the more complicated spin-vibronic levels. Despite the basic ideas being outlined in the 1960s, it is only with the advent of high-level theory and femtosecond spectroscopy that the importance of the spin-vibronic mechanism for ISC in both fundamental as well as applied research fields has been revealed with significant impact across chemistry, physics, and biology. In this review article, we present the theory and fundamental principles of the spin-vibronic mechanism for ISC. This is followed by empirical rules to estimate the rate of ISC within this regime. The most recent developments in experimental techniques, theoretical methods, and models for the spin-vibronic mechanism are discussed. These concepts are subsequently illustrated with examples, including the ISC mechanisms in transition metal complexes, small organic molecules, and organic chromophores.