Intersystem crossing (ISC), formally forbidden within nonrelativistic 9 quantum theory, is the mechanism by which a molecule changes its spin state. It plays an 10 important role in the excited state decay dynamics of many molecular systems and not 11 just those containing heavy elements. In the simplest case, ISC is driven by direct spin− 12 orbit coupling between two states of different multiplicities. This coupling is usually 13 assumed to remain unchanged by vibrational motion. It is also often presumed that spin-14 allowed radiationless transitions, i.e. internal conversion, and the nonadiabatic coupling 15 that drives them, can be considered separately from ISC and spin−orbit coupling owing 16 to the vastly different time scales upon which these processes are assumed to occur. 17 However, these assumptions are too restrictive. Indeed, the strong mixing brought about 18 by the simultaneous presence of nonadiabatic and spin−orbit coupling means that often 19 the spin, electronic, and vibrational dynamics cannot be described independently. Instead of considering a simple ladder of states, 20 as depicted in a Jablonski diagram, one must consider the more complicated spin-vibronic levels. Despite the basic ideas being 21 outlined in the 1960s, it is only with the advent of high-level theory and femtosecond spectroscopy that the importance of the 22 45 3.1.2. Time-Dependent Methods I 46 3.1.3. Including Temperature J 47 3.2. Quantum Dynamics Methods J 48 3.2.1. Multi-Configurational Time-Dependent 49 Hartree Approach J 50 3.2.2. Including Temperature K 51 3.2.3. Spin-Vibronic Model Hamiltonian L 52 3.3. On-the-f ly Dynamics Methods M 53 3.3.1. Trajectory Surface Hopping M 54 3.3.2. Methods Based upon Gaussian Wave-55

The short-time dynamics through a conical intersection of a macrosystem with a vast number of nuclear degrees of freedom (modes) is investigated. For convenience, the macrosystem is decomposed into a system carrying a few modes and a "bath." By transforming the bath modes to new ones, it is shown that only three effective bath modes contribute to the conical intersection. They govern--together with the system's modes--the short-time dynamics of the macrosystem. The remaining bath modes do not directly couple the electronic states and become relevant at longer times. An extensive numerical example is presented.

Ultrafast intersystem crossing (ISC) processes coupled to nuclear relaxation and solvation dynamics play a central role in the photophysics and photochemistry of a wide range of transition metal complexes. These phenomena occurring within a few hundred femtoseconds are investigated experimentally by ultrafast picosecond and femtosecond transient absorption or luminescence spectroscopies, and optical laser pump-X-ray probe techniques using picosecond and femtosecond X-ray pulses. The interpretation of ultrafast structural changes, time-resolved spectra, quantum yields, and time scales of elementary processes or transient lifetimes needs robust theoretical tools combining state-of-the-art quantum chemistry and developments in quantum dynamics for solving the electronic and nuclear problems. Multimode molecular dynamics beyond the Born-Oppenheimer approximation has been successfully applied to many small polyatomic systems. Its application to large molecules containing a transition metal atom is still a challenge because of the nuclear dimensionality of the problem, the high density of electronic excited states, and the spin-orbit coupling effects. Rhenium(I) α-diimine carbonyl complexes, [Re(L)(CO)3(N,N)](n+) are thermally and photochemically robust and highly flexible synthetically. Structural variations of the N,N and L ligands affect the spectroscopy, the photophysics, and the photochemistry of these chromophores easily incorporated into a complex environment. Visible light absorption opens the route to a wide range of applications such as sensors, probes, or emissive labels for imaging biomolecules. Halide complexes [Re(X)(CO)3(bpy)] (X = Cl, Br, or I; bpy = 2,2'-bipyridine) exhibit complex electronic structure and large spin-orbit effects that do not correlate with the heavy atom effects. Indeed, the (1)MLCT → (3)MLCT intersystem crossing (ISC) kinetics is slower than in [Ru(bpy)3](2+) or [Fe(bpy)3](2+) despite the presence of a third-row transition metal. Counterintuitively, singlet excited-state lifetime increases on going from Cl (85 fs) to Br (128 fs) and to I (152 fs). Moreover, correlation between the Re-X stretching mode and the rate of ISC is observed. In this Account, we emphasize on the role of spin-vibronic coupling on the mechanism of ultrafast ISC put in evidence in [Re(Br)(CO)3(bpy)]. For this purpose, we have developed a model Hamiltonian for solving an 11 electronic excited states multimode problem including vibronic and SO coupling within the linear vibronic coupling (LVC) approximation and the assumption of harmonic potentials. The presence of a central metal atom coupled to rigid ligands, such as α-diimine, ensures nuclear motion of small amplitudes and a priori justifies the use of the LVC model. The simulation of the ultrafast dynamics by wavepacket propagations using the multiconfiguration time-dependent Hartree (MCTDH) method is based on density functional theory (DFT), and its time-dependent extension to excited states (TD-DFT) electronic structure data. We believe that the interplay be...

A novel time-dependent hybrid quantum/classical propagation scheme based on Bohmian quantum trajectories is presented. The quantum subsystem is described by a wave packet depending on the quantum variables x and, via the total potential energy of the system, parametrically on the classical trajectories X(t). The wave packet is used to calculate de Broglie-Bohm quantum trajectories x(t) which are used to calculate the force acting on the classical variables. Quantum corrections of the classical equation of motion are also included. The method is applied to a simple case of two coupled oscillators. Comparison between exact quantum and approximate results demonstrates that these MQCB ͑Mixed Quantum/Classical Bohmian͒ trajectories provide a good description of the energy exchange between the two oscillators.

Ultrafast luminescence decay and intersystem crossing processes through the seven low-lying singlet and triplet excited states of [Re (X)(CO)3(bpy)] (X = Cl, Br, I; bpy = 2,2'-bipyridine) are interpreted on the basis of time-dependent density functional theory (TD-DFT) electronic structure calculations performed in acetonitrile and including spin-orbit coupling (SOC) effects within the zeroth-order approximation. It is shown that the red shift of the lowest part of the spectra by SOC increases from X = Cl (0.06 eV) to X = Br (0.09 eV) and X = I (0.18 eV) due to the participation of the triplet sublevels to the absorption. The six lowest "spin-orbit" states remain largely triplet in character and the maximum of absorption is not drastically affected by SOC. While the energy of the excited states is affected by SOC, the character of these states is not significantly modified: SOC mixes states of the same nature, namely metal-to-ligand-charge-transfer/halide-to-ligand-charge-transfer (MLCT/XLCT). This mixing can be large, however, as illustrated by the S1/T2 (a(1)A″/a(3)A') mixing that amounts to about 50:50 within the series Cl > Br > I. On the basis of the optimized structures of the six lowest excited states an interpretation of the emission signals detected by ultrafast luminescence spectroscopy is proposed. It is shown that whereas the experimental Stokes shift of 6000 cm(-1) observed for the three complexes is well reproduced without SOC correction for the Cl and Br complexes, SOC effects have to be taken into account for the iodide complex. The early signal of ultrafast luminescence detected immediately after absorption at 400 nm to the S2 state, covering the 500-550 nm energy domain and characterized by a decay τ1 = 85 fs (X = Cl) and 128 fs (X = Br), is attributed to S2 calculated at 505 and 522 nm, respectively, and to some extend to T3 by SOC. The intermediate band observed at longer time-scale between 550 and 600 nm with emissive decay time τ2 = 340 fs (X = Cl) and 470 fs (X = Br) can be assigned to T2 calculated at 558 and 571 nm, respectively. The S1 state could also participate to this band by SOC. In both complexes the long-lived emission at 600-610 nm is attributed to the lowest T1 state calculated at 596 and 592 nm for the chloride and bromide complexes, respectively, and shifted to ∼610 nm by SOC. Important SOC effects characterize the luminescence decay of [Re (I)(CO)3(bpy)], the mechanism of which differs significantly of the one proposed for the two other complexes. The A' spin-orbit sublevel of T3 state calculated at 512 nm with an oscillator strength of 0.17 × 10(-1) participates to the first signal characterized by a rapid decay (τ1 = 152 fs) with a maximum at 525 nm. The intermediate band covering the 550-600 nm region with a decay time τ2 = 1180 fs is assigned to the "spin-orbit" S1 state calculated at 595 nm. The S2 absorbing state calculated at 577 nm could contribute to these two signals. According to the spin-orbit sublevels calculated for T1 and T2, both states contribute to the long-...

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.

The short-time dynamics through a conical intersection of a macrosystem comprising a large number of nuclear degrees of freedom (modes) is investigated. The macrosystem is decomposed into a "system" part carrying a limited number of modes, and an "environment" part. An orthogonal transformation in the environment's space is introduced, as a result of which a subset of three effective modes can be identified which couple directly to the electronic subsystem. Together with the system's modes, these govern the short-time dynamics of the overall macrosystem. The remaining environmental modes couple, in turn, to the effective modes and become relevant at longer times. In this paper, we present the derivation of the effective Hamiltonian, first introduced by Cederbaum et al. [Phys. Rev. Lett. 94, 113003 (2005)], and analyze its properties in some detail. Several special cases and topological aspects are discussed.

The lowest-lying spectral transitions in [ReX(CO)(3)(bpy)] (X = Cl, Br, I; bpy = 2,2'-bipyridine) complexes were calculated by means of spin-orbit time-dependent density functional theory (SO-TD-DFT) and spin-orbit multistate complete active space second-order perturbation theory (SO-MS-CASPT2). Computational results are compared with absorption spectra measured in different solvents and used to qualitatively explain the temperature dependence of the phosphorescence decay parameters that were measured for the whole series of complexes. Spin-orbit excited-state calculations interpret their electronic absorption spectra as arising from a bunch of spin mixed states with a singlet component of only 50-90% (depending on the halide), and attribute the phosphorescence decay to thermal population of spin-mixed states with a substantial singlet character.