In this Colloquium, the wave-function-based multiconfigurational time-dependent Hartree approaches to the dynamics of indistinguishable particles (MCTDH-F for fermions and MCTDH-B for bosons) are reviewed. MCTDH-B and MCTDH-F or, together, MCTDH-X are methods for describing correlated quantum systems of identical particles by solving the time-dependent Schrödinger equation from first principles. MCTDH-X is used to accurately model the dynamics of real-world quantum many-body systems in atomic, molecular, and optical physics. The key feature of these approaches is the time dependence and optimization of the single-particle states employed for the construction of a many-body basis set, which yields nonlinear working equations. The historical developments that have led to the formulation of the MCTDH-X method and motivate the necessity for wave-function-based approaches are briefly described. The derivation of the unified MCTDH-F and MCTDH-B equations of motion for complete and also specific restricted configuration spaces are sketched. The strengths and limitations of the MCTDH-X approach are assessed via benchmarks against an exactly solvable model and via convergence checks. Applications to some instructive and experimentally realized quantum many-body systems are highlighted: the dynamics of atoms in Bose-Einstein condensates in magneto-optical and optical traps and of electrons in atoms and molecules. The current development and frontiers in the field of MCTDH-X are discussed: theories and numerical methods for indistinguishable particles, for mixtures of multiple species of indistinguishable particles, the inclusion of nuclear motion for the nonadiabatic dynamics of atomic and molecular systems, as well as the multilayer and second-quantized-representation approaches, and the orbital-adaptive time-dependent coupled-cluster theory.

The nonadiabatic photoinduced dynamics occurring in the coupled 11A2 and 11B1 excited states of SO2 is investigated using ab initio quantum dynamical methods. To this end, large scale calculations of the potential energy surfaces have been carried out at the multireference configuration interaction level. All vibrational degrees of freedom of the molecule are considered in the potential energy surface calculations and the quantum dynamical treatment. To deal with the symmetry-allowed conical intersection which occurs between the potential energy surfaces, we use the diabatic picture in the framework of regularized diabatic states. Wave-packet propagation on the coupled surfaces was performed and allowed to reproduce with good accuracy the complex absorption band observed experimentally in the 29 000–42 000 cm−1 range. This provides a basis for a subsequent theoretical treatment of the high order harmonic spectra of SO2.

The nonadiabatic photoinduced ring opening occurring in the two lowest excited singlet states of furan is investigated theoretically, using wave-packet propagation techniques. The underlying multidimensional potential energy surfaces (PESs) are obtained from ab initio computations, using the equation-of-motion coupled cluster method restricted to single and double excitations (EOM-CCSD), reported in earlier recent work [E. V. Gromov, A. B. Trofimov, F. Gatti, and H. Köppel, J. Chem. Phys. 133, 164309 (2010)10.1063/1.3493451]. Up to five nuclear degrees of freedom are considered in the quantum dynamical treatment. Four of them represent in-plane motion for which the electronic states in question (correlating with the valence 1B2(V) and Rydberg 1A2(3s) states at the C2v ground-state molecular configuration) have different symmetries, A′ and A′′, respectively. The fifth mode, representing out-of-plane bending of the oxygen atom against the carbon-atom plane, leads to an interaction of these states, as is crucial for the photoreaction. The nonadiabatic coupling and conical intersection cause an electronic population transfer on the order of ∼10 fs. Its main features, and that of the wave-packet motion, are interpreted in terms of properties of the PES. The lifetime due to the ring-opening process has been estimated to be around 2 ps. The dependence of this estimate on the nuclear degrees of freedom retained in the computations is discussed.

Even though the sulfur dioxide molecule has been extensively studied over the last decades, its photo-excitation dynamics is still unclear, due to its complexity, combining conical intersections, and spin-orbit coupling between a manifold of states. We present a comprehensive ab initio study of the intersystem crossing of the molecule in the low energy domain, based on a wave-packet propagation on the manifold of the lowest singlet and triplet states. Furthermore, spin-orbit couplings are evaluated on a geometry-dependent grid, and diabatized along with the different conical intersections. Our results show for the first time the primordial role of the triplet 3B2 state and furthermore predict novel interference patterns due to the different intersystem crossing channels induced by the spin-orbit couplings and the shapes of the different potential energy surfaces. These give new insight into the coupled singlet-triplet dynamics of SO2.