In this Colloquium, the wavefunction-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. We briefly describe the historical developments that have lead to the formulation of the MCTDH-X methods and motivate the necessity for wavefunction-based approaches. We sketch the derivation of the unified MCTDH-F and MCTDH-B equations of motion for complete and also specific restricted configuration spaces. The strengths and limitations of the MCTDH-X approach are assessed via benchmarks against an exactly solvable model and via convergence checks. We highlight some applications to instructive and experimentally-realized quantum many-body systems: the dynamics of atoms in Bose-Einstein condensates in magneto-optical and optical traps and of electrons in atoms and molecules. We discuss the current development and frontiers in the field of MCTDH-X: 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, the so-called multilayer generalizations to the MCTDH-F and MCTDH-B methods, and the time-dependent orbital-adaptive coupled cluster theory are discussed.

The nonadiabatic photoinduced dynamics occurring in the coupled 1(1)A(2) and 1(1)B(1) excited states of SO(2) 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 SO(2).