Dynamical pruning of the multiconfiguration time-dependent Hartree (DP-MCTDH) method: An efficient approach for multidimensional quantum dynamics.

We present two strategies for combining dynamical pruning with the multiconfiguration time-dependent Hartree (DP-MCTDH) method, where dynamical pruning means on-the-fly selection of relevant basis functions. The first strategy prunes the primitive basis that represents the single-particle functions (SPFs). This is useful for smaller systems that require many primitive basis functions per degree of freedom, as we will illustrate for NO2. Furthermore, this allows for higher-dimensional mode combination and partially lifts the sum-of-product-form requirement onto the structure of the Hamiltonian, as we illustrate for nonadiabatic 24-dimensional pyrazine. The second strategy prunes the set of configurations of SPF at each time step. We show that this strategy yields significant speed-ups with factors between 5 and 50 in computing time, making it competitive with the multilayer MCTDH method.

Efficient molecular quantum dynamics in coordinate and phase space using pruned bases.

We present an efficient implementation of dynamically pruned quantum dynamics, both in coordinate space and in phase space. We combine the ideas behind the biorthogonal von Neumann basis (PvB) with the orthogonalized momentum-symmetrized Gaussians (Weylets) to create a new basis, projected Weylets, that takes the best from both methods. We benchmark pruned time-dependent dynamics using phase-space-localized PvB, projected Weylets, and coordinate-space-localized DVR bases, with real-world examples in up to six dimensions. For the examples studied, coordinate-space localization is the most important factor for efficient pruning and the pruned dynamics is much faster than the unpruned, exact dynamics. Phase-space localization is useful for more demanding dynamics where many basis functions are required. There, projected Weylets offer a more compact representation than pruned DVR bases.