TDAP stands for "Time Dependent Ab-initio Package", which is a suite of computer software targeting for dynamic simulations of electron-ion system from first principles. It employs a real time real space implementation of time-dependent density functional theory based on numerical atomic basis sets.

The Born-Oppenheimer approximation, which assumes that the motion of the nuclei and electrons in a molecule or solid can be separated, is the most fundamental hypothesis in quantum physics and chemistry. However, in many situations, such as chemical or biological processes involving electron or proton transfer with significant tunneling or nonadiabatic effects, zero point motion in a chemical bond containing available energy smaller than that predicted by the potential depth, and the continuous rearrangement of a complex network of hydrogen bonds in water (inherently a quantum mechanical phenomenon), the Born-Oppenheimer approximation may often fail due to neglecting quantum mechanical electron-nucleus correlation effects. In such processes, the molecular system owns enough energy to explore the unusual regions of the configuration space, the adiabatic potential energy surface (PES) driving the time evolution of the system branches, and the nuclear wave packet splits among the manifolds of possible states.

The theoretical treatment of the time-dependent nonadiabatic phenomena is a formidable challenge at many levels, from the description of the excited states to the time propagation of the corresponding physical properties. Given that the full quantum mechanical solution of such problems for large systems is out of question, several semi-classical approaches have been developed in the last half century to tackle the problem.

TDAP is a real-time ab initio approach for electron-nucleus dynamic simulations beyond the Born-Oppenheimer approximation, which follows Ehrenfest dynamics and represents a mean-field theory of the mixed quantum-classical system, with forces on the nuclei are averaged over many possible adiabatic electronic states induced by nuclei motion.

TDAP employs local atomic basis sets and real-time propagation of wave functions for solving the time-dependent Kohn-Sham (TDKS) equations, which endows it several advantages over available conventional methods:

The adoption of overwhelmingly efficient atomic orbital basis sets, which are small in size and fast in performance, enables simulations of either periodic system or a finite-sized supercell with large vacuum space without heavy calculation cost while maintaining relatively high accuracy.

Real time excited state trajectories are achieved with many-electron density self-consistently propagating at every electronic and nuclear steps and forces calculated from mean-field theory, offering a direct microscopic picture on the ultrafast dynamics of electrons and nuclei upon photo-excitation.

Relatively high efficiency for parallelization can be achieved because the occupied molecular orbitals are propagated independently at a time and can be distributed evenly over several processors with little mutual communication.

Photo-absorption spectra and polarizability of the computed systems can be calculated within the same scheme. Nonlinear effects can also be treated precisely.

TDAP behaves well in treating dynamic processes such as interface electron injection, electron-hole recombination and charge transfer induced chemical reactions, where a single path dominates in the reaction dynamics. However, in mean-field regime, Ehrenfest dynamics describes nuclear paths using a single averaged trajectory even when the nuclear wavefunction has broken up into distinct parts. Therefore, the approach fails to deal with situations where multiple paths are involved in the excited states, especially when state-specific nuclear trajectories are of interest. It also lacks a detailed balance for quantum electronic states For alternative strategies where trajectories other than Ehrenfest dynamics are needed to model nonadiabatic processes, the readers are referred to methods which explicitly include electronic transitions such as trajectory surface hopping.