Sparse adaptive basis set methods for solution of the time dependent Schrodinger equation

Scalable numerical solutions to the time dependent Schrodinger equation remain an outstanding goal in theoretical chemistry. Here we present a method which utilises recent breakthroughs in signal processing to consistently adapt a dictionary of basis functions to the dynamics of the system. We show that for two low-dimensional model problems the size of the basis set does not grow quickly with time and appears only weakly dependent on dimensionality. The generality of this finding remains to be seen. The method primarily uses energies and gradients of the potential, opening the possibility for its use in on-the-fly ab initio quantum wavepacket dynamics.

Automated summary

Scalable numerical solutions to the time dependent Schrodinger equation remain an outstanding goal in theoretical chemistry. Here we present a method which adaptively adjusts a dictionary of basis functions to the dynamics of the system using recent breakthroughs in signal processing. Our results show that for two low-dimensional model problems, the size of the basis set does not grow quickly with time and is weakly dependent on dimensionality. The method primarily utilizes energies and gradients of the potential, suggesting its potential application in on-the-fly ab initio quantum wavepacket dynamics.