Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Theoretical physics

Background:

• Solving the time-dependent Schrödinger equation is crucial in quantum mechanics.
• Traditional methods use static or dynamic basis functions.
• A previous approach used dynamic trajectories to create static basis sets.

Purpose of the Study:

• To develop a more efficient method for solving the time-dependent Schrödinger equation.
• To reduce the size of basis sets required for accurate wave function propagation.
• To improve upon existing trajectory-guided basis set methodologies.

Main Methods:

• Employing short-time classical trajectories to generate new basis functions.
• Utilizing Matching Pursuit to periodically minimize the basis set size.
• Propagating the wave function using an adaptive, dynamically generated basis set.

Main Results:

• The new scheme generates adaptive and minimal basis sets.
• Basis sets were approximately an order of magnitude smaller than the original method.
• Accurate wave function propagation was achieved for benchmark problems.

Conclusions:

• The adaptive strategy offers significant advantages for wave function propagation.
• This method provides a more efficient approach to solving the time-dependent Schrödinger equation.
• The reduction in basis set size enhances computational efficiency.