Development of a general time-dependent absorbing potential for the constrained adiabatic trajectory method.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Theoretical physics

Background:

• Solving the time-dependent Schrödinger equation is crucial for understanding quantum systems.
• The Floquet formalism is a powerful tool for analyzing systems under periodic perturbation.
• Non-orthogonal basis sets and Fourier decomposition are common techniques in computational quantum dynamics.

Purpose of the Study:

• To introduce and validate the constrained adiabatic trajectory method (CATM) for solving the time-dependent Schrödinger equation.
• To develop a general form for an inherent absorbing potential applicable to dispersed boundary conditions.
• To demonstrate the method's efficacy using calculations on the H(2)(+) molecular ion.

Main Methods:

• Utilizing the Floquet formalism and Fourier decomposition within a non-orthogonal basis set.
• Applying matrix manipulation and deriving a general form for an inherent absorbing potential.
• Separating CATM propagation into steps to manage the size of the Fourier basis.

Main Results:

• The derived absorbing potential can reproduce any dispersed boundary conditions.
• The method transforms wavefunctions into desired states with exponentially decreasing errors.
• Successful application of CATM to the H(2)(+) molecular ion under laser pulse illumination.

Conclusions:

• The constrained adiabatic trajectory method provides an effective approach for quantum dynamics simulations.
• The developed absorbing potential enhances the accuracy and applicability of the CATM.
• This method offers a viable computational strategy for studying molecular ions interacting with laser fields.