A simple and efficient evolution operator for time-dependent Hamiltonians: the Taylor expansion.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Molecular dynamics

Background:

• Time-dependent Hamiltonian operators, crucial for modeling molecular interactions with electric fields, lack a compact evolution operator expression.
• The Magnus expansion, while formal, is computationally challenging for high-order calculations.
• Existing numerical methods like Runge-Kutta and split-operator have limitations in accuracy, time step size, and applicability.

Purpose of the Study:

• To present a novel and efficient Taylor expansion method for computing the evolution operator with time-dependent Hamiltonians.
• To demonstrate the method's advantages over traditional approaches in terms of simplicity, implementation, and time step size.
• To validate the method's effectiveness through model systems and a realistic molecular application.

Main Methods:

• Developed a Taylor expansion approach for the evolution operator and wave function around the initial time.
• Applied the method to a two-level quantum system and Gaussian wave packet propagation in a harmonic potential.
• Utilized the method to calculate time-averaged absorbed energy in fluoroproprene.

Main Results:

• The Taylor expansion method is straightforward to implement and does not require specific Hamiltonian representations (e.g., diagonal kinetic energy).
• The method allows for significantly larger time steps compared to traditional numerical techniques.
• Demonstrated accurate results for model systems and a practical application in molecular spectroscopy.

Conclusions:

• The Taylor expansion method provides a robust and efficient alternative for solving the time-dependent Schrödinger equation.
• This approach overcomes limitations of existing numerical methods, enabling more accurate and feasible simulations of quantum systems.
• The method shows promise for advanced applications in computational chemistry and molecular physics.