The multi-configurational time-dependent Hartree approach revisited

Area of Science:

• Quantum Dynamics
• Computational Chemistry
• Theoretical Physics

Background:

• The multi-configurational time-dependent Hartree (MCTDH) approach is crucial for simulating high-dimensional quantum dynamics.
• The standard derivation involves a regularization procedure to handle singularities arising from unoccupied single-particle functions (SPFs).

Purpose of the Study:

• To present an alternative derivation of the MCTDH equations of motion.
• To introduce a method for optimizing the choice of unoccupied SPFs.
• To discuss the impact of optimized SPFs on MCTDH equations and their regularization.

Main Methods:

• Derivation of MCTDH equations of motion using second-order time-dependence analysis of single-particle density matrices.
• Identification of optimal unoccupied SPFs based on this analysis.
• Application of generalized equations within the multi-layer MCTDH framework.

Main Results:

• A new set of equations is derived from the second-order analysis, enabling optimal selection of unoccupied SPFs.
• The choice of unoccupied SPFs influences the structure and regularization of the MCTDH equations.
• Numerical examples illustrate the effects of initial SPF choices.

Conclusions:

• The alternative derivation provides a more robust foundation for MCTDH simulations.
• Optimizing unoccupied SPFs can lead to improved accuracy and efficiency in quantum dynamics.
• The presented method is applicable to the multi-layer MCTDH framework.