Optimal Mode Combination in the Multiconfiguration Time-Dependent Hartree Method through Multivariate Statistics:...

Area of Science:

• Computational Chemistry
• Quantum Dynamics
• Multivariate Statistics

Background:

• The multiconfiguration time-dependent Hartree (MCTDH) method and its multilayer extension (ML-MCTDH) are essential for simulating nuclear quantum dynamics in complex, high-dimensional systems.
• These methods reduce computational cost by using time-dependent variational orbitals and layered effective degrees of freedom.
• However, optimal selection of mode grouping and tensor tree structures remains challenging and relies heavily on user expertise.

Purpose of the Study:

• To develop a novel, objective protocol for guiding the design of tensor-network decompositions in MCTDH and ML-MCTDH methods.
• To provide a reliable and convenient approach for optimizing the computational efficiency of nuclear quantum dynamics simulations.

Main Methods:

• The study details a new protocol employing multivariate statistical techniques, specifically factor analysis and hierarchical clustering.
• These statistical methods are used to guide the optimal design of complex 'system-of-systems' tensor-network decompositions.

Main Results:

• The new statistical protocol offers a systematic approach to mode grouping and tensor tree selection, moving beyond subjective intuition.
• The protocol's effectiveness and applicability were demonstrated through tests on water and protonated water clusters exhibiting large amplitude motions.

Conclusions:

• The developed statistical protocol provides a robust and convenient method for optimizing tensor-network structures in high-dimensional quantum dynamics.
• This approach enhances the efficiency and reliability of MCTDH and ML-MCTDH simulations for complex molecular systems.