A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Standard multiconfiguration time-dependent Hartree (MCTDH) methods face challenges with large basis sets and potentials not expressible as sums of products (SOPs).
• The exponential scaling of direct product bases with the number of atoms limits accuracy and applicability.

Purpose of the Study:

• To develop a novel MCTDH approach combining a pruned basis and collocation for improved computational efficiency and broader potential applicability.
• To overcome limitations of existing pruned basis and collocation strategies by integrating them.

Main Methods:

• A pruned basis approach is combined with a collocation grid (Smolyak grid) to reduce basis size and enable calculations with non-SOP potentials.
• The method avoids numerical integration and quadrature, relying on sequential evaluation of matrix-vector products.
• Nested collocation points and hierarchical basis functions facilitate efficient matrix inversion for function representation.

Main Results:

• The pruned, collocation-based (PC-)MCTDH approach successfully mitigates the direct-product basis size problem.
• The method allows for quantum dynamics calculations with potentials that are not SOPs.
• The validity of the PC-MCTDH approach was confirmed by calculating vibrational energies for CH2NH.

Conclusions:

• The developed PC-MCTDH method offers a significant advancement in quantum dynamics simulations, particularly for systems with complex potentials.
• The technique provides a more efficient and versatile alternative to standard MCTDH calculations.
• The matrix inversion technique may have applications beyond chemical physics.