A collocation-based multi-configuration time-dependent Hartree method using mode combination and improved relaxation

Area of Science:

• Quantum chemistry
• Computational physics
• Molecular dynamics

Background:

• The multi-configuration time-dependent Hartree (MCTDH) method is powerful for quantum dynamics but has limitations.
• Its computational cost scales exponentially with system size.
• Standard MCTDH requires potential energy surfaces in a specific sum-of-product (SOP) form.

Purpose of the Study:

• To develop a more efficient and versatile computational method for quantum dynamics.
• To overcome the exponential scaling and SOP form limitations of the original MCTDH.
• To enable accurate calculations for larger molecular systems and general potential energy surfaces.

Main Methods:

• Introduced mode combination (MC) to group coordinates, reducing computational cost.
• Integrated MC with a collocation approach to eliminate the need for integrals.
• Formulated the new MC collocation multi-configuration time-dependent Hartree (MC-C-MCTDH) method.
• Employed a variant of improved relaxation with point-based residual evaluation.
• Utilized discrete variable representation-like and Leja points for multi-dimensional collocation.

Main Results:

• The MC-C-MCTDH method demonstrates non-exponential cost scaling with the number of atoms.
• It accommodates general potential energy surfaces without requiring the SOP form.
• No integrals or quadratures are necessary, simplifying calculations.
• Accurate vibrational energy eigenstates were computed for methyl radical, methane, and acetonitrile.
• The method proved efficient for these molecular systems.

Conclusions:

• MC-C-MCTDH offers a significant advancement in computational quantum dynamics.
• The method is more scalable and versatile than the original MCTDH.
• It enables accurate and efficient calculations for larger and more complex molecular systems.
• The use of collocation and mode combination provides a robust framework for future studies.