Using a pruned basis and a sparse collocation grid with more points than basis functions to do efficient and accurate...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• The multi-configuration time-dependent Hartree (MCTDH) method is crucial for simulating quantum dynamics.
• Standard MCTDH methods can suffer from point-set errors, particularly with complex potential energy surfaces.
• Previous collocation MCTDH approaches required direct product bases for both grids and wavefunctions.

Purpose of the Study:

• To develop a novel collocation MCTDH method that minimizes point-set errors.
• To enable MCTDH calculations with general potential energy surfaces without integral computations.
• To allow the use of more collocation points than basis functions with pruned bases.

Main Methods:

• A new collocation multi-configuration time-dependent Hartree (MCTDH) method is proposed.
• The method utilizes a larger basis for collocation points than for wavefunctions.
• A novel pseudo-inverse is employed to handle pruned bases and grids, allowing more points than basis functions.

Main Results:

• Errors in calculating vibrational states of CH2NH were reduced by two orders of magnitude.
• Error reduction was achieved by increasing the number of collocation points without increasing the basis size.
• The method's effectiveness was demonstrated even with unrefined time-independent points.

Conclusions:

• The proposed collocation MCTDH method effectively reduces point-set errors in quantum dynamics.
• This approach offers a significant improvement for simulating molecular vibrations and other quantum phenomena.
• The method provides a more accurate and efficient way to perform complex quantum chemical calculations.