Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Smolyak's method (1963) addresses exponential scaling in calculations by using sums of small direct products.
• This approach was applied to quantum dynamics in 2009 and has seen subsequent use.
• Previous applications have been limited in system size and complexity.

Purpose of the Study:

• To extend the application of Smolyak's method to larger and more complex quantum systems.
• To accurately compute the tunneling splitting of malonaldehyde in full dimensionality.
• To validate a novel computational approach by comparing results with experimental data.

Main Methods:

• Implemented Smolyak's method combined with on-the-fly kinetic energy operator calculation.
• Utilized a Block-Davidson procedure for obtaining eigenstates.
• Developed and employed custom Fortran codes (ElVibRot and Tnum-Tana).

Main Results:

• Successfully computed the tunneling splitting of malonaldehyde in 21 dimensions.
• Obtained values of 21.7±0.3 cm⁻¹ and 2.9±0.1 cm⁻¹ for the normal and mono-deuterated isotopologues.
• Demonstrated excellent agreement between calculated and experimental tunneling splitting values.

Conclusions:

• The combination of Smolyak's method, on-the-fly calculations, and Block-Davidson procedure enables accurate computations for complex systems.
• This approach pushes the boundaries for calculating tunneling splitting in large molecular systems.
• The study validates the computational methodology for future applications in quantum chemistry and dynamics.