Permutationally Invariant, Reproducing Kernel-Based Potential Energy Surfaces for Polyatomic Molecules: From...

Area of Science:

• Computational chemistry
• Quantum chemistry
• Molecular modeling

Background:

• Constructing accurate, high-dimensional molecular potential energy surfaces (PESs) for polyatomic molecules is computationally demanding.
• Reproducing kernel Hilbert space (RKHS) interpolation offers an efficient method for PES construction but typically requires data on regular grids, leading to prohibitive computational costs for high-level electronic structure calculations.
• Existing methods struggle with the large number of reference energies needed for complex systems.

Purpose of the Study:

• To develop an efficient and robust scheme for constructing high-dimensional molecular potential energy surfaces (PESs).
• To overcome the computational limitations of traditional RKHS interpolation for large molecular systems.
• To enable the accurate modeling of systems with up to 10 atoms.

Main Methods:

• Utilizing reproducing kernel Hilbert space (RKHS) interpolation.
• Incorporating both energies and gradients of molecular systems to reduce the number of required input data points.
• Implementing and testing the permutational symmetry in kernel products for molecular systems.
• Applying the scheme to construct high-dimensional PESs for systems up to 10 atoms.

Main Results:

• An efficient and robust scheme for constructing high-dimensional PESs has been developed.
• The inclusion of gradients alongside energies significantly reduces the number of input data points required for RKHS interpolation.
• The method successfully constructs PESs for systems with up to 10 atoms.
• Permutational symmetry was correctly implemented and demonstrated for the CH4 molecule.

Conclusions:

• The presented scheme overcomes the computational limitations of RKHS interpolation for constructing high-dimensional PESs.
• The use of energies and gradients, along with correct implementation of permutational symmetry, makes the approach computationally feasible for larger molecular systems.
• This method facilitates accurate molecular modeling and electronic structure calculations for complex chemical systems.