Using Hessian update formulae to construct modified Shepard interpolated potential energy surfaces: application to...

Area of Science:

• Computational chemistry
• Chemical physics
• Surface science

Background:

• Modified Shepard interpolation using second-order Taylor expansions is effective for potential energy surfaces.
• Extending interpolation to gas-surface dynamics with mobile surface atoms significantly increases problem dimensionality and computational cost.
• Accurate Hessian (second derivative matrix) evaluations are a major bottleneck.

Purpose of the Study:

• To develop a computationally efficient method for constructing potential energy surfaces in gas-surface dynamics.
• To reduce the computational burden associated with accurate Hessian calculations.
• To enable more complex simulations of systems with mobile surface atoms.

Main Methods:

• Utilized approximate Hessians derived from established Hessian update formulas.
• Combined approximate Hessians with a single accurate Hessian evaluation.
• Applied this approach to gas-surface dynamics simulations.

Main Results:

• Demonstrated that using approximate Hessians significantly reduces computational cost.
• Showed that the combination of approximate and single accurate Hessians is effective.
• Successfully avoided the need for repeated expensive accurate Hessian determinations.

Conclusions:

• Approximate Hessians offer an effective strategy to mitigate high computational costs in gas-surface dynamics.
• This method provides a practical solution for constructing potential energy surfaces in complex systems.
• The approach facilitates more feasible simulations of dynamic processes involving mobile surfaces.