Interpolation of multi-sheeted multi-dimensional potential-energy surfaces via a linear optimization procedure.

Area of Science:

• * Theoretical Chemistry
• * Quantum Chemistry
• * Spectroscopy

Background:

• * High-dimensional analytic potential-energy surfaces are essential for molecular dynamics simulations.
• * Previous methods, while advanced, faced challenges with multi-sheeted surfaces and conical intersections.
• * Polynomial invariant theory has enabled significant progress in constructing permutationally invariant surfaces.

Purpose of the Study:

• * To generalize existing methods for constructing multi-sheeted, multi-dimensional potential-energy surfaces.
• * To develop a technique that avoids nonlinear optimization issues common in diabatic surface construction.
• * To enable the accurate modeling of systems with seams of conical intersections.

Main Methods:

• * Expansion of characteristic polynomial coefficients using invariant polynomials (molecular point group or permutation group).
• * Construction of multi-sheeted adiabatic potential-energy surfaces via the Frobenius companion matrix.
• * Application of the method to a specific system, avoiding ab initio data fitting challenges.

Main Results:

• * A novel, generalized method for constructing multi-sheeted potential-energy surfaces.
• * Avoidance of nonlinear optimization problems in the construction process.
• * Successful application to generate a three-sheeted, nine-dimensional surface for the methane cation's ground state.

Conclusions:

• * The developed method offers a robust approach for multi-sheeted potential-energy surface construction.
• * This technique is particularly valuable for systems exhibiting conical intersections.
• * The study provides a practical example demonstrating the method's efficacy.