Permutationally invariant polynomial representation of polarizability tensor surfaces for linear regression analysis

Area of Science:

• Computational chemistry
• Theoretical chemistry
• Quantum chemistry

Background:

• Molecular dipole polarizability tensor surfaces (PTS) are crucial for understanding molecular electronic properties.
• Existing non-linear models can be computationally intensive and lack unique solutions.

Purpose of the Study:

• To introduce a novel, linearly parameterized functional form for Cartesian PTS.
• To develop a computationally efficient and accurate method for calculating PTS.

Main Methods:

• Linearization of the Applequist power series ansatz for PTS.
• Least-squares fitting procedure for parameter determination.
• Calculation of CH4 PTS using the linear model with extensive training data.

Main Results:

• The linear PTS model provides a unique solution to the least-squares fitting problem.
• Computational complexity is reduced, comparable to potential energy and dipole moment surface calculations.
• Achieved high accuracy (~0.3% RMSE) on a test set, outperforming the non-linear model (~1% RMSE).

Conclusions:

• The proposed linear PTS model offers a computationally efficient and accurate alternative to non-linear methods.
• This approach simplifies the analysis of molecular electronic properties.
• The method demonstrates excellent performance for methane (CH4) polarizability calculations.