Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Accurate computation of molecular electronic properties is crucial for materials design.
• Frequency-dependent hyperpolarizabilities determine nonlinear optical (NLO) responses, such as second-harmonic generation (SHG).
• Basis set choice significantly impacts the accuracy of quantum chemical calculations.

Purpose of the Study:

• To benchmark Dunning correlation-consistent Gaussian basis sets for frequency-dependent second-order hyperpolarizabilities.
• To develop and apply methods for analyzing basis set errors in NLO property calculations.
• To understand the convergence behavior of basis sets for SHG properties across diverse molecules.

Main Methods:

• Benchmarking Dunning basis sets against multiresolution analysis (MRA) as a reference.
• Utilizing a unit-sphere representation to analyze the directional structure of basis set errors.
• Introducing relative RMS total error and signed projection errors for quantitative error assessment.
• Employing unsupervised clustering to identify distinct convergence patterns.

Main Results:

• Basis set errors in hyperpolarizabilities are often anisotropic and directionally localized.
• Four distinct convergence behaviors were identified across 68 molecules.
• Doubly augmented basis sets generally outperform singly augmented sets.
• Core-polarization functions are essential for accurate calculations on second-row elements.

Conclusions:

• Directional error analysis provides deeper insights into basis set performance than global metrics.
• Clustering reveals diverse convergence characteristics, aiding basis set selection for NLO properties.
• This framework enhances the understanding and prediction of basis set convergence for nonlinear optical response.