H₃ ⁺ as a five-body problem described with explicitly correlated Gaussian basis sets

Area of Science:

• Computational chemistry
• Quantum mechanics
• Molecular physics

Background:

• The molecular Schrödinger equation is fundamental to understanding molecular behavior.
• Explicitly correlated Gaussian (ECG) basis sets offer a way to improve the accuracy of quantum chemical calculations.
• The hydronium ion (H3+) is a simple yet important molecular system for testing theoretical methods.

Purpose of the Study:

• To analyze the strengths and weaknesses of various ECG basis sets for solving the molecular Schrödinger equation.
• To develop a numerically stable algorithm for utilizing large and complex ECG basis sets in molecular calculations.
• To demonstrate the efficiency of the developed algorithm for excited states of H2 and H3+.

Main Methods:

• Evaluation of different types of ECG basis sets: plain, global vector representation, floating, and complex parameters.
• Development of a numerically stable algorithm for large-scale ECG basis set calculations.
• Visualization of results using particle density plots.

Main Results:

• Identification of advantages and disadvantages of various ECG basis set formulations.
• Successful development of a stable and efficient algorithm for complex ECG basis sets.
• Demonstration of the algorithm's efficiency on calculating excited states of H2 and H3+.

Conclusions:

• ECG basis sets are a valuable tool for molecular quantum mechanics, with specific types offering distinct benefits.
• The developed algorithm significantly enhances the feasibility of using advanced ECG basis sets in computational chemistry.
• This work provides a robust computational framework for studying small molecular systems like H3+.