# H$_3^+$ as a five-body problem described with explicitly correlated Gaussian basis sets

## TL;DR

This paper evaluates various explicitly correlated Gaussian basis sets for solving the Schrödinger equation of H$_3^+$, developing a stable algorithm to efficiently handle complex basis sets for polyatomic systems.

## Contribution

It introduces a numerically stable algorithm enabling the use of large complex ECG basis sets in molecular calculations of H$_3^+$.

## Key findings

- ECG basis sets have specific advantages and shortcomings.
- The new algorithm improves numerical stability for complex ECGs.
- Efficient calculations demonstrated for H$_2$ and H$_3^+$ states.

## Abstract

Various explicitly correlated Gaussian (ECG) basis sets are considered for the solution of the molecular Schr\"odinger equation with particular attention to the simplest polyatomic system, H$_3^+$. Shortcomings and advantages are discussed for plain ECGs, ECGs with the global vector representation, floating ECGs and their numerical projection, and ECGs with complex parameters. The discussion is accompanied with particle density plots to visualize the observations. In order to be able to use large complex ECG basis sets in molecular calculations, a numerically stable algorithm is developed, the efficiency of which is demonstrated for the lowest rotationally and vibrationally excited states of H$_2$ and H$_3^+$.