# The building principle of triatomic trilobite Rydberg molecules

## TL;DR

This paper explores the structure and stability of triatomic Rydberg molecules with trilobite-like electron densities, developing a predictive building principle for their equilibrium geometries based on electronic structure analysis.

## Contribution

It introduces a simple building principle for predicting triatomic Rydberg molecule configurations, based on properties of diatomic trilobite molecules and electronic structure calculations.

## Key findings

- Potential energy landscape has oscillatory shape supporting various stable geometries.
- Localized vibrational states are identified with energy spacings around 100 MHz.
- The building principle accurately predicts equilibrium configurations.

## Abstract

We investigate triatomic molecules that consist of two ground state atoms and a highly excited Rydberg atom, bound at large internuclear distances of thousands of \AA ngstroms. In the molecular state the Rydberg electron is in a superposition of high angular momentum states whose probability densities resemble the form of trilobite fossils. The associated potential energy landscape has an oscillatory shape and supports a rich variety of stable geometries with different bond angles and bond lengths. Based on an electronic structure investigation we analyze the molecular geometry systematically and develop a simple building principle that predicts the triatomic equilibrium configurations. %based on the properties of diatomic trilobite molecules. As a representative example we focus on $^{87}$Rb trimers correlated to the $n=30$ Rydberg state. Using an exact diagonalization scheme we determine and characterize localized vibrational states in these potential minima with energy spacings on the order of 100 MHz$\times h$.