January 4, 2022

A 15+-Year-Old Problem Finally Resolved

Researchers achieved complete assignment of infrared spectrum of hydronium-water “magic number” cluster reported in 2004

Hydronium ions interact with surrounding water molecules to form “magic number” clusters of exceptional stability.

Hydronium ions interact with surrounding water molecules to form “magic number” clusters of exceptional stability.

(Illustration by Stephanie King | Pacific Northwest National Laboratory)

The Science                                

In aqueous solutions, hydrogen ions (H+)—often referred to as protons—separate from dilute acids and associate with water molecules to make hydronium ions (H3O+). A hydronium ion can then interact with surrounding water molecules to form cluster networks. For a certain number of water molecules solvating the hydronium ion, clusters of exceptional stability—“magic number” clusters—are formed. Despite the intense interest in these systems, the results produced from infrared (IR) spectroscopy of these clusters are too complex to understand through conventional means, and therefore many details of their structure cannot be determined. Scientists have developed a novel protocol to calculate the vibrational IR spectra of large hydrogen bonded clusters based on high-level electronic structure methods for the underlying potential energy surface. They then demonstrated its accuracy in assigning—for the first time—the complete experimental spectrum of the H+(H2O)21 cluster originally reported in 2004.

The Impact

The use of this novel protocol may elucidate IR band assignments for complex systems and consequently affect our understanding of their molecular structures. These calculations can provide definitive structural proof to clarify previously controversial and unclear band assignments of proton motions. The spectral signature of the excess proton offers deeper insight into the nature of charge accommodation in the extended hydrogen-bonding network underpinning this water cluster. This also provides an understanding of the local structure of water in diverse environments, such as the water/air interface and water droplets in an amorphous aqueous medium.  


The spectroscopic features of protonated water species in dilute acid solutions have been long sought after to understand the microscopic behavior of a proton in water. Researchers developed a new protocol for the calculation of the IR spectra of complex systems using gas phase water clusters H+(H2O)n as a model system. The IR spectra of these hydronium-water clusters were first reported in 2004, but they were too complex to fully analyze and understand. The novel protocol combines the fragment-based Coupled Cluster method with anharmonic vibrational quasi-degenerate perturbation theory. Its accuracy was demonstrated through the complete and accurate assignment of the IR spectrum of the H+(H2O)21 cluster. The site-specific IR spectral signatures reveal two distinct structures for the internal and surface four-coordinated water molecules. These are ice-like and liquid-like, respectively. The effect of the inter-molecular interaction between surrounding water molecules is also addressed by this protocol. For instance, a vibrational resonance is found between the O-H stretching fundamental and the bending overtone of the nearest neighboring water molecule. Environmental effects are incorporated by atomic point charges, accounting for the electronic polarization and hydrogen-bond cooperativity effects. This makes the truncation after the dimer terms far more accurate than a simple summation of bare monomer/dimer energies.


Sotiris Xantheas
Advanced Computing, Mathematics and Data Directorate, Pacific Northwest National Laboratory


This work was supported by the Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences at Pacific Northwest National Laboratory.

This work was also supported by:

  • the National Natural Science Foundation of China
  • the National Key R&D Program of China
  • Shanghai Municipal Natural Science Foundation
  • “Double First-Class” University project
  • the Fundamental Research Funds for China Pharmaceutical University
  • the Fundamental Research Funds for the Central Universities
  • the Japan Society for the Promotion of Science KAKENHI

This research used resources of the National Energy Research Scientific Computing Center, the Supercomputer Centers of East China Normal University and China Pharmaceutical University.

Published: January 4, 2022

Liu J, J Yang, X C Zeng, S S Xantheas, K Yagi, and X He. 2021. "Towards complete assignment of the infrared spectrum of the protonated water cluster H+(H2O)21." Nature Communications, 12(1), DOI: 10.1038/s41467-021-26284-x