Posner molecules: From atomic structure to nuclear spins

TL;DR

This paper studies Posner molecules, calcium phosphate clusters, using computational methods to understand their structure, vibrational spectra, interactions, and potential for long-lived nuclear spin coherence relevant for quantum computing and medical imaging.

Contribution

It provides a detailed first-principles analysis of Posner molecules, revealing their atomic structure, vibrational properties, and the potential for long coherence times of nuclear spins in biological environments.

Findings

Posner molecules have a stable atomic structure with specific vibrational modes.

The $^{31}$P nuclear spins in Posner molecules can maintain long coherence times.

Potential applications include quantum computing and medical imaging.

Abstract

We investigate "Posner molecules", calcium phosphate clusters with chemical formula Ca$_9$(PO$_4$)$_6$. Originally identified in hydroxyapatite, Posner molecules have also been observed as free-floating molecules $in$ $vitro$. The formation and aggregation of Posner molecules have important implications for bone growth, and may also play a role in other biological processes such as the modulation of calcium and phosphate ion concentrations within the mitochondrial matrix. In this work, we use a first-principles computational methodology to study the structure of Posner molecules, their vibrational spectra, their interactions with other cations, and the process of pairwise bonding. Additionally, we show that the Posner molecule provides an ideal environment for the six constituent $^{31}\text{P}$ nuclear spins to obtain very long spin coherence times. $In$ $vitro$, the spins could provide a platform for liquid-state nuclear magnetic resonance quantum computation. $In$ $vivo$, the spins may have medical imaging applications. The spins have also been suggested as "neural qubits" in a proposed mechanism for quantum processing in the brain.