Nanochemistry and biotechnology

Quantum Nature of Stability Mechanisms of Posner’s Clusters Structure

Karbivskyy V.L., Kurgan N.A., Romansky A.A., Karbovska L.I.
G.V. Kurdymov Institute for Metal Physics of the NAS of Ukraine,
03680, blvd. Vernadsky, 36, Kiev, Ukraine 
E-mail: karb@imp.kiev.ua  

It is considered that 31P nuclear spins in Ca9(PO4)6 molecules, better known as "Posner molecules", could form the basis of a quantum mechanism for neural processing in the brain and the formation of the thought process [1]. Since the spins in different Ca9(PO4)6 molecules can become entangled and remain so for periods that hugely exceed typical 31P spin relaxation times, these molecules are unique contenders for protecting the neural qubits for a very long time and thus can serve as working quantum memory [2].
The role of the d-shell of calcium in the formation of the stability mechanisms of Ca9(PO4)6 molecules is investigated by spectral and theoretical methods. A detailed analysis of the electronic structure of Posner molecules is performed. The limitations of the application of quantum-mechanical calculations using the methods of the density functional theory for the description of the long-range component of the interaction of calcium with the surroundings are established. It is determined that the stability of the structure of these molecules is determined largely by the two-valley effective potential of calcium d-electrons. 
During the collapse of the d-electron, the overlap of the 3d-radial wave function with the 3p-electron function significantly increases. This leads to an increase in the electrostatic interaction between these shells. Consequently, the collapse of the d-electron in the 3р53d isoelectronic series leads to an increase in the role of the electrostatic interaction in comparison with the spin–orbit interaction. Consequently, the presence of two valleys on the effective potential curve of calcium 3d-electrons may have a consequence in the anomalous stability of the structure of Ca9(PO4)6 molecules to defects and external perturbations.

1.	Player Th. C., Hore P. J. Posner qubits: spin dynamics of entangled Ca9(PO4)6 molecules and their role in neural processing // Journal of the Royal Society Interface. – 2018. – 15, 147. https://doi.org/10.1098/rsif.2018.0494 
2.	Fisher M. P. Quantum cognition: The possibility of processing with nuclear spins in the brain // Annals of Physics. – 2015. – 362. - P. 593-602.