Evaluation of the detachment energy of hydrated phosphate anion over a wide range of cluster size and revisiting solvent–berg model: a theoretical study

Abstract

An explicit analytical expression has been obtained for vertical detachment energy (VDE) that can be used to calculate the same over a wide range (both stable and unstable regions) of cluster sizes including the bulk from the knowledge of VDE for a finite number of stable clusters (n = 16–23). The calculated VDE for the bulk is found to be very good in agreement (within 1%) with the available experimental result and the domain of instability lies between n = 0 and n = 15 for the hydrated clusters, PO^{3 −}₄ · nH₂O. The minimum number (n₀) of water molecules needed to stabilise the phosphate anion is 16. We are able to explain the origin of solvent–berg model and anomalous conductivity from the knowledge of first stable cluster. We have also provided a scheme to calculate the radius of the solvent–berg for phosphate anion. The calculated conductivity using Stokes–Einstein relation and the radius of solvent–berg is found to be very good in agreement (within 4%) with the available experimental results.

Keywords:

• semi-grand canonical ensemble
• solvent–berg model
• Stokes–Einstein relation
• conductivity

Acknowledgements

The author would like to thank computer centre BARC for providing the ANUPAM parallel computational facility. Prof(s). B.N. Jagatap, S.K. Ghosh, T. Bandyopadhyay, A.K. Samanta and J.A. McCammon are gratefully acknowledged for helpful discussion and encouragements.

Additional information

Funding

The work was supported by Department of Atomic Energy, India under grant [XII-N-R&D-02.04/Theoretical and Computational Chemistry of Complex Systems].