Quantifying cooperativity in water clusters: an attempt towards obtaining a generalised equation

Abstract

The current study describes the development of a general equation of cooperativity energy (CE) for an n-mer system based on the difference between interaction energy of the system and the sum of interaction energy of its dimeric subunits. The counterpoise corrected generalised CE equation of n-mer system has also been developed. In order to validate these two generalised equations, we have considered four different kinds of water clusters, viz. W1D, W2D, W2D-H and W3D, ((H₂O)_n: n = 3–10), with the increasing cluster size as well as changing arrangements. The CE obtained from the two generalised equations follow the trend W3D > W2D-H > W2D > W1D. The deviation at n = 6 for W3D clusters in the plot of CE with cluster size has also been observed for O–H stretching frequencies, electron density and the Laplacian of the electron density plots. The contrastingly higher CE for cyclic pentamer compared to hexamer is in accordance with earlier observations as well as computed average hydrogen bond lengths. We have observed that the average charge value is more on oxygen atoms of pentamer than hexamer resulting in the shortening of hydrogen bond in pentamer and hence the CE values are more for pentamer than hexamer. We have shown that CE has the capability to quantify the cooperativity effect in water clusters.

Keywords:

• cooperativity
• anticooperativity
• cooperativity energy
• hydrogen bonding
• water clusters

Acknowledgements

CSIR, New Delhi is thanked for financial support in the form of GENESIS (BSC-121), a 12th five-year project. This work is dedicated to Dr Sourav Pal on the occasion of his 60th birth anniversary.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental data

In the supplemental data, the equations for n = 6–10, the figures and the different energy components of W1D, W2D, W2D-H and W3D are also presented. Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/00268976.2015.1072648

Additional information

Funding

This work was supported by Council of Scientific & Industrial Research (CSIR), India [GENESIS (BSC-0121)].