Direct and Reliable Method for Estimating the Hydrogen Bond Energies and Cooperativity in Water Clusters, Wn, n = 3 to 8.

No direct method for estimating the individual O-H···O hydrogen bond (H-bond) energies in water clusters (Wn) exists in the literature. In this work, we propose such a direct method based on the molecular tailoring approach, which also enables the estimation of the cooperativity contributions. The calculated H-bond energies at MP2(full)/aug-cc-pVTZ and CCSD(T)/aug-cc-pVDZ levels for Wn, n = 3 to 8, agree well with one another and fall between 0.3 and 11.6 kcal mol-1 with the cooperativity contributions in the range of -1.2 and 7.0 kcal mol-1. For gauging the accuracy of our H-bond energies for a cluster, the H-bond energy sum is added to the sum of monomer energies, and the results are compared with the respective total energy. These two values agree with each other to within 8.3 mH (∼5 kcal mol-1), testifying the accuracy of our estimated H-bond energies. Further, these H-bond strengths show a good correlation with the respective O-H stretching frequencies and the molecular electron density values at the (3, -1) O-H···O H-bond critical point.