Cyclic Cooperativity Contributions Determine the Hydrogen Bond Strengths in Molecular Clusters

In a recent communication (Phys. Chem. Chem. Phys., 2024, 26, 21332), we proposed a method for calculating the energy of a hydrogen bond (HB), which is common to two or more cyclic networks of HBs in water (H2O)_n clusters. For this purpose, the sum of the cooperativity contributions of these cyclic structures, estimated using the molecular tailoring approach (MTA)-based method, was added to the energy of this HB in the respective water dimer isolated from the cluster. The HB energies calculated in this fashion (E_HB^Synergetic) were in excellent agreement with their actual cluster counterparts (E_HB^cluster). In this work, we test the generality of this methodology. For this purpose, we employed the clusters of ammonia (NH₃)_n, hydrogen sulphide (H₂S)_n, mixed (H₂S)_m(H₂O)_n, (NH₃)_m(H₂O)_n, methanol-water (CH₃OH)_m(H₂O)_n, and hydrogen fluoride-water (HF)_m(H₂O)_n exhibiting HBs of variable strength (1 to 19 kcal/mol). The HB energies in all these molecular clusters calculated using the present method were found to be accurate. The absolute difference between the E_HB^Synergetic and E_HB^cluster values in these clusters is found to be less than 0.5 kcal/mol. Importantly, the present method not only enables the accurate HB energy estimation in molecular clusters but also offers qualitative guidelines for this purpose. The latter are based on the nature of cyclic cooperativity, exhibiting either full cyclic (FCC), partial cyclic cooperativity (PCC) or anti-cooperativity (AC).