Cyclic cooperativity contributions determine the hydrogen bond strengths in molecular clusters

In a recent communication (A. Shivhare, B. Dehariya, S. R. Gadre and M. M. Deshmukh, 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) clusters. For this purpose, the sum of the cooperativity contributions (CCs) 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 (ESynergeticHB) were in excellent agreement with their actual cluster counterparts (EclusterHB). In this work, we test the generality of this methodology. For this purpose, we employed 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^-1). The HB energies in all these molecular clusters calculated using the present method were found to be accurate. The absolute difference between the ESynergeticHB and EclusterHB values in these clusters is found to be less than 0.5 kcal mol^-1. Importantly, the present method not only enables 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 cooperativity (FCC), partial cyclic cooperativity (PCC) or anti-cooperativity (AC).