Hydration shell model for expeditious and reliable individual hydrogen bond energies in large water clusters

Recently, we have developed and tested a method, based on the molecular tailoring approach (MTA-based) to directly estimate the individual hydrogen bond (HB) energies in molecular clusters. Application of this MTA-based method to large molecular clusters is prohibitively difficult due to the evaluation of the energy of large-sized fragments. We propose here a smaller model system called the shell model, to overcome this difficulty. The shell model represents the first hydration shell of water molecules involved in the formation of HB under consideration. Utilizing the shell model as a parent system, fragmentation is carried out, in a fashion similar to the actual MTA-based method, to estimate individual HB energies in large water clusters (W, n = 10-16, 18 and 20). The estimated individual HB energies in these W clusters, employing the shell model, fall between 0.2 and 12.5 kcal mol^-1 at the MP2/aug-cc-pVTZ level, with no net loss in the cooperativity contribution. We have also applied this shell model-based approach to estimate individual HB energies in the two lowest energy conformers of ammonia octamers (NH₃)₈ and mixed hydrogen fluoride-water clusters. The estimated individual HB energies employing the shell model, in all these molecular clusters studied in this work, are in good agreement with their actual MTA-based counterparts. The typical difference is less than 1 kcal mol^-1. Importantly, the shell model has a huge computational time advantage over the actual MTA-based method and it requires only modest hardware.