Two-Step ONIOM Method for the Accurate Estimation of Individual Hydrogen Bond Energy in Large Molecular Clusters

The study of molecular clusters to understand the properties of condensed systems has been the subject of immense interest. To get insight into these properties, the knowledge of various noncovalent interactions present in these molecular clusters is indispensable. Our recently developed molecular tailoring approach-based (MTA-based) method for the estimation of the individual hydrogen bond (HB) energy in molecular clusters is useful for this purpose. However, the direct application of this MTA-based method becomes progressively difficult with the increase in the size of the cluster. This is because of the difficulty in the evaluation of single-point energy at the correlated level of theory. To overcome this caveat, herein, we propose a two-step method within the our own N-layer integrated molecular orbital molecular mechanics (ONIOM) framework. In this method, the HB energy evaluated by the MTA-based method employing the actual molecular cluster at a low Hartree–Fock (HF) level of theory is added to the difference in the HB energies evaluated by the MTA-based method, employing an appropriate small model system, called the shell-1 model, calculated at high (MP2) and low (HF) levels of theory. The shell-1 model of a large molecular cluster is made up of only a few molecules that are in direct contact (by a single HB) with the two molecules involved in the formation of an HB under consideration. We tested this proposed two-step ONIOM method to estimate the individual HB energies in various molecular clusters, viz., water (W_n, n = 10–16, 18 and 20), (H₂O₂)₁₂, (H₂O₃)₈, (NH₃)_n and strongly interacting (HF)₁₅ and (HF)_m(W)_n clusters. Furthermore, these estimated individual HB energies by the ONIOM method are compared with those calculated by the MTA-based method using actual molecular clusters. The estimated individual HB energies by the ONIOM method, in all these clusters, are in excellent linear one-to-one agreement (R² = 0.9996) with those calculated by the MTA-based method using actual molecular clusters. Furthermore, the small values of root-mean-square deviation (0.06), mean absolute error (0.04), |ΔE_max| (0.21) and Sε (0.06) suggest that this two-step ONIOM method is a pragmatic approach to provide accurate estimates of individual HB energies in large molecular clusters.