Fragments‐in‐fragments method for efficient and reliable estimates of individual hydrogen bond energies in large molecular clusters

Abstract

The knowledge of individual hydrogen bond (HB) strength in molecular clusters is indispensable to get insights into the bulk properties of condensed systems. Recently, we have developed the molecular tailoring approach based (MTA-based) method for the estimation of individual HB energy in molecular clusters. However, the direct use of this MTA-based method to large molecular clusters becomes progressively difficult with the increase in the size of a cluster. To overcome this caveat, herein, we propose the use of linear scaling method (such as the original MTA method) for the estimation of single-point (SP) energies of large-sized parent molecular cluster and their respective fragments. Because the fragments of the MTA-based method, for the estimation of HB energy, are further fragmented, this proposed strategy is called as Fragments-in-Fragments (Frags-in-Frags) method. The SP energies of fragments and parent cluster calculated by the Frags-in-Frags approach were utilized to estimate the individual HB energy. The estimated individual HB energies, in various molecular clusters, by Fragsin-Frags method are found to be in excellent linear agreement with their MTA-based counterparts (R 2 = 0.9975 of 348 data points). The difference being less than 0.5 kcal/ mol in most of the cases. Furthermore, RMSD is 0.43 kcal/mol, MAE is 0.33 kcal/mol, and the standard deviation is 0.44 kcal/mol. Importantly, the Frags-in-Frags method not only enables the reliable estimation of HB energy in large molecular clusters but also requires less computational time and can be possible even with off-the-shelf hardware.

Molecular Tailoring Approach for the Direct Estimation of Individual Noncovalent Interaction Energies in Molecular Systems

“…The order of the error in the estimation of SP energies of two primary and one binary fragments of HB energy evaluation by the Frags-in-Frags method is similar to that of the parent cluster. This similar order of errors in SP energy leads to error cancellation in the estimation of energy of HBs in the (H 2 O) 20 cluster; for details see ref and discussion in the Supporting Information. The Frags-in-Frags method was also tested on other molecular clusters such as (H 2 O) n ( n = 10–16, 18, 20), (NH 3 ) 20 , (H 2 O 2 ) 12 , and (H 2 O 3 ) 8 clusters.…”

“…The reason for this impressive computational economy of the Frags-in-Frags method is attributed to the use of the MTA methodology, coupled with the possibility of the occurrence of many common (identical) fragments, whose energies are to be evaluated only once. 46 The MTA-based methodology and the computational strategies developed to overcome its limitations are now available in the form of an automated H-BEE (acronym of hydrogen bond energy estimation) Python code for molecular clusters. 92 The H-BEE software eliminates the laborious manual fragmentation and avoids tedious manual tracking of the common fragments in the Frags-in-Frags method.…”

“…Another strategy is called the Fragments-in-Fragments (Frags-in-Frags) method wherein the original MTA method developed by Gadre and co-workers − is employed for evaluating the energy of the parent cluster and its MTA-based fragments using eq . It may be noted that the fragmentation scheme for the SP energy evolution of the parent cluster and its fragments for the HB energy evaluation must remain unaltered.…”

“…However, there is no reliability check on the these energy estimates. 46 Further, these empirical equations are applicable only when a (3,−1) BCP is present. Recently, the HB energies estimated by the Espinosa method are found 46 to be largely overestimated and the sum of all HB energies does not match the total binding energy of a molecular cluster.…”

“…The first term is the classical Coulombic interaction between groups involved in the formation of an HB, with the second one being the exchange–correlation energy. However, there is no reliability check on the these energy estimates . Further, these empirical equations are applicable only when a (3,–1) BCP is present.…”