Two-Step Hybrid Method for the Energetics of Individual Noncovalent Interactions in Molecular Crystals

Abstract

We present a two-step method for the direct estimation of the energy of individual non-covalent interactions (NCIs) such as hydrogen bond (HB), CH…π or π…π interactions in any given molecular crystal. The first step of this method is to calculate the energy of a NCI by a molecular tailoring approach based (MTA-based) method utilizing a sufficiently large molecular crystal structure. This calculation is performed at the low Hartree–Fock (HF) level. In the next step, the energy of the same referenced NCI is evaluated by the MTA-based method employing a suitable monomeric or dimeric species. This calculation is usually performed at both the high (B3LYP, MP2 or CCSD(T)) and low (HF) levels. Note that the NCI energies in monomeric or dimeric species are significantly different from those in the actual crystal. The difference in the energy calculated in the second step at high and low levels is added to the energy of this NCI calculated (at HF level) in the first step employing a large molecular crystal. The energies of NCIs calculated by this two-step method are compared with their actual crystal counterparts. For this purpose, molecular crystals of L-Histidine (LH), nitromalonamide (NMA) and salicylic acid (SA) are chosen as test cases. It is found that the proposed two-step method provides very accurate energy of individual NCIs in these molecular crystals. For instance, the estimated energies of NCIs by the proposed two-step method are in excellent linear agreement with their actual crystal counterparts (R² = 0.9983). Furthermore, RMSD and standard deviation are 0.22 and 0.24 kcal/mol, respectively, with a mean and maximum absolute error being 0.15 and 0.51 kcal/mol, respectively. Importantly, the two-step method is computationally efficient and saves nearly 50% of computational time vis-à-vis its full calculation counterpart employing the actual molecular crystal.