A systematic investigation of cooperativity between two types of hydrogen bonding in the nonlinear clusters of an aromatic molecule: Pyrazole

Abstract

Crystalline pyrazole consists of nonlinear chains of an aromatic molecule. It includes two independent molecules which in turn causes two different types of hydrogen bonds (HBs). These two types of HBs with slight differences in their NH⋯N geometries can be considered as interesting ones in the recent studies of cooperativity between different HBs. These HBs are investigated in several pyrazole clusters by electronic structure calculations. Parameters such as structure, binding energy, charge transfer, chemical shielding and electric field gradient (EFG) parameters calculated at the second order Moller–Plesset perturbation (MP2) and density functional (DF) levels of theory. Both the basis set superposition error (BSSE) and zero point vibrational energy (ZPVE) corrections on the cooperativity enhancement were considered. Changes of different properties of clusters against crystal size were investigated by proposed diagrams fitted to a logarithmic function which renders their extrema in the crystal limit. In each cluster, pyrazole molecules for which their parameters are more affected by cooperativity enhancement were explored employing these fitted diagrams. Most calculated energetic and spectroscopic parameters were in good linear correlations with both the structural parameters and charge transfer along HB (qn(N2)→σ∗(N1–H1)). These correlations in the cases of nuclear magnetic resonance (NMR) and nuclear quadrupolar resonance (NQR) parameters, were explained in the terms of natural charges of bonding (σ(N1H1)) and antibonding (σ*(N1H1)) orbitals. Organizing calculated data for mental clusters with similar molecules and HB types produced better regression values in all linear correlations. According to the experimental CQ of N(2) in solid state and zero charge transfer in the gas phase, the value of charge transfer in the crystalline pyrazole and gas phase value of CQ of N(2) were assessed, respectively. Diagrams of the structural parameters against either crystal size or HB cooperativity propose that experimental structure in the case of both hydrogen and heavy nuclei positions is in doubt and should be revisited.