Electron density and its reduced density gradient in the study of π–π interactions

Abstract

(Figure presented.) interactions are unique dispersive interactions that are important for biological systems and materials, but the study of this interaction is not trivial. It is well-known that density functional theory (DFT) does not describe these interactions correctly and only with empirical dispersion corrections, it produces accurate energies. Moreover, little is known about the error in the electron density ((Figure presented.)). Non-Covalent Interaction method (NCI) has been used to analyze (Figure presented.) stacking from the electron density. However, for these interactions, the information that can be extracted with this method is quite limited. We compare the DFT and CCSD intermolecular (Figure presented.). The correlation between both densities is close to one, but DFT underestimates its value. To evaluate, if the strength of the (Figure presented.) interaction can be qualitatively inferred from density related scalar fields, we study the correlation between these fields ((Figure presented.) multiplied by the sign of the second eigenvalue of its hessian, (Figure presented.), the laplacian of (Figure presented.), (Figure presented.), the virial field, (Figure presented.), the Lagrangian, (Figure presented.), and the Hamiltonian, (Figure presented.), kinetic energy density) and the interaction energy. Surprisingly, all the scalar fields have a better correlation with the energy than (Figure presented.). This quantity is normally plotted over the reduced density gradient (RDG) isosurface in the NCI method to get an insight of intermolecular interactions, but the other scalar fields give a better picture of the energetic nature of (Figure presented.) interactions. Moreover, we show that (Figure presented.) cannot be used as an indicator of repulsive interactions (positive values), because for the studied (Figure presented.) systems, the more energetic the interaction is, the more positive (Figure presented.).