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

pi - pi 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 (rho(r)). Non-Covalent Interaction method (NCI) has been used to analyze p 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 (rho(r)). The correlation between both densities is close to one, but DFT underestimates its value. To evaluate, if the strength of the pi - pi interaction can be qualitatively inferred from density related scalar fields, we study the correlation between these fields (rho(r)) multiplied by the sign of the second eigenvalue of its hessian, sign (lambda(2))rho, the laplacian of (rho(r)), del(2)(rho(r)), the virial field, V(r), the Lagrangian, G(r), and the Hamiltonian, K(r), kinetic energy density) and the interaction energy. Surprisingly, all the scalar fields have a better correlation with the energy than sign (lambda(2))rho. 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 pi - pi interactions. Moreover, we show that sign(lambda(2))rho. cannot be used as an indicator of repulsive interactions (positive values), because for the studied pi systems, the more energetic the interaction is, the more positive sign(lambda(2))rho.

Automated summary

π-π interactions are important for biological systems and materials, but studying them is challenging. Density functional theory (DFT) fails to describe these interactions accurately, and little is known about the error in the electron density. The Non-Covalent Interaction method (NCI) has limited capability in analyzing these interactions.