The best known choice for extension of E v [ρ] into the noninteger domain is the one of ref. 18 -namely, forming an ensemble of the ground-state density matrix of the N-electron system with either the density matrix of the ground state of the (N + 1) system or the ground state of the (N -1) system. This procedure leads to piecewise linear energy behaviour. This choice precludes application of the Euler-Lagrange variation method because the derivative ∂ E/∂ N does not exist (is discontinuous at the integer point). More extensive discussion of these matters is given in ref. (3.9.3) Liu : Two schemes for partitioning the total energy in DFT have been applied to understand different chemical processes and transformations. From these schemes, a unified view of molecular conformational stability has emerged, in which the electrostatic interaction plays the dominant role, while the contributions of steric repulsion and quantum effects are minor indispensable. This was also recently utilized to analyse the effects of cooperativity, 479 frustration, 480 and homochirality. Regioselectivity, nucleophilicity, and electrophilicity have also been quantified by information gain and Hirshfeld charge. Recent studies of density-based quantities for aromaticity and antiaromaticity yielded two opposite propensities, one for aromaticity and the other for antiaromaticity, depending on the number of π-electrons. 193 (3.9.4) Chermette : As pointed out in contribution (3.9.3), for most molecular systems, the electrostatic interactions dominate over steric repulsion and other quantum effects. Accordingly, an analysis of the molecular perturbation introduced by a small charge (typically ±0.1e) leads to interesting insights in the understanding of reactivity.