They have been characterized by a wide arsenal of experimental tools (almost all flavors of spectroscopies, see Ref. [7][8][9] for typical examples) as well as by multifarious theoretical approaches [10]: molecular orbitals analysis [11], energetic decompositions [12], conceptual DFT [13,14], Bader's atoms-in-molecules (QTAIM) theory [15][16][17][18], etc., each of them conveying complementary insight to unravel their physical nature. Among them, the σ-hole concept [19][20][21][22][23][24], forged and developed by Politzer and coworkers, has achieved a high popularity, owing to its simplicity, its versatility and its ubiquity (since it is also at work in other non-covalent bonds like pnicogen and carbon bonds), and it has clearly represented a considerable breakthrough for the understanding of these non-conventional interactions.Let us recall that the σ-hole is plainly defined as a region of positive molecular electrostatic potential (MEP) on the outer side of the halogen atom. This space region is thus prone to interact with the lone electron pair(s) carried by the partner. Recently, a similar analysis (also valid for homologous noncovalent bonds) has been proposed using, as the primary physical observable, the electron density Laplacian ∇ 2 ρ(� r) [25][26][27][28] instead of MEP, leading to the so-called lump-hole interaction paradigm [29]: the electron-deficient region at the periphery of the halogen atom is then viewed as a "hole" that can be filled by the electron-rich Lewis base's lump. Indeed, it is very well known that charge depletion areas are easily characterized by positive ∇ 2 ρ(� r) values, while charge concentration occurs when ∇ 2 ρ(� r) is negative.The aim of this paper is to provide formal evidence that the two descriptions (σ-hole point of view based on MEP, lump-hole viewpoint based on density Laplacian) are actually closely related and to hint how the latter can be used to evaluate interaction energies in the framework of Bader's atoms-in-molecules (QTAIM) [30,31] theory. Note Abstract In this paper, we discuss the physical meaning of the electron density Laplacian values in the valence region of halogen atoms and its relevance for the interpretation of halogen bonds formation. To this aim, formal relationships between Laplacian, electrostatic potential and molecular energies are derived, in particular within the framework of Bader's atoms-in-molecules theory. Simple one-dimensional models are finally provided to illustrate the semiquantitative usefulness of such tools.