As a result, the ELF can range from 0 to 1, where 0.5 occurs when D σ = D 0 σ , in other words, ELF = 0.5 is the probability of finding two electrons with the same spin in a particular region of space for the system of interest as if calculated for a uniform electron gas. The first important aspect to notice is that the ELF, by definition, does not provide any direct information about the presence or absence of electron pairs. In fact, ELF ∼1 can be found in regions of space occupied by a single, isolated electron (e.g. a hydrogen atom in a box, Figure ). However, it is generally assumed that in a multi-electron system the region of space populated by an electron of spin α is automatically invaded by an electron of β spin, hence the common, but incorrect, assertion that ELF always plots regions where electron pairs are likely to be found. Though it is formally allowed for α and β electrons to share the same spatial position, the ELF, per se, does not specifically quantify the probability of finding such electron pairs. Consequently, since the formulation of the ELF is based on the probability that the electrons in a given spatial region have the same spin, it can instead be understood as a measure of the excess of local kinetic energy generated by Pauli exclusion. A second important aspect to consider is that at any point in space the ELF will always have a non-zero value as long as some electron density is present. Therefore, plotting values of the ELF below 0.5 does not mean that electrons are localized, but it only signifies that the electron density is very flat and dilute (less dense than in a uniform electron gas) in that specific region of space. Any other region of space that does not behave like a freeelectron gas will have ELF > 0.5. For example, ELFs as high as 0.7 can be found in pure metals and superconductors. Higher ELF values, ∼0.9, can be found for lone pairs in water, around an isolated hydrogen atom with its single electron, between two sp 3 bonded carbon atoms in diamond, and in interstitial regions when 1 atm metals are squeezed to high densities (Figure ). Since values of ELF close to 1 occur only when P σσ cond (r, s) ∼ 0, they only provide information about the Pauli exclusion in a specific region. Therefore, the value of the ELF alone is not sufficient to unambiguously classify a chemical system as being an electride, despite the fact that it is has been widely exploited for this purpose. This aspect becomes particularly evident upon the topological analysis of the electron density and the ELF properties of Ca under pressure. Looking at the ELF values alone, might lead one to conclude that Ca-fcc at 0 GPa has a higher localization of electrons than Ca-bcc at 25 GPa, as previously proposed. On the other hand, the topology of the electron density reveals that the critical point (cp) in the fcc structure has a lower value of the electron density than both of the cps found in the bcc phase (c.f. ρ(r) values given in Figure ). Moreover, the topological analysis reveals that the cp found at the center of the Ca octahedron of the fcc phase is located at a minimum of the electron density (cp = (3,+3) in QTAIM's notation, where the first value tells us that the scalar function is 3D, and the second value is the sum of the algebraic signs of the non-zero curvatures). This cp, characterized by a positive Laplacian of the electron density (∇ 2 ρ(r) value given in Figure ), therefore corresponds to a minimum of the electron density -the topological opposite of a charge concentration point.