During the development of a new TB method (working title: g-xTB), we observed the latter issue in CEH-v1: For a diatomic system like LiNa, artificial CT occurs from the slightly higher lying Li valence 2s level to the sodium, leading to the unphysical heterolytic dissociation into Li + and Na -above 5.0 Å. As apparent from the gray lines in Fig. , the increasing CT (solid line) runs in parallel with the quickly diminishing fundamental gap (dashed line) at larger distances (0.02 eV above 5 Å). One approach to mitigate this issue in a single-diagonalization approach is an increased electronic temperature, which "smears out" the occupation over the energy levels. For close-lying levels, Fermi statistics at a sufficiently high electronic temperature (4000 K for CEH-v2) yields an almost equal population of both levels. The increased electronic temperature in CEH-v2 (blue lines) limits the CT to < 0.2e - in the dissociation limit, even though the HOMO-LUMO gap is even smaller than in CEH-v1 (0.01 eV at 10 Å). Beyond the electronic temperature, CEH-v2 uses an explicit electrostatics term and a slightly more diffuse basis set to delay the decay of the off-diagonal Hamiltonian matrix elements. This leads to a larger and more slowly decaying fundamental gap and also a limitation of artificial CT at shorter distances (< 0.1e -below 5Å). As expected, both EEQ and ωB97M-V correctly dissociate also with an equal population at lithium and sodium.