AbstractDFT results and the analysis of the energetic and structural landscape of the title complexes are reported. It is shown that the minima of the ground state potential energy surface occur at positions corresponding to tetragonally compressed structures of D2d symmetry, with rather distinct electronic stabilization energies in respect to the tetrahedral parent complexes. The structural distortion and the accompanying energetic effects are found to increase with increasing ligand hardness, i.e. from Br– to Cl– to F–. The results are discussed and compared by conventional vibronic coupling and angular overlap model calculations. The Jahn–Teller interaction between the 2T2 ground state and the ϵ‐vibrational mode of tetrahedral CuX42– splits the 2T2 ground state; this coupling is supported by 3d–4s mixing, which softens the ground state potential energy surface along the ϵ normal mode [formally a T2(d9) ⊕ ϵ ⊕ T2 (d8s1) pseudo Jahn–Teller coupling interaction in Td]. The vibronic activity may also occur along the trigonal τ2 modes, which leads to C3v‐ or, if both types of pathway are involved, C2v‐ [2T2 ⊕ (ϵ + τ2) coupling] distorted structures, which are very weak as compared to D2d deformations. Theoretical results are validated and used to explain the structural diversity and electronic spectra reported for CuCl42– in various crystal structures. A strain model, which differentiates between an elastic and a binding component, is qualified for getting an understanding for the appearance of structures from tetrahedral to square planar. In the considered cases, it is generally the elastic strain component, which governs the structural and energetic scene, though the binding strain increment is not negligible sometimes (e.g. Cs2CuCl4). Predictions in respect to corresponding compounds with F– and Br– ligands are made.