Abstract: Spin-1/2 chains with alternating antiferromagnetic (AFM) and ferromagnetic (FM) couplings have attracted considerable interest due to the topological character of their spin excitations. Here, using density functional theory and density-matrix renormalization-group (DMRG) methods, we have systematically studied the dimerized chain system ${\mathrm{Na}}_2{\mathrm{Cu}}_2{\mathrm{TeO}}_6$ with a $d^9$ electronic configuration. Near the Fermi level, in the nonmagnetic phase the dominant states are mainly contributed by the Cu $3d_{x^2-y^2}$ orbitals highly hybridized with the O $2p$ orbitals, leading to an “effective” single-orbital low-energy model. By calculating the relevant hoping amplitudes, we explain the size and sign of the exchange interactions in ${\mathrm{Na}}_2{\mathrm{Cu}}_2{\mathrm{TeO}}_6$. In addition, a single-orbital Hubbard model is constructed for this dimerized chain system where the quantum fluctuations are taken into account. Both AFM and FM couplings (leading to an $\uparrow \text{−}\downarrow \text{−}\downarrow \text{−}\uparrow$ state) along the chain were found in our DMRG and Lanczos calculations, in agreement with density functional theory and neutron-scattering results. The hole pairing binding energy $\mathrm{\Delta }E$ is predicted to be negative at Hubbard $U\sim 11\mathrm{eV}$, suggesting incipient pairing tendencies.