It is known that within the interacting electron model Hamiltonian for the one-dimensional $\frac{1}{4}$-filled band, the singlet ground state is a Wigner crystal only if the nearest-neighbor electron-electron repulsion is larger than a critical value. We show that this critical nearest-neighbor Coulomb interaction is different for each spin subspace, with the critical value decreasing with increasing spin. As a consequence, with the lowering of temperature, there can occur a transition from a Wigner crystal charge-ordered state to a spin-Peierls state that is a bond-charge-density wave with charge occupancies different from the Wigner crystal. This transition is possible because spin excitations from the spin-Peierls state in the $\frac{1}{4}$-filled band are necessarily accompanied by changes in site charge densities. We apply our theory to the $\frac{1}{4}$-filled band quasi-one-dimensional organic charge-transfer solids, in general, and to 2:1 tetramethyltetrathiafulvalene (TMTTF) and tetramethyltetraselenafulvalene cationic salts, in particular. We believe that many recent experiments strongly indicate the Wigner crystal to bond-charge-density Wave transition in several members of the TMTTF family. We explain the occurrence of two different antiferromagnetic phases but a single spin-Peierls state in the generic phase diagram for the 2:1 cationic solids. The antiferromagnetic phases can have either the Wigner crystal or the bond-charge-spin-density wave charge occupancies. The spin-Peierls state is always a bond-charge-density wave.

• Received 21 September 2007

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