Magnetic susceptibility of alkali-TCNQ salts and extended Hubbard models with bond order and charge density wave phases

The molar spin susceptibilities $\chi (T)$ of Na-TCNQ, K-TCNQ and Rb-TCNQ(II) are fit quantitatively to 450 K in terms of half-filled bands of three one-dimensional Hubbard models with extended interactions using exact results for finite systems. All three models have bond order wave (BOW) and charge density wave (CDW) phases with boundary $V=V_c(U)$ for nearest-neighbor interaction $V$ and on-site repulsion $U$. At high $T$, all three salts have regular stacks of $\mathrm{T}\mathrm{C}\mathrm{N}{\mathrm{Q}}^{-}$ anion radicals. The $\chi (T)$ fits place Na and K in the CDW phase and Rb(II) in the BOW phase with $V\approx V_c$. The Na and K salts have dimerized stacks at $T<T_d$ while Rb(II) has regular stacks at 100K. The $\chi (T)$ analysis extends to dimerized stacks and to dimerization fluctuations in Rb(II). The three models yield consistent values of $U$, $V$ and transfer integrals $t$ for closely related $\mathrm{T}\mathrm{C}\mathrm{N}{\mathrm{Q}}^{-}$ stacks. Model parameters based on $\chi (T)$ are smaller than those from optical data that in turn are considerably reduced by electronic polarization from quantum chemical calculation of $U$, $V$ and $t$ on adjacent $\mathrm{T}\mathrm{C}\mathrm{N}{\mathrm{Q}}^{-}$ ions. The $\chi (T)$ analysis shows that fully relaxed states have reduced model parameters compared to optical or vibration spectra of dimerized or regular $\mathrm{T}\mathrm{C}\mathrm{N}{\mathrm{Q}}^{-}$ stacks.