A modified Hubbard model with linear coupling to both lattice phonons and molecular vibrations is applied to the structural and electronic instabilities of organic charge-transfer (CT) salts such as tetrathiafulvalene-chloranil (TTF-CA). The potential energy surface (PES) of the correlated model is found exactly in finite one-dimensional (1D) systems with a mean-field approximation for 3D Coulomb interactions and parameters close to first or second-order phase transitions. The PES near a first-order transition has multiple minima with different values of $\rho$, the degree of CT in the ground state. The energy of metastable domains is related to their length $L$, to the discontinuity $\Delta \rho$ at the transition, and to the energy $2E_w$ of two domain walls. Sharp and relaxed domain walls are modeled by free spinless fermions coupled to both phonons and molecular vibrations whose ground-state PES is obtained in chains of up to 1000 sites. When $\Delta \rho$ is sufficiently small, metastable domains become thermally accessible at low temperature where the Boltzmann population of electronic excitations is negligible. The pressure-induced transition of TTF-CA is discussed in terms of an equilibrium between stable and metastable domains with different $\rho$, using previous parameters for the temperature-induced transition, where metastable domains are not accessible thermally. In either correlated or uncorrelated models, linear coupling of electrons to slow, harmonic coordinates for lattice and molecular vibrations leads to strongly anharmonic PES near an electronic or structural instability. CT salts with neutral-ionic transitions illustrate competition between a lattice phonon that drives a second-order Peierls transition and molecular vibrations that favor a first-order $\Delta \rho$.

• Received 29 January 2007

DOI:https://doi.org/10.1103/PhysRevB.75.155119