Motivated by recent experimental studies of hydrogen-bonded molecular conductors κ-X3(Cat-EDT-TTF)2[X=H, D], interplays of protons and correlated electrons, and their effects on magnetic, dielectric, and optical properties, are studied theoretically. We introduce a model Hamiltonian for κ-X3(Cat-EDT-TTF)2, in which molecular dimers are connected by hydrogen bonds. Ground-state phase diagram and optical conductivity spectra are examined by using the mean-field approximation and the exact diagonalization method in finite-size cluster. Three types of the competing electronic and protonic phases, charge density wave phase, polar charge-ordered phase, and antiferromagnetic dimer-Mott insulating phase are found. Observed softening of the interdimer excitation due to the electron-proton coupling implies reduction of the effective electron-electron repulsion, i.e., "Hubbard U," due to the quantum proton motion. Contrastingly, the intradimer charge excitation is hardened due to the proton-electron coupling. Implications of the theoretical calculations to the recent experimental results in κ-X3(Cat-EDT-TTF)2 are discussed.
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