First-principles study of hydrogen-bonded molecular conductor $\kappa -{\mathrm{H}}_3{(\text{Cat}-\text{EDT}-\text{TTF}/\text{ST})}_2$

We theoretically study hydrogen-bonded molecular conductors synthesized recently, $\kappa -{\mathrm{H}}_3{(\text{Cat}-\text{EDT}-\mathrm{TTF})}_2$ and its diselena analog, $\kappa -{\mathrm{H}}_3{(\text{Cat}-\text{EDT}-\mathrm{ST})}_2$, by first-principles density functional theory calculations. In these crystals, two H(Cat-EDT-TTF/ST) units share a hydrogen atom with a short O–H–O hydrogen bond. The calculated band structure near the Fermi level shows a quasi-two-dimensional character with a rather large interlayer dispersion due to the absence of insulating layers, in contrast with conventional molecular conductors. We discuss effective low-energy models based on H(Cat-EDT-TTF/ST) units and its dimers, respectively, where the microscopic character of the orbitals composing them are analyzed. Furthermore, we find a stable structure which is different from the experimentally determined structure, where the shared hydrogen atom becomes localized to one of the oxygen atoms, in which charge disproportionation between the two types of H(Cat-EDT-TTF) units is associated. The calculated potential energy surface for the H atom is very shallow near the minimum points; therefore the probability of the H atom can be delocalized between the two O atoms.

Figure 1

(a) Crystal structure of $\kappa$-type ${\mathrm{H}}_3$(Cat-EDT-TTF)${}_2$ ($\kappa$-S) measured at 50 K. (b) Molecular structure of ${\mathrm{H}}_3$(Cat-EDT-TTF/ST)${}_2$.

Figure 2

View of the crystal structure along the $a$ axis showing the $bc$ plane. Definitions of (a) intermolecular and (b) interdimer bonds are presented.

Figure 3

(a) First-principles band structure of $\kappa -{\mathrm{H}}_3$(Cat-EDT-TTF)${}_2$. (b) Energy diagram of isolated monomer ${\mathrm{H}}_2$(Cat-EDT-TTF) and its dimer, ${\mathrm{H}}_4$(Cat-EDT-TTF)${}_2$, where all the O–H bonds were set to be 1.0 Å. (c) First-principles band structure of $\kappa -{\mathrm{H}}_3$(Cat-EDT-ST)${}_2$. (d) Schematic energy diagram of isolated monomer ${\mathrm{H}}_2$(Cat-EDT-ST) and its dimer, ${\mathrm{H}}_4$(Cat-EDT-ST)${}_2$. In both band structures (a) and (c), dotted curves show the fitted results for the four-band model, and dashed curves show the fitted results of the two-band (dimer) model. The origin of the vertical axis with a dashed line shows the Fermi level.

Figure 4

Notation of interlayer bonds of $\kappa -{\mathrm{H}}_3$(Cat-EDT-TTF)${}_2$. $l_1$ and $l_2$ are those between the H(Cat-EDT-TTF) units, whose former is that connected by the shared H atom. $L_1$ and $L_2$ denote the two different interdimer bonds.

Figure 5

Partial density of states of $\kappa -{\mathrm{H}}_3$(Cat-EDT-TTF)${}_2$ with the space group $C2/c$. The atom assignments are shown in the figure (see also Table 3). The origin of the vertical axis with a dashed line shows the Fermi level.

Figure 6

Structural properties around hydrogen bonds in H-localized structure ($P\overline{1}$) of $\kappa -{\mathrm{H}}_3$(Cat-EDT-TTF)${}_2$. The shared H atom (H1) is located at the fractional coordinate of (0.010, –0.008, 0.241) [(0.000, –0.010, 0.250) in the optimized $C2/c$ structure].

Figure 7

Band structures of optimized (a) $C2/c$ and (b) H-localized ($P\overline{1}$) structures of $\kappa -{\mathrm{H}}_3$(Cat-EDT-TTF)${}_2$. To see how the degenerated bands split by the symmetry lowering, the band structure along the common symmetric line is plotted [different from Fig. 3]. (c) Local density of states (LDOS) of the H(Cat-EDT-TTF) with $C2/c$ (solid curve) and $P\overline{1}$ structures. The latter contains two parts, ${\mathrm{H}}_2$(Cat-EDT-TTF) (dashed curve) and H(Cat-EDT-TTF) (broken curve). (d) LDOS of the TTF part, which is summation of the partial DOS from C–$p$, S–$p$, O–$p$, and H–$s$ states belonging to each TTF part. The origin of the vertical axis with a dashed line shows the Fermi level.

Figure 8

Potential energy curves for the shared H atom in $\kappa -{\mathrm{H}}_3$(Cat-EDT-TTF)${}_2$. Solid circles show potential energies for the optimized $C2/c$ structure. Open squares show potential energies for the $P\overline{1}$ structure. The origin of the longitudinal axis is set to be the minimum point of the $P\overline{1}$ structure. The horizontal axis is the fractional $z$ coordinate of the shared H atom located between two O atoms. H ($z$) = 0.25 corresponds to the center between two O atoms.