Optical characterization of platinum-halide ladder compounds

Varieties of quasi-one-dimensional halogen $\left(X\right)$-bridged transition-metal $\left(M\right)$ complexes, $\left({\mathrm{C}}_8{\mathrm{H}}_6{\mathrm{N}}_4\right){\left[\mathrm{Pt}\left({\mathrm{C}}_2{\mathrm{H}}_8{\mathrm{N}}_2\right)X\right]}_{2}X{\left(\mathrm{Cl}{\mathrm{O}}_4\right)}_3\bullet {\mathrm{H}}_2\mathrm{O}$ $(X=\mathrm{Br},\mathrm{Cl})$ and $\left({\mathrm{C}}_{10}{\mathrm{H}}_8{\mathrm{N}}_2\right){\left[\mathrm{Pt}\left({\mathrm{C}}_4{\mathrm{H}}_{13}{\mathrm{N}}_3\right)\mathrm{Br}\right]}_2{\mathrm{Br}}_4\bullet 2{\mathrm{H}}_2\mathrm{O}$, comprising two-leg ladders of mixed-valent platinum ions, are described in terms of a multiband extended Peierls-Hubbard Hamiltonian. The polarized optical-conductivity spectra are theoretically reproduced, and the ground-state valence distributions are reasonably determined. The latter variety, whose interchain valence arrangement is out of phase, is reminiscent of conventional $MX$ single-chain compounds, while the former variety, whose interchain valence arrangement is in phase, reveals itself as a $d\text{−}p\text{−}\pi$-hybridized multiband ladder material.

Figure 1

(Color online) Hartree-Fock calculation of a ground-state phase diagram on the $t_{MM}^{\text{rung}}\text{−}{V}_{MM}^{\text{rung}}\text{−}{V}_{MM}^{\mathrm{diag}}$ cube within a single-band model, where $t_{MM}^{\text{leg}}$ is taken as unity and the region of no physical interest is shaded. A simple consideration of competing IP-CDW and OP-CDW states is also presented, where Coulomb energy losses and transfer energy gains within $d$ electrons are illustrated.

Figure 2

(Color online) Modeling of $MX$ ladders, where $M=\mathrm{Pt}$; $X=\mathrm{Br},\mathrm{Cl}$; and $L=\mu \text{−}\mathrm{bpym}$, bpy. An electron with spin $s=\uparrow$, $\downarrow \equiv \pm$ is created on the $M{d}_{z^2}$ and $X{p}_z$ orbitals on the $l\text{th}$ leg in the $n\text{th}$ unit by $a_{n:lMs}^{†}$ and $a_{n:lXs}^{†}$, respectively, and on the $n\text{th}$-rung $L\pi$ orbital by $a_{n:Ls}^{†}$. The resultant electron density is given by $a_{n:lMs}^{†}{a}_{n:lMs}\equiv n_{n:lMs}$, $a_{n:lXs}^{†}{a}_{n:lXs}\equiv n_{n:lXs}$, and $a_{n:Ls}^{†}{a}_{n:Ls}\equiv n_{n:Ls}$. The on-site energies (electron affinities) of isolated atoms and molecules are given by ${\epsilon }_A$ $(A=M,X,L)$, and the electron hoppings between these levels are modeled by $t_{A{A}^{\prime }}$ [$A=M,X$; $A^{\prime }(\ne A)=X,L$]. $U_A$ and $V_{A{A}^{\prime }}$ $(A,A^{\prime }=M,X,L)$ describe the on-site and different-site Coulomb interactions, respectively. The halogen-ion displacements $u_{n:l}$ affect electrons through intersite $(\alpha ,\gamma )$ and intrasite $\left(\beta \right)$ coupling constants, accompanied by elastic energy $\propto K$.

Figure 3

(Color online) Hartree-Fock (HF) and single-excitation configuration-interaction (CI) calculations of the polarized optical-conductivity spectra parallel (∥) and perpendicular (⊥) to ladder legs within the single-band model, where $t_{MM}^{\text{leg}}=0.75\mathrm{eV}$ $\left(0.66\mathrm{eV}\right)$, $t_{MM}^{\text{rung}}∕t_{MM}^{\text{leg}}=0.35$ (0.16), $U_M∕t_{MM}^{\text{leg}}=1.40$ (1.20), $V_{MM}^{\text{leg}}∕t_{MM}^{\text{leg}}=0.35$ (0.35), $V_{MM}^{\text{rung}}∕t_{MM}^{\text{leg}}=0.30$ (0.25), $V_{MM}^{\mathrm{diag}}∕t_{MM}^{\text{leg}}=0.26$ (0.10), and $\beta ∕\sqrt{t_{MM}^{\text{leg}}K}=1.10$ (1.00) for IP CDW (OP CDW). Hartree-Fock calculations of the relevant dispersion relations are also shown in an attempt to understand the spectral features of ${\sigma }_{\parallel }\left(\omega \right)$, where bare arrows and those with a cross attached denote major optical absorptions and optically forbidden transitions, respectively.

Figure 4

(Color online) Hartree-Fock (HF) and single-excitation configuration-interaction (CI) calculations of the polarized optical-conductivity spectra parallel (∥) and perpendicular (⊥) to ladder legs for IP-CDW states in comparison with experimental observations (exp) of $\left(\mathrm{bpym}\right){\left[\mathrm{Pt}\left(\mathrm{en}\right)X\right]}_2$.

Figure 5

(Color online) Hartree-Fock (HF) and single-excitation configuration-interaction (CI) calculations of the polarized optical-conductivity spectra parallel (∥) and perpendicular (⊥) to ladder legs for an OP-CDW state in comparison with experimental observations (exp) of $\left(\mathrm{bpy}\right){\left[\mathrm{Pt}\left(\mathrm{dien}\right)\mathrm{Br}\right]}_2$.

Figure 6

(Color online) Hartree-Fock calculations of the dispersion relation ${ϵ}_k$ and the local (total) density of states ${\rho }_{n:lA}\left(ϵ\right)$ $[\rho \left(ϵ\right)\equiv {\sum }_{n,l,A}{\rho }_{n:lA}\left(ϵ\right)]$ for the (a) IP-CDW and (b) OP-CDW states describing $\left(\mathrm{bpym}\right){\left[\mathrm{Pt}\left(\mathrm{en}\right)\mathrm{Cl}\right]}_2$ and $\left(\mathrm{bpy}\right){\left[\mathrm{Pt}\left(\mathrm{dien}\right)\mathrm{Br}\right]}_2$, respectively. Major optical absorptions with ${\mathit{E}}_{\mathrm{in}}\parallel \mathit{c}$ and ${\mathit{E}}_{\mathrm{in}}\perp \mathit{c}$ are indicated by solid and dotted arrows, respectively, in Figs. 4, 5 as well as here.

Figure 7

(Color online) Single-excitation configuration-interaction calculations (solid lines) of the polarized optical-conductivity spectra parallel to ladder legs for IP-CDW states in comparison with an experimental observation (a dotted line) of $\left(\mathrm{bpym}\right){\left[\mathrm{Pt}\left(\mathrm{en}\right)\mathrm{Cl}\right]}_2$, where (a) $U_M$, (b) $\beta$, and (c) $\alpha$ are tuned, while the rest are fixed at set A in Table .

Figure 8

(Color online) Single-excitation configuration-interaction calculations (solid lines) of the polarized optical-conductivity spectra parallel to ladder legs for IP-CDW states in comparison with an experimental observation (a dotted line) of $\left(\mathrm{bpym}\right){\left[\mathrm{Pt}\left(\mathrm{en}\right)\mathrm{Cl}\right]}_2$, where (a) $U_X$ and (b) ${\epsilon }_X$ are tuned, while the rest are fixed at set A in Table .

Figure 9

(Color online) Single-excitation configuration-interaction calculations (solid lines) of the polarized optical-conductivity spectra parallel to ladder legs for IP-CDW states in comparison with an experimental observation (a dotted line) of $\left(\mathrm{bpym}\right){\left[\mathrm{Pt}\left(\mathrm{en}\right)\mathrm{Cl}\right]}_2$, where (a) $U_L$, (b) ${\epsilon }_L$, and (c) $t_{ML}$ are tuned, while the rest are fixed at set A in Table .

Figure 10

(Color online) Single-excitation configuration-interaction calculations (solid lines) of the polarized optical-conductivity spectra parallel to ladder legs for IP-CDW states in comparison with an experimental observation (a dotted line) of $\left(\mathrm{bpym}\right){\left[\mathrm{Pt}\left(\mathrm{en}\right)\mathrm{Cl}\right]}_2$, where all the parameters but $V_{MX}^{\text{leg}}$ are fixed at set A in Table .