Vibronic Interactions in Polynuclear Mixed‐Valence Clusters

A Mixed-Valence Octanuclear Iron−Oxo Pyrazolate: Assessment of Electronic Delocalization by Structural and Spectroscopic Analysis

“…The timescale of electronic spectroscopy (~10 -15 s), which classifies 2 — as weakly coupled system, is our current best estimate of the electron-transfer rate. Examples of other delocalized systems exhibiting valence localization of the ground state at the XPS time scale exist in the literature 12. The present study provides an entry to the spectroscopic investigation of oxo-analogues of the well studied and biologically relevant Fe 4 S 4 -cubanes 4.…”

Ferromagnetic Nanoscale Electron Correlation Promoted by Organic Spin-Dependent Delocalization

“…This Hamiltonian yields a modified energy spectrum with twice the number of S T states generated by the HDvV Hamiltonian. 22,31,32,34–36 $$\begin{array}{c}\hfill {Ĥ}_{S_T=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\begin{array}{ccc}false|S_T,S_A,S_{B}false\rangle \hfill & \hfill true|\frac{3}{2},1,\frac{1}{2}true\rangle \hfill & \hfill true|\frac{3}{2},\frac{1}{2},1true\rangle \hfill \\ true|\frac{3}{2},1,\frac{1}{2}true\rangle \hfill & \hfill -J\hfill & \hfill H_{\text{italicAB}}\hfill \\ true|\frac{3}{2},\frac{1}{2},1true\rangle \hfill & \hfill H_{\text{italicAB}}\hfill & \hfill -J\hfill \end{array}\hfill \\ \hfill {Ĥ}_{S_T=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\begin{array}{ccccc}false|S_T,S_A,S_{B}false\rangle \hfill & \hfill true|\frac{1}{2},1,\frac{1}{2}true\rangle \hfill & \hfill true|\frac{1}{2},\frac{1}{2},1true\rangle \hfill & \hfill true|\frac{1}{2},0,\frac{1}{2}true\rangle \hfill & \hfill true|\frac{1}{2},\frac{1}{2},0true\rangle \hfill \\ true|\frac{1}{2},1,\frac{1}{2}true\rangle \hfill & \hfill -J\hfill & \hfill \frac{H_{\text{italicAB}}}{2}\hfill & \hfill 0\hfill & \hfill \frac{\sqrt{3}}{2}{H}_{\mathit{\text{AB}}}\hfill \\ true|\frac{1}{2},\frac{1}{2},1true\rangle \hfill & \hfill \frac{H_{\mathit{\text{AB}}}}{2}\hfill & \hfill -J\hfill & \hfill \frac{\sqrt{3}}{2}{H}_{\mathit{\text{AB}}}\hfill & \hfill 0\hfill \\ true|\frac{1}{2}\hfill \end{array}\hfill \end{array}$$…”

“…7 requires some comment, as it differs substantially from that commonly encountered for transition metal systems that have been observed to display spin-dependent delocalization. 32,38 This difference is due to the comparatively weak “single-site” exchange resulting from the 1,4-phenylene bridge 39 and parameterized by the magnitude of J NN(A)-SQ(A) . Coupled with the magnitude of H AB , this leads to a strong configurational mixing between the |S T =1/2, S A =1, S B =1/2> and |S T =1/2, S A =0, S B =1/2> states, and this wavefunction mixing is clearly evident in Figure 12.…”

Vibrational detection and control of spin in mixed-valence molecular transistors

“…2,3,7 In contrast, the antisymmetric mode, Q − , couples to the internal charge imbalance n 1 − n 2 . Together with the intramolecular tunneling, t, this results in the PJT effect, 17 i.e., Hamiltonian ͑2͒ mixes electronic and vibrational states of the mode Q − .…”

“…Importantly, in mixedvalence molecules J H is much larger than the other energy scales, J H ӷ ͉J͉ , , t ͑typical values: J H ϳ 1 eV, J , t ϳ 1 -100 meV, ϳ tens of meV͒. 17,23,24 This scale separation derives from the intraionic origin of J H ͑direct Hund exchange͒, in contrast to the intramolecular processes involved in the exchange J and hopping t. We assume a ferromagnetic coupling, J H Ͼ 0, i.e., a less than half filled ionic shell. The excitations where S i and s i are aligned antiparallel can therefore be neglected.…”