Dissipative electron transfer dynamics in mixed valence dimers: Microscopic approach to the solid state problem

Abstract

We propose a microscopic analytical approach to the description of the low-temperature dissipative intracluster electron transfer dynamics in centrosymmetric one-electron mixed-valence (MV) dimers. The dissipative system (bath) is supposed to consist of the acoustic phonons of the crystal surrounding that are coupled to the delocalized electron(s) of a MV dimer. Although the concept of the bath is the spin-boson model is more generic, the present consideration is relevant, for example, to a MV bi-center impurity in an ionic crystal. The model allows us to develop an approximate microscopic approach within which the relaxation processes are explicitly taken into account without additional assumption regarding spectral function of the bath. It is assumed that initially the extra electron is localized on a certain center and then the time-dependent localization probability (averaged value of the electron dipole moment) is evaluated with the emphasis on the damping of the amplitude of the Rabi oscillations. The approach assumes the following conditions: (i) the vibrational spectrum of the crystal does not show the presence of local modes; (ii) the itinerant electron is weakly coupled to the long-waves acoustic phonons which is peculiar to fully delocalized Robin and Day class III MV systems; (iii) the Debye energy ℏωD exceeds the electronic resonance energy gap 2β (β is the electron transfer parameter). We have demonstrated that the dissipation in this case is super-ohmic with the low-frequency spectral function J(ω) ∝ ω(5). The time dependences of the localization probabilities show nearly picosecond damped oscillations. The longitudinal relaxation time T1 has been shown to be two times shorter than the decoherence time T2 thus giving the upper bound for T2, T2 ≤ 2T1.

Electron transfer within a reaction path model calibrated by constrained DFT calculations: application to mixed-valence organic compounds

“…In this work, we model the dissipative dynamics based on the Bloch-Redfield approach, [65][66][67] which has proven its usefulness in various applications. [68][69][70][71] It is based not only on a weak coupling assumption, but also on the Markov approximation, valid when the bath correlation functions decay rapidly as compared to the typical system timescales. Note that this constraint can be overcome by non-Markovian methods, [72][73][74][75] and the vibronic Hamiltonian developed in this work could in the future be directly used within this framework.…”

Electric Field Control of Spin-Dependent Dissipative Electron Transfer Dynamics in Mixed-Valence Molecules

“…As an advantageous system, one can mention the MV vanadium dimer, formulated as [(PY 5 Me 2 ) 2 V 2 (μ-5,6-dimethylbenzimidazolate)]­(PF 6 ) 4 , which has been reported by Long et al The imidazolate is a compact, symmetric, and conjugated bridging ligand, for which manipulation of the character of the frontier orbitals is available, and therefore, the double exchange can be tuned by chemical means (see details in ref ). In this MV dinuclear vanadium­(III)–vanadium­(II) ( d 2 – d 3 ) complex, the double exchange stabilizes the high-spin state with S = 5/2, with respect to the lower-spin states with S = 3/2 and S = 1/2, which are excited states lying around 100 cm –1 above the ferromagnetic ground state . In view of our study, it is important that the role of the vibronic coupling has been underlined.…”

“…In this MV dinuclear vanadium(III)−vanadium(II) (d 2 −d 3 ) complex, the double exchange stabilizes the high-spin state with S = 5/2, with respect to the lower-spin states with S = 3/2 and S = 1/2, which are excited states lying around 100 cm −1 above the ferromagnetic ground state. 34 In view of our study, it is important that the role of the vibronic coupling has been underlined. It was indicated that this is a gap, which is actually reduced by the vibronic coupling with respect to the double exchange splitting expected in the electronic spectrum.…”

“…Therefore, the description of the dynamics is based on the quantum-mechanical model of a MV complex, but along with the intramolecular interactions, the coupling with the environment or thermal bath (solvent modes, phonons, etc.) is to be included to account for the irreversible energy dissipation. − Such dissipation represents a common phenomenon in the dynamics of complex systems in physics, chemistry, and biology. , The MV systems exhibiting electron delocalization provide examples of ultrafast ET dynamics, including short-time electronic coherence and dephasing, − the phenomena which are currently the focus of research in view of possible molecular implementations of quantum-dot cellular automata based on MV systems . It should be emphasized that the dissipative dynamics is one of the actual topic in a wide and well developed area of the Jahn–Teller (JT) and pseudo-JT effects − closely related to the problem of localization vs tunneling and measurements of the physical values in different time-scales.…”

“…The study of the dynamics will be performed in the framework of the Redfield theory for the reduced density matrix that has been initially proposed for the description of nuclear magnetic resonance phenomenon and more recently has been successfully used for modeling of ultrafast ET dynamics. − ,,− It has been demonstrated by Egorova et al that the approach based on multilevel Redfield equations, is adequate for the description of ultrafast photoinduced ET reactions in the appropriate parameter range. In the present study, we will use the multilevel version of the Redfield theory operating with the spin-vibronic energy levels obtained by the numerical solution of the dynamic vibronic problem for a magnetic MV dimer coupled to a thermal bath.…”