Quantum rate efficiency of the charge transfer mediated by quantum capacitive states

On the fundamentals of quantum rate theory and the long-range electron transport in respiratory chains

“…The b and l terms of the electron coupling of the molecular film are obtained (or inferred) independently, as discussed in ref. 14, from where it was demonstrated a good agreement (B3% of differences) between the parameters inferred from a capacitivederived impedance analysis and that obtained independently. For instance, G/G 0 and N are obtained from impedance or complex capacitance spectra, as shown in Fig.…”

“…which not only establishes a direct correlation between the exchange (or ambipolar) current i 0 and c * , as is required for an appropriate physical description of the meaning of charge transfer resistance R ct = 1/G 0 of a single electron in the field of electrochemistry, 11,14 but eqn ( 12) also establishes the meaning of i 0 directly as a function of n through the elementary charge of the electron e. Noteworthy is that i 0 = en, where i 0 p c * is established as e/l, which is the electron density in the quantum channel.…”

“…This nature implies that i 0 of a single electron is not only ambipolar (see the ESI, † SI.3) but also has a time-dependent meaning that implies electric current dynamics with a net value at the Fermi level within equivalent amounts of electron and hole carriers flowing in opposite directions. The physical meaning of the latter statement for redox reactions 14 is that there is the transport of electron (reduction) and hole (oxidation) carriers flowing in opposite directions at the equilibrium of the reaction whereas the rate of the reaction is purely defined in terms of chemical kinetics (name exchange current), where the meaning of the ambivalence of electric current is generally disregarded. In other words, the oxidation and reduction electric currents are of the same magnitude but in the opposite direction for electrochemical reaction at equilibrium, implying the presence of an exchange current of i 0 , which in terms of physical terminology is ambipolar and related to g e , as discussed in Section 2.…”

“…2 (a) D and A states comprising a quantum channel with a short path length l (no longer than 3 nm) for ET through a potential energy of the barrier (eV) that defines a tunneling electron coupling between D and A such that k = exp(Àbl), where b is a constant that defines the properties of the barrier; and m D and m A are the chemical potentials states D and A, defining a chemical potential difference that complies with Dm = ÀeV = e 2 / C q . 11,14 For an adiabatic or ballistic quantum conductance with a perfect transmittance k B 1, the conductance through the barrier is theoretically stated as G 0 = g s e 2 /h B 77.5 mS. 11,14 (b) D (oxidation) and A (reduction) states of the redox reaction Ox + e , Red has been demonstrated to possess electrodynamics that follows relativistic quantum mechanics. 11,15 Fig.…”

Quantum rate as a spectroscopic methodology for measuring the electronic structure of quantum dots

“…11 Furthermore, quantum rate theory has been useful for the study of quantum electrochemical principles, 11,15 for example demonstrating that charge transfer resistance is essentially a specific setting of the quantum conductance principle. 16 This has provided the basis for the design of improved electrochemical interfaces for electron transport 17 with multiple applications.…”