Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics

Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested

A modified Ehrenfest formalism for efficient large-scale ab initio molecular dynamics

We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave-functions, which can become the bottleneck for very large systems. Alternatively, one can handle the electron-ion dynamics within the Ehrenfest scheme where no explicit orthogonalization is necessary, however the time step is too small for practical applications. Here we preserve the desirable properties of Ehrenfest in a new scheme that allows for a considerable increase of the time step while keeping the system close to the Born-Oppenheimer surface. We show that the automatically enforced orthogonalization is of fundamental importance for large systems because not only it improves the scaling of the approach with the system size but it also allows for an additional very efficient parallelization level. In this work we provide the formal details of the new method, describe its implementation and present some applications to some test systems. Comparisons with the widely used Car-Parrinello molecular dynamics method are made, showing that the new approach is advantageous above a certain number of atoms in the system. The method is not tied to a particular wave-function representation, making it suitable for inclusion in any AIMD software package.Comment: 28 pages, 5 figures, published in a special issue of J. Chem. Theory Comp. in honour of John Perde

Trifluorocoumarino Cryptands as Photoprotonic Molecules: Basic Features and Theoretical Considerations

The coupling between the fluorescence properties of the (trifluoromethyl)coumarino fluorophore and the protolytic state of the ion binding moiety of two fluorescent cryptands, F221 and F222, is investigated experimentally by carrying out steady-state and time-resolved fluorescence measurements. The high-intensity fluorescence emission of the diprotonated state of the these alkali ion-selective indicators, characterized by quantum yields of 0.6 and 0.83 as well as by lifetimes of 5.3 and 5.6 ns, are markedly quenched upon deprotonation, which leads to the monoprotonated state with quantum yields of 0.07 and 0.02 as well as lifetimes of 1.0 and 0.19 ns, respectively. The corresponding pKa1 values are 7.07 for F221 and 5.85 for F222. The formation of the fully deprotonated state of the fluorescent cryptands, characterized by pKa2 values of 10.6 and 9.3, respectively, is accompanied by a comparatively small additional reduction of the fluorescence quantum yield and lifetime. As a framework for the understanding of the pH-dependent fluorescence parameters, we suggest the concept of fluorescence quenching via photoinduced electron transfer (PeT), where the quenching process is assumed to be controlled by the pH-dependent availability of nonprotonated bridgehead N-atoms of the cryptand. These N-atoms act as electron donors with respect to the excited fluorophore, which functions as electron acceptor. In order to quantify the PeT energetics in the case of F221 and its monoprotonated state, one-electron oxidation and reduction potentials are determined by cyclic voltammetry for the parent cryptand [2.2.1] and the fluorophore derivative I as suitable model compounds, respectively. Experimental redox data are supplemented by simple estimations of the electrostatic energy contributions for the intramolecular radical ion pair produced through photoinduced charge separation and by corrections for the hydration energies. The resulting thermodynamic driving forces for PeT in the deprotonated F221 and its monoprotonated form show that PeT is favored for both of these species in water, where only a minor endergonic shift is observed for the monoprotonated as compared to the fully deprotonated compound. Therefore, the fully de- and the monoprotonated state of these fluorescent cryptands are regarded as being responsible for the reduction of the fluorescence quantum yield and the appearance of the second lifetime τ2 at high pH. In contrast, PeT is expected to be completely blocked for the diprotonated state of these (trifluoromethyl)coumarino cryptands