K. L. Sebastian

Resonance energy transfer from a dye molecule to graphene

We study the distance dependence of the rate of resonance energy transfer from the excited state of a dye to the pi system of graphene. Using the tight-binding model for the pi system and the Dirac cone approximation, we obtain the analytic expression for the rate of energy transfer from an electronically excited dye to graphene. While in traditional fluorescence resonance energy transfer, the rate has a (distance)(-6) dependence, we find that the distance dependence in this case is quite different. Our calculation of rate in the case of the two dyes, pyrene and nile blue, shows that the distance dependence is Yukawa type. We have also studied the effect of doping on energy transfer to graphene. Doping does not modify the rate for electronic excitation energy transfer significantly. However, in the case of vibrational transfer, the rate is found to be increased by an order of magnitude due to doping. This can be attributed to the nonzero density of states at the Fermi level that results from doping.

Long range resonance energy transfer from a dye molecule to graphene has (distance)−4 dependence

In our previous report on resonance energy transfer from a dye molecule to graphene [J. Chem. Phys.129, 054703 (2008)], we had derived an expression for the rate of energy transfer from a dye to graphene. An integral in the expression for the rate was evaluated approximately. We found a Yuwaka-type dependence of the rate on the distance. We now present an exact evaluation of the integral involved, leading to very interesting results. For short distances (z<20 A), the present rate and the previous rate are in good agreement. For larger distances, the rate is found to have a z(-4) dependence on the distance, exactly. Thus we predict that for the case of pyrene on graphene, it is possible to observe fluorescence quenching up to a distance of 300 A. This is in sharp contrast to the traditional fluorescence resonance energy transfer where the quenching is observable only up to 100 A.

Electrochemical electron transfer: Accounting for electron–hole excitations in the metal electrode

The transfer of an electron from a metal electrode to an ion in a polar liquid is probably the most important process in electrochemistry. As the electrons in the metal have a continuum of allowed energy levels, this transfer may be accompanied by the creation/annihilation of electron–hole excitations in the metal. Calculation of the rate of electron transfer, with these excitations and the solvent accounted for properly is a difficult problem to treat using the usual approaches of molecular reaction dynamics, as one now has a continuum of potential energy surfaces, on which the dynamics has to be considered. We suggest an approach in which the electron–hole excitations are treated as bosons. Using this, we have derived an expression for the rate, which accounts both for solvent dynamics and electron–hole excitations. Our analysis amounts to a solution of the problem of calculating the electronic transmission coefficient κ, for a continuum of crossing diabatic surfaces. Calculations of the rate using our ...

Electron transfer in the reflection of atoms from metal surfaces

Abstract The resonance mechanism for positive and negative ionization of an atom reflected from a metal surface is treated in the time-dependent Hartree-Fock approximation assuming that the atom moves on its classical trajectory. A simple model is parameterized to describe 30–500 eV Na atoms reflected from tungsten, and the ionization probabilities are calculated by numerical integration of the equation of motion of the time evolution operator. Significant ionization can only occur if either the ionization level, or the affinity level of the atom crosses the Fermi level beyond the range of the atom-metal hopping interaction. On clean tungsten, the former situation applies, and the probability of positive ionization is nearly unity, and of negative ionization nearly zero.

On the proof of the principle of maximum hardness

It has been suggested that molecules arrange their electronic structure to be such that they have the maximum hardness, this being referred to as the principle of maximum hardness. This principle has been claimed to have been proved rigorously. We show that the proof is in error.

Resonance energy transfer from a fluorescent dye molecule to plasmon and electron-hole excitations of a metal nanoparticle

The authors study the distance dependence of the rate of electronic excitation energy transfer from a dye molecule to a metal nanoparticle. Using the spherical jellium model, they evaluate the rates corresponding to the excitation of l=1, 2, and 3 modes of the nanoparticle. The calculation takes into account both the electron-hole pair and the plasmon excitations of the nanoparticle. The rate follows conventional R(-6) dependence at large distances while small deviations from this behavior are observed at shorter distances. Within the framework of the jellium model, it is not possible to attribute the experimentally observed d(-4) dependence of the rate to energy transfer to plasmons or electron-hole pair excitations.

Surface science lettersTheory of ion neutralisation scattering from surfaces

A method for the calculation of the probability of neutralisation of an ion, which is scattered from the surface of a solid is presented. It assumes the ion to move along a classical trajectory and solves for the time evolution operator for the electronic system. For one electron Hamiltonians the solution can be carried out exactly. Results are presented for scattering from a semi-infinite linear chain.

Path integral representation for fractional Brownian motion

Fractional Brownian motion (FBM) is a generalization of the usual Brownian motion. A path integral representation that has recently been suggested for it is shown to be not for the FBM but for a different generalization of the Brownian motion. A new path integral representation is given and its measure has fractional derivatives of the path in it. The measure shows that the process is Gaussian but is, in general, non-Markovian, even though Brownian motion itself is Markovian. It is shown how the propagator for the motion of free FBM may be evaluated. This is somewhat more complex than for the usual path integrals, due to the occurrence of fractional derivatives. We also find the propagator in the presence of a linear absorption (potential), and for FBM on a ring.

Pulling a polymer out of a potential well and the mechanical unzipping of DNA

Motivated by experiments on DNA under torsion, we consider the problem of pulling a polymer out of a potential well by a force applied to one of its ends. If the force is less than a critical value, then the process is activated, and has an activation energy proportional to the length of the chain. Above this critical value, the process is barrierless and will occur spontaneously. We use the Rouse model for a description of the dynamics of the peeling out, and study the average behavior of the chain by replacing the random noise by its mean. The resultant mean-field equation is a nonlinear diffusion equation, and hence rather difficult to analyze. We use physical arguments to convert this to a moving boundary value problem, which can then be solved exactly. The result is that the time t(po) required to pull out a polymer of N segments scales like N2. For models other than the Rouse model, we argue that t(po) approximately N1+nu.

Time-dependent survival probability in diffusion-controlled reactions in a polymer chain: Beyond the Wilemski–Fixman theory

Brownian dynamics simulation results of the time-dependent survival probability (Sp(t)) of a donor–acceptor pair embedded at the two ends of a Rouse chain are compared with two different theories, one of which is the well-known Wilemski–Fixman (WF) theory. The reaction studied is fluorescence energy transfer via the Forster mechanism, which has a R–6 distance (R) dependence of the reaction rate. It has been reported earlier [G. Srinivas, A. Yethiraj, and B. Bagchi, J. Chem. Phys. 114, 9170 (2001)] that while the WF theory is satisfactory for small reaction rates, the agreement was found to become progressively poorer as the rate is increased. In this work, we have generalized the WF theory. We suggest an approximate, reduced propagator technique for three-dimensional treatment (instead of 3N dimensions, where N is the number of monomers in the polymer chain). This equation is solved by combining a Greens function solution with a discretized sink method. The results obtained by this new scheme are in better agreement with the simulation results.