Pavel A. Frantsuzov

Universal emission intermittency in quantum dots, nanorods and nanowires

Virtually all known fluorophores exhibit mysterious episodes of emission intermittency. A remarkable feature of the phenomenon is a power-law distribution of on- and off-times observed in colloidal semiconductor quantum dots, nanorods, nanowires and some organic dyes. For nanoparticles, the resulting power law extends over an extraordinarily wide dynamic range: nine orders of magnitude in probability density and five to six orders of magnitude in time. Exponents hover about the ubiquitous value of -3/2. Dark states routinely last for tens of seconds—practically forever on quantum mechanical timescales. Despite such infinite states of darkness, the dots miraculously recover and start emitting again. Although the underlying mechanism responsible for this phenomenon remains a mystery and many questions persist, we argue that substantial theoretical progress has been made.

Explanation of quantum dot blinking without the long-lived trap hypothesis

A simple model explaining the experimental data on QDs luminescence blinking is suggested. The model does not assume the presence of the long-lived electron traps. The bleaching of the QD luminescence is a result of the Auger assisted radiationless relaxation of the excitation through the deep surface states. Possible ways of the experimental verification of the model are discussed.

Model of Fluorescence Intermittency of Single Colloidal Semiconductor Quantum Dots Using Multiple Recombination Centers

We present a new physical model resolving a long-standing mystery of the power-law distributions of the blinking times in single colloidal quantum dot fluorescence. The model considers the nonradiative relaxation of the exciton through multiple recombination centers. Each center is allowed to switch between two quasistationary states. We point out that the conventional threshold analysis method used to extract the exponents of the distributions for the on times and off times has a serious flaw: the qualitative properties of the distributions strongly depend on the threshold value chosen for separating the on and off states. Our new model explains naturally this threshold dependence, as well as other key experimental features of the single quantum dot fluorescence trajectories, such as the power-law power spectrum (1/f noise).

Quantum statistical mechanics with Gaussians: Equilibrium properties of van der Waals clusters

The variational Gaussian wave-packet method for computation of equilibrium density matrices of quantum many-body systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time beta=(k(B)T)(-1) starting at the classical limit beta=0. For an N-particle system a Gaussian exp[(r-q)(T)G(r-q)+gamma] is represented by its center qinR(3N), the width matrix GinR(3Nx3N), and the scale gammainR, all treated as dynamical variables. Evaluation of observables is done by Monte Carlo sampling of the initial Gaussian positions. As demonstrated previously at not-very-low temperatures the method is surprisingly accurate for a range of model systems including the case of double-well potential. Ideally, a single Gaussian propagation requires numerical effort comparable to the propagation of a single classical trajectory for a system with 9(N(2)+N)/2 degrees of freedom. Furthermore, an approximation based on a direct product of single-particle Gaussians, rather than a fully coupled Gaussian, reduces the number of dynamical variables to 9N. The success of the methodology depends on whether various Gaussian integrals needed for calculation of, e.g., the potential matrix elements or pair correlation functions could be evaluated efficiently. We present techniques to accomplish these goals and apply the method to compute the heat capacity and radial pair correlation function of Ne(13) Lennard-Jones cluster. Our results agree very well with the available path-integral Monte Carlo calculations.

Thermodynamics and equilibrium structure of Ne38 cluster: quantum mechanics versus classical.

The equilibrium properties of classical Lennard-Jones (LJ38) versus quantum Ne38 Lennard-Jones clusters are investigated. The quantum simulations use both the path-integral Monte Carlo (PIMC) and the recently developed variational-Gaussian wave packet Monte Carlo (VGW-MC) methods. The PIMC and the classical MC simulations are implemented in the parallel tempering framework. The classical heat capacity Cv(T) curve agrees well with that of Neirotti et al. [J. Chem. Phys. 112, 10340 (2000)], although a much larger confining sphere is used in the present work. The classical Cv(T) shows a peak at about 6 K, interpreted as a solid-liquid transition, and a shoulder at approximately 4 K, attributed to a solid-solid transition involving structures from the global octahedral (Oh) minimum and the main icosahedral (C5v) minimum. The VGW method is used to locate and characterize the low energy states of Ne38, which are then further refined by PIMC calculations. Unlike the classical case, the ground state of Ne38 is a liquidlike structure. Among the several liquidlike states with energies below the two symmetric states (Oh and C5v), the lowest two exhibit strong delocalization over basins associated with at least two classical local minima. Because the symmetric structures do not play an essential role in the thermodynamics of Ne38, the quantum heat capacity is a featureless curve indicative of the absence of any structural transformations. Good agreement between the two methods, VGW and PIMC, is obtained. The present results are also consistent with the predictions by Calvo et al. [J. Chem. Phys. 114, 7312 (2001)] based on the quantum superposition method within the harmonic approximation. However, because of its approximate nature, the latter method leads to an incorrect assignment of the Ne38 ground state as well as to a significant underestimation of the heat capacity.

Universal binary theory of photochemical charge separation and distribution

Using integral formalism we developed the encounter theory of reversible photoionization followed by charge recombination. This is a problem that can not be approached with conventional (differential) formalism, unless ionization is highly exothermic and thus irreversible. In this limit, the integral theory supplemented by the recipe for calculating the ion distribution may be successfully reduced to the differential theory used in our previous work. However, there is no alternative to integral theory when ionization is quasiresonant and the back electron transfer to the excited state should be accounted for. Using the contact approximation we calculated the free-energy dependence of the Stern-Volmer constant of reversible photoionization accompanied by charge recombination.

Equilibrium properties of quantum water clusters by the variational Gaussian wavepacket method

The variational Gaussian wavepacket (VGW) method in combination with the replica-exchange Monte Carlo is applied to calculations of the heat capacities of quantum water clusters, (H(2)O)(8) and (H(2)O)(10). The VGW method is most conveniently formulated in Cartesian coordinates. These in turn require the use of a flexible (i.e., unconstrained) water potential. When the latter is fitted as a linear combination of Gaussians, all the terms involved in the numerical solution of the VGW equations of motion are analytic. When a flexible water model is used, a large difference in the timescales of the inter- and intramolecular degrees of freedom generally makes the system very difficult to simulate numerically. Yet, given this difficulty, we demonstrate that our methodology is still practical. We compare the computed heat capacities to those for the corresponding classical systems. As expected, the quantum effects shift the melting temperatures toward the lower values.

Correlations between Subsequent Blinking Events in Single Quantum Dots

We explain the long-range correlations found by Stefani and his co-workers between blinking times of single colloidal quantum dot emission. Our explanation is based on the multiple recombination center model we recently suggested. The model produces positive correlations between subsequent on--on and off--off times and negative on--off correlations, as observed in the experiment. We also reproduce qualitatively the dependence of correlations between subsequent on--on, on-off, and off--off times on the number of switching events separating them.

Spatial dispersion of electron transfer probability

Abstract Recombination and ionization rate constants were calculated taking into account the spatial dispersion of reaction free and reorganization energies. The conditions were found under which the reactions are contact and the contact estimation of their rate is invalid. The spatial dispersion of transfer probability was shown to be responsible for the smoothing of the multichannel structure of the free energy “gap” dependence of the rate constant.

Accumulation and distribution of energy quenching products

Abstract The quantum yield of irreversible energy quenching, as well as the accumulation and distribution of its products, were studied by means of differential and integral encounter theories and a competing approach based on the superposition approximation. The lower-order concentration corrections to the Stern–Volmer constant are found, but only the non-binary contributions to them are different. Such a difference between the theories was shown to have an impact on the accumulation and final distribution of the charged products, especially at short distances. This effect is of principle importance but does not affect significantly the main results of any encounter theory.