Interaction of theory and experiment: examples from single molecule studies of nanoparticles

Abstract

This article is in part the author's perspective on the revolution that has occurred in theoretical chemistry during the past half-century. In this period much of theoretical chemistry has moved from its initial emphasis on analytic treatments, resulting in equations for physical chemical and chemical phenomena, to the detailed computation of many different systems and processes. In the best sense the old and the new are complementary and their coexistence can benefit both. Experiment too has seen major developments. One of the newer types of experiment is that of single molecule studies. They range from those on small inorganic and organic nanoparticles to large biological species. We illustrate some of the issues that arise, using the topic of 'quantum dots' (QDs), and choosing a particular inorganic nanoparticle, CdSe, the most studied of these systems. Its study reflects the problems that arise in experiment and in theories in this field. The complementary nature of the conventional ensemble experiments and the new single molecule experiments is described and is illustrated by trajectories for the two types of experiments. The research in the QD field is both experimentally and theoretically a currently ongoing process, for which the answers are not fully known in spite of the large body of research. The detailed role of surface states is part of the problem. The field continues to yield new and unexpected results. In a sense this part of the article is an interim report that illustrates one analytic approach to the topic and where computer calculations and simulations can be expected to provide added insight.

Figure 1.

CdSe quantum dot with ZnS coating and various attachments for sensing. Adapted from Gao et al. (2004). Reprinted with permission.

Figure 2.

Fluorescence intermittency distribution of ‘off’ times for CdSe(ZnS) QD showing intermittency at (a) room temperature and (b) 10 K. Self-similarity is seen in the expanded view. (c) Normalized off-time probability distribution for different QDs, the straight line having a slope of −1.5 and the inset showing the distribution of powers in this power law; (d) off-time probability distribution for different temperatures of QDs; (e) off-time probability distribution for different QD radii at room temperature (Shimizu et al. 2001). Reprinted with permission.

Figure 3.

Power law plot slope for ‘on’ and ‘off’ distributions. The distributions are shown for two different temperatures and two different incident intensities. (a) Off-time distribution. (b) On-time distribution. Black square, 10 K, 175 W cm⁻²; inverted triangle, increased laser power; triangle, increased temperature (Shimizu et al. 2001). Reprinted with permission.

Figure 4.

Tunnelling spectroscopy of a CdSe nanocrystal, showing the tunnelling resonances corresponding to the discrete energy levels of the QD (Liljeroth et al. 2006). Reprinted with permission.

Figure 5.

The QD is ‘off’ because the indicated Auger transition can occur when a trap is occupied. Here, the occupied trap is in the form of a Se⁻ in a site formerly occupied by a dangling Se²⁻ at the surface of the QD. The Se²⁻ has trapped a hole. Open circle, electron; filled circle, hole.

Figure 6.

Auger-based trapping mechanism, converting here a dangling Se²⁻ ion to a Se⁻, with the extra electron now occupying a state S_e in the conduction band. Open circle, electron; filled circle, hole.

Figure 7.

Free energy curves for the two states that are in resonance at the intersection. An example of the two states is given in equation (4.1).

Figure 8.

Auger-based mechanism for detrapping, converting a dangling Se⁻ to a dangling Se²⁻. Open circle, electron; filled circle, hole.

Figure 9.

Power spectral density of fluctuations in fluorescence measured for three individual QDs. Solid lines are fitted power laws to low-frequency and high-frequency portions of the power spectra, and horizon dashed lines are expected shot-noise levels (Pelton et al. 2007).