Quantum mechanical size effects

Give some examples of applications that exploit quantum mechanical size effects. 

Quantum efficiencies Quantum efficiency Quantum electronics Quantum fluids Quantum mechanics Quantum size effect Quantumwell... 

We can obtain a crude estimate the time required for a precise quantum mechanical calculation to analyse possible syntheses of bryosta-tin. First, the calculation of the energy of a molecule of this size will take hours. Many such calculations will be required to minimise the energy of a structure. A reasonable estimate may be that a thousand energy calculations would be required. Conformation searching will require many such minimisations, perhaps ten thousand. The reactivity of each intermediate will require a harder calculation, perhaps a hundred times harder. Each step will have many possible combinations of reagents, temperatures, times, and so on. This may introduce another factor of a thousand. The number of possible strategies was estimated before as about a million, million, million. In order to reduce the analysis of the synthesis to something which could be done in a coffee break then computers would be required which are 10 times as powerful as those available now. This is before the effects of solvents are introduced into the calculation. 

Gorer S, Hodes G (1994) Quantum size effects in the study of chemical solution deposition mechanisms of semiconductor films. J Phys Chem 98 5338-5346... 

What makes metal nanoclusters scientifically so interesting The answer is that they, in many respects, no longer follow classical physical laws as all bulk materials do, but are correctly to be considered by means of quantum mechanics. This is not only valid for metals. In principle any other solid or in some cases even liquid material exhibit so-called nano-effects when reaching a critical size. Nanoscience and nanotechnology are based on those effects. In the course of only 1-2 decades nanosciences and nanotechnology have developed to such an extent that our daily life already is and will be increasingly influenced in a way that cannot be compared with any other technological development in mankind s history [2]. A few examples will help to better understand what is meant. 

Quantum mechanical/molecular mechanical study on the Favorskii rearrangement in aqueous media has been carried out.39 The results obtained by QM/MM methods show that, of the two accepted mechanisms for Favorskii rearrangement, the semibenzilic acid mechanism (a) is favored over the cyclopropanone mechanism (b) for the a-chlorocyclobutanone system (Scheme 6.2). However, the study of the ring-size effects reveals that the cyclopropanone mechanism is the energetically preferred reactive channel for the a-chlorocyclohexanone ring, probably due to the straining effects on bicycle cyclopropanone, an intermediate that does not appear on the semibenzilic acid pathway. These results provide new information on the key factors responsible for the behavior of reactant systems embedded in aqueous media. 

Figure 20. The (So —> S2) absorption spectrum of pyrazine for reduced three- and four-dimensional models (left and middle panels) and for a complete 24-vibrational model (right panel). For the three- and four-dimensional models, the exact quantum mechanical results (full line) are obtained using the Fourier method [43,45]. For the 24-dimensional model (nearly converged), quantum mechanical results are obtained using version 8 of the MCTDH program [210]. For all three models, the calculations are done in the diabatic representation. In the multiple spawning calculations (dashed lines) the spawning threshold 0,o) is set to 0.05, the initial size of the basis set for the three-, four-, and 24-dimensional models is 20, 40, and 60, and the total number of basis functions is limited to 900 (i.e., regardless of the magnitude of the effective nonadiabatic coupling, we do not spawn new basis functions once the total number of basis functions reaches 900).

Macroscopic descriptions of matter and radiation are adequate without taking the discontinuous nature of matter and/or radiation into account. However, when dealing with particles approaching the size of elementary quanta, the quantum effects become increasingly important and must be taken into account explicitly in the mechanical description of these particles. Unlike relativistic mechanics, quantum mechanics cannot be used to describe macroscopic events. There is a fundamental difference between classical and non-classical, or quantum, phenomena and the two systems are complimentary rather than alternatives. 

In the quantum mechanical continuum model, the solute is embedded in a cavity while the solvent, treated as a continuous medium having the same dielectric constant as the bulk liquid, is incorporated in the solute Hamiltonian as a perturbation. In this reaction field approach, which has its origin in Onsager s work, the bulk medium is polarized by the solute molecules and subsequently back-polarizes the solute, etc. The continuum approach has been criticized for its neglect of the molecular structure of the solvent. Also, the higher-order moments of the charge distribution, which in general are not included in the calculations, may have important effects on the results. Another important limitation of the early implementations of this method was the lack of a realistic representation of the cavity form and size in relation to the shape of the solute. 

The level of accuracy that can be achieved by these different methods may be viewed as somewhat remarkable, given the approximations that are involved. For relatively small organic molecules, for instance, the calculated AGsoivation is now usually within less than 1 kcal/mole of the experimental value, often considerably less. Appropriate parametrization is of key importance. Applications to biological systems pose greater problems, due to the size and complexity of the molecules,66 156 159 161 and require the use of semiempirical rather than ab initio quantum-mechanical methods. In terms of computational expense, continuum models have the advantage over discrete molecular ones, but the latter are better able to describe solvent structure and handle first-solvation-shell effects. 

A particularly interesting feature of the theory [9] is the incorporation of deviations from Coulomb scattering due to the nonvanishing size of the projectile nucleus. The very fact that the theory is based on the Dirac equation and that spin dependences enter nontrivially indicates that quantum mechanics is essential here. Moreover, at the highest energies considered, pair production becomes important, i.e., an effect that does not have a classical equivalent [57]. 

Instead, optical measurement was applied to clarify the formation mechanism of Agl nanoparticles in diluted suspensions. Figure 4.4.10A shows the absorption spectra of the 1-day aged suspension containing 3.33 X 10-4 M Ag+ and 6.67 X 10-4 M I- as a function of RSH concentration. When the content of RSH increased from 0 to 6.67 X I0-3 M (curves a-d), the absorption spectra of Agl particles blue-shifted, suggesting the quantum size effect. The relationship between the particle diameter, d (A), and the concentration of RSH, c (A/), was plotted in the inset, which shows the double-logarithmic linear line of d versus c. The aggregation number is found to be proportional to the cube of the size. The same relationship was reported on the formation of CdS nanoparticles (37). These correlations indicate that Agl and CdS have the same ionic nature and have the same reaction modules of thiols. 

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