Applications of nanotechnology in water and wastewater treatment

Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited-state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited-state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. In this article we describe the GW approximation which has turned out to be a fruitful approximation to the self-energy. The Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. Self-consistency issue and new developments beyond the GW approximation are also discussed as well as the success and shortcomings of the GW approximation.

https://iopscience.iop.org/article/10.1088/0034-4885/61/3/002/pdf

The GW method

In this Review, we summarize recent work on modeling of organic/metal and organic/organic interfaces. Some of the models discussed have a semiempirical approach, that is, experimentally derived values are used in combination with theory, and others rely completely of calculations. The models are categorized according to the types of interfaces they apply to, and the strength of the interaction at the interface has been used as the main factor. We explain the basics of the models, their use, and give examples on how the models correlate with experimental results. We stress that given the complexity of organic/metal and organic/organic interface formation, it is crucial to know the exact way in which the interface was formed before choosing the model that is applicable, as none of the models presented covers the whole range of interface interaction strengths (weak physisorption to strong chemisorption).

Energy‐Level Alignment at Organic/Metal and Organic/Organic Interfaces

Experimental studies of the superconductive properties of fullerides are briefly reviewed. Theoretical calculations of the electron-phonon coupling, in particular for the intramolecular phonons, are discussed extensively. The calculations are compared with coupling constants deduced from a number of different experimental techniques. It is discussed why ${\mathrm{A}}_{3}$${\mathrm{C}}_{60}$ are not Mott-Hubbard insulators, in spite of the large Coulomb interaction. Estimates of the Coulomb pseudopotential ${\mathrm{\ensuremath{\mu}}}^{\mathrm{*}}$, describing the effect of the Coulomb repulsion on the superconductivity, as well as possible electronic mechanisms for the superconductivity, are reviewed. The calculation of various properties within the Migdal-Eliashberg theory and attempts to go beyond this theory are described.

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Superconductivity in fullerides

We review studies of the electromagnetic response of various classes of correlated electron materials including transition metal oxides, organic and molecular conductors, intermetallic compounds with $d$- and $f$-electrons as well as magnetic semiconductors. Optical inquiry into correlations in all these diverse systems is enabled by experimental access to the fundamental characteristics of an ensemble of electrons including their self-energy and kinetic energy. Steady-state spectroscopy carried out over a broad range of frequencies from microwaves to UV light and fast optics time-resolved techniques provide complimentary prospectives on correlations. Because the theoretical understanding of strong correlations is still evolving, the review is focused on the analysis of the universal trends that are emerging out of a large body of experimental data augmented where possible with insights from numerical studies.

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Electrodynamics of correlated electron materials

The band gap of solid ${\mathrm{C}}_{60}$ is found to be 2.3\ifmmode\pm\else\textpm\fi{}0.1 eV. The on-site molecular ${\mathrm{C}}_{60}$ Coulomb interaction (U) as determined from the KVV ${\mathrm{C}}_{60}$ Auger spectrum is found to be 1.6\ifmmode\pm\else\textpm\fi{}0.2 eV. This value of U is shown to lead to Frenkel-type molecular excitons in the 1.5--2 eV range. These results lead us to suggest that doped ${\mathrm{C}}_{60}$ should be considered as a highly correlated system with U/W comparable to that in high-${\mathit{T}}_{\mathit{c}}$ cuprates and that stoichiometric ${\mathrm{K}}_{3}$${\mathrm{C}}_{60}$ is a Mott-Hubbard insulator with a gap of about 0.7 eV.

/pdf/band-gap-excitons-and-coulomb-interaction-in-solid-c60-4h64ni19ro.pdf

Band gap, excitons, and Coulomb interaction in solid C60.

With a Second-Harmonic Generation (SHG) experiment the electric-dipole forbidden 1T1g excitonic state at hω=1.81 eV of solid C60 can be probed1. We show that the SHG line shape depends strongly on the degree of rotational order. For decreasing temperature we observe a strong enhancement of the SH intensity, an overall blue shift, and below the rotational-ordering phase-transition temperature (260 K) the SH resonance splits into two peaks. The origin of the splitting will be discussed in terms of a possible Davydov splitting due to the four molecules per unit cell in the low temperature phase, and a mixing of the nearly-degenarate 1T1g and 1Gg free molecule states because of the lower symmetry in the solid. The exciton band structure is calculated with a charge transfer mediated propagation mechanism as suggested by Lof et al.2 and with one-electron (-hole) transfer integrals determined from band structure calculations. Comparison with our experimental SHG data leads to a reasonable agreement and shows that a mixing of 1T1g and 1Gg states may explain the splitting at low temperature.

/pdf/excitons-in-c60-studied-by-temperature-dependent-optical-33o6xun5s6.pdf

Excitons in C60 studied by temperature-dependent optical second-harmonic generation

The bandgap of solid C60 is found to be 2.3±0.1 eV. The on-site molecular C60 Coulomb interaction (U) as determined from the KVV C60 Auger spectrum is found to be 1.6 ±.2 eV. This value of U is shown to be consistent with Frenkel type molecular excitons in the 1.5–2 eV range. These results lead us to suggest that doped C60 should be considered as a highly correlated system with U/W comparable to that in high Tc cuprates. The Auger spectroscpoy results are consistent with a rather long range Coulomb interaction on a single bucky ball indicating that a Hubbard model is not suitable to describe the electronic structure of a C60 molecule.

B. Koopmans

Papers

Band gap, excitons, and Coulomb interaction in solid C60.

Excitons in C60 studied by temperature-dependent optical second-harmonic generation

Correlation Effects in Solid C60