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Theoretical X-ray Absorption Spectroscopy of Liquid Water Using First-Principles Calculations
Published in Fausto Martelli, Properties of Water from Numerical and Experimental Perspectives, 2022
For the most practical calculations, the self-consistent procedure is complicated. The huge computational cost prohibits the GW method from being applied to complex systems. Several alternative attempts have been made based on the physically motivated approximations. Actually, the GW approximation could also be interpreted as a combination of the Hartree-Fock approximation and a dynamically screened Coulomb interaction (Onida et al. 2002). In this approach, the GW self-energy could be evaluated via the Coulomb-hole plus screened exchange (COHSEX) approximation: ∑COHSEX(r1,r2)=∑COH(r1,r2)+∑SEX(r1,r2)
Semimetal Electronics
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
Alfonso Sanchez-Soares, Christian König, Conor O’Donnell, Jean-Pierre Colinge, James C. Greer
To sum up, we have found that the electronic properties of a confined material can be very different from their bulk counterpart. The general features of band structures like the position of charge carrier pockets in momentum space may be modified, and the symmetry and character of states at band edges may change. The quantum mechanical nature of electrons changes the energy spacing between the VB and CB, and states within bands discretize with the formation of subbands. Although the models presented here are not sufficient to accurately describe the band structure of a real material, they illustrate the main relevant concepts. More sophisticated theoretical frameworks such as density functional theory (DFT) and many-body theories like the GW approximation are state-of-the-art methods to calculate the electronic structure of both bulk and nanostructured materials, and take into account interactions between electrons that were completely neglected in the simple model presented here.
Recent Advances in the Computational Characterization of π-Conjugated Organic Semiconductors
Published in John R. Reynolds, Barry C. Thompson, Terje A. Skotheim, Conjugated Polymers, 2019
Jean-Luc Bredas, Xiankai Chen, Thomas Körzdörfer, Hong Li, Chad Risko, Sean M. Ryno, Tonghui Wang
However, as mentioned in the Introduction, situations are often encountered in organic electronics where we are interested in the charge transfer between two molecules and/or polymer chain segments, be it in the context of donor-acceptor interfaces, small-gap polymers, or dopant-introduced semiconductor thin films. Here, the key is the ability to predict the level alignments, the extent of charge transfer across an interface, the interface dipoles, and the energies of the CT and charge-separated excited states. Since the ∆SCF approach is not applicable in these instances, alternative approaches are required. An accurate method for the evaluation of charged excitation energies is many-body perturbation theory in the GW approximation.96,97 However, due to large basis set requirements, these calculations are numerically much more expensive than DFT, even when carried out in a non-self-consistent way at the G0W0 level.
Effects of rotational conformation on electronic properties of 4,4′-bis(carbazol-9-yl)biphenyl (CBP): the single-molecule picture and beyond
Published in Molecular Physics, 2021
Rodrigo Cortés-Mejía, Sebastian Höfener, Wim Klopper
A solution to the dilemma of CT vs. computational scaling is given by the Bethe-Salpeter equation (BSE) based on GW for which no CT problem arises and the scaling is significantly reduced compared to wavefunction methods [17, 18]. In this scheme, first the electron self-energy operator is constructed within the GW approximation and the one-particle Green's function is calculated, yielding the quasi-particle (QP) energies that correspond to single-electron ionisation energy and electron affinity [19]. In a second step, the two-particle interaction is constructed, and the BSE for the two-particle Green's function is solved, resulting in the neutral excitation energies [19, 20]. Overall, the GW approximation is used to evaluate the QP spectrum of holes and electrons, while solving the BSE for the two-particle Green's function gives the electron-hole interactions [19]. Assessment of intramolecular CT-type excitations using the GW-BSE theoretical framework has proven to produce results that are in excellent agreement with experimental measurements by reproducing correctly the long-range behaviour of charge transfer excitations [20, 21].
DFT study of electronic and optical properties of CH3NH3SnI3 perovskite
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
Roozbeh Sabetvand, Mohammad Ebrahim Ghazi, Morteza Izadifard
The value of band gap is one of the important parameters for light absorber substance in solar cells. The band structure for CH3NH3SnI3 cubic structure was calculated using the LDA, GGA, and GW approximations along the R – Γ – X – R – Γ – M path (Grimme 2006). The band structures obtained by GGA and GW approximations are shown in Figures 4 and 5, respectively. As shown in these figures, the wave vector for the valance band maximum (VBM) and the conduction band minimum (CBM) are similar, at the (0,0,0) point of the Brillouin zone, and hence, CH3NH3SnI3 in the cubic phase has a direct band-gap at the Gamma (Γ) point. The band gap values from LDA, GGA and GW approximations were calculated. Comparison of these results show that the band-gap obtained by GGA (1.02 eV) is bigger than that obtained by LDA (0.77 eV), and hence, has a better consistency with the previous reports (Ahmad and Mobin 2020). As mentioned earlier, the standard DFT usually gives lower band gap value for structures due to the self-correlation error of electrons and the inherent lack of derivative discontinuity (Argaman and Makov 2000). However, the band gap obtained by GW approximation is 1.38 eV, which is in a good consistency with the experimental results (Eg = 1.30 eV) (Ahmad and Mobin 2020). In fact, the GW approximation determines the self-energy of a many-body system of electrons, which improve the calculations accuracy.
Simulation of the crystal structure formation from the small lithium clusters
Published in Molecular Physics, 2019
Methods based on many-body perturbation theory [12] are seems to be more appropriate to use. For example, the GW approximation (GWA) is derived from many-body perturbation theory. In this approximation, the self-energy is a product of the single particle Green function (G) and the screened Coulomb interaction (W) [13]. The GWA offers a quite adequate description of the electronic structure for a large number of materials [14]. However, calculations based on these methods are too expensive to be widely used for these purposes.