Electronic structure computations methods

The development that led to the emergence of DFT to its current status as the most widely used electronic structure computational method is that due to KS [274]. The ansatz used by KS replaces the interacting problem with an auxiliary independent particle one, with all the many-body effects included in an exchange-correlation functional. In practice, the KS scheme introduces an equivalent orbital picture (rigorously established), with the resulting KS equations solved self-consistently. 

Simply doing electronic structure computations at the M, K, X, and T points in the Brillouin zone is not necessarily sufficient to yield a band gap. This is because the minimum and maximum energies reached by any given energy band sometimes fall between these points. Such limited calculations are sometimes done when the computational method is very CPU-intensive. For example, this type of spot check might be done at a high level of theory to determine whether complete calculations are necessary at that level. 

The periodic electronic structure calculations methods constitute the other available approach." These methods require a relative high computational effort, beside progress in computer power allows calculations on systems of size of interest." The advantage of periodic approach method is that the entire... 

Computation of Reaction Potential Energy Surfaces. As transition states cannot be observed, there is no experimental means of establishing their structure. Computational methods can be applied for descriptions of intermediates and transition stmctures. Structural attributes such as bond lengths, bond orders, electron density distribution, and orbital occupancy can be found for transition stmctures and intermediates, as was described in Sections 3.1.2.5 for stable molecules. The evaluation of a... 

Since the relevant dimensional parameter is 1/D, the pseudoclas-sical large-Z) limit is closer to D = 3 than is the hyperquantum low-D limit. As in Fig. 3, for D finite but very large, equivalent to a very heavy electronic mass, the electrons are confined to harmonic oscillations about the fixed positions attained in the D oo limit. We call these motions Langmuir vibrations, to acknowledge his prescient suggestion 70 years ago [89] that the electrons could...rotate, revolve, or oscillate about definite positions in the atom. In a dimensional perturbation expansion the first-order term, proportional to 1/D, corresponds to these harmonic vibrations, whereas higher-order terms correspond to anharmonic contributions. Standard methods for analysis of molecular vibrations [90] thus become directly applicable to electronic structure. These methods are semiclassical in form and far simpler, both conceptually and computationally, than the conventional orbital formulation. 

The way the electrons distribute in a molecule reflects its physical and chemical properties. For example, dipole moments and electron deficient sites are relevant properties in a molecule that affect the way it interacts with the reaction partners, and these properties are determined by the molecular charge distribution. Quantum mechanics allows the computation of the electron density, which tells the way electrons distribute in the molecule. However, the electron density can only be obtained from an electronic structure computation, and simpler methods are also required to estimate the atomic charges in complex systems. 

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