Correction schemes electron correlation

The advantage over the HF scheme is that whereas in conventional ah initio theory we must resort to costly perturbation theory or configuration interaction expansions, in DFT electron correlation is already included explicitly in the exchange-correlation functional. The key problem is instead to find an appropriate expression for xc. As stated above, when we have the correct functional we should be able to extract the exact energy, the exact ground state density, and all properties for our system. 

The major advantage of a 1-RDM formulation is that the kinetic energy is explicitly defined and does not require the construction of a functional. The unknown functional in a D-based theory only needs to incorporate electron correlation. It does not rely on the concept of a fictitious noninteracting system. Consequently, the scheme is not expected to suffer from the above mentioned limitations of KS methods. In fact, the correlation energy in 1-RDM theory scales homogeneously in contrast to the scaling properties of the correlation term in DPT [14]. Moreover, the 1-RDM completely determines the natural orbitals (NOs) and their occupation numbers (ONs). Accordingly, the functional incorporates fractional ONs in a natural way, which should provide a correct description of both dynamical and nondynamical correlation. 

For a better understanding of the nature of the adsorption forces between TNB and the siloxane surface of clay minerals, the decomposition scheme of Sokalski et al. [199] was applied. The results of such energy decomposition are presented in Table 6. They are in complete agreement with qualitative conclusions presented above. One may see that two dominant attractive contributions govern the adsorption of TNB. As it is expected, one is an electrostatic contribution, and the other one is contribution, which includes components that originate from the electronic correlation. The electronic correlation related contributions include the dispersion component and a correlation correction to electrostatic, exchange, and delocalization terms of the interaction energy. 

An approach to address the proper r decay of the exchange-correlation potential is the LC scheme, where LC indicates a long-range correction. HF exchange is only applied to long-range electron correlation, with a functional defined as... 

Density Functional theory [4] (DFT) has been widely recognized as a powerful alternative computational method to traditional ab initio schemes, particularly in studies of transition metal complexes where large size of basis set and an explicit treatment of electron correlation are required. The local spin density approximation [5] (LDA) is the most frequently applied approach within the families of approximate DFT schemes. It has been used extensively in studies on solids and molecules. Most properties obtained by the LDA scheme are in better agreement with experiments [4a] than data estimated by ab initio calculations at the Hartree-Fock level. However, bond energies are usually overestimated by LDA. Thus, gradient or nonlocal corrections [6] have been introduced to rectify the shortcomings in the LDA. The non-... 

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