Highly Correlated Correlation Potentials

Molecule LDAXC LDAXC +4 -IP EXX LDAC EXX PBEC —IP Expt. 

The +A indicates the addition of an energy shift to the functional potential. Auxiliary basis functions for the density fitting technique (see Sect. 2.7) are used. Excerpt from Hamel et al. (2002) and Kim et al. (1999) 

In the ab initio DFT, the exact exchange (EXX) potential and frequently its hybridization with the Hartree-Fock exchange potential is used as the exchange potential. The EXX potential that Gorling and Levy developed is a Kohn-Sham orbital-dependent potential (Gorling and Levy 1994 Ivanov et al. 1999), 

This equation is based on the OEP method, as recognized from its similarity to Eq. (7.40). Even though the EXX potential produces valence orbital energies that are exactly similar to those of the Hartree-Fock exchange potential, it provides core orbital energies that are much different from the Hartree-Fock ones. Combining 

This hybridization drastically improves the results of core orbital energies. 

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What causes the poor-quality HOMO energies for hydrogen and the rare gases As shown in Table 7.6, similar problems are also found in the calculations of core orbital energies. Note that even ab initio density functional theory using highly correlated correlation potentials also provides poor-quality core orbital energies... 

The local density approximation is highly successful and has been used in density functional calculations for many years now. There were several difficulties in implementing better approximations, but in 1991 Perdew et al. successfully parametrised a potential known as the generalised gradient approximation (GGA) which expresses the exchange and correlation potential as a function of both the local density and its gradient ... 

The descriptors used should not be highly collinear with each other, for two reasons. First, this can lead to statistical instability and overprediction, and second, collinearity makes mechanistic interpretation difficult. For example, Cronin and Schultz [41] have pointed out that although a good correlation could be obtained between the skin sensitization potential and the hydrophobicity of a series of bromoalkanes, a correlation between skin sensitization potential and molecular weight had exactly the same statistics, because hydrophobicity and molecular weight are very highly correlated in homologous series. 

A small problem arises when the crystal thickness and temperature factors are refined simultaneously, because these parameters are highly correlated. Raising both the thickness and the temperature factors results in almost the same least-squares sum. This is not an artifact of the calculation method but lies in the behavior of nature. Increasing the Debye-Waller factor of an atom means a less peaked scattering potential, which in turn results in a less sharply peaked interaction with the ncident electron wave. It can be shown that a thickness of 5 nm anc B=2 will give about the same results as a thickness of 10 nm and B=6 A. ... 

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