Exchange correlation potential selection

The partial cancellation of correlation effects arising from the 1- and 2-matrices is a well-known fact in Kohn-Sham theory [1, 2, 72], As is to be expected, it also appears in the Kohn-Sham-type equations for an orbit cty. We would like to emphasize, nevertheless, that all terms in Eq. (82) can be explicitly calculated. In principle, therefore, within a particular orbit cty, the exchange-correlation energy term as well as the Kohn-Sham-type exchange-correlation potential can be explicitly obtained. The accuracy of the results depends, clearly, on our selection of the orbit-generating functions W 6 c Cn and W e c Sn. 

The present review has been very selective, stressing the rationale behind density-functional methods above their applications and excluding many important topics (both theoretical and computational). The interested reader may refer to anyone of the many books [91-93] or review articles [94-101] on density-functional theory for more details. Of special importance is the extension of density-functional theory to time-dependent external potentials [102-105], as this enables the dynamical behavior of molecules, including electronic excitation, to be addressed in the context of DFT [106-108]. As they are particularly relevant to the present discussion, we cite several articles related to the formal foundations of density-functional theory [85,100,109-111], linear-scaling methods [63,112-116], exchange-correlation energy functionals [25, 117-122], and qualitative tools for describing chemical reactions [123-126,126-132]. 

It is the coupling network that dictates the possibilities to select correlations to be observed. The key idea is to produce a mutually complementary pair of spectra, e.g. HNCA and HN(CO)CA. The former displays both intra- and inter-residue correlations and the latter exclusively the inter-correlations. Alternatively, an exclusive inter-HNCA can be recorded. The pair of spectra displaying for each amide nuclei resonances both intra- and inter-carbon resonances allow one to trace the polypeptide backbone from one residue to another. The sequential walk is interrupted at prolines and at times potentially due to exchange broadening. 

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