Isopycnic localization

In conclusion, the results available suggest that the initial integration into open chromatin regions (such as those corresponding to the GC-richest isochores) is favoured even for a GC-poor provirus. Stability of integration and expression are, however, associated with an isopycnic localization. 

The causes of the compartmentalized, isopycnic localization of viral sequences... 

For each QTAIM atom in diamond the DAFH analysis delivers 5 orbitals with essential occupations. One of them has occupation very close to 2 and is almost completely confined in the QTAIM basin, thus corresponding to a core orbital. Each of the four other orbitals has occupation number 0.94 and is located between two nearest C atoms (Fig. 9, left). Around 48% of its norm is recovered in the basin of the reference QTAIM atom and 43% of the norm is in the basin of elosest C atom. Therefore, more than 90% of its norm is eonfined in the basins of the two bonded C atoms. The complement sum of occupation numbers of two such orbitals from each participating atom yields the number very close to 2, which nicely describes the localized 2c-2e bond, similar to the isopycnic localized orbital in Fig. 8. The DAFH analysis easily recovers... 

Fig. 8 One of the orbitals resulting from the isopycnic localization transformation. Shown is the amplitude isosurface of level 0.12, colored by the orbital phase. [Color figure can be viewed in the electronic version.].

Fig. 4. Localization of WAP27 and WAP20 in the crude microsome fractions and the relation with marker-enzyme activities in three organelles (ER, tonoplast, and Golgi). SDS-PAGE of fractionated proteins by isopycnic linear sucrose density gradient centrifugation of microsome fraction of mulberry cortical parenchyma cells was performed using 6-pL samples in each fraction. Immunoblot analysis was performed with anti-WAP27 and anti-WAP20 antibodies. (From ref. [1], with permission from the American Society of Plant Physiologists.)...

Cioslowski, J. Isopycnic orbital transformations and localization of natural orbital. Int. J. Quant. Ghent. Symp. 1990, 24,15. 

Their conceptual and computational importance notwithstanding. neither MOs nor NOs are useful in analysis of electronic wavefunctions. On the other hand, one-electron functions furnished by unitary transformations of MOs and the so-called isopycnic transformations of NOs have found widespread applications in quantum chemistry. These specialized orbitals are primarily used in studies of bonding and electron localization. 

An alternative approach was suggested by Cioslowski and Mixon, who introduced the so called covalent bond order C(A,B), whose values are calculated from the localized natural orbitals and associated populations 0, resulting from so-called isopycnic transformation of the original natural orbitals. 

The first step of the analysis consists in the diagonalization of the matrix that represents the hole (eqn (10)) in appropriate basis (usually canonical orbitals). This primary diagonalization yields the set of eigenvalues and eigenfunctions that are, in the second step subjected to the isopycnic transformation. Its aim is to transform the primary eigenvectors, that are usually delocalized over the nearest neighborhood of the reference basin, into the set of more localized functions whose resemblance with localized orbitals often allows the association with classical concepts of bonds, lone pairs etc., in terms of which chemists are used to classify the molecular structures. 

Therefore x(R) is the only nontrivial eigenvector of DAFH and an isopycnic transformation is not necessary in this case. Thus x(R) defines the expansion of the DAFH orbital/r(r) in terms of the local orhitals y... 

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