It is shown that the quantum mechanical requirement for the spatial localization of an electron in a many-electron system is that the Fermi correlation hole for the electron be totally contained within the same spatial region. Correspondingly, the extent to which this requirement is not met provides a quantitative measure of its delocalization over the remaining space of the system. The localizability of the Fermi hole is a property of the pair density and the total localization of some number of electrons N ( Q ) in a region (Q) of real spacejs obtEined only when the exclusion principle acts so as to reduce the average pair population of (a) to its limiting value of N ( R ) ( N ( Q ) -I). It is shown that the partitioning of a system which most closely approaches the limit of spatially localized subsets of electrons may be determined by demanding that the fluctuation in the average population of each of the spatial regions be a minimum. The extent to which the (Hartree-Fock) charge distributions of LiH, BeH2, BH3, BH4-, CH4, NH3,OHz. FH, Ne, N2, and Fz may be regarded as arising from the localization of individual a,@ pairs of electrons in distinct spatial regions is determined. The model of spatially localized pairs is appropriate for LiH, BeH2, BH3, and BH4-, it is borderline for CH4, but in the remaining systems, the motions of the valence electrons are so strongly inter-correlated, the localized pair model ceases to afford a suitable description. For example, the properties of the charge and pair densities of H2O provide no physical basis for the view that there are two separately localized pairs of nonbonded electrons in this system. The same analysis indicates that a wave function constructed from N / 2 intra-correlated pair functions would fail to recover the major fraction of the correlation energy in this latter set of molecules.In this paper we investigate the extent to which the electronic charge distribution of a molecular system may be regarded as arising from the localization of individual pairs of electrons in well-defined and nonoverlapping regions of space. W e do this in the following way. We determine the average number of pairs in a given region of space by integration of the quantum mechanical expression for the pair density over that region. W e next show that this average number of pairs is dependent upon the correlative interactions between the electrons and in particular, that the decomposition of a total system which most closely approaches the limit of spatially localized pairs of electrons is attained by maximizing the extent to which the integrated Fermi correlation hole of each electron in a given pair is localized within the same spatial domain. Finally, we show that this latter condition is attained by demanding that the fluctuation in the average population of each of the spatial regions be a minimum.Daudel and co-workers'%2 have reasoned that there should be some "best" decomposition of the physical space of a system into a number of mutually exclusive spaces called loges. The "...
We have determined the nucleotide sequence of two Bacillus subtilis promoters (veg and tms) that are utilized by the principal form of B. subtilis RNA polymerase found in vegetative cells (sigma 55-RNA polymerase) and have compared our sequences to those of several previously reported Bacillus promoters. Hexanucleotide sequences centered approximately 35 (the "--35" region) and 10 (the "--10" region) base pairs upstream from the veg and tms transcription starting points (and separated by 17 base pairs) corresponded closely to the consensus hexanucleotides (TTGACA and TATAAT) attributed to Escherichia coli promoters. Conformity to the preferred --35 and --10 sequences may not be sufficient to promote efficient utilization by B. subtilis RNA polymerase, however, since three promoters (veg, tms and E. coli tac) that conform to these sequences and that are utilized efficiently by E. coli RNA polymerase were used with highly varied efficiencies by B. subtilis RNA polymerase. We have also analyzed mRNA sequences in DNA located downstream from eight B. subtilis chromosomal and phage promoters for nucleotide sequences that might signal the initiation of translation. In accordance with the rules of McLaughlin, Murray and Rabinowitz (1981), we observe mRNA nucleotide sequences with extensive complementarity to the 3' terminal region of B. subtilis 16S rRNA, followed by an initiation codon and an open reading frame.
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