Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coherent view of crystal chemistry and ab initio analyses of Pb(II) and
  Bi(III) Lone Pair in square planar coordination   The stereochemistry of 6s2 (E) lone pair of divalent Pb and trivalent Bi
(PbII and BiIII designated by M*) in structurally related PbO, PbFX (X= Cl, Br,
I), BiOX (X= F, Cl, Br, I) and Bi2NbO5F is rationalized. The lone pair LP
presence determined by its sphere of influence E, equal to those of oxygen or
fluorine anions, was settled by its center then giving M*-E directions and
distances. Detailed description of structural features of both elements in the
title compounds characterized by [PbEO]n and [BiEO]n layers allowed to show the
evolution of M*-E distance versus the changes with the square pyramidal SP
coordination polyhedra. All are different, in red PbO one finds {PbEO4E4}
square antiprism, a {[Bi.E]O4X4Xapical} monocapped square antiprism in PbFX and
BiOX and {BiEO4F4}square antiprism in Bi2NbO5F. To analyze the crystal
chemistry results, the electronic structures of these compounds were calculated
within density functional theory DFT. Real space analyses of electron
localization illustrate a full volume development of the lone pair on PbII
within {PbEO4E4} in PbOE, {PbEF4X4} in PbFXE and Bi(III) within {BiEO4X4}
square antiprisms, contrary to Bi(III) within {[Bi.E]O4F4Fapical} monocapped
square antiprism. Larger hardness (larger bulk modules B0) and band gap
characterize BiOF versus PbO due to the presence of F which brings antibonding
Bi-F interactions oppositely to mainly bonding Bi-O. In PbFX and BiOX series
there is a systematic decrease of B0 with the increasing volume following the
nature and size of X which is decreasingly electronegative and increasingly
large. The electronic densities of states mirror these effects through the
relative energy position and relative electronegativities of F/X and O/X
leading to decrease the band gap.

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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph