The Contribution To Bond Valences By Lone Electron Pairs
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The Contribution To Bond Valences By Lone Electron Pairs Xiqu Wang* Department of Chemistry, University of Houston, Houston, TX 77204-5003, U.S.A. Friedrich Liebau Institut für Geowissenschaften, Universität zu Kiel, D-24106 Kiel, Germany. ABSTRACT Bond valence sums (BVS) calculated for lone-pair cations are found increasingly higher than their formal valences as the retraction of the lone electron pair (LEP) from the nucleus is more pronounced. The increase in BVS is interpreted as a continuous increase of an effective valence of an atom that is a measure of its actual ability to bind other atoms without changing its formal valence. How the LEP of a lone-pair cation affects the effective valence of other atoms in a structure is studied by bond valence calculations for specific structures. For structures rich in alkali cations, it is found that the high effective valence of the lone-pair cations tends to be balanced by low effective valence of alkali cations. The LEP transfers bonding power or effective valence from the alkali cations to the lone-pair cations by joining the coordination sphere of the alkali cations.
INTRODUCTION The bond valence model that has a root in Pauling’s electrostatic valence rule [1] is an empirical method widely and successfully used to describe and interpret crystal structures. The model was thoroughly reviewed in a recent monograph by Brown [2]. According to the bond valence model, an inorganic structure is considered an arrangement of atoms linked by bonds between atoms with opposite signs of valences. A bond valence is assigned to each bond so that the bond valence sum for all bonds around an atom equals the absolute value of the valence of the atom. By setting the atomic valence equal to the oxidation number or formal valence forV, the following empirical relationship between bond valence and bond length is widely used: (1) Sij = exp [(r0 – Dij) / b] where Dij is the length of the bond between atoms i and j, Sij is the bond valence, and r0 and b are empirical parameters derived from well-refined structures. b is taken as a constant equal to 0.37Å and normally independent of bond types, whereas r0 is tabulated for every bond type (cation anion pair). The tabulated r0 value for an A–X bond type is derived by averaging individual r0i values calculated for every available [AXn] polyhedron according to (2) r0i = b {[ ln (forV / [Σj exp (– Dij) / b)]} where b = 0.37 Å [2-4]. For the majority of inorganic structures, bond valence sums (BVS) calculated by using equation (1) are satisfactorily close to the formal valences forV of the corresponding atoms. Large deviations can usually be attributed to chemical or steric reasons [2]. For example, if the hydrogen atom of a hydroxyl group OH- in a structure is not located the calculated BVS for the O atom will be remarkably lower than the formal valence 2 v.u. If the ignored hydrogen atom is involved in an O-H…X hydrogen bond the calculated BVS for the X atom will also be lower than the formal valence. Systematic deviations of BVS from f
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