Bond critical point properties

IV. BOND CRITICAL POINT PROPERTIES OF THE ELECTRON DENSITY... 

They compute Laplacian and bond critical point properties of sulfide bonds containing first- and second-row main group M-cations and compare them with oxide bonds. The Laplacian maps of the distributions show that the VSCC of the sulfide anion is highly polarised and extends into the internuclear region of the M-S bonds, coalescing with the VSCCs of the more electronegative first-row cations. On the other hand, maps for a corresponding set of oxide molecules show that the oxide anion tends to be less polarised and more locally concentrated in the vicinity of its valence shell, particularly when bonded to second-row M-cations. 

Another more quantitative strategy that has been used to determine whether a pair of atoms is bonded or not is based on the bond critical point properties of the electron density distribution. According to Bader (1998), two atoms are indicated to be bonded if... 

Bond critical point properties and electron density distributions... 

The bond critical point properties of an electron density distribution are evaluated at the bond critical point, rc, of a bonded interaction. Collectively, they consist of the curvatures and the Laplacian of the distribution, the value of /9(rc) and the bonded radii of the bonded atoms. The curvatures of p(rc) determine the local concentration or local depletion of the electron density distribution in the vicinity of the bond critical point measured in three mutually perpendicular directions. As observed by Bader and Essen (1984), the curvatures in these directions are found by evaluating the eigenvalues and eigenvectors of the Hessian matrix of p(rc), Hy = p(r l dXjdxj, (ij = 1,3). The three... 

Bond critical point properties calculated for molecules... 

Figure 11. The observed MO bond length nsed to prepare Fignre 3 plotted against the bond critical point properties (a) the bond radins of the oxide anions, rj(0), (b) 2, the... 

Etschmann BE, Maslen EN (2000) Atomic radii from electron densities. Aust J Phys 53 317-332 Feth S, Gibbs GV, Boisen MB, Hill FC (1998) A study of the bonded interactions in nitride molecules in terms of bond critical point properties and relative electronegativities. Phys Chem Miner 98 234-241... 

Gibbs GV, Tamada O, Boisen MB, Hill FC (1999a) Lapladan and bond critical point properties of the electron density distributions of sulfide bonds A comparison with oxide bonds. Amer Mineral 84 435-446... 

Kirfel A, Lippmann T, Blaha P et al (2005) Electron density distribution and bond critical point properties for forsterite, Mg2Si04. Phys Chem Miner 32 301-313 Gibbs GV, Downs RT, Cox DF et al (2008) Experimental bond critical point and local energy density properties determined for Mn-O, Fe-O, and Co-O bonded interactions for tephroite, Mn2Si04, fayalite, Fe2Si04, and olivine, Co2Si04 and selected organic metal complexes. J Phys Chem Al 12 8811-8823... 

Gibbs GV, Boisen MB Jr, Hill FC et al (1998) SiO and GeO bonded interactions as inferred from the bond critical point properties of electron density distributions. Phys Chem Miner 25 574-584... 

Because of the nonquantitative nature of A/o(r) maps , the X-ray diffraction data recorded for coesite was used to genraate a total electron density distribution, p(r), for the mineral. In an analysis of the bond critical point properties of the distribution, Downs located the critical points along each of its Si—O bonds, determined the value of the electron density and the Laplacian of /o(r) at each of these critical points, V pfr, ), and mapped —V p(r) over the domain of each of its Si—O—Si skeletal units. A mapping of the total electron density distribution and its topological properties has a distinct advantage over a mapping of the deformation density in that The derivation of a unique and physically meaningful difference (deformation) electron density is a problem that cannot be solved since the choice of the promolecular reference density always implies some... 

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