Atomic charges definitions

Free Energies of Solvation in Water, in kcal/mole," Obtained by Classical Monte Carlo Simulations Using Two Different Atomic Charge Definitions... 

Analogous to the topological atomic charge definition is that of topological bond orders, defined as the limit of... 

P. Politzer and R. S. Mulliken, J. Chem. Phys., 55,5135 (1971). Comparison of Two Atomic Charge Definitions, as Applied to the Hydrogen Fluoride Molecule. 

A key distinguishing characteristic of atomic charge definitions is their intended usage in describing some aspect of the electronic charge distribution, i.e., the spatial variation of electron density p(r). In the most superficial usages, this distribution is replaced by supposed point charges (Dirac delta functions) at each nucleus, namely. 

Two other atomic properties have been used in the definition of atom type, thereby increasing its fuzziness relative to that in the ap and tt descriptors - atomic log P contribution (yielding hydrophobic pairs, hps, and torsions, hts) and partial atomic charges (charge pairs, cps, and charge torsions, cts). 

Such a matrix is not independent on the coordinate system, but the trace is. Cioslowski has proposed a definition of atomic charges as one-third of the trace over the APT, denoted Generalized Atomic Polar Tensor (GAPT) charges.The charge on atom A is defined as... 

Population Analyses Population analyses are used to gain a detailed understanding of the electronic properties of a molecule. A common feature of most of these analytic tools is the definition of atomic charges. Because there is no... 

On trying to assign an oxidation number to the copper atom one finds that the atomic charges, as calculated with the MuUiken definition 183), are remarkably small ... 

This is true for our procedure for calculating partial atomic charges in a-bonded molecules (16). The method starts from Mulliken s definition of electronegativity, x> derived from atomic ionization potentials, IP, and electronegativities, EA (Equation 3)(17). 

The operators for the potential, the electric field, and the electric field gradient have the same symmetry, respectively, as those for the atomic charge, the dipole moment, and the quadrupole moment discussed in chapter 7. In analogy with the moments, only the spherical components on the density give a central contribution to the electrostatic potential, while the dipolar components are the sole central contributors to the electric field, and only quadrupolar components contribute to the electric field gradient in its traceless definition. 

The function F consists of the last two terms of (10.22) divided by y, with a change in sign. It is convenient to rewrite F using the definition of net atomic charge, Zeff — = After some algebra one obtains... 

Clearly not Atomic charges are not molecular properties, and it is not possible to provide a unique definition (or even a definition which will satisfy all). It is possible to calculate (and measure using X-ray diffraction) molecular charge distributions, that is, the number of electrons in a particular volume of space, but it is not possible to uniquely partition them among the atomic centers. 

See Atomic metallic ion emission Anomalous corrugation theory 31, 142 breakdown 146 graphite, and 31, 144 Apparent barrier height 63,171 anomalously low 171 attractive force, and 49, 209 definition 7 image force, and 72 repulsive force, and 171, 198, 209 square-barrier problem, in 63 Apparent radius of an atomic state 153 Atom charge superposition I 11 analytic form 111 Au(lll), in 138 in atomic beam scattering 111 Atom-beam diffraction 107 apparatus 109... 

Although the number of valence electrons present on an atom places definite restrictions on the maximum formal oxidation state possible for a given transition element in chemical combination, in condensed phases, at least, there seem to be no a priori restrictions on minimum formal oxidation states. In future studies we hope to arrive at some definitive conclusions on how much negative charge can be added to a metal center before reduction and/or loss of coordinated ligands occur. Answers to these questions will ultimately define the boundaries of superreduced transition metal chemistry and also provide insight on the relative susceptibility of coordinated ligands to reduction, an area that has attracted substantial interest (98,117-119). 

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