Wigner correlation

Most of the present implementations of the CPA on the ab-initio level, both for bulk and surface cases, assume a lattice occupied by atoms with equal radii of Wigner-Seitz (or muffin-tin) spheres. The effect of charge transfer which can seriously influence the alloy energetics is often neglected. Several methods were proposed to account for charge transfer effects in bulk alloys, e.g., the so-called correlated CPA , or the screened-impurity model . The application of these methods to alloy surfaces seems to be rather complicated. 

Wigner s study of the correlation energy in the alkali metals was a pioneering work of great importance, and the degree of difficulty of this field is perhaps best demonstrated by the fact that, during the last two decades, little improvement has been achieved in his correlation formula III. 12. The formula is nevertheless rather crude, and Wigner himself estimates the overall accuracy to be within 20 per cent. 

Wigner s study of the correlation effects for high-electron densities is closely connected to the standard methods described in Section III.E., and the main errors come from the restricted form of the wave function (Eq. III.7) and the fact that this function does not represent a pure spin state. Hence, Wigner obtains only an upper bound for the correlation energy in this case. 

Bohm-Pines" plasma model seems at first sight to be very different from the expansion methods treated here, but in Section III.E(2b) it was shown that it is rather closely connected with the method using correlation factor. Similar to Wigner s formula, it probably gives reasonable values for the correlation energy for the... 

Mitler, H., Phys. Rev. 99, 1835, "Correlation energy of He." Application of Wigner s idea for two-electron case. 

Krisement, O., Phil. Mag. 2, 245, Some remarks about electron correlation. A comparative survey of the theories of Wigner (1934) and of Bohm and Pines by means of modulating factor. 

Water, electronic correlation, 324 methane-propane ternary system, 23 superposition of configuration, 295 Wigner s theory, cellular method," 252, 304, 306, 318... 

Activation energy values for the recombination of the products of carbonate decompositions are generally low and so it is expected that values of E will be close to the dissociation enthalpy. Such correlations are not always readily discerned, however, since there is ambiguity in what is to be regarded as a mole of activated complex . If the reaction is shown experimentally to be readily reversible, the assumption may be made that Et = ntAH and the value of nt may be an indication of the number of reactant molecules participating in activated complex formation. Kinetic parameters for dissociation reactions of a number of carbonates have been shown to be consistent with the predictions of the Polanyi—Wigner equation [eqn. (19)]. 

Van der Woude and Miedema [335] have proposed a model for the interpretation of the isomer shift of Ru, lr, Pt, and Au in transition metal alloys. The proposed isomer shift is that derived from a change in boundary conditions for the atomic (Wigner-Seitz) cell and is correlated with the cell boundary electron density and with the electronegativity of the alloying partner element. It was also suggested that the electron density mismatch at the cell boundaries shared by dissimilar atoms is primarily compensated by s —> electron conversion, in agreement with results of self-consistent band structure calculations. 

The Woodward-Hoffmann rules have intellectual roots that can be traced back to Wigner-Witmer correlation rules (E. Wigner and E. E. Witmer, Z. Phys. 51 [1928], 859) and general correlation-diagram concepts (R. S. Mulliken, Rev. Mod. Phys. 4 [1932], 1) as employed, e.g., by K. F. Herzfeld, Rev. Mod. Phys. 41 (1949), 527. Alternative MO... 

The first term is the exchange part, which is known exactly for the homogeneous gas, and the second term is the Wigner approximation for the correlation energy. For further discussion we refer to the literature [4-6]. 

In the low-density limit (r, — ), correlation and exchange are of comparable strength, and are together independent of exc is then nearly equal to the electrostatic energy per electron of the Wigner crystal [33-36] ... 

We recently presented a correlation method based on the Wigner intracule, in which correlation energies are calculated directly from a Hartree-Fock waveftmction. We now describe a self-consistent form of this approach which we term the Hartree-Fock-Wigner method. The efficacy of the new scheme is demonstrated using a simple weight function to reproduce the correlation energies of the first- and second-row atoms with a mean absolute deviation of 2.5 m h. 

Electron correlation is inherently a multi-electron phenomenon, and we believe that the retention of explicit two-electron information in the Wigner intracule lends itself to its description (i). It has been well established that electron correlation is related to the inter-electronic distance, but it has also been suggested (4) that the relative momentum of two electrons should be considered which led us to suggest that the Hartree-Fock (HF) Wigner intracule contains information which can yield the electron correlation energy. The calculation of this correlation energy, like HF, formally scales as N. ... 

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