Coulombic parameter, calculation

Table 2. The Coulomb parameters for CJJJ, as obtained from the DF calculations of Ref. [1]...

In the present calculation both e-e and e-v interactions are included for the HOMO shell of C6o- E-e exchange terms are treated essentially exactly, in the assumptions that (i) inter-band couplings can be neglected, and only act as a renormalization of the Coulomb parameters and that (ii) the latter are independent of the charge n in the HOMO. In principle, due to both orbital and geometrical relaxation, the effective... 

Oxidation potentials are recognized to be correlated with the highest occupied levels of electrons, which may be evaluated according to the Hiickel molecular orbital calculation. In this paper the calculations were carried out with the following values (18) as the Coulomb parameters. 

On the other hand, all the phosphonitrilic chlorides display comparable aromaticity. The assumption of a particular difference in electronegativity between phosphorus and nitrogen allows the calculation of 5r-electron energies in terms of the appropriate resonance integrals. Table VI compares the aromatic hydrocarbons and the phosphonitrilic chlorides. The calculated energies per electron relative to the Coulomb parameters o and p are expressed in terms of the appropriate resonance... 

The LDA-I-U orbital-dependent potential (7.74) gives the energy separation between the upper valence and lower conduction bands equal to the Coulomb parameter U, thus reproducing qualitatively the correct physics for Mott-Hubbard insulators. To construct a calculation in the LDA-I-U scheme one needs to define an orbital basis set and to take into account properly the direct and exchange Coulomb interactions inside a partially filled d- f-) electron subsystem [439]. To realize the LDA-I-U method one needs the identification of regions in a space where the atomic characteristics of the electronic states have largely survived ( atomic spheres ). The most straightforward would be to use an atomic-orbital-type basis set such as LMTO [448]. 

For the determination of equilibrium properties, NVT (constant number of particles, volume and temperature) and NPT (constant number of particles, pressure and temperature) ensembles were used. For these ensembles, the use of a non-Hamiltonian system is required. Temperature was controlled with a thermostat based on a Nose-Hoover chain [17]. In each case, calculations were performed with a time step fixed at 1.2 fs. A rigid-ion model based on the Bom-Mayer potential (Equation 3.4.1) was used. This model takes into account the Van der Waals and Coulomb parameters. 

One of the most efficient algorithms known for evaluating the Ewald sum is the Particle-mesh Ewald (PME) method of Darden et al. [8, 9]. The use of Ewald s trick of splitting the Coulomb sum into real space and Fourier space parts yields two distinct computational problems. The relative amount of work performed in real space vs Fourier space can be adjusted within certain limits via a free parameter in the method, but one is still left with two distinct calculations. PME performs the real-space calculation in the conventional manner, evaluating the complementary error function within a cutoff... 

The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser-Parr-Pople method, and by the introduction of a new empirical parameter to differentiate resonance integrals between a orbitals and tt orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyri-dazine, pyrimidine and pyrazine. The results obtained were refined by a limited Cl calculation, and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both the n TT and n tt singlet transitions. The relative energies of the tt and the lone pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the lone pairs in these compounds is discussed. 

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