Madelung contribution

The on-site energy Dp for atomic species Q at the lattice site R consists of the band, core, double-counting, non-spherical and Madelung contributions, respectively. 

Fig. 11. The equation of state of UN. The curve labelled total is the equation of state. The uranium d and f contributions are also shown. The curves labelled spd are the s and p contributions plus the contribution of d electrons on the anion. The Madelung contribution is shown separately...

We see that the simple rectangular d band model reproduces the behaviour found by experiment and predicted by Miedema s semi-empirical scheme. However, we must stress that the model does not give credence to any theory that bases the heat of formation of transition-metal alloys on ionic Madelung contributions that arise from electronegativity differences between the constituent atoms because in the metallic state the atoms are perfectly screened and, hence, locally charge neutral. Instead, the model supports... 

In many cases more refined molecular orbital models give a better agreement between theory and experiment. Self-consistent field- 80 81> or CNDO-82> calculations as well as other ab initio calculations 83>84) were performed and the results of several different approaches for phosphorous compounds were critically evaluated by M. Pelavin 77). For the nitrogen compounds two different linear relationships, one for cations and for neutral molecules, the other for anoins, were observed 82), a phenomenon which might be explained with a Madelung contribution. 

As before in Sect.7.3, (8.30,39,40) must be solved-self-consistently using for instance the LMTO technique described in Sect.8.2. Owing to the simplifying assumptions of the atomic-sphere approximation, the only added complication is the Madelung contribution from point charges positioned at the centres of the atomic spheres. 

With the use of (142) the Madelung contribution to the ground-state energy becomes ... 

The approximate electronic-pressure formula, eq. (46), is slightly modified for compounds by inclusion of the Madelung contribution, and becomes... 

The modifications of the electron-ion interactions in the presence of the interface also contribute to the electrostatic term. The total electrostatic energy gives the Madelung contribution to the interfacial energy. It is unfavourable to adhesion when it is high. 

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