The rectangular d band model of cohesion

The simplest model for describing the strength of interatomic bonding in transition metals is based on the evaluation of the bond integrals dda, ddjr, ddd [3]. 

The total energy per atom consists of attraction contribution (13.3) and repulsive contribution, 

The d states of transition metals retain much of their atomic character in the solid. 

The results of simulating for transition metals illustrate a large difference between the s and p valence orbitals that are delocalized and the d states that are much more localized. Exchange and correlation of electrons are much more expressed in highly localized orbitals. 

Although the noble metals such as silver and copper have filled d bands, their bond shares important features in common with the elements to their left in the Mendeleev periodic table. 

The d bond energy is the energy of the d electrons that is measured with respect to the centre of gravity of the band, that is 

The sp-d hybridization energy is the contribution that results from turning on the hybridization matrix elements in eqn (7.25), resulting in the mixing between the NFE sp and d bands. As expected, it is negative, taking the approximately constant value of about 2 eV across the series. 

The parabolic variation in the cohesive energy across the 4d series is driven by the d-bond contribution alone, as is clearly demonstrated by Fig. 7.11. The sizeable drop in the cohesive energy towards the middle of the 3d series is a free-atom phenomenon, resulting from the special stability of Cr and Mn atoms with their half-full d shells. The simplest model for describing the bonding of transition metals is, therefore, to write the binding energy per atom as 

The d bond energy depends on the strength of the bond integrals dd 7, ddtr, and dd 5, which determine the density of states in eqn (7.32). 

Within the rectangular d band model the bond energy is proportional to the bandwidth, IF, through eqn (7.33). We may relate the bandwidth to 

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