Interatomic Potentials for Simple Metals Sample Clauses

Interatomic Potentials for Simple Metals. ‌ In Eq.(2.52), we introduced the cohesive energy Ecoh. The goal of this section is to prove that Ecoh for an sp-valent metal can be written as the sum of a term dependent on the atomic volume Ω plus a long-ranged pair potential v2 [189, 190] ΣE ({R}, Ω) = E (Ω) + v (Rcoh vol 22N 1 ′ ij ij, Ω) . (2.82) The volume term Evol is the largest contribution to the cohesive energy and v2 is responsible for structural energy differences. In this section, we shall prove that the cohesive energy takes this form and derive analytic expressions for Evol and v2 using results from the previous sections. All terms in the binding energy are now known in terms of the pseudopotential. There are certain terms that can be seen to be equal and opposite. To proceed, we need to partition all structural and volume components. We will first do this in reciprocal-space and then in real-space. In addition, we will tem- porarily assume that the pseudopotential is local and then generalise our expressions to the non-local case.