# Energy of a Fe supercell?

1. Jun 6, 2013

### pillow47

In a fcc or bcc lattice of Fe atoms (or Cobalt or Aluminum, or potentially any element) , for a supercell of 16 Fe atoms with periodic boundary condition, how do you estimate the total ground state energy of the system? The total energy is defined to include the kinetic energy of the electrons and potential energy due to the Columbic interactions among electron-electron, electron-nuclei, and nuclei-nuclei. The kinetic energy of the nuclei is not included under the Born-Oppenheimer approximation. What experimental values can be cited or theoretical calculations done to give a rough estimate of the total energy on the order of magnitude? Ab initio is one way, but I want to find out other ways to confirm with the ab initio results.

I tried to use the first a few ionization energies of Fe to estimate the binding energy due to one atom and then multiply by 16 to get the total energy of the system. But of course, this calculation doesn't include the potential energy due to atom-atom interaction. Also, I was told that things in solids dramatically change and the single-atom approximation doesn't have much truth to it. So I'm wondering if there is a better way to make an estimate of the total energy of the system.

2. Jun 6, 2013

### Useful nucleus

Experimentally what you need to look for is the so called cohesive energy. Theoretically one needs a Hamiltonian with an explicit function for the potential energy to evaluate the cohesive energy. If the so-called ab initio methods are not appealing, one can use a classical force field in which the atom is represented by a point (or a finite number of points) without internal structure. A famous example for metals is the so-called EAM (Embedded Atom Method) potential.
For iron in particular , you might need to consult the work of Auckland who developed several potentials for iron that are widely accepted.
Except very few ideal cases, no theoretical calculations can be carried analytically and numerical simulations are needed.

3. Jun 10, 2013

The "total ground state energy" depends on what theoretical method you are using. In general, you can't meaningfully compare absolute ab initio energies for heavy atoms like Fe with those obtained from experiments (too many non-Coulombic terms are left out of the Hamiltonian). Most codes used for solid state calculations would report only the energies of valence electrons, since the core electrons are usually replaced by a pseudopotential.

In addition, the experimental data for total atomic ionization are only precise to ~10 eV or so for an atom like Fe.

Schwinger's classic paper on the topic of atomic binding energies may be of interest: Phys. Rev. A 32 (1985) 47.

4. Jun 10, 2013