# [Pw_forum] Comparison of total energies

Nicola Marzari nicola.marzari at epfl.ch
Thu Jul 6 00:41:26 CEST 2017

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Dear Chukwuemeka,

there are two possibilities:

1) if you are comparing the same stoichiometries, but different
arrangements (e.g. 1 A atom, 1 B atom, 1 C atom, 1 D atom, or a
multiple of these in a supercell) you just need to compare
the energies out of PWscf for different arrangements; in
each case, you want to calculate for the particular arrangement you
chose the energy at relaxed atomic positions, and relaxed unit cell
vectors. This would allow you to identify the best candidate among your
trials (but of course you wouldn't know if there are better candidates,
or if the system is thermodynamically stable with respect to
decomposition in other, simpler compounds).

2) if you have a more complex case, where you are comparing compounds
with different stoichiometries, you want to compare formation energies.
For that, you could e.g. choose for each element its energy per atom at
the ground-state structure of the elemental system (eg for Si, it would
be the diamond lattice at equilibrium). So, for each of the 4 elements
you need the energies of their elemental ground-state structure per atom
(for Si, you divide by 2, since you have 2 atoms in the unit cell), and
then you want to compare formation energies defined as

E(A_i,B_j,C_k,D_l)-i*E(A)-j*E(B)-k*E(C)-l*E(D)

where E(A_i,B_j,C_k,D_l) is the energy of your compound (at equilibrium)
with an integer number i of atoms A, j atoms B, k atoms C, and l atoms
D, and E(A) is the energy of the elemental compound for A at
equilibrium, divided by the number of atoms that the elemental compound
A as in the unit cell (same for E(B), ....). If the formation energy is
negative, you would know that your system is stable, at 0K, with respect
to decomposition in the end compounds - but you still wouldn't know
if it is stable or not with respect to say decomposing into different
binary compounds, or combinations of unaries, binaries, and ternaries.

For more in-depth understanding, have a look at:
http://oqmd.org/analysis/gclp/

nicola

On 05/07/2017 23:59, Chukwuemeka Okoye wrote:
> Dear All,
>
> I am using Quantum Espresso to perform calculations on quaternary
> Heusler compounds. My question is, can I compare the total energies of
> different types of atom arrangement in other to determine the most
> stable configuration(correct ground state) between Type-I, Type-II and
> Type-III?
> Thanks.
>
> CMI Okoye
> /------------------------------
> Chukwuemeka M I *Okoye*
> /
> /Department of Physics and Astronomy,
> /
> /University of Nigeria,
> /
> /Nsukka, Enugu State,
> /
> /Nigeria/
> Telephone: +234 7038766990
> E-mail: cmi.okoye at unn.edu.ng <mailto:cmi.okoye at unn.edu.ng>
>
>
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>

--
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Prof Nicola Marzari, Chair of Theory and Simulation of Materials, EPFL
Director, National Centre for Competence in Research NCCR MARVEL, EPFL
http://theossrv1.epfl.ch/Main/Contact http://nccr-marvel.ch/en/project

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