# [CP2K:8672] How to calculate Fermi energy of metals?

Matt W MattWa... at gmail.com
Wed Feb 8 22:59:57 UTC 2017

```Hi,

the OP might need to be a bit careful with the definition of the fermi
energy and explain what they are after. I think there are different
conventions around.

I think the free-electron models he referred to, and that 7 eV for copper
number, measure the chemical potential / fermi energy relative to the
bottom of the band. So it corresponds to something like the energy from the
lowest 4s copper states up to the highest occupied states. What you would
use it for, I am not quite sure.

So I think it is not the same thing as a physical measure relative to the
vacuum, i.e. work function.

Matt

On Wednesday, February 8, 2017 at 10:15:19 PM UTC, Ari Paavo Seitsonen
wrote:
>
> Dear Ashish Dabral,
>
>   The only way _I_ know is to calculate a system with surface (well, two,
> slab model) and then align the Fermi energy via the potential in the middle
> of the slab - should be thick enough so that in the middle it is converged
> - and the potential in the middle of the vacuum. So the value of "Fermi
> energy" would be the work function. I guess that one would get the same
> value if one would then take the difference of the potential in the middle
> of the slab and potential in the vacuum, and then uses that after aliging
> the difference between the potential and the Fermi energy in a bulk system.
>
>   With GGA one usually gets too small values of the work function if I
> remember correctly (self-interaction/asymptotics), by about 0.5-1 eV
> depending on the material.
>
>     Greetings,
>
>        apsi
>
> 2017-02-08 17:17 GMT+01:00 ashish dabral <ashis... at gmail.com
> <javascript:>>:
>
>> Hi,
>>
>> I would like to know how to calculate the fermi energy of metals using
>> cp2k.
>> For example, Cu has a fermi energy of around 7.0eV, which can also be
>> calculated using the general formula involving carrier concentration (
>> https://en.wikipedia.org/wiki/Fermi_energy, the
>> three dimensional case.) I would like to know how can I obtain this value
>> (approximate) from the bulk metal unit cell.
>>
>> Thanks
>>
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>
>
>
> --
>
> -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-
>   Ari Paavo Seitsonen / Ari.P... at iki.fi <javascript:> /
> http://www.iki.fi/~apsi/
>     Ecole Normale Supérieure (ENS), Département de Chimie, Paris
>     Mobile (F) : +33 789 37 24 25    (CH) : +41 79 71 90 935
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