# Vacuum level for charged systems

Nuri Yazdani nuri.a.... at gmail.com
Thu Feb 2 12:37:21 UTC 2017

```Hi all,
First to summarize the question: how/can one extract the vacuum level from
a calculation done on a charged (non periodic!) system, such that the
energies taken from two calculations with different amounts of charge can
be compared on an absolute scale to one another? Also, if someone could
provide a reference for where this or a similar situation has been looked
Why I want to know this is explained in more detail below.

I am doing calculations on charged molecules, including HF. I am trying to
look into the reorganization energy associated with hopping of carrier from
one charge molecule to another. To estimate this, I calculate the energies
for a charged (+1e-) and neutral molecule:

E0{A,n} = E{A,n}+E{F,ref}, where E{A,n} are the energy spectra I get from
CP2k for the neutral molecule, and E{F,ref} is the reference level to vacuum

E0{C,n} = E{C,n}+E{C,ref}, where E{C,n} are the energy spectra I get from
CP2k for the charged molecule, and E{F,ref} is the reference level to
vacuum for that calculation

If there are N occupied molecular orbitals in the neutral molecule, than
the reorganization energy can be approximated as:

lambda = Sum{1:N}(E{C,n}+E{C,ref}) + Sum{1:N+1}(E{A,n}+E{A,ref}) -
Sum{1:N+1}(E{C,n}+E{C,ref}) - Sum{1:N}(E{A,n}+E{A,ref})
lambda = Sum{1:N}(E{C,n}-E{A,n}) + Sum{1:N+1}(E{A,n}-E{C,n})  - E{C,ref} +
E{A,ref}

So the end product is directly proportional to the difference in reference
energies.

Cheers,
Nuri
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