GW: Ionization Potential and Electron Affinity
**********************************************

ADF Spectroscopy GW Quasi-particles Ionization potential Electron
affinity

Ionization potential (IP) and electron affinity (EA) of molecules can
be predicted with reasonable accuracy using the G_0W_0 method [1] [2],
especially if as starting point a (range separated) hybrid functional
is used. Note that functionals that use XCfun (like LCY-BP86 and CAMY-
B3LYP) can not be used as starting point.

One can also do eigenvalue-only self-consistent GW (evGW) with ADF,
which is typically a factor 5 to 10 more expensive than G_0W_0, but
which has the advantage that it is less starting-point dependent.
Starting from AMS2022 one can also do quasiparticle self-consistent GW
(qsGW) with ADF, which is more expensive than evGW, but the results of
a qsGW are starting-point independent, and is usually the most
accurate one.

Next in AMS2022 it also possible to go beyond the GW approximation for
the self-energy and take into account the screened interaction to
second order, with an even more expensive method called G3W2. See the
ADF manual on GW for more details.

In AMS2023.102 a bug was fixed regarding GW. An incorrect Fermi energy
was used, which also affected BSE.

In this tutorial we will show how to compute the IP and EA of Azulene
with ADF using G_0W_0@PBE0.

See also:

  * ADF manual on GW

  * Recommendations for GW calculations

  * Video tip of the week

Warning:

  The implemented GW algorithm is very sensitive to numerical noise
  and on the numerical (MBPT) settings. Using the same numerical
  settings, quasiparticle energies from partially self-consistent GW
  calculations performed on different hardware can differ by a few
  meV. See also the ADF manual on GW and ADF manual on MBPT settings.


Set up and run the calculation
==============================

Let's start by importing the structure of the Azulene molecule from
our molecules database:

   **1.** Start **AMSinput** (**SCM → New Input**)
   **2.** In the **search box** [image: Search][image] search for "Azulene" and select **C10H8: Azulene**
   **3.** Symmetrize the molecule by clicking on [image: SymmTool][image]

Let's now set up the calculation details in the main panel:

   **1.** **Task → Single Point**
   **2.** **XC functional → Hybrid → PBE0**
   **3.** **Basis set → TZ2P**
   **4.** **Frozen core → None**
   **5.** **Numerical quality → Good**
 [image]

Typically for EA one may need a larger basis set than TZ2P, see the
section Recommendations for GW calculations in the ADF manual. For
precision reasons (at least) a good numerical quality is recommended.

To enable the G_0W_0 calculation:

   **1.** In the panel bar select **Properties → GW**
   **2.** In the GW panel, check the **Calculate GW quasi-particle energies** checkbox
   **3.** **Self consistency → G0W0**

   [image]

Use **Self consistency → EVGW** for evGW, and use **Self consistency →
QSGW** for qsGW. Use **Self energy → G3W2** for G3W2, typically used
in combination with qsGW. In case of (any variant of) GW, in order to
avoid numerical issues, the dependency key is set in ADF (and the
RIHartreeFock%DependencyThreshold is increased), see the
Recommendations for GW calculations in the ADF manual. One can change
these dependency values using the panel bar **Details → Accuracy**.

We are now ready to run the calculation:

   **1.** **File → Save** and give the job an appropriate name, e.g. "Azulene"
   **2.** **File → Run**
   **3.** Wait for the calculation to finish (you can monitor the progress via the logfile, **SCM → Logfile**)


Results
=======

The results of the calculation are written both to the text output
file and to the binary "adf.rkf" file. To see the G_0W_0 results in
the output file:

   **1.** **SCM → Output**
   **2.** In AMSoutput, search for "GW Quasi-Particle Spectrum"

   [image]

The ionization potential (IP) equals the negative of the G_0W_0 quasi-
particle HOMO energy:

   \text{IP} = -\text{HOMO}_{\text{G}_0\text{W}_0} = 7.07 \text{[eV]}

The electron affinity (EA) equals the negative of the G_0W_0 quasi-
particle LUMO energy:

   \text{EA} = -\text{LUMO}_{\text{G}_0\text{W}_0} = 0.55 \text{[eV]}

These values are in good agreement with the CCSD(T) results from [1]
(IP=7.55 [eV] and EA=0.54 [eV]) and with experimental results cited in
[1] (IP=7.42-7.44 [eV] and EA=0.69-0.80 [eV]).

[1] Joseph W. Knight, Xiaopeng Wang, Lukas Gallandi, Olga
    Dolgounitcheva, Xinguo Ren, J. Vincent Ortiz, Patrick Rinke,
    Thomas Körzdörfer, and Noa Marom, *Accurate Ionization Potentials
    and Electron Affinities of Acceptor Molecules III: A Benchmark of
    GW Methods*, J. Chem. Theory Comput. 2016, 12, 2, 615–626

[2] Arno Förster, Lucas Visscher, *Low-order scaling G0W0 by pair
    atomic density fitting*, arXiv.org (2020)
