Eu3+ Luminescence properties with Ligand Field DFT
**************************************************

ADF Spectroscopy Excitations Lanthanides XANES Luminescence Inorganic
LEDs

Eu^3+ compounds are often used in trichromatic phosphors for lighting
purposes, where they are known for red-color emission. The red
emission results from the Eu 4f^6 → 4f^6 transitions involving the
ground states 7F_J (with J designating the spin-orbit components,
i.e., 0, 1, 2, . . . , 6), and low-lying excited state 5D_0. In this
tutorial, we are going to calculate the energy levels of Eu^3+
compounds by using LFDFT, in order to understand the mechanism of the
electron transition process. As example for application, we consider
the luminescence properties of the compound
[Eu(NO3)3(phenanthroline)2]. More detailed calculation procedure can
be found in Ref. [1].

[image]

[Eu(NO3)3(phenanthroline)2] has an open-shell electronic structure,
where the Eu 4f orbitals are occupied with 6 valence electrons. In
accord with the LFDFT method we have to define an average of
configuration type calculation. We use the keyword “IRREPOCCUPATIONS”
in ADF to set fractional electron occupations of the molecular
orbitals. For [Eu(NO3)3(phenanthroline)2], 338 electrons are
restricted to closed shell, and 6 valence electrons are evenly
distributed over the seven molecular orbitals that are identified with
large atomic 4f characters and thus constitute the active subspace of
the ligand-field calculation.


LFDFT atomic database installation
==================================

To run LFDFT you need to first install the LFDFT atomic database on
the machine where you run the calculation.


Setting up the calculation
==========================

We start by downloading the input structure "Eu-complex.xyz", a file
that contains the cartesian coordinates of the Eu^3+ complex
[Eu(NO3)3(phenanthroline)2].

   Start AMSinput and import the coordinates
   **1.** Go to **File → Import Coordinates** and select 'Eu-complex.xyz'
   **2.** Change to panel **Model → Coordinates**
   **3.** Check that the Eu atom is the first atom

Remark: the first atom in a LFDFT calculation needs to be the atom of
interest, Eu in this case.

[image]

Before the actual Ligand Field DFT calculation (LF-DFT), a preliminary
DFT calculation is run. From this calculation the occupation numbers
of the molecular orbitals are obtained. The occupation numbers are
then used to set up the LF-DFT calculation. This can be a cheap
calculation, as long as the basis set is all electron and the symmetry
is NOSYM. There is no need for a converged SCF.

   Set up the preliminary DFT calculation
   **1.** Change to [image: ADFPanel][image]
   **2.** Change to panel **Model → Main**
   **3.** Select **Frozen core → None**
   **4.** Change to panel **Details → Symmetry**
   **5.** Select **NOSYM** from the symmetry panel
   **6.** Change to panel **Details → SCF**
   **7.** Enter "1" for 'Maximum number of SCF cycles'
   **8.** **File → Save** and **File → Run**
 [image][image][image]

The calculation will not converge (because of the difficult open-shell
electronic structure and 1 SCF cycle), but the output can be used to
set fractional occupations to the molecular orbitals later. Once the
calculation is finished, click OK to the error message that the SCF
did not converge.

Important is to change the number of SCF cycles back to the original
value.

   **1.** In panel **Details → SCF**
   **2.** IMPORTANT: Enter "300" for 'Maximum number of SCF cycles'
 [image]

Next we will try to use the settings as were used in Ref. [1] for PBE.
The calculation is performed in water using COSMO as solvation method.

   **1.** Change to panel **Model → Main**
   **2.** Select **XC functional → GGA → PBE**
   **3.** Select **Basis set → TZ2P**
   **4.** Select **Frozen core → None**
   **5.** Change to panel **Model → Solvation**
   **6.** Select **Solvation method → COSMO**
   **7.** Select **COSMO Solvent → Water**
 [image][image]

LFDFT requires an average of configuration (AOC) run. The occupation
numbers will reflect an AOC where 338 (= 169*2) electrons are in
doubly occupied orbitals, and 6 valence electrons are evenly
distributed over the 7 molecular orbitals that are identified with
large atomic 4f characters.

The MO indices in the LFDFT settings should be the fractionally
occupied levels of the AOC calculation. In the LFDFT run spin-orbit
coupling will be included. In the results we want to see all spin-
orbit splitted levels even if they are close. Therefore a small
degeneracy threshold is chosen.

   **1.** Change the panel to **Model → Spin and Occupation**
   Click OK if an error message appears
   **2.** Change the occupations for levels 170, 171, 172, 173, 174, 175, and 176 to "6/7"
   **3.** Change to panel **Properties → Ligand Field DFT**
   **4.** In the panel **Shell 1**, set **MO indices → 170 171 172 173 174 175 176**
   **5.** Set **n → 4**
   **6.** Set **l → 3**
   **7.** Set **Spin-Orbit scaling factor → 1.0**
   **8.** Set **Degeneracy threshold → 0.00001**
 [image][image]

   **1.** **File → Save** and **File → Run**


Results
=======

Once the calculation is finished (may take several minutes), the
molecular orbitals and the occupation numbers of the 4f orbitals can
be found in the output file.

   **1.** Open [image: SCMMenu][image] **→  Output**
   **2.** Search for **List of selected MOs**
 [image]

Scroll down to molecular orbitals #170, 171, ..., 176 to verify that
they have predominantly Eu f character and are occupied with
fractional 6/7 = 0.86 electrons.

   **1.** Open [image: SCMMenu][image] **→  Spectra**
   **2.** Set **Axes → Horizontal Unit → 1/cm**

Below the figure in AMSspectra a list of all the calculated energy
levels is given. This includes all levels of the Eu 4f^6 configuration
split by spin-orbit coupling and ligand field, in total 3003 values.

[image]

The lowest 49 levels all have expectation values of <S^2> close to 12
and <L^2> close to 12, which means a high ^7F character.

Similarly, if one scrolls down one can find that levels 50-58 have
high ^5D character.

[image]

The calculated levels can be compared to the calculated ones for PBE
in the paper. The lowest ^7F levels in cm-1 are 0, 144, 323, 698,
versus 0, 214, 393, 700 for PBE in the paper, and the lowest ^5D
levels are at 16205, 17744, 17832, 17996 versus 16081, 17705, 17716,
17806 for PBE in the paper. The agreement is reasonable, however,
apparently small differences in the calculation can lead to somewhat
larger differences in the energy of the levels, and can easily lead to
a difference of a few 100 cm-1.

In the output one can find a more detailed spectral analysis of the
results.

   **1.** Open [image: SCMMenu][image] **→  Output**
   **2.** Search for **Spectral term analysis**
 [image]

In this results block, the energy levels are projected on to the
atomic solution, giving rise to the listed percentage characters.

Instead of PBE one can also use, for example, the hybrid PBE0, and use
the same settings as before.

   **1.** Change to panel **Model → Main**
   **2.** Select **XC functional → Hybrid → PBE0**
   **3.** **File → Save As** and **File → Run**

This, however, will take much more time (may take several tens of
minutes). One could skip this part and only look at the results. Note
again that small differences in the calculation can lead to somewhat
larger differences in the energy of the levels.

[image][image]

Again the lowest 49 levels have a high ^7F character and levels 50-58
have high ^5D character. Now labeling the levels with a J value makes
more sense than in the PBE calculation. The lowest level has an
expectation values of <J^2> close to 0 thus this level could be
labeled as ^7F_0, levels 2-4 have  an expectation values of <J^2>
close to 2 thus this level could be labeled as ^7F_1, etcetera.

The table compares a subset of LFDFT/PBE0 energy levels with the
experimental values reported in Ref. [1].

+-----------------------------------+-----------------------------------+-----------------------------------+
| State                             | PBE0 (cm ^-1)                     | Exp (cm ^-1)                      |
|===================================|===================================|===================================|
| ^7F_0                             | 0                                 | 0                                 |
+-----------------------------------+-----------------------------------+-----------------------------------+
| ^7F_1                             | 267                               | 295                               |
+-----------------------------------+-----------------------------------+-----------------------------------+
|                                   | 380                               | 367                               |
+-----------------------------------+-----------------------------------+-----------------------------------+
|                                   | 513                               | 444                               |
+-----------------------------------+-----------------------------------+-----------------------------------+
| ^7F_2                             | 965                               | 947                               |
+-----------------------------------+-----------------------------------+-----------------------------------+
|                                   | 968                               | 981                               |
+-----------------------------------+-----------------------------------+-----------------------------------+
|                                   | 1045                              | 1016                              |
+-----------------------------------+-----------------------------------+-----------------------------------+
|                                   | 1109                              | 1080                              |
+-----------------------------------+-----------------------------------+-----------------------------------+
|                                   | 1190                              | 1111                              |
+-----------------------------------+-----------------------------------+-----------------------------------+
| ...                               |                                   |                                   |
+-----------------------------------+-----------------------------------+-----------------------------------+
| ^5D_0                             | 16534                             | 17241                             |
+-----------------------------------+-----------------------------------+-----------------------------------+
| ^5D_1                             | 18137                             | 18945                             |
+-----------------------------------+-----------------------------------+-----------------------------------+
|                                   | 18172                             |                                   |
+-----------------------------------+-----------------------------------+-----------------------------------+
|                                   | 18211                             |                                   |
+-----------------------------------+-----------------------------------+-----------------------------------+

[1] H. Ramanantoanina, *LFDFT-A Practical Tool for Coordination
    Chemistry*, Computation 2022, 10, 70.
