L-Edge X-Ray spectrum NEXAFS
****************************

ADF Spectroscopy Excitations

XANES or NEXAFS is a process where core electrons are excited by X-ray
photons. Knowing the X-ray spectrum can help in determining the
electronic structure of the atoms in a molecule. In this tutorial we
will calculate the excitations of a Si 2p core electron of SiCl4 using
the ADF engine. X2C spin-orbit coupled relativistic calculations will
be performed. Compared to ZORA the relativistic methods X2C and RA-X2C
give a better description of core orbitals. First the transition
potential method (TP) will be used and next TD-DFT.

The cheap TP method is useful especially for K-Edge X-ray spectra, but
also for L-Edge it will give a reasonable spectrum, however, the
relative intensities for the spin-orbit splitted levels of the 2p are
typically not so great. With the more expensive TD-DFT method one can
improve these relative intensities for L-Edge 2p electrons.

Note:

  This tutorial is also available in video format.


Step 1: Setting up the system
=============================

   1. Start AMSinput
   2. Download the coordinates "SiCl4.xyz" and import them into AMSinput
   3. Click on the Symmetrize tool [image: SymmTool][image] (the system should have "T(D)" symmetry)
   4. Select **Relativity →  Spin-Orbit**
   5. Select **Frozen Core →  None**
   6. In panel **Details →  Relativity** select **Formalism →  X2C**
 [image]

   In panel **Model →  Regions**
   7. Select the whole molecule and click on the [image: AddButton][image] button to create a new region and call it "SR"
 [image]

   8. In panel **Multilevel →  Fragments** check the 'Use fragments' checkbox
   9. Save the job as "SO" and run it


Step 2: Selecting the orbital labels
====================================

In order to excite a 2p electron we need to know the orbital labels
first.

   1. Select the **SO.SR** job in AMSjobs
   2. View the orbital diagram with **SCM →  Levels**
   3. In AMSlevels, set **Axes → Unit eV** and **View → Labels → Show**

The diagram should look like this:

[image]

The Si 2p orbitals are labeled as 1P and form the 5T2 labeled orbitals
in SiCl4 and have energies of around -100 eV. We performed spin-orbit
relativistic calculations which will have split these orbitals and
changed their labels.

   1. Select the **SO** job in AMSjobs
   2. View the orbital diagram with **SCM →  Levels**
   3. In AMSlevels, set **Axes → Unit eV** and **View → Labels → Show**
   4. Zoom in on the -100 eV region
 [image]

We see that the 5T2 orbitals have been split into 7U3/2 and 5E5/2
spinors. We will use these labels now to excite a 2p electron.


Step 3: TP method
=================

The TP method is fast and one can easily afford a large basis set. The
TP method is approximate and using LDA will not make the approximation
much worse. One should not use the TP method with a hybrid functional.
In the TP method 0.5 electron will be removed, in this case 0.5
electron from the (almost) degenerate Si 2p orbitals (spinors).

   1. Open a new (!) AMSinput window and import the SiCl4 molecule
   2. Select **Relativity →  Spin-Orbit**
   3. Select **Basis Set →  QZ4P**
   4. Select **Frozen Core →  None**
   5. In panel **Details →  Relativity** select **Formalism →  X2C**
   In **Model →  Spin and Occupation**
   6. Click the 'folder' button next to 'Occupations info file' and select "SO.results/adf.rkf"
   7. Change "5E5/2" to "11/6"
   8. Change "7U3/2" to "11/3"
 [image]

   In **Properties →  Excitations (UV/Vis), CD**
   9. Select **Type of excitations →  AllowedOnly**
   10. Select **Method →  Delta eps**
   11. Change 'Number of excitations' to "40"
 [image]

   In **Details → Select Excitations**
   12. Select **Selection method →  Modify Excitation**
   13. Enter "7U3/2 5E5/2" as 'Occupied orbitals'
 [image]

   14. Save the file as 'TP_SiCl4_2p' and run the calculation

Here we have selected the orbitals to excite from. We have removed, in
total, 1/2 electron from the Si 2p orbitals. These Si 2p orbitals (in
the scalar relativistic calculation these are the 5T2 orbitals) were
split into a four-fold degenerate 7U3/2 spinor and a two-fold
degenerate 5E5/2 spinor. Therefore we have removed 1/6 electron from
5E5/2 and 1/3 electron from 7U3/2.

[image]

The X-ray spectrum can be seen with **SCM → Spectra** (Horizontal unit
"eV", and Width "0.3") and shows the L-edge of the SiCl4 molecule. It
can be compared against experimental spectra (for example, R. Püttner,
M. Domke, and G. Kaindl, Phys. Rev. A 57, 297 (1998)). The calculated
excitation energies are in reasonable agreement, however, the relative
intensities (of the first 4 peaks) are not so great. The difference in
energy between the lowest two peaks is due to the spin-orbit splitting
of the Si 2p orbital, which is calculated to be a bit more than 0.6
eV.


Step 4: TD-DFT
==============

The TP method that was used in the previous step is fast and gives a
reasonable spectrum if one compares it to experiment, but for L-edge
2p the calculated relative intensities (of the first 4 peaks) are not
so great. The intensities can be improved for L-edge 2p if TD-DFT is
used. Here the SAOP model potential is used, since it is also good for
Rydberg states and is relatively cheap to calculate. Note, however,
that TD-DFT is much slower than the TP method. Make sure to open a new
AMSinput window.

   1. Open a new (!) AMSinput window and import the SiCl4 molecule
   2. Select **XC functional →  Model →  SAOP**
   2. Select **Relativity →  Spin-Orbit**
   3. Select **Basis Set →  QZ4P**
   4. Select **Frozen Core →  None**
   5. In panel **Details →  Relativity** select **Formalism →  X2C**
   In **Properties →  Excitations (UV/Vis), CD**
   6. Select **Type of excitations →  AllowedOnly**
   7. Select **Method →  Davidson**
   8. Change 'Number of excitations' to "40"
   In **Details → Select Excitations**
   9. Select **Selection method →  Modify Excitation**
   10. Enter "7U3/2 5E5/2" as 'Occupied orbitals'
   11. Save the file as "TDDFT_SiCl4_2p" and run the calculation
 [image]

Again the X-ray spectrum can be seen with **SCM → Spectra**
(Horizontal unit "eV", and Width "0.3") and shows the L-edge of the
SiCl4 molecule. It can be compared against experimental spectra (for
example, R. Püttner, M. Domke, and G. Kaindl, Phys. Rev. A 57, 297
(1998)). The calculated excitation energies are shifted compared to
experiment with about 10 eV, and are thus in worse agreement than the
results with the TP method. However, the relative intensities (of the
first 4 peaks) are improved with respect to the results with the TP
method.

It is not uncommon to shift the calculated spectrum in such cases. It
depends on the XC functional and to a lesser extent on the basis set
how large this shift is. If results for excitations of a certain
orbital of a given element are compared for different molecules one
typically uses the same shift in energy. Compared to SAOP the much
more expensive TD-DFT calculations with a hybrid functional with
approximately 50% HF exchange seem to give improved excitation
energies, if these are compared to experiment. Note that also the very
cheap TP method seem to be capable of doing that.
