PolTDDFT: damped complex polarizabilities Au_12
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ADF Spectroscopy UV/Vis Excitations Absorption POLTDDFT

In this Tutorial we calculate the absorption spectrum of Au_12 using
PolTDDFT, which is a fast algorithm to solve the TD-DFT equations. We
will look at some of the analysis options that PolTDDFT has to offer,
like the so called individual component maps of oscillatory strength
(ICM-OS, see Ref. [1]), transition contribution maps (TCM), and an
analysis of the spectra per region, using the fragment projection
analysis approach (see Ref. [2]).

Note:

  See also the webinar by Mauro Stener regarding PolTDDFT


Set calculation options
=======================

For PolTDDFT it very important is to use specially made auxiliary fit
sets. Here we will use the POLTDDFT/DZ frozen core basis set for Au.
The model exchange-correlation potential LB94 will be used, which is
often used in PolTDDFT calculations. LB94 has an asymptotically
correct Coulomb tail and is thus superior to purely gradient-corrected
xc-functionals (such as PBE) in describing low-lying unoccupied
electronic states.

In order to use the region analysis option we divide Au_12 in 2
regions: the 3 inner gold atoms in one region and the other 9 in
another region.

   Start AMSinput.
   Obtain Au_12 by copy-pasting the following coordinates into AMSinput:

   Au       3.90924307       1.34478417       0.00000000
   Au       1.60055482       2.77224227       0.00000000
   Au      -0.79000428       4.05789589       0.00000000
   Au      -3.11923879       2.71311172       0.00000000
   Au      -0.77594464       1.34397554       0.00000000
   Au       1.55188928      -0.00000000       0.00000000
   Au       3.90924307      -1.34478417       0.00000000
   Au       1.60055482      -2.77224227       0.00000000
   Au      -0.77594464      -1.34397554       0.00000000
   Au      -3.20110964      -0.00000000       0.00000000
   Au      -3.11923879      -2.71311172       0.00000000
   Au      -0.79000428      -4.05789589       0.00000000

   Use the panel bar **Model →  Regions**
   Select the 3 inner gold atoms
   Click the [image: AddButton][image]  button to add a region, and rename Region_1 to "Au3"
   **Select →  Invert Selection**
   Add a region, and rename Region_2 to "Au9"
 [image]

   Use the Main [image: ADFPanel][image] panel
   **XC functional →  Model →  LB94**
   **Basis set →  POLTDDFT →  POLTDDFT/DZ**
   Use the panel bar **Properties →  POLTDDFT**
   Check the 'UV/Vis and CD spectrum' checkbox
   Check the 'Analysis' checkbox
   Check the 'Region analysis' checkbox
 [image][image]

We are now ready to run the calculation.

   Save your input as "Au12" using **File →  Save As...**.
   Run the calculation with **File →  Run**.
   Wait for the calculation to finish.


Results
=======

Once the PolTDDFT calculation has finished, the absorption spectrum
can be viewed.

   Open [image: SCMMenu][image] **→  Spectra**
 [image]

Here we see an analysis of the absorption spectrum per region, using
the fragment projection analysis approach (see Ref. [2]). The most
important part comes from region Au9 -> region Au9 (orange,
"Au12_reg2_2"), which is not unexpected because there are more atoms
in region Au9 than in region Au3, but it is larger than expected
(expected is around (9*9)/(12*12)=56%).

Right of the absorption spectrum one can find a two-dimensional ICM-OS
plot for the X component. If one selects the highest peak (point 70 at
3.45 eV) in the absorption spectrum the ICM-OS plot for the X
component at frequency 3.45 eV will be shown. Next one can select the
TCM plot for the X component at frequency 3.45 eV. Of course, for a
full analysis at a certain frequency one should also look at the Y and
Z component. Here, due to symmetry, the Y component will give the same
information as the X component. The contributions to the oscillator
strength from the Z component are small.

   Select the AMSspectra window
   Select point 70 (frequency 3.45 eV) in the table below the absorption spectrum
   Under the right figure make sure that 'icm-os' and 'x' are selected
   Next select 'tcm' and 'x' and press the 'Update' button
 [image][image]

ICM-OS (Ref. [1]) allows one to analyze and better understand the
features of electronic transitions. It allows one to decompose a
specific absorption peak in terms of electronic single orbital
transitions labeled by the energy of the occupied (x-axis) and virtual
(y-axis) orbitals involved. The diagonal line shows where the
excitation energy matches a difference in occupied and virtual
energies. In addition to the weight of each pair of orbitals in the
oscillator strength, ICM-OS also accounts for the signs of the
associated dipole contributions, which may result in constructive (in
red) or destructive (in blue) interference among excited
configurations. TCM is more focused on a description of the excited
state in terms of electronic single orbital transitions (with only
positive contributions) than being suited to rationalize the
mechanisms which are behind absorption.

   Open **SCM →  Output**
   Find the PolTDDFT analysis for the X component at frequency 3.45 eV.
 [image]

In the output one can find

* **%**: the relative character of a single orbital transition (SOT),
  like the TCM plot is showing,

* **contr to f**: how much this SOT character contributes to the
  oscillator strength, like the ICM-OS plot is showing.

To know the energy of an orbital it helps to open an AMSLevels window.

   Open **SCM →  Levels**
   Hide the fragment stacks: **View → Hide/Show all Fragments**
   Show the labels: **View → Labels → Show**
 [image]

Note that irreps for D(3H) in ADF are sometimes written as AA1, AAA1,
AA2 AAA2, EE1, and EEE1, they stand for A1', A1'', A2', A2'', E1', and
E1''. So the SOT "24e' -> 17a1'" is from the orbital 24EE1 to the
orbital 17AA1

One can imagine that for a larger gold cluster the number of SOTs that
may be important at a certain frequency may grow rapidly. In that case
the TCM plot and ICM-OS plot are easier to understand.

[1] S. Theivendran, L. Chang, A. Mukherjee, L. Sementa, M. Stener, A.
    Fortunelli, and A. Dass, *Principles of Optical Spectroscopy of
    Aromatic Alloy Nanomolecules:* Au_36-x Ag_x (SPh-tBu)_24, Journal
    of Physical Chemistry C 122, 4524 (2018)

[2] L. Sementa, G. Barcaro, O. Baseggio, M. De Vetta, A. Dass, E.
    Aprà, M. Stener, and A. Fortunelli, *Ligand-Enhanced Optical
    Response of Gold Nanomolecules and Its Fragment Projection
    Analysis: The Case of* Au_30 (SR)_18, Journal of Physical
    Chemistry C 121, 10832 (2017)
