QTAIM (Bader), localized orbitals and conceptual DFT
****************************************************

ADF Bonding Analysis Catalysis Bader analysis QTAIM Fukui function
Dual descriptor

This tutorial will show you how to perform a QTAIM analysis, compute
localized orbitals and conceptual DFT descriptors using ADF.


QTAIM analysis of an Adenine–Thymine base pair
==============================================

   Start AMSinput with the [image: ADFPanel][image] panel active.

Next we need the structure of the Adenine–Thymine (AT) base pair:

   **1.** Click on the **Structure** tool [image: StructTool][image] and select **DNA → AT**
   **2.** Click on the molecule drawing area to add the AT base pair

You should now see the AT base pair in the molecule drawing area.

[image]

Not all QTAIM options can be used in combination with relativistic
effects, so in this Tutorial we disable them:

   In the main panel, select **Relativity → None**

Now we want to activate the QTAIM analysis to find the critical points
and bond paths. To find where this option is located, search for it:

   Activate the search box [image: Search][image] (cmd/ctrl-F)
   Type 'criti' in the search box
   Click on the first hit: 'QTAIM'
   (Alternatively, click on **Properties → QTAIM** )

AMSinput will switch to the panel that displays the option you are
looking for (to calculate the AIM critical points and paths). The
matching input options will be marked with blue text. Note that the
input option search will restrict the search to panels that belong to
the current method (ADF, BAND, DFTB, ...)

   Tick the **Perform QTAIM analysis** check-box
   Set the **Analysis level** to **Full** (to get atomic properties, basins and other descriptors in addition to the critical points and paths)
 [image]

Now we are ready to run the calculation.

   To run the calculation: **File → Run**

A dialog will pop up in which you must specify a filename to use for
your job, for example 'AT':

   Enter 'AT' as a Filename, press the Save button

After hitting the save button the calculation will start. You will get
a new AMSjobs window that allows you to manage your jobs and keep
track of their state (for example, queued or running). For a running
job, there will be two lines showing the progress. To get more
information you can show the logfile in a new window:

   Click on the two lines showing the progress

Depending on your computer, the calculation should be ready after a
few minutes at most.

Once the calculation is finished, use AMSview to visualize the
results. To visualize the critical points and bond paths:

   Switch to AMSview: **SCM → View**
   In AMSview, click on **Properties → QTAIM (Topology)**
 [image]

The critical points and bond paths are shown (the molecule balls and
sticks representation is hidden). The different types of critical
points (atom CP, bond CP, ring CP and cage CP) are indicated by
different colors:

* atom CP: white

* bond CP: red

* ring CP: green

The bond paths are colored by density, by default. You can get extra
information about a CP or a point along the bond path by clicking on
it.

To inspect the basin partitioning itself:

   In AMSview, click on **Properties → QTAIM Sampling**
   Keep **Show basins** enabled to display the reconstructed QTAIM basin surfaces
   Optionally enable **Show points** to also display the sampling points, and adjust **Basin opacity** to make the atoms and points easier to see

We will now add a plane showing the electronic density:

   Click on **Fields → Grid → Medium**
   Click on **Add → Plane: Contours**
   In the controls at the right of AMSview, click on **Select Field → Density → Density SCF**
   Change the number of contour lines from 15 to 30
 [image]

This concludes the AT QTAIM tutorial. To close all its windows:

   **SCM → Quit**


Benzene QTAIM charge analysis and NBOs
======================================

   Start AMSinput
   Make a benzene molecule (for example by searching for it with cmd/ctrl-F)
   In the main panel set **Frozen Core → None** and **Relativity → None**

   Panel bar **Properties → QTAIM**
   Check the 'Perform QTAIM analysis' option
   Set the **Analysis level** to **Extended**

   Panel bar **Properties → Localized Orbitals, NBO, ROSE**
   Check the 'Perform NBO analysis' option
   Request Boys-Foster localized orbitals

   Run this setup (**File → Run**)

When the calculation is done (it should run very fast), we use AMSview
to examine the QTAIM charges and compare them with Mulliken charges:

   Open the results with AMSview
   Show the QTAIM atomic charges (**Properties → Atom Info → QTAIM Charge → Show**)
   Color the atoms by QTAIM charges (**Properties → Color Atoms By → QTAIM Charge**)
   Show the Mulliken charges (**Properties → Atom Info → Mulliken Charge → Show**)
 [image]

Note:

  This part requires you to have a license for the NBO6 program. You
  can contact license@scm.com for more information.

Next we inspect the NBOs and Boys-Foster localized orbitals. To remove
the charge display we close and open AMSview, but you could also have
used the View menu to remove them by hand:

   Close AMSview
   Open the results again with AMSview
   Add an isosurface with phase
   Use the field menu in the new controls,
   and observe the labels present with the NBOs and NLMOs
   Open a NBO similar to BD Cn - Hn
   Improve the grid by using **Fields → Grid → Fine**
 [image]

You can also visualize the **NLMOs** or the **Boys-Foster localized
orbitals** (which are just called Localized Orbitals in the fields
menu.


Rationalizing a typical SN2 reaction using condensed Conceptual DFT descriptors
===============================================================================

The chemical reactivity of reactants or key intermediates can be
analyzed using condensed (over QTAIM basins) Conceptual DFT
descriptors such as Fukui functions or Dual Descriptor. We strongly
suggest the use of the Dual Descriptor, which gives at one glance a
more complete description of reactivity behaviors. All the following
calculations are based on frontier molecular orbitals (FMOs) using
Koopmans approximation, which presents advantages (fast calculations)
and drawbacks (in particular if FMOs are degenerated or quasi-
degenerated).

An alternative way, based on finite difference linear (FDL)
approximation, is available in ADF: Fukui Functions and Dual
Descriptor. The FDL approximation offers a more rigorous approach, but
it requires three calculations (systems with N electrons (reference),
N+δ electrons and N-δ electrons (0<δ<=1)) and shows other drawbacks.
For instance, adding one electron to the reference system may lead to
unconverged SCF procedure, or the corresponding spin states might be
unobvious. Besides, some ambiguity remains about which atomic basins
(relaxed or unrelaxed) should be used when adding or removing
electrons.

   Start AMSinput
   Draw the N,N-dimethylbutylamine molecule (nucleophile)
   Pre-optimize the structure by clicking on [image: PreOptimTool][image]

   Select the Geometry Optimization task

   Panel bar **Properties → Conceptual DFT**
   Check the ‘Conceptual DFT’ option
   Set the ‘Analysis level’ option to Extended
 [image]

   Run this setup: **File → Run**, use 'nucleophile' as file name for your job and wait until it is ready.

At the end of the optimization process, all the QTAIM properties will
be calculated.

   Start AMSview: **SCM → View**

Show the condensed (over QTAIM atomic basins) ‘Fukui Fminus function’
indices that characterize the nucleophilicity of atomic sites:

   **Properties → Atom Info → Fukui- (FMO) → Show**
   **Properties → Color Atoms By → Fukui- (FMO)**
   **Properties → Atom Info → Name → Show**
 [image]

On this picture, we clearly see that the nitrogen site is the most
nucleophilic one. To obtain a more complete picture at one glance, we
can visualize the condensed values of the dual descriptor (DD) that
corresponds, using the Koopmans’ theorem, to the difference between
FMOs electron densities.

To this end, first hide the previous values and display the condensed
DD values:

   **Properties → Atom Info → Fukui- (FMO) → Hide**
   **Properties → Atom Info → Dual (FMO) → Show**
   **Properties → Color Atoms By → Dual (FMO)**
 [image]

Positive values correspond to atomic sites where electrophilicity is
predominant, while negative values correspond to atomic sites where
nucleophilicity is predominant (again, the nitrogen atom is highly
nucleophilic).

In a new input window, now make the benzyl chloride (electrophile):

   **SCM → New input**
   Make benzyl chloride by copying the following coordinates and pasting them in the AMSinput molecule drawing area:

   C      -0.70294970       0.03823073       0.00000000
   C      -0.02771734      -1.20050280       0.00000000
   C       1.37040750      -1.24326069       0.00000000
   C       2.10941268      -0.05859271      -0.00000000
   C       1.45241936       1.17312771      -0.00000000
   C       0.05527963       1.22223527      -0.00000000
   C      -2.21056076       0.15917615      -0.00000000
   Cl     -2.96962094       0.22007043       1.61845248
   H      -0.56397603      -2.13845972       0.00000000
   H       1.88164983      -2.19732981       0.00000000
   H       3.19110656      -0.09523365      -0.00000000
   H       2.02573037       2.09116490      -0.00000000
   H      -0.43823632       2.18658642      -0.00000000
   H      -2.49816320       1.08415158      -0.54318756
   H      -2.64194499      -0.70811986      -0.54318753

   Pre-optimize the structure by clicking on [image: PreOptimTool][image]

   Select the Geometry Optimization task

   Panel bar **Properties → Conceptual DFT**
   Check the ‘Conceptual DFT’ option
   Set the ‘Analysis level’ option to Extended

   Run this setup: **File → Run**, use '‘electrophile’' as file name for your job and wait until it is ready.

At the end of the optimization process, all the QTAIM properties will
be calculated.

   Start AMSview: **SCM → View**

Show the condensed (over QTAIM atomic basins) ‘Fukui+ (FMO) function’
values that characterize the electrophilicity of atomic sites:

   **Properties → Atom Info → Fukui+ (FMO) → Show**
   **Properties → Color Atoms By → Fukui+ (FMO)**
   **Properties → Atom Info → Name → Show**
 [image]

On this picture, two carbon sites (C(4) and C(7)) have similar Fukui+
indices. Moreover, chlorine has a strong electrophilic character due
to the existence of a sigma hole in the outer part of its valence
shell along the C-Cl bond. Therefore, it is difficult to unambiguously
determine the reactivity of this molecule by the sole QTAIM condensed
Fukui+ values. In that case, the dual descriptor is quite useful,
providing a balanced picture, since it allows evaluating the
predominant reactivity behavior at each atomic site.

To this end, first hide the previous values and display the condensed
DD values:

   **Properties → Atom Info → Fukui+ (FMO) → Hide**
   **Properties → Atom Info → Dual (FMO) → Show**
   **Properties → Color Atoms By → Dual (FMO)**
 [image]

As already mentioned, positive values correspond to atomic sites where
electrophilicity is predominant, while negative values correspond to
atomic sites where nucleophilicity is predominant.

In this picture we clearly see, as expected from chemical intuition,
that C(7) is highly electrophilic (compared to the other carbon
atoms). This site will thus undergo a nucleophilic attack during the
SN2 reaction with the N,N-dimethylbutylamine molecule, leading to the
formation of a quaternary ammonium salt.

Besides, we can also observe that the chlorine atom is predominantly a
nucleophilic site (due to its lone pairs) despite the presence of an
electrophilic sigma hole.

   **SCM→ Quit All**
