Interacting Quantum Atoms (IQA)
*******************************

ADF Bonding Analysis Interacting Quantum Atoms

This tutorial will show you how to perform interacting quantum atoms
calculations with two simple examples: water and PF_5 . You will run
them and check the results in the output files.

See also:

  See the documentation for Interacting Quantum Atoms (IQA) for more
  information about the method.

This feature can only be used with Relativity None.


Step 1: Build H_2O
==================

   Start AMSinput.
   Add an oxygen atom using O tool then add the hydrogens (ctrl/cmd + E).
   Choose the Geometry Optimization task in main section.
   Set **Relativity: None**, **Basis set: DZP**, and **Frozen core: None**.
   Save and Run.
 [image]

At the end of the calculation:

   Click the orange **Update molecule** button at the top of the main ADF panel to load the optimized structure.
   Use **File → Save As...** to give the job a new name.
   To restart the SCF from the first job, go to **Model → Restart** and select the "*.results/adf.rkf" file as **Engine restart**.


Step 2: Calculate all interactions in H_2O
==========================================

   Choose the Single Point task in main section.
   In the panel bar, select **Properties → QTAIM**.
   Check the Calculate Interacting Quantum Atoms (IQA) check-box.
   Save again and Run.
 [image]


Step 3: Analyze the results
===========================

When the calculation has finished, check the results:

   Open the output file: **SCM → Output** .
   Go to the IQA section of the output (**Properties → Interacting Quantum Atoms (IQA)** ).
 [image]

All results are expressed in a.u. unless otherwise specified (for
example, kcal/mol). By default, in addition to intra-atomic (‘self’)
terms, the total interatomic interaction energy, its covalent and non-
covalent parts are printed for each atom pair.

For instance, the total interaction energy between O1 and H2 atoms
should be close to -288 kcal/mol at this level of theory
(LDA/DZP/Normal Grid). The ‘covalent’ part (exchange) is equal to -135
kcal/mol (47% of the total energy) while the electrostatic
contribution (‘ionic part’) corresponds to -153 kcal/mol (53% of the
total energy).

It is interesting to note that the repulsive H2-H3 interaction is
quite large (73 kcal/mol), due to substantial QTAIM charges on
hydrogen atoms (+0.55 e- for each hydrogen). The classical Coulomb
part of the energy (+ 74 kcal/mol) is larger than the total
interaction energy, explaining why the energy percentage is greater
than 100%. It is in fact counterbalanced by stabilizing but rather
small exchange energy (less than 1 kcal/mol, consistent with the non-
bonded character of the interaction). Finally, we can notice that the
electrostatic contribution can be roughly estimated by a point charge
model (with QTAIM charges) and Coulomb’s law q(H2) x q(H3) / rH2-H3 »
64 kcal/mol.


Step 4: Build PF_5, optimize and calculate all interactions
===========================================================

We will now look at the P-F bonds in the PF_5  molecule.

Note that you can combine the geometry optimization with an IQA
calculation, which we will now do for PF_5.

   Close all previous windows and start again AMSinput.
   Build a trigonal bipyramidal structure: [image: StructTool][image] Structure Tool → Metal Complexes →  ML5 trigonal bipyramidal.
   Change the central atom into a P atom.
   Change ligands into F atoms.
   Choose the Geometry Optimization task in main section.
   Set **Relativity: None**, **Basis set: DZP**, and **Frozen core: None**.
 [image]

   In the panel bar, select **Properties → QTAIM**.
   Check the **Calculate: Interacting Quantum Atoms (IQA)** check-box.
   Set Print to **verbose**.
   Save and Run.
 [image]

At the end of the calculation, AMSinput will ask whether to use the
new coordinates. Select **No**.


Step 5: Analyze the results and compare equatorial and axial P-F bonds
======================================================================

When the calculation has finished, check the results:

   Open the output file: **SCM → Output**
   Search for the IQA section
 [image]

In this verbose mode, more information is printed: individual terms
for intra- and inter-atomic interactions are printed and a total
energies section is added.

[image]

The bonds with equatorial fluorine atoms can be recognized by the
interatomic distance of 2.95. These bonds are predominantly ionic
(87-88%) with interaction energies between -748 and -760 kcal/mol
(-756 kcal/mol on average). The difference between equatorial bonds
can be explained by the fact that the assignment of the integration
points located near the border between two QTAIM basins is somewhat
arbitrary. The different can be reduced by increasing the numerical
quality to Good and VeryGood. Please note that this inter-atomic
energy should not be confused with a bond formation energy that
includes the variations of intra-atomic terms during the bond
formation and substantial secondary interactions between the incoming
fluorine atom and other fluorine atoms.

The axial P-F bonds are longer than the equatorial ones. Therefore, we
may expect them to be weaker and the IQA energy decomposition analysis
confirms our chemical intuition. Indeed, the covalent contribution to
the interaction decreases (from about -97 kcal/mol to -87 kcal/mol)
and so does the classical Coulomb interaction (from -650 kcal/mol to
-640 kcal/mol). This results in a substantial decrease of the total
inter-atomic interaction from -756 kcal/mol to -727 kcal/mol, in
agreement with the bond length increase.

Regarding accuracy of the results, classical Coulomb interaction
energies (Non-Cov. part) can be extremely sensitive to the choice of
the basis set. This can be seen in the following table (geometry
optimized at the LDA/DZP level; normal numerical quality):

   XC/Basis           P-F(eq) min      P-F(eq) max         P-F(ax)
   PBE0/DZP           -730             -743                -713
   PBE0/TZP           -728             -769                -735
   PBE0/TZ2P          -786             -816                -773
   PBE0/QZ4P          -793             -796                -774

The quality of the integration grid is also important for evaluating
the electrostatic (Non-Cov. part) contribution. We recommend the
numerical quality VeryGood when accurate energies are required. The
Normal level can be used for semi-quantitative purposes. This can be
seen in the following table obtained at the PBE0/DZP level (for a
geometry optimized at the LDA/DZP level and a normal numerical
quality):

   Quality           P-F(eq) min      P-F(eq) max         P-F(ax)
   Basic             -687             -766                -700
   Normal            -731             -743                -714
   Good              -719             -728                -697
   VeryGood          -723             -725                -718

It's noteworthy that the asymmetry between equatorial atoms (P-F(eq)
min and max) becomes rather small at the numerical quality VeryGood.
