Interacting Quantum Atoms (IQA)¶

Step 1: Build H2O¶

Start AMSinput

Add an oxygen atom using O tool then add the hydrogens (ctrl/cmd + E)

Choose the Geometry Optimization task in main section

Choose the DZP basis set, and no frozen core

Set Relativity → None

Save and Run

At the end of the job, AMSinput will ask whether to read the new coordinates.

Check the Restart engine with engine results option.

Select Yes, new job. This creates a new job with the optimized geometry. The SCF will be restarted from the converged solution. Check that the correct restart file is given under Model → Restart.

Step 2: Calculate all inter-atomic interactions in H2O¶

Choose the Single Point task in main section (mandatory for an IQA calculation)

In the panel bar, select Properties → QTAIM

Check the Calculate Interacting Quantum Atoms (IQA) checkbox

Save again and Run

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) )

All results are expressed in a.u. unless otherwise specified (kcal/mol). By default, only the total interaction energy as well as the exchange (covalent part) and classical Coulomb electrostatic contributions (ionic part) are listed for each atom pair. No intra-atomic (‘self’) terms are evaluated.

For instance, the total interaction energy between O1 and H2 atoms corresponds to -287 kcal/mol at this level of theory (LDA/DZP/Normal Grid). The ‘covalent’ part (exchange) is equal to -136 kcal/mol (47% of the total energy) while the electrostatic contribution (‘ionic part’) corresponds to -151 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 PF₅¶

We will now look at the P-F bonds in the PF₅ molecule.

Close all previous windows and start again AMSinput

Build a trigonal bipyramidal structure: 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

Choose the DZP basis set, and no frozen core

Set Relativity → None

Save and Run

At the end of the job, AMSinput will ask whether to read the new coordinates.

Check the Restart engine with engine results option.

Select Yes, new job.

Step 5: Select two atoms (P and equatorial F) and calculate this specific interaction¶

Choose the Single Point task in main section (again, it is mandatory for an IQA calculation)

In the panel bar, select Properties → QTAIM

Check the Calculate Interacting Quantum Atoms (IQA) check-box

Select the central P atom and only one of the equatorial F

To include only these two atoms in the calculation, click the add button

Set Print to Verbose

Save again and Run

Step 6: Analyze the results (a single P-Feq bond in PF₅ )¶

When the calculation has finished, check the results:

Open the output file: SCM → Output

Search for the IQA section

In this verbose mode, more information is printed. A third section is added (total energies). The various energy contributions are summed up and listed, keeping in mind that ‘self’ contributions are missing. Moreover, this calculation is limited to a single inter-atomic interaction.

Coming back to bonding analysis, the P-Feq bond is predominantly ionic (87%) with a total interaction energy of -760 kcal/mol. 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.

Step 7: Compare equatorial and axial P-F bonds¶

As a final exercise, one can calculate the inter-atomic interaction between the central P atom with one of the axial F atoms.

Please close all previous results and go back to the AMSinput window

In the panel bar, select Properties → QTAIM

Click on the – button to deselect atoms and select again P with one axial F atom.

Click on the + button to select them.

Save and Run again

At the end of the job, open the output file: SCM -> Output Search for the IQA section.

The P-Fax bond length is longer than the P-Feq one. Therefore, we may expect a weaker P-Fax bond compared to P-Feq.

The IQA energy decomposition analysis confirms our chemical intuition. Indeed, the covalent contribution to the interaction decreases (from -96 kcal/mol to -87 kcal/mol) as well as the classical Coulomb interaction (from -664 kcal/mol to -640 kcal/mol). This results in a substantial decrease of the total inter-atomic interaction, from -760 kcal/mol to -727 kcal/mol in agreement with the bond length increase.

From a more practical point of view, classical Coulomb interaction energies may be extremely sensitive to the choice of the basis set. This can be seen in the following table (fixed geometry at PBE0/TZ2P; Grid normal):

Xc/Basis           P-Feq                                  P-Fax
                   Ex       Ecoul     Einter              Ex      Ecoul    Einter
PBE0/DZP           -91      -734      -825                -75     -724     -799
PBE0/TZP           -90      -754      -844                -74     -736     -810
PBE0/TZ2P          -86      -792      -878                -72     -769     -841
PBE0/QZ4P          -83      -830      -913                -71     -790     -861

The quality of the integration grid is also important for evaluating this electrostatic contribution. We recommend a “good quality” which seems sufficient. A “normal” level can be used for semi-quantitative purposes. This can be seen in the following table, Geometry & Single Point calculations using PBE0/TZ2P:

Quality           P-Feq                                  P-Fax
                  Ex       Ecoul     Einter              Ex      Ecoul    Einter
Basic             -90       -688      -778               -83     -622     -705
Normal            -86       -792      -878               -72     -769     -841
Good              -82       -831      -913               -70     -784     -854
Excellent         -80       -830      -910               -69     -790     -859