Fragment Analysis in ADF¶

Build the Structure¶

The structure is perfectly tetrahedral. You should be able to build the molecule yourself using the techniques described in earlier tutorials.

One possible way:

1. Start AMSinput

2. Build a tetrahedral metal complex: → Metal Complexes → ML4 tetrahedral

3. Change the central atom into a Ni atom

4. Select one ligand

5. Select all ligands: Select → Select Atoms Of Same Type menu command

6. Change them in CO ligands: Atoms → Replace By Structure → Ligands → CO

7. Symmetrize the system by clicking on

8. Choose the Geometry Optimization task

9. Save and Run

10. When the run has finished, click ‘Yes, New Job’ to import the optimized coordinates

Alternatively, copy-paste the following coordinates in AMSinput:

Ni  0.0000000000000  0.0000000000000  0.0000000000000
O  -1.7186781693251  1.7186781693251  1.7186781693251
O   1.7186781693251 -1.7186781693251  1.7186781693251
O  -1.7186781693251 -1.7186781693251 -1.7186781693251
O   1.7186781693251  1.7186781693251 -1.7186781693251
C   1.0473110733159  1.0473110733159 -1.0473110733159
C  -1.0473110733159 -1.0473110733159 -1.0473110733159
C   1.0473110733159 -1.0473110733159  1.0473110733159
C  -1.0473110733159  1.0473110733159  1.0473110733159

Your molecule should look something like this:

Define fragments¶

The fragments that ADF uses are based on the regions that you define. In this example we will generate four new regions: one for each of the CO ligands. The regions for the CO ligands will get special names to make sure that ADF recognizes them as one fragment repeated four times.

The Ni atom will not be in a region. AMSinput will automatically create atomic fragments for all atoms not in a region.

Repeated fragments are indicated with the fragment name followed by |n, with n the number of the copy (see also the ADF user manual on fragments). All copies must match such that one fragment can be positioned exactly over another fragment by rotation and translation. ADF checks for this, AMSinput does not. In this particular example all four CO fragments are obviously identical by symmetry.

Now one new region has been defined: the CO region for the ligands. The next step is to split the ligand region into four repeated regions:

This should result in the following regions:

Set up the fragment analysis run¶

The next step is very easy: we will tell ADF to perform a Single Point calculation (fragment analysis in ADF only works with a single point calculation), and we tell AMSinput to use the regions that we just defined as fragments:

In the Fragments panel you will see that one fragment is present, without charge: the repeated CO fragment. ADF will use basic atomic atoms for any atoms not put in another fragment. Thus, the Ni atom will be an atomic fragment.

Remark: Typically SFO site energies give more insight if each fragment only occurs once. Therefore and one can visualize SFO site energies with AMSlevels only in such cases. Here the CO fragment occurs 4 times, and one will get unnormalized SFOs. If one checks the ‘Calculate SFO site energies’ check box in this case one can only see the SFO site energies in the output.

Run the fragment analysis and view the results¶

Next you will Save and Run the calculation. When you do this, AMSinput will actually save two different calculations:

• The CO calculation (with matching .ams and .run file)

• The Ni(CO)₄ fragment analysis calculation (with matching .ams and .run file)

You do not need to run the calculation for the CO fragment first, it will automatically be executed when needed.

This calculation results in the normal .rkf and .out output files. You can view them with the SCM → View and SCM → Output commands. More interesting in the case of a fragment analysis is the interaction diagram that you can view using AMSlevels:

In the center you see the levels of the whole molecule, on the sides you see the CO fragment and the Ni-atom fragment.

The red interaction lines tell you which molecular orbitals come from which fragment orbitals. The brightness of the line is directly related to the contribution %.

The blue interaction lines together show the orbital interaction, and are drawn when a bonding and anti-bonding combination can be made. The strength of this interaction is calculated by taking the geometric average of the 4 contributions. Compared to the normal average, the geometric average places more emphasis on equal contributions. This will give 50-50 contributions the strongest interaction, and 0-100 contributions no interaction at all. The strongest interaction is drawn, and weaker interactions can be drawn by using the menu or the shortcuts (AMSlevels: View → Interactions → Increase # Significant). In this case there are several interactions which are almost equally strong. Depending on the exact geometry you may find a different strongest interaction.

In the output file you can find detailed information about the composition of the molecular levels in terms of the fragment orbitals.

Build the structure¶

We will now perform a similar fragment calculation for a PtCl₄ H₂ ^2- molecule. The following is a picture of the PtCl₄ H₂ ^2- molecule, after optimization with ADF:

To make this molecule, an easy way is to start with an octahedral complex to ensure symmetry. Next make changes to get this molecule, ending with a geometry optimization with ADF:

1. Build an octahedral metal complex using the Structures button ( → Metal Complexes → ML6 octahedral)

2. Change the central atom into a Pt atom

3. Change four dummies in a plane into Cl atoms

4. Remove one of the remaining dummies

5. Change the remaining dummy in OH, via Atoms → Replace by structure → Ligands → OH (this will ensure the final two H’s do not break symmetry)

6. Change the O atom into an H atom

7. Symmetrize the system by clicking on

Note that pre-optimization using UFF will make the geometry worse, if you wish you can pre-optimize using Mopac. But the ADF geometry optimization will also converge without pre-optimization.

Or, copy-paste the following coordinates and symmetrize the system by clicking on (do not forget to set the charge to -2):

Pt  0.0         0.0         0.70977802
Cl  2.39841436  0.0         0.75420182
Cl  0.0         2.39841436  0.75420182
Cl -2.39841436  0.0         0.75420182
H   0.0         0.0        -2.26954689
Cl  0.0        -2.39841436  0.75420182
H   0.0         0.0        -1.45703842

After copy-pasting the H atoms will not be bonded in the picture. That is no problem as ADF does only look at the atom positions.

Define fragments¶

Define the PtCl₄ ^2- and H₂ fragments in the Regions panel:

Now the fragments are defined. Next, we set up the fragment analysis calculation:

1. Select the Main panel

2. Select the Single Point task

3. Panel bar MultiLevel → Fragments (or click the button)

4. Check the Use fragments check box

5. Change the charge of the PtCl4 fragment to -2

6. Save

If you skipped the geometry optimization step and copy-pasted the coordinates, be sure to set the overall overall charge to -2 in the main panel!

When you click on the Open button (the big dot) next to the PtCl4 fragment, you can inspect the PtCl4 fragment setup:

For more complex calculations, you could make additional changes to your fragment runs.

Run the fragment analysis and view the results¶

Next you will Run the calculation:

After the calculation has finished, you can view the resulting interaction diagram:

Only interactions between visible levels are shown. So, if you zoom out no interactions will be visible for some of the levels. That is the reason that you will need to use the Show Interactions menu command.

We needed to shift the H₂ levels to accommodate that in the final complex (in this case PtCl₄ H₂ ^2-) the fragment H₂ experiences an electrostatic shift due to the -2 charge, which is absent from the H₂ fragment calculation. The interaction diagram should look something like the following:

Instead of shifting the H₂ levels, one can also look at the so called SFO site energies. The SFO site energy is defined as the diagonal Fock matrix element of the Fock matrix of the full complex in SFO representation. This is a more realistic description on how in the final molecule the H₂ fragment experiences the -2 charge (each level is not shifted with the same amount).

If you move the mouse over a molecular orbital (MO) level one can find out more detailed information about the composition of the MO level in terms of the symmetrized fragment orbitals (SFOs). Also in the output file you can find such information.

Set up the calculation¶

Copy-paste the following coordinates:

C       0.000000000   0.000000000  -0.23931600
H      -0.521322100  -0.902956364  -0.56271600
H      -0.521322100   0.902956364  -0.56271600
H       1.042644200  -0.000000000  -0.56271600
I       0.000000000   0.000000000   1.92746400

Define the CH₃ and I fragments in the Regions panel:

Now the fragments are defined. Next, we set up the unrestricted fragment analysis calculation.

Prepared for bonding¶

The electron configuration of the fragments will be chosen such that the valence I p_z orbital has 1 alpha electron, and the highest occupied Methyl orbital has 1 beta electron. Note that this electron configuration of the fragments means that they are so called ‘prepared for bonding’ in order to minimize the Pauli repulsion in the electron pair bond, which in this case is a sigma-bond in the z-direction.

Note that the GUI shows a label ‘Spin’ which in fact should be ‘Spin polarization’. If fragments are used symmetry has been set by the GUI to NOSYM. In this case, however, we would like to use symmetry. If one uses real spin-unrestricted fragments the calculation on the full complex must also be calculated spin-unrestricted.

In the electron configuration of the I atomic fragment we want the p_z alpha orbital to be occupied, and the p_z beta orbital to be unoccupied. In order to make such an electron configuration the I atomic fragment is not calculated in atomic symmetry but calculated in a subsymmetry, in this case D∞h (D(LIN)), in which p_z is in a different irrep (SIGMA.u) than p_x and p_y (PI.u). The symmetry requirements in ADF for calculating an atom in D∞h symmetry are such that the atom should be in the origin. For convenience the I atomic fragment is precalculated in D∞h symmetry without specifying the electronic configuration. Next the electronic configuration of this calculation is adjusted to the desired electronic configuration.

Remark: due to a bug in AMSinput in AMS2023.101 these (integer) occupation numbers are not saved in the I fragment. This is fixed in AMS2023.102 (or bug fixed AMS2023 binary with r113153 or higher). If this bug is present when running the calculation for the I fragment the warning message: ‘Warning: partially occupied orbitals’ may appear, and in the output file of the I fragment one can find that fractional occupation numbers are used.

Run the calculation¶

Next you will Run the calculation:

After the calculation has finished, you can view the resulting interaction diagram:

The spin alpha and spin beta SFO energies are sometimes very different. However, the spin alpha and spin beta SFO site energies are not that different, see next figure.

The SFO site energy is defined as the diagonal Fock matrix element of the Fock matrix of the full complex (in this case CH₃I) in SFO representation. Using SFO site energies will give a more realistic description of the the spin alpha and spin beta fragment orbitals energies in the final closed shell molecule.

If you move the mouse over a molecular orbital (MO) level one can find out more detailed information about the composition of the MO level in terms of the symmetrized fragment orbitals (SFOs). The most important contributions are given including an overlap S(sfo) of the SFOs that participate the most. A ‘+’ or ‘-’ sign directly after an overlap value between two different SFOs indicates whether the contributions of these two SFOs form a bonding combination (‘+’) or anti-bonding combination (‘-’) in the MO.

The 4A1 MO is (mostly) a bonding combination of a I p_z fragment orbital (a p_z orbital has irrep label SIGMA.u in symmetry D(LIN)) and a Methyl 2A1 fragment orbital. Although the 4A1 alpha MO and the 4A1 beta MO are spatially the same, the decomposition in terms of SFOs is (slightly) different, since the spin alpha and spin beta SFOs are not spatially the same.