Fragment Analysis in ADF
************************

ADF Inorganic Chemistry Bonding Analysis Fragments AMSlevels

This tutorial will show you how to perform a Fragment Analysis using
ADF and visualize the results. This Tutotial may fail in case file
names or directory names contain spaces. The three examples used here
are:

Ni(CO)_4
   A fragment analysis with one Ni fragment and one CO fragment
   repeated four times.

PtCl_4 H_2 ^2-
   A fragment analysis with one PtCl_4 ^2- fragment and one H_2
   fragment. This is a good example on how to specify the charges of
   the fragments.

CH_3I
   A fragment analysis with one CH_3 fragment and one I fragment. This
   is a good example to show how to use spin-unrestricted fragments.

Tip:

  These tutorials can also be run from the command-line. See

  * How to run examples from the command-line

  * Example: Compound Fragments: Ni(CO)4

  * Example: Fragments: PtCl4H2 2-

  * Example: unrestricted fragments: CH3I


Ni(CO)_4
========


Build the Structure
-------------------

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

See also: Building structure tutorials

One possible way:

   **1.** Start AMSinput
   **2.** Build a tetrahedral metal complex: [image: StructTool][image] **→ 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 [image: SymmTool][image]
   **8.** Choose the **Geometry Optimization** task
   **9.** Save and Run
   **10.** When the job has finished, in AMSinput click on [image: UpdateMolecule][image]

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:

   [image]


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.

   **1.** Panel bar **Model → Regions**
   **2.** Select all atoms
   **3.** Click the "+" button to add a new region (containing all atoms)
   **4.** Select the Ni atom
   **5.** Remove the Ni atom from Region_1: click the "-" button on the right side of the 'Region_1'
   **6.** Change the name of 'Region_1' into 'CO'

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:

   **1.** Press the triangle on the right side of the CO region line
   **2.** In the pop-up menu, use the **Split By Molecule** command

This should result in the following regions:

   [image]


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:

   **1.** Open the 'Main' panel
   **2.** Select the **Single Point** task
   **3.** Panel bar **MultiLevel → Fragments**
   **4.** Check the 'Use fragments' check box

Tip:

  The [image: MoreBtn][image] to the right of Task links to the
  Fragments panel if the task is "Single Point"

   [image]

In the Fragments panel you will see that one fragment is present,
without charge: the repeated CO fragment. ADF will use basic atomic
fragments 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.

   **1.** Save
   **2.** Run
   **3.** Wait for the calculation to finish (note that first the fragment calculation (CO) is executed, followed by the final fragment analysis)

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:

   **SCM → Levels**

   [image]

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.


PtCl_4 H_2 ^2-
==============


Build the structure
-------------------

We will now perform a similar fragment calculation for a PtCl_4 H_2
^2- molecule. The following is a picture of the PtCl_4 H_2 ^2-
molecule, after optimization with ADF:

   [image]

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:

   In a new AMSinput window (**SCM → New Input**)
   **1.** Build an octahedral metal complex using the Structures button ([image: StructTool][image] **→ 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 [image: SymmTool][image]

   **1.** Choose the **Geometry Optimization** task
   **2.** Set the **total charge** to **-2**
   **3.** Run
   **4.** When the job has finished, in AMSinput click on [image: UpdateMolecule][image]

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 [image: SymmTool][image] (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 PtCl_4 ^2-  and H_2    fragments in the Regions panel:

   **1.** Panel bar **Model → Regions**
   **2.** Select the Pt and Cl atoms
   **3.** Use the '+' button to add a new region, and name it 'PtCl4'
   **4.** Select the two H atoms
   **5.** Use the '+' button to add a new region, and name it 'H2'
   **6.** Clear the atom selection (click in empty space)

   [image]

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 [image: MoreBtn][image] button)
   **4.** Check the **Use fragments** check box
   **5.** Check the **Calculate SFO site energies** check box
   **6.** Change the **charge** of the PtCl4 fragment to **-2**
   **7.** 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!**

   [image]

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

   **1.** Click on the Open button (the big dot next to the PtCl4 fragment) in the 'Fragments' panel
   **2.** Check the charge of the fragment in the newly opened AMSinput (should be -2)
   **3.** Close the PtCl4 fragment AMSinput window

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:

   Run

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

   **1.** Use the **SCM → Levels** command
   **2.** Use the mouse (drag with left mouse, scroll wheel, drag with right mouse)
   **3.** Change to energy axis to Hartree: **Axes → Unit → Ha**
   **4.** zoom in on the interesting region (roughly from -0.5 to 0.4)
   **5.** Select the PtCl4H2 column (by clicking on the name at the bottom)
   **6.** Use the **View → Interactions → Show** menu command
   **7.** Right-click in the H2 column, **Shift Stack...**, shift the H2 levels by +0.28

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 H_2 levels to accommodate that in the final
complex (in this case PtCl_4 H_2 ^2-) the fragment H_2 experiences an
electrostatic shift due to the -2 charge, which is absent from the H_2
fragment calculation. The interaction diagram should look something
like the following:

   [image]

Instead of shifting the H_2 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 H_2 fragment experiences the -2 charge (each level
is not shifted with the same amount).

   **1.** Select **View → Site Energies**
   **2.** zoom in on the same region (roughly from -0.5 to 0.4)

   [image]

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.


CH_3I
=====

We will now perform an unrestricted fragment analysis for a CH_3I
molecule.

Here we will use real spin-unrestricted fragments. An alternative
approach is to use spin-restricted fragments in combination with the
FRAGOCCUPATIONS key  in which the spin-unrestricted occupations are
defined.


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

   In the **Main** panel:
   **1.** **Task → Single Point**
   **2.** **XC functional → GGA:BP86**
   **3.** **Basis set → TZ2P**
   **4.** **Frozen core → Small**
   **5.** **Numerical quality → Good**

   [image]

Define the CH_3 and I fragments in the Regions panel:

   **1.** Panel bar **Model → Regions**
   **2.** Select the I atom
   **3.** Use the '+' button to add a new region, and name it 'I'
   **4.** Invert the selection: **Select → Invert Selection** menu command
   **5.** Use the '+' button to add a new region, and name it 'Methyl'
   **6.** Clear the atom selection (click in empty space)

   [image]

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.

   **1.** Panel bar **MultiLevel → Fragments**
   **2.** Check the 'Use fragments' check box
   **3.** Change the spin polarization of the I fragment to 1
   **4.** Change the spin polarization of the Methyl fragment to -1
   **5.** Check the 'Calculate SFO site energies' check box

   [image]

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.

   **1.** Panel bar **Details → Symmetry**
   **2.** **Symmetry → AUTO**
   **3.** In the **Main** panel:
   **4.** Check the 'Unrestricted' check box
   **5.** **File → Save** as CH3I

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.

   **1.** Panel bar **MultiLevel → Fragments**
   **2.** Click on the Open button (the big dot next to the I fragment) in the 'Fragments' panel
   **3.** In the newly opened AMSinput window:
   **4.** Put the I atom in the origin (select the I atom, then **Edit → Set Origin → X,Y and Z**)
   **5.** Panel bar **Details → Symmetry** Molecular symmetry **Symbol → D(LIN)**
   **6.** Run the I fragment calculation
   **7.** After the calculation has finished (still for the I fragment calculation):
   **8.** Panel bar **Model → Spin and Occupation**
   **9.** Change the electron configuration from 4/3 to 2 beta electrons in PI.u
   **10.** Change the electron configuration from 2/3 to 0 beta electrons in SIGMA.u
      (horizontal scrolling may be needed)
   **11.** Close and save the I fragment AMSinput window

   [image]


Run the calculation
-------------------

Next you will Run the calculation:

   Open the CH3I AMSinput window
   Run

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

   **1.** Use the **SCM → Levels** command
   **2.** **Axes → Unit → eV**
   **3.** Use the mouse (drag with left mouse, scroll wheel, drag with right mouse)
   **4.** zoom in on the interesting region (roughly from -10 to -1 eV)
   **5.** **View → Labels → Show**

   [image]

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.

   **1.** Use the **SCM → Levels** command
   **2.** Select **View → Site Energies** menu command
   **3.** zoom in on the same region (roughly from -10 to -1 eV)
   **4.** **View → Labels → Show**

   [image]

The SFO site energy is defined as the diagonal Fock matrix element of
the Fock matrix of the full complex (in this case CH_3I) 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.

   [image]

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.
