Energy Decomposition Analysis (EDA)
***********************************

ADF Bonding Analysis Energy Decomposition Analysis

This Tutorial may fail in case file names or directory names contain
spaces.

* EDA with restricted fragments (ammonia borane)

* EDA with unrestricted fragments (ethane)

* EDA-NOCV: natural orbitals for chemical valence (metal complexes)


EDA with restricted fragments
=============================

This tutorial explains how to perform an energy decomposition analysis
(EDA) [1] of ammonia borane, in which ammonia and borane have a donor-
acceptor interaction with each other. In this way, you can examine
which interactions result in a stable complex.

The **bond energy** (or **binding energy**) of H_3N-BH_3 is defined
as:

   \Delta E = E_{\text{H}_3\text{N}-\text{BH}_3} - E_{\text{NH}_3}
   -E_{\text{BH}_3}

in which E_NH3 and E_BH3 are the energies of the optimized reactants,
and E_H3N-BH3 is the energy of the optimized complex.

Note:

  If you simply optimize a H_3N-BH_3 complex with ADF, the printed
  bond energy is *not* calculated from the above equation. Instead, it
  is calculated with respect to spherically symmetric spin-restricted
  atomic fragments. See more below.

The bond energy consists of the **preparation energy** (or strain
energy, deformation energy), and the **interaction energy**:

   \Delta E = \Delta E_{\text{prep}} + \Delta E_{\text{int}}

The **preparation energy** is the amount of energy that is required to
deform the NH_3 and BH_3 from their equilibrium structure to the
geometry they have in the complex. The **interaction energy** is the
change in energy when the prepared fragments (NH_3 and BH_3 in the
complex geometry) are combined to form the complex. A quantitative
energy decomposition analysis (EDA) divides the **interaction energy**
in the **electrostatic** interaction, **Pauli repulsion**, and
attractive **orbital interactions (oi)**:

   \Delta E_{\text{int}} = \Delta V_{\text{elstat}} + \Delta
   E_{\text{Pauli}} + \Delta E_{\text{oi}}

The electrostatic interaction, which is usually attractive, is the
energy between the unperturbed charge distributions of the prepared
fragments. The Pauli repulsion is responsible for steric repulsion, it
consists of the destabilizing interactions between occupied orbitals
of the fragments. The orbital interaction accounts for charge transfer
and polarization.


Geometry Optimizations of NH_3, BH_3 and H_3N-BH_3
--------------------------------------------------

To calculate \Delta E, the energies of optimized NH_3, BH_3 and H_3N-
BH_3 need to be calculated. Note that another basis set and functional
can be used as well. Symmetry will be used, which may help in the
analysis.  Open AMSinput (**SCM → New Input**), and perform the
following steps:

   **1.** Create NH_3: search [image: Search][image] for "ammonia", click "H3N: Ammonia (ADF)"
   **2.** **Symmetrize** the system by clicking on [image: SymmTool][image]
   **3.** Select **Task →  Geometry Optimization**
   **4.** Select **XC functional →  GGA:BP86**
   **5.** Select **Basis set →  TZP**
   **6.** Select **Numerical quality →  Good**
   **7.** Run the calculation with **File →  Run** (save with the name "ammonia")
   **8.** Click 'Yes' to 'Save changes (required to run)'

Repeat the above steps for BH_3:

   Create BH_3: [image: StructTool][image] **→ Metal Complexes →  ML3 Trigonal Planar**.
   Select the central atom, **Atoms →  Change Atom Type** to B, then change the three "ligands" to H.
   Repeat steps 2-7 above (save with the name "borane").

Repeat the above steps for H_3N-BH_3.

   To create H_3N-BH_3, you could:
   a) combine the previous two systems by copying and pasting,
      add a bond between N amd B and make sure the geometry is staggered
   b) search for ethane and choose Ethane (ADF), replace one atom by N and the other by B
   Symmetrize the system by clicking on [image: SymmTool][image].
   Repeat steps 2-7 (save with the name "ammoniaborane").
 [image]


EDA: single-point calculation with molecular fragments
------------------------------------------------------

When the H_3N-BH_3 calculation has finished, a button above 'Task'
will appear displaying 'Update molecule'. Click on it and then perform
a single point calculation.

   **1.** Set **Task →  Single Point**.

   [image]

   **2.** Go in the panel bar to **Model →  Regions**
   **3.** Select the atoms of NH_3 and click the [image: AddButton][image] button next to Regions, and rename Region_1 to "NH3"
   **4.** Select the atoms of BH_3 and click also on the [image: AddButton][image] button, and rename Region_2 to "BH3".
 [image]

   **5.** Go in the panel bar to **MultiLevel →  Fragments**
   **6.** Check the 'Use fragments' check box
   **7.** Run the calculation (save with the name "EDA_ammoniaborane")
   **8.** Click 'Yes' to 'Save changes (required to run)'

   [image]

The job actually runs three separate calculations. First, single point
calculations of NH_3 and BH_3 in their prepared geometry are run. The
"adf.rkf" files of those single point computations are then used for
the fragment analysis.


Bond energy, preparation energy, interaction energy
---------------------------------------------------

The energy of a calculation can be found at the bottom of the logfile
(**SCM → Logfile**), in the output (**SCM → Output**), or in the
binary output file (**SCM → KFbrowser**).

To **tabulate the energies from all previous calculations**, either

* use one of the above methods to get the energy for each calculation

* **Build a spreadsheet summary**: In AMSjobs (**SCM → Jobs**), select
  the "ammonia", "borane", "ammoniaborane", "EDA_ammoniaborane",
  "EDA_ammoniaborane.NH3", and "EDA_ammoniaborane.BH3" jobs by holding
  Ctrl and clicking on them. Then go to **Tools → Build spreadsheet**,
  set the **Energy unit** to **kcal/mol**, and click **Do It**. Save
  with the name "report.xlsx". Follow the instruction in the
  spreadsheet if numbers are not displayed correctly, see also the GUI
  documentation on spreadsheets.

   [image]Spreadsheet summary of all calculations. Not all properties
   are shown here and the "Notes" and energy calculations were
   manually added.

   \Delta E = E_{\text{H}_3\text{N}-\text{BH}_3} - E_{\text{NH}_3}
   -E_{\text{BH}_3}

The **bond energy** \Delta E of H_3N-BH_3 was calculated to be
**-31.80 kcal/mol** with these settings. (-838.47 - (-444.53) -
(-362.14) = -31.80)

The **preparation energy for BH**_3 (**12.72 kcal/mol**, calculated as
-349.42-(-362.14)) is much **larger** than that for **NH**_3 (**0.11
kcal/mol**). This is because the  structure of the fully relaxed NH_3
is only slightly different from the structure of the NH_3 fragment in
H_3N-BH_3.  However, the structure of the fully relaxed flat BH_3
(symmetry D_3h) is substantially different than the structure of the
BH_3 trigonal pyramidal fragment in H_3N-BH_3 (symmetry C_3v):

[image]

The **interaction energy** is simply the "bond energy" output by ADF
for the "EDA_ammoniaborane" job.  This is because that job **used the
reactants in the prepared geometries as fragments**.


EDA Analysis
------------

The energy decomposition of the interaction energy of H_3N-BH_3 can be
found in the output file of the fragment analysis (job
"EDA_ammoniaborane", **SCM → Output**, followed by **Properties →
Bonding Energy Decomposition**). You can find for instance that H_3N-
BH_3 has an interaction energy of -44.62 kcal/mol, which consists of a
Pauli repulsion of 108.10 kcal/mol, an electrostatic interaction of
-77.53 kcal/mol, and an orbital interaction of -75.19 kcal/mol. Note
that these numbers may be slightly different if a different geometry
is used, or if different precision parameters are used.

[image]

The orbital interaction is decomposed into contributions from
different irreducible representations of the molecular point group. In
this case the contributions from A1 (\sigma, \sigma^*-orbitals) are
much more important than those from E1 (\pi, \pi^*-orbitals).

With **AMSlevels** the molecular orbital diagram can be visualized, in
which one can see a donor-acceptor interaction and (repulsive)
interactions between occupied orbitals.

   **1.** **SCM →  Levels**
   **2.** In AMSlevels, click on **View →  Labels →  Show**
 [image]

By right-clicking the BH_3 2A1 fragment orbital (LUMO of BH_3,
acceptor orbital) you can select the corresponding SFO (symmetrized
fragment orbital), which can be visualized with AMSview.  Similarly,
you can select the NH_3 2A1 fragment orbital (HOMO of NH_3, donor
orbital).  After some manipulations, using 50% opacity, you can get
the following two AMSview windows that show these fragment orbitals.

[image]


EDA with unrestricted fragments
===============================

This tutorial explains how to perform an energy decomposition analysis
(EDA) of a molecule with unrestricted fragments, for example the CH_3
groups of ethane. Hereby, the user can examine which interactions
result in the stable molecule. To see an explanation of these
different interactions or to do an EDA without unrestricted fragments,
see the EDA of Ammonia Borane tutorial.


Geometry Optimization
---------------------

The geometry of the reactants and the product (complex) must be
optimized. Note that another basis set and functional can be used as
well. Symmetry will be used, which may help in the analysis.

For ethane:

   **1.** In AMSinput make the structure or search for the structure in the search box [image: Search][image] in the panel bar
   **2.** Symmetrize the system by clicking on [image: SymmTool][image]
   **3.** Select **Task →  Geometry Optimization**
   **4.** Select **XC functional →  GGA:BP86**
   **5.** Select **Basis set →  TZP**
   **5.** Select **Numerical quality →  Good**
   **7.** Run the calculation with **File →  Run** (give an appropriate name to your calculations)
   **8.** Click 'Yes' to 'Save changes (required to run)'
   **9.** When the run has finished, click 'Update molecule' to import the optimized coordinates and save it
 [image]

For CH_3 (methyl) an unrestricted calculation is needed:

   **1.** In AMSinput make the structure or search for the structure in the search box [image: Search][image] in the panel bar
   **2.** Symmetrize the system by clicking on [image: SymmTool][image]
   **3.** Select **Task →  Geometry Optimization**
   **4.** Check the **Unrestricted** box.
   **5.** Enter "1.0" as Spin polarization
   **6.** Select **XC functional →  GGA:BP86**
   **7.** Select **Basis set →  TZP**
   **8.** Select **Numerical quality →  Good**
   **9.** Run the calculation with **File →  Run** (give an appropriate name to your calculations)
   **10.** Click 'Yes' to 'Save changes (required to run)'
   **11.** When the run has finished, click 'Update molecule' to import the optimized coordinates and save it
 [image]

The bond energy of C_2H_6 can be calculated by subtracting the
energies of the reactants (two CH_3) from the energy of the complex.
The energies can be found at the bottom of the logfile or in the
output.

   \Delta E = E_{C_2H_6} - 2 E_{CH_3}

The bond energy of C_2H_6 was calculated to be -93.53 kcal/mol with
these settings. (-920.23 - 2*(-413.35)) = -93.53)


EDA
---

Single point calculations of the CH_3 groups in the geometry they have
in the product are needed to perform an EDA. Note that one sometimes
need to change the electron configuration of the fragments to make
them so called 'prepared for bonding' in order to minimize the Pauli
repulsion in the electron pair bond. This is not needed in this simple
example.

   **1.** Set up a new calculation with the optimized **ethane** molecule
   **2.** Select the Task **Single Point**
   **3.** Check the **Unrestricted** box.
   **4.** Select **XC functional →  GGA:BP86**
   **5.** Select **Basis set →  TZP**
   **6.** Select **Numerical quality →  Good**

   [image]

   **7.** Go in the panel bar to **Model →  Regions**
   **8.** Select the atoms of one CH_3 group and click the [image: AddButton][image] button next to Regions
   **9.** Select the atoms of the other CH_3 group and click also on the [image: AddButton][image] button
 [image]

   **10.** Go in the panel bar to **MultiLevel →  Fragments**
   **11.** Check the 'Use fragments' check box (A warning will popup regarding NOSYM symmetry)
   **12.** Enter as spin polarization "1" for one of the fragments and "-1" for the other fragment
 [image]

The symmetry has been adjusted to NOSYM. However, we want to use
symmetry. Besides setting the symmetry to AUTO, in this case we also
need to symmetrize the coordinates again, since using fragments will
lower the symmetry of ethane that ADF can use from D_3d to C_3v. Note
that in this case the symmetrization will only reorient the geometry
in order to fulfill the molecular orientation requirements in ADF such
that ADF can use symmetry.

   **13.** Go in the panel bar to **Details →  Symmetry**
   **14.** Select **Symmetry →  AUTO**
   **15.** Symmetrize the system by clicking on [image: SymmTool][image]
   **16.** Save it and run the calculation


Analysis
--------

The different energies, where the interaction energy of the CH_3
groups of ethane consists of, are noted in the output (**SCM** →
**Output**, followed by  **Properties → Bonding Energy
Decomposition**). It can be noticed that the interaction energy of
-111.43 kcal/mol is build out of 180.02 kcal/mol Pauli repulsion,
-125.43 kcal/mol electrostatic interaction, and -166.02 kcal/mol
orbital interactions.

The orbital interaction is decomposed into contributions from
different irreducible representations of the molecular point group. In
this case the contributions from A1 (\sigma, \sigma^*-orbitals) are
much more important than those from E1 (\pi, \pi^*-orbitals).

[image]

The bond energy was calculated previously to be -93.53 kcal/mol and
accordingly the preparation energy can be calculated to be 17.90
kcal/mol (=-93.53-(-111.43)). The preparation energy for one CH_3
fragment is 8.95 kcal/mol, the difference between the bond energy of
the CH_3 trigonal pyramidal fragment (-404.40 kcal/mol) and the fully
relaxed planar CH_3 molecule (-413.35 kcal/mol). The preparation
energy of the other CH_3 fragment is the same. Note that the energies
of the fragments can be found at the bottom of the logfile or in the
output of the fragments. Also note that these numbers may be slightly
different if a different geometry is used, or if different precision
parameters are used.

With AMSlevels (**SCM → Levels**) the molecular orbital diagram can be
visualized, in which one can see an electron-pair bond and (repulsive)
interactions between occupied levels.

[image]


Dispersion correction
=====================

Dispersion energy can be of importance in complexes with weak bonds.
The dispersion energy is a long-ranged electron correlation effect.
When using, for example, a DFT-D3 functional or a DFT-D4 functional
the dispersion corrected energy will also be a part of the interaction
energy:

   \Delta E_{int} = \Delta V_{elstat} + \Delta E_{Pauli} + \Delta
   E_{oi} + \Delta E_{disp}

The dispersion corrected interaction energy will be printed in the
output file just as the electrostatic interaction, Pauli repulsion,
and orbital interactions. The dispersion corrections are XC functional
dependent, and contain fitted parameters. For many XC functionals such
parameters are available in AMS.


EDA-NOCV: natural orbitals for chemical valence
===============================================

An energy decomposition analysis - natural orbitals for chemical
valence (EDA-NOCV), also known as extended transition state - natural
orbitals for chemical valence (ETS-NOCV), can be used to analyze the
transition metal-ligand ([TM]-L) bonds in transition metal complexes.
This method combines the energy decomposition analysis [1] with the
natural orbitals for chemical valence [2]. This tutorial will show how
to use the EDA-NOCV method for a Fischer-type carbyne complex and a
Schrock-type carbyne complex, based on the paper of Jerabek et al. [3]

The EDA-NOCV/ETS-NOCV method gives insight in the orbital interactions
for non-symmetric molecules, because the deformation density is
decomposed into different components (*σ*, *π*, *δ*) of the chemical
bond. In the ETS-NOCV: Natural Orbitals for Chemical Valence
documentation  more information about this method can be found.

In carbyne complexes, various types of orbital interaction between a
ligand and the TM can be distinguished:

* donor–acceptor complexes possessing dative bonds (Fischer‐type
  carbynes)

* electron‐sharing bonds (Schrock‐type carbynes)

Here we follow Ref. [3], in order to see whether the results of the
EDA-NOCV calculations may provide a useful classification of the TM
compounds into the these two types of molecules. Note that this
example focuses on the understanding of [TM]-L bonds and compares
results using different electron configurations of the fragments. This
example does not calculate bond energies.

Some remarks on the analysis. The EDA depends on the fragments chosen,
whether neutral or charged fragments are used, and which spin state
they have. For the EDA-NOCV method it is necessary that the sum of the
number of spin-α orbitals in the fragments is the same as in number of
spin-α orbitals the full complex, likewise for the number of spin-β
orbitals. If there is (near) degeneracy between different electron
configurations of the fragments, for the analysis it is best to use
the electron configuration of the fragments such that they are so
called 'prepared for bonding' in order to minimize the Pauli repulsion
in the electron pair bond. For example, if one has two fragments which
both have unpaired electrons, one typically would put the unpaired
electrons of the first fragment in the spin-α orbitals and the
unpaired electrons of the second fragment in the spin-β orbitals. In
this example this will be used, but not all possible reasonable
electron configurations will be investigated, which might have been
better 'prepared for bonding'. Note that here so called 'real'
unrestricted fragments will be used, which was not possible in the ADF
version that was used in Ref. [3]. This means that the energies in the
EDA that will be reported here are not directly quantitatively
comparable to those in Ref. [3].

An EDA-NOCV will be performed on the Fischer-type carbyne complex
Br(CO)_4W-CPh and on the Schrock-type carbyne complex
Cl_3(dme)W-CCMe_3 with fragments in 1. the singlet state (dative
bonding), 2. the quartet state (electron-sharing bonding), and 3. the
doublet state (mixed dative/electron-sharing bonding).

* The optimized geometry of Br(CO)_4W-CPh can be downloaded "here"

* The optimized geometry of Cl_3(dme)W-CCMe_3 can be downloaded "here"

Single Point calculations will be performed on these optimized
complexes.


1. Dative bonding
-----------------

These calculations are based on the paper of Jerabek et al. [3] and
therefore the following level of theory is used.

Perform the following steps for both complexes you just downloaded:
Br(CO)_4W-CPh and Cl_3(dme)W-CCMe_3

   **1.** Open the geometry of the complex in AMSinput
   **2.** Make sure that the Task is set at **Single Point**
   **3.** Select the **GGA:BP86-D3(BJ)** XC functional and **TZ2P** Basis set
   **4.** Make sure that the Relativity is set at **Scalar**
   **5.** Select **Frozen Core →  None** and **Numerical quality →  Good**
   **6.** Go in the panel bar to **Model →  Regions**
   **7.** Select the atoms of the ligand (C-*t*Bu or C-Ph group) and click the [image: AddButton][image] button next to Regions
   **8.** Select all other atoms of the complex (by Select → Invert Selection) and click the [image: AddButton][image] button again
 [image]

   **9.** Go in the panel bar to **MultiLevel →  Fragments**
   **10.** Tick the **Use fragments** box (the Check charge and spin box and no symmetry will be set)
   **11.** Enter as charge for the ligand fragment "1.0" and for the other fragment "-1.0"
 [image]

   **13.** Go in the panel bar to **Properties →  ETS-NOCV**
   **14.** Select an **Closed-Shell** ETS-NOCV analysis
   **15.** Tick the **T/V analysis** box.
   **16.** Run the calculation
   Note that one may have SCF problems for the fragment [Cl_3(dme)W]^-1

In this case both charged fragments are calculated in the singlet
state.


SCF problems
~~~~~~~~~~~~

The fragment [Cl_3(dme)W]^-1 has problems with SCF convergence. It is
difficult (or impossible) to converge the SCF with an aufbau solution.
Therefore one can use an explicit non-aufbau electron configuration.
Note that the following is an expert option. If you do not include the
next expert steps you may get a different non-aufbau solution, and
thus a different energy decomposition analysis for Cl_3(dme)W-CCMe_3
for this case of charged fragments.

   Relevant only for the fragment [Cl_3(dme)W]^-1 of Cl_3(dme)W-CCMe_3
   Open the fragment [Cl_3(dme)W]^-1 AMSinput
   Go in the panel bar to **Details →  Run Script**
   Enter in Engine ADF part:
   "IrrepOccupations"
   "A 148 0 0 2 2"
   "End"
   Select **File →  Save**
   Close the fragment [Cl_3(dme)W]^-1 AMSinput
   Open the Cl_3(dme)W-CCMe_3 AMSinput
   Run the calculation
 [image]


2. Electron-sharing bonding
---------------------------

To do an analysis of the [TM]-L complexes from an electron-sharing
bonding perspective, follow these steps:

   **1.** Open the main input for the dative ETS-NOCV calculation
   **2.** In the Main panel bar tick the box for an **Unrestricted**  calculation
 [image]

   **3.** Go in the panel bar to **MultiLevel →  Fragments**
   **4.** Set the charges to "0" for both fragments
   **5.** Enter as **spin polarization** for the ligand fragment "3.0" and for the other fragment "-3.0"
   **6.** Save as a different file, and run
 [image]

In this case both neutral fragments are calculated in the quartet
state (more precisely they have |S_z|=3/2).


3. Dative/Electron‐sharing bonding
----------------------------------

To analyze bonding from the mixed dative/electron-sharing perspective,
simply change the spins from the electron-sharing calculation to 1 and
-1, save as a different file, and run

   **1.** Open the main input for the electron-sharing ETS-NOCV calculation
   **2.** Go In the panel bar **MultiLevel →  Fragments**
   **3.** Enter as **spin polarization** for the ligand fragment "1.0" and for the other fragment "-1.0"
   **4.** Save as a different file, and run

such that both neutral fragments are calculated in the doublet state
(more precisely they have |S_z|=1/2). Note that the fragment CCMe_3
has near degenerate solutions in case it is calculated in the doublet
state, and that one solution may have a corresponding electron
configuration that may be better 'prepared for bonding' than another.
This will not be investigated further.


EDA
---

The different energy terms of the interaction between the ligand and
its transitions state complex are noted in the output (Properties →
Bonding Energy Decomposition). The following energy terms will be
found for Br(CO)_4W-CPh and Cl_3(dme)W-CCMe_3 (in kcal/mol):

+---------------------------+---------------------------+---------------------------+---------------------------+
| Br(CO) _4 W-CPh           | Dative                    | Electron-sharing          | Dative/Electron‐sharing   |
|===========================|===========================|===========================|===========================|
| Δ*E*_int                  | -261.9                    | -191.0                    | -154.8                    |
+---------------------------+---------------------------+---------------------------+---------------------------+
| Δ*E*_Pauli                | 232.8                     | 230.3                     | 292.5                     |
+---------------------------+---------------------------+---------------------------+---------------------------+
| Δ*V*_elstat               | -211.0                    | -173.3                    | -214.7                    |
+---------------------------+---------------------------+---------------------------+---------------------------+
| Δ*E*_oi                   | -275.3                    | -239.6                    | **-224.3**                |
+---------------------------+---------------------------+---------------------------+---------------------------+
| Δ*E*_disp                 | -8.4                      | -8.4                      | -8.4                      |
+---------------------------+---------------------------+---------------------------+---------------------------+

+---------------------------+---------------------------+---------------------------+---------------------------+
| Cl _3 (dme)W-CCMe _3      | Dative                    | Electron-sharing          | Dative/Electron‐sharing   |
|===========================|===========================|===========================|===========================|
| Δ*E*_int                  | -427.4                    | -194.7                    | -177.1                    |
+---------------------------+---------------------------+---------------------------+---------------------------+
| Δ*E*_Pauli                | 303.4                     | 302.2                     | 690.4                     |
+---------------------------+---------------------------+---------------------------+---------------------------+
| Δ*V*_elstat               | -251.2                    | -224.4                    | -436.2                    |
+---------------------------+---------------------------+---------------------------+---------------------------+
| Δ*E*_oi                   | -468.6                    | **-261.3**                | -420.1                    |
+---------------------------+---------------------------+---------------------------+---------------------------+
| Δ*E*_disp                 | -11.2                     | -11.2                     | -11.2                     |
+---------------------------+---------------------------+---------------------------+---------------------------+

**The method which results in an orbital interaction closer to zero
gives the commonly accepted chemical interpretation** (dative or
electron-sharing), see Ref. [3].

For the Fischer-type carbyne complex Br(CO)_4W-CPh the orbital
interaction is closer to zero for the dative/electron sharing  bonding
with an orbital interaction of -224.3 kcal/mol (vs -239.6 or -275.3
kcal/mol).

For the Schrock-type carbyne complex Cl_3(dme)W-CCMe_3 the orbital
interaction is closer to zero for the electron-sharing bonding with an
orbital interaction of -261.3 kcal/mol (vs -420.1 or -468.6 kcal/mol).


EDA-NOCV Fischer‐type carbyne complex
-------------------------------------

The best description for the Fischer‐type carbyne complex Br(CO)_4W-
CPh is found for neutral fragments in their electronic doublet state
(|S_z|=1/2), which engage in a mixture of dative bonding (σ donation
and π backdonation) and one electron‐sharing π bond, as can be seen in
the next NOCV analysis.

   Go to AMSjobs
   Select the Br(CO)_4W-CPh job with neutral fragments in their electronic doublet state (the third job, dative/electron-sharing bonding)
   Open AMSview (**SCM →  View**)
   Select **Fields →  Grid →  Medium**
   Select **Add →  Isosurface: With Phase**
   In the 'Select Field' category, select **NOCV Def Densities...**
   Select NOCV_Def_Density with largest eigenvalue
   Change isosurface value to 0.01
   Repeat this for NOCV_Def_Density with the 5 highest eigenvalues

The direction of the charge flow from fragments to full complex in the
next pictures is from red → blue. The orbital interaction energy
contributions from each NOCV pair can be found in the output
(Properties → ETS - NOCV).

[image]

α-Δρ ΔE=-80 kcal/mol (|v|=1.00), electron‐sharing π bond caused by
drops in both ΔT=-36 kcal/mol and ΔV=-44 kcal/mol. The transfer of a
whole electron (|v|=1.00) indicates that there probably is an electron
configuration of the fragments that may be better 'prepared for
bonding', however, that will not be investigated here further.

[image][image]

left: β-Δρ ΔE=-30 kcal/mol (|v|=0.54), ΔT=-613 kcal/mol, ΔV=583
kcal/mol; right: β-Δρ ΔE=-39 kcal/mol (|v|=0.53), ΔT=-703 kcal/mol,
ΔV=664 kcal/mol; π backdonation driven by drop in kinetic energy

[image][image]

left: β-Δρ ΔE=-30 kcal/mol (|v|=0.34), ΔT=206 kcal/mol, ΔV=-236
kcal/mol; right: α-Δρ ΔE=-29 kcal/mol (|v|=0.34), ΔT=238 kcal/mol,
ΔV=-267 kcal/mol; σ donation on metal accompanied by the lowering of
potential energy


EDA-NOCV Schrock‐type carbyne complex
-------------------------------------

The best description for the Schrock‐type carbyne complex
Cl_3(dme)W-CCMe_3 is found for neutral fragments in their electronic
quartet state ((|S_z|=3/2), which engage in one electron-sharing σ
bond and two electron‐sharing π bonds, as can be seen in the next NOCV
analysis.

   Go to AMSjobs
   Select the Cl_3(dme)W-CCMe_3 job with neutral fragments in their electronic quartet state (the second job, electron-sharing bonding)
   Open AMSview (**SCM →  View**)
   Select **Fields →  Grid →  Medium**
   Select **Add →  Isosurface: With Phase**
   In the field select menu on the bottom: select **NOCV Def Densities...**
   Select NOCV_Def_Density with largest eigenvalue
   Change isosurface value to 0.01
   Repeat this for NOCV_Def_Density with the 6 highest eigenvalues

The direction of the charge flow from fragments to full complex in the
next pictures is from red → blue. The orbital interaction energy
contributions from each NOCV pair can be found in the output
(Properties → ETS - NOCV).

[image][image][image][image]

top-left: α-Δρ ΔE=-32 kcal/mol (|v|=0.65), ΔT=880 kcal/mol, ΔV=-912
kcal/mol; top-right: β-Δρ ΔE=-37 kcal/mol (|v|=0.65), ΔT=-1188
kcal/mol, ΔV=1151 kcal/mol; bottom-left: α-Δρ ΔE=-30 kcal/mol
(|v|=0.62), ΔT=817 kcal/mol, ΔV=-847 kcal/mol; bottom-right: β-Δρ
ΔE=-51 kcal/mol (|v|=0.55), ΔT=-1071 kcal/mol, ΔV=1020 kcal/mol; two
electron‐sharing π bonds

[image][image]

left: β-Δρ ΔE=-73 kcal/mol (|v|=0.54), ΔT=-825 kcal/mol, ΔV=752
kcal/mol; right: α-Δρ ΔE=-33 kcal/mol (|v|=0.42), ΔT=378 kcal/mol,
ΔV=-411 kcal/mol; one electron-sharing σ bond

-[ References ]-

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    Theory: Predicting and Understanding Chemistry*, Reviews in
    Computational Chemistry 15, 1 (2000)

[2] M. Mitoraj, A. Michalak, *Donor–Acceptor Properties of Ligands
    from the Natural Orbitals for Chemical Valence*, Organometallics
    26, 6576 (2007)

[3] P. Jerabek, P. Schwerdtfeger, G. Frenking, *Dative and Electron-
    Sharing Bonding in Transition Metal Compounds*, Journal of
    Computational Chemistry 40, 247 (2019)

[4] D.Rodrigues Silva, L. de Azevedo Santos, M.P. Freitas, C. Fonseca
    Guerra, T.A. Hamlin, *Nature and Strength of Lewis Acid/Base
    Interaction in Boron and Nitrogen Trihalides*, Chemistry – An
    Asian Journal 15, 23 (2020)

[5] F.M.Bickelhaupt, E.J. Baerends, *The Case for Steric Repulsion
    Causing the Staggered Conformation of Ethane*, Angewandte Chemie
    International Edition 42, 35 (2003)
