Periodic Energy Decomposition of the Tetrahydrofuran/Si(001) System¶

Model¶

We begin the Tutorial by loading the atomic model for the Si(001)-THF adsorption complex from a periodic xyz-file.

This structure was obtained by cuts along the [001] Miller plane in order to create a six-layer slab. The atoms at the bottom of this slab was then saturated by adding hydrogen atoms at the experimental Si-H bond length of Silane (1.48 Å). The unit cell was extended to form a 2x4 supercell model. This resulting slab model was then relaxed while keeping the bottom two Si-layers and the hydrogen atoms fixed. On the surface of the slab there are two exposed Si-atoms, which form a characteristic alternating buckled structure. A further analysis reveals that this buckling (or symmetry breaking) is the consequence of each of the exposed Si-atoms having an unpaired electron. In consequently, one of these unpaired electrons transfers to the neighboring Si-atom and forming a lone pair with the other unpaired electron there. The Si center where the lone pair is located becomes more nucleophile and gets pushed upwards (Si_up) while its more electrophile neighbor (Si_down) moves slightly towards the slab.

Due to the electrophile nature of Si_down the THF molecule was then added on top of this site with its O-atom oriented towards Si_down. Afterwards, the resulting adsorption complex was relaxed to yield the structure provided for this tutorial.

The periodic structure is loaded by opening the file THF_Si001_DativeBond.xyz with amsinput. As this structure file includes lattice vectors, this will automatically switch to the calculation options for BAND. Next, the regions of the adsorption complex need to be defined in order to analyze the interactions between them with PEDA.

In the options tab of amsinput

Model → Regions

Remove any existing regions by clicking on the “-” button on their left

Select all atoms of the THF molecule

Click on the “+” button and name the newly defined region e.g. molecule

Unselect and select all Si-atoms and the H-atoms at the bottom of the slab

Click on the “+” button and name the newly defined region e.g. slab

Settings¶

Based on the regions defined above, PEDA will invoke three individual DFT calculations, one for each fragment and one for the whole adsorption complex, respectively.

We specify the options for the DFT calculations as follows:

In the options tab of amsinput

Click on Main

Select XC functional: → GGA-D → PBE-D3(BJ)

Basis set: → TZ2P

Frozen core: → Small

Numerical quality: → Good

PEDA itself can handle an arbitrary k-space grid, which is often necessary for cases like metallic surfaces. However, PEDA-NOCV is only implemented for a Gamma-only k-space grid. We set this option as follows:

In the options tab of amsinput

Click on Details → K-Space Integration

Select K-Space: → Gamma Only

Also any symmetry treatment needs to be disabled:

In the options tab of amsinput

Click on Details → Symmetry

Untick Use Symmetry

We proceed by enabling the usage of fragments in BAND:

In the options tab of amsinput

Click on MultiLevel → Fragments

Tick Use Fragments

Finally, PEDA-NOCV needs to be activated as follows:

In the options tab of amsinput

Click on Properties → PEDA-NOCV

Tick Perform PEDA-NOCV Analysis

After everything is set, save the input with File → Save As… and start the calculation with File → Run.

PEDA Terms¶

After completing the calculation we can examine the results as follows:

SCM → Output to switch to AMSoutput

Properties → PEDA Energy Terms

Here E_int denotes the total interaction energy between the two fragments, i.e. between the Si(001) slab and THF. PEDA subdivides this interaction into components corresponding to the Pauli repulsion E_Pauli as well as dispersion E_disp, electrostatic E_elstat, and orbital interactions E_orb, which are found in almost perfect agreement with the original study:

Due to the elecrophile character of Si_down we can expect a dative bond between the THF O-atom and this site. Indeed, the E_orb and E_elstat interactions are found both rather high with values of several hundred kJ/mol and the latter slightly dominating (54-55%), which are typical features of dative bonds.

NOCV Orbitals¶

To analyze the dative bond between Si_down and THF further, we proceed by examining the natural orbital for chemical valence (NOCV).

In AMSouput SCM → View to switch to AMSview

Fields → Grid → Medium (or Fine)

Add → Isosurface: With Phase

This creates an empty field to plot which can be adjusted in the bar at the bottom:

In the field options bar

Change the isosurface value from 0.03 to 0.0025

Select Field … → NOCV Def Densities…

This will open a window containing the different NOCV orbital pairs sorted according to their contribution to the deformation density:

In the window Select NOCV Deformation Density

Double-click on the first entry (largest contribution), NOCV_(1,1)**2 - NOCV_(1920,1)**2

This will show a plot of the NOCV pair contribution to the deformation density:

This plot is to be interpreted as follows: Red lobes show an electron depletion due to the fragment interactions while blue lobes represent an increased electron density. The above plot shows that electrons are removed from the surroundings of the O-center (and to a lesser extend from Si_down) and accumulated in between these two atoms, which is a clear indication for the formation of a bond. We can examine this bond further by looking at the two NOCV orbitals that form the NOCV pair.

Add → Isosurface: With Phase to add another field options bar

In new field options bar: Change the isosurface value from 0.03 to 0.07

Click on Select Field … → NOCV Orbitals…

In the selection list: double-click on the first NOCV orbital (most negative contribution)

Repeat these steps for the last NOCV orbital (with the largest contribution)

For a given pairs of NOCVs the one with the lower index corresponds to the electron donor orbital and the orbital with the higher index is its electron accepting partner. The NOCV on the left thus derives from the lone pair at the O-center, while the orbital on the right side originates from unoccupied orbitals of the Si_down atom.