Analysis of NMR parameters with Localized Molecular Orbitals
************************************************************

ADF Spectroscopy Natural Bonding Orbitals (NBO) Natural Localized
Molecular Orbitals (NLMO) Nuclear magnetic resonance (NMR)


Introduction
============

Note:

  This part requires you to have a license for the NBO6 program. You
  can contact license@scm.com for more information.

Localized molecular orbitals, such as Natural Bonding Orbitals (NBO)
or Natural Localized Molecular Orbitals (NLMO) can be helpful in
analyzing and interpreting properties computed in electronic structure
calculations.

This tutorial analyzes the effects of NH_2 and NO_2 substituents in
ortho-, meta-, and para-positions on NMR chemical shifts of aromatic
carbon atoms in a benzene ring. These shifts in aromatic systems are
commonly believed to originate from a depletion or accumulation of
electrons in the π-orbitals at these atoms. We examine this claim by
means of NMR calculations with **ADF** and NBO/NLMO analysis tools.

This tutorial loosely follows the following publication: R. V.
Viesser, L. C. Ducati, C. F. Tormena and J. Autschbach *The unexpected
roles of σ and π orbitals in electron donor and acceptor group effects
on the 13C NMR chemical shifts in substituted benzenes*, Chem. Sci.
Phys. 8, 6570-6576 (2017).


Step 1: Preparations
====================

The molecular structures needed for this tutorial can be downloaded by
clicking on the following links:

   Download "Benzene.xyz"
   Download "Aniline.xyz"
   Download "Nitrobenzene.xyz"

These structures have **already been optimized and properly aligned**.
In general, you should optimize the structures first.

Note:

  The analysis of NMR and EFG results in terms of localized molecular
  orbitals requires some care about the alignment of the molecules
  when comparing results between different systems as in our case.
  This is, for example, because the analysis in terms of NLMOs is
  origin dependent. To obtain comparable orbital contributions one has
  furthermore to ensure that the different molecules are oriented in
  the same way. In AMSinput you can use the options **Edit →  Align**
  and **Edit →  Set Origin** to achieve this when performing localized
  orbital analysis with your custom models.

The main idea is now to compute the NMR shielding parameters for three
different carbon atoms in the ring, C(1), C(4), and C(5), which are in
ortho-, meta-, and para-position to the substituent at atom C(3):

   [image]


Step 2: Calculation Settings
============================

We need to perform three ADF calculations, one for each molecule (i.e.
Benzene, Aniline, and Nitrobenzene).

Let us start with **Benzene**:

   Start **AMSinput**
   Click on **File → Import Coordinates...** and select the file **Benzene.xyz** you just downloaded

Next, select the following settings in the main AMSinput panel

   In the **Main ADF panel**:
   **Task →  Single Point**
   **XC functional → Hybrid →  PBE0**
   **Basis set → TZ2P**
   **Frozen core → None**
   **Numerical quality → Good**

Note:

  An all-electron basis set is desirable because a hybrid functional
  is used. Using an all-electron basis set also improves the quality
  of the NMR results.

Note:

  A scalar relativistic treatment (Relativity → Scalar) is required to
  perform the NBO analysis of the NMR shifts.

In order to compare the computed NMR results with their experimental
counterparts (which were measured in Chloroform solution), we enable
the COSMO solvation model:

   Click on **Model → Solvation**
   **Solvation method → COSMO**
   **COSMO solvent → Chloroform**

We now select the atoms for which we want to compute the NMR
properties:

   In the menu bar: **Properties → Atom Info → Name → Show**
   In the panel bar: **Properties → NMR**
   Select atoms **C(1)**, **C(4)**, and **C(5)** in the molecular editor
   **NMR shielding for atoms:** click on the **+** button
   **Print:** tick **Isotropic shielding constants** and **Full shielding tensors**

   [image]

and enable the NBO analysis of the NMR properties:

   In the panel bar: **Properties → Localized Orbitals, NBO, ROSE**
   **Perform NBO analysis**: Tick **yes**
   **Analyse property →  NMR**

   [image]

Finally, we need to disable the automatic symmetry treatment of ADF:

   Click on **Details →  Symmetry**
   **Symmetry → NOSYM**

Now that all options are set, save the job:

   **File → Save As...**
   Save e.g. as "Benzene"
   Click **OK** in the popup window to confirm using the FULL FOCK matrix

For the other two systems (i.e. Aniline, and Nitrobenzene), we can
avoid having to set again most computational options:

   Select and delete all atoms
   **File → Import Coordinates...**
   Select "Aniline.xyz" and click **Open**
   In the menu bar: **Properties →  Atom Info →  Name →  Show**
   Panel bar: **Properties →  NMR**
   Select atoms **C(1)**, **C(4)**, and **C(5)** in the molecular editor
   **NMR shielding for atoms:** click on the **+** button
   **File →  Save As...**
   Save e.g. as "Aniline"
   Repeat for "Nitrobenzene.xyz"


Step 3: Running the Calculations
================================

We are now ready to run all three calculations

   Switch to AMSjobs using the SCM menu
   Select the three jobs **Benzene**, **Aniline**, and **Nitrobenzene**
   **Job → Run**


NMR Results
===========

After all three calculations are completed (this can take 10 minutes
up to several hours, depending on your hardware), we can explore the
output file:

   In AMSjobs click on the job **Benzene**
   Switch to AMSoutput using the SCM menu **SCM → Output**

In the AMSoutput window, we can see the output file. We can search for
text on it by using the text box localized at the bottom. For example,
we can go directly to the NMR section by searching the text "N M R",
or go to the beginning of the shielding tensor calculation section for
each atom with "****  N U C L E U S :". Notice that in the latter
case, there is one section for each of the three nuclei C(1), C(4),
and C(5), and you can reach each one of them by using the small
triangles to the right of the searching text box.

We can also retrieve the isotropic shielding constants directly by
clicking on the properties listed on the top menu of AMSoutput:

   In AMSoutput, click on **Other Properties → NMR shielding (NMR program)**

   [image]

Repeating the previous click, we can retrieve the result for each
atom.

In the case of Benzene the atoms C(1), C(4), and C(5) are all
equivalent, thus yielding shielding isotropic constants σ_i of the
same value. This is different in the case of the other two systems,
whose shielding constants are retrieved analogously from the
corresponding output files. The following are the expected results:

+----------------+----------------+---------------------+
| Compound       | Substitution   | σ_i (ppm)           |
|================|================|=====================|
| Benzene        |                | 54.302              |
+----------------+----------------+---------------------+
| Aniline        | o-NH_2         | 69.391              |
|                +----------------+---------------------+
|                | m-NH_2         | 53.198              |
|                +----------------+---------------------+
|                | p-NH_2         | 66.490              |
+----------------+----------------+---------------------+
| Nitrobenzene   | o-NO_2         | 57.630              |
|                +----------------+---------------------+
|                | m-NO_2         | 53.927              |
|                +----------------+---------------------+
|                | p-NO_2         | 46.071              |
+----------------+----------------+---------------------+

The chemical shifts δ_i are then computed relative to the
unsubstituted Benzene molecule as follows:

δ_i = σ_Benzene - σ_i + δ_Benzene

Here σ_Benzene is the isotropic value of the chemical shielding
computed σ_i for Benzene (54.302 ppm in our case), and δ_Benzene =
128.55 ppm is the experimental chemical shift relative to TMS for ^13C
in Benzene.

Note:

  It is important to note that the trends analyzed herein are not
  affected by the nature of the intermediate reference.

This yields the following results:

+----------------+----------------+--------------------------+----------------------------+
| Compound       | Substitution   | exp ^13C-shift           | calc ^13C-shift            |
|================|================|==========================|============================|
| Benzene        |                | 128.55                   | 128.55 (by definition)     |
+----------------+----------------+--------------------------+----------------------------+
| Aniline        | o-NH_2         | 115.29                   | 113.46                     |
|                +----------------+--------------------------+----------------------------+
|                | m-NH_2         | 129.45                   | 129.65                     |
|                +----------------+--------------------------+----------------------------+
|                | p-NH_2         | 118.73                   | 116.36                     |
+----------------+----------------+--------------------------+----------------------------+
| Nitrobenzene   | o-NO_2         | 123.65                   | 125.22                     |
|                +----------------+--------------------------+----------------------------+
|                | m-NO_2         | 129.48                   | 128.92                     |
|                +----------------+--------------------------+----------------------------+
|                | p-NO_2         | 134.76                   | 136.78                     |
+----------------+----------------+--------------------------+----------------------------+

The experimental NMR shifts are reproduced with an error margin of
about 2 ppm, and the trend between the different substitutions is
reproduced: the NH_2 group leads to a significant decrease in the
chemical shifts in ortho- and para- position. The meta-position
remains almost unaffected by the NH_2 group. This is also observed for
the meta-position near a NO_2 substitution, while the chemical shifts
are lowered at the ortho-atom and increased at the para-position.

To rationalize this finding, we proceed to examine the contributions
of individual orbitals to these substituent effects.


NLMO/NBO Analysis
=================

We first look at the individual NLMO contributions to the isotropic
shielding tensors. Each output file contains the NLMO and NBO
decomposition of the isotropic shielding tensors (and other
quantities) for the atoms C(1), C(4), and C(5).

The NMR shielding tensors consist of diamagnetic and paramagnetic
(+SO) contributions. Diamagnetic terms are larger but mostly dominated
by contributions from core orbitals and they are essentially not
affected by the local environment of an atom. As we are interested in
substitution effects, i.e. changing environments around an atom, we
focus on the diamagnetic terms here as these are most influential on
the magnitude and direction of the chemical shifts.

   Switch to AMSoutput for the job **Aniline**
   Type "NLMO contributions to" in the search bar
   Use the arrows in the search bar to get the entries for the **Isotropic Shielding Tensor**

   [image]

We find that the paramagnetic part of the isotropic shielding tensor
at atom C(1) is mostly determined by contributions originating from
three bonding NLMOs formed between C(1) and its three neighbors C(3),
C(4), and H(7). See labels "C  1- C  3", "C  1- C  4", and "C  1- H
7" respectively. Analogous results are obtained for C(4) and C(5) as
well as for the corresponding atoms in the Nitrobenzene molecule.

One finds similar results when examining the NBO contributions to the
isotropic shielding tensors. These contributions can be obtained by
searching for "NBO contributions to" in the search bar of ADFOutput.

Note:

  The following table summarizes characteristics of the common
  NBO/NLMO types, showing the number of centers, quantum shell,
  Lewis(L)/non-Lewis(NL) donor-acceptor type, and the program output
  label:

  +-------------------------+-----------+-----------+--------+---------+
  | NBO Type                | Centers   | Shell     | L/NL   | Label   |
  |=========================|===========|===========|========|=========|
  | core                    | 1-c       | core      | L      | CR      |
  +-------------------------+-----------+-----------+--------+---------+
  | nonbonded (lone pair)   | 1-c       | valence   | L      | LP      |
  +-------------------------+-----------+-----------+--------+---------+
  | bond                    | 2-c       | valence   | L      | BD      |
  +-------------------------+-----------+-----------+--------+---------+
  | antibond                | 2-c       | valence   | NL     | BD*     |
  +-------------------------+-----------+-----------+--------+---------+
  | Rydberg                 | 1-c       | Rydberg   | NL     | RY      |
  +-------------------------+-----------+-----------+--------+---------+


Inspecting NLMOs
================

We now examine in more detail the NLMOs with the largest
contributions.

   In **AMSjobs**, select the job **Aniline**
   Open **AMSview** using the SCM menu, click on **SCM → View**
   In AMSview, click on **Add →  Isosurface: With Phase**
   In the field bar at the bottom: **Select Field ...  →  NLMOs..**

The selection window allows you to pick individual orbitals for
plotting in AMSview

   [image]

A visual inspection of the three NLMOs with the largest contribution
to the isotropic shielding tensor reveals that they all have a
pronounced σ-orbital character:

   In AMSview in the field bar at the bottom:
   Enter "0.06" as isovalue

   [image]

Opposed to that, the π-orbitals of the aromatic system can be clearly
identified as well, e.g. for NLMO #11 in the above listing of
contributions

   [image]

As the results discussed above show, such π-orbitals are not
contributing much to the isotropic shielding tensors.

The corresponding analysis in terms of NBOs can be done in exactly the
same way

   In the field bar at the bottom: **Select Field ...  →  NBOs..**
   Select NBO from list

and suggests exactly the same finding

In conclusion, the chemical shifts due to substitutions on an aromatic
ring are mainly influenced by contributions from σ-bonding orbitals
rather than π-orbitals.


Further Reading
===============

R. V. Viesser, L. C. Ducati, C. F. Tormena and J. Autschbach *The
unexpected roles of σ and π orbitals in electron donor and acceptor
group effects on the 13C NMR chemical shifts in substituted benzenes*,
Chem. Sci. Phys. 8, 6570-6576 (2017).

J. A. Bohmann, F. Weinhold and T. C. Farrar *Natural chemical
shielding analysis of nuclear magnetic resonance shielding tensors
from gauge-including atomic orbital calculations*, J. Chem. Phys. 107,
1173-1184 (1997).

J. Autschbach *Analyzing NMR shielding tensors calculated with two-
component relativistic methods using spin-free localized molecular
orbitals*, J. Chem. Phys. 128, 164112 (2008).

R. V. Viesser, L. C. Ducati, C. F. Tormena and J. Autschbach *The
halogen effect on the 13C NMR chemical shift in substituted benzenes*,
Phys. Chem. Chem. Phys. 20, 11247 (2018).
