Example 1 - Ethanol

Fig1. Proton spectrum of ethanol

The discovery that one could actually see chemical shifts in hydrogen spectra was made in 1951 at Stanford University by Packard, Arnold, Dharmatti (shown in Fig1.). In this tutorial, we will try to reproduce this result.

Getting outputs

This tutorial will go through the calculations for ethanol, using these 2 files:

ethanol.cell

%BLOCK LATTICE_ABC
6 6 6
90 90 90
%ENDBLOCK LATTICE_ABC

%BLOCK POSITIONS_ABS
H 3.980599 4.178342 3.295079
H 5.033394 3.43043 4.504759
H 5.71907 4.552257 3.315353
H 3.720235 5.329505 5.509909
H 4.412171 6.433572 4.317001
H 5.911611 5.032284 6.242202
C 4.84694 4.350631 3.941136
C 4.603025 5.518738 4.882532
O 5.746254 5.812705 5.6871
%ENDBLOCK POSITIONS_ABS

%BLOCK KPOINTS_LIST
0.25 0.25 0.25 1.0
%ENDBLOCK KPOINTS_LIST

ethanol.param

xcfunctional    = PBE
fix_occupancy   = true
opt_strategy    = speed
task            = magres
cutoff_energy   = 300 eV

Look at the cell and param files. Note that the only special part of the ethanol.param file is

task = magres

Run a standard castep calculation for ethanol. Look at the ethanol.castep output file. Towards the end, you should be able to find the isotropic chemical shielding, anisotropy, and asymmetry in a table like this:

====================================================================
|                      Chemical Shielding Tensor                   |
|------------------------------------------------------------------|
|     Nucleus                            Shielding tensor          |
|  Species            Ion            Iso(ppm)   Aniso(ppm)  Asym   |
|    H                1               29.45       8.84      0.14   |
|    H                2               30.10       8.07      0.20   |
|    H                3               29.94       7.12      0.06   |
|    H                4               26.83       8.02      0.95   |
|    H                5               27.24      -7.07      0.90   |
|    H                6               31.93      13.99      0.46   |
|    C                1              157.27      33.77      0.70   |
|    C                2              110.73      69.91      0.42   |
|    O                1              268.63     -50.78      0.96   |
====================================================================

Here we are only interested in the isotropic values for the hydrogen atoms

You may also find this information (as well as extra detail) in the file ethanol.magres, which contains tables such as

============
Atom: H        1
============
H        1 Coordinates      3.981    4.178    3.295   A

TOTAL Shielding Tensor

              30.1276      1.2172      3.7366
               1.9301     27.4802      2.4707
               4.0710      2.2023     30.7511

H        1 Eigenvalue  sigma_xx      26.1030 (ppm)
H        1 Eigenvector sigma_xx       0.3550      0.6810     -0.6405
H        1 Eigenvalue  sigma_yy      26.9119 (ppm)
H        1 Eigenvector sigma_yy       0.6932     -0.6514     -0.3085
H        1 Eigenvalue  sigma_zz      35.3439 (ppm)
H        1 Eigenvector sigma_zz       0.6273      0.3345      0.7033

H        1 Isotropic:       29.4529 (ppm)
H        1 Anisotropy:       8.8365 (ppm)
H        1 Asymmetry:        0.1373

for each atom. You can see here that it also gives the same information - the isotropic value for atom 1 is the same. You may note that the isotropic value is the average of the diagonal values in the total shielding tensor.

You might wish to open the ethanol.magres with MagresView.

Analysis

Next we identify which (hydrogen) ion corresponds to which part of the molecule - in the case of ethanol, we find out which ones correspond to CH₃ CH₂ and OH. This can be done by uploading the cell file to VESTA or MagresView and clicking each atom.

NMR vesta demonstration

Here you can see that one of the CH₃ hydrogens is atom 3. If you do the same for all of them, you should find that atoms 1, 2 and 3 are the CH₃ hydrogens, 4 and 5 are the CH₂ hydrogens and 6 is the OH hydrogen.

It is important to check if the results are converged. Running a convergence test plot ranging the

cut_off_energy = 200 eV

from 200 to 1600eV gives the plot

Ethanol convergence plot

Here a cut off energy of 600 eV is reasonable - it's still relatively fast and should be fairly well-converged. 800eV is better converged. The cut off is quite high due to the presence of oxygen.

Next we will look at the converged isotropic hydrogen shieldings. We will compare them to experiment. The three methyl (CH₃) protons undergo fast exchange; they "rotate" faster than the nuclear magnetic moment processes. The magnetic moment will therefore "see" an average chemical shielding. The same is true of the CH₂ protons.

Then we can average the CH₃ and CH₂ chemical shieldings. For example, the shieldings of the CH₂ hydrogens (atoms 4 and 5) are found in the ethanol.castep file (shown above) to be 26.83ppm and 27.24ppm: the average CH₂ shielding is 27.04ppm. CH₃, meanwhile, has an average of 29.83ppm. Lastly, the single OH hydrogen has a value of 31.93ppm. We now have 3 unique chemical shieldings (though in your case the values will likely slightly differ)

We now need to convert the chemical shieldings $\sigma_{iso}$ ; to chemical shifts $\delta_{iso}$ on the experimental scale. We use the relation: $\delta_{iso}$ = $\sigma_{iso}$ - $\sigma$ . A suitable $\sigma_{ref}$ for ¹H is 30.97ppm.

Fig2. H NMR spectrum of liquid ethanol

Fig2. ¹H NMR spectrum of liquid ethanol

Fig2. shows a modern high-resolution ¹H spectrum for liquid ethanol. Note that the peaks are split due to J-coupling - the interaction of the ¹H magnetic moments. The three peaks are roughly at 1.2ppm, 3.7ppm and 5ppm - in this tutorial the shifts were found to be 1.14ppm (the CH₃ shielding), 3.94ppm (CH₂) and -0.96ppm (OH). The OH hydrogen clearly has a very different result while the other 2 roughly agree. The OH hydrogen shift is very sensitive to hydrogen bonding. It is has a very different value in as isolated molecule (as per our calculation) compared to liquid ethanol. The experimental value in a non-polar solvent should be closer to our isolated molecule - but note that the measurement is sensitive to even small traces of absorbed water, which will affect the OH shift.