# NMR shifts with relativistic DFT

See also this FAQ on recommend settings for NMR calculations.

## Scalar relativistic & spin-orbit coupling calculations of NMR chemical shifts

In this tutorial you will learn how to optimize the geometry of a molecule and calculate NMR chemical shifts. You will study the effect of the relativistic approximation and of the exchange-correlation functional used: the PBE GGA or the PBE0 hybrid GGA.

The excercise addresses how the chemical shift of the hydrogen halides series is affected by relativistic spin-orbit coupling, following the problem formulated in Jochen Autschbach‘s chapter in High Resolution NMR Spectroscopy edited by Rubén Contreras.

## Geometry optimization and NMR chemical shifts for the H-X series

First, we create a new ADF Input

Open ADFJobs SCM → New Input

Build an HF molecule: press ‘h’ to switch to the building mode and click somewhere in the black canvas to draw an H atom. Now click ‘f’ to attach a fluorine atom to the H. Click somewhere close to the H.

Next we set up the geometry optimization. Select the following options in the main input panel:

Preset → Geometry Optimization XC potential in SCF: → GGA → PBE Relativity (ZORA): → Scalar Basis set: → QZ4P Frozen core: → none Integration: → Becke Good

That is, you will perform a geometry optimization with the PBE functional and the ZORA scalar relativistic Hamiltonian, using an all-electron QZ4P basis set with a ‘Good Becke’ grid. Your Geometry optimization input should look something like this:

Now we will define the NMR calculation to be performed after the geometry optimization. First select the H atom by clicking on it. Switch to the NMR input panel, and select the NMR shielding tensor to be calculated:

Click on the + next to 'NMR Shieldings for atoms:' Select the two tick boxes to print Isotropic shielding constants and the Full shielding tensor

Your NMR input should look something like this:

By clicking Ctrl + R or Cmd + R you will run this calculation, being prompted to save your input on the way.

The last two lines of the logfile will be shown in ADFJobs under your job. If you click SCM → Logfile you will get the complete logfile which picks up the latest information from the calculation as it proceeds.

The geometry optimization and the NMR calculation following that should finish in a minute or so. In the logfile you will see the NMR Shielding.

You will also be prompted to Read in the new coordinates, so that the geometry in your input window will be updated. Then, if you select both atoms you can read the interatomic distance from the geometry input box on the bottom right. If you have performed the calculations for the entire H-X series, you can also extract the geometric data and NMR shifts in one go by using the ADFreport tool (see below).

## Run calculations for the other hydrogen halides

Starting from HF, you can go down the periodic table by either making new inputs, or changing the halide. If you right-click on fluorine, and then click change atom type you will get a pop-up periodic table and clicking on Cl will change F to Cl. This will not change the interatomic distance, so it is recommended you pre-optimize before running the DFT calculations.

Save the new molecule under a different job name: File → Save as and run it (Ctrl + R or Cmd + R).

In the same manner, you can replace Cl by Br and then Br by I. These calculations will take increasingly more time to complete. Collect the distances and NMR Shielding. We will compare the distances to the experimental H-X distances from the NIST Chemistry Webbook, type in the molecular formula and look for the equilibrium distance r_{e}. The NMR shieldings will be compared with the experimental chemical shift with respect to H-F, which are -2.58, -6.43, and -15.34 ppm. The absolute experimental shielding for HF is reported as 28.72ppm

## Vary the relativistic approach and density functional (xc)

You will have found that the PBE distances are slightly longer than the experimental ones and that the scalar-relativistic NMR shieldings for HBr and HI are overestimated.

Now we will change the xc functional and relativistic treatment. The easiest is probably to take the converged geometries for the PBE + SR (scalar-relativistic treatment) and change the xc or the relativistic treatment, or both. This can be done in the Main input panel, under XC potential in SCF: → Hybrid → PBE0 and Relativistic treatment: → Spin-Orbit Make sure you save each new input file under a different name:

File → Save as before you run it (Ctrl + R or Cmd + R). The spin-orbit coupling NMR calculations will warn you that symmetry will be switched off. Click OK to proceed. Hybrid calculations (PBE0) will take longer than GGA calculations (PBE). Spin-orbit calculations will take much longer than scalar relatvistic ones.

Convince yourself that PBE0 (a hybrid functional) gives bond distances in excellent agreement with experiment. PBE also gives good results, but slightly overestimates the bond lengths.

Also convince yourself that switching the relativistic treatment from scalar relativistic to spin-orbit coupling hardly affects the geometries even for the heaviest I atom, but it strongly influences NMR shielding. In particular it gives NMR shieldings in good agreement with experiment for the heavier halides, where the scalar relativistic treatment is insufficient.

## Analyze multiple jobs with ADFreport

If you want to analyze the 16 calculations in one go, you can make use of the ADFreport tool in ADFJobs (the window with your jobs listed):

Tools → New Report Template Type in a name in the top-left entry (e.g. NMR and distance) Untick everything, tick 'NMR Chemical Shift' (if you want other things reported, leave those ticks on) In the bottom field type distance#1#2 to report the distance between atoms 1 and 2. Click OK to Save this report template

Select all (16) jobs, and click Tools → Build NMR and distance Report (or whatever you called your report template). You will get an html file reporting all distances and NMR chemical shifts in your default browser.

If you have calculated chemical shifts with scalar relativistic, spin-orbit coupling, PBE, and PBE0 Hamiltonians, you can compare them with the experimental values which you can find tabulated in the paper by Wolff and Ziegler in J. Chem. Phys. **109**, 895-905 (1998). Your findings should look something like this.