Benzene: NMR Chemical Shifts¶
An NMR calculation gives the absolute magnetic shielding σ of every nucleus. Spectra report chemical shifts δ relative to a reference compound, so two calculations at the same level are needed: the molecule of interest and the reference, tetramethylsilane (TMS). Then
δ = σ(TMS) − σ(molecule).
Copy and run¶
dft/pbe0/6-31g* nmr
geom="""
C 1.392883 0.000000 0.000000
C 0.696465 1.206259 0.000000
C -0.696465 1.206259 0.000000
C -1.392883 0.000000 0.000000
C -0.696465 -1.206259 0.000000
C 0.696465 -1.206259 0.000000
H 2.479666 0.000000 0.000000
H 1.239913 2.147463 0.000000
H -1.239913 2.147463 0.000000
H -2.479666 0.000000 0.000000
H -1.239913 -2.147463 0.000000
H 1.239913 -2.147463 0.000000
"""
Download benzene-nmr.oqp · Download tms-nmr.oqp (TMS, 17 atoms, same first line)
openqp benzene-nmr.oqp
openqp tms-nmr.oqp
nmr computes GIAO (gauge-including atomic orbital) shieldings, which do not
depend on the choice of coordinate origin. Both geometries were optimized at
PBE0/6-31G*. Benzene takes about 25 seconds and TMS about 40 seconds.
What you get¶
The end of each log has the isotropic shielding of every atom, in ppm. The
column to use is total_coupled, which includes the response of the orbitals to
the magnetic field (coupled-perturbed Kohn–Sham). For benzene:
Isotropic shielding (GIAO, ppm) [exact-exchange c_x = 0.2500]
Atom Z sigma_dia para_uncoupled para_coupled total_uncoupled total_coupled
1 6.0 256.824629 -143.610570 -184.723650 113.214059 72.100980
2 6.0 256.835108 -143.625026 -184.741975 113.210082 72.093133
...
7 1.0 29.549782 -3.924546 -4.810611 25.625236 24.739171
8 1.0 29.545189 -3.921758 -4.807423 25.623431 24.737766
OQP Studio can color the atoms by these values and print them on the structure:
Equivalent atoms agree to 0.01 ppm; the small spread comes from the DFT integration grid. Averaging over equivalent atoms:
| Nucleus | σ(benzene) | σ(TMS) | δ = σ(TMS) − σ | Experiment (CDCl₃) |
|---|---|---|---|---|
| ¹H | 24.738 ppm | 32.109 ppm | 7.37 ppm | 7.34 ppm |
| ¹³C | 72.10 ppm | 194.49 ppm | 122.4 ppm | 128.4 ppm |
TMS has four equivalent carbons and twelve equivalent hydrogens; its geometry here is not exactly Td, and the individual values spread by 0.2 ppm (C) and 0.02 ppm (H) around the averages above.
Reading the result¶
The ¹H shift is close to experiment. The ¹³C shift is 6 ppm too low; ¹³C
shieldings depend more strongly on the functional and the basis set than ¹H
shieldings, so test a larger basis set such as cc-pvtz before relying on
absolute ¹³C values. The experimental values are for solution, while the
calculation is for an isolated molecule.
Cross-check¶
To test the GIAO implementation, the benzene calculation was repeated at the
Hartree–Fock level (hf/6-31g* nmr) in OpenQP and in PySCF 2.13 at the same
geometry. Both give σ(C) = 73.519 ppm and σ(H) = 25.083 ppm.
Try next¶
- Compute the shifts of a substituted benzene, such as toluene, at the same level; the TMS reference values above can be reused.
- Repeat the benzene run at the Hartree–Fock level,
hf/6-31g* nmr, and compare with the values in the cross-check above.
See also: NMR, IR, and Raman,
properties.