Introduction to Computational Quantum Chemistry
Lesson 9: Response properties: NMR
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NMR
Widely used structure determination method
Uses very high magnetic fields to probe magnetically active nuclei
Each type of nucleus gives specific signal in spectrum
Position and shape of the signal is given by electronic and nuclear
structure of the surroundings of the nucleus
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What can be obtained
Izotropic chemical shifts
Chemical shift tensors
J-coupling
g-tensor (EPR)
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Properties
NMR properties are very sensitive to:
Chosen geometry
Wavefunction (tighten convergence criteria, if possible)
Solvent effects/crystal effects (especially exchangeable moieties)
Dynamic effects
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Energy levels
Difference between states is ∆E = γhB0
Where:
γ is the magnetogyric ratio of a nucleus
h is Planck’s constant
B0 is the external magnetic field
Small energies for excitations - perturbation to the wavefunction
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Chemical shielding (σ)
Difference in frequency of bare nucleus and nucleus under
investigation
σ(ppm) = 106 ∗ (νNUC − νCOM )/νNUC
Magnetic field felt by the nucleus is (1 − σ) ∗ B0
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Chemical shielding tensor
IUPAC convention:
σ11 ≥ σ22 ≥ σ33 (1)
σ11: direction of least shielding
σ33: direction of highest shielding
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Chemical shift (δ)
Difference between the shielding of nucleus under investigation
and nucleus in reference compound:
δ(ppm) = 106 ∗ (σCOM − σSTD)/(1 − σSTD)
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Isotropic tumbling
In solution the dipolar couplings caused by CSA vanish
In solid state the dipolar couplings are reduced by magic angle
spinning (MAS)
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Methods
For DFT improved results with climbing Jacob’s ladder
Always try to use as high basis set as possible
Make sure you wavefunction is well converged
Increase the convergence criteria
Calculate the chemical shifts against well-behaving reference
Martin Novák (NCBR) Response properties: NMR 18. listopadu 2014 10 / 14
Practical task
Calculate the NMR properties of acetic acid
Consider
Equilibrium geometry
Dimer
Microsolvated acetic acid with 2 water molecules
Use the preoptimized geometries distributed in IS
Calculate the spin-spin J-couplings as well
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Input
In your inputfiles include:
b3lyp 6-311++g(d,p) method
Very tight linear equations for SCF
D3 dispersion correction
Ultrafine integration grid
PCM water solvation model
Calculation of only J-couplings for nonoxygen atoms of acetic acid
(see documentation of NMR in Gaussian, do NOT calculate for
dimer)
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Reference compound
Good reference from computational point of view:
Small and symmetric
Rigid molecule (elimination of dynamic effects)
Only electrostatic interactions with surroundings (elimination of
charge transfer effects)
Benzene in benzene
Use the very same setup as for acetic acid (except PCM), use
“tight” convergence for optimization
δ13C = 127.83, δ1H = 7.15
δCOM (ppm) = σSTD − σCOM + δSTD
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Results
Compare the experimental values with predicted ones:
1H: 2.08 and 11.7 ppm
13C: 20.0 and 180.0 ppm
Why some geometries give better results?
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