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
Typical nuclei: 1H, 13C, 15N, 31P
Each type of nucleus gives specific signal in spectrum
Position and shape of the signal is given by electronic and nuclear
structure surrounding the nucleus
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What can be obtained
Izotropic chemical shifts
Chemical shielding tensors
J-coupling
g and A-tensors (EPR, paramagnetic NMR)
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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 = −γω
Where:
γ is the magnetogyric ratio of a nucleus
h is Planck’s constant
B0 is the external magnetic field
ω is the Larmor precession frequency
Small energies for excitations - perturbation to the wavefunction
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Chemical shielding tensor (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
IUPAC convention:
σ11 ≥ σ22 ≥ σ33
σ11: direction of least shielding
σ33: direction of highest shielding
σ11 = 286 ppm
σ22 = -65 ppm
σ33 = -65 ppm
σISO = 52 ppm
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Powder pattern
IUPAC convention:
σ11 ≥ σ22 ≥ σ33
σ11: direction of least shielding
σ33: direction of highest shielding
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Isotropic tumbling
Due to fast tumbling in solution, the shielding gets isotropically
distributed
In solid state the anisotropy is reduced by magic angle spinning
(MAS)
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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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Methods
Improved results with climbing Jacob’s ladder (DFT and ab initio)
Always try to use as high basis set as possible
STO are superior to GTO
Make sure you wavefunction is well converged
Increase the SCF convergence criteria
Calculate the chemical shifts against well-behaving reference
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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 input files include:
b3lyp 6-311++g(d,p) method
Tighten the SCF convergence to 10−8
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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