Introduction to Computational Quantum Chemistry
Lesson 9: Response Properties: NMR
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 1
NMR Spectroscopy
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
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 2
Properties that can be obtained
isotropic Chemical Shifts
chemical Shielding Tensors
J-coupling
g and A-tensors (EPR, paramagnetic NMR)
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 3
In Silico NMR Properties
calculated NMR atomic properties are very sensitive to:
chosen geometry
wavefunction (tighten convergence criteria, if possible)
solvent effects/crystal effects (especially exchangeable
moieties)
dynamic effects
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 4
Energy Levels (α − β)
difference between states is ∆E = γ B0 = −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
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 5
NMR Chemical Shift
∆E = γ (1 − σ)B0 = −γω
magnetic field felt by the nucleus is (1 − σ) ∗ B0 as a result
of chemical shielding σ
difference in frequency of bare nucleus and nucleus under is:
σ(ppm) = 106
∗ (νnuc − νcom)/νnuc
chemical shift:
δ(ppm) = 106
∗ (σref − σsample)
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 6
Chemical Shift Anisotropy
IUPAC convention:
σ11 ≥ σ22 ≥ σ33
σ11: direction of least shielding, σ33: direction of highest
shielding
the average of these is the "isotropic" value
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 7
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)
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 8
Chemical shift (δ)
difference between the shielding of nucleus under investigation and
nucleus in reference compound:
δ(ppm) = 106
∗ (σCOM − σST D)/(1 − σST D)
In Silico 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
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 9
ACTIVITY I - Acetic Acid
use the series of optimize geometries provided (Acetic Acid)
for NMR calculation your input files must 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)
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 10
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
NOTE: δ13
Cref = 127.83, δ1
H = 7.15
δcom(ppm) = σref − σcom + δref
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 11
Assesment - Acetic Acid
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?
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 12
END
(Prepared by Radek Marek Research Group)
Lesson 09 - Response Properties: NMR 13