Solid State NMR of Glass - Modelling NMR spectra of glass...
Transcript of Solid State NMR of Glass - Modelling NMR spectra of glass...
Solid State NMR of GlassModelling NMR spectra of glass from first-principles
Thibault Charpentier
CEA / IRAMIS / SIS2MLaboratoire de Structure et Dynamique par Resonance Magnetique
GDR Verre, 9-13 April 2011
Introduction
Basics of NMR: Interactions, MAS, MQMAS
NMR of disordered Materials
NMR from first-principles
Molecular Dynamics versus NMRContent of the tutorial
I Basics of NMR interactions and spectra of solids
I 1D-2D NMR experiments: Static, MAS and MQMAS spectra
I NMR of disordered Materials
I Structure: Molecular Dynamics Simulations (TD)
I NMR parameters: DFT GIPAW calculations (TD)
I NMR parameters & Simulations: specific NMR softwarepackages (fpNMR) (TD)
I Principles of pulsed NMR
I NMR Hamiltonian Art . . .
The Zeeman Interaction and Larmor FrequencyThe NMR spectrum of an isolated nucleus . . .
∆m ± 1
0
0
I=32
B0≠0
B0=0
∣m=3/2 ⟩
∣m=1/2 ⟩
∣m=−1/2 ⟩
∣m=−3/2 ⟩
0
The Zeeman effect
0
E=−N⋅B0
0=−N2
B0
The Larmor frequency and its NMRspectrum.
No information on the chemical surrounding
(~) H = −~γN~I · ~B0
NMR and the Periodic TableOne-half and quadrupolar nuclei
I Isotope, Nuclear Spin
I Natural Abundance
I Gyromagnetic ratio γ(rad/s/T)ω0 = 2πν0 = −γB0
I Quadrupolar MomentQ (see Pyykko)
Pulsed NMRThe Basic NMR Experiment . . . One pulse !
M0: Nuclear Magnetization at Equilibrium
s s-msms-h
p
B0 M0 M0
BRF
M0
FFT
S t
S
~M(0) = M0~z~M(τp) = M0~x
S(t) = M0e−iν0te
− tT2
S(ν) =
∫ ∞
0dt S(t)e−i2πνt ≈
N−1∑k=0
S(tk)e−i2πνtk = L (ν − ν0)
Lineshape L(ν): Gaussian, Lorentzian . . .
Pulsed NMRThe Basic NMR Experiment: Fourier Transform
0 5000 10000 15000Time (µs)
-50-40-30-20-1001020304050Chemical shift ( ppm )
23Na in Na2MoO4
S(t) S(ν)
NMR Interactions for NMR spectroscopistsEffects of the local magnetic fields . . .
Electrons
Phonons
Nuclear Spins I Nuclear Spins SNMRNMR
EPR
MicroWaves, ....
Bloc
B0BRF
0
E=−N⋅B0Bloc
loc
The NMR spectrum
Information on the chemical surrounding
(~) H = −~γN~I ·
~B0 + ~Bloc
= HZ + Hinter.
(~) H = HZ + HCS + HQ + HJ + HD + . . .
CS: Chemical Shift, Q: Quadrupolar, J: J couplings, D: Dipolar
NMR interactions for Quantum ChemistsThe effective Hamiltonian
HS(NMR) = −~∑
i
γi~Ii (1− σ) ~B0 +
∑i ,|Ii |≥1
~IiQii~Ii
+~2
2
∑i
∑j 6=i
γiγj~Ii (Dij + Jij)~Ij
~B0 External static magnetic field
~BRF (t) External radiofrequency magnetic field (NMR signal)
Internal Interactions
~Ii Nuclear spin operators ~µi = γi~~Iiσ Nuclear magnetic shielding tensor (chemical shift)
Dij Nuclear magnetic dipolar coupling tensor (structure)
Jij Indirect nuclear spin-spin coupling tensor
Qii Nuclear quadrupolar coupling tensor ( |Ii | ≥ 1 )
The nature of NMR interactionsSecond-rank tensors (i.e. matrices) define NMR interactions.
~B(A)loc = A~X =
Axx Axy Axz
Ayx Ayy Ayz
Azx Azy Azz
·
Xx
Xy
Xz
HA = −γN~×~I · A · ~X
A ~X Interaction
1 ~B0,~BRF Zeeman interaction
σ ~B0 Magnetic Shielding DFT
Q ~I Quadrupolar interaction DFT
D ~S Dipolar interaction (spatial) structure
J ~S Indirect J couplings (through bond) DFT
DFT calculations output A in its tensorial (matrix) form relative to a
reference frame(x , y , z) (crystal axes).
NMR Interactions: The Principal Axes System (PAS) IThe principal values
AZZ
AYYAXX
B0B0
z
x
y
A =
AXX 0 0
0 AYY 0
0 0 AZZ
Isotropic Aiso = 1
3Tr [A]
Anisotropy δA = AZZ − Aiso
Asymmetry ηA = (AXX − AYY ) /δA
with 0 ≤ ηA ≤ 1
Calculations output the tensor in a reference frame (unit-cell definition).Its diagonalization (3D rotation) provides the principal values (Aα,α) and
its orientation with respect to the reference frame.Convention: |AZZ − Aiso | ≥ |AXX − Aiso | ≥ |AYY − Aiso |
AisoAZZAYY AXX
NMR Interactions are Anisotropic . . .. . . NMR spectra of a single molecule (crystal)
O
C
O
C
O
C
zz yy xx
B0B0
B0
The NMR frequency depends on the orientation with respect to ~B0
ν − ν0 = νint(Ω)Single crystal NMR exists . . . but amorphous materials ?
NMR Interactions: The Principal Axes System (PAS) IIThe relative orientation of the PAS
APAS = Aiso1
+ δA
− 1
2 (1 + ηA) 0 0
0 − 12 (1− ηA) 0
0 0 1
A = X−1
A APASXA
XA = R(αA, βA, γA)
= exp(−iαAIz)
× exp(−iβAIy )
× exp(−iγAIz)
(x , y , z): reference frame axis(αA, βA, γA): Euler angles
A NMR interaction is characterized by 6 parameters:Aiso , δA, ηA, αA, βA, γA.
For a single interaction, (αA, βA, γA) does not affect the powderlineshape but can be determined for single crystal NMR.
NMR Interactions are Anisotropic . . .. . . NMR spectrum (CSA) of a powder
B0
x
y
z
,
=90° =0 °
The powder average
S(t) =
∫sin θdθdφ
× exp −iν(θ, φ)t
NMR Interactions are Anisotropic . . .. . . but in liquids only the isotropic part in effective
Motional averaging
I Motions affect the anisotropiclineshape.
I In the case of fast motionalaveraging (vs Larmorfrequency), a narrow line at theisotropic frequency.
I Brownian Motion in liquid
I Motions (fluctuations) induce
Relaxation
H (Ω(t)) = Hiso + Hani (Ω(t)) withHani (Ω(t)) = 0 at the Larmor time scale ( 1/ν0)
The Zeeman Truncation in High Field NMROnly the part along B0 is NMR active to first order.
AZZ
AYYAXX
B0B0
z
x
y
Azz
In case of 1-spin interaction,only Azz (in the referenceframe) contributes to firstorder to the NMR frequency.
Because B0 Bloc (or HZ Hint), wehave the secular approximation
Hint ≈ H(1)CS + H
(1)Q + H
(2)Q + H
(1)J + H
(1)D . . .
Typical strength of NMR interactionsI Z: 10-1000 MHz
I CS: kHz
I Q: MHz (up to second order)
I D: kHz
I J: Hz
NMR Interactions in generalAn overview . . .
H (λ) = C (λ) × R (λ) (Ω)× T(λ)
C (λ) Constant Obtained from DFT (σ,Q)
R(λ) (Ω) Spatial Dependence Manipulated through (sample) motions
R(λ) (Ω) = 1 Isotropic Brownian motions in liquids
T(λ) Spin operators Manipulated through RF (spin rotation)
T(σ) Iz Chemical shift
T(Q) I 2z First order quadrupolar interaction
T(Q) Iz , I3z Second order quadrupolar interaction
T(D,J) IzSz Dipolar (heteronuclear) or J interactions
T(D)II
IAz IB
zDipolar (homonuclear) interaction
+ 14
(IA+ IB− + IA
−IB+
)
The Shielding / Chemical Shift TensorNMR frequency
The secular contribution of the magnetic shielding is:
HCS = γ~Iσ~B0 ≈ γB0σzz(Ω)Iz
σzz(Ω) = σXX sin2 θ cos2 φ + σYY sin2 θ sin2 φ + σZZ cos2 θ
= σiso +δCS
2
((3 cos2 θ − 1) + ηCS sin2 θ cos 2φ
)= σiso + δCSR20(Ω)
NMR measure the chemical shift tensor δ (ppm):
δexpiso (ppm) = 106
(ν − νref
νref
)νref is a frequency reference value obtained from one tabulated
reference compound, generally in liquid or in a solid (narrow peak,e.g. NaCl for 23Na.
The shielding / Chemical Shift TensorNMR static lineshape
-200 -100 0 100 200ppm
-200 -100 0 100 200ppm
δCSA > 0 δCSA < 0
η = 0
η = 0.5
η = 1
The magnetic shieldingRelationshield with the chemical environment
-120-110-100-90-80-70-6029Si chemical shift δiso (ppm)
O-
O-SiO-
O-
O-
SiOSiO-
O-
O-
SiOSiOSi O-
Si OSiOSiOSi O-
Si OSiOSiOSi O Si
Q(0) Q(1) Q(2) Q(3) Q(4)
Q(1) SiOSi=180o
Q(0)
Q(1)
Q(2)
Q(3)
Q(4)
Tetrahedral silicon Q(n) units in silicates
The quadrupolar interactionfrom electric field gradient. Only for I ≥ 1.
Because of its large strength (kHz-MHz), quadrupolar Hamiltonianare often accounted for up to second order (23Na,17O,27Al,11B. . . )
depending on the local environment of the nucleus.
The electric field gradient V is a symmetric traceless(VXX + VYY + VZZ = 0) tensor.
CQ =eQ
hVZZ , ηQ =
VXX − VYY
VZZ,Viso = 0
CQ : quadrupolar couping constant, ηQ : quadrupolar asymmetryparameter.
The quadrupolar interactionTo first order. Only for I ≥ 1.
The firt-order secular quadrupolar Hamiltonian is
H(1)Q =
CQ
6I (2I − 1)× R20 (Ω)× T20 , T20 =
√1
6
(3I 2
z − I (I + 1))
This I 2z yields the NMR frequency as
νm,m−1 − ν0 =1− 2m
2νQR20 (Ω) = ν
(1)Q (Ω)
The central transition −12 ↔
12 is not affected by H
(1)Q .
0Q1
20−
Q1
2
I=1
0
0Q
10−Q1
I=32
The quadrupolar interactionTo second order.
The second-order secular quadrupolar Hamiltonian is (morecomplex)
H(2)Q =
1
ω0
(CQ
6I (2I − 1)
)2
×∑
l=0,2,4
AlRl0(Ω)
Rl0(Ω) =−l∑k=l
Bkl (η)Dk
l0 (Ω) ,Dkl0 : Wigner rotation matrix elements
Al = f (I 3z , Iz) and isotropic shift (SOQS) δ
(2)Q = A0B0
0 (η)
The NMR frequency of the central transition can be written as
ν−1/2,+1/2(Ω)− ν0 = a0 + a2R20(Ω) + a4R40(Ω)
The quadrupolar interactionfrom electric field gradient
-2000-1000010002000kHz
-200-1000100ppm
Central
-5/2 <-> -3/2
-3/2 <-> -1/2
-1/2 <-> +1/2
+1/2 <-> +3/2
+3/2 <-> +5/2
Satellite
Satellite
Satellite
Satellite
I=5/2
CQ = 5 MHz
B0 = 11.75 Tη=0.0
η=0.2
η=0.4
η=0.6
η=0.8
η=1.0
Central Transition
Quadrupolar + CSA NMR spectrumInterplay of interactions
NMR lineshapes are also sensitive to the relative orientation of the CSAPAS with respect to the EFG (quadrupolar) PAS.
-400-300-200-1000100200ppm
I=5/2
CQ = 5 MHz η = 0.1
δCSA = 100 ppm
ηCSA =0.4
B0 = 11.72 T
(α,β,γ) = (0,0,0)
(α,β,γ) = (0,90,0)
-1/2 <-> 1/2
B0
ZZ
YYXX
V ZZ
V YYV XX
Xσ,c = R(ασ,c , βσ,c , γσ,c)
XQ,c = R(αQ,c , βQ,c , γQ,c)
The relative orientation reads
Xσ,Q = Xσ,c × X−1Q,c
= R(ασ,Q , βσ,Q , γσ,Q)
Quadrupolar + CSA NMR spectrumInterplay of interactions
-1000001000093Nb chemical shift (ppm)
LaNbO4
-6000-30000300093Nb chemical shift (ppm)
MgNb2O4
-10000093Nb chemical shift (ppm)
YNbO4
18.8 T
14.1 T
9.4 T
7 T
J.V. Hanna et al. Chem. Eur. J. 16 (2010) 3222
Multiple magnetic fields acquisition required to determine accurately
both tensors (8 parameters !).
High Resolution NMRWhy Magic Angle Sample Spinning ?
R20(Ω) ∝ 3 cos2 θ − 1Method: Reduce all orientation to an effective magic angle
orientation !
-150-100-50050100150
θM
3 cos2(θM ) - 1 = 0
High Resolution NMRMagic Angle Sample Spinning: a coherent averaging approach
A (Ω(t)) = Aiso1 + A(θM) + A(t)
AZZ
AYYAXX
B0B0
z
x
y
At
At A
B0
M
Coherent Averaging
Magic Angle: A(θM) = A = 0 (Fast) Spinning A(t) = 0
Effective A reduces (to first order) to Aiso1.
High Resolution NMRMagic Angle (Sample) Spinning for I=1/2
Spinning sidebands
ROT
ROT
CSA + Dipolar ( 13C-13C )
νROT ≤ δA: spinning sidebands at k × νROT
νROT > δA: narrow lines
(Experimental) Solid State NMR
High Resolution NMRMagic Angle Spinning for quadrupolar nuclei: The central transition
-150-100-50050ppm
-300-200-1000100ppm
I=5/2
CQ = 5 MHz
B0 = 11.75 T
η=0.8
η=0.6
η=0.4
η=0.2
η=0.0 B0 = 17.6 T
B0 = 11.7 T
B0 = 7.05 T
η=1.0
High Resolution NMR of quadruplar nucleiMagic Angle Spinning for quadruplar nuclei: The satellite transitions
-100001000kHz
460470480kHz
I=5/2
CQ = 5 MHz
B0 = 11.75 T
+3/2 <-> +5/2
-1/2 <-> -3/2+1/2 <-> +3/2
-3/2 <-> -5/2
νROT = 40 kHz
η=1.0
Satellite Transitions
"spinning sidebands
manifold"
High Resolution NMR of quadruplar nucleiMagic Angle Spinning: one example
27Al NMR in NaAlH4
High Resolution NMR of quadrupolar nucleiHow to reduce the linewidth ?
ppm
* *
* spinning sidebands
STATIC
MAS
0 20 40 60 80θ (degree)
-0,4
-0,2
0
0,2
0,4
0,6
0,8
1
d400(θ)
d200(θ)
30.56° 54.74°
70.12°
static: νCT = νiso + a2R20(Ω) + a4R40(Ω)
MAS: νCT = νiso + a4 R40(Ω)
High Resolution NMR of quadrupolar nucleiThe Multiple Quantum MAS (MQMAS) approach
3/2
−3/2
−1/2
1/2
3/2
−3/2
−1/2
1/2
2D NMR: S(t1, t2) = exp −i ν3Q t1 × exp −i ν1Q t2
2D FFT yields a 2D spectrum S(ν1, ν2)
High Resolution NMR of quadrupolar nucleiPrinciples of MQMAS NMR
-1100-1050-1000-950MAS (1Q) dimension (ppm)
2900
2950
3000
3050
3100
3150
3200
3Q d
imen
sion
(ppm
)
-1100-1050-1000-950MAS (1Q) dimension (ppm)
110
120
130
140
Isot
ropi
c di
men
sion
(ppm
)
ν3Q(Ω)
ν1Q(Ω)
Shear Transformation
Both transitions have the same anisotropy!
ν(1Q=CT ) = ν(1Q)iso + a4(1Q) R40(Ω)
ν(3Q=TQ) = ν(3Q)iso + a4(3Q) R40(Ω)
High Resolution NMR of quadrupolar nucleiMQMAS at work in a crystalline sample
Solid State NMR of disordered materials
Each site characterized by a NMR parameter distribution.
11B MAS NMR in Borosilicate GlassesDirect access to boron speciation
Identifying the structural units forming
the glass network
-100102011B δ / ppm
[4]B
[3]B
[3]B
[4]B
"Resolved" Spectrum
O
B
MAS @ B0= 11.75 T
-100102011B δ / ppm
MAS @ B0 = 18.8 T
High Field MAS NMR:
Boron speciation resolvedMD Picture, J.M. Delaye, CEA/DEN
Solid State NMR of disordered materialsMAS NMR: mechanisms of broadening?
-100-50050100Chemical Shift (ppm)
17O MAS NMR @ 11.72T
SiO2
Glass
CristobaliteSample D. Neuville (IPGP)
-50-40-30-20-100102030Chemical Shift (ppm)
11B MAS NMR @ 11.75 T
La(BO2)3
Sample. D Caurant (ENSCP)
Crystal
Glass
BO3
BO4-
Need of 2D NMR to elucidate the contribution of EFG and chemical shift
distribution.
High Resolution NMR in glassThe power of oxygen-17 MQMAS NMR
Modeling and Quantifying 17O MQMAS SpectroscopyQuantification + Spin dynamics + NMR Distribution F. Angeli, T. Charpentier et al. JNCS 2008
-200204060MAS dimension / ppm
-50
-40
-30
-20
-10
Isot
ropi
c di
men
sion
/ pp
m
17O MQMAS @ 11.75T
-60-40-20Isotropic dimension / ppm
0 1 2 3 4 5 6 717O CQ / MHz
20
30
40
50
60
70
80
17O
δIS
O /
ppm
3D NMR parameter distribution
-200204060MAS dimension / ppm
-50
-40
-30
-20
-10
Isot
ropi
c di
men
sion
/ pp
m
-40-20020406080MAS dimension / ppm
0 2 4 6 817O CQ / MHz
0
0,1
0,2
0,3
0,4
Sign
al /
arb.
uni
ts
Experiment
Simulation
SiOSiSiOB
SiONa
11%
SiOSi
SiOBSiO
+ Na+
SiOSi
SiOB
SiONa
SiOSi
SiOB
MQMAS Efficiency ProfileSiONa
SiOSiSiOB
SiONa
59%
30%
Correlated model of distribution p(CQ , η, δiso)
Quantifying glass topological disorder
1 2 3 4 5 6 717O Quadrupolar Coupling Constant CQ / MHz
0
20
40
60
80
100
120
17O
Isot
ropi
c C
hem
ical
shi
ft δ is
o / pp
m
Si-O-SiSi-O-B
B-O-B
Si-O-Na+
Si-O-Na+,Ca++
MQMAS @ B0= 11.75 T
Glass Topology
I Reconstruction of the NMRparameter distribution
I Correlating the local disorder to theNMR spectrum line shape ?
I Π(NMR) ⇒ Π(Structure) ?
Understanding NMR / Structure relationshipsQuantum Mechanical calculations: the Cluster Approach
Si(OH)3-O-Si(OH)3
120 130 140 150 160 170 1804
5
6
7
17O
Qua
d. C
onst
ant C
Q /
MH
z
1,5 1,6 1,7 1,84
5
6
7
120 130 140 150 160 170 180Si-O-Si angle (degree)
0
0,2
0,4
0,6
0,8
1
17O
η Q
uad.
Asy
mm
etry
1,5 1,6 1,7 1,8Si-O distance (angstroem)
0
0,2
0,4
0,6
0,8
1
η(Si-O-Si)
CQ(Si-O-Si) CQ(Si-O)
η(Si-O)
17O CQ and ηQ NMR parameters are allmost exclusively controlled by
local properties: (Si-O-Si bond angle and Si-O bond length)
Understanding NMR / Structure relationshipsThe Phenomenological Approach: using Crystalline Reference Compounds.
17O CQ(θ)
Coesite SiO2
130 140 150 160 170 180Si-O-Si angle ( θ ) / degree
5
5,2
5,4
5,6
5,8
6
17O
Qua
drup
olar
cou
plin
g co
nsta
nt /
MH
z
ExperimentCQ = A ( 1/2 + cosθ / (cosθ-1) )(α)
17O η(θ)
Coesite SiO2
130 140 150 160 170 180Si-O-Si angle ( θ ) / degree
0
0,05
0,1
0,15
0,2
0,25
17O
Qua
drup
olar
asy
mm
etry
par
amet
er η
Experimentηq = B (1-cosθ/(cosθ-1))β
But 17O NMR: very limited number of experimental data !
Combining MD simulations with fp NMR calculationsGIPAW: C.J. Pickard & F. Mauri, PRB 2001
DFT NMR CalculationsIn General
The Quadrupolar Interaction (Electric Field Gradient) Tensor fromfirst principles calculations :
Q(k)αβ =
eQ
h〈Ψ0|
δ(1)Eα
δrβ|Ψ0〉 =
eQ
hVαβ
Eα Electric field, depends on the fundamental states only (easy)The Chemical Shielding Tensor from first principles calculations:
σ(k)αβ =
δ(2)E0
δµk,αB0,β=
δ2〈Ψ0|H|Ψ0〉δµk,αδB0,β
.
Second order derivative (Response Theory)
DFT NMR CalculationsEFG from electronic density n0(r)
I Kohn-Sham Orbitals / Plane wave
φj(r) =∑
k∈IBZ
e−ikr uj ,k(r)
uj ,k(r) =∑G
Cj ,k(G ) e−iGr withG ≤ Gmax
n0(r) =∑occ
|φj(r)|2
I Electric Field Gradient
Vα,β(rN) =
∫dr
n0(r)
|r − rN |
δα,β − 3
(rα − rN,α)(rβ − rN,β)
|r − rN |2
DFT NMR CalculationsFrom electronic density n0(r)
Principles of a NMR shielding tensor calculation (first-order in BO)(~rN position of the nucleus)
1. computation of the induced (quantum) current density ~j (1)(~r)
2. computation of the induced magnetic field
~B(1)in (~rN) =
1
c
∫d3r j (1)(~r)×
~rN −~r
|~rN −~r |3(1)
3. The absolute chemical shielding tensor σ is obtained through
~B(1)in (~rN) = −σ(~rN)~B0 (2)
The GIPAW methodGauge Including Projector Augmented Wave C.J. Pickard & F. Mauri, PRB 2001
I DFT using GGA (PBE) or LDAfunctionals.
I Plane Waves Expansion (e−ik.r)I 3D FFT, Parallel CodeI Periodic Boundary Conditions
I Pseudopotential approximation ofcore electrons
I GI-PAWI PAW: Reconstruction of the
wave function at the nucleusI GI: Gauge InvarianceI All-electron approach
-100 -50 0 5017O δ / ppm
-200 0 20017O δ / ppm
Experiment
α-cristobalite SiO2
GIPAW
Exp.: Spearing et al. Phys. Chem. Minerals 1992.
STATIC MAS
Accuracy: GIPAW outperforms all previous approaches
GIPAW CalculationsPractice
I Convergence of NMR versus Plane wave cutoff, k-grid
I Outputs: magnetic shielding σ, EFG V tensor
I Experimental Observable: chemical shift δ, Quadrupolar parametersCQ , η
δiso(calc) = σiso(ref )− σiso(calc)
CQ =eQ
hVZZ
σiso(ref ), Q from reference compound(s) with accurateexperimental NMR parameters and structure.
I (DFT) Optimized structures provides better NMR predictions thanX-ray structures.
I Periodic boundary conditions: GIPAW performs (much) better thancluster approximation
I Challenges: Finite Temperature (calculation at 0K), Disorder.
DFT NMR CalculationsThe (art of) pseudopotential approximation
I Choice of valence(core) configuration
I choice of cutoff radii
for r > rcut
φPS(r) = φAE (r)
for r < rcut
φPS(r) smooth
GIPAW ApplicationsImportance of the design of accurate pseudopotentials
Some elements are difficult (transition element), need of optimizedpseudopotentials (ultra-soft)
Importance of good convergence
L. Truflandier, M. Paris, F. Boucher, Density functional theory investigation of 3d transition metal NMR shielding
tensors in diamagnetic systems using the gauge-including projector augmented-wave method, Phys. Rev. B. 76
(2007) 035102.,
GIPAW ApplicationsZORA (Zero-Order Relativistic Approximation) Relativistic correction
Absolute magnetic shielding versus (relative) chemical shift
500 1000 1500 200077Se σiso (ppm) Experiment
500
1000
1500
2000
77Se
σis
o (ppm
) GIP
AW
nonrelativisticrelativistica=1.1267a=1.1134
1000 2000 3000 4000125Te σiso (ppm) Experiment
0
1000
2000
3000
4000
125 Te
σis
o (ppm
) GIP
AW
nonrelativisticrelativistica=1.0057a=0.9904
SeH2
Se(CH3)2
SeF6
SeF4
SeHCH3
TeH2
Te(CH3)2
Te(CH3)4
TeF6
(TeCF2)2
J.R. Yates, C.J. Pickard, M.C. Payne, F. Mauri,Relativistic nuclear magnetic resonance chemical shifts of heavy
nuclei with pseudopotentials and the zeroth-order regular approximation, J. Chem. Phys. 118 (2003) 5746
GIPAW ApplicationsAssessment of the GIPAW method
Set of reliable NMR data are needed to assess the GIPAW method
J.V. Hanna, K.J. Pike, T. Charpentier, T.F. Kemp, M.E. Smith, B.E.G. Lucier, R.W. Schurko, L.S. Cahill, A 93Nb
Solid-State NMR and Density Functional Theory Study of Four- and Six- Coordinate Niobate Systems, Chem. Eur.
J. 16 (2010) 3222-3239.
GIPAW ApplicationsNMR Crystallography: assign NMR peak to crystallographic sites.
Use of DFT GIPAW in support of advanced 2D NMR techniques
F. Pourpoint, A. Kolassiba, C. Gervais, T. Azais, L. Bonhomme-Coury, C. Bonhomme, F. Mauri, First Principles
Calculations of NMR Parameters in Biocompatible Materials Science: The Case Study of Calcium Phosphates, β-
and γ-Ca(PO3)2. Combination with MAS-J Experiments, Chemistry of Materials. 19 (2007) 6367-6369.
GIPAW ApplicationsNMR Crystallography: NMR supported structure refinment
Use of NMR shifts to refine structures
Soon in glasses ?E. Salager, R.S. Stein, C.J. Pickard, B. Elena, L. Emsley, Powder NMR crystallography of thymol, Phys. Chem.
Chem. Phys. 11 (2009) 2610
GIPAW ApplicationsAccouting for motional averaging
Use of MD trajectory and averaging to account for finite temperature(motion) effects
Ave
rag
e ch
emic
al s
hie
ldin
g /
pp
m
Sta
ndar
d d
evia
tion
of t
he
mea
n /
pp
m
Number of configurations
64 25619264 M. Robinson, P.D. Haynes, Dynamical effects
in ab initio NMR calculations: Classical force
fields fitted to quantum forces, J. Chem.
Phys. 133 (2010) 084109.
Must be developped for Glasses ( but coming soon. . . ).
GIPAW ApplicationsCorrelation between low-energy vibrations and disorder
Disorder correlated to vibrational properties ? A NMR answer . . .
S. Cadars, A. Lesage, C.J. Pickard, P. Sautet,
L. Emsley, Characterizing Slight Structural
Disorder in Solids by Combined Solid-State
NMR and First Principles Calculations, The
Journal of Physical Chemistry A. 113 (2009)
902-911.
GIPAW ApplicationsChemical disorder in ceramics
Sensitivity of NMR to next-nearest neighbors
(a)
(d)
(a)
(e)
S.W. Reader, M.R. Mitchell, K.E. Johnston, C.J. Pickard, K.R. Whittle, S.E. Ashbrook, Cation Disorder in
Pyrochlore Ceramics: 89Y MAS NMR and First-Principles Calculations, The Journal of Physical Chemistry C. 113
(2009) 18874-18883.
GIPAW ApplicationsEffect of surface. ZnSe Nanoparticules
Solid-state NMR: strong disorder (line broadening) despite with highdegree of positional order
Electronic disorder spreads beyond 1 nm below the surface
S. Cadars, B.J. Smith, J.D. Epping, S. Acharya, N. Belman, Y. Golan, B.F. Chmelka, Atomic Positional Versus
Electronic Order in Semiconducting ZnSe Nanoparticles, Phys. Rev. Lett. 103 (2009) 136802.
Combining Molecular Dynamics with NMR-GIPAW
17O NMR in alkali tetrasilicate glassClassical vs Ab Initio S. Ispas, T. Charpentier et al. Solid State Sci. 2009
-40-200204060 MAS dimension (ppm)
-50
-40
-30
-20
-10
0Isot
ropi
c di
men
sion
(ppm
)
-40-200204060MAS dimension (ppm)
-50
-40
-30
-20
-10
0Isot
ropi
c di
men
sion
(ppm
)
EPCP
1,52 1,56 1,6 1,64 1,68
Si-NBO distance (Å)
2
3
4
Cq (M
Hz)
CPEP
-60-50-40-30-20-10010Isotropic dimension (ppm)
Simulation
Experimental
Exp.
EP
NBO BO
NBO
BO (a)
(b)
(c)
(d)
CP
fpNMR provides complementary data (diffraction) for assessing MD
models
A Monte Carlo / MD Hybrid ApproachModeling Glass Structure: Bond Switching Algorithm
0 200 400 500 510 520 530Time (ps)
0
1000
2000
3000
4000
Tem
pera
ture
(K)
NMR
Molecular Dynamics : Monte Carlo + Ab Initiosupercell ~ 100 - 1000 atoms
Relaxation
ab initio MD Car-Parinello
Random Network Generation
0K
Bond Switching Algorithm
E0[ρ(r)]
V = α (∆rij)2+β(∆Θijk)
2
Defect Free Vitreous SilicaContinuous Random Network
Simulation of NMR SpectraThe simple approach
-120-80-400408017O δMAS / ppm
-60
-40
-20
0
20
40
17O
δIS
O /
ppm
DAS @ 9.4 T
-120-80-400408017O δMAS / ppm
-60
-40
-20
0
20
4017
O δ
ISO /
ppm
DAS @ 9.4 T
Experiment
Clark et al. PRB 2004
Simulation of NMR SpectraKernel Density Estimate Approach
3 4 5 6 717O CQ / MHz
20
30
40
50
60
70
17O
δis
o / pp
m
CQ , η, δisoi ⇒ p (CQ , η, δiso)
Kernel: p(x) =∑
i
KHi(x− xi)
I (~ν) =
∫p (CQ , η, δiso)
× Ith (~ν;CQ , η, δiso)
Simulation of NMR SpectraKernel Density Estimate Approach
Direct Simulation
-120-80-400408017O δMAS / ppm
-60
-40
-20
0
20
40
17O
δIS
O /
ppm
DAS @ 9.4 T
KDE simulation
-120-80-400408017O δMAS / ppm
-60
-40
-20
0
20
40
17O
δIS
O /
ppm
DAS @ 9.4 T
Experiment
-120-80-400408017O δMAS / ppm
-60
-40
-20
0
20
40
17O
δIS
O /
ppm
DAS @ 9.4 T
Experiment
Clark et al. PRB 2004
Analysis of NMR parameter distributionKernel Density Estimate Approach
Theoretical points
3 4 5 6 717O CQ / MHz
0
0,2
0,4
0,6
0,8
1
17O
η
Estimated Distribution
3 4 5 6 717O CQ / MHz
0
0,2
0,4
0,6
0,8
1
17O
η
Introduction of a correlated 3D NMR parameter distribution:
p (CQ , η, δiso) = G (CQ − CQ)× G (η − fη(CQ))× G (δiso − fδ(CQ))
Quantitative analysis of Experimental data
-120-80-400408017O δMAS / ppm
-60
-40
-20
0
20
40
17O
δIS
O /
ppm
DAS @ 9.4 T
Experiment
Clark et al. PRB 2004
-120-80-400408017O δMAS / ppm
-60
-40
-20
0
20
40
17O
δIS
O /
ppm
DAS @ 9.4 T
Fit
Charpentier et al. JPC 2009
Experimental data can be well described in term of geometricaldisorder only.
Reconstructing the Bond Angle Distribution (BAD)NMR / Structure relationships F.Angeli, O. Villain et al., Geochem. Chim. Acta 2011
A new Tool: the first-principles (fp) NMR approachCombining Molecular Dynamics simulations (MD) with fp NMR calculations.
0 100 200 300 400 500 600 610 620 630Time (ps)
0
1000
2000
3000
4000
Tem
pera
ture
(K)
Melt & Quench Method
LiquidEquilibration
Quench
Relaxation
rigid ions
Relaxation to 0K
NMR
first-principles (ab-initio)
Classical MD
Rate 10 K/ps
Vij + ( Vijk )
Oc(2-Y)-+Os
Y-
Shell model
O2-
core shell (m=0)
DFT GeometryOptimization
DFT-NMR GIPAW
43Ca MQMAS in CaSiO3 Glass
-4004080120MAS dimension / ppm
-40
0
40
80
120
Isot
ropi
c di
men
sion
/ pp
m
+++
CS
QIS
-4004080120MAS dimension / ppm
-40
0
40
80
120
Isot
ropi
c di
men
sion
/ pp
m
+
CS
QIS
43CaMQMAS
-4004080120MAS dimension / ppm
-40
0
40
80
120
Isot
ropi
c di
men
sion
/ pp
m
+
CS
QIS
-4004080120MAS dimension / ppm
-40
0
40
80
120
Isot
ropi
c di
men
sion
/ pp
m
+
CS
QIS
CaO6
CaO5CaO7
⇒ Including polarization effects (O2−): Improved Q(n) description.A. Tilocca, N.H. de Leeuw, A.N. Cormack , PRB 2006, 73, 104209.
⇒ The fpNMR package: Analysis of MD-GIPAW outputs
J Phys Chem B 108, 4147, 2004; J Phys Chem C 113, 7917, 2009; PCCP 12, 6054, 2010
Topology of vitreous B2O3 G. Ferlat, T. Charpentier et al., PRL 2008
Topology of vitreous B2O3
0 10 20 30
q / A-1
0
0,5
1
1,5
2
S(q)
/ ar
b. u
nits
ExpMD
fring = 22%
0 10 20 30
q / A-1
0
0,5
1
1,5
2
S(q)
/ ar
b. u
nits
ExpMD
fring = 75%
S(q): poor sensitivity to Bond Angle ?
Topology of vitreous B2O3
-400-200020040017O chemical shift / ppm
ExpMD
fring = 22%
O(ring)
O(non-ring)
-400-200020040017O chemical shift / ppm
ExpMD
fring = 75%
O(ring)
O(non-ring)
NMR: high sensitivity to Bond Angle
Molecular Dynamics versus NMRGIPAW provides an integrated approach to analyse NMR data
MAS NMR
MD-GIPAW
Molecular Dynamics versus NMR
Many 1D-2D NMR approches
STATIC, MAS, MQMAS, STMAS, DOR, DAS, MQDOR...
DFT Calculations Structure
NMR Hamiltonian
NMR Simulations
DFT vs Experiments
Many 1D-2D NMR approches
STATIC, MAS, MQMAS, STMAS, DOR, DAS, MQDOR...
DFT vs Experiments