Solid State NMR of Glass - Modelling NMR spectra of glass...

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Solid State NMR of Glass Modelling NMR spectra of glass from first-principles Thibault Charpentier CEA / IRAMIS / SIS2M Laboratoire de Structure et Dynamique par R´ esonance Magn´ etique GDR Verre, 9-13 April 2011

Transcript of Solid State NMR of Glass - Modelling NMR spectra of glass...

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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

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Introduction

Basics of NMR: Interactions, MAS, MQMAS

NMR of disordered Materials

NMR from first-principles

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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 . . .

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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

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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)

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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 . . .

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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)

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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

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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 )

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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).

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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

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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 ?

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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.

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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

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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)

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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

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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+

)

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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.

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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

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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

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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.

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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

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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)

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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

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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)

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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 !).

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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

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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.

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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

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(Experimental) Solid State NMR

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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

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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"

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High Resolution NMR of quadruplar nucleiMagic Angle Spinning: one example

27Al NMR in NaAlH4

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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)

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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)

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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)

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High Resolution NMR of quadrupolar nucleiMQMAS at work in a crystalline sample

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Solid State NMR of disordered materials

Each site characterized by a NMR parameter distribution.

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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

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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.

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High Resolution NMR in glassThe power of oxygen-17 MQMAS NMR

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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)

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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) ?

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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)

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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 !

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Combining MD simulations with fp NMR calculationsGIPAW: C.J. Pickard & F. Mauri, PRB 2001

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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)

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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

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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)

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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

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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.

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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

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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.,

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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

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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.

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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.

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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

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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. . . ).

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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.

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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.

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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.

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Combining Molecular Dynamics with NMR-GIPAW

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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

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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

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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

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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)

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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

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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))

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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.

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Reconstructing the Bond Angle Distribution (BAD)NMR / Structure relationships F.Angeli, O. Villain et al., Geochem. Chim. Acta 2011

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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

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Topology of vitreous B2O3 G. Ferlat, T. Charpentier et al., PRL 2008

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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 ?

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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

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Molecular Dynamics versus NMRGIPAW provides an integrated approach to analyse NMR data

MAS NMR

MD-GIPAW

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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