13th Oxford School on Neutron Scattering

St. Anne's College, University of Oxford 2 - 13 September 2013

Chemical Applications of Neutron ScatteringPart 1

Elastic Scattering and Structural Studies

Alberto AlbinatiUniversity of Milan, Department of Chemistry

Neutron Properties

• Zero Electric Charge: Negligible absorption, scattering from the bulk.

• @ 293.6 K for a “neutron gas”:

E = 25 meV, v ≈ 2.2 km s-1, ν ≈ 200 cm –1 ≈ 6 x 1012 Hz, λ = h/mv ≈ 1.8 Å

• Neutron Scattering is a Nuclear Process:

• De Broglie Wavelength is Comparable with Interatomic Distances: Bragg Scattering.

• The Energy of Thermal Neutrons is Comparable with the Energy of Molecular and Lattice Vibrations (Phonons): Inelastic Coherent & Incoherent Scattering Can Probe Lattice and Molecular Vibrations

Atomic Scattering Factors for X-rays

( ) ( ) exp 2 ( )f i dρ π= ∫S r S r r

2

0

sin 2 ( )( ) 4 ( )2 ( )

Srf S r r drSrππ ρ

π

∞

= ∫

From R. Pynn . Neutron Scattering: a Primer. Los Alamos Science (1990)(www.mrl.ucsb.edu/~pynn)

COHERENT and INCOHERENT NEUTRON SCATTERING

( ) [ ]

[ ]

2

'

2

'

'

e p

p

xp

e

ex

xR R'R,R

R R RR R

'

RQ.R Q.(R

Q.(R-R

R')

')RR

d b i b b id

b b ib

σ= = − =

Ω

= +

∑

∑

∑

∑

∑

2 2R R

Rb N b=∑

[ ]

[ ] [ ]

''

'2 2'

' '

2

exp

exp exp

R R

R

RR

R RRR R R

b b i

i N b N b iN b

=

= = − +

∑

∑ ∑∑

Q.(R-R')

Q.(R-R') Q.(R-R')

( ) ( )22

2 2 expRR

N bN bd id

bσ= +

Ω− ∑ Q.R

( ) ( )222 Incoherent Scattering Cross Section N b b N b b− = −

“bR” varies from isotope to isotope

assuming no correlation ‹bRbR’› = ‹bR›‹bR’› = ‹bR›2

Neutron Scattering Cross Sections

24coh bσ π=

COHERENT CROSS SECTIONS

Coherent Scattering depends on the correlation between the positions of the same nucleus at different times and the positions of different nuclei at different times.

STRUCTURAL INFORMATION.

INCOHERENT CROSS SECTIONS

( )224incoh b bσ π= −

Incoherent Scattering arises from the random distribution of different isotopes with different scattering lengths. Incoherent Scattering depends on the correlation between the positions of the same nucleus at different times.

SPECTROSCOPY

Neutron Incoherent Cross-Sections

Bragg Scattering in Crystals

R = n + rR ≡ atomic position n ≡ lattice vector ≡ n1a1 + n2a2 + n3a3r(xyz) ≡ atomic position in the unit cell

.

n

r

R

2 2 2 2

b e exp ( ) b exp ( ) exp ( ) b exp ( )iR r r

dI i i i idσ = = == = Ω

∑ ∑ ∑ ∑ ∑Q.

R n r n

R

rnQ. Q. Q. Q.r rn

4 sinπ ϑλ

=Q

2πλ

=k

Bragg Scattering in Crystals

2πsinϑλ

=S

2 2 2 21 2 3

2 2 2

sin N sin N sin Nexp ( )sin sin sin

h k lih k lπ π ππ π π

=∑n

nQ.

if Q = H

32

1 2 3(2 )N N N ( )Vcell

dI Fdσ π δ = = Ω

∑ HH

-Q H

b exp ( )cohrF i=∑H

rH r FH ≡ Structure Factor

In Crystallography:

b exp2πi( ) b exp2πi( )coh cohhkl j j j j j j

j jF hx ky lz= = + +∑ ∑rS * * *

1 2 3h k l= + +S a a a

1 2 3x y z= + +r a a a

Bragg Scattering in Crystals

and finally atoms do “move”….

b ex ( ) ( )pr rF i T=∑Hr

H r Q

where “Tr(Q)” is the temperature factor of atom “r”.

for an harmonic crystal

Tr(Q) = exp(-2π⟨Q•r)⟩2)

The Temperature Factor and the P.D.F.(Probability Density Function)

T(Q) = exp-½[⟨(Q • u)2⟩]

p.d.f. of an atom ( pκ(u) ) is the probability of finding an atom in the volume element d3u when it is displaced by u from its rest position.

If ρ0(u) ≡ scattering density

ρ κ(u) = ρ0(u) ∗ pκ(u)

F.T. (ρ κ (u)) = FT(ρ0,κ(u)) x FT(p κ(u))

T(Q) = ∫ pκ(u) expi(Q•u) d3u

pκ(u) = (2π3)-1∫ T(Q) exp-i(Q•u) d3Q

( )23

2 22( ) 2 exp

2up u uu

π

= ⟨ ⟩ − ⟨ ⟩

p.d.f. for a SHO is gaussian

Probability Density Function

Temperature factor for an isotropically vibrating atom.Both curves are Gaussians in the harmonic approximation

Temperature Factors and Atomic Vibrations

2 2

T 2 22

4 sin( ) exp 2 ( ) exp ( )isoT u uκπ ϑπ κ κλ

= − = − = H H H

2

2

sinexp B ϑλ

−

22 coth

8 2ih hu

kTν

π µν ⟨ ⟩ =

U = t + l ∧ r

T( ) exp 2anisTκ π = − H H UH

There are not enough of them! The fluxes are too low and the experiments take too long!

The samples needed are too big!

For powder diffraction at least 100 mg; For single crystal elastic a few mg

For single crystal inelastic 100 -1000 mg.

Disadvantages of neutron scattering

G. Lander

BNL Single XXl Diffractometer on H6

ADVANCES IN COORDINATION CHEMISTRY ARE LINKED TO

ADVANCES IN INSTRUMENTATION

D19 “Old Banana Detector”

D19 New Detector 2007

trans - W(C-Mesityl)(dmpe)2H

D19 @20K

V = 2667 Å3; C2/c

W – H1 1.84 (2) ÅW – C5 1.868 (9)C4 – C5 1.461 (8)

VIVALDI @ ILL

[(C5Me4SiMe3)YH2]4]

R e f le c tio n s a t o n e s c a t te r in g a n g le (9 0 ° ) re s o lv e d a t d i f fe re n t T O F ' s

P o r t i o n o f r e c i p r o c a l s p a c e sa m p le d fo r

2θ < 2θ < 2θ a n d t < T O F < t

m inm in m a x

m a x2θm a xm in2θ

2θm a xm in2θ

In c i d e n t B e a m

1 /λ m in

1 /λ m a x

S p h e r e o f r e f l e c t i o n a t t m a x

S p h e r e o f r e f l e c t i o n a t tm in

Ewald Spheres

VIVALDI

Typical neutron Laue pattern from (C5Me4(SiMe3) -Y)4H11[C5Me4(SiMe3)*W], Stewart, Bau et al.

SXD - ISIS

Absorption

( )1 p q

V

A e dVV

µ− += ∫0 220 ψ

Extinction I

•Reduction of Intensity by scattering not by absorption

•Primary Extinction: Weakening of Intensity by Multiple Reflections in the Crystal

Extinction I

00

1

02

I I ItI I It

σ σ

σ σ

∂= − +

∂∂

= − +∂

Zachariasen 19671) Spherical Crystal2) Ideal Perfect Crystal

s ≡ diffracting power

1Intensity reduction ( ) = 1 t

φ σσ+

Extinction II•Secondary Extinction: Weakening of the beam due to the shielding of the inner planes by the outer planes•Most important for strong reflections at low sinθ/λ

Mosaic Crystal

Type IDepends mainly on g(mosaic spread)

Zachariasen 1967

Type IIDepends mainly on t(radius of mosaic blocks)

I = Iobs(1 + 2gIcalc)

Fcrctd = Fok[1 + 0.001|Fc2|λ3/sin2θ]-1/4

Zachariasen 1967

(Shelxl)

RuH

HP

PRu

P

P

RuHH

P

P

Ru

P

P

H

HHHH

C2H4

H2

HHHH

C2H4

H2

1

2

3

4

Reactivity of "Ru(PCyp)3" vs. "Ru(PCy)3"

Selective Deuteration of "RuH6"

RuH

H

P

P

HHH

H

1

2

2'

3

3'

D2 / solvent

RuD

D

P DDHH

DDHH

DD

H H

PDD

HH

DDH

HDD

HH

DDDD

12 3

3'2'

pentane

3bar D2

C6D6 C6D6sol.

Pentane/stirring3 d

3bar D23h

M-D≈91%

M-D≈91%C-D≈32%

D≈92%

C6D6

" RuH2(H2)2((Cyp)3)2 " vs. " RuD2(D2)2((Cyp)3)2 "

MD MH MD MH 0.840(2) Å 0.825(7) Å P-Ru-P 168.87(3)° 168.9(1)°0.840(2) Å 0.835(7) Å

C-H Activation Pathway in "RuH6 – trans-P"

The Structure of Na2Mg2NiH6

bcoh (Mg) = 5.375(4)bcoh(D) = 6.674(6)

Na – Mg 2.66 ÅNa – H ~ 3.3 ÅMg – H > 2.72 Å

a) exp. XRD pattern b) correct model c) Mg/D

K. Yvon & al. Inorg Chem. 48, 5052 (2009)

X-rays see the Centroid of Charges displaced in the direction of the bond

Positional and thermal parameters from X-ray diffraction may be biased

Positional and thermal parameters from neutron diffraction (nuclear scattering)

are not biased

In real molecules:

• Atoms participate in charge transfers

• Atoms deviate from spherical symmetries (lone pairs, incomplete shells)

• Atoms form covalent bonds sharing electron densities

Electron Density in Crystals: X-Ray Scattering

𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐(𝐇𝐇) = 𝑗𝑗𝑓𝑓𝑗𝑗exp(2𝜋𝜋𝜋𝜋𝐇𝐇 · 𝐫𝐫𝑗𝑗)𝑇𝑇𝑗𝑗(𝐇𝐇)

where fj’s are calculated for spherical atoms

Electron Density in Crystals: X – N Maps

, , , ,( ) exp(2 )calc j j jatoms

F f i Tπ= ∑ XN N NrH H

r𝑗𝑗,N ≡ r (x𝑗𝑗,y𝑗𝑗, z𝑗𝑗) neutron values - unbiased

Fcalc, N ideal molecule built from spherical atoms and neutron unbiasedparameters → correct geometry and no electron redistribution

Fobs, X obtained from X-ray diffraction are the F.T. of the actual electrondistribution

, ,1( ) ( ) exp( 2 )deformation obs calcF F iV

ρ π= − −∑NN

X-X

Hr H r

P. Coppens Science 158, 1577 (1967)

A Few Types of Hydrogen-Bonds

M

H-OH

Potential Energy Landscapes for Hydrogen Bonds

O

O

O

OH

Malic acid

D

O

H

OH

PhD

O

H

O

Ph

H

Proton Transfer in Terephtalic Acid

B.H. Meier & al., Chem. Phys. Lett. 108, 522 (1984)

KH2PO4 (KDP) – Ferroelectric Phase Transition

Bacon & Pease

Non- Classical “Weak” Interactions

ALn M Hδ− δ+HCl

M

H

H

Mδ+

δ−

M

H-OH

M

AH

LN

CHO

HA L =

N

CH

O

Pt PEt3

Cl

Cld(M….H) ≈ 2.5 – 2.9 Å

Pt(NH3)(gly)Cl2•(H2O)

D19 @ 20KPt – N1 2.040(2) Å

Pt – H1 2.89(1) Å

N – C 1.480(3) Å

1.30 x 0.50 x 0.50 mm

Angew. Chem. Int. Ed. 2010, 49, 7440

Proton Transfer to CpRuH(CO)(PCy3)

Shubina, Limbach & al. Eur. J. Inorg. Chem. (2001) 1753

Reactions Involving Hydrido-Complexes

Homogeneous HydrogenationR2

R1

H

R2R1+ H2

[RhCl(PR3)3]

Olefin PolymerizationR

R R RH H HAlCl3

["Al-(CH2)n-H"]

Olefin HydroformilationR2

R1

CHO

H

R2R1+ H2 + CO +

CHO

R2R1[CoH(CO)4]

Materials for Hydrogen Storage(new entry)

3

2

iX

4 3 6

T 1 2NaAlH Na AlH + Al + H

3 3

Types of Metal - Hydrogen Interactions.

Classical Metal Hydrides:

Ln MH

H

Ln M H(n) MLn

(H)n

MM

M

M

L

L

L

L

(n+)

"Non- Classical" Metal Hydrides: MH

HM

H

H

Non- Classical “Weak” Interactions:

Ln M Hδ− Xδ+H

P

P

ClCl Cl

Cl

IrH

H

H

H

HH

Irδ+P

P

X-ray Structure of [(Cl5C6)(PMet3)2Pt-H-Pt(PMet3)2(C6Cl5)]+

X-ray Structure of [(Cl5C6)L2Pt - H - Ag - H - Pt(C6Cl5)]+ (R.T. data)

Schematic Catalytic Cycle for Homogeneous Hydrogenation

Metals break H-H bonds but HOW?

H-H Distances (Å) from Single XXl Neutron Diffraction

[Ru(dppe)2(H)(H2)]+ 0.82(3) [Os(en)2I(H2)]+ 1.224(7)

[Ru(cp*)(dppm)2(H2)]+ 1.08(3) [Os(en)2(OAc)(H2)]+ 1.34(2)

Ir(PiPr3)3Cl2(H)(H2) 1.11(3) [Os(PMe2Ph)3(H)5]+ ≥1.49(4)

Ir(PiPr3)2I(H)2(H2) 0.856(9) Ir(PiPr3)2Br(H)2(H2) 0.819(8)

Backdonation is critical for the stability of M-H2 Complexes

η2 0.8 – 0.9Å stretched 1.0 – 1.2Å weak interactions ≥ 1.3Å ≥1.7Å

The Structure of RuH2(H2)2((Cyp)3)2D19 @20K

H – H 0.825(7) 0.835(7) Å

Ru - (H1) 1.730(5) 1.753(5) Å

Ru - (H2) 1.745(5) 1.764(5) Å

Ru - H 1.628(4) 1.625(4) Å

P - Ru - P 168.9(1)°

Ru(H)2(H2)(P(cyp)3)2: a Parametric Study on D19

20K

100K

60K

180K

RuH2(H2)2(P(Cyp)3)2

20K 60K 100K 180K

H11 – H12 0.825(8) 0.796(8) 0.794(8) 0.73(5)

Ru – H1 1.628(4) 1.618(4) 1.626(4) 1.69(2)

Ru – P1 2.307(3) 2.309(3) 2.310(2) 2.325(8)

P1 – Ru – P2 168.9(1) 168.8(1) 168.72(9) 178.0(5)

H - H Distances (Å) and TLS Correction

Fe(PEtPh2)3(H)2(H2) 0.82 (1) 1.05

[Fe(dppe)2(H)(H2)][BF4] 0.82 (2) 0.85 0.90

[Os(dppe)2(H)(H2)][PF6] 0.79 (2) 0.96 0.99

[Os(dppe)2(Cl)(H2)][PF6] 1.15 (3) 1.24 1.19

[Os(en)2(I)(H2)] 1.224 (7) 1.272

[Ru(cp*)(dppm)2(H2)][BF4] 1.08 (3) 1.09 1.02

Zilm, K.W.; Millar, J.M. Adv. Magn. Opt. Reson. 1990, 15, 163

Uncorrected TLS Solid State NMR

T [K]0 50 100 150 200

δ [A2]

0

1

2

3

) sT

ε

ε

δ0

Θ'E

Σx(T) = AgVδ(1/ω,T)V’g’A’ + ε

Molecular Motion from the Temperature Dependence of ADP’s

ADPs, determined experimentally at several temperatures

Low frequency, large-amplitude vibrations(ω), e.g. librations, translations and deformations (V)

Intramolecular, high frequency vibrations and disorder (ε) (~temperature independent)

H.B. Bürgi, S. Capelli Acta Cryst. A56, 403 (2000)

Molecular Motion from the Temperature Dependence of the ADPs

1(( ,) ) TX T TT Tω−= +∑ Ag gδ AV V ε

c(2

) oth2

j

j b

hhk T

Tω

ω

= δ

X TT

= +

∑

T SA A ε

S L

Σ(T) observed atomic mean square displ. at multiple TA transformation matrix from atomic to normal modes coordsV eigenvectors matrixε 3x3 upper triangular tensor

contribution to ADPs from high ν small amplitude vibrationsδ(T) diagonal matrix of mean square normal modes displacements

For each normal mode j

Considering only T and L

Burgi & Capelli Acta Cryst A, 403 (2000)

Naphthalene : ADP’s and rms difference surfaces

10 K 5 K

X-ray (SR) Neutron

30 K

150 K

The Structure of RuH2(H2)2((Cyp)3)2D19 @20K

1) Rigid-body description: the motion of the molecule as a whole is defined by 6 degrees of freedom :

Lx, Ly, Lz, Tx, Ty, Tz

Serious problems in describing the out-of-plane displacements of the H atoms involved in the di-hydrogen groups

ε(H) 0.017(2) 0.001(1) 0.005(1)0.019(2) -0.006(1)

0.058(2)

2) Rigid-body + internal rotations of the di-hydrogen groups:8 degrees of freedom:Lx, Ly, Lz, Tx, Ty, Tz, U1, U2

Significant improvement in the description of the out-of-plane displacements in the di-hydrogen groups

ε(H) 0.018(2) 0.000(1) 0.000(1)0.018(2) 0.005(1)

0.028(2)

normal mode frequencies for di-hydrogen rotations: 104 and 170 cm-1

MODELS OF MOTION USED TO ANALYSE THE 20, 60 AND 100K NEUTRON DATA

(with both THMA and ADP-analysis)

[Albinati A., Capelli S.C., Mason S.A., (2013) in preparation. ]

Model T (K) R (%) Goof Obs Par Obs/Parratio

Degrees of freedom

A 2060

100

413633

5.165.015.82

54 20 2.70 6 librations, 6 translations, 8 coupling terms

B 2060

100

231917

3.833.393.83

54 32 1.69 6 librations, 6 translations, 8 coupling terms + 6 components of the librations of the di-hydrogen groups

C all 12 1.62 162 28 5.79 1 librational frequency, 3 translational frequencies, 24components of the 4 temperature-independent ε-tensors

D all 9 1.16 162 32 5.06 3 librational frequencies, 3 translational frequencies, 2eigenvector components, 24 components of the 4temperature-independent ε-tensors

Models used for the ADP’s analysis

T RU-H11 RU-H12 RU-H21 RU-H22(K) TLS ADP TLS ADP TLS ADP TLS ADP

________________________________________________________20 1.7397 1.7475 1.7618 1.7709 1.7732 1.7819 1.7537 1.7610 60 1.7322 1.7412 1.7606 1.7710 1.7699 1.7786 1.7488 1.7562

100 1.7435 1.7540 1.7543 1.7682 1.7673 1.7755 1.7491 1.7580

T H11-H12 H21-H22(K) TLS ADP Exp TLS ADP Exp_____________________________________________20 0.831 0.899 0.825(8) 0.840 0.911 0.835(8)60 0.804 0.887 0.796(8) 0.826 0.902 0.820(8)

100 0.806 0.916 0.794(8) 0.820 0.910 0.812(8)

Bond Distances (Å) Corrected for Libration

Dihydrogen Ligands:Low Frequency Normal Modes

170.3 cm-1104.5 cm-1

P

P

RuH12

H11

H21

H22

H1H2

H-H Distances (Å) vs. JHD (Hz)

W(CO)3(PiPr3)2(H2) 0.82 (1) 34.0

[Fe(dppe)2(H)(H2)]+ 0.82 (2) 30.5

[Ru(dppe)2(H)(H2)]+ 0.82 (3) 32.0

[Os(dppe)2(H)(H2)]+ 0.79 (2) 25.5

d (H-H) JHD

We need more information…….

Another technique

End of Part 1