13th Oxford School on Neutron Scattering

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

Chemical Applications of Neutron ScatteringPart 2

Mainly Inelastic Scattering:Spectroscopy and Dynamics

Alberto AlbinatiUniversity of Milan, Department of Chemistry

Chemical Applications of Neutron Scattering

Part 2: Inelastic Scattering

• INS Spectroscopy: Transition Metals Hydrides

• Rotational Tunnelling and the Nature of the M-H2

Bond

• Combined use of Diffraction, Spectroscopy and ab-

initio calculations

• Hydrogen Storage

Incoherent Scattering 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.

NO INTERFERENCE EFFECTS ≡ SPECTROSCOPY

INS spectrum from a hypothetical molecular crystal

Inelastic and Quasielastic Neutron Spectroscopy

∆E hτ π≈ 2

Time Scale τ Resolution ∆E Spectroscopic Technique

10-11 sec 10 - 100 meV Direct Geometry TOF

10-9 sec 0.3 - 20 meV Backscattering Crystal Analyzer

10-7 sec 5 neV - 1 meV Spin Echo

Q =4πλ

ϑsin

MomentumTransfer Q(Å-1)

Distance (Å) Regime

0.05 100 Continous or Macrospic Diffusion

5 1 Atomic or Microscopic Diffusion

INELASTIC INCOHERENT NEUTRON SCATTERING:

•The energy of the thermal neutrons is comparable to that of the lattice and molecular vibrations.•The incoherent part of the scattering cross-section (σinc) arises from the random distribution of different isotopes with different scattering lengths.

•The incoherent part of the scattering cross-section describes the singleparticles dynamics: Vibrational and rotational spectroscopy.•The intensity scattered by each mode depends on the value of the incoherent scattering cross-section ( σinc ) and the atomic displacements.•The incoherent cross section for Hydrogen is very large: modes involving H atoms will dominate the INS Spectrum

σinc (H) = 80.27 (barn)

σinc (D) = 2.05 (barn)

σ(inc) σ(coh) σ(abs)

Inelastic neutron scattering measures atomic motion

22 )' ( ,coh

coh

d kb Nd dE

Sk

ωσω

=

Q

22 )' ( ,incoh

inc hi

o

d kb Nd dE k

Sω

ωσ =

Q

Inelastic coherent scattering measures correlated motions of atoms

Inelastic incoherent scattering measures self-correlationse.g. vibrations, diffusion

( )1 ( , ), )2

( i tG t e d dtS ωωπ

−= ∫∫ Q rQ r r

( )1 ( , )2

( , )ii t

sG t dS e d tω

πω −= ∫∫ Q rr rQ

Correlation Functions

Scoh (Q, ω) F.T. G (r, t)

Sinc (Q, ω) F.T. Gs (r, t)

• G(r, t) ≡ Probability of finding an atom at r and at time t when there is an atom at r = 0 at t = 0.

• Gs(r, t) ≡ Probability of finding an atom at r and at time t if the same atom was at r = 0 at t = 0.

INCOHERENT INELASTIC NEUTRON SCATTERING

( ) ( )2d 1 , ,

d d 4f

coh coh inc incf i

kS S

E kσ σ ω σ ω

π= + Ω

Q Q

( )( ) ( )( ) ( ) ( )

22 ' 2 2 2

,

1 1d 2 2 x . expd d 2

inc jinc rj r

j rj r

n bk Q uE k m

σ δ ω ωω

+ ± = −

Ω ∑ ∑q

q Q u qq

( ) ( )2 22 '2d 1 1 exp 2

d d 2 2 2inc

inc

Q u Zk b n W NE k m

ωσω

= + ± − Ω

2 '2d ( , )

d dinc

inc inck b S

E kσ ω=Ω

Q ( ) ( )2 2, exp 2incS Q u Wω = −Q

for a powder sample we can average

at very low T for hydrogenous materials

The INS Difference-Spectrum of [P2N2Zr]2 (µ-H)(µ-N2H)

21 2 coth

8 2h hu

kTν

π µν =

The Structure of [Co(CO)15H]−

D. Hart & al.JACS 1981, 103 1458

[Co6(CO)15]2- + H+ → [HCo6(CO)15]-

NMR (solution) δ ~ +3

Hydride δ ~ -5 -40

Formyl δ ~ +5 +10

Cs[Co6(CO)15H]IN1 - ILL (30g)J. Howard (1983)

I.R. K[Co6(CO)15H] (CsI )Longoni & Stanghellini (1987)

K[Co6(CO)15H]Be Filter - LANSCE (1987)

800 1400 cm-1

15 K

TOSCA

TFXA

TOSCA at ISIS

INS & I.R. Spectra of X[Co6(CO)15H]

K[Co6(CO)15H] in CsI

900 1000 1100 1200 1300 1400-0.1

0.0

0.1

0.2

0.3

0.4

0.5

S(Q

,ω) (

a. u

.)

ω (cm-1)

H-D PPNCo6[CO]15 DFT calculation

T = 20K

INS & I.R. Spectra of X[Co6(CO)15H]

K[Co6(CO)15H] in CsI

900 1000 1100 1200 1300 1400-0.1

0.0

0.1

0.2

0.3

0.4

0.5

S(Q

,ω) (

a. u

.)

ω (cm-1)

H-D PPNCo6[CO]15 DFT calculation

T = 20K

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

INS Spectra of M-(H2) Complexes

M-(η2-H2) Bonding

Non-classical Hydrides and Rotational Tunnelling Spectroscopy

Rotational Tunnelling: Single Particle Rotation

For a single particle model (i.e.: V(ω) describes the system):

i i iεΗΦ = Φwhere

2 ( )B V ϕΗ = ∇ +

( )( ) 1 cos2j

V jV jn nϕ ϕ= −∑ n=2 twofold potentialn=3 threefold potential

2 / (2 )B I=

B: H2 (7.3 meV) > NH4+, NH3 (0.782 meV) > CH4, -CH3 (0.655 meV)

The level splitting is proportional to V(φ) and B

Single Particle Rotation: Twofold potential

For a 1D rotor in a twofold-potential:

21( ) cos 22V Vϕ ϕ=

2

221 cos 22B V Eϕ

ϕ ∂− + Ψ = Ψ ∂

Eigenvalues (in units of B) are determined by the ratio V(f)/B

W. Press Single Particle Rotations in Crystals (Springer)Prager, Heidemann Chem. Rev. 97, 2933 (1997)

The new IN5 Spectrometer

INSTITUT MAX VON LAUE - PAUL LANGEVIN

Detectors

Effective Height 3.0 m~3000 L 3He + 570 L CF4

4.75 bar 3He + 1.25 bar CF4

147.5° Hor - ± 20.55° vert

Rotational Tunnelling in [Fe(H)2(H2)L3] and [Ru(H2)(H)(dppe)2]+

Rotational Tunnelling in Ru(H2)2(H)2(Pcyp3)2

-1.0 -0.5 0.0 0.5 1.00.00

0.02

0.04

S(Q

,ω)

energy transfer, meV

RuH6,λ=6.5Α 4K 32K 43K 53K

Rotational Tunnelling in Ru(H)2(H2)2L2

L = P(cyp)3L = P(cy)3

-0.6 -0.4 0.0 0.4 0.6meV

L = P(cy)2(tBut)

Vφ = 0.99, 1.09 kcal/mol

VIBRATIONAL FREQUENCIES and TUNNEL SPLITTINGS for M-H2 COMPLEXES

Compound ν(H-H) τ(H-H) ωt Vt[cm-1] (IR) [cm-1] [cm-1] [kcal/mol]

W(CO)3(P iPr3)2(H)2 2695 370 - 340 0.73 2.4

W(CO)3(PCy3)2(H)2 2690 380 - 325 0.89 2.2

[Fe(PP3)(H)(H2)]+ 276 - 259 1.15 1.9

[Ru(PP3)(H)(H2)]+ 225 – 184 2.58 1.6

IrBr(P iPr3)2(H)2(H2) 18.9 0.53

IrI(P iPr3)2(H)2(H2) 9.8 0.98Ir

P

PX

H HH

H

[(CH3)4Pb] Prager, Heidemann Chem Rev (1997)

(iPr3P)2IrI(H)2(H)2

Dihydrogen-Hydride Exchange in (iPr3P)2IrX(H)2(H)2

Ir

R3P

PR3

H(1)

H(2)

H(3)H(4)

X Ir

R3P

PR3

H(1) H(2)

H(3)

H(4)

X

A

Ir

R3P

PR3

H(1)H(2)

H(3)

H(4)

XB

Ir

R3P

PR3

H(1)

H(2)

H(3)

H(4)

X

C

Ir

R3P

PR3

H(1)H(2)

H(3)

H(4)

X

(iPr3P)2IrX(H)2(H)2

IrH

H

HH

X

PiPr3

PiPr3

X Cl Br I

Rotat. tunnelling freq. 20 19 6(ω, cm-1)

Rotat. barrier V2exp 0.51(3) 0.48(3) 1.00(4)

(kcal/mole)

Rotat. barrier Vcalc 0.37 (2.04) 0.42 (2.11) 0.66 (2.32)(PMe3 / PH3 kcal/mole)

H-H (exp) 0.78 (INS) 0.819(8) 0.856(9)

H-H (calc) 0.853 0.857 0.862

(iPr3P)2IrX(H)2(H)2: Observed and CalculatedExchange Energies (QENS & B3LYP)

Data @ 100, 175, 210, 250 K ∆Ea = 1.5(2) Kcal/mol

B3LYP/BS4 (reactant, intermediate, TS’s)∆ETS = 1.87 kcal/mol

Dihydrogen-Hydride Exchange in (iPr3P)2IrX(H)2(H)2

Ir

R3P

PR3

H(1)

H(2)

H(3)H(4)

X Ir

R3P

PR3

H(1) H(2)

H(3)

H(4)

X

A

Ir

R3P

PR3

H(1)H(2)

H(3)

H(4)

XB

Ir

R3P

PR3

H(1)

H(2)

H(3)

H(4)

X

C

Ir

R3P

PR3

H(1)H(2)

H(3)

H(4)

X

Rotational Tunnelling in Ru(H2)2(H)2(Pcyp3)2

*( )

0( )E T

kTT e − Γ = Γ

-1.0 -0.5 0.0 0.5 1.00.00

0.02

0.04

S(Q

,ω)

energy transfer, meV

RuH6,λ=6.5Α 4K 32K 43K 53K

ω = 0.73 0.83 meVV = 0.99 1.09 kcal/mol

E* = 1.6 kcal/molH/H2 exchange

H/H2 Exchange Mechanism

ΔE†(exp) = 1.65 KcaΔE†(calc) = 2.7 Kca

Rotational Tunnelling and QENS for Tp*Rh(H2)H2

2 4 6 8 10 12 14

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

Ln(W

L)

1000/T

Ea=0.23kcal/mol

Ea=0.42kcal/mol

ω = 0.8 meV

Tp*Rh(H2)H2: Exchange Path

E* = 3.9 kcal mol-1

Classical vs. non-classical: [PP3Co(H)2]+ and [ PP3Co(H2)]+

Co

P

HP

PP

Co

P

PP

P

H H

Co

P

HP

PP

H

PF6- BPh4

-

Red solid White solid

HOTf THF

White Form: [PP3Co(H)2]BPh4

Co – H 1.47 (7) Å (av)

Red Form: [PP3Co(H)2]PF6

H – H 0.65(8) Å 0.807 Å (calc)

Red Form: [PP3Co(H)2]PF6White Form: [PP3Co(H)2]BPh4

[PP3Co(H)2]BPh4 – H.P. Raman Spectrum

1500 1600 1700 1800 1900 2000 2100

0

2000

4000

6000

8000

10000

Pressure evolution of the H-Co-H stretching

Pressure (kbar)

23.0

20.8

18.8

16.2

13.2

10.7

8.8

6.0

4.6

1.9

Raman shift (cm-1)

The Hydrogen Storage Problem

Hydrogen as an Energy Vector

•Jules Verne The Mysterious Island (1 874).“… hydrogen and oxygen which constitute [water], used singly or together, will furnish an inexhaustible source of heat and light…”

•Max Pemberton The Iron Pirate (1 893).hydrogen from coal “ …fuels the most powerful engines

that have yet been placed on a battleship …”

Hydrogen Production

Burning 3.8L gasoline produces ~ 9Kg of CO2

Energy wise 3.8L gasoline ~ 1Kg of H2

CH4 + H2O CO + 3H2CO + H2O CO2 + H2

H2/CO2 = 2/1

•Biomasses•Photovoltaic•Electrolysis + Nuclear Power (Solar Energy)

J.J. Romm “The Hype about Hydrogen” (2004) Ch.4

1 Kg of H2 by electrolysis ≡ 32 Kg of CO2

Thermodynamics and kinetics of the adsorption /desorption process. -20<Qst(∆H) <-40 kJ/mol H2; Dchem>10-9cm2/s.

Capacity >6% wt, 60kg H2/m3 at RT, P<100 bar. ∼ 10% wt , at least, for the bare storage material itself.

Structural stability upon cycling/activation; Resistance against poisoning agents H2O, CO, CO2, N2, etc. Cost and Environment safety.

Parameters Values and Methods

Microscopically probe the interactions between H2 and individual adsorption sites – INS and Model calculations .

Proposed H2 Storage Materials

Mg2NiH4 LaNi5H6 H2(l) H2 (200 atm)

4Kg Hydrogen

2NaAlH4 2NaH + 2Al + 3H2↑

[Weller (2006)]

[Yaghi (2001)]

[Chem. Rev. (2004, 2012)]

0 20 40 60 80 100 1200.0

0.2

0.4

0.6

0.8

1.0

-9

-20

-17

-22

-23

Frac

tiona

l Site

Occ

upan

cy

Pressure, bar

-33, -31-35kJ/mol H2

-26

Van der Waals–a few kJ, electrostatic-<10 kJ/mol H2

Graphite, activated carbons, CarbonNanotubes, Na+ , Li+… -exchangedZeolites

Interstitial hydrides-LaNi5, Non-classical hydrides: M-(η2-H2) complexes of Transition Metals

Very likely a combination ofelectronic and dispersiveinteractions. Most challenging tomodel and characterize. It washoped that MOF’s would fall here.

Expected Interactions and Associated Thermodynamics

Rotational Energy Levels of the Hydrogen Molecule

Symmetry Properties Rotational Energy LevelsE = BJ(J+1)

Introduction of a Barrier to Rotation of the H2 Molecule

H2 Absorption in Nanoporous Materials

J. Eckert & al. JACS (2005)

8 10 12 14 16 18 20

S(Q,ω)

, arb.

units

Neutron energy loss, meV

SWNT

AC

Graphite

SWCNT

0 20 40 60 80 100 1200.0

0.2

0.4

0.6

0.8

1.0

-9

-20

-17

-22

-23

Frac

tiona

l Site

Occ

upan

cy

Pressure, bar

-33, -31-35kJ/mol H2

-26

Van der Waals–a few kJ, electrostatic-<10 kJ/mol H2

Graphite, activated carbons, CarbonNanotubes, Na+ , Li+… -exchangedZeolites

Interstitial hydrides-LaNi5, Non-classical hydrides: M-(η2-H2) complexes of Transition Metals

Very likely a combination ofelectronic and dispersiveinteractions. Most challenging tomodel and characterize. It washoped that MOF’s would fall here.

Expected Interactions and Associated Thermodynamics

Chemisorption of H2 in Fe -ZSM-5

ω = 4.2(2) cm-1 8.3(2) cm-1

NEAT @5K - λ = 5.1Å

Van der Sluys & al. JACS 1990, 112, 4831

Chemisorption of Molecular Hydrogen in: Cu–ZSM5H2/Cu 0.4

H2/Cu 2.0

ωτ ±0.80 cm-1 ±1.37 cm-1

IN5 @4K - λ = 7.0Å

-0.5 0.0 0.5

10 ÷4 K

45 ÷10 K

92 ÷47 K150 ÷92 K

200 K

Dihydrogen Adsorption Isotherms - H2 in Cu-ZSM5

Isosteric Heat of adsorptionH2 on Cu 39±4 - 73±4 kJ/mol

Pressure, bar0 14

H2/Cu

Q in

kJ/

mol

Abso

rbed

H2,

cc (S

TP)

:

Chem Phys Lett 449, 182 (2007)

Molecular Chemisorption at Unsaturated Transition Metal Binding Sites

Sorption Based Materials with Greater H2 - Binding Energy

(can reach > 20 kJ/mol)

⇓ ⇓ ⇓Bind Multiple DihydrogenLigands

Lighter Metals: alkali,alkaline earth hybrids

Density too high? Not enough binding sites?

Framework modifications: anionic frameworks, different metals…

⇓Combine two or more of these approaches in one material

The Effect of Framework Catenation

PCN-6 (15K) PCN-6’ (15K)

JACS (2008)

O. Yaghi (2010)O. Yaghi (2010)

Weak-H2 Chemisorption - HKUST-1

Peak at ~ 9.1 meV

Cu-BTCAimed at achieving heats of

adsorption of ~20 kJ/mol H2

S.S.-Y. Chui et al. Science 283, 1148 (1999)

ZIF-68

ZIF-69

ZIF’s: Zeolite Type Frameworks

Cl substitution on benzene ring in ZIF-69Banerjee & al. Science 319, 939, 2008.

-2

0

2

4

6

8

10

12

14

16

0 100 200 300 400 500 600 700 800P (torr)

Up

tak

e (

mg

g-1

ST

P)

Adsorption-69

Desorption-69

Adsorption-68

Desorption -68Adsorption-70

Desorption-70

ZIF-70

INS of H2 in ZIF-68, ZIF-69

Possible binding sites: ZnN4 cluster, Im, -NO2, organic, and -Cl (ZIF-69)

NEAT Spectrometer (BENSC) T = 5K

CPO-27-Co [Co2(dhtp)(H2O)•8(H2O)] (dhtp = 2,5- dihydroxyterephthalic acid)

P.C. Dietzel & al. Chem. Comm.(2006)

Georgiev, Albinati Eckert

CPO-27- M[M2(dhtp)(H2O)•8(H2O), M = Mg, Ni, Co]

(dhtp = 2,5- dihydroxyterephthalic acid)

Georgiev, Albinati Eckert

Dr. S. Rizzato, University of Milan

Dr. P. A. Georgiev, University of Milan

Dr. T. F. Koetzle, Argonne National Laboratory

Dr. W. Klooster, Amethyst Scientific Consulting LLP, Singapore

Dr. S. Capelli, Institut Laue – Langevin

Dr. S. A. Mason, Institut Laue – Langevin

Dr. G. J. McIntyre, Institut Laue – Langevin

Dr. J. Ollivier, Institut Laue – Langevin

Dr. J. Eckert, Los Alamos National Laboratory

Prof. P. S. Pregosin. ETH – Zürich

Prof. H. Berke, University of Zürich

Dr. B. Chaudret, CNRS Toulouse

Dr. S. Sabo - Etienne, CNRS Toulouse

Dr. M. Grellier, CNRS Toulouse

Prof. B. L. Mojet, University of Twente

Prof. K. C. Caulton, Indiana University

Prof. M. B. Hall, Texas A&M

Prof. R. Morris, University of Toronto

Funded by:

C.N.R., M.U.R,

EU FP5-RTM, NATO