interaction induced localisation of protons - temperature ... · helium solvation effects ukasz...

Motivation Localisation at Low Temperatures Localisation in Superfluid Helium

Interaction Induced Localisation of Protons Electronvolt Neutron Spectroscopy, Abingdon 2014 | Ł. Walewski 1

Interaction Induced Localisationof Protons Temperature and SuperfluidHelium Solvation Effects

Łukasz WalewskiRuhr-University Bochum

VI Workshop in Electronvolt Neutron Spectroscopy, Abingdon 2014


Motivation – Superfluid Helium EnvironmentHelium Nano Droplet Isolation (HENDI) Spectroscopy1

Ultra-cold & Ultra-gentle Matrix

adapts perfectly to the solute→ QM ground state delocalisationtransparent from IR to UV→ refractive index close to 1spectral line half-width < 0.25 cm−1

→ ultra-cold, weak interactionsabsorbs binding energy→ evaporative coolingalmost free rotation of the solute→ zero viscosity

1Review: J. P. Toennies, A. F. Vilesov, Angew. Chem. Int. Ed. 43 (2004) 2622Interaction Induced Localisation of Protons Electronvolt Neutron Spectroscopy, Abingdon 2014 | Ł. Walewski 2


Motivation – What Could Be Influenced ?

Nuclear Quantum EffectsQuantum mechanical treatment ofthe atomic nuclei, as opposed tothe classical point particleviewpoint, affects:

molecular structurenuclear delocalisationreactivity. . .

Nuclear quantum effects will beinvestigated for the first time atsuperfluid helium temperatures.

classicalnuclei

quantumnuclei

Ł. W., H. Forbert, D. Marx, J. Phys.Chem. Lett. 2 (2011) 3069



Motivation – What Could Be Influenced ?

Nuclear Quantum EffectsQuantum mechanical treatment ofthe atomic nuclei, as opposed tothe classical point particleviewpoint, affects:

molecular structurenuclear delocalisationreactivity. . .

Realistic description of theelectronic structure is necessary.

0

2

4

6

8

−0.4 −0.2 0 0.2 0.4

P (

δ )

δ [ Å ]

T = 100 K

quantumclassical

Ł. W., H. Forbert, D. Marx,ChemPhysChem 14 (2013) 817



Motivation – What Are We Specifically Interested In ?Aggregation induced chemical reactions 1

-160

-140

-120

-100

-80

-60

-40

-20

0

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

En

erg

y (

kJ m

ol-1

)

Simulation Steps/1000

Energ

y (

kJ/m

ol)

0 10 20Simulation Steps/1000

0

−20

−40

−60

−80

−100

−120

−140

+

+

+

SIP

PA

Cooling in He Droplet

successive aggregationof H2O moleculesessentially barrierlessprocessformation of thepartially aggregated(PA) structureHCl dissociation

this mechanism can not be accessed by exploring the PESof a fixed number of H2O’s

1H. Forbert, M. Masia, A. Kaczmarek, N. N. Nair and D. Marx, JACS 133 (2011) 4062Interaction Induced Localisation of Protons Electronvolt Neutron Spectroscopy, Abingdon 2014 | Ł. Walewski 5


Ultra-Low Temperatures vs Interatomic InteractionsT = 1.67 K Reff [ Å ] L

H 2.68 1.00

H2 1.97 0.73

H2O 1.26 0.47

HCl 1.26 0.47

Effective radius of a bound nucleus

Reff =√

3 3

√3

4π

∫Ω

d3~r

Ω ≡ ∀~r : P(~r)≥Pmax · e−12

Free atom radius of gyration

Rfreeg =

Λ√8π

=

√h2/2πmkBT√

8π

Localisation index

L = Reff/Rfreeg

Ł. W., H. Forbert, D. Marx, Mol. Phys. 111 (2013) 2555Interaction Induced Localisation of Protons Electronvolt Neutron Spectroscopy, Abingdon 2014 | Ł. Walewski 6


Strikingly Strong Localisation Due to Hydrogen Bonds

T = 1.67 K

Nucleus Reff [ Å ] LCl(1) 0.31 0.69O(2) 0.31 0.45O(3) 0.34 0.50O(4) 0.37 0.55O(5) 0.40 0.59H(6) 0.30 0.11H(7) 0.41 0.15H(8) 0.31 0.12H(9) 0.36 0.13H(10) 0.37 0.14H(11) 0.35 0.13H(12) 0.48 0.18H(13) 0.66 0.25H(14) 0.67 0.25



Strikingly Strong Localisation Due to Hydrogen Bonds

ClH

T = 1.67 K

Effective size of H smaller thanthat of Cl ?

Nucleus Reff [ Å ] LCl(1) 0.31 0.69O(2) 0.31 0.45O(3) 0.34 0.50O(4) 0.37 0.55O(5) 0.40 0.59H(6) 0.30 0.11H(7) 0.41 0.15H(8) 0.31 0.12H(9) 0.36 0.13H(10) 0.37 0.14H(11) 0.35 0.13H(12) 0.48 0.18H(13) 0.66 0.25H(14) 0.67 0.25



Interaction-Induced Localisation

H2O· · ·HOH0

6

121.67 K

OH

0

6

12

0 0.5 1

P (

Rg

/ Rgfr

ee H

)

Rg / Rgfree H

107 K

H2O· · ·HCl0

6

121.67 K

ClH

0

6

12

0 0.5 1

P (

Rg

/ Rgfr

ee H

)

Rg / Rgfree H

107 K

Ł. W., H. Forbert, D. Marx, Mol. Phys. 111 (2013) 2555Interaction Induced Localisation of Protons Electronvolt Neutron Spectroscopy, Abingdon 2014 | Ł. Walewski 9


Interaction-Induced Localisation

T 1.67 K 100 KReff (Cl) 0.31 Å 0.06 ÅReff (H) 0.30 Å 0.22 Å

Ł. W., H. Forbert, D. Marx, J. Chem. Phys., in revisionInteraction Induced Localisation of Protons Electronvolt Neutron Spectroscopy, Abingdon 2014 | Ł. Walewski 10


Simulating Pure Superfluid Helium

Indistinguishable identical particles→ Bose–Einstein statistics

ZBE = Trsym e−βH =1N!

∑P

∫dR⟨

R∣∣∣e−βH∣∣∣PR

⟩

T = 3.33 K T = 2.11 K T = 1.18 K

Review: D. M. Ceperley, Rev. Mod. Phys. 67 (1995) 279Interaction Induced Localisation of Protons Electronvolt Neutron Spectroscopy, Abingdon 2014 | Ł. Walewski 11


Simulating Pure Superfluid Helium

Indistinguishable identical particles→ Bose–Einstein statistics

ZBE = Trsym e−βH =1N!

∑P

∫dR⟨

R∣∣∣e−βH∣∣∣PR

⟩

1.0

2.0

3.0

4.0

2.17 1 3

Cv

T [ K ]

0.2

0.4

0.6

0.8

1.0

2.17 1 3

ρs / ρ

T [ K ]

T = 2.11 K

Review: D. M. Ceperley, Rev. Mod. Phys. 67 (1995) 279Interaction Induced Localisation of Protons Electronvolt Neutron Spectroscopy, Abingdon 2014 | Ł. Walewski 12


Simulating Molecules in Superfluid Helium – A Hybrid Method

Hybrid Interactions (à la QM/MM)

solute: Born-Oppenheimerenergy of the groundelectronic state (QM)solvent: effective He–He pairpotential (MM)solute–solvent: parameterizedinteraction potential 1

fitted using highly accurateSAPT and CC dataaccounts for different soluteconfigurations

1A. D. Boese, H. Forbert, M. Masia, A. Tekin, D. Marx, G. Jansen PCCP, 13 (2011) 14550Interaction Induced Localisation of Protons Electronvolt Neutron Spectroscopy, Abingdon 2014 | Ł. Walewski 13


Simulating Molecules in Superfluid Helium – A Hybrid Method1

Hybrid Sampling (MD/MC)

solute: ab initio PIMDsolvent: bosonic PIMC

e−β(HBO+HHe−He+Hinter)

Correct sampling of the canonicaldensity matrix for the total system

→ Implemented in our in house CP2K version1Ł. W., H. Forbert, D. Marx, Comp. Phys. Comm., doi: 10.1016/j.cpc.2013.12.011



Additional Localisation Due to Superfluid Helium?

0.2

0.4

0.6

0.8

L

LgpLHe

1 3 5 7 9 11 13

0.2

δL

Atom Index

Relative effect on the order of 10-20%



Additional Localisation Due to Superfluid Helium

0.00

0.05

0.10

0 0.25 0.5 0.75 1∆

L =

Lg

p −

LH

eLgp

H, O, Cl

The weaker localisation in GP, the stronger the He effect



Next Step: Cryochemical Reactions

PA SIP

T = 1.67 K + 4He solvation

Acid Dissociation Mechanism

HCl + 4 H2O→ Cl− + H3O+ + 3 H2Oapproach of an H2O towards HClO−H· · ·Cl hydrogen bond creationHCl dissociation→ proton transferH3O+ formation→ proton transfer

−0.2

0.0

0.2

0.4

0 1 2 3 4 5 6

δ [

Å ]

t [ ps ]

Ł. W., H. Forbert, D. Marx, Comp. Phys. Comm., and in preparationInteraction Induced Localisation of Protons Electronvolt Neutron Spectroscopy, Abingdon 2014 | Ł. Walewski 17


AcknowledgementsPeople

Dominik Marx, RUB

Harald Forbert, RUB

Georg Jansen, UDE

Daniel Boese, UDE

Software & Resources

CP2K Team

LiDOng@Uni-Dortmund

CHEOPS@Uni-Köln

BoViLab@RUB

Funds


interaction induced localisation of protons - temperature ... · helium solvation effects ukasz...

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