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Title HF dissociation in water clusters by computer simulations Authors(s) Elena, Alin Marin Publication date 2013 Publisher University College Dublin. School of Physics Link to online version http://dissertations.umi.com/ucd:10000 Item record/more information http://hdl.handle.net/10197/6782

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HF Dissociation in Water Clusters by Computer Simulations∗

Alin M Elena

School of Physics Scoil na Fisice Principal supervisor:

• Prof. Giovanni Ciccotti

Supervisor:

• Dr. Simone Meloni

University College Dublin July 10, 2013

∗Submitted for publication to the Journal of the American Chemical Society

Outline 1

Motivation

2

Methods Developed and Used Collective Variables Restrained hybrid Monte Carlo Rate Constant Calculation

3

Results Collective Variable Model Equilibrium Constant Mechanism of the Reaction Reaction Rate Constat

HF Dissociation in Water Clusters... July 10, 2013 0 / 20

Motivation

Acid dissociation

(AH)aq GGGB F GGG (A−)aq + (H+)aq

atmosphere water rock CO2 CO2 +H2O GGGB F GGG H2CO3 H3O+ HCO−

3

chemical weathering

carbon cycle biological systems

HF Dissociation in Water Clusters... July 10, 2013 1 / 20

Motivation

HF dissociation

Atmospheric chemistry, pockets in proteins... Testing ground for development of models for dissociaiton reaction in bulk

• P. Ayotte, M. Hébert & P. Marchand, J. Chem. Phys. 2005, 125, p. 184501
• S. Odde et al., J. Phys. Chem. A, 2006, 110, p. 7918

HF Dissociation in Water Clusters... July 10, 2013 2 / 20

Motivation

Dissociation of HF in HF(H2O)7

reactants products

J.-L. Kuo & M. L. Klein, J. Chem. Phys. 2004, 120, p. 4690 HF Dissociation in Water Clusters... July 10, 2013 3 / 20

Motivation

Objectives

Equilibrium constant Reaction mechanism Reaction rate constant

HF Dissociation in Water Clusters... July 10, 2013 4 / 20

Methods Developed and Used Collective Variables

Outline 1

Motivation

2

Methods Developed and Used Collective Variables Restrained hybrid Monte Carlo Rate Constant Calculation

3

Results Collective Variable Model Equilibrium Constant Mechanism of the Reaction Reaction Rate Constat

HF Dissociation in Water Clusters... July 10, 2013 4 / 20

Methods Developed and Used Collective Variables

Description of a process by collective variables

z ρθ(z) F(z) reactants (r) products (p) kBT kBT ∆F∗

dF(z) dz = − lim

βk→∞

∫dx k(θ(x)− z)e−βU(x)e− βk

2 (θ(x)−z)2

∫dx e−βU(x)e− βk

2 (θ(x)−z)2

Uk(x, z)=U(x)+ k 2(θ(x)− z)2 ρθ(z)= 1 𝒶∫ dx e−βU(x)δ(θ(x)− z) 𝒶 =∫ dx e−βU(x) F(z)= − 1 β ln ρθ(z) F(zB)− F(zA)= ∫

zB zA

dzdF dz

HF Dissociation in Water Clusters... July 10, 2013 5 / 20

Methods Developed and Used Restrained hybrid Monte Carlo

Outline 1

Motivation

2

Methods Developed and Used Collective Variables Restrained hybrid Monte Carlo Rate Constant Calculation

3

Results Collective Variable Model Equilibrium Constant Mechanism of the Reaction Reaction Rate Constat

HF Dissociation in Water Clusters... July 10, 2013 5 / 20

Methods Developed and Used Restrained hybrid Monte Carlo

Restrained hybrid Monte Carlo

Random momenta extracted from a Maxwell-Boltzmann distribution at inverse temperature β Collective move corresponding to a short MD trajectory with the guiding Hamiltonian ℋg(x, p)= U(x)+ K(p) Acceptance probability is PA(xi+1, pi+1|xi, pi)= min{1, e−βδℋa} δℋa = ℋa(xi+1, pi+1)− ℋa(xi, pi) ℋa(x, p)= Uk(x, z)+ K(p) δt determines the acceptance rate ℋa(x, p)≠ ℋg(x, p)

• S. Duane, Phys. Lett. B, 1987, 195, p. 216
• B. Mehlig, D. W. Heermann & B. Forrest, Phys. Rev. B, 1992, 45, p. 679

HF Dissociation in Water Clusters... July 10, 2013 6 / 20

Methods Developed and Used Rate Constant Calculation

Outline 1

Motivation

2

Methods Developed and Used Collective Variables Restrained hybrid Monte Carlo Rate Constant Calculation

3

Results Collective Variable Model Equilibrium Constant Mechanism of the Reaction Reaction Rate Constat

HF Dissociation in Water Clusters... July 10, 2013 6 / 20

Methods Developed and Used Rate Constant Calculation

Rate constant calculation

θ(x)= z F(z) krp kpr ∆F∗ z∗ zr Vr zp Vp reactants (r) products (p)

{ ̇ nr(t) = −krpnr(t) + kprnp(t) ̇ np(t) = krpnr(t) − kprnp(t) Nr+Np ≈ 1 Nr = 1 𝒶∫

Vr

dx e−βU(x) Np = 1 𝒶∫

Vp

dx e−βU(x) krp = ν 2Nr kpr = ν 2Np ν = lim

τ→∞

Nrp

τ

τ

• E. Vanden-Eijnden & F. A. Tal, J. Chem. Phys. 2005, 123, p. 184103

HF Dissociation in Water Clusters... July 10, 2013 7 / 20

Methods Developed and Used Rate Constant Calculation

TST with dynamical corrections

ν = ∫ dxdv ̇ θ(x)ξp(x, v)ξr(x, −v)ρ(x, v)δ(θ(x)− z∗) =∫dxdv ̇ θ(x)ξp(x, v)ξr(x, −v)ρ(x, v)δ(θ(x)− z∗) ∫dxdv ρ(x, v)δ(θ(x)− z∗) ∫ dxdv ρ(x, v)δ(θ(x)− z∗) = 〈 ̇ θ(x)ξp(x, v)ξr(x, −v) 〉z e−βF(z∗) ξp(x, v)is the probability to reach p before z∗ starting from (x, v) ξr(x, −v)is the probability to reach r before p starting from (x, −v) ν = e−βF(z∗) Ns

Ns

∑

i=1

̇ θ(xi)χi

pχi r

̇ θ(xi(t = 0))= θ(xi(δt))− θ(xi(−δt)) 2δt

HF Dissociation in Water Clusters... July 10, 2013 8 / 20

Results Collective Variable

Outline 1

Motivation

2

Methods Developed and Used Collective Variables Restrained hybrid Monte Carlo Rate Constant Calculation

3

Results Collective Variable Model Equilibrium Constant Mechanism of the Reaction Reaction Rate Constat

HF Dissociation in Water Clusters... July 10, 2013 8 / 20

Results Collective Variable

Collective variable for acid dissociation

reactants F O1 O2 O3 products F O1 O2 O3

HF Dissociation in Water Clusters... July 10, 2013 9 / 20

Results Collective Variable

Collective variable for acid dissociation

w1

α

w1

ζ

w2

α

w2

ζ

w3

α

w3

ζ

• G. Berghold, C. Mundy, A. Romero, J. Hutter & M. Parrinello, Phys. Rev. B, 2000, 61, p. 10040

〈ℋKS〉α = 〈wα | ℋKS(x) | wα〉 〈ℋKS〉ζ = 〈wζ | ℋKS(x) | wζ〉 wχ(r)= ∑

i

cχ,iϕi(r) ξi(x)= 〈ℋKS〉ζ − 〈ℋKS〉α

ξi < 0 covalent bond at α ξi > 0 covalent bond at ζ θ(x) =

3

∑

i=1

ξi(x)

HF Dissociation in Water Clusters... July 10, 2013 10 / 20

Results Model

Outline 1

Motivation

2

Methods Developed and Used Collective Variables Restrained hybrid Monte Carlo Rate Constant Calculation

3

Results Collective Variable Model Equilibrium Constant Mechanism of the Reaction Reaction Rate Constat

HF Dissociation in Water Clusters... July 10, 2013 10 / 20

Results Model

Computational details

Restrained hybrid Monte Carlo developed and implemented in CP2K DFT-GPW, HCTH120 exchange correlation functional, GTH pseudo-potentials, m-TZV2P basis set, cubic box of side 14.0 Å and a plane wave cut-off of 300 Ry 24k hMC steps per z point to converge the mean force (relative error ≈ 10−4) Almost uniform grid in z space, [-16.6,16.3] eV, with an average step of 0.95 eV k = 50 eV−1 for the biased potential T = 25, 75, 150, 225 and 300 K

HF Dissociation in Water Clusters... July 10, 2013 11 / 20

Results Equilibrium Constant

Outline 1

Motivation

2

Methods Developed and Used Collective Variables Restrained hybrid Monte Carlo Rate Constant Calculation

3

Results Collective Variable Model Equilibrium Constant Mechanism of the Reaction Reaction Rate Constat

HF Dissociation in Water Clusters... July 10, 2013 11 / 20

Results Equilibrium Constant

Free energy profile

−15 −10 −5 5 10 15 −10 10 20 30 z [eV] F(z) kBT T=25 K T=75 K T=150 K T=225 K T=300 K

−15 −10 −5 5 10 15

z [eV] F(z) [eV]

HF Dissociation in Water Clusters... July 10, 2013 12 / 20

Results Equilibrium Constant

pKa

25 50 75 100 125 150 175 200 225 250 275 300 −6 −5 −4 −3 −2 −1 1 2 3 4 T [K] pKa cluster (comp.) bulk (exp.) Ka = 𭒬

p

𭒬

r

pKa = − log Ka

HF Dissociation in Water Clusters... July 10, 2013 13 / 20

Results Equilibrium Constant

Contributions to the free energy

25 50 75 100 125 150 175 200 225 250 275 300 −0.2 −0.15 −0.1 −5 ⋅ 10−2 5 ⋅ 10−2 T [K] ∆F / ∆E / T∆S [eV] ∆F ∆E T∆S

HF Dissociation in Water Clusters... July 10, 2013 14 / 20

Results Equilibrium Constant

Entropy

Sh−vib =

Nm

∑

i=1 {

βhνie−

βhνi 2

1 − e−

βhνi 2

− ln(1 − e−

βhνi 2 )

}

75 100 125 150 175 200 225 250 275 300 −0.2 −0.15 −0.1 −5 ⋅ 10−2 T [K] T∆S [eV] free energy calculations normal mode analysis intra-molecular modes inter-molecular modes

HF Dissociation in Water Clusters... July 10, 2013 15 / 20

Results Mechanism of the Reaction

Outline 1

Motivation

2

Methods Developed and Used Collective Variables Restrained hybrid Monte Carlo Rate Constant Calculation

3

Results Collective Variable Model Equilibrium Constant Mechanism of the Reaction Reaction Rate Constat

HF Dissociation in Water Clusters... July 10, 2013 15 / 20

Results Mechanism of the Reaction

Mean path

low z high z

x(z) = ⟨x⟩z

HF Dissociation in Water Clusters... July 10, 2013 16 / 20

Results Mechanism of the Reaction

Hydrogen bond chain length

−15 −10 −5 5 10 15 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 z [eV] L(z) [Å] T=25 K T=75 K T=150 K T=225 K T=300 K L(z) =

3

∑

i=1

di(z) =

3

∑

i=1

‖rα

i (z) − rζ i (z)‖1/2 2 HF Dissociation in Water Clusters... July 10, 2013 17 / 20

Results Mechanism of the Reaction

ξi vs z

−5 5 300 K F − H − O1 O1 − H − O2 O2 − H − O3 −5 5 225 K −5 5 150 K −15 −10 −5 5 10 15 −5 5 75 K z [eV] 〈ξi(x) 〉z [eV]

ξi(x) = 〈ℋKS〉ζ − 〈ℋKS〉α

HF Dissociation in Water Clusters... July 10, 2013 18 / 20

Results Mechanism of the Reaction

Intermediate state

−15 −10 −5 5 10 15 2.4 2.5 2.6 2.7 2.8 2.9 3 −15 −10 −5 5 10 15 2.4 2.5 2.6 2.7 2.8 2.9 3 z [eV] 225 K 300 K O − O [H9O4]+

• M. Eigen, Angew. Chem. Int. Ed. Engl. 1964, 3, p. 1

HF Dissociation in Water Clusters... July 10, 2013 19 / 20

Results Reaction Rate Constat

Outline 1

Motivation

2

Methods Developed and Used Collective Variables Restrained hybrid Monte Carlo Rate Constant Calculation

3

Results Collective Variable Model Equilibrium Constant Mechanism of the Reaction Reaction Rate Constat

HF Dissociation in Water Clusters... July 10, 2013 19 / 20

Results Reaction Rate Constat

Reaction rate constant

50 100 150 200 250 300 10−2 100 102 104 106 108 1010 T [K] krp [s−1] 50 100 150 200 250 300 5 10 15 20 25 30 T [K] ∆F∗ kBT

• T. Joutsuka & K. Ando, J. Chem. Phys., 2011, 115, p. 671
• M. Eigen, W. Kruse, G. Maass & L. de Maeyer, Progress in Reaction Kinetics, 1964, vol. II, p. 285

HF Dissociation in Water Clusters... July 10, 2013 20 / 20

Summary

Summary

We studied dissociation reaction of HF in water clusters by using statistical mechanics of rare events combined with ab initio MD RhMC was implemented in CP2K We developed a CV which is able to monitor and steer the reaction without any strong a priori knowledge of the mechanism HF is a stronger acid in cluster than in bulk HF gets a strong acid at lower T

HF Dissociation in Water Clusters... July 10, 2013 20 / 20

Summary

Summary

Weak acidity of HF has an entropic origin Negative ∆S is due to two opposite contributions a positive intra-molecular one and a dominant negative inter-molecular The deprotonation process is ”cooperative” but asynchronous and triggered by the compression of HB chain Reaction rate constant in cluster is higher than in bulk

HF Dissociation in Water Clusters... July 10, 2013 20 / 20

Acknowledgements

Acknowledgements

Giovanni and Simone

HF Dissociation in Water Clusters... July 10, 2013 20 / 20

Questions

Q&A

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