Provided by the author(s) and University College Dublin Library in accordance with publisher policies. Please cite the published version when available. 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 Downloaded 2020-11-01T20:35:50Z The UCD community has made this article openly available. Please share how this access benefits you. Your story matters! (@ucd_oa) Some rights reserved. For more information, please see the item record link above.
HF Dissociation in Water Clusters by Computer Simulations ∗ Alin M Elena School of Physics Scoil na Fisice Prof. Giovanni Ciccotti Principal supervisor: Dr. Simone Meloni Supervisor: 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 biological systems carbon cycle atmosphere CO 2 water CO 2 + H 2 O GGGB F GGG H 2 CO 3 HCO − H 3 O + 3 chemical weathering rock 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 ( H 2 O ) 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
= − lim Methods Developed and Used Collective Variables Description of a process by collective variables ρ θ ( z )= 1 reactants (r) products (p) 𝒶 ∫ d x e − βU ( x ) δ ( θ ( x )− z ) 𝒶 =∫ d x e − βU ( x ) F ( z )= − 1 F ( z ) ρ θ ( z ) β ln ρ θ ( z ) ∆F ∗ k B T z B dz d F F ( z B )− F ( z A )= ∫ k B T d z z A z 2 ( θ ( x )− z ) 2 ∫ d x k ( θ ( x )− z ) e − βU ( x ) e − βk d F ( z ) d z 2 ( θ ( x )− z ) 2 ∫ d x e − βU ( x ) e − βk βk →∞ U k ( x , z )= U ( x )+ k 2 ( θ ( x )− z ) 2 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 ℋ g ( x , p )= U ( x )+ K ( p ) Acceptance probability is P A ( x i + 1 , p i + 1 | x i , p i )= min { 1, e − βδ ℋ a } δ ℋ a = ℋ a ( x i + 1 , p i + 1 )− ℋ a ( x i , p i ) ℋ a ( x , p )= U k ( x , z )+ K ( p ) δt determines the acceptance rate ℋ a ( x , p )≠ ℋ g ( 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
{ 𝒶 ∫ 𝒶 ∫ ̇ ̇ Methods Developed and Used Rate Constant Calculation Rate constant calculation N r + N p ≈ 1 n r ( t ) = − k rp n r ( t ) + k pr n p ( t ) N r = 1 n p ( t ) = k rp n r ( t ) − k pr n p ( t ) d x e − βU ( x ) V r N p = 1 reactants (r) products (p) d x e − βU ( x ) k rp V p ν k pr k rp = 2N r F(z) ν k pr = ∆F ∗ 2N p N rp τ ν = lim τ τ →∞ V r V p θ ( x )= z z r z p z ∗ 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 = ∫ d x d v ̇ θ ( x ) ξ p ( x , v ) ξ r ( x , − v ) ρ ( x , v ) δ ( θ ( x )− z ∗ ) =∫ d x d v ̇ θ ( x ) ξ p ( x , v ) ξ r ( x , − v ) ρ ( x , v ) δ ( θ ( x )− z ∗ ) ∫ d x d v ρ ( x , v ) δ ( θ ( x )− z ∗ ) ∫ d x d v ρ ( x , v ) δ ( θ ( x )− z ∗ ) θ ( x ) ξ p ( x , v ) ξ r ( x , − v ) 〉 z e − βF ( z ∗ ) = 〈 ̇ ξ p ( x , v ) is the probability to reach p before z ∗ starting from ( x , v ) ξ r ( x , − v ) is the probability to reach r before p starting from ( x , − v ) N s ν = e − βF ( z ∗ ) θ ( x i ) χ i p χ i r N s i = 1 θ ( x i ( t = 0 ))= θ ( x i ( δt ))− θ ( x i (− 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 F F O 1 O 1 O 3 O 3 O 2 O 2 reactants products HF Dissociation in Water Clusters... July 10, 2013 9 / 20
α α ∑ α Results Collective Variable Collective variable for acid dissociation 〈 ℋ KS 〉 α = 〈 w α | ℋ KS ( x ) | w α 〉 〈 ℋ KS 〉 ζ = 〈 w ζ | ℋ KS ( x ) | w ζ 〉 w χ ( r )= ∑ c χ,i ϕ i ( r ) i w 1 w 1 ζ ξ i ( x )= 〈 ℋ KS 〉 ζ − 〈 ℋ KS 〉 α w 2 ξ i < 0 covalent bond at α ξ i > 0 covalent bond at ζ 3 w 3 w 2 ζ ζ θ ( x ) = ξ i ( x ) w 3 i = 1 G. Berghold, C. Mundy, A. Romero, J. Hutter & M. Parrinello, Phys. Rev. B , 2000, 61 , p. 10040 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 T=25 K 30 T=75 K T=150 K T=225 K 20 T=300 K k B T F ( z ) F(z) [eV] 10 0 − 10 − 15 − 10 − 5 0 5 10 15 z [eV] − 15 − 10 − 5 0 5 10 15 z [eV] HF Dissociation in Water Clusters... July 10, 2013 12 / 20
𭒬 Results Equilibrium Constant pK a p K a = 𭒬 pK a = − log K a r 4 3 2 1 cluster (comp.) bulk (exp.) 0 pK a − 1 − 2 − 3 − 4 − 5 − 6 25 50 75 100 125 150 175 200 225 250 275 300 T [K] HF Dissociation in Water Clusters... July 10, 2013 13 / 20
Results Equilibrium Constant Contributions to the free energy 5 ⋅ 10 − 2 0 ∆F / ∆E / T∆S [ eV ] − 5 ⋅ 10 − 2 − 0 . 1 − 0 . 15 ∆F ∆E − 0 . 2 T∆S 25 50 75 100 125 150 175 200 225 250 275 300 T [K] HF Dissociation in Water Clusters... July 10, 2013 14 / 20
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