# How to determine diffusion rates computationally? - Lorentz Center

код для вставкиHow to determine diffusion rates computationally? Grain-Surface Networks and Data for Astrochemistry, Lorentz Center, Leiden, 29-07-2013 Leendertjan Karssemeijer Theoretical Chemistry, Institute for Molecules and Materials Radboud University Nijmegen Institute for Molecules and Materials 1 Introduction How to determine diffusion rates computationally? вЂў Diffusion is a fundamental process in solid state astrochemistry. вЂў Many rates and barriers are still missing in models and are (crudely) estimated. вЂў Experiments difficult to perform and often not available. Institute for Molecules and Materials 2 Introduction How to determine diffusion rates computationally? вЂў Diffusion is a fundamental process in solid state astrochemistry. вЂў Many rates and barriers are still missing in models and are (crudely) estimated. вЂў Experiments difficult to perform and often not available. вЂў Diffusion process can be studied at various levels of detail. Insight in processes at the atomistic level. вЂў Individual processes can be studied (experiments probe averages). Importance of quantum effects can be evaluated. вЂў Differentiate between bulk and surface diffusion. Institute for Molecules and Materials 2 Introduction How to determine diffusion rates computationally? вЂў Diffusion is a fundamental process in solid state astrochemistry. вЂў Many rates and barriers are still missing in models and are (crudely) estimated. вЂў Experiments difficult to perform and often not available. вЂў Diffusion process can be studied at various levels of detail. Insight in processes at the atomistic level. вЂў Individual processes can be studied (experiments probe averages). Importance of quantum effects can be evaluated. вЂў Differentiate between bulk and surface diffusion. Institute for Molecules and Materials 2 Introduction How to determine diffusion rates computationally? вЂў Diffusion is a fundamental process in solid state astrochemistry. вЂў Many rates and barriers are still missing in models and are (crudely) estimated. вЂў Experiments difficult to perform and often not available. вЂў Diffusion process can be studied at various levels of detail. Insight in processes at the atomistic level. вЂў Individual processes can be studied (experiments probe averages). Importance of quantum effects can be evaluated. вЂў Differentiate between bulk and surface diffusion. Institute for Molecules and Materials 2 Introduction Introduction Analysis techniques Simulation techniques Conclusions Challenges Institute for Molecules and Materials 3 Analysis techniques Introduction Analysis techniques Microscopic approach Mean squared displacement Velocity autocorrelation function Indirect methods Simulation techniques Conclusions Challenges Institute for Molecules and Materials 4 Analysis techniques Microscopic approach Microscopic approach Particle hopping in a periodic potential. вЂў Diffusion constant easily found: D = a02 khop вЂў khop and a0 determined computationally. khop = ОЅ в€’Ed kT в€’в†’ D = D0 exp в€’Ed kT Prefactor D0 (в€ј 10в€’3 cm2 sв€’1 ) combination of attempt frequency, jump distance a0 and dimensionality. Institute for Molecules and Materials 5 Analysis techniques Microscopic approach Microscopic approach Particle hopping in a periodic potential. вЂў Diffusion constant easily found: D = a02 khop вЂў khop and a0 determined computationally. khop = ОЅ в€’Ed kT в€’в†’ D = D0 exp в€’Ed kT Prefactor D0 (в€ј 10в€’3 cm2 sв€’1 ) combination of attempt frequency, jump distance a0 and dimensionality. Straightforward approach. khop and a0 can be determined accurately, including quantum effects (possibly averaged). Only useful for very simple and crystalline systems. Institute for Molecules and Materials 5 Analysis techniques Mean squared displacement Mean squared displacement From a microscopic point of view, the Einstein relation relates the mean squared displacement of particles in time to the diffusion coefficient: D = lim tв†’в€ћ 1 в€‚ |r(t) в€’ r(0)| 2d в€‚t d dimensionality of the system (2 for surface, 3 for bulk diffusion). Straightforward to implement. r(t) is usually available from simulations. Long simulation times needed for proper averaging (problematic for solids and at low temperatures). Institute for Molecules and Materials 6 Analysis techniques Velocity autocorrelation function Mean squared displacement is related to the velocity of the particles. In one dimension: 2 t x 2 (t) = vx (t )dt 0 t t = vx (t )vx (t )dt dt 0 0 t t vx (t )vx (t ) dt dt . =2 0 0 But vx (t )vx (t ) only depends on t в€’ t so: vx (t )vx (t ) = vx (t в€’ t )vx (0) . From the Einstein relation: в€ћ D= vx (t)vx (0) 0 velocity autocorrelation function Institute for Molecules and Materials 7 dt. Analysis techniques Velocity autocorrelation function Velocity autocorrelation function In general, Green-Kubo relation for the diffusion constant: D= 1 d в€ћ v(t) В· v(0) dt. 0 Vibrational power spectrum is also easily obtained: 1 P(П‰) = в€љ 2ПЂ в€ћ v(t) В· v(0) e iП‰t dt. в€’в€ћ Relation to the vibrational power spectrum of the system. v(t) not always available from simulations. Long simulation times needed to reduce noise. Institute for Molecules and Materials 8 Analysis techniques Indirect methods Indirect methods The mean squared displacement (MSD) and velocity autocorrelation (VAC) methods are most used. Other (indirect) possibilities: вЂў Model TPD experiments by Kinetic Monte Carlo with temperature dependent rate constants. вЂў Solve FickвЂ™s second law: в€‚c в€‚2c = D 2, в€‚t в€‚x with the appropriate boundary conditions to obtain c(r, t). Solution can be fit to experiments. вЂў Rate equation models with diffusion parameter. Institute for Molecules and Materials 9 Simulation techniques Introduction Analysis techniques Simulation techniques Molecular Dynamics Kinetic Monte Carlo Indirect techniques Conclusions Challenges Institute for Molecules and Materials 10 Simulation techniques Molecular Dynamics Molecular Dynamics: Atomistically detailed simulations possible. Interaction schemes of all accuracies (ab-initio, DFT, forcefields). Diffusion easily calculated from MSD of VAC. Long sampling is computationally expensive (problematic for dust grain simulations). Institute for Molecules and Materials 11 Simulation techniques Molecular Dynamics Quantum wavepacket dynamics for H atom surface diffusion on graphite (Matteo Bonfanti and Rocco Martinazzo, J. Phys. Chem. C., 111, 2007) вЂў Accurate ab-initio PES. вЂў Diffusion barrier determined (4 meV) вЂў Rate of single hopping/tunneling process, khop , calculated by wavepacket propagation. вЂў D = a02 khop = 1.7 Г— 10в€’4 cm2 sв€’1 . Institute for Molecules and Materials 12 Simulation techniques Molecular Dynamics Quantum wavepacket dynamics for H atom surface diffusion on graphite (Matteo Bonfanti and Rocco Martinazzo, J. Phys. Chem. C., 111, 2007) вЂў Accurate ab-initio PES. вЂў Diffusion barrier determined (4 meV) вЂў Rate of single hopping/tunneling process, khop , calculated by wavepacket propagation. вЂў D = a02 khop = 1.7 Г— 10в€’4 cm2 sв€’1 . Very accurate description of interactions. Quantum approach. No вЂ™realвЂ™ dynamics simulation needed. Only possible from simple crystalline systems (defects not included). Institute for Molecules and Materials 12 Simulation techniques Molecular Dynamics Classical Molecular Dynamics of atomic oxygen diffusion in amorphous solid water (Myung Won Lee and Markus Meuwly, Faraday Discuss., , 2014). вЂў Individual jumps observed. вЂў D = a02 khop . вЂў khop and a0 averaged over observed jumps. Institute for Molecules and Materials 13 Simulation techniques Molecular Dynamics Classical Molecular Dynamics of atomic oxygen diffusion in amorphous solid water (Myung Won Lee and Markus Meuwly, Faraday Discuss., , 2014). вЂў Individual jumps observed. вЂў D = a02 khop . вЂў khop and a0 averaged over observed jumps. Accurate description of interactions. Diffusion mechanism can be understood. Temperature not low enough. Only limited number of jumps observed. System only partially sampled: possible bias. Simulation times not long enough to sample MSD. Institute for Molecules and Materials 13 Simulation techniques Kinetic Monte Carlo Kinetic Monte Carlo: Atomistic detail possible. Interaction schemes of all accuracies (ab-initio, DFT, forcefields, parametrized model). Diffusion easily calculated from MSD. Finding diffusion transition states is computationally expensive. Estimating rates not straighforward. Institute for Molecules and Materials 14 Simulation techniques Kinetic Monte Carlo Kinetic Monte Carlo algorithm Institute for Molecules and Materials 15 Simulation techniques Kinetic Monte Carlo Kinetic Monte Carlo algorithm Defining steps: 1 Define states вЂў Off-lattice (most structural detail) вЂў On-lattice (less structural detail) Institute for Molecules and Materials 15 Simulation techniques Kinetic Monte Carlo Kinetic Monte Carlo algorithm Defining steps: 1 2 Define states вЂў Off-lattice (most structural detail) вЂў On-lattice (less structural detail) вЂў Determining processes: вЂў Specify before simulation (lattice KMC, NEB) вЂў On-the-fly (Adaptive KMC) вЂў Determining rates: вЂў Harmonic TST вЂў Quantum Harmonic TST вЂў Instanton theory вЂў ... Institute for Molecules and Materials 15 Simulation techniques Kinetic Monte Carlo Kinetic Monte Carlo algorithm Defining steps: 1 2 3 Define states вЂў Off-lattice (most structural detail) вЂў On-lattice (less structural detail) вЂў Determining processes: вЂў Specify before simulation (lattice KMC, NEB) вЂў On-the-fly (Adaptive KMC) вЂў Determining rates: вЂў Harmonic TST вЂў Quantum Harmonic TST вЂў Instanton theory вЂў ... All processes need to be known for proper time evolution. Institute for Molecules and Materials 15 Simulation techniques Kinetic Monte Carlo H2 O surface diffusion on ice 1h (E.R. Batista and H JВґ onsson, Comput. Mater. Sci., 20, 2001) вЂў Binding sites explored in forcefield. вЂў Nudged elastic band calculation to obtain barriers. вЂў Harmonic rate constant: kAв†’B = ОЅ exp в€’EAв†’B kT . Institute for Molecules and Materials 16 Simulation techniques Kinetic Monte Carlo H2 O surface diffusion on ice 1h (E.R. Batista and H JВґ onsson, Comput. Mater. Sci., 20, 2001) вЂў Binding sites explored in forcefield. вЂў Nudged elastic band calculation to obtain barriers. вЂў Harmonic rate constant: kAв†’B = ОЅ exp вЂў D = 1 4t в€’EAв†’B kT в€†r(t) = 10 (T = 140 K). в€’9 . cm2 sв€’1 вЂў Diffusion barrier: 180 meV. Institute for Molecules and Materials 16 Simulation techniques Kinetic Monte Carlo H2 O surface diffusion on ice 1h (E.R. Batista and H JВґ onsson, Comput. Mater. Sci., 20, 2001) вЂў Binding sites explored in forcefield. вЂў Nudged elastic band calculation to obtain barriers. вЂў Harmonic rate constant: kAв†’B = ОЅ exp вЂў D = 1 4t в€’EAв†’B kT в€†r(t) = 10 (T = 140 K). в€’9 . cm2 sв€’1 вЂў Diffusion barrier: 180 meV. Accurate description of interactions (TIP4P forcefield). Long timescale simulations: sampling MSD possible. Crystal inhomogeneities included. Binding sites need to be known before the simulation (Some sites may be missed). Institute for Molecules and Materials 16 Simulation techniques Kinetic Monte Carlo Adaptive Kinetic Monte Carlo вЂў No prior knowledge of diffusion steps вЂў Potential energy surface explored automatically, to find transition states. вЂў Example: CO diffusion on ice 1h (L.J. Karssemeijer et al., Phys. Chem. Chem. Phys., 14, 2012). Institute for Molecules and Materials 17 Simulation techniques Kinetic Monte Carlo Adaptive Kinetic Monte Carlo вЂў No prior knowledge of diffusion steps вЂў Potential energy surface explored automatically, to find transition states. вЂў Example: CO diffusion on ice 1h (L.J. Karssemeijer et al., Phys. Chem. Chem. Phys., 14, 2012). Institute for Molecules and Materials 17 Simulation techniques Kinetic Monte Carlo Adaptive Kinetic Monte Carlo вЂў No prior knowledge of diffusion steps вЂў Potential energy surface explored automatically, to find transition states. вЂў Example: CO diffusion on ice 1h (L.J. Karssemeijer et al., Phys. Chem. Chem. Phys., 14, 2012). Institute for Molecules and Materials 17 Simulation techniques Kinetic Monte Carlo вЂў KMC algorithm generates random walk trajectories of the CO molecule. вЂў Diffusion coefficient can be obtained from the mean squared displacement: D = lim tв†’в€ћ 1 |r(0) в€’ r(t)|2 . 4t 140 Mean Squared Displacement (nm2) 600 Y displacement (nm) 400 200 0 -200 -400 -600 -800 -200 0 200 400 600 100 80 60 40 20 0 800 1000 1200 X displacement (nm) Institute for Molecules and Materials 120 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (s) 18 1 Simulation techniques Kinetic Monte Carlo Temperature (K) behavior. вЂў Effective energy barrier can be extracted. вЂў Diffusion on amorphous ice is impossible to simulate below 30 K. Diffusion constant (cm2s-1) вЂў Diffusion constant follows Arrhenius 10-4 50.0 30.0 25.0 20.0 10-9 10-14 10-19 10-24 10-29 20.0 30.0 40.0 50.0 1000/T (1/K) Hexagonal ice Amorphous ice System Hexagonal ice Amorphous ice Institute for Molecules and Materials 15.0 Effective diffusion barrier (meV) 49 В± 2 103 В± 13 19 60.0 Simulation techniques Kinetic Monte Carlo вЂў On amorphous ice, diffusion is limited by strong binding pore sites. Diffusion constant (cm2s-1) Temperature (K) 10-4 50.0 30.0 25.0 20.0 10-9 10-14 10-19 10-24 10-29 20.0 30.0 40.0 50.0 1000/T (1/K) Hexagonal ice Amorphous ice System Hexagonal ice Amorphous ice Institute for Molecules and Materials 15.0 Effective diffusion barrier (meV) 49 В± 2 103 В± 13 19 60.0 Simulation techniques Kinetic Monte Carlo Temperature (K) strong bonding sites to increase mobility. Diffusion constant (cm2s-1) вЂў Increase CO coverage by occupying 10-4 50.0 30.0 25.0 20.0 10-9 10-14 10-19 10-24 10-29 20.0 30.0 40.0 50.0 1000/T (1/K) Hexagonal ice Amorphous ice System Hexagonal ice Amorphous ice Institute for Molecules and Materials 15.0 Effective diffusion barrier (meV) 49 В± 2 103 В± 13 19 60.0 Simulation techniques Kinetic Monte Carlo Temperature (K) occupied with CO. вЂў One additional CO remains mobile. вЂў Occupying the pore sites increases mobility dramatically. Diffusion constant (cm2s-1) вЂў Three or six strongest binding sites are 10-4 50.0 30.0 25.0 20.0 10-9 10-14 10-19 10-24 10-29 20.0 30.0 40.0 50.0 1000/T (1/K) Hexagonal ice Amorphous ice Amorphous ice (3 occupied sites) Amorphous ice (6 occupied sites) System Hexagonal ice Amorphous ice Amorphous ice (3 occupied sites) Amorphous ice (6 occupied sites) Institute for Molecules and Materials 15.0 Effective diffusion barrier (meV) 49 В± 2 103 В± 13 67 В± 7 64 В± 12 19 60.0 Simulation techniques Kinetic Monte Carlo Off-lattice Kinetic Monte Carlo: Atomistic detail. Sufficiently long timescale to probe surface diffusion under astrochemical conditions. Can reveal mechanisms (trapping). Finding transition state computationally expensive. Bulk processes still beyond reach. Institute for Molecules and Materials 20 Simulation techniques Kinetic Monte Carlo On-lattice Kinetic Monte Carlo: вЂў Larger systems then off-latice KMC. вЂў Predefined event parameters. Institute for Molecules and Materials 21 Simulation techniques Kinetic Monte Carlo Figure: (Thanja Lamberts et al., Phys. Chem. Chem. Phys., 15, 2013) On-lattice Kinetic Monte Carlo: вЂў Larger systems then off-latice KMC. вЂў Predefined event parameters. вЂў Species confined to predefined lattice. вЂў No realistic interaction potentials. Institute for Molecules and Materials 21 Simulation techniques Kinetic Monte Carlo ВЁ Segregation in H2 O:CO2 ice mixtures (K. I. Oberg et al., A&A, 505, 2009) вЂў Lattice KMC simulations. 0.20 вЂў Diffusion included in bulk (swapping) and 0.15 bulk + surface surface surface (swapping) 0.10 Segregated amount (a.u.) вЂў Both bulk and surface processes needed to reproduce experiments. Predefined event parameters: Barrier type Energy / K H2 Oв€’H2 O Ebinding 1000 CO2 в€’CO2 Ebinding 500 H2 O Ehop 2400 CO2 Ehop 1200 H2 Oв€’CO2 Eswap 3600 CO2 в€’H2 O Eswap 3600 Institute for Molecules and Materials bulk 0.05 0 1.5 1.0 0.5 0 22 0 50 100 150 200 Time (min) 250 300 Simulation techniques Kinetic Monte Carlo Lattice KMC simulation of TPD experiments (E. Gavardi et al., Chem. Phys. Lett., 477, 2009) вЂў KMC simulation with varying temperature (A.P.J. Jansen, Comput. Phys. Commun., 86, 1995). вЂў Binding energies and diffusion barrier from DFT simulations. вЂў KMC simulates H2 formation and TPD profiles are obtained. вЂў Ortho- to para-dimer diffusion gives second peak in TPD. вЂў Insight in process obtained from KMC simulation. Institute for Molecules and Materials 23 Simulation techniques Kinetic Monte Carlo Lattice KMC simulation of TPD experiments (E. Gavardi et al., Chem. Phys. Lett., 477, 2009) вЂў KMC simulation with varying temperature (A.P.J. Jansen, Comput. Phys. Commun., 86, 1995). вЂў Binding energies and diffusion barrier from DFT simulations. вЂў KMC simulates H2 formation and TPD profiles are obtained. вЂў Ortho- to para-dimer diffusion gives second peak in TPD. вЂў Insight in process obtained from KMC simulation. Institute for Molecules and Materials 23 Simulation techniques Kinetic Monte Carlo On-lattice Kinetic Monte Carlo Long timescales, can probe bulk processes. Computationally efficient. Rates as input: close relation to rate equation models. Assumptions have to be made on mechanisms. Institute for Molecules and Materials 24 Simulation techniques Indirect techniques Indirect computational methods to find diffusion parameters вЂў Solutions to FickвЂ™s second law to understand experiments: вЂў Simple analytical solution, can be fit to experiments. вЂў Gives quantitative understanding. Possible future methods? вЂў Extracting diffusion constants from MSD in lattice KMC simulations. вЂў Analyzing power spectrum from MD simulations. Institute for Molecules and Materials 25 Simulation techniques FickвЂ™s second law: Indirect techniques в€‚c(x, t) в€‚ 2 c(x, t) . = D(T ) в€‚t в€‚x 2 General solution: в€ћ [Ai sin(О»i x) + Bi cos(О»i x)] exp(в€’О»2i Dt). c(x, t) = i=в€’в€ћ Initial value problem: boundary conditions and initial concentration profile determine full solution. Institute for Molecules and Materials 26 Simulation techniques FickвЂ™s second law: Indirect techniques в€‚c(x, t) в€‚ 2 c(x, t) . = D(T ) в€‚t в€‚x 2 General solution: в€ћ [Ai sin(О»i x) + Bi cos(О»i x)] exp(в€’О»2i Dt). c(x, t) = i=в€’в€ћ Initial value problem: boundary conditions and initial concentration profile determine full solution. вЂў Isothermal desorption experiments through ASW (CO,NH3 ,H2 CO,HNCO) (F Mispelaer et al., A&A A13, (2013);L.J. Karssemeijer et al., ApJ 781, (2014)). ВЁ вЂў Mixing experiments: CO into ASW (Lauck, Oberg et al, 2014, in prep). Institute for Molecules and Materials 26 Simulation techniques Indirect techniques CO diffusion and desorption through ASW (L.J. Karssemeijer et al., ApJ, 781, 2014). Institute for Molecules and Materials 27 Simulation techniques . Indirect techniques вЂў Boundary conditions: вЂў Initial concentration in bottom slab: c(x, 0) = c0 , 0, if if 0 < x в‰¤ d, d < x < h. вЂў Desorption at x = h: c(h, t) = 0. вЂў No flux at x = 0: в€‚c(0, t) = 0. в€‚x Institute for Molecules and Materials 27 Simulation techniques . Indirect techniques вЂў Boundary conditions: вЂў Initial concentration in bottom slab: c(x, 0) = c0 , 0, if if 0 < x в‰¤ d, d < x < h. вЂў Desorption at x = h: c(h, t) = 0. вЂў No flux at x = 0: 1 Concentration c(x,t) в€‚c(0, t) = 0. в€‚x вЂў Solution (Вµi = (2i + 1)ПЂ/2h): в€ћ c(x, t) = i=0 2c0 sin (Вµi d) cos (Вµi x) exp в€’Вµ2i Dt , Вµi h Institute for Molecules and Materials 0.6 x=d 0.4 0.2 0 27 Time t =0 t = 0.02 t = 0.05 t = 0.1 t = 0.4 t = 2.0 0.8 Ice height x Simulation techniques . Indirect techniques вЂў Boundary conditions: вЂў Initial concentration in bottom slab: c(x, 0) = c0 , 0, if if 0 < x в‰¤ d, d < x < h. 1 Concentration c(x,t) вЂў Desorption at x = h: c(h, t) = 0. вЂў No flux at x = 0: в€‚c(0, t) = 0. в€‚x i=0 x=d 0.4 0.2 Ice height x 1 2c0 sin (Вµi d) cos (Вµi x) exp в€’Вµ2i Dt , Вµi h Species in ice в€ћ 0.6 0 вЂў Solution (Вµi = (2i + 1)ПЂ/2h): c(x, t) = Time t =0 t = 0.02 t = 0.05 t = 0.1 t = 0.4 t = 2.0 0.8 вЂў Species in ice (в€јIR band area): Species in ice 0.8 0.6 0.4 0.2 h A(t) = 0 c(x, t)dx 0 в€ћ = i=0 2c0 (в€’1)n sin (Вµi d) exp в€’Вµ2i Dt Вµ2i hd Institute for Molecules and Materials 27 0 0.2 0.4 0.6 0.8 1 1.2 Time 1.4 1.6 1.8 2 Simulation techniques Indirect techniques 1 . 32 K 37 K Concentration c(x,t) вЂў Solution fit to experimental results. 40 K 50 K Time t =0 t = 0.02 t = 0.05 t = 0.1 t = 0.4 t = 2.0 0.8 0.6 x=d 0.4 0.2 Band area (cmв€’1 ) 0 Ice height x 1 Species in ice Species in ice 0.8 0 5 10 15 20 25 Time (min) 30 Institute for Molecules and Materials 35 0.6 0.4 0.2 40 0 27 0 0.2 0.4 0.6 0.8 1 1.2 Time 1.4 1.6 1.8 2 Simulation techniques Indirect techniques Solutions to FickвЂ™s second law to understand experiments Useful to to quantitatively understand experiments. Simple model, little parameters. Fit to IR band area gives a lot of uncertainty. How applicable is the model? Diffusion not the only process. Only one diffusing species. No concentration dependence in the model. Complicating model does not necessarily improve understanding. Institute for Molecules and Materials 28 Conclusions Conclusions вЂў Several analysis techniques and simulation methods available. вЂў Computer simulations can help unveil properties of molecular diffusion on the atomic scale. вЂў Tradeoff between detail/accuracy and system size/timescales (limits on included local structure, inhomogeneities, trapping, restructuring, crystalization) вЂў Long timescales under astrophysical conditions problematic. вЂў Lot of recent work and work in progress. вЂў Diffusion is still too poorly understood. Institute for Molecules and Materials 29 Challenges Challenges for computing diffusion processes Institute for Molecules and Materials 30 Challenges Challenges for computing diffusion processes вЂў How to simulate bulk processes? вЂў Is there real bulk diffusion or effective surface diffusion along pores? вЂў Lattice Kinetic Monte Carlo, but... вЂў Unclear what processes to include? вЂў What parameters to give them? вЂў Molecular Dynamics... вЂў Time scales long enough? вЂў Accelerated methods? Institute for Molecules and Materials 30 Challenges Challenges for computing diffusion processes вЂў How to simulate bulk processes? вЂў Is there real bulk diffusion or effective surface diffusion along pores? вЂў Lattice Kinetic Monte Carlo, but... вЂў Unclear what processes to include? вЂў What parameters to give them? вЂў Molecular Dynamics... вЂў Time scales long enough? вЂў Accelerated methods? вЂў What structure of the ice to include in atomistically detailed simulations? Institute for Molecules and Materials 30 Challenges Challenges for computing diffusion processes вЂў How to simulate bulk processes? вЂў Is there real bulk diffusion or effective surface diffusion along pores? вЂў Lattice Kinetic Monte Carlo, but... вЂў Unclear what processes to include? вЂў What parameters to give them? вЂў Molecular Dynamics... вЂў Time scales long enough? вЂў Accelerated methods? вЂў What structure of the ice to include in atomistically detailed simulations? вЂў What are the essential physical processes? How to input detailed simulation results into simplistic models вЂў More detailed simulations can give a lot of insight, but results have to be useful/used. Institute for Molecules and Materials 30 Thank you for your attention Questions? Challenges VAC and Power spectrum вЂў VAC also gives power spectrum P(П‰). вЂў Maybe used for interpretation of new THz ice results (M.A. Allodi et al., Phys. Chem. Chem. Phys., 16, 2014). вЂў Possible new way to characterize bulk diffusion? вЂў Requires accurate potentials. . . Institute for Molecules and Materials 32 Challenges Adaptive Kinetic Monte Carlo CO diffusion on water ice. вЂў Amorphous and crystalline samples. вЂў Binding energies evaluated. вЂў Nanoporous sites important. Hexagonal ice Amorphous ice Institute for Molecules and Materials 33

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