Ab initio molecular dynamics

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1 Ab initio molecular dynamics Kari Laasonen, Physical Chemistry, Aalto University, Espoo, Finland (Atte Sillanpää, Jaakko Saukkoriipi, Giorgio Lanzani, University of Oulu) Computational chemistry is a field that use quantum mechanical methods to study molecules properties and reactions In most of the calculations the studied molecules are in vacuum which is seldom the case with real molecules We need computational chemistry in realistic environment The molecules also moves so often we need to simulate the molecular dynamics (MD) The main advantage of AIMD is that chemical reactions can be studied.

2 Ab Initio Molecular Dynamics combining periodic DFT-GGA and MD. the atoms are treated classically, (Born-Oppenheimer approximation) F = Ma, F = - d V/d R electrons are included and they are treated using DFT (also HF and hybrid functionals are possible) E KS (,R) forces are calculated in DFT level F = - d E KS (,R) / d R the core electrons are described with effective core potentials we need to either optimize the electrons at every time step or to use the Car-Parrinello method expensive calculations Wavefunctions do not change much between time steps the previous wf s are an excellent start for the new ones. => Fast convergence (5-10 iterations)

3 Ab Initio Molecular Dynamics CPMD smooth effective core potentials and plane wave basis set. Car- Parrinello algorithm, time step ca. 0.1 fs CP2K hard effective core potentials and gaussian basis set. Time step ca. 1 fs. Note: the wavefunctions has to be computed at every time step! accuracy of GGA is usually good Van der Waals interactions are missing. We use DFT + empirical corrections a la Grimme full arsenal of MD techniques and electronic structure analysis methods are implemented thermostats, constraints, thermodynamic integration, Wannier functions, TD-DFT

4 Computational aspects CP2K code Developed mostly in Zurich, Prof. Hutter s group Free to download (from the address above) Tutorials: 2nd CP2K Tutorial: Enabling the Power of Imagination in MD Simulations. Very complex code ( lines of code, Fortran 95) Huge amount of features Difficult to compile and difficult to learn to use Important help from CSC (compilation)

5 Computational aspects CP2K code Efficient code but in normal application not very good parallel scaling. We are interested of some simulation of 200+ waters and few MD steps. One simulation should not take more month (wall clock time, Cray XX). CP2K scaling A supercomputer is essential 100 Good scaling up to 1024 cores (10 s/step is makes few 100 ps simulations possible) Time 10 64water 128water NaCl+475w 1024water Cores

6 Ab Initio Molecular Dynamics examples: Al 2 O n H m Cl water, Al 5 O n H m Cl k water, PBE-GGA various simulations, simulation time scale ca. 100 ps CPMD or CP2K code, computations with Cray XT5/XT4

7 Ab initio molecular dynamics of acidic systems Hydrofluoric Acid HF acid is a very interesting because at low concentrations it is a weak acid (ph ca. 3) but at high concentration it become very strong acid. HF and water mix with all concentrations. Sillanpää, A., Simon, C., Klein, M.L., Laasonen, K. J. Phys. Chem. B 106, , (2002). Simon, C., Klein, M.L., ChemPhysChem, 6, , (2005). Hydrochloric Acid HCl is a typical strong acid. It s soluability limit is ca. 30 mol % We have done DCl:D 2 O simulations with concentrations of 4:28, 7:25 and 10:22 at ca. 300 K and 10:22 at 470 K and 910 K. Sillanpää, A., Laasonen, K. Phys.Chem.Chem.Phys., 6, , (2004). Heuft, J.M., Meijer, E.J., Phys.Chem.Chem.Phys., 8, , (2006).

8 Mixture of Hydrofluoric and Hydrochloric Acid Simulations: 1 HF, 3 HCl, 28 waters,15 ps, NVT, 330 K 3 HF, 4 HCl, 25 w, 12 ps + 25 ps NVT, 330 K 6 HF, 8 HCl, 18 w, 50 ps, NVT, 350 K, 20 ps, NVE, 320 K 6 HF, 8 HCl, 18 w, 40 ps annealing + 60 ps, NVT, 350 K 14 HF, 0 HCl, 18 w, 2x50 ps, NVT 350 K (in all simulations dt = fs (5 au), = 500 au) PBE GGA and Vanderbilt pseudopotentials, cut-off 35 Ry all hydrogens were replaced with deuteriums we wanted to see how HF is behaving in acid environment K. Laasonen, J. Larrucea, A. Sillanpää, J. Phys. Chem. B, 120, (2006)

9 Structure heavy atoms O-O distances are much shorter than in water (similar as in concentrated HF(aq) and HCl(aq)) O coordination is very sensitive to the acid concentration: 2.7 (1/3), 2.2 (3/4), 1.1 (6/8), 1.4 (14/0) (const. cut-off 3.0 Å) 3.2 (1/3), 2.3 (3/4), 0.9 (6/8), 1.6 (14/0) (integral to the first minimum) only 1 oxygen around water in the 6/8 simulation! (in pure water ca. 4)

10 OH pair correlation functions Good correlation with hydronium concentration (hydronium is defined by using OH cutoff of 1.25) The water molecules start loosing their meaning!! O-O coordination ca 1. H H H H Protons are getting very close to heavy atoms.

11 Free energy profiles for hydrogen. F( q) P( q) RT ln max ( P( q)) In acids the protons are very mobile, OHO barrier is around 1 kj/mol in the mixture simulation

12 Some general comments on acid AIMD simulations You do not do such simulations with empirical potentials Doable with AIMD Limitations: time scale, accuracy of GGA

13 Ab initio molecular dynamics aluminum oxide chemistry in aqueous solution Al oxides are widely used chemicals for water cleaning (coagulation) Not much are known of their formation chemistry We have a lot of new mass spectrometer data of these complexes which needs computations to resolve the molecular structures

14 Ab initio molecular dynamics aluminum oxide chemistry in aqueous solution loosely bound proton (acidic) normal proton (water) 1.48 Å Distance (Å) Distance (Å) 1.35 Å Time (ps) Time (ps)

15 Ab initio molecular dynamics aluminum oxide chemistry in aqueous solution fast proton jump correlated to Cl escape attempt O-Cl Distance (Å) O-H 1.65 Å 1.98 Å ** 1.68 Å 3.0 Å Time (ps)

16 Constrained MD simulation One can fix some geometrical parameters and compute the force to this constraint. MetaDynamics allows treatment of more complex reaction. Free energy difference is an integral of this force Tedious calculations since they need long simulation to get good averaging. The constraint can slowly grow or it can be fixed (the later turned out to be more efficient) Al - Cl H H O Al --- Cl H H O

17 Constrained MD simulation Test the hysteresis grow and reduce the constraint. The result should be the same

18 Constrained MD simulation Also the static calculations need long simulations fs

19 Aluminum oxide chemistry in aqueous solution reaction barriers very large ligand effect: Al 1 ClOHw, Al 2 Clw 2 small barriers Cl s will dissociate 14 ± 3 kj mol ± 5 kj mol J. Saukkoriipi and K. Laasonen, J. Phys. Chem. A, 112, (2008), G (kj/mol) ,2 2,4 2,6 2,8 3,0 3,2 Distance (Å)

20 Metadynamics Laio, Parrinello, PNAS 99, 12562, 2002 Biased dynamics Choose few collective variables that will describe the problem of interest Run dynamics Add small repulsive gaussians to the system in places where you have been At the end the you will get the free energy profile (from the gaussians) A good review: Laio and Gervasio, Rep. Prog. Phys (2008)

21 Metadynamics The critical point, the choice of the collective variable The Z shape potential: 1 CV going from A to B cause easily too high barrier since CV do not go backwards 2 CV better can map this problem Deep problem: real system is very high dimensional, most of them are not relevant, BUT how many are. And how many CV s are need. The MetaDynamics (in CP2K) works with 2 CV s

22 Example: Al3On reactions (Giorgio Lanzani) CV:s 1: d(al1-al2)-d(al1-al3) 2: root mean displacement of the atoms forming the Al-O ring (reference: ring like Al3On) Why such CV s Alchemy making different molecules and finding good descriptors of them (experience in Hutter s group, especially M. Iannuzzi, has been very useful) After long (few 100 s ps) we receive very interesting and complex potential Surface. To produce this data with distance constrains would have been impossible.

23 Free energy surface of the considered Al--trimeric cluster at 300 K. The geometries corresponding at the local minima (marked in red) and saddle points (blue) are reported as well.

24 Conclusions The AIMD is a very poverfull tool for small systems (less than 1000 atoms and less than 5000 electrons) Time scale is limited to 1 ns The accuracy is dermined by the DFT-GGA (+vdw) Access to structural, dynamic and electronic properties Access to energy barriers

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