QM/MM approaches in ab initio molecular dynamics

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1 CP2K UK Workshop 2014! August, Imperial College, London /MM approaches in ab initio molecular dynamics Marcella Iannuzzi! University of Zurich!! Teodoro Laino! IBM Zurich Research Laboratory

2 MM:overview GEEP Application: covd Conclusion MM Schemes Outline Overview of the /MM methodology! Available /MM Electrostatic Schemes! GEEP: CP2K /MM driver! Charged Oxygen Vacancies in SiO2

3 Nobel Prize in Chemistry 2013 Martin Karplus, Harvard U., Cambridge, MA, USA Micheal Levitt, Stanford U., Stanford, CA, USA Arieh Warshel, U. Southern Ca., Los Angeles, CA, USA Development of Multiscale Models of Complex Chemical Systems

4 /MM Combine and MM Combine Quantum Mechanics and Molecular Mechanics /MM full atomistic by classical FF Separate system in and MM part, single out electro Vtreated (R) =byv (R) + VMM (R) + Vint (R) Define potential energy surface

5 Combine and MM : modelling of electronic rearrangements! MM: efficient inclusion of wider environment! Choice of method (semi empirical, DFT, QC)! Choice of the force field! Partitioning and treatment of the boundary

6 MM:overview GEEP Application: covd Conclusion MM Schemes 738,000 atoms - 50 nanometers Ligand binding affinity in docking! Free energy simulations! Complex biomolecular structures P.D. Blood and G.A. Voth, PNAS, 103, 2006, pp

7 MM:overview GEEP Application: covd Conclusion MM Schemes Environment effects on reaction energetics

8 MM:overview GEEP Application: covd Conclusion MM Schemes MM: overview 0.11 million atoms! 5 regions: effects of O implantation into Si! adaptive regions simox technology Yoshio Tanaka (AIST) and Aiichiro Nakano (USC)

9 MM Environment U(R N )= X i U 1 (R i )+ X i X X X U 3 (R i, R j, R k )+... j>i U 2 (R i, R j )+X i j>i k>j U(R N, n p )

10 MM Environment U(R N )= X i U 1 (R i )+ X i X X X U 3 (R i, R j, R k )+... j>i U 2 (R i, R j )+X i j>i k>j X X X X "!! #! U(R N, n p ) U(R N ) = + + X j>i X i2bonds X s2torsion k (b) i 2 (l i l i,0 ) 2 + X j2angles V s 2 (1 + cos(n s! s)) 4" ij " ij R ij 12 ij R ij 6 # k (a) j 2 ( j j,0 ) 2 + q iq j 4" 0 R ij! :[(k (b),l 0 ) bon ;(k (a), 0 ) ang ;(V s, s) tor ;(", ) pair ; q at ]

$Topology RESI ALA 0.00 GROUP ATOM N NH1-0.47! ATOM HN H 0.31! HN-N ATOM CA CT1 0.07! HB1 ATOM HA HB 0.09! / GROUP! HA-CA--CB-HB2 ATOM CB CT3-0.27! \ ATOM HB1 HA 0.09! HB3 ATOM HB2 HA 0.09! O=C ATOM HB3 HA 0.$

11 Topology RESI ALA 0.00 GROUP ATOM N NH1-0.47! ATOM HN H 0.31! HN-N ATOM CA CT1 0.07! HB1 ATOM HA HB 0.09! / GROUP! HA-CA--CB-HB2 ATOM CB CT3-0.27! \ ATOM HB1 HA 0.09! HB3 ATOM HB2 HA 0.09! O=C ATOM HB3 HA 0.09! GROUP! ATOM C C 0.51 ATOM O O BOND CB CA N HN N CA BOND C CA C +N CA HA CB HB1 CB HB2 CB HB3 DOUBLE O C IMPR N -C CA HN C CA +N O DONOR HN N ACCEPTOR O C IC -C CA *N HN IC -C N CA C IC N CA C +N IC +N CA *C O IC CA C +N +CA IC N C *CA CB IC N C *CA HA IC C CA CB HB IC HB1 CA *CB HB IC HB1 CA *CB HB

12 MM CP2K input &FORCE_EVAL METHOD FIST!!! &MM &FORCEFIELD PARM_FILE_NAME acn.pot PARMTYPE CHM &CHARGE ATOM CT CHARGE &END CHARGE &CHARGE ATOM YC CHARGE &END CHARGE &CHARGE ATOM YN CHARGE &END CHARGE &CHARGE ATOM HC CHARGE &END CHARGE &END FORCEFIELD!!! &POISSON &EWALD EWALD_TYPE SPME ALPHA.44 GMAX 32 O_SPLINE 6 &END EWALD &END POISSON &END MM &SUBSYS &CELL ABC &END CELL &TOPOLOGY CONNECTIVITY PSF CONN_FILE_NAME acn_topology.psf COORD_FILE_NAME acn_topology.pdb COORDINATE pdb &END TOPOLOGY &END SUBSYS STRESS_TENSOR ANALYTICAL &END FORCE_EVAL

13 Subtractive /MM E total = E MM,tot + E () E MM() MM FF also for active region! density not polarised

14 Subtractive /MM E total = E MM,tot + E () E MM() MM FF also for active region! &MULTIPLE_FORCE_EVALS FORCE_EVAL_ORDER &END MULTIPLE_FORCE_EVALS! &FORCE_EVAL METHOD MIXED &MIXED MIXING_TYPE GENMIX &GENERIC # X: Energy force_eval 2 # Y: Energy force_eval 3 # Z: Energy force_eval 4 MIXING_FUNCTION X+Y-Z VARIABLES X Y Z &END GENERIC &END MIXED &SUBSYS &TOPOLOGY CONNECTIVITY PSF CONN_FILE_NAME topo.psf COORD_FILE_NAME totsys.xyz &END TOPOLOGY &CELL ABC &END CELL &END SUBSYS &END FORCE_EVAL density not polarised! &FORCE_EVAL METHOD FIST &MM &END MM &SUBSYS &TOPOLOGY CONNECTIVITY PSF CONN_FILE_NAME topo.psf COORD_FILE_NAME totsys.xyz &END TOPOLOGY &CELL ABC &END CELL &END SUBSYS &END FORCE_EVAL! &FORCE_EVAL METHOD QS &DFT &END DFT!! &SUBSYS &TOPOLOGY COORD_FILE_NAME qmsys.xyz &END TOPOLOGY &CELL ABC &END CELL &END SUBSYS &END FORCE_EVAL! &FORCE_EVAL METHOD FIST &MM &END MM &SUBSYS &TOPOLOGY CONNECTIVITY PSF CONN_FILE_NAME qmtopo.psf COORD_FILE_NAME qmsys.xyz &END TOPOLOGY &CELL ABC &END CELL &END SUBSYS &END FORCE_EVAL

15 MM:overview GEEP Application: covd Conclusion MM Schemes Additive /MM E total = E MM,tot + E () + E /MM E MM() = E el MM() + Evdw MM() + Eb MM() Electrostatic coupling is the most involved term! Mechanical embedding possible! Linked atom scheme! vdw might need ad hoc parameterisation

16 MM:overview GEEP Application: covd Conclusion MM Schemes Outline Overview of the /MM methodology! Available /MM Electrostatic Schemes! GEEP: CP2K /MM driver! Charged Oxygen Vacancies in SiO2

17 MM:overview GEEP Application: covd Conclusion MM Schemes Available Electrostatic Schemes on the same cell on which is defined box Cost N MM * P 1 MM box

18 MM:overview GEEP Application: covd Conclusion MM Schemes Available Electrostatic Schemes Spherical Cutoff box Cost N c MM * P1 MM box

19 MM:overview GEEP Application: covd Conclusion MM Schemes Available Electrostatic Schemes Multi-pole! Expansion box MM box A. Laio, J. VandeVondele, U. Rothlisberger, J. Chem. Phys., 116, 2002, pp. 6941

20 MM:overview GEEP Application: covd Conclusion MM Schemes Outline Overview of the /MM methodology! Available /MM Electrostatic Schemes! GEEP: CP2K /MM driver! Charged Oxygen Vacancies in SiO2

21 MM:overview GEEP Application: covd Conclusion MM Schemes /MM

22 MM:overview GEEP Application: covd Conclusion MM Schemes /MM E TOT (R, R MM )=E (R )+E MM (R MM )+E /MM (R, R MM ) E /MM (R, R MM )= X MM q MM Z n(r) r R MM dr + X,MM u vdw (R, R MM )

23 MM:overview GEEP Application: covd Conclusion MM Schemes /MM Gaussians Plane Waves

24 Gaussian charge distribution n(r, R MM )= rc,mm p 3 e ( r R MM /r c,mm ) 2 v MM (r, R MM )= Erf r RMM r c,mm r R MM prevent spill out problem! accelerate calculations of electrostatics

25 MM:overview GEEP Application: covd Conclusion MM Schemes GEEP Sum of functions with different cutoffs, derived from the new Gaussian expansion of the electrostatic potential Energy [a.u.] ṽ MM (g) = 4 g 2 exp g 2 r 2 c,mm 4! Distance

26 MM:overview GEEP Application: covd Conclusion MM Schemes GEEP Sum of functions with different cutoffs, derived from the new Gaussian expansion of the electrostatic potential ṽ MM (g) = 4 g 2 exp g 2 r 2 c,mm 4! G vectors Distance T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 1, 2005, pp

27 MM:overview GEEP Application: covd Conclusion MM Schemes Multigrid Framework N i+1 =8N i T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 1, 2005, pp

28 MM:overview GEEP Application: covd Conclusion MM Schemes Multigrid Framework interpolate restrict interpolate restrict interpolate restrict Cubic Splines T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 1, 2005, pp

29 Collocation in the Box Z E /MM (R, R MM )= n(r, R )V /MM (r, R MM )dr potential on the finest grid V /MM i (r, R MM )= X MM v i MM(r, R MM ) box optimal! grid levels!! 60-80% of time

30 box

31 box

32 compact Gaussian! functions

33 compact Gaussian! functions

34 compact Gaussian! functions

35 compact Gaussian! functions

44 Scaling ~ Nc3

45 V /MM (r, R MM )= Xfine i=coarse fine Y 1 k=i I k k real space interpolation from coarsest to finest! 1V /MM i (r, R MM )

46 V /MM (r, R MM )= Xfine i=coarse fine Y 1 k=i I k k real space interpolation from coarsest to finest! 1V /MM i (r, R MM )

47 V /MM (r, R MM )= Xfine i=coarse fine Y 1 k=i I k k 1V /MM i (r, R MM )

48 V /MM (r, R MM )= Xfine i=coarse fine Y 1 k=i I k k 1V /MM i (r, R MM )

49 V /MM (r, R MM )= Xfine i=coarse fine Y 1 k=i I k k 1V /MM i (r, R MM )

50 Electrostatic Potential interpolation! 20-40% of time

51 &MM! &CELL ABC &END CELL USE_GEEP_LIB 9 ECOUPL GAUSS! &MM_KIND H RADIUS 0.44 &END MM_KIND &MM_KIND O RADIUS 0.78 &END MM_KIND! &_KIND H MM_INDEX 8 9 &END _KIND &_KIND O MM_INDEX 7 &END _KIND! &END MM! &MM.. &END MM! &DFT. &END DFT! &SUBSYS &CELL ABC &END CELL! &TOPOLOGY COORD_FILE_NAME sys.pdb COORDINATE pdb &END TOPOLOGY &END SUBSYS

52 MM:overview GEEP Application: covd Conclusion MM Schemes Extension to PBC How to handle the electrostatic potential in presence of periodic boundary conditions (PBC)? Ewald Summation scheme:

53 MM:overview GEEP Application: covd Conclusion MM Schemes Extension to PBC How to handle the electrostatic potential in presence of periodic boundary conditions (PBC)? Ewald Summation scheme: Reciprocal space Real space

54 MM:overview GEEP Application: covd Conclusion MM Schemes /MM fully periodic MM MM MM MM MM MM MM MM MM T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

55 Total ES Energy n(r) =n (r)+n MM (r)

56 Total ES Energy n(r) =n (r)+n MM (r) ±n B background charge

57 Total ES Energy n(r) =n (r)+n MM (r) ±n B background charge E TOT = 1 2 Z Z drdr 0 n(r)n(r0 ) r r 0 Z Z E MM = 1 2 E = 1 Z Z 2 E /MM = Z Z drdr 0 (nmm (r)+n B,MM )(n MM (r 0 )+n B,MM ) r r 0 drdr 0 (n (r)+n B, )(n (r 0 )+n B, ) r r 0 drdr 0 (n (r)+n B, )(n MM (r 0 )+n B,MM ) r r 0

58 MM:overview GEEP Application: covd Conclusion MM Schemes MM/MM fully periodic MM MM MM MM MM MM MM MM MM T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

59 MM:overview GEEP Application: covd Conclusion MM Schemes /MM fully periodic MM MM MM MM MM MM MM MM T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

60 MM:overview GEEP Application: covd Conclusion MM Schemes GEEP with PBC T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

61 MM:overview GEEP Application: covd Conclusion MM Schemes GEEP with PBC smooth! coarsest grid T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

62 MM:overview GEEP Application: covd Conclusion MM Schemes /MM real space term V /MM rs (r, R MM )= X LappleL cut MM 2 X 4 X Ng r RMM + L 2 3 A g exp 5 G 2 g T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

63 MM:overview GEEP Application: covd Conclusion MM Schemes /MM reciprocal space term T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

64 MM:overview GEEP Application: covd Conclusion MM Schemes /MM reciprocal space term low cutoff function! only few k vectors! needed T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

65 !!! &MM &CELL ABC &END CELL ECOUPL GAUSS USE_GEEP_LIB 6 &MM_KIND NA RADIUS &END MM_KIND &MM_KIND CL RADIUS &END MM_KIND &PERIODIC GMAX 0.5 &MULTIPOLE EWALD_PRECISION RCUT 8.0 NGRIDS ANALYTICAL_GTERM &END MULTIPOLE &END PERIODIC! &END MM

66 MM:overview GEEP Application: covd Conclusion MM Schemes GEEP Summary GEEP to speed up the evaluation of a function on a grid! The speed up factor is ~ (Nf/Nc) 3 =2 3(Ngrid-1)! Usually 3-4 grid levels are used corresponding to a speed up of ~ 10 2 times faster than the simple collocation algorithm (Interpolations and Restrictions account for a negligible amount of time)! Since the residual function is different from zero only for few k vectors, the sum in reciprocal space is restrained to few points.! Small computational overhead between the fully periodic and non-periodic

67 MM:overview GEEP Application: covd Conclusion MM Schemes Sources of Errors Cutoff of grid level appropriate to the cutoff of the mapped Gaussian (~ points per linear direction)! Error in Cubic Spline interpolation! Cutoff of the coarse grid level comparable to the cutoff of the long range function.

68 MM:overview GEEP Application: covd Conclusion MM Schemes fully periodic T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

69 MM:overview GEEP Application: covd Conclusion MM Schemes fully periodic T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

70 MM:overview GEEP Application: covd Conclusion MM Schemes De-coupling and re-coupling T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

71 MM:overview GEEP Application: covd Conclusion MM Schemes De-coupling and re-coupling T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

72 MM:overview GEEP Application: covd Conclusion MM Schemes Bloechl Scheme!!!!!! Density fitting in g-space of the total density! ˆn(r, R )= X q g (r, R ) Reproduce the correct Long-Range electrostatics! Q l = W = Z Z drr l Y l (n(r, R ) ˆn(r, R )) drr 2 (n(r, R ) ˆn(r, R )) minimise! Decoupling and Recoupling using these charges P. E. Bloechl, J. Chem. Phys., 103 (17), 1995, pp T. Laino, F. Mohamed, A. Laio and M. Parrinello, J. Chem. Th. Comp., 2 (5), 2006, pp

73 MM:overview GEEP Application: covd Conclusion MM Schemes Charged OV Migration of charged oxygen vacancy defects in silica dimer! deloc. el. E δ T. Laino, D. Donadio, I-Feng W. Kuo, Phys. Rev. B, 2007

74 MM:overview GEEP Application: covd Conclusion MM Schemes Charged OV Migration of charged oxygen vacancy defects in silica dimer! deloc. el. E δ E 1 T. Laino, D. Donadio, I-Feng W. Kuo, Phys. Rev. B, 2007

75 MM:overview GEEP Application: covd Conclusion MM Schemes Charged OV Migration of charged oxygen vacancy defects in silica dimer! deloc. el. E δ E 1 E 1 * T. Laino, D. Donadio, I-Feng W. Kuo, Phys. Rev. B, 2007

76 MM:overview GEEP Application: covd Conclusion MM Schemes

77 MM:overview MM Schemes GEEP Application: covd Conclusion

78 MM:overview GEEP Application: covd Conclusion MM Schemes NEB: Minimum Energy Path T. Laino, D. Donadio, I-Feng W. Kuo, Phys. Rev. B, 2007

79 MM:overview GEEP Application: covd Conclusion MM Schemes NEB: Minimum Energy Path T. Laino, D. Donadio, I-Feng W. Kuo, Phys. Rev. B, 2007

80 Image Charge & MM molecule + EAM metal nitrobenzene/au(111) Siepmann Sprik., JCP (1995) 102 Golze Iannuzzi Passerone Hutter, JCTC (2013) : DFT optimized structures of the five investigated molecules adsorbed on a m surface: (a) nitrobenzene, (b) thymine, (c) guanine, (d) benzene on Au(11 (e) water on Pt(111). Color code: orange: C, white: H, blue: N, red : O, y Au, grey: Pt. 52, for large N, computing the single Gaussian potentials v on the full g

81 Image Charge & MM molecule + EAM metal nitrobenzene/au(111) IC (r) = X CImet exp Imet VH (r) + VIC (r) = Z r RImet 2 (r0 ) + IC (r0 ) 0 dr = V0 0 r r IC induce polarization, solved selfconsistently Siepmann Sprik., JCP (1995) 102 Golze Iannuzzi Passerone Hutter, JCTC (2013) : DFT optimized structures of the five investigated molecules adsorbed on a m surface: (a) nitrobenzene, (b) thymine, (c) guanine, (d) benzene on Au(11 (e) water on Pt(111). Color code: orange: C, white: H, blue: N, red : O, y Au, grey: Pt. 52, for large N, computing the single Gaussian potentials v on the full g

, JCP (1995) 102 Golze Iannuzzi Passerone Hutter, JCTC (2013) : DFT optimized structures of the five investigated molecules adsorbed on a m surface:

82 Image Charge & MM molecule + EAM metal nitrobenzene/au(111) IC (r) = X CImet exp Imet VH (r) + VIC (r) = Z r RImet 2 (r0 ) + IC (r0 ) 0 dr = V0 0 r r IC induce polarization, solved selfconsistently Siepmann Sprik., JCP (1995) 102 Golze Iannuzzi Passerone Hutter, JCTC (2013) : DFT optimized structures of the five investigated molecules adsorbed on a m surface: (a) nitrobenzene, (b) thymine, (c) guanine, (d) benzene on Au(11 IC-MM IC+V:H O, y VH on Pt(111). Color code: orange: C, white: H, blue: N,Vred (e)dft water Au, grey: Pt. 52, for large N, computing the single Gaussian potentials v on the full g

83 IC distribution Z Z (VH (r) (VH (r) + VIC (r) V0 ) gi (r) + X J CJ V0 ) gi (r) = Z Z gj (r0 )gi (r) drdr0 0 r r linear set of eq. (CG iterative scheme) arameters. (a) Dependence of total energy and x-gradients (of an etal atom) on parameter. The x-gradients refer to the image charge n, see Eq. 9. (b) Execution time of a single point calculation of thymine performed on Cray XK6 system. Note that a double logarithmic scale. ations and performance ariable in the IC-/MM scheme is the width of the Gaussian charge 53

84 H2O cluster on Pt(111) H 2 O, Pt EAM, H 2 O-Pt Siepmann-Sprik + IC 1H 2 O 2H 2 O 12H 2 O kj/mol E int E ads E int E ads E H bond E int E ads E H bond /MM IC-/MM full DFT

85 1 2 e 27 of 36 Journal of Chemical Theory and Computation honeycomb arrangement 10 70% on-top site occupied density Figure 11: 29 Structural and electronic properties obtained for a water film on Pt(111). (a) Typical snapshot of30 the water/pt(111) simulation cell. (b) Snapshot of the water adlayer. (c) Plane-averaged water density rw along the surface normal. The arrows indicate the division of the water film in 31 4 different layers. (d) Plane-averaged particle density rp for O and H atoms. (e) Plane-integrated 32 difference Dr 1D between water and Pt(111). electronic density elec the water molecules in these regions are expected to be massively overstructured. Further away 35 Liquid Water at Pt(111) from the surface, the density oscillations decay rapidly. For distances larger than 10 Å, the density 55

86 H-bond distribution 56

CP2K: Selected Developments

CP2K: Selected Developments Jürg Hutter Department of Chemistry University of Zurich Outline Introduction History and Performance Current and Future Developments Post-Hartree-Fock Methods GW Methods RPA