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About handling on the Grid  quantum molecular knowledge related to molecular simulators

About handling on the Grid  quantum molecular knowledge related to molecular simulators. Authors: A. Laganà 1 , A. Costantini 1 , O. Gervasi 2 Location: 1) Department of Chemistry, University of Perugia, Perugia, Italy

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About handling on the Grid  quantum molecular knowledge related to molecular simulators

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  1. About handling on the Grid quantum molecular knowledge related to molecular simulators Authors: A. Laganà1, A. Costantini1, O. Gervasi2 Location: 1) Department of Chemistry, University of Perugia, Perugia, Italy 2) Department of Mathematics and Computer Science, University of Perugia, Perugia, Italy

  2. THE STARTING POINT SIMBEX: design and implementation of a Simulator of Molecular Beam Experiments for atom diatom reactions using classical trajectories (demo at first EGEE meeting) GEMS: design and partial implementation of a Grid Enabled Molecular Simulator using both quantum and classical trajectory methods to mimic molecular processes GEMMS: design and feasibility studies of Grid Empowered Molecular and Matter Sciences in a cooperative fashion using in-house and commercial packages To change: View -> Header and Footer

  3. WORKFLOW OF SIMBEX Input Interaction Dynamics Measurables Virtual Monitor To change: View -> Header and Footer

  4. The INTERACTION module START Is there a suitable LEPS Pes? NO INTERACTION YES Import the LEPS parameters DYNAMICS To change: View -> Header and Footer

  5. The DYNAMICS module Are classical trajectory calculations appro- priate? NO DYNAMICS YES TRAJ: application performing atom diatom classical trajectory integration OBSERVABLES To change: View -> Header and Footer

  6. TRAJECTORY DISTRIBUTION Master: Worker: DO traj_index =1, traj_number RECEIVE status message IF worker “ready” THEN generate seed SEND seed to worker ELSE GOTO RECEIVE endIF endDO SEND “ready” status message RECEIVE seed integrate trajectory update indicators SEND “ready” status message GOTO RECEIVE To change: View -> Header and Footer

  7. GRIDIFYING the TRAJ kernel Define quantities of general use TRAJ Iterate over initial conditions the integration of individual trajectories (ABCTRAJ, etc.) return To change: View -> Header and Footer

  8. The MEASURABLE module Is the observable a state-to-state one? NO OBSERVABLES YES DISTRIBUTIONS: VM for scalar and vector product distributions, and state-to-state crosssections END: EXTEND THE CALCULATIONTO OTHER PROPERTIES Do calculated and measured properties agree? YES END: TRY WITH ANOTHER SURFACE NO To change: View -> Header and Footer

  9. THE H+ICl REACTION THE VIRTUAL MONI-TORS BUILD IN REAL TIME THE PRODUCT ANGULAR DISTRIBU-TIONS OF THE VA-RIOUS CHANNELS H+ICl→HI+Cl H+ICl→H + ICl H+ICl→HCl+I To change: View -> Header and Footer

  10. THE MOLECULAR BEAM EXPERIMENTof Perugia MEASURABLES • Angular and time of flight product distributions INFORMATION OBTAINABLE - Primary reaction products • Reaction mechanisms • Structure and life time of transients • Internal energy distribution of products • Key features of the potential To change: View -> Header and Footer

  11. From representation to simulation SIMULATION OF MOLECULAR PROCESSES REPRESENTATION OF EXPERIMENTAL APPARATUSES VISUALIZATION OF MOLECULAR STRUCTURES To change: View -> Header and Footer

  12. Types of molecular visualization • Type of molecular representations: • Balls and Sticks (BS) • Wire frame (WF) • Space filling (SF) • SF+WF • Colored wire frame • Properties • Transparency • Labels • The atoms are colored using the RASMOL CPK coloring scheme

  13. Simulation of molecular processes A direct (versus the previous complex) mechanism for reactive processes To change: View -> Header and Footer

  14. The analysis of the potential surface The evolution of the arrier to reaction as a function of the collision angle To change: View -> Header and Footer

  15. The minimum energy path (MEP) in the BO space To change: View -> Header and Footer

  16. Fixed target geometry isoenergetic contours To change: View -> Header and Footer

  17. CONTOURS AND MEPS A coordinate smoothly connecting reactants to products Remaining coordinates are mutually orthogonal (bifurcations difficult to handle) • LEPS surface • Isometric contours • Choosing a proper set of coordinates To change: View -> Header and Footer

  18. PRESENT ADVANCES EXTEND European collaboration to GEMS (Grid Enabled Molecular Simulations) using quantum means • WG1 PHOTODYN: Computational photochemistry and photobiology • WG2 QDYN: Quantum dynamics engines for Grid enabled molecular simulators • WG3 ELAMS: E-science and Learning approaches in Molecular Science • WG4 DECIQ: Code interoperability in Computational Quantum Chemistry • WG5 CCWF: Computational Chemistry Workflows and Data Management • WG6 AIMD4GRID: Ab initio Molecular Dynamics for the Grid The D37 (GRIDCHEM) COST CMST action To change: View -> Header and Footer

  19. QUANTUM SCATTERING - time-independent: time is factored out of the wavefunction and the problem becomes a single energy stationary one - time-dependent: the time dependent Schrödinger equation is integrated at a given initial state by following the evolution in time of the wavepacket The wavefunction  carries all the needed information on the scattering process. To change: View -> Header and Footer

  20. DYNAMICS module Are classical trajectory calculations appro- priate? TI: application carrying out time-independent quantum calculations (atom-diatom) Is the calculation single initial state? NO NO DYNAMICS YES YES TD: application carrying out time- dependent quantum calculations (atom-diatom) TRAJ: application using classical trajectory calculations OBSERVABLES To change: View -> Header and Footer

  21. THE TIME DEPENDENT METHOD Collocate the wavepacket Time propagate the wavepacket Carry out its analysis at the product asymptote To change: View -> Header and Footer

  22. TIME DEPENDENT PSEUDOCODE Master: Worker: DO init_cond =1, N_initcond RECEIVE status message IF worker “ready” THEN SEND init_cond to worker ELSE GOTO RECEIVE endIF endDO SEND “ready” status message RECEIVE init_cond integrate in time generate the S matrix element SEND “ready” status message GOTO RECEIVE To change: View -> Header and Footer

  23. Gridified time dependent method Define quantities of general use TD • Iterate over initial conditions • the integration over time • propagation (RWAVEPR, etc.) return To change: View -> Header and Footer

  24. Gridified time independent method Define quantities of general use including the integration bed TI Iterate over the reaction coor- dinate to build the interaction matrix Broadcast coupling matrix Iterate over total energy value the integration of scattering equations return To change: View -> Header and Footer

  25. The N+N2 reaction Grid based molecular simulators: the nitrogen atom reactions Leonardo Pacifici A QUANTUM STUDY OF REACTIONS CONTRIBUTIONS TO HEAT DISSIPATION AROUND REENTERING SPACECRAFTS To change: View -> Header and Footer

  26. State to state probabilities Grid based molecular simulators: the nitrogen atom reactions Leonardo Pacifici E(v) 0.146 eV V=0 V=1 0.433 eV V=2 0.717 eV V=3 0.997 eV 1.270 eV V=4 V=5 1.543eV To change: View -> Header and Footer

  27. Grid based molecular simulators: the nitrogen atom reactions Leonardo Pacifici Threshold energies Etr 1.359 eV V=0 V=1 0.950 eV V=2 0.772 eV V=4 0.199 eV To change: View -> Header and Footer

  28. Rate coefficients ● ● To change: View -> Header and Footer

  29. A Model quantum problem OUTLINE • H+/D+ ions flowing through a carbon nanotube • A quantum scattering problem solved using a 3D time-dependent technique (the problem has been already solved using classical approaches) • Implementation of a quantum scattering formalism based on polar cylindrical coordinates to single out resonances, interferences and tunneling To change: View -> Header and Footer

  30. THE NANOTUBES • Carbon nanotubes are cylindrical aggregates of carbon atoms • They can be seen as a wrapped around plane of graphite. - The p orbitals of the carbon atoms are perpendicular to the C plane and and form an aromatic like layer. To change: View -> Header and Footer

  31. Carbon nanotubes are highly stable and show several highly interesting technological properties as new materials. An interesting application is as hydrogen storage f. To change: View -> Header and Footer

  32. NANOTUBES AS QUANTUM SIEVES - Nanotube have been considered for separation of mixtures of molecules of similar shape. • They can bind, in fact, differently to the internal part of the nanotube and alter the partition function. • Such an effect is expected to be particularly pronounced for H/D isotopic variants. To change: View -> Header and Footer

  33. SCATTERING IN CYLINDRICAL SYMMETRY PROBLEMS In thenanotube problem the symmetry is about cylindrical The most suitable coordinates are the polar cylindrical ones (r,,z) The projection of the total angular momentum on z is a good quantum number To change: View -> Header and Footer

  34. THE ELECTRONIC STRUCTURE The ab initio calculation of the electronic structure of a carbon nanotube at the level of 'chemical accuracy' is highly demanding in terms of computational resources Most often DFT techniques are used to handle the problem (A.D. Becke, J. Chem. Phys. 1993, 98, 5648). S. K. Gray et al calculated the bound states of an H2 molecule placed inside a carbon nanotube (with all its degrees of freedom) (T. Lu, E.M. Goldfield and S. K. Gray, J. Phys. Chem. B 2003, 107, 12989). To change: View -> Header and Footer

  35. A FORCE FIELD APPROACH We used for our study an atom-atom additive semiempirical force field. All interactions are formulated as van der Waals one between the H+ ion and the C atom. The functional form used is a Lennard-Jones 6-12 : The value of the parameters are (JACS 1995):  = 3.90310-5 h  = 3.157 a0 To change: View -> Header and Footer

  36. BASIS SET The z component of the wavefunction is given by plane waves: with k being the momentum along z. The radial component is a Bessel function and the angular component is an imaginary expomential R is the nanotube radius K is the angular momentum component on z ρn is the nth zero of the Bessel function JK To change: View -> Header and Footer

  37. RADIAL FUNCTION To change: View -> Header and Footer

  38. THE HAMILTONIAN The Hamiltonian for a particle in cylindrical soordinates reads: with - By substituting f by r1/2f the first derivative disappears - By adopting cylindrical polar instead of cartesian coordinates it does appear a centripetal term towards the center of the cylinder - At non zero total angular momentum values the centripetal term is absorbed inside the cetrifugal one To change: View -> Header and Footer

  39. THE WAVEPACKET - The initial (t=0) wavepacket is placed at one end of the nanotube - Its shape is that of an eigenfunction of the polar component of the Hamiltonian with a given component of the total angular momentum and a given radial excitation (that of the corresponding Bessel function) - Its z component is a Gaussian times a phase factor (corresponding to the linear momentum) To change: View -> Header and Footer

  40. THE PROPAGATION The wavepacket is propagated as usual using the propagator - The potential operator is diagonal when represented on a grid • Translation along z and r is dealt using a bidimensional Fourier transform • Rotation (centrifugal term) is dealt using a one dimensional Fourier transform • An absorbing imaginary potential is placed at both ends of the nanotube. To change: View -> Header and Footer

  41. OUTGOING FLUX MONITORING At each time t of the propagation the expectation value of the flux operator is calculated using the expression where  is a threshold Heaviside function and z is the point at which the analysis occurs (square brackets indicate operator commutation) To change: View -> Header and Footer

  42. OUTGOING FLUX PLOTS: angular momentum H+ - Elong=0.04 h Etransv=0.01 h L=0 L=5 L=10 L=30 0.001 0.000 An increase of the value of the angular momentum quantum number slightly delays the flux (the increase of the centrifugal potential pushes the wavepacket closer to the nanotube walls). -0.001 -0.002 -0.003 0.000 -0.001 -0.002 Outgoing Flux -0.003 0.000 -0.001 -0.002 -0.003 0.000 -0.001 -0.002 -0.003 0 500 1000 1500 2000 Time (atomic units) To change: View -> Header and Footer

  43. OUTGOING FLUX PLOTS: transversal excitation H+ - Elong=0.04 h Etransv=0.03 h Transversal excitation also slightly delays the flux and introduces some wiggles To change: View -> Header and Footer

  44. OUTGOING FLUX PLOTS: longitudinal energy H+ - Elong=0.08 h Etransv=0.01 h A doubling of the longitudinal energy shifts the flux of a factor √2. To change: View -> Header and Footer

  45. OUTGOING FLUX PLOTS: isotopic effectD+, Elong = 0.04 h, Etrasv = 0.01 h A doubling of the mass shifts the flux of a factor √2 To change: View -> Header and Footer

  46. THE EXTENDED WORKFLOW In an extended approach the whole workflow is considered including • the generation of the potential energy values and their functional representation • the integration of full (classical) dimensional motion equations for many atom systems • statistical averaging to build observable quantities • visual techniques to single out relevant patterns

  47. Extended INTERACTION module START Take force field data and procedures from related databases Are ab initio calculations available? Are ab initio calculations feasible? NO NO Is there a suitable Pes? NO INTERACTION YES YES YES Import the PES routine CALL FITTING CALL SUPSIM DYNAMICS To change: View -> Header and Footer

  48. Gridified Ab initio approach Define the characteristics of the ab initio calculation, the coordinates used and the Variable’s intervals SUPSIM Iterate over the system geometries geometries the call of ab initio suites of codes (GAMESS, etc) return To change: View -> Header and Footer

  49. Gridified FITTING portal YES YES YES Are remai- ning values inaccurate? Do ab initio values have the proper sym- metry? Are asym- ptotic values accurate? FITTING NO NO NO Modify asym- ptotic values Modify short and long range values Enforce the proper symmetry Application using fitting programs to generate a PES routine Return To change: View -> Header and Footer

  50. EXTENDED DYNAMICS module DYNAMICS NO NO Are classical trajectory calculations appro- priate? Is it A many Body problem? NO Is the calculation single initial state? YES YES YES TD: application carrying out time- dependent quantum calculations (atom-diatom) DL_POLY: application using classical mechanics to many body systems TI: application carrying out time-independent quantum calculations (atom-diatom) TRAJ: application using classical few body trajectory calculations OBSERVABLES To change: View -> Header and Footer

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