INELASTIC AND REACTIVE ELE-MENTARY PROCESSES IN ATOM- DIATOM, DIATOM-DIATOM COLLISIONS AND BEYOND

1. INELASTIC AND REACTIVE ELE-MENTARY PROCESSES IN ATOM- DIATOM, DIATOM-DIATOM COLLISIONS AND BEYOND Antonio Laganà* Dipartimento di Chimica University of Perugia lag@unipg.it *Antonio Riganelli, Dimitris Skouteris, Leonardo Pacifici, Noelia Faginas Lago, Stefano Crocchianti

2. MULTISCALE SIMULATIONS Electronic structure Nuclear dynamics Kinetics of non elementary processes Fluid dynamics, electrodynamics, etc. Macroscopic properties of realistic systems

3. SUMMARY • A priori molecular simulations: theoretical means • The N + N2 collisions: beyond quasiclassical • The need for accurate potential energy surfaces • Some diatom-diatom, atom-polyatom processes • Towards complex molecular systems • Concurrent computing • Metalaboratories for molecular calculations • Grid enabled molecular simulators

4. TRAJECTORY CALCULATIONS • A + BC (i)  AB (f) + C (reactive) The atom- diatom case •  AC (f) + B (reactive) •  A + BC (f) (non reactive) •  A + B + C (dissociative) The Hamilton equations dRx/dt=PRx/µA,BC dPRx/dt=-∂V/∂Rx dRy/dt=PRy/µA,BC dPRy/dt=-∂V/∂Ry dRz/dt=PRz/µA,BC dPRz/dt=-∂V/∂Rz drx/dt=Prx/µBC dPrx/dt=-∂V/∂rx dry/dt=Pry/µBC dPry/dt=-∂V/∂ry drz/dt=Prz/µBC dPrz/dt=-∂V/∂rz Integrate the above differential equations from a given configuration of the reactants until a final reactive, non reactive or dissociation configuration is reached

5. QUANTUM METHODS Time dependent {W} – set of position vectors of the nuclei or any other choice of coordinates Hn - nuclear Hamiltonian Factor out time and choose a different continuity va-riable (or transformation from reactants to products) Time independent

6. THE DYNAMICAL QUANTITIES • PROBABILITY: Pif=Nif/N or =|Sif|2 • CROSS SECTION: σif=πb2maxPif • RATE COEFFICIENTS: averaging σif(E) over discrete distributions and integrating over continuous distributions Reaction and Molecular Dynamics, Springer, 2000

7. RECENT DYNAMICAL STUDIES • N + N2 , H+H2, O+O2 • H2+OH, H2+H2, OH+HCl, OH+CO • Cl + CH4

8. Nitrogen atom Nitrogen molecule reaction Previous calculations: extended quasiclassical trajectory calculations of state to state rate coefficients (available for distribution)

9. : exact quantum calculations v=0-5 j=0,1,2 • Initial quantum states • LEPS surface • Zero total angular momentum • Time dependent approach in Jacobi coordinates • Collision energy interval E=1.359-1.759 eV • Iterations: ~2000

10. THE TIME DEPENDENT METHOD Collocate the wavepacket Time propagate the wavepacket Carry out its analysis at the product asymptote

11. : state to state probabilities 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

12. : threshold energies Etr 1.359 eV V=0 V=1 0.950 eV V=2 0.772 eV V=4 0.199 eV

13. Product vibrational distributions (1.65 eV)

14. Time dependent 3D Time independent RIOS

15. RIOS: state to state probabilities (v=0)

16. RIOS vs 3D product vibrational distributions

17. State specific probabilities. Effect of rotation

18. FITTING A NEW POTENTIAL ENERGY SURFACE (PES) • Fit the parameters of the PES to ab initio data • Adopt process coordinates instead of arrangement coordinates (like Jacobi coordinates) • Use bond order (BO) variables defined as nij=exp[-βij(rij-reij)] and their polar version ρ=[n122 + n232]½α=atan(n23/n12)

21. OH + HCl

22. POLYATOMIC REACTION FUNCTIONAL FORMS • ROtating BO (ROBO) and Largest Angle Generalization ROBO (LAGROBO). • Many Process Expansion (MPE) W=ξWξVξ

30. MOVING TO LARGER SYSTEMS • Simplify the interaction • Decompose the domain

31. THE FORCE FIELD • The most popular formulations of force fields separate intra- from inter-molecular forces • Intramolecular terms are associated to functional forms fitted to ab initio data • Intermolecular are expressed as sums of two body semiempirical (usually of the Lennard Johnes type) functionals

32. Interaction representation • Many body expansion truncated to the second term • Two body interactions are of the atom(ion) – atom(ion) type • Portability among different systems

33. n Isomer GP E(1/cm) 1 (1׀0) C6v -356 2 (1|1) D6h -711 2 (2|0) C3v -665 Isomer (2|0) EnergyminimizationArnC6H6 Isomer (1|1)

34. OTHER NEW GLOBAL POTENTIALS • Atom-bond pseudo two-body (Pirani et al.) V({r}) = ∑k∑mLkm(rkm,,αkm) L = Lennard Johnes potential, k = atom index, m = bond index 2. Full Bond Order potential (ALLBO) (Laganà et al.) V({r}) = ∑k∑lL kl(nkl) P = Bond order potential, k = atom index, l = bond index nkl is the Bond Order variable of the kl atomic pair

35. CONCURRENCY IN MOLECULAR CALCULATIONS • 1. NATURAL CONCURRENCY FROM EXTENSIVE TRAJECTORY CALCULATIONS • 2. MULTILEVEL CONCURRENCY IN QUANTUM CALCULATIONS

36. SISD (Single Instruction stream Single Data stream) CU Control Unit PU Processing Unit MM Memory Module IS Instruction stream DS Data stream CU IS PU DS MM

37. SIMD (Master - workers) DS1 PU1 MM1 DS2 CU IS PU2 MM2 DSn PUn MMn

38. MIMD (Cooperative workers) CU IS1 PU1 DS1 MM1 IS2 DS2 CU PU2 MM2 DSn ISn CU PUn MMn

39. MPI QUASICLASSICAL PSEUDOCODE 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

40. COLLABORATIVE INITIATIVES TO DEVELOP REALISTIC A PRIORI SIMULATORS • Innovative approaches to chemical (as well as to physical, aerospace, medicinal, biological, etc.) problems need the cooperation of knowledge and computer resources. • The concentration of human and hardware resources is no longer practical for logistic, economic and psycological reasons.

41. METACHEM Metalaboratories for complex computational applications in Chemistry

42. THE METALABORATORY • The METALABORATORY is a cluster of geographically distributed laboratories having complementary expertise and software programs and having some hardware resources grafted on a computing grid.

43. THE STRUCTURE OF A METALABORATORY • Several computational science laboratories acting as reservoirs of specific expertise relevant to the realization of a given project. • One particularly skilled computer science laboratory (or Large Scale Computing Facility) acting as the regulator of the grid. • Other laboratories having complementary expertises (for example an experimental laboratory).

44. ONGOING MOLECULAR SCIENCE METALABORATORIES • CI Calculations (Carsky). • DIRAC (Faegri). • SIMBEX (Gervasi) • Atmospheric processes (Aguilar) • Elchem (Laganà) • Chemical knowledge (Rossi)

45. The CHEMISTRYcommunity Simbex Murqm Dirac Elchem Icab Dysts Comovit

46. LABS per NATIONALITY (51) 1 Isr,Pl,Sk,Nl 2 Cz,Ch, Fr, Dk, A, Sw, No 3 Hu 4 Gr 5 E 6 D, Uk, 9 I

47. SIMBEX: SIMUL. MOLECULAR BEAM EXPERIMENTS • Managing an a priori simulation to be inter- faced with the experi- ment in crossed mole- cular beam measure- ments Exper. Simul.

48. The GEMS.0 demo application REQUEST: a potential fitted to beam experiments Interaction Dynamics Observables NO Theoretical and experimental results agree? YES SUPPLY: the potential and related monitors

49. The INTERACTION module START NO Force field- application taking empirical data from database to generate a PES Are ab initio calculations available? Are ab initio calculations feasible? NO Is there a suitable Pes? NO INTERACTION YES YES YES Application using fitting programs to generate a PES routine Ab initio application using programs for electronic structure Import the PES routine DYNAMICS

50. The DYNAMICS module Are quantum dynamics calculations inappropriate? TI: application carrying out time-independent quantum calculations Is the calculation single initial state? NO NO DYNAMICS YES YES TD: application carrying out time- dependent quantum calculations ABCtraj: quasiclassical trajectory calculations OBSERVABLES