Maykel L. González-Martínez 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions OUTLINE 1. MOTIVATION 2. QUASI-CLASSICAL TRAJECTORY METHOD - ANGLE-ACTIONS & CARTESIAN COORDINATES - ECCPST 3. RESULTS - CH 2 CO  CH 2 + CO… P(E trans ; j CO ) distributions 4. SUMMARY & PERSPECTIVES 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions WHAT, WHY…? (OBJECT) Planetary atmospheres, interstellar media First-principles amazingly-accurate theoretical predictions 3- to 4-atom systems: Highly detailed experimental results 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions Molecules of biological interest‏ WHAT, WHY…? (OBJECT) 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions Nano-objects WHAT, WHY…? (OBJECT) 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions Clusters WHAT, WHY…? (OBJECT) 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions High interpretative power, intuition… ‘Simplicity’ Extensivity Prediction (‘smart’ influence)‏ Uni-, bi-molecular reactions, etc… WHAT, WHY…? (METHOD) Relatively low computational expense 6 th IMP, Feb. 1-5, C. Habana

0 < t < T max (R ≤ R max ) 2.- Hamilton/Newton equations of motion N traj = N tot 3.- Statistics: From microscopic variables to observables Quasi-Classical Trajectory Method (QCTM)‏ t = (QC) initial conditions Intro Motivation Theory Results Conclusions 6 th IMP, Feb. 1-5, C. Habana

Unimolecular dissociation of ketene 6 th IMP, Feb. 1-5, C. Habana Intro Motivation Theory Results Conclusions

6 th IMP, Feb. 1-5, C. Habana Intro Motivation Theory Results Conclusions E b ~ few hundred cm -1 Δ ST ≈ 3150 cm -1 (Reproduced from I. -C. Chen, et al J. Chem. Phys. 89, 314 (1988)‏) RESULTS: E exc < E th (S 0 )  barrier (T 1 ) E exc ~ E th (S 0 ) cm -1 P diss (S 0 ) ~ 80% ↑ E exc : loose  tight TS Effective barrierless polyatomic unimolecular reaction in a single PES

Intro Motivation Theory Results Conclusions 6 th IMP, Feb. 1-5, C. Habana A. V. Komissarov et al. J. Chem. Phys. 124, (2006)‏ RESULTS: ketene… P(E Trans ; j CO )

J. Chem. Phys. 126, (2007)‏ Intro Motivation Theory Results Conclusions 6 th IMP, Feb. 1-5, C. Habana A. A. Hoops et al. J. Chem. Phys. 114, 9020 (2001)‏

Intro Motivation Theory Results Conclusions J. Chem. Phys. 126, (2007)‏ RESULTS: NCO, P(E Trans ) ‘explained’… 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions Some problems… QCTM (+ GW): application to polyatomics 6 th IMP, Feb. 1-5, C. Habana Angle-action variables Ideal for initial conditions Not ideal for propagation Preferable for final statistics GW requires ~ 10 times more trajectories/vibration… 10 4 ! Microcanonical distribution at the TS Cartesian coordinates Not ideal for initial conditions Ideal for propagation OK for final statistics No general transformation from AA to CC!

RESULTS: photo-fragmentation of ketene J. Chem. Phys. 130, (2009)‏ Intro Motivation Theory Results Conclusions 6 th IMP, Feb. 1-5, C. Habana

CH 2 (x 1 - -) CO(x 4 ) CH 2 (- - x 3 ) CH 2 (- x 2 -) Intro Motivation Theory Results Conclusions J. Chem. Phys. 130, (2009)‏ 6 th IMP, Feb. 1-5, C. Habana

j 2 j 1  1 J J z l Intro Motivation Theory Results Conclusions J. Chem. Phys. 130, (2009)‏ 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions Hipothesis: Time-reversed dynamics yields MC ‘distro’ at TS Hamilton-Brumer… Microcanonical distribution at the products QCTM: Exit-channel corrected PST I. Hamilton and P. Brumer, J. Chem. Phys. 82, 595 (1985) accepted (t’  -t)rejected 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions Some advantages… QCTM: Exit-channel corrected PST Initial conditions  R | TS  flexibly (re-)defined Threshold behavior Partitioning into product normal modes No discretizing + no binning/weighting at t = T max Avoids the strong interaction region 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions Phys. Chem. Chem. Phys. 12, 115 (2010) 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions QCTM: A modification to the PES Phys. Chem. Chem. Phys. 12, 115 (2010) 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions Phys. Chem. Chem. Phys. 12, 115 (2010) 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions QCTM: How to ‘add’ the rotational resolution? Phys. Chem. Chem. Phys. 12, 115 (2010) 6 th IMP, Feb. 1-5, C. Habana

ETET j = 0 j = 2 Least-biased Quantum P(ET)P(ET) ETET E T = E - hw /2 - B v j(j+1) Least-biased Quantum with convolution Least-biased Classical with convolution or E T = E - ‘exact’ ro-vibrational energy QCTM: P(E Trans ; v) in ABC A + BC(v) h Intro Motivation Theory Results Conclusions 6 th IMP, Feb. 1-5, C. Habana Phys. Chem. Chem. Phys. 12, 115 (2010)

Ratio = LB quantum with convolution LB classical with convolution ETET 1 QCTM P(ET)P(ET) LB quantum with convolution LB classical with convolution QCTM Final curve = Intro Motivation Theory Results Conclusions 6 th IMP, Feb. 1-5, C. Habana QCTM: P(E Trans ; v) in ABC A + BC(v) h ETET Phys. Chem. Chem. Phys. 12, 115 (2010)

Intro Motivation Theory Results Conclusions QCTM: How to ‘add’ the rotational resolution? Phys. Chem. Chem. Phys. 12, 115 (2010) 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions Phys. Chem. Chem. Phys. 12, 115 (2010) 6 th IMP, Feb. 1-5, C. Habana

Intro Motivation Theory Results Conclusions Phys. Chem. Chem. Phys. 12, 115 (2010) 6 th IMP, Feb. 1-5, C. Habana

Angle-action variables to Cartesian coordinates for polyatomics Problems in S 0 PES of CH 2 CO Alternative methodology to apply QCTM to polyatomics: (1) t = 0: angle-actions to Cartesian coordinates; (2) 0 < t < T max : ‘association’ perspective (Hamilton & Brumer); (3) t = T max : QC formulae to ‘insert’ rotational resolution. (1)+(2)+(3) = ¡Ro-vibrational resolution without binning/weighting! SUMMARY & PERSPECTIVES Intro Motivation Theory Results Conclusions 6 th IMP, Feb. 1-5, C. Habana

SUMMARY & PERSPECTIVES New ab initio PES for CH 2 CO(S 0 ) PESs y aplication to C 2 H 2  C 2 H + H ECCPST to direct processes Multi-PES reactions Intro Motivation Theory Results Conclusions 6 th IMP, Feb. 1-5, C. Habana

Prof. Jesús Rubayo Soneira InSTEC, C. Habana, CUBA. Dr. Pascal Larrégaray ISM, Bordeaux, FRANCE. Prof. Jean-Claude Rayez ISM, Bordeaux, FRANCE. Dr. Laurent Bonnet ISM, Bordeaux, FRANCE. 6 th IMP, Feb. 1-5, C. Habana Intro Motivation Theory Results Conclusions

Instituto Superior de Tecnologías y Ciencias AplicadasUniversité Bordeaux 1 Inter-University Agreement on International Joint Doctorate Supervision between the Instituto Superior de Tecnologías y Ciencias Aplicadas (CUBA) and the Université Bordeaux 1 (FRANCE)‏ Departamento de Física General Instituto Superior de Tecnologías y Ciencias Aplicadas PNCB/2/04 project of the Departamento de Física General del Instituto Superior de Tecnologías y Ciencias Aplicadas (CUBA) MANY THANKS FOR YOUR ATTENTION 6 th IMP, Feb. 1-5, C. Habana Intro Motivation Theory Results Conclusions