Maykel L. González-Martínez

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

OUTLINEOUTLINE

1. MOTIVATION

2. QUASI-CLASSICAL TRAJECTORY METHOD - ANGLE-ACTIONS & CARTESIAN COORDINATES - ECCPST

3. RESULTS - CH2CO CH2 + CO… P(Etrans; jCO) distributions

4. SUMMARY & PERSPECTIVES

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

WHAT, WHY…? WHAT, WHY…? (OBJECT)(OBJECT)

Planetary atmospheres, interstellar media

First-principles amazingly-accurate theoretical predictions

3- to 4-atom systems:3- to 4-atom systems:

Highly detailed experimental results

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

Molecules of biological interest

WHAT, WHY…? WHAT, WHY…? (OBJECT)(OBJECT)

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

Nano-objects

WHAT, WHY…? WHAT, WHY…? (OBJECT)(OBJECT)

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

Clusters

WHAT, WHY…? WHAT, WHY…? (OBJECT)(OBJECT)

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

High interpretative power, intuition…

‘Simplicity’ Extensivity

Prediction (‘smart’ influence)

Uni-, bi-molecular reactions, etc…

WHAT, WHY…? WHAT, WHY…? (METHOD)(METHOD)

Relatively low computational expense

6th IMP, Feb. 1-5, 2010. C. Habana

0 < t < Tmax (R ≤ Rmax)

2.- Hamilton/Newton equations of motion

Ntraj = Ntot

3.- Statistics: From microscopic variables to observables

Quasi-Classical Trajectory Method (QCTM)

t = 01.- (QC) initial conditions

Intro Motivation Theory Results Conclusions 6th IMP, Feb. 1-5, 2010. C. Habana

Unimolecular dissociation of ketene

6th IMP, Feb. 1-5, 2010. C. HabanaIntro Motivation Theory Results Conclusions

6th IMP, Feb. 1-5, 2010. C. HabanaIntro Motivation Theory Results Conclusions

Eb ~ few hundred cm-1

ΔST ≈ 3150 cm-1

(Reproduced from I. -C. Chen, et al J. Chem. Phys. 89, 314 (1988))

RESULTS:

Eexc < Eth(S0) barrier (T1)

Eexc ~ Eth(S0) + 200 cm-1

Pdiss(S0) ~ 80%

↑Eexc: loose tight TS

Effective barrierless polyatomic unimolecular reaction in a single PES

Intro Motivation Theory Results Conclusions 6th IMP, Feb. 1-5, 2010. C. Habana

A. V. Komissarov et al. J. Chem. Phys. 124, 014303 (2006)

RESULTS: ketene… P(ETrans; jCO)

J. Chem. Phys. 126, 041102 (2007)

Intro Motivation Theory Results Conclusions 6th IMP, Feb. 1-5, 2010. C. Habana

A. A. Hoops et al. J. Chem. Phys. 114, 9020 (2001)

Intro Motivation Theory Results Conclusions

J. Chem. Phys. 126, 041102 (2007)

RESULTS: NCO, P(ETrans) ‘explained’…

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

Some problems…Some problems…

QCTM (+ GW): application to polyatomics

6th IMP, Feb. 1-5, 2010. C. Habana

Angle-action variables • Ideal for initial conditions• Not ideal for propagation• Preferable for final statistics

GW requires ~ 10 times more trajectories/vibration… 104!

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, 114103 (2009)

Intro Motivation Theory Results Conclusions 6th IMP, Feb. 1-5, 2010. C. Habana

CH2(x1 - -) <scissor>

CO(x4)

CH2(- - x3) <asym. stretch>

CH2(- x2 -)<sym. stretch>

Intro Motivation Theory Results Conclusions

J. Chem. Phys. 130, 114103 (2009)

6th IMP, Feb. 1-5, 2010. C. Habana

j2 <CO rot.>j1 <CH2 rot.> 1 <j1 proj.>

J <tot. ang. momentum> Jz <J proj.> l <tot. orbital>

Intro Motivation Theory Results Conclusions

J. Chem. Phys. 130, 114103 (2009)

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

Hipothesis: Time-reversed dynamics yields MC ‘distro’ at TS

Hamilton-Brumer…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) rejected6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

Some advantages…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 = Tmax

Avoids the strong interaction region

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

Phys. Chem. Chem. Phys. 12, 115 (2010)

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

QCTM: A modification to the PES

Phys. Chem. Chem. Phys. 12, 115 (2010)

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

Phys. Chem. Chem. Phys. 12, 115 (2010)

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

QCTM: How to ‘add’ the rotational resolution?

Phys. Chem. Chem. Phys. 12, 115 (2010)

6th IMP, Feb. 1-5, 2010. C. Habana

ET j = 0j = 2

Least-biased Quantum

ET

ET = E - hw/2 - Bvj(j+1)

Least-biased Quantumwith convolution

Least-biased Classicalwith convolution

or ET = E - ‘exact’ ro-vibrational energy

QCTM: P(ETrans; v) in ABC A + BC(v)h

Intro Motivation Theory Results Conclusions 6th IMP, Feb. 1-5, 2010. C. Habana

Phys. Chem. Chem. Phys. 12, 115 (2010)

Ratio =LB quantum with convolution

LB classical with convolution

ET

1

QCTM

LB quantum with convolution

LB classical with convolutionQCTM Final curve =

Intro Motivation Theory Results Conclusions 6th IMP, Feb. 1-5, 2010. C. Habana

QCTM: P(ETrans; v) in ABC A + BC(v)h

ET

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)

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

Phys. Chem. Chem. Phys. 12, 115 (2010)

6th IMP, Feb. 1-5, 2010. C. Habana

Intro Motivation Theory Results Conclusions

Phys. Chem. Chem. Phys. 12, 115 (2010)

6th IMP, Feb. 1-5, 2010. C. Habana

• Angle-action variables to Cartesian coordinates for polyatomics

• Problems in S0 PES of CH2CO

• Alternative methodology to apply QCTM to polyatomics: (1) t = 0: angle-actions to Cartesian coordinates; (2) 0 < t < Tmax: ‘association’ perspective (Hamilton & Brumer);

(3) t = Tmax: QC formulae to ‘insert’ rotational resolution.

(1)+(2)+(3) = ¡Ro-vibrational resolution without binning/weighting!

SUMMARY & PERSPECTIVES

Intro Motivation Theory Results Conclusions 6th IMP, Feb. 1-5, 2010. C. Habana

SUMMARY & PERSPECTIVES

• New ab initio PES for CH2CO(S0)

• PESs y aplication to C2H2 C2H + H

• ECCPST to direct processes

• Multi-PES reactions

Intro Motivation Theory Results Conclusions 6th IMP, Feb. 1-5, 2010. C. Habana

Prof. Jesús Rubayo SoneiraInSTEC, C. Habana, CUBA.

Dr. Pascal LarrégarayISM, Bordeaux, FRANCE.

Prof. Jean-Claude RayezISM, Bordeaux, FRANCE.

Dr. Laurent BonnetISM, Bordeaux, FRANCE.

6th IMP, Feb. 1-5, 2010. C. HabanaIntro Motivation Theory Results Conclusions

• Inter-University Agreement on International Joint Doctorate Supervision between the Instituto Superior de Tecnologías y Instituto Superior de Tecnologías y Ciencias AplicadasCiencias Aplicadas (CUBA) and the Université Bordeaux 1Université Bordeaux 1 (FRANCE)

• PNCB/2/04 project of the Departamento de Física GeneralDepartamento de Física General del Instituto Superior de Tecnologías y Ciencias AplicadasInstituto Superior de Tecnologías y Ciencias Aplicadas (CUBA)

MANY THANKS FOR

YOUR ATTENTION

6th IMP, Feb. 1-5, 2010. C. HabanaIntro Motivation Theory Results Conclusions