DYNAMICS AROUND CRITICAL FEATURES OF ENERGY LANDSCAPES

DYNAMICS AROUND CRITICAL FEATURES OF ENERGY LANDSCAPES

BRUXELLES N. Vaeck

ORSAY D. Lauvergnat

Y. Justum

B. Lasorne

M. Desouter-Lecomte

LYON M.-C. Bacchus

K. Piechowska

LIEGE G. Dive

I. RESEARCH AREA OF THE TEAM

II. METHODOLOGY

III. CRITICAL REGIONS OF ENERGY LANDSCAPES

IV. OBJECTIVES IN THE RADAM NETWORK

I. RESEARCH AREA OF THE TEAM

II. METHODOLOGY

III. CRITICAL REGIONS OF ENERGY LANDSCAPES

IV. OBJECTIVES IN THE RADAM NETWORK

I. RESEARCH AREAI. RESEARCH AREA

Quantum description of elementary processes in gas phase

1) Electrons: ab initio quantum chemistry calculations of PES

2) Nuclei : wave packet dynamics

Chemical reactivity = exploration of an energy landscape by a wave packet possibly guided by a laser field

Chemical reactivity = exploration of an energy landscape by a wave packet possibly guided by a laser field

Particular regions leading to

quantum effects

Dynamics involving few active degrees

of freedom

Ultrafast processes

t < 1 ps

Ultra fast local quantum dynamicsUltra fast local quantum dynamics

Molecular system H

Segregation between active (q) and inactive (Q) coordinatesq : at least the n principal coordinates involved in the reaction path

II. METHODOLOGY II. METHODOLOGY

Rigid or flexible constraints

Constrained subsystem

Hconstrained+ Dissipation

II. METHODOLOGYII. METHODOLOGY

Select n active coordinates q

Hconstrained nDHconstrained nD

= VnD(q)

ab initio

= VnD(q)

ab initio

+ TnD

+ TnD

Compute a PES VnD(q)

Choose rigid or flexible kinematical model Qeq(q) = Qc or ∂Qeq(q)/∂q ≠ 0

Construct the corresponding constrained KEOTnD

II. METHODOLOGYII. METHODOLOGY

n n

nD i j i eqi ,j 1 i=

ij i2

11H + V (f ( ) f ( ) v( ) )

q q qq

TNUM generates numerically but exactly the values of the coefficients of the differential operators at any grid point.

D. Lauvergnat & A. Nauts, J. Chem. Phys. 116, 8560 (2002)

D. J. Rush et K. B. Wiberg, J. Phys. Chem. A 101, 3143 (1997), J. R. Durig et W. Zhao, J. Phys. Chem. 98, 9202 (1994)S. Sakurai N. Meinander et J. Laane, J. Chem. Phys. 108, 3537 (1998)M. L. Senent, CPL 296, 299 (1998), D. Luckhaus, J. Chem. Phys. 113, 1329 2000

Constrained Hamiltonians

III. CRITICAL FEATURES OF ENERGY LANDSCAPESIII. CRITICAL FEATURES OF ENERGY LANDSCAPES

Rate constant

Tunneling

A. Regions of strong non adiabatic

interaction

A. Regions of strong non adiabatic

interaction

B. Bifurcating regions

B. Bifurcating regions

C. Transition statesC. Transition states

IVR between reaction coordinate and deformationElectron transfer

Ultra fast internal conversion

Conversion of an optical signal into mechanical motion

Non B-O B-O

A. Regions of strong non adiabatic interactionA. Regions of strong non adiabatic interaction

Conical intersectionConical intersection

M.-C. Bacchus

K. Piechowska

CASSCF/cc-pvtz

Avoided crossingAvoided crossing

dCO dCBr or dCCl

M.-C. Bacchus

N. Vaeck

CASSCF/cc-pvdz

V2D

Up funnel

Ultra Fast

decay

Diabatic trapping or up-funnel process

Diabatic trapping or up-funnel process

Paradoxical decrease of product yield at increasing excitation energy

Photoisomerization of the Yellow proteine chromophore (p-trans coumaric acid) in S1 state

up-funnel S1/S2 and turn around towards another channel

C. Ko et al. JACS 125, 12710 (2003)

Avoided crossingAvoided crossing

Coordonnée de réaction

En

erg

ie p

ote

nti

ell

e

R

E

Coordonnée de réaction

En

erg

ie p

ote

nti

ell

e

R

E

CH2

Cl

O

Br

BrCH2CO+Cl

Br+CH2COCl

n*(C-Br) n*(C-Cl)

n*(CO)

h

= 248 nm

Competitive dissociation of bromoacetyl chloride

Experimental branching ratio

Cl:Br = 1.0:0.4

Diabatic trappingDiabatic trapping

A’’A’’

A’A’

C C

HH

O

Cl

Br

CH2

Cl

O

Br

BrCH2CO+Cl

Br+CH2COCl

n*(C-Br) n*(C-Cl)

n*(CO)

hM.D. Person, P.W. Kash & L.J. Butler, J. Chem. Phys. 97, 355 (1992) CISD/STO-3G*

W.-J. Ding et al, Journal Chemical Physics 117, 8745 (2002) CAS(8,7)/6-31G* MRCI

B. Lasorne, et al, J. Chem. Phys. 120, 1271, 2004 CASSCF/cc-pvdz (18)

Diabatic trappingDiabatic trapping

Active coordinates Two 2D subspaces

Spectator modesTwo deformations frozen at the Franck-Condon geometry

Other modes optimized in the first A" excited state

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

qx / 10-10 m

q y / 1

0-10 m

diabats in orthogonal coordinates

1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6

1

1.2

1.4

1.6

1.8

2

2.2

CBr / 10-10

m

CO/10

-10 m

adiabat 1

1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6

1

1.2

1.4

1.6

1.8

2

2.2

CBr / 10-10 m

CO

/ 1

0-10 m

adiabat 2

1.5 2 2.5 3 3.5

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

CCl / 10-10 m

CO

/ 1

0-10 m

adiabat 1

1.5 2 2.5 3 3.5

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

CCl / 10-10 m

CO

/ 1

0-10 m

adiabat 2

1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6

1

1.2

1.4

1.6

1.8

2

2.2

CBr / 10-10 m

CO

/ 1

0-10 m

diabats

COCO

COCO

Barrier

Barrier

Seam

Seam

Dynamics of photodissociation

Dynamics of photodissociation

CBrCBr

CClCCl

M.-C. Bacchus

N. Vaeck

CASSCF/cc-pvdz

―: t = 0 ―: 12 fs ―: 24 fs ―: 36 fs ―: 48 fs --: 84 fs --: 96 fs

3 4 5 6 7 8

2.5

3

3.5

4

4.5

5

qx / a.u.

q y /

a.u

.

CO/ CBr subspace

0.1

0.15

0.15

3 4 5 6 7 8

2.5

3

3.5

4

4.5

5

qx / a.u.

q y /

a.u

.

CO/CBr subspace

0.1

0.1

0.15

0.15

0.15

0.15 0.15

0.1

0.15

0.15

Dynamics of photodissociationDynamics of photodissociation

CO CBrCO CBr

Ratio of the dissociative fluxes in

the CO/CBr and CO/CCl sides

Experimental branching ratio

Cl:Br = 1.0:0.4

F-C

Dynamics in excited statesDynamics in excited statesWorks in prospectWorks in prospect

in collaboration with QCEXVAL

University of Valencia, Spain

M. Merchán y L. Serrano-Andrés, J. Am. Chem. Soc. 125, 8108

(2003)

CytosineCytosine

Adenine/(H2O)nAdenine/(H2O)n

H. Kang, K.T. Lee , S.K. Kim, Chem. Phys. Letters 359,

213 (2002).

Pump probe experience on adenine/(H20)n

Bifurcation of valleysBifurcation of valleys

C O

H

HH

B. Bifurcating regions : Valley Ridge Inflection PointB. Bifurcating regions : Valley Ridge Inflection Point

Bifurcation of ridgesBifurcation of ridges

V2D

G. Dive

QCISD 6-31G*

G. Dive

B3LYP 6-31G*

Bifurcating regionsBifurcating regions

Dynamics of a wave packet around a VRI region

V2D

spreadi

ng

Time of spreading in a flat region

Width when entering the VRI region

Curvature of the ridge

Time of flight along the ridge

Lenght of the ridge

Gradient along the ridge

Kinetic energy

Competition between

B. Lasorne, G. Dive, D. Lauvergnat and M. Desouter-Lecomte, J. Chem. Phys. 118, 5831 (2003)

TS2: TS1:

1.9631.6372.895

2.652

P

P

P’

P’

TS1

TS1

TS2

TS2

VRI

VRI

Bifurcating regionsBifurcating regions

Dimerisation of cyclopentadiene

P. Caramella, P. Quadrelli & L. Toma, JACS 124, 1130 (2002)

0 fs

10 fs

20 fs

30 fs

40 fs

50 fs

60 fs

70 fs

0 fs

10 fs

20 fs

30 fs

40 fs

50 fs

60 fs

70 fs

Bifurcating regionsBifurcating regions

Offers a rich variety of behaviours according to the shape of the wave packet

Key regions for branching ratios in the unsymmetrical case

Key regions in the control by laser field ?

20 40 60 80 100 120 140 160 180

-150

-100

-50

0

50

100

150

Key regions in the control by laser field ?Key regions in the control by laser field ?

TargetWave packet

Target

Target

InitialWave packet

After 500 fs

zz

xx

yy

H transfer

C. Regions around transition states C. Regions around transition states

Reaction coordinate s

V

tunneling

tunneling

Rate constant including tunneling

( )( )

( )

N Ek E

h E

( )E

( )N E

( ) ( - )nD jj

N E N E

by TSWP method using the flux

operator eigenvectors

B. Lasorne, F. Gatti, E. Baloïtcha, H.D. Meyer and M. Desouter-Lecomte, J. Chem.Phys. 2004 In press

0

0.1

0.2

0.3

0.4

0.5

-1 -0.5 0 0.5 1

Reaction coordinate (ua)

Ener

gy (e

V)

H exchange between hydroxyl radical and adenine.

0

0.2

0.4

0.6

0.8

1

1.2

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Energy above reactive complex (eV)

N1D

(E)

Complex absorbing potential

Complex absorbing potential

2

1 1 1

2 ˆ ˆ( ˆ ˆ() 2 ( ) )

D DDE HN E r E Ft HF

1( )

DN E

s = s#

constrained reaction path Hamiltonian

G. Dive B3LYP/6-31G**

Active coordinate : reaction coordinate s

tunneling

2

2 1 ( ) ( ) ( )

s s sT f s f s v s

Hydroxyl radical on nucleobases and ribose.

-1

-0.5

0

0.5

-8 -6 -4 -2 0 2 4 6 8

Coordonnée de réaction

Energie

(eV

)

reaction coordinate

E ev

C1

Works in prospectWorks in prospect Rate constantsRate constants

OUR OBJECTIVES IN THE RADAM NETWORKOUR OBJECTIVES IN THE RADAM NETWORK

Preliminary step: collect data at microscopic levelPreliminary step: collect data at microscopic level

Target :

understand the mechanisms of elementary processes involving quantum effects after irradiation of biomolecules

compute and hopefully control branching ratio and rate of

photodissociation

photoisomerization

electron, proton and H transfer

Target :

understand the mechanisms of elementary processes involving quantum effects after irradiation of biomolecules

compute and hopefully control branching ratio and rate of

photodissociation

photoisomerization

electron, proton and H transfer

Tools :

Quantum dynamics in reduced dimensionality

in fundamental and excited states

including a laser field

dissipative effects

around conical intersections, avoided crossings and bifurcating regions

Tools :

Quantum dynamics in reduced dimensionality

in fundamental and excited states

including a laser field

dissipative effects

around conical intersections, avoided crossings and bifurcating regions

Further step: macroscopic levelFurther step: macroscopic level

Inclusion of these data in kinetic schemes for cellular processes reaction chains or selforganization

Thank you for your attentionThank you for your attention