Mario Barbatti Institute for Theoretical Chemistry University of Vienna

Photochemistry: Photochemistry: adiabatic and nonadiabatic adiabatic and nonadiabatic molecular dynamics with molecular dynamics with

multireference ab initio methods multireference ab initio methods Mario BarbattiMario Barbatti

Institute for Theoretical ChemistryUniversity of Vienna

COLUMBUS in BANGKOK (3-TSCOLUMBUS in BANGKOK (3-TS22CC22))Apr. 2 - 5, 2006Apr. 2 - 5, 2006

Burapha University, Bang Saen, ThailandBurapha University, Bang Saen, Thailand

OutlineOutline

First Lecture: An introduction to molecular dynamicsFirst Lecture: An introduction to molecular dynamics1. Dynamics, why?2. Overview of the available approaches

Second Lecture: Towards an implementation of surface Second Lecture: Towards an implementation of surface hopping dynamicshopping dynamics

1. The NEWTON-X program 2. Practical aspects to be adressed

Third Lecture: Some applications: theory and experiment

• On the ambiguity of the experimental raw data • On how the initial surface can make difference• Intersection? Which of them?• Readressing the DNA/RNA bases problem

OutlineOutline

First Lecture: An introduction to molecular dynamicsFirst Lecture: An introduction to molecular dynamics1. Dynamics, why?2. Overview of the available approaches

Second Lecture: Towards an implementation of surface Second Lecture: Towards an implementation of surface hopping dynamicshopping dynamics

1. The NEWTON-X program 2. Practical aspects to be adressed

Third Lecture: Some applications: theory and experiment

• On the ambiguity of the experimental raw data • On how the initial surface can make difference• Intersection? Which of them?• Readressing the DNA/RNA bases problem

Part IPart IAn Introduction to An Introduction to Molecular DynamicsMolecular Dynamics

Cândido Portinari, Café, 1935

Dynamics, why?Dynamics, why?

SingletTriplet

Photoinduced chemistry and physicsPhotoinduced chemistry and physics

avoided crossing 102-104 fsconical intersection 10-102 fs

PA – photoabsorption 1 fs

VR – vibrational relaxation 102-105 fs

Energy (eV)

0

10

Nuclear coordinates

PhFl

PA

VR

Fl – fluorescence 106-108 fsintersystem crossing 105-107 fs

Ph – phosforescence 1012-1017 fs

ab initio dynamicsab initio dynamics

When is it not adequate to reduce the dynamics to the motion on a sole adiabatic potential energy surface?

• Electron transfer (high kinetic energy);• Dynamics at metal surfaces (high DoS);• Photoinduced chemistry (multireference states)Photoinduced chemistry (multireference states). • Radiationless processes in moleculesRadiationless processes in molecules and solids (conical intersections);

Dynamics, why?Dynamics, why?

Why dynamics simulations are needed?

• Estimate of specific times (lifetimes, periods);• Estimate of the kind and relative importance of the several available nuclear motions (reaction paths, vibrational modes).

Main objective: relaxation pathMain objective: relaxation path

Ben-Nun, Molnar, Schulten, and Martinez. PNAS 99,1769 (2002).

An example to start: the An example to start: the ultrafast deactivation of ultrafast deactivation of

DNA/RNA basesDNA/RNA bases

An example: photodynamics of DNA basisAn example: photodynamics of DNA basis

Lifetimes of the excited state of DNA/RNA basis:

Maybe the fast deactivation times for the DNA/RNA basis can provide some explanation to the photostability of DNA/RNA under the UV solar radiationUV solar radiation.

N

N

NH

N

NH2

N

NH

NH2

O N

NH

NH

N

NH2

O

Canuel et al. JCP 122, 074316 (2005)

NH

NH

O

O

CH3

NH

NH

O

O


What has theory to say?

*/S0 crossing

Marian, JCP 122, 104314 (2005)Chen and Li, JPCA 109, 8443 (2005)Perun, Sobolewski and Domcke, JACS 127, 6257 (2005)

C2



n*/S0 crossing

Chen and Li, JPCA 109, 8443 (2005)Perun, Sobolewski and Domcke, JACS 127, 6257 (2005)

reaction coordinate



N

N

N9

N

NH2

H

*/S0 crossing

Sobolewski and Domcke, Eur. Phys. J. D 20, 369 (2002)



0 200 400 600 800 1000 1200 1400

-466.70

-466.68

-466.66

-466.64

-466.62

-466.60

-466.58

-466.56

-466.54

-466.52

-466.50

-466.48

-466.46

-466.44

Ene

rgy

(a.u

.)

Time (fs)

Our own simulations (TD-DFT(B3LYP)/SVP) do not show any crossing at all.



• The static calculations have being done in good levels, for instance: MRCI in Matsika, JPCA 108, 7584 (2004); CAS(14,11) in Chen and Li, JPCA 109, 8443 (2005); DFT/MRCI in Marian, JCP 122, 104314 (2005).

• However, the system can present conical intersections but never access them due to energetic or entropic reasons.

• The dynamics calculations are not reliable enough: they miss the MR and the nonadiabatic characters.

To address the problem demands nonadiabatic dynamics with MR methods.

We will come back to the adenine deactivation later …We will come back to the adenine deactivation later …

Overview of the Overview of the available approachesavailable approaches

The minimum energy path: the The minimum energy path: the midpoint between static and midpoint between static and

dynamics approachesdynamics approaches

Minimum energy path in two stepsMinimum energy path in two steps

Celany et al. CPL 243, 1 (1995)

Emax

Emin

v0

Hypersphere

R1

R2

R1eq

R2eq

1. Determine the initial displacement vector (IRD)

2. Search for the minimum energy path

Schlegel, J. Comp. Chem. 24, 1514 (2003)

Minimum energy pathMinimum energy path

Garavelli et al., Faraday Discuss. 110, 51 (1998).

Three qualitatively distinct MEPs

Minimum energy pathMinimum energy path

Garavelli et al., Faraday Discuss. 110, 51 (1998).Cembran et al. JACS 126, 16018 (2004).

Advantages: • Explore the most important regions of the PES.• Its equivalent to “one trajectory damped dynamics”.• Clear and intuitive.

Disadvantages:• Only qualitative temporal information.• Neglects the kinetic energy effects.• No information on the importance of each one of multiple MEPs.• No information on the efficiency of the conical intersections.

SiCHSiCH44: : MRCI/CAS(2,2)/6-31G*MRCI/CAS(2,2)/6-31G*

0 30 60 900

1

2

3

4

5

6

Ene

rgy

(eV

)

Rigid torsion (degrees)

Also for SiCH4 one expects the basic scenario torsion+decay at the twisted MXS.

68% of trajectories follow the torsional coordinate, but do not reach the MXS die to the in-phase stretching-torsion motion.

The lifetime of the S1 state is 124 fs.

This and other movies are available at:homepage.univie.ac.at/mario.barbatti

SiCHSiCH44: MRCI/CAS(2,2)/6-31G*: MRCI/CAS(2,2)/6-31G*

The other 32% follow the stretch-bipyramidalization path. And reaches quickly the bipyramid. region of seam.

The lifetime of the S1 state is 58 fs.

1.724

1.0851.477

115.8° 115.6°

1.652

1.084

1.513

97.5° 115.3°

2.340

1.5111.134

96.0°92.0°

= 47.3° = 89.4°Si

Si

Si

C

C

C

1.724

1.0851.477

115.8° 115.6°1.724

1.0851.477

115.8° 115.6°

1.652

1.084

1.513

97.5° 115.3°1.652

1.084

1.513

97.5° 115.3°

2.340

1.5111.134

96.0°92.0°

2.340

1.5111.134

96.0°92.0°

= 47.3° = 89.4°Si

Si

Si

C

C

C

This and other movies are available at:homepage.univie.ac.at/mario.barbatti

SiCHSiCH44

Type T Type B

Zechmann, Barbatti, Lischka, Pittner and Bonačić-Koutecký, CPL 418, 377 (2006)

The time-dependent self-The time-dependent self-consistent field: the basis for consistent field: the basis for

everythingeverything

),,(),,( tHt

ti RrRr

eN

eN

n

ir

N

IR

I

HKVKK

tVmM

HiI

),,(22 1

2

1

2 RrTime dependent Schrödinger equation (TDSE)

t

dtHittt0

'exp),(),(),,( rR,RrRr

Total wave function

Time-dependent SCFTime-dependent SCF

reN HK

ti

RVK

ti e

Time-dependent self consistent field (TD-SCF)

Dirac, 1930

Time evolution - I

• Wave packet propagation

1) The nuclear wave function is expanded as:

f is the number of nuclear coordinates (<< 3N).

Wave packet dynamicsWave packet dynamics

f

ffjj

ff

jjjj RRtAt..

)(1

)1(..

111

...)(, R

tRR ikjk

kj kk

, MCTDH (multiconfigurational time-dependent Hartree)(Meyer, Manthe and Cederbaum, CPL 165, 73 (1990))

2) Solve TDSE using . Hermite/Laguerre polynomials (DVR, discrete variable representation) Plane waves (FFT, fast Fourier transform)

Advantage: it is the most complete treatmentLimitation: it is quite expansive to include all degrees of freedom

C. Lasser, TU-München

Wave packet dynamicsWave packet dynamics

Wave packet: example HBQWave packet: example HBQ H

N

O

de Vivie-Riedle, Lischka et al. (2006)

Time evolution - II

• Multiple Spawning dynamics (Martínez et al., JPC 100, 7884 (1996))

Multiple spawningMultiple spawning

tGtAt CC

tN

j

kj

kj

k

,,,,1

PRRR

N

CCCkj tRRiPtRRNG

3

1,,

2,

4/1

exp2

The centroids RC and PC are restricted to move classically.

Advantage: very reliable quantitative resultsLimitation: it is still quite expansive

Nuclear wave function is expanded as a combination of gaussians:

Time evolution - III

• Mean Field; Surface Hopping.

Semiclassical approachesSemiclassical approaches

N

C tRRt3

1,,

R

RC is restricted to move classically.

Advantage: large reduction of the computational effortLimitation: they cannot account for nuclear quantum effects

Nuclear wave function is restricted to be a product of functions:

),(exp),(),( tSitAt RRR

Classical limit of the Schrödinger equationClassical limit of the Schrödinger equationNuclear wave function in polar coordinates

I

R

IIe

I

R

AA

MH

MS

tS II

22

22

r

02

11 2

IR

IIRR

I

SAM

SAMt

AIII

0

2

2

Ie

I

R HM

StS I

r

0i)Hamilton-Jacob

dtdMH I

IeI

RrR

2

Newton

eH

ti

reN HK

ti

ii)

RVK

ti e

N

C tRRt3

1,,

R

Classical TDSE limit and minimum actionClassical TDSE limit and minimum action

0

2

2

Ie

I

R HM

StS I

r

Hamilton-Jacob

dtdMH I

IeI

RrR

2

Newton

t

dttLS0

')'( (Classical action)

Min(S): Euler-Lagrange equation

k

kk ttct );(),(),,( rRRr

TDSE and Multiconfigurational expansionTDSE and Multiconfigurational expansion

eH

ti

ikikiik dHicc

where

kiiRkrikki td hRR

Time derivative Nonadiabatic coupling vector

iekki HH

*ikki cca Population:

ikikiijijjikikj HiaHiaa hRhR

• Two electronic states are coupled via non-diagonal terms in the Hamiltonian Hij and by the nonadiabatic coupling vector hij.

• Diabatic representation: i hij = 0.• Adiabatic representation: {i} Hij = 0 (i ≠ j).

Mean Field (Ehrenfest) dynamicsMean Field (Ehrenfest) dynamics

Advantage: Computationally cheapLimitation: wrong assymptotical description of a pure state (there is no decoherence)Solution (?): Impose a demixing time (Jasper and Truhlar, JCP 122, 044101 (2005))

ji

jijiSC HaV,

dtdMV I

ISCI

RR

2

• At each time, the dynamics is performed on an average of the states:

• In the adiabatic representation Hii = Ei(R), Ei, and hji are obtained with traditional quantum chemistry methods.

• aji is obtained by integrating

• Nuclear motion is obtained by integrating the Newton eq.


k

kk ttct );(),(),,( rRRr

SC

jijeijie

V

HccH

I

II

R

rRrR

,

*

Surface hoppingSurface hopping

iiSC HV


dtdMV I

ISCI

RR

2

• At each time, the dynamics is performed on one unique adiabatic state.

• In the adiabatic representation Hii = Ei(R), Ei, and hji are obtained with traditional quantum chemistry methods.

• aji is obtained by integrating

• Nuclear motion is obtained by integrating the Newton eq.

• The transition probability between two electronic states is calculated at each time step of the classical trajectory.

• The system can hop to other adiabatic state.

Advantages: Computationally cheap; correct assymptotic behavior; easy interpretation of resultsLimitations: Forbidden hops; ad hoc conservation of energy

We will discuss this approach in detail later…

Mean Field and Surface hoppingMean Field and Surface hopping

t

E

t

E

Mean Fieldsystem evolves in a pure state(superposition of several states)

Surface Hoppingsystem evolves in mixed state (several independent trajectories)

What are we loosing?What are we loosing?

k

kk ttt ),();(),,( RrRr

Let`s start again, but now with a multiconfigurational wave function.

),,(),,( tHt

ti RrRr

),(exp),(),( tSitAt kkk RRR

And with

Multiconfigurational approach in polar coordinatesMulticonfigurational approach in polar coordinates

the same equation as before

I k

kR

IIkek

I

kRk

AA

MH

MS

tS I

22

22

r

Ekk

kIlk

Iklk

IkR

Ikl

IkR

Iklk

I

IkR

k

IIkRkR

I

k

SSiDAMiA

MiSA

M

SAM

SAMt

AIII

,

2

exp2

1

211

hh

new terms

where iRkIkl I

D 2lRkIkl I

h andHigh order coupling

Approximation 1: Classical independent trajectoriesApproximation 1: Classical independent trajectories

kIlk

Iklk

IkR

Ikl

IkR

Iklk

I

IkR

k

IIkRkR

I

k

SSiDAMiA

MiSA

M

SAM

SAMt

AIII

,

2

exp2

1

211

hh

I k

kR

IIkek

I

kRk

AA

MH

MS

tS II

22

22

r

where iRkIkl I

D 2lRkIkl I

h and


Example: Surface hopping. Mean Field.

kIlk

Iklk

IkR

Ikl

IkR

Iklk

I

IkR

k

IIkRkR

I

k

SSiDAMiA

MiSA

M

SAM

SAMt

AIII

,

2

exp2

1

211

hh

I k

kR

IIkek

I

kRk

AA

MH

MS

tS II

22

22

r

= 0= 0

where iRkIkl I

D 2lRkIkl I

h and


Example: Surface hopping. Mean Field.

kIlkkR

Iklk

IIkR

k

I

k SSiSAM

SAMt

AI

,

2 exp12

1

h

0

2

2

Ikek

I

kRk HMS

tS I

r

kIlk

Iklk

IkR

Ikl

IkR

Iklk

I

IkR

k

IIkRkR

I

k

SSiDAMiA

MiSA

M

SAM

SAMt

AIII

,

2

exp2

1

211

hh

I k

kR

IIkek

I

kRk

AA

MH

MS

tS II

22

22

r

Approximation 2: Classical coupled trajectoriesApproximation 2: Classical coupled trajectories

where iRkIkl I

D 2lRkIkl I

h and

kIlk

Iklk

IkR

Ikl

IkR

Iklk

I

IkR

k

IIkRkR

I

k

SSiDAMiA

MiSA

M

SAM

SAMt

AIII

,

2

exp2

1

211

hh

I k

kR

IIkek

I

kRk

AA

MH

MS

tS II

22

22

r

where iRkIkl I

D 2lRkIkl I

h and


= 0= 0

Example: Bohmian Dynamics; Velocity Coupling Approximation (VCA, Burant and Tully, 2000).

kIlkkR

Iklk

I

IkR

k

IIkRkR

I

k

SSiSAM

SAM

SAMt

AIII

,

2

exp1

211

h

0

2

2

Ikek

I

kRk HMS

tS I

r

where lRkIkl I

h


Example: Bohmian Dynamics; Velocity Coupling Approximation (VCA, Burant and Tully, 2000).

kIlk

Iklk

IkR

Ikl

IkR

Iklk

I

IkR

k

IIkRkR

I

k

SSiDAMiA

MiSA

M

SAM

SAMt

AIII

,

2

exp2

1

211

hh

I k

kR

IIkek

I

kRk

AA

MH

MS

tS II

22

22

r

where iRkIkl I

D 2lRkIkl I

h and

Approximation 3: Coupled trajectoriesApproximation 3: Coupled trajectories

Example: Classical Limit Schrödinger Equation (CLSE, Burant and Tully, 2000)

One problem: get Dkl

2Ikl

IklD h (Yarkony, JCP 114, 2601 (2001)

Tully, Faraday Discuss. 110, 407 (1998).

Burant and Tully, JCP 112, 6097,(2000)

Comparison between methodsComparison between methods

wave-packet

surface-hopping (adiabatic)mean-field

Landau-Zener

surface-hopping (diabatic)

Worth, hunt and Robb, JPCA 127, 621 (2003).

Comparison between methodsComparison between methods

Oscillation patterns are not necessarily quantum interferences

Butatriene cation

Barbatti, Granucci, Persico, Lischka, CPL 401, 276 (2005).

Ethylene

Hierarchy of methodsHierarchy of methods

Quantum

Classical

Multiple spawning (MS)

tGtAt CC

tN

j

kj

kj

k

,,,,1

PRRR

R1

R2

t

Surface hopping and Ehrenfest dynamics Ct RRR ,

independent trajectories

R1

R2

t

Bohmian dynamics (CLSE, VCA) Ct RRR ,

interacting trajectories

R1

R2

t

Wave packet (MCTDH)

fff

jjf

fjjjj RRtAt

..

)(1

)1(..

111

...)(, R

R1

R2

t

Next lecture:Next lecture:• How to implement the surface hopping dynamics• The on-the-fly surface-hopping dynamics program NEWTON-X

This lecture:This lecture:• Dynamics reveal features that are not easily found by static methods• From the full quantum treatment to the classical approach, there are several available methods• Semiclassical approaches (classical nuclear motion + quantum electron treatment) show the best cost-benefit ratio

Documents

Mario Barbatti Institute for Theoretical Chemistry University of Vienna