Mario Barbatti Institute for Theoretical Chemistry University of Vienna
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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
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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
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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
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Part IPart IAn Introduction to An Introduction to Molecular DynamicsMolecular Dynamics
Cândido Portinari, Café, 1935
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Dynamics, why?Dynamics, why?
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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
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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).
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Main objective: relaxation pathMain objective: relaxation path
Ben-Nun, Molnar, Schulten, and Martinez. PNAS 99,1769 (2002).
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An example to start: the An example to start: the ultrafast deactivation of ultrafast deactivation of
DNA/RNA basesDNA/RNA bases
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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
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An example: photodynamics of DNA basisAn example: photodynamics of DNA basis
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
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An example: photodynamics of DNA basisAn example: photodynamics of DNA basis
What has theory to say?
n*/S0 crossing
Chen and Li, JPCA 109, 8443 (2005)Perun, Sobolewski and Domcke, JACS 127, 6257 (2005)
reaction coordinate
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An example: photodynamics of DNA basisAn example: photodynamics of DNA basis
What has theory to say?
N
N
N9
N
NH2
H
*/S0 crossing
Sobolewski and Domcke, Eur. Phys. J. D 20, 369 (2002)
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An example: photodynamics of DNA basisAn example: photodynamics of DNA basis
What has theory to say?
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.
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An example: photodynamics of DNA basisAn example: photodynamics of DNA basis
What has theory to say?
• 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 …
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Overview of the Overview of the available approachesavailable approaches
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The minimum energy path: the The minimum energy path: the midpoint between static and midpoint between static and
dynamics approachesdynamics approaches
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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)
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Minimum energy pathMinimum energy path
Garavelli et al., Faraday Discuss. 110, 51 (1998).
Three qualitatively distinct MEPs
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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.
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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
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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
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SiCHSiCH44
Type T Type B
Zechmann, Barbatti, Lischka, Pittner and Bonačić-Koutecký, CPL 418, 377 (2006)
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The time-dependent self-The time-dependent self-consistent field: the basis for consistent field: the basis for
everythingeverything
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),,(),,( 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
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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
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C. Lasser, TU-München
Wave packet dynamicsWave packet dynamics
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Wave packet: example HBQWave packet: example HBQ H
N
O
de Vivie-Riedle, Lischka et al. (2006)
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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:
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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:
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),(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
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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
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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).
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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.
ikikiijijjikikj HiaHiaa hRhR
k
kk ttct );(),(),,( rRRr
SC
jijeijie
V
HccH
I
II
R
rRrR
,
*
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Surface hoppingSurface hopping
iiSC HV
ikikiijijjikikj HiaHiaa hRhR
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…
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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)
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What are we loosing?What are we loosing?
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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
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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
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Approximation 1: Classical independent trajectoriesApproximation 1: Classical independent trajectories
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
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Approximation 1: Classical independent trajectoriesApproximation 1: Classical independent trajectories
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
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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
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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 2: Classical coupled trajectoriesApproximation 2: Classical coupled trajectories
= 0= 0
Example: Bohmian Dynamics; Velocity Coupling Approximation (VCA, Burant and Tully, 2000).
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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
Approximation 2: Classical coupled trajectoriesApproximation 2: Classical coupled trajectories
Example: Bohmian Dynamics; Velocity Coupling Approximation (VCA, Burant and Tully, 2000).
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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)
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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)
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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
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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
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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