Angel Rubio

Support: DGES, UPV, EC-RTN (NANOPHASE,COMELCAN, M-DNA)

Advances in Molecular Electronics, ADMOL, Dresden (February 23-27 2004)

Dpto. de Física de Materiales, Universidad del País

Vasco, Donostia International Physics Center (DIPC),

and Centro Mixto CSIC-UPV/EHU, Donostia, Spain

http://dipc.ehu.es/arubio E-mail: arubio@sc.ehu.es

Excited state dynamics of nanostructures and extended systems within TDDFT

Motivation Motivation Ab-initio approach for non-equilibrium electron dynamics

e-

e-

e-

excited states

Ground state

transport

Optical spectroscopy. Photoelectron and time-resolved spectroscopiesElectron-phonon coupling (adiabatic/nonadiabatic)Photo-induced dynamics (Ultrafast dynamics) (Resonant-tranport)

e.g. Photoisomerisation in bio-photoreceptorsMOLECULAR TRANSPORT (time-scales!!!!)

hv

Time-dependent scheme; TDDFT? Comparison with MBPT

●(Landauer): Non equilibrium Green's Functions ●Lippman-Schwinger self-consistent approach (Massimiliano di Ventra)●Maximum Entropy Scheme: steady-state-current from DM (Bokes and Godby)●Many-Boby Kubo-formula: Current-current correlation function●TDDFT? -----TD-Current-DFT (see K. Burke)

G=2 e2

hTr [GRw

LwG Aw

Rw]

First principles description of Molecular transport ??????QUESTIONS?

✔Ground-state DFT? J(r,t); virtual exc.✔Temperature e-phon coupling?✔Dissipation??✔Finite bias (resonant)✔AC transport✔Role of contacts✔MOLECULE

See for a review: G. Onida, L. Reining and AR, Rev. Mod. Phys. 74, 601 (2002)

Electronic properties of a many body system: ab-initio approach

Ground state

density n(r)yes, LDA, GGA's

n(r,t) and/or j(r,t)

G1, total energy

G2

yes

Excited states

Corrections toKS eigenvalues?

Yes, non-linear phenomena and time-resolved spectroscopies

Quasiparticle excitationsIP and EAoptical absorption

yes, in some cases!

Scheme

DFT

TDDFT

MBPT

QM

Problems

XC-func.

(r,r') (w)dependence

Comput.

Method: TDDFT

✔TDDFT: N-particles equation is mapped to a set of coupled one-particle equations.

✔Drawback: HKS

contains an unknown term!

✔Current approximations have proven to be reliable.✔ LDA, GGA, metaGGA, orbital-dependent,... for the static kernel.✔Currend Density-Functional Theory: !!!!!!✔Adiabatic approximation to handle ( = ignore) time non-locality.

✔It is scalable (more promising, in this aspect, that quantum chemistry approaches and many-body perturbation theory)

i ℏ ∂∂t=H i ℏ ∂

∂t

i=H

KS [ { j}]i, i=1,⋯N

?

HKS=ℏ2

2 mi∇−

e

c ℏA

2

Vexternal

Vhartree

Vexchange

Vcorrelation

Gross et al (1985)-to date

✔ Numerical description of functions: real space discretization (1D-3D).✔ Auxiliary use of LCAO/ FFTs. QM/MM for biomolecular structures✔ Electon-ion coupling: pseudopotentials. Spin-Orbit .........

✔Classical description of electromagnetic field.(Absence of radiative-decay channel!)

✔Classical description of nuclei (point particles): Ehrenfest path:

✔Solution of the TD-KS equations by unitary propagation schemes

Implementation

M.A.L. Marques, A. Castro, G. Bertsch, AR, Comp. Phys. Comm. 151, 60 (2002)www.tddft.org/programs/octopus

Fat =−⟨t ∣∇ a

H∣t ⟩ t =Det {it }

it t =e

−iHKS t t t /2e−iHKS t t /2

it

Nanostructures

How good is the performance of present DFT XC-functionals?

G. Onida, L. Reining and AR, Rev. Mod. Phys. 74, 601 (2002)

=0

0v f

xc

Linear optical response: general aspects

Transport: Current + E-field

0r , r ', w=∑ij f j− f i

ic r jr ir ' j

c r '

i− j−w

– LDA- thick solid line– EXX- dotted line– Bethe-Salpeter – Experiments

Optical response: (Benzene)

7eV

� (HOMO)

M.A.L Marques, A. Castro, G.F. Bertsch and AR, Comp. Phys. Comm. (2002);K. Yabana and G. F. Bertsch, Int. J. Quantum Chem. 75, 55 (1999)

� * (LUMO)

A "poor" condensed matter physicist view !!!!

Biological molecules: photoreceptors

QM/MM + TDDFT approach

M.A.L Marques, X. Lopez, D. Varsano, A. Castro, and A. R. Phys. Rev. Lett. 90, 158101 (2003)

Linear optical response: Towards understanding biomolecule colours

(Aequorea victoria: jellyfish)Green Fluorescent Protein (GFP).

Towards understanding biomolecular colours: the GFP case

HOMO-LUMO

T.M.H. Creemers et al, Proc. Natl. Acad. Sci.. USA (1999)

QM/MM approach

Azobenzene: spectroscopy along femtosecond-laser induced photoisomerization

Proc. Natl. Acad. Sci., 99, 7998 (2002).

Azobenzene dyes are known to isomerize at the central N-N bond within fractions of picoseconds at high quantum yield [T. Nägele et al, Chem. Phys. Lett. 272, 489 (1997)]. One example is the APB optical trigger:

HOMO

LUMO

Azobenzene: spectroscopy along femtosecond-laser induced photoisomerization

CIS

Next step: QM/MM calculation of the chromophore+peptide system

TRANS

HOMO-LUMO T=0

Isomerisation of Formaldimine

HOMO-LUMO T=300K

Bulk Part?

MBPT and fxc

Time-dependent approach for extended systems: a gauge formalismG.F. Bertsch, J.I. Iwata, AR, K. Yabana, PRB62, 7998 (2000)

E t =−1

c

d Ad t

The Lagrangian of a periodic system in a volume V under a uniform field is

The equation of motion are:

For the electric field is:

L=∑i

i∣i ℏ ∂∂t−

1

2 mp

e

cA

2

−Vion∣

i−E

Hartree−E

xc

V

8c2d Adt

2

i ℏ∂∂t

i=[ 1

2 mp

e

cA

2

VionV

HV

xc ]i

d2 A

dt 2=−4e

2 n

mA−4c

e

V∑

i

i∣pm∣

i

d Edt=−4j j=

−e

V∑

i

i∣pm∣

i−

e2

cn Aand

Lithium Diamond

Non-local fxc for extended systems:

Many-Body approach to the Exchange-Correlation Kernel of TDDFT

TDDFT

MBPT

Bethe-Salpeter Equation

Iterative equation for fxc

A. Marini, R. Del Sole and AR, PRL (2003)

L. Reining, V. Olevano, AR, G. Onida, PRL88, 0664041 (2002) and to be published.

For a review see G. Onida, L. Reining and AR, Rev. Mod. Phys. 74, 601 (2002)

Static non-local fxc for extended systems:

= 0.2

= 0.2

fxc=−/q2

=0

G W0

G Wv fxc

=

BSETDDFT Experiment

TDDFT, scalar fxc

Bound excitons in TDDFT

A. Marini, R. Del Sole and AR, PRL (2003)

www.tddft.org/programs/octopus

Conclusions

Ongoing work on applications to:

Time-resolved spectroscopies: pump-probe simulations.

High-harmonic generation from quantum dots.

QM/MM: for excited-state dynamics in biomolecules: photoisomerisation

Control chemical reactivity:Pulse optimization in laser induced reaction

Non-linear effects in One-dimensional systems

Time-dependent Molecular transport !!!!!!!!!

Quantum nuclei, etc......

TDDFT is a powerfool tool to handle the combined dynamics of electron/ion in response to external electromagnetic fields of nanostructures, biological molecules and extended systems.

Problem: we need better fxc functionals based on either DFT (or current-DFT) or MBPT approaches

Acknowledgements

A. Castro, A. Marini, X. López, L Wirtz, D. Varsano Department of Material Physics, Centro Mixto CSIC-UPV, University of the Basque

Country, and Donostia International Physics Center (DIPC), Donostia, Spain

L. Reining, V. Olevano

G.F. Bertsch, K. Yabana

École Polytechnique, Palaiseau, France

Physics Department and Institute for Nuclear Theory University of Washinton, Seattle (USA)

R. Del Sole and G. OnidaIstituto Nazionale per la Fisica della Materia e Dipartimento di Fisica

dell'Università di Roma ``Tor Vergata'', Roma, Italy

M. A. L. Marques, C.A. Rozzi, and E. K. U. GrossInstitut für Theoretische Physik, Freie Universität, Berlin, Germany