Excited state dynamics of nanostructures and extended systems within TDDFT

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de Física de Materiales, Universidad del País

(DIPC), and Centro Mixto CSIC-UPV/EHU, Donostia,

1 Excited state dynamics of nanostructures and extended systems within TDDFT Angel Rubio Dpto. de Física de Materiales, Universidad del País Vasco, Donostia International Physics Center (DIPC), and Centro Mixto CSIC-UPV/EHU, Donostia, Spain Support: DGES, UPV, EC-RTN (NANOPHASE,COMELCAN, M-DNA) Advances in Molecular Electronics, ADMOL, Dresden (February )

2 Motivation Ab-initio approach for non-equilibrium electron dynamics excited states e- hv transport eeground state Optical spectroscopy. Photoelectron and time-resolved spectroscopies Electron-phonon coupling (adiabatic/nonadiabatic) Photo-induced dynamics (Ultrafast dynamics) (Resonant-tranport) e.g. Photoisomerisation in bio-photoreceptors MOLECULAR TRANSPORT (time-scales!!!!) Time-dependent scheme; TDDFT? Comparison with MBPT

First principles description of Molecular transport?????? (Landauer): Non equilibrium Green's Functions 2 QUESTIONS? Ground-state DFT? J(r,t); virtual exc. Temperature e-phon coupling? Dissipation?

3 First principles description of Molecular transport?????? (Landauer): Non equilibrium Green's Functions 2 QUESTIONS? Ground-state DFT? J(r,t); virtual exc. Temperature e-phon coupling? Dissipation?? Finite bias (resonant) AC transport Role of contacts MOLECULE 2e R A G= Tr [G w w G w w ] L R h 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)

5 Electronic properties of a many body system: ab-initio approach Scheme Ground state DFT density n(r) yes, LDA, GGA's Excited states Problems Corrections to KS eigenvalues? XC-func. TDDFT n(r,t) and/or j(r,t) MBPT G1, total energy G2 QM See for a review: yes Yes, non-linear phenomena and time-resolved spectroscopies (r,r') (w) dependence Quasiparticle excitations IP and EA optical absorption Comput. yes, in some cases! G. Onida, L. Reining and AR, Rev. Mod. Phys. 74, 601 (2002)

Method: TDDFT TDDFT: N-particles equation is mapped to a set of coupled

Current approximations have proven to be reliable.

6 Method: TDDFT TDDFT: N-particles equation is mapped to a set of coupled oneparticle equations. i ℏ =H t i ℏ =H, i=1, N KS j i t i [ { }]? Drawback: HKS contains an unknown term! 2 ℏ e H = i A V V V KS external hartree exchange 2m cℏ 2 V correlation 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) Gross et al (1985)-to date

7 Implementation 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: F t = t H t a a t =Det { t } i Solution of the TD-KS equations by unitary propagation schemes t t =e i ih KS t t t / 2 e ih KS t t / 2 t i M.A.L. Marques, A. Castro, G. Bertsch, AR, Com p. Phys. Com m. 151, 60 (2002)

8 Nanostructures How good is the performance of present DFT XC-functionals? G. Onida, L. Reining and AR, Rev. Mod. Phys. 74, 601 (2002)

9 Linear optical response: general aspects = v f r, r ', w = ij f j f i xc ci r j r i r ' cj r ' i j w LDA- thick solid line EXX- dotted line Bethe-Salpeter Experiments Transport: Current + E-field

10 Optical response: (Benzene) * (LUMO) 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)

11 Biological molecules: photoreceptors A "poor" condensed matter physicist view!!!! QM/MM + TDDFT approach M.A.L Marques, X. Lopez, D. Varsano, A. Castro, and A. R. Phys. Rev. Lett. 90, (2003)

12 Linear optical response: Towards understanding biomolecule colours (Aequorea victoria: jellyfish) Green Fluorescent Protein (GFP).

13 Towards understanding biomolecular colours: the GFP case HOMO-LUMO T.M.H. Creemers et al, Proc. Natl. Acad. Sci.. USA (1999) QM/MM approach

$Azobenzene dyes are known to isomerize at the central N-N bond within fractions of$ picoseconds at high quantum yield [T. Nägele et al, Chem. Phys. Lett.

14 Azobenzene: spectroscopy along femtosecond-laser induced photoisomerization 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 Proc. Natl. Acad. Sci., 99, 7998 (2002).

15 Azobenzene: spectroscopy along femtosecond-laser induced photoisomerization CIS TRANS Next step: QM/MM calculation of the chromophore+peptide system

16 Isomerisation of Formaldimine HOMO-LUMO T=0 HOMO-LUMO T=300K

17 Bulk Part? MBPT and fxc

18 Time-dependent approach for extended systems: a gauge formalism G.F. Bertsch, J.I. Iwata, AR, K. Yabana, PRB62, 7998 (2000) The Lagrangian of a periodic system in a volume V under a uniform field is e V d A L= i ℏ p A V E E i i ion i Hartree xc 2 t 2 m c 8 c dt A 1 d t = E c dt The equation of motion are: [ ] 1 e 2 iℏ = p A V V V ion H xc i t i 2 m c 2 d A dt 2 = 4 e 2 n e p A 4 c i m i m V i For the electric field is: de = 4 j dt 2 j = e p e n A and i i m i V c

19 Lithium Diamond

20 Non-local fxc for extended systems:

21 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)

22 Static non-local fxc for extended systems: = GW 0 GW 0 v f f = /q xc xc = 0.2 = 0.2 L. Reining, V. Olevano, AR, G. Onida, PRL88, (2002) and to be published. For a review see G. Onida, L. Reining and AR, Rev. Mod. Phys. 74, 601 (2002) 2

23 Bound excitons in TDDFT = TDDFT BSE Experiment TDDFT, scalar fxc A. Marini, R. Del Sole and AR, PRL (2003)

24 Conclusions 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 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...

25 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 M. A. L. Marques, C.A. Rozzi, and E. K. U. Gross Institut für Theoretische Physik, Freie Universität, Berlin, Germany L. Reining, V. Olevano École Polytechnique, Palaiseau, France R. Del Sole and G. Onida Istituto Nazionale per la Fisica della Materia e Dipartimento di Fisica dell'università di Roma ``Tor Vergata'', Roma, Italy G.F. Bertsch, K. Yabana Physics Department and Institute for Nuclear Theory University of Washinton, Seattle (USA)

Angel Rubio. Motivation. I. Illustration of the physics for nano- and bio-structures. II. Extended systems: problems and new developments

Angel Rubio. Motivation. I. Illustration of the physics for nano- and bio-structures. II. Extended systems: problems and new developments Lectures on Applications of TDDFT Angel Rubio 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