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Excited states dynamics in time-dependent density functional theoryM. A. L. Marquesmarques@tddft.orgFreie Universität – Berlinhttp://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.1/15


Co-workersT. Burnus and E. K. U. Gross.Freie Universität, Berlin, GermanyA. Castro and A. Rubio.Donostia International Physics Center (DIPC), and University of theBasque Country, San Sebastián, Spainhttp://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.2/15


octopushttp://www.tddft.org/programs/octopushttp://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.5/15


Photo-dissociation I – Na + 2A. Assion et al, Phys. Rev. Lett. 86, 5695 (2002)http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.6/15


Photo-dissociation II – Na + 2http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.7/15


Photo-dissociation III – He + 3J. Chem. Phys. 103, 3450 (1995)http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.8/15


Photo-dissociation IV – He + 3Linear Response Laser (I 0 =9×10 10 W/cm 2 )∆X(t)0.020.010-0.01-0.02-0.03420-2ω=ω resI = I 0ω=(1/3)ω resI = I 0ω=(5/3)ω resI = I 0ω=ω resI = 10 I 0-40 20 40 60 0 20 40 60Time (fs)http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.9/15


The ELFDefine the function [Becke, Edgecombe, JCP 92, 5397 (1990)]elf σ =1 +1[ ]Cσ (r) 2Cσuni (r)Where Cσ uni (r) = 3 5 (6π2 ) 2/3 n 5/3σ (r) is the kinetic energy density of the uniform gas.With this definition, 0 ≤ elf ≤ 1.high localization ⇔ C σ ∼ 0 ⇔ elf ∼ 1completely delocalized ⇔ C σ ∼ Cσ uni ⇔ elf = 1/2When the wavefunction is a Slater determinant one obtains in the static caseC detσ =N σ∑i=1|∇ϕ iσ (r)| 2 − 1 4[∇n σ (r)] 2n σ (r)http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.10/15


The ELFDefine the function [Becke, Edgecombe, JCP 92, 5397 (1990)]elf σ =1 +1[ ]Cσ (r) 2Cσuni (r)Where Cσ uni (r) = 3 5 (6π2 ) 2/3 n 5/3σ (r) is the kinetic energy density of the uniform gas.With this definition, 0 ≤ elf ≤ 1.high localization ⇔ C σ ∼ 0 ⇔ elf ∼ 1completely delocalized ⇔ C σ ∼ Cσ uni ⇔ elf = 1/2When the wavefunction is a Slater determinant one obtains in the time-dep. caseCσ detN σ= ∑∣ ∇ϕiσ,t (r) ∣ 2 − 1i=14[∇n σ (r,t)] 2n σ (r,t)− [ j σ(r,t)] 2n σ (r,t)http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.10/15


Examples (static case)[ A. Savin, R. Nesper, S. Wengert, and T, F. FässlerAngew. Chem. Int. Ed. Engl. 36, 1808 (1997) ]http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.11/15


Examples (time-dependent)(1) C 2 H 2 in a strong laser field (2) Scattering of a high energy protonon C 2 H 4http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.12/15


C 2 H 2 in a strong laser fieldLaser: ω = 17 eV, T = 8 fs, I = 1.2 × 10 14 Wcm −2http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.13/15


C 2 H 2 in a strong laser fieldLaser: ω = 17 eV, T = 8 fs, I = 1.2 × 10 14 Wcm −2http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.13/15


C 2 H 2 in a strong laser fieldLaser: ω = 17 eV, T = 8 fs, I = 1.2 × 10 14 Wcm −2http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.13/15


C 2 H 2 in a strong laser fieldLaser: ω = 17 eV, T = 8 fs, I = 1.2 × 10 14 Wcm −2http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.13/15


C 2 H 2 in a strong laser fieldLaser: ω = 17 eV, T = 8 fs, I = 1.2 × 10 14 Wcm −2http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.13/15


Scattering of a proton on C 2 H 4Kinetic energy: 2 keVhttp://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.14/15


Scattering of a proton on C 2 H 4Kinetic energy: 2 keVhttp://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.14/15


Scattering of a proton on C 2 H 4Kinetic energy: 2 keVhttp://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.14/15


Scattering of a proton on C 2 H 4Kinetic energy: 2 keVhttp://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.14/15


Scattering of a proton on C 2 H 4Kinetic energy: 2 keVhttp://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.14/15


Scattering of a proton on C 2 H 4Kinetic energy: 2 keVhttp://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.14/15


The ELF in momentum spaceC 2 H 2http://www.tddft.org/programs/octopusAarhus, 13 April 2004 – p.15/15


The ELF in momentum spaceC 2 H 2 Na 4Aarhus, 13 April 2004 – p.15/15http://www.tddft.org/programs/octopus


The ELF in momentum spaceC 2 H 2 Na 4 Na 8Aarhus, 13 April 2004 – p.15/15http://www.tddft.org/programs/octopus

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