The Particle-Hole Map: a computational tool to visualize electronic excitations

Transcription

1 The Pcle-Hole Mp: compuol ool o vsulze elecoc excos Cse A. Ullch Uvesy of Mssou Besque Sepembe 06 Yoghu L Tj Uvesy

2 Oule Vsulzo/epeo mehods of elecoc excos The pcle-hole mp: defos Exmples d pplcos Y. L d C.A. Ullch Chem. Phys Y. L d C.A. Ullch J. Chem. Theoy Compu Y. L D. Moghe S. Pl S. Guh d C.A. Ullch Mol. Phys Y. L d C.A. Ullch submed o JCP 06

3 Molecul opcl specoscopy 3 Uses wek lse s Pobe Sysem Respose hs peks elecoc exco eeges Spec c be clculed usg TDDFT Phoobsopo coss seco N N 4 Theoy Expeme Theoy Eegy ev Vslev e l. PRB Rozz e l. Nue Commu. 03

4 Rel-me smulo of exco dymcs 4 Would lke o vsulze e-h p moo el me CT exco ceo dffuso dssoco D-A efces mpo fo udesdg ogc phoovolcs sysems ω

5 Rel-me smulo of exco dymcs 5 Would lke o vsulze e-h p moo el me CT exco ceo dffuso dssoco D-A efces mpo fo udesdg ogc phoovolcs sysems Rel D-A sysems e complex d eque kg lce elxo o ccou. Wh should we be lookg? Semcoducg polyme doo e- Fulleee ccepo

6 Chge-sfe excos 6 Zcbceochlo- Bceochlo complex lgh-hvesg pls d puple bce CT excos e dffcul wh TDDFT: LDA d GGA fl. Deuw d Hed-Godo JACS 004

7 Tso deses d dffeece deses 7 Exmple: MEH-PPV L e l Comp. M. Sc so desy lowes exced se chge desy dffeece

8 8 ] / [ 0 D D D f ELF j σ σ σ σ σ σ σ σ τ + Locl ques lke TDELF o he desy self show he moo of chges d os o he bekg of bods Chge flucuos c be see fom so deses o desy dffeeces chge sfe c ofe be see fom MO s Bu whee do elecos d holes come fom o go o? How do we defy eleco-hole ps o excos? Need olocl fomo. Tme-Depede Eleco Loclzo Fuco TDELF T. Buus M.A.L. Mques E.K.U. Goss PRA R 005 Vsulzo of eleco dymcs: TDELF 8

9 Eleco-hole dsbuos fo exco 9 LF Eh Schlefe Sdgh d Abeg PRB Rohlfg d Loue PRB Obed fom soluos of he GW-Behe-Slpee eq.

10 Tso Desy Mx TDM 0 Ψ TDM ssoced wh specfc exco : Γ My-body egeses: -body desy mx opeo: Ψ 0 Ψ ˆ ρ Ψ Hˆ Ψ 0 E Ψ + ˆ ρ ψˆ ψˆ 0 R. McWeey RMP F. Fuche JCP Dgolzg he TDM bss of ul obls gves he ul so obls. R.L. M JCP

11 TDDFT fomlsm fo exco eeges Ω Y X 0 0 Y X A K K A * * Exco eeges follow fom egevlue poblem Csd 995: + + xc f d d K K A ω ε ε δ δ * 3 3 so desy: [ ] Ω + Ω Ω Y X * * δ

12 Koh-Shm TDM S. Tek d S. Mukmel Chem. Rev F. Fuche JCP F. Plsse M. Wom d A. Deuw JCP Γ KS [ X Ω + Y Ω ] * * The dgol elemes e pcple exc so deses: KS Γ Γ δ Ω The off-dgol elemes e geel o exc: KS Γ Γ

13 Y. L d C.A. Ullch Chem. Phys Tme-depede TDM 3 E e 0 0 ˆ Ψ Ψ Γ ρ KS Tme-depede TDM: E KS KS e 0 0 ˆ Φ Φ Γ ρ Whee 0 Φ Φ e me-depede d goud-se Koh- Shm Sle deems: { } de j Φ v v v j j xc H + + +

14 TDM fo low-eegy exced ses of PPV 0 4 TDHF clculo S.Tek d S.Mukmel Chem. Rev S. Tek K. Igumeshchev d S. Mukmel PRB

15 Two chcesc legh scles 5 Coheece Legh L c Deloclzo Legh L d

16 TDM fo low-eegy exced ses of PPV 0 6 S. Tek K. Igumeshchev d S. Mukmel PRB TDHF gves oveboud excos No boud excos ALDA e-h epulso Hybd fucols hve boud excos

17 Tso Desy Mx 7 TDM s esy o compue d epese Allows o vsulze excoc chce of exco eleco-hole wve fuco The TDM does o ell us whee eleco d hole e comg fom: dffcul o ssess chge-sfe chce of exco New vsulzo ool complemey o TDM: he pcle-hole mp PHM

18 TDKS equo: V m j s j + whee N j j j Cosde he followg sum of jo pobbles: { } 0 0 N P goud-se pobbly desy of h KS obl poso desy flucuo of h me-depede KS obl The me-depede pcle-hole mp I 8

19 Fo smll peubo we c leze: c c c c u o δ δ δ whee he obl flucuos volvg lly uoccuped ses e obed by pojeco: N j u d δ The me-depede pcle-hole mp II The obl flucuos volvg occuped ses do cobue o he le desy espose e d hece dscded 9

20 The me-depede pcle-hole mp III 0 N { 0 + } δ u c. c. 0 Ξ Sum of jo pobbly deses h KS pcle oges poso d moves dug he exco pocess o poso. Ξ 0 0 sg fom goud se Ξ d 3 0 om cosevo 3 Ξ d δ exc desy espose

21 The fequecy-depede pcle-hole mp We expd + 0 N u e C ω δ If he sysem s he elecoc egemode of he h exced se e Ω Ω δ δ Usg sum ule d compg wh he Csd equo fom TDDFT [ ] 0 0 0* 0* 0 Y X Ω + Ω Ω Ξ

22 Devo fom -pcle RDM I d -ode pcle-hole so desy mx bewee wo Sle deems: 0 ˆ ˆ ˆ ˆ ; 0; Φ Φ + + ψ ψ ψ ψ γ ph * * * * + + γ γ γ γ

23 Devo fom -pcle RDM II Pojeco oo occuped KS obls: * ; 0 l occ l ph l P P γ ; Ω Ω Ξ l ph occ l l P P γ 3 * l l l P PHM: obl-pojeced pcle-hole -TDM [ ] * * Y X Ω + Ω

24 PHM: D exmples 4 N 8

25 PHM: D exmples 5 PHM TDM

26 PHM: how o ed 6 eges o δ hs deco whee e/h s gog o x eges o zeo hs deco blue: elecos ed: holes x whee e/h s comg fom

27 PHM: D exmples 7 PHM TDM

28 D exmple: me-depede PHM 8 TDKS popgo sg fom goud se wh lse pulse esoce

29 The PHM 3D: how o plo 9 Plo PHM fo fxed efeece po: Ξ 0 Ω Aom-ceeed bss fo KS obls: Assume zeo ovelp of bss fucos o dffee omc ses d plo PHM sml o TDM s y. Fo el-spce gd defe spl cose gg. Ech b s umbeed d we plo he vege of he PHM ove he b. C use boxes slces o Wge-Sez cells. j N M ς η A l l k l jk l k

30 C H 4 C F 4 chge sfe complex 30 Ξ 0 Ω

31 PDPP-BBT vesus TDPP-BBT 3 Boh e doo-ccepo molecules wh vey sml opcl spec. Bu TDPP hs 0x bgge esposvy phoocue. Why?

32 PDPP-BBT vesus TDPP-BBT: expeme 3

33 PDPP-BBT vesus TDPP-BBT moomes 33

34 PDPP-BBT vesus TDPP-BBT dmes 34

35 P3HT C 60 chge sfe complex 35

36 Exesos & Geelzos 36 Sghfowd exesos: Movg ucle Sp-depede Ulfs me-depede wek esy Sog excos: c use P ' Rozz e l. Nue Commu. 05

37 Boud excos peodc sysems 37 -bd gh-bdg model π π k PHM TDM Z.H. Yg Y. L d C.A. Ullch J. Chem. Phys Z.H. Yg F. Sole d C.A. Ullch Phys. Rev. B

38 38 LF 5x5 supecell EWF PHM

39 Summy 39 TDM povdes mge of exco wve fuco. PHM s del fo chge-sfe pocesses. I c ell us whee elecos d holes e comg fom d whee hey e gog o he ole of dvdul chemcl us he exco pocess Boh e esy o pply s pos-tddft ules d povde complemey fomo C be ppled el me o lluse exco dymcs. Applcos he ulfs sog-feld egme e possble Y. L d C.A. Ullch Chem. Phys Y. L d C.A. Ullch J. Chem. Theoy Compu Y. L D. Moghe S. Pl S. Guh d C.A. Ullch Mol. Phys Y. L d C.A. Ullch submed o JCP 06