Methods of quantum dynamics and simulation of pump-probe spectra
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1 Mhods of quau dacs ad sulao of pup-pob spca Chsoph M Laboao Collsos Aéas Réacvé Uvsé Paul Saba Toulous Cas Auus 008
2 Mhods of quau dacs ad sulao of pup-pob spca I. Ioduco Las / olcul aco -- lco / ucl spaao -- coupld chal quaos -- sulao of pup pob spca -- ucal plao II. Mhods of wav pack popaao -- sadad hods: SOD Cak-cholso FFT-SO -- hods fo hh dsoal pobls: TD-SCF MCTD III. Oulook ad fuh dvlops -- 6D quau wp: vbaoal pdssocao of 4 ao copl -- Local cool ad wh a d qu/classcal popaao sch
3 I. I. Ioduco 3 Co: Foscod las aco wh aoc ad olcula sss classcal MD wav pack popaao dacs subc o vos dacs of cd sas puls shapd IR cao IVR lcoc / vbaoal laao pdssocao... p-----ho
4 I. Ioduco 4 Foscod spcoscop olcula sss A: obsvao of la pocsss of chcal acv a h aoc scal al W wa o hav accss a: vbao ocal aa bak ad foao of bods sosao IVR asos bw lcoc sas: IC ISC vbaoal lcoc laao Pcpl of pup-pob ps: Two -dlad ulasho las pulss Pup puls: s olcula dacs Pob puls: pobs quau sa a dff dla s scals: foscod: 0-5 s pcoscod: 0 - s
5 I. Ioduco 5 ucal sulaos: Elcoc sucu calculaos Modl acos SE Foc flds dscpo of h ss aco wh copl-shapd las pulss dpd appoach quau wav pack dacs wak flds: dpd pubao ho classcal dacs p
6 6 dpol aco aloa E μ s α α α μ q lcoc/ucla spaao: lcoc sucu calculao Ψ V μ μ Ψ Ψ s E μ & s μ E & c s V P P also: T V μ E & I. Ioduco Las / olcul aco c s V P P ss aloa:
7 7 I. Ioduco Las / olcul aco V μ E & δ Pops of : ad spcfcall : V T μ E & a V o-adabac coupls Ĥ
8 I. Ioduco Las / olcul aco a ˆ E μ V E μ 8 Vbaoal cao IR o-adabac coupls Elcoc cao vs-uv ucla dacs o h lcoc oud sa o-adav aso ucla dacs cd sas dacs d: ucla wav fuco o l. sufac V cao las Epsso vald fo hh ss al wav fuco
9 I. Ioduco Las / olcul aco 9 ucla dacs o h lcooc oud sa o-adav aso ucla dacs cd sas A pup pob: choos wo las pulss wh vaabl dla o sud h cobd lcoc / ucla dacs A coh cool: choos copl shapd las pulss o duc a pdfd dacs w a spcfc chal
10 0 Eμ ˆ ucla dacs lcoc oud sa ucla dacs lcocall cd sas 0 0 ˆ d T Eμ E μ E μ ˆ ˆ p h.. 0 ˆ 0 ˆ d Eμ ˆ δ δ Eμ ˆ ˆ δ δ δ δ μ E I. Ioduco Las / olcul aco ˆ δ δ quau popaao I boh cass: a V ˆ μ E μ E Vbaoal cao IR Elcoc cao vs-uv o-adabac coupls
11 II. Mhods of wav pack popaao Mhods of wav pack popaaos hav a wd a of applcaos wll bod las puls acos wh aoc / olcula sss.: aoc ad olcula phscs: [s also: D. J. Tao Ioduco o Quau Mchacs: A T Dpd Pspcv Uvs Scc Pss Sausalo 006] -- lasc / lasc collsos acv sca -- spcoscop va colao fucos -- plc dpd pubaos las acos coh cool Opcs: Mawll s quao...
12 II. Mhods of wav pack popaao Eapl: popaao of lcoac wavs aosucus D& B& c c E D εe B μ ψ E 0 c μ c ε 0 ψ& ψ ca b scald o b ha Ca b foulad fo dspsv da Applcao: lh assso houh aosucud apus [A. G. Bosov S. V. Shabaov J. Cop. Phs ]
13 3 ˆ δ δ U [ ] app app U U o should b cosvd popaao o ac dscsao o should alwas b covd fo δ 0 quau popaao U U app app δ δ II. Mhods of wav pack popaao
14 II. Mhods of wav pack popaao 4 popaaos av lobal - scod od dff - plc Cal - Spl-Opao - sho av Laczos - Laczos - Chbchff - -dpd slf coss fld TD-SCF - Mulcofuao dpd a MCTD Ca also b usd fo h popaao of ds acs
15 II. Mhods of wav pack popaao 5 Scod od dffc SOD: dvao: ˆ Δ ˆ Δ Δ Δ Δ Δ ˆ Δ hod: Δ Δ Δ chaacscs: -- soa: -- opaos: -- sabll: Δ ˆ Δ < Ea
16 II. Mhods of wav pack popaao 6 Cal Cak-cholso : dvao: Δ ˆ ˆ Δ ˆ Δ ˆ Δ Δ Δ ˆ ˆ Δ Δ Δ pobl: vso Δ Δˆ Δ hod: chaacscs: -- soa: -- opaos: -- o-cosv -- sc w. Δ ξ Δ ξ ˆ ξ ˆ Δ Δ ξ
17 dvao: II. Mhods of wav pack popaao FFT-Spl Opao FFT-SO : ˆ T V ˆ Δ ΔT Δ Δ V Δ V 7 Fou psao: Δ h k π ΔV π Δ 0 0 Δ V Δ V FFT T Δ FFT Δ V hod: Δ V FFT ΔT FFT Δ Δ V chaacscs: -- soa: -- opaos: -- sabl o-cosv -- sc w ulplcaos FFT o! Δ Δ [M. D. F J. A. Flck A. S J. Copu. Phs ] Ĥ
18 II. Mhods of wav pack popaao 8 Ovvw / copaso: avaas désavaas SOD flbl: a psao dpd sall sp Cak-colso plc flbl: a psao dpd ua ao a v sp FFT-SO FFT: ffc o a-vco ulplcao dpd ua qudsa ds : o coss-s
19 II. Mhods of wav pack popaao Quau wav pack fo hh-dsoal pobls: 9 pacls 3-6 al DoF 0 pos/bass fcs p DoF calculao of spcu / dacs poal scal 3 6 Mb CPU : sc Gb CPU :0 das Appoaos q 3 ~0 ~0 40 Gb CPU : ~0 0 as appoa dacs: TD-SCF MCTD dacs ducd dsoal s podc haoc appoao classcal chacs acos d quau/classcal dacs
20 0 II. Mhods of wav pack popaao: TD-SCF TD-SCF: suppos wf ca b dscbd b a poduc R: hs dcoposo s o uqu! cosas Schöd quao bcos: Schöd q. D s placd b coupld D quaos Dacs o DoF s dd b h dac a fld ov h oh DoF v f s dpd ad a -dpd! ca b usd fo up o ~00 DoF! dsavaa: appoa o had o sa a cosd DoF fo h psao of h basc da bu h usfulss ls h so o a DoF 0 & & a a & & & Oh foulaos s
21 II. Mhods of wav pack popaao: MCTD cosd DoF fo h psao of h basc da bu h usfulss ls h so o a DoF MCTD: ul-cofuaoal paso of h wavfuco R: hs s o uqu! cosas a Schöd quao bcos: -- coupld quaos fo h a -- fo ad M bco copl: MCDT bcos a ac sadad hod bco dpd & δ M & δ flbl a psao s possbl dff psaos fo dff DoF possbl a soa qus: fo b ad M b bass fcs/d pos * b M* M b *M vs. b *M b all: << b M<<M b U. Mah.-D. M L. S. Cdbau J. Ch. Phs D. M U. Mah L.S. Cdbau Ch. Phs. Ls
22 II. Mhods of wav pack popaao: TD-SCF MCTD: ul-cofuaoal paso of h wavfuco R: hs s o uqu! cosas Schöd bcos: M a δ & M a a & P ρ & M δ & M P ρ & * M M a a * a a P M P M a a * ρ a a * ρ cosd DoF fo h psao of h basc da bu h usfulss ls h so o a DoF
23 II. Mhods of wav pack popaao 3 quau wav pack hods os: psao os os h calculao of h popaao avaas / dsadvaas fasbl fo oda ub of DoF: -3 fo o ha 3 DoF: MCTD ls: appoaos Rfcs: Méhods d popaao d paqus d ods: C. Ca ucal Gd hods ad h applcao o h Schöd quao Kluw 993. C. Lfos R.. Bssl C. Ca M. D. F R. Fs A. Guldb A. ach G.Jolcad W. Kal.-D. M. Lpk O. Roco R. Kosloff J. Cop. Phs R. Kosloff J. Ch. Phs Mulcofuao -dpd a: M.. Bck A. Jäckl G. A. Woh.-D. M Phs. Rpos U. Mah.-D. M L. S. Cdbau J. Ch. Phs D. M U. Mah L.S. Cdbau Ch. Phs. Ls
24 4 III. Oulook fuu dvlops Dacal pocsss of o copl sss -- Mo ds of fdo -- o-solad sss ffcs of vo dcohc Cool b copl shapd las pulss spcal os IR UVXUV h s I θ I θ R R Vbaoal pdssocao of I Full-dsoal quau a 6D puls shapd IR cao b-co Local cool sch Md qu/cl dacs
25 III. Oulook fuu dvlops Epl: vbaoal pdssocao of I odl ss o sud h sovla-solu acos wak va d Waals aco: Challs: zo-po ffcs poa quau of vbao of I s ouh o dssoca o a as ao sol colad dacs of h wo aos I θ I θ R R 5 Quau a `full dsoal fc calculao fo appoa schs pocssus sudd: vbaoal pdssocao of : I B I B0 I B9 [C. M U. Mah J. Ch. Phs ]
26 6 III. Oulook fuu dvlops R R θ I I θ s s s θ θ θ μ μ μ μ θ θ θ I I R R R R R R θ θ θ θ λ γ λ γ γλ R R V C R R Sall coodoés o-ohooal: dsac I-I c of ass I - al al bw h I-I- plas R R θ θ R
27 III. Oulook fuu dvlops 7 wav pack popaao us h MCTD sch 6 D ψ R R θ θ 6 L 6 a L 6 R 3 3 R 4 4 θ 5 5 θ 6 6 cooda R R θ θ SPF b. of bass fc. psao 5 49 fc. pops d I FFT FFT 4 80 Ld DVR 4 80 Ld DVR 6 9 FFT ub of cofuaos: 9000 aloa a sadad hod: ~
28 III. Oulook fuu dvlops 8 ν IVR ν0 ν0 ν9 dc ν9 R R aspoc lf of h soac: I B : ~55 ps pocss: I Bν I B ν0 : IVR pocss: I Bν I Bν9 : dc dacal pocss qus QM ad full dsoal!
29 III. Oulook fuu dvlops 9 Epl: Mulphoo IR cao of bco wh shapd pulss Wh? CO vbao as local pob of po vo suds of vbaoal laao: laao pahwas flow of duc cofoal chas? oud sa chs a: dpos as uch h COsch as possbl : cofoal chas? oud sa dssocao? laao pahwas c sl vbaoal sas o coh supposos of sas subsqu asus of sa solvd laao s dcohc: ssv asu of vo / po dacs
30 III. Oulook fuu dvlops 30 ahaoc quau oscllao CO h copl ~30 aos FPI-CO sub-u of po ~00 aos odl: [] [fuu wok: full po solvao] CO FPI po clos vo: DFT B3LYP al-lad pops π-backbod [] po: Cha odfs FP dpol o cas fluc. lcc flds [] M. D. Fa Au. Rv. Phs. Ch 5 00 J.R. ll al. J. Phs. Ch K. A. Mcha al JACS D.E. Salla J.E Saub Bophs. J [] M. C. z C. M. J. Ch. Phs
31 III. Oulook fuu dvlops 3 Md quau-classcal dacs quau: ψ q V q L μ q L E E ψ q ψ q Schöd quao q : CO sch wh FPI-CO copl q 0 q f q L μ q L E po classcal: wos quaos & q L o back-aco: V foc s valuad a CO qulbu poso [clud backaco fuu] sp sulao:. Cha wh CO fd. ulpl quau wav pack calculaos wh flucuaos poal dpol oao q
32 ulpl WP popaaos wh dff III. Oulook fuu dvlops Obsvabls ds acs ad Local cool ψ q ds a ρ ψ Aρ obsvabls A local cool fo If o chooss: h w hav: f A 0 d d d 0 ψ ψ Aψ [ ] ρ 0 cosθ ψ [ μ 0] cosθ ψ [ μ 0] E ψ E f ψ d 0 0 Eal fld sus ha of spcfc od: Local cool sch wh Q/C [] R. Kosloff S. A. Rc P. Gaspad S. Ts D. Tao Ch. Phs M. Suawaa Y. Fuua J. Ch. Phs P. Goss. Sh. Rabz K. Mas G. M. ua Phs. Rv A ad los o... 3
33 III. Oulook fuu dvlops 33 sulaos: 000 d qu/classcal us fo soopcall od sapl [ μ ] 0 E ± f cosθ ψ ψ f chos o su puls lhs of: ps.5 ps ps.5 ps ad cosa s: 40 μ paas of IR puls shap ps of M. Joff LOB Pas [] ps.5ps.0ps.5ps [c - ] W plos of LCT pulss copaso wh o-flucua ss soopc [] C. Valo al PAS
34 III. Oulook fuu dvlops 34 fuu : -- dvlop of d quau / classcal appoachs -- applcao o alsc sss -- cool dsspav vos -- cobao of MCTD ad classcal chacs fud: AR Fch s: pos doc poso
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Major: All Engineering Majors. Authors: Autar Kaw, Luke Snyder
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