Yoshio Teki* and Takafumi Matsumoto

Transcription

1 horticl tudy of th ynmic Elctron-pin-Polriztion vi oublt-urtt untum-mixd tt nd th im-rsolvd ER pctr of th urtt High-pin tt Yoshio ki* nd kfumi Mtsumoto ivision of Molculr Mtril cinc Grdut chool of cinc Osk City nivrsity --8 ugimoto umiyoshi-ku Osk 8-88 pn E-mil: upplmntry Informtion t h tim-rsolvd ER spctr nd th dtils of th spctrl simultions of nd th prnt -rdicl th dtils of th ignfild/xct-digonliztion hybrid mthod th dtil drivtion of th unitry trnsformtion mtrixs nd dynmic lctron polriztion dnsity mtrixs by th prturbtion pproch th rsults of th molculr orbitl clcultions r prsntd s th supplmntry informtion. h dpndnc of th tim-rsolvd ER spctr of th C stt t ns on th lctron trnsfr rt constnt is lso prsntd in this supplmntry informtion.

2 I im-rsolvd ER spctr nd th dtils of th spctrl simultions of nd th prnt -rdicl. b c d.... Mgntic Fild / Figur Obsrvd tim-rsolvd ER spctrum of nd dtils of th spctrl simultion. Obsrvd RER spctrum ftr lsr xcittion of th bsorption bnd = nm of th bodipy componnt A; b imultion obtind by th suprimposition of c d nd with th wight of.. nd. rspctivly; c imultion spctrum obtind by th slctiv popultion to th high-fild spin-sublvls; d simultion spctrum obtind by th slctiv popultion to zro-fild spin-sublvls nhncd spin-orbit intrsystm crossing mchnism; simultion of polrizd doublt stt with g =.. b c d / / /.... Mgntic Fild / Figur Obsrvd tim-rsolvd ER spctrum of nd dtils of th spctrl simultion Y. kmoto nd Y. ki ChmPhysChm publishd onlin. OI:./cphc.7. Obsrvd RER spctrum obtind t. s by th xcittion of = nm. b imultion obtind by th suprimposition of c nd d with th wight of.78 :. rspctivly. b imultion spctrum obtind by th slctiv popultion to th high-fild spin-sublvls novl mchnism through ion-pir stt; c simultion spctrum obtind by th slctiv popultion to zro-fild spin-sublvls nhncd spin-orbit intrsystm crossing mchnism.

3 Abs. b Emi..... Mgntic Fild / Figur Obsrvd tim-rsolvder spctrum of th prnt -rdicl nd th spctrl simultion. im-rsolvd ER t K in -MHF glss mtrix. b imultion. h simultion spctrum ws obtind by th slctiv popultion to zro-fild spin-sublvls nhncd spin-orbit intrystm crossing mchnism.

4 II tils of th ignfild/xct-digonliztion hybrid mthod h ignfild/xct-digonliztion hybrid mthod 8 is combintion of th ignfild mthod 7 xct clcultion of th ER rsonnc filds nd th numricl digonliztion of th spin-hmiltonin. In this mthod th rsonnc fild B Rs for ch trnsition of MsMs ws dirctly clcultd by solving th following ignfild qution 7 : A ZBRs CZ whr A nd C r givn by th following supr-oprtors. A EEFEEF nd C GEEG* Hr E is unit mtrix nd is th givn microwv frquncy. h oprtors G nd F r th fild dpndnt nd indpndnt prts of th spin Hmiltonin rspctivly. By solving th ignfild qution q th rsonnc filds BRs r obtind. h trnsition probbilitis I wr vlutd by numriclly digonliztion of th spin Hmiltonin mtrix t ch clcultd rsonnc ignfild.

5 * * * * * * B III tils of th Prturbtion Approch hv trtd th cs of H x < H f << H z. hus H f nd H x wr trtd s prturbtion trms. According to th convntionl prturbtion thory th following qutions hv bn drivd. h nrgis E - E nd ignfunctions > - > r givn by qs. B Bl in th Appndix of th min txt. h unitry trnsformtion mtrix from th bsis rprsnttion to th bsis rprsnttion is obtind to th first ordr using qs. B Bl. sing this qution nd th projction oprtor givn in q. A in th Appndix of th min txt t C of q. is obtind to th first ordr on th bsis rprsnttion s ˆ B P B t C his qution shows tht th first ordr trm zz of th fin-structur tnsor is not contribut to th dnsity mtrix which xprss th EP of th stt undr th finit fild. Espcilly it should b notd tht th digonl componnts of th dnsity mtrix th popultions of * * * * * * * * * * * *

6 th ignstts of th stt is indpndnt to th. h d-cohrnc procss lds to th dnsity mtrix t C which is givn by q. in th min txt s follows. t C sing qs. A nd th dnsity mtrix t C on th high-fild spin-ignstts rprsnttion / > / > -/ > -/ > / > nd -/ > is obtind to th first ordr s t C t C * 7 8 * his qution shows tht th EP gnrtd on th stts is minly trnsfrrd to th M = / spin sublvls of th high-fild wvfunctions of th C stts / > nd / > which lds to non-boltzmnn popultion EP. hus th M vlu is consrvd during this procss. h min off-digonl trms r 7 / / 8 nd 7 / / 8. Howvr ths trms do not contribut to th tim-rsolvd ER spctrum of th C stts s th stdy stts ftr th d-cohrnc. ` * 7 8 * * In th C stts th xchng intrction is much lrgr thn othr intrctions. Hr w hv trtd th cs of H Z > H f nd H f s prturbtion trm for H Z. h mixing trm V hs bn lso incorportd s th prturbtion for H x. According to th prturbtion thory th nrgis E / - E -/ nd th ignfunctions / > - -/ > r givn by qs. B Bl in th Appndix of th min txt. using qs. B Bl. h unitry trnsformtion mtrix from th bsis to th bsis is obtind to th first * * 7 8 * / * * 7 8 *

7 7 ordr using qs. B Bl: sing qs. nd 7 C t is obtind to th first ordr on th bsis rprsnttion by C C C t t t h d-cohrnc procss during t t lds to th slctivly popultd C spin ignstts which is rprsntd by q. on th bsis rprsnttion shown in th min txt s follows. 7 * * * * * * * * * * H * * 7 8 * * * * * * * 7 8 * * * * * 7 8 * * 8 * * 8 * * 8 * *

8 C t

9 Orbitl Enrgy / V IV Rsults of th b-initio molculr orbitl clcultions b OV - - OV -7 otl Enrgy: E = -.87.u. Figur -HOMO nd b MO lvl digrm of th ground stt of

10 Orbitl Enrgy / V b MO igrm of BOIPY-An-OV urtt Excitd tt OV - - OV - otl Enrgy: E = -.88.u. Figur pin dnsity distribution nd b molculr orbitls nd nrgy lvls of th qurtt photo-xcitd stt of.

11 Orbitl Enrgy / V b otl Enrgy: EBLYP = u. Figur pin dnsity distribution nd b molculr orbitls nd nrgy lvls of th nothr photo-xcitd stt of which is constructd from th photo-xcitd triplt stt of th BOIPY moity nd th spin-doublt rdicl moity. his photo-xcitd stt is highr in nrgy bout..u..7 V thn th qurtt stt dtctd by tim-rsolvd ER.

12 Orbitl Enrgy / V b MO igrm of Nphtlimid-An-Vr Ground tt - - α β otl Enrgy: EBLYP = -.8.u. Figur 7 -HOMO nd b MO lvl digrm of th ground stt of

13 Orbitl Enrgy / V b MO igrm of Nphtlimid-An-Vr urtt tt otl Enrgy: EBLYP = -.8.u. Figur 8 pin dnsity distribution nd b molculr orbitls nd nrgy lvls of th qurtt photo-xcitd stt of.

14 V pndnc of th tim-rsolvd ER spctr of th C stt t ns on th lctron trnsfr rt constnt sing th solution = C = nd th initil condition = P nd C = on th bsis rprsnttion w simultd th dpndnc of th tim-rsolvd ER spctr of th C stt on k E. Figur shows th dpndnc of th tim-rsolvd ER spctr of th C stt on th lctron trnsfr rt constnt. In this clcultion th durtion tim ws st to b ns. As shown in this Figur th most similr on to thos obtind by th polriztion trnsfr ftr th d-cohrnc of th stt shown in Figurs -f is Figur j. Howvr th cntr rgion of th spctrum is diffrnt from thos shown in Figurs -f. hus only th incomplt dphsing ws obtind t ns. x h x i x b c x 7 x 7 j x d x 7 k x x 7 l x f x g x.... Mgntic Fild /.... Mgntic Fild / Figur pndnc of th simultion spctr of th C stt on k E. h durtion tim ws st to b ns. C =. cm - nd E C =. cm - wr usd for th fin-structur prmtr of th C stt. nd vlus wr fixd to b. cm -. MHz nd GHz rspctivly. k E =.x 7 s - b k E =.x s - c k E =.x s - d k E =.x s - k E =.x s - f k E =.x s - g k E =.x s - h k E =.x s - i k E =.x s - nd j k E =.x 8 s - k k E =.x 7 s - nd l k E =.x s - rspctivly.