Ultrafast Vibrational Frequency Shifts Induced by Electronic Excitations: Naphthols in Low Dielectric Media

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1 pubs.acs.org/jpca Ultrafast Vbratonal Frquncy Shfts Inducd by Elctronc Exctatons: Naphthols n Low Dlctrc Mda Dquan Xao, Mrabll Prmont-Schwarz, Erk T. J. Nbbrng,*, and Vctor S. Batsta*, Dpartmnt of Chmstry, Yal Unvrsty, P.O. Box 2817, Nw Havn, Connctcut , Untd Stats Max Born Insttut f ur Nchtlnar Optk und Kurzztspktroskop, Max Born Strass 2A, D Brln, Grmany ABSTRACT: W study th solvnt-nducd frquncy shfts of th OH-strtchng mod of 1-naphthol and 2-naphthol n nonpolar/wakly polar solvnts, subjct to lctronc xctaton, wth ultrafast UV/md-nfrard pump prob spctroscopy and thortcal modlng basd on Pulln s prturbatv tratmnt of vbratonal solvatochromc ffcts. Th modl s paramtrzd at th dnsty functonal thory (DFT) lvl, ncludng th B3LYP/TZVP and TD-B3LYP/TZVP dscrptons, for th naphthol chromophors n th S -and 1 L b -stats and accounts for both th statc and th optcal dlctrc rspons of th solvnt on tm scals comparabl to that of th OH-strtchng vbratonal motons. Th favorabl comparson btwn xprmntal and thortcal valus of th solvnt-nducd vbratonal frquncy shfts suggsts that th ultrafast dlctrc rspons of th solvnt contrbuts prdomnantly to th solvatochromc shfts n solvnts of modrat polarty whr spcfcsolut solvnt ntractons ar absnt. 1. INTRODUCTION Photoacdty s a trm that was cond to hghlght a unqu proprty of aromatc alcohols, namly, that thy show a pronouncd ncras n acdty upon lctronc xctaton. 1 6 Changs n acdty for photoacds dssolvd n watr rang from ΔpK a =pk a (S 1 ) pk a (S ) ,8 Ths gvs rs to xctd stat proton transfr ractons thrby nablng studs of thr ultrafast dynamcs Whl much rsarch has bn dvotd to proton transfr n photoacd bas complxs n th gas phas, rcnt xprmntal and thortcal vdnc support hydrogn transfr mchansms nstad of th xpctd proton transfr, wth a nt lctron and proton transfr wth bass lk amns In contrast, photoacds typcally rlas a proton n solvnts wth a hgh dlctrc constant, most notably n watr. 21 To undrstand such nt sparaton of th postv solvatd proton and th ngatvly chargd photobas, solvaton of th racton products must b of major mportanc. 22 As such, to xplan photoacdty on should not only am for a quanttatv dtrmnaton of th ntrnsc lctronc dnsty ffcts affctd by photoxctaton but also for a full xploraton of th mcroscopc paramtrs govrnd by solvaton. Studyng th couplng btwn th lctronc and nuclar dgrs of frdom of a solut mbddd n a solvnt by UV/vs spctroscopy s wll stablshd Solvaton of photoacd molculs has bn nvstgatd usng lctronc spctroscopy and analyzd wth smmprcal dscrptons basd on lnar fr nrgy rlatonshps, such as th Kamlt Taft approach Howvr, solvaton can also b probd by lookng at th frquncy poston of th vbratons of a solut, whr th solvatochromc frquncy shfts ar typcally 2 ordrs of magntud smallr than thos obsrvd by lctronc spctroscopy. Th hydrogn strtchng vbratons of th proton donatng hydroxyl OH or (protonatd) amn NH 3 + groups would provd a drct nsght nto th local ntractons of photoacd molculs. W prsnt xprmntal and thortcal rsults of transnt IR spctroscopy of th OH-strtchng mod of 1-naphthol (1N) and 2-naphthol (2N) (s Schm 1), th two prototyp photoacds In ordr to undrstand th basc ntrnsc lctronc charg rdstrbuton as wll as solut solvnt couplngs, w frst dscuss rsults n solvnts of low polarty, whr spcfc solut solvnt ntractons,.., hydrogn bonds, ar undrstood not to tak plac. Quantum chmcal calculatons on 1N and 2N ar prsntd to stmat th changs n lctron dnsty dstrbutons causd by lctronc xctaton. W thn analyz th solut solvnt couplngs by th Onsagr solvaton modl, whr th solut s rprsntd by a pont dpol mbddd n a sphrcal Onsagr cavty ntractng wth a dlctrc contnuum rprsntng th surroundng solvnt molculs Whl th xprmntal vbratonal frquncy shfts for wakly hydrogn bondd molcular systms n th lctronc ground stat hav bn lnkd to a prturbaton thory of th solvatd oscllator potntal, no such rlatonshp dscrbng how th obsrvd frquncy shfts ar rlatd to molcular paramtrs xsts for th xctd stat. W follow th (stady-stat) prturbatv dscrpton by Pulln and rfn t wth th tm-dpndnt thory by van dr Zwan and Hyns 48 to tak nto account th ffcts of solvnt shll rarrangmnts. W thn compar th xprmntally masurd solvnt-nducd OH strtchng frquncy shfts of 1N n th S -and S 1 -stats wth thortcal prdctons usng quantum chmcal calculatons, as wll as wth prvously rportd rsults obtand on 2N. 49 Fnally, w dscuss th dffrncs obsrvd btwn 1N and 2N. Spcal Issu: Fmto1: Th Madrd Confrnc on Fmtochmstry Rcvd: Sptmbr 1, 211 Rvsd: Octobr 9, 211 Publshd: Novmbr 1, 211 r 211 Amrcan Chmcal Socty 2775 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

2 Th Journal of Physcal Chmstry A Schm 1. Chmcal Structurs of cs and trans Conformrs of 1N and 2N numrcally by fnt dffrncs ðμ k Þ x ¼ μ k ðx þ δx Þ μ k ðx δx Þ 2δx ð2þ 2. METHODS: THEORY AND EXPERIMENT 2.1. Computatonal Mthods. Gomtry optmzaton and calculatons of ground stat molcular proprts, ncludng lctronc nrgs, transton dpol momnts, lctrostatc potntal (ESP) atomc chargs, dpol momnts, dpol drvatvs wth rspct to normal mods, vbratonal normal mods, and solvaton nrgs wr obtand at th DFT (B3LYP/ TZVP) lvl of thory, as mplmntd n Gaussan 9. 5 Analogous xctd stat calculatons wr prformd at th TD-DFT (B3LYP/TZVP) lvl. Th polarzabl contnuum modl (PCM) was usd for computatons of solvaton nrgs and for gomtry optmzaton n dlctrc contnuum mda. Th ordr of th xctd stats, 1 L a and 1 L b, n th nrgy laddr of both th cs- and trans-rotamrs of 1N or 2N was found to b swtchd wth rspct to th nrgtc ordr probd by xprmnts. 15,51 Ths bhavor was studd prvously and attrbutd to an undrstmaton of th ntracton btwn onc componnts n th 1 L a -stat du to th mpropr asymptotc form of standard functonals. 52 Howvr, th dstnct lctronc symmtry of ths stats nabld us to dntfy th 1 L b stat and comput th molcular paramtrs n ths stat at th TD- DFT lvl, ncludng dpol momnts as wll as th frst and scond dpol drvatvs. Th anharmonc forc constant and th harmonc constant wr calculatd by th anharmonc vbratonal analyss mplmntd n th Gaussan 9 program usng th kyword frq(= anharmonc). For th anharmonc vbratonal analyss, th HF/6-31g mthod was usd for th ground stat, and th CIS/6-31g mthod was usd for th xctd stat. Onc th frst drvatvs of th dpol momnt wth rspct to th kth normal mod (μ k = μ/ Q) wr calculatd by th kyword IOP(7/33 = 1) n Gaussan 9, th scond dpol momnt drvatvs wr computd as follows: μ k ¼ ðμ k Þ Q ¼ ðμ k Þ l k ð1þ x whr l k s th transformaton matrx from th Cartsan coordnat to th normal mod coordnat, and th drvatv n th Cartsan coordnat (μ k )/( x ) was calculatd 2.2. Exprmntal Mthods. 1-Naphthol (99%), 2-naphthol (99%), n-hxan, cyclohxan, C 2 Cl 4, CHCl 3,CH 2 Cl 2, and 1,2- dchlorothan (Ragnt Plus; g99%) wr all purchasd from Aldrch. Stady-stat lctronc absorpton spctra wr rcordd wth a doubl-bam UV/vs spctromtr (Prkn-Elmr), and msson spctra wr rcordd wth a spctrofluoromtr (Spx Fluorolog). W obsrv a sgnfcantly lowr msson quantum yld and a dvaton of th msson band shap compard to that of th othr solvnts n CHCl 3 and C 2 Cl 4 (total fluorscnc qunchng was obsrvd n CCl 4 ), whch unfortunatly prcluds th prcs dtrmnaton of th lctronc Stoks shft n ths solvnts. Th qunchng bhavor of som halocarbon solvnts wth naphthaln and ts drvatvs has prvously bn rportd n th ltratur 53,54 and s tntatvly ascrbd to a spcal xcplx ntracton btwn ths halocarbon solvnts and th aromatc systm n th S 1 -stat, thrby shortnng th lctronc xctd stat lftm. Ultrafast nfrard spctra wr rcordd usng an xprmntal stup dscrbd prvously. 55 Elctronc xctaton of 1N and 2N was achvd wth pulss (3 μj, 5 fs) gnratd by sum frquncy mxng of th fundamntal of a 1 khz amplfd T: sapphr lasr (Tsunam oscllator wth Sptfr Pro rgnratv and boostr amplfr stags; Spctra Physcs) and vsbl pulss gnratd by a noncollnar optcal paramtrc amplfr (NOPA). Th xctaton wavlngth was tund to th lowst nrgy pak of th 1 L b transton for ach solvnt thrby nsurng mnmal xcss nrgy (318 to 33 nm). Th pump pulss wr snt to a dlay ln and thn focusd onto th sampl wth a bam damtr of approxmatly 2 μm. Tunabl mdnfrard pulss wr gnratd by a doubl-pass optcal paramtrc amplfcaton followd by dffrnc frquncy mxng of sgnal and dlr. Th prob and rfrnc pulss wr obtand usng rflctons from a ZnS wdg and focusd onto th sampl by mans of an off-axs parabolc mrror (focal damtr, 15 μm). Th prob and rfrnc pulss wr dsprsd n a polychromator (8 1 cm 1 rsoluton), and spctrally rsolvd absorbanc changs wr rcordd smultanously for ach shot usng a lqud ntrogn coold HgCdT doubl array dtctor (2 31 pxls). Th tm rsoluton was dtrmnd to b 15 fs basd on th cross-corrlaton btwn th UV-pump and IRprob pulss masurd n a ZnS smconductor placd at th sampl poston. A prstaltc pump was usd to crculat th sampl through a flow cll (1 mm thck CaF2 wndows sparatd by a 3 μm thck Tflon spacr) to guarant that a nw sampl volum was xctd for vry lasr shot. Concntratons of only 2 mm wr usd n ordr to mnmz th slf-assocaton found to occur n th nonpolar solvnts such as n-hxan or cyclohxan. In addton, gvn th formaton of a photoproduct stckng to th cll wndow, a wll-known phnomnon n aromatc systms wth lctron donatng substtunts, 56,57 th sampl holdr was movd up and down durng th masurmnt. Also, th lctronc and stady-stat nfard spctra wr montord bfor and aftr th masurmnt to nsur that th natur of th soluton dd not chang dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

3 Th Journal of Physcal Chmstry A Th solutons usd n th xprmnts wr chckd for watr contamnaton. Furthrmor, th ffct of watr was vrfd through a controlld xprmnt whr known quantts of watr wr addd to a soluton of 1N n CH 2 Cl 2.Itwasfoundthatth complxaton constant was qut small and that watr dd not chang th natur of th OH-strtchng band of uncomplxd 1N. 3. SOLVENT-INDUCED VIBRATIONAL FREQUENCY SHIFTS: PULLIN VAN DER ZWAN HYNES PERTUR- BATIVE APPROACH Thortcal dscrptons of solvnt-nducd vbratonal frquncy shfts hav oftn rld on a prturbatv approach, whr th solut solvnt ntracton s tratd as a prturbaton to th vbratonal Hamltonan of a gas phas molcul. 58 Whn a dtald mcroscopc dscrpton of th solut solvnt ntracton s not avalabl, solvnt contnuum modls ar of us. Krkwood 59 and Baur and Magat 6 wr th frst to us th Onsagr racton fld modl of a pont dpol rprsntng th solut mbddd n a sphrcal cavty surroundd by a contnuous solvnt mdum charactrzd by a macroscopc dlctrc constant. Pulln gnralzd ths prturbatv approach for polyatomc polarzabl molculs wth anharmonc vbratonal potntals, dssolvd n a contnuum solvnt wth a frquncy-dpndnt dlctrc constant. 43,44 Buckngham smlarly usd an xplct quantum chmcal tratmnt of a datomc molcul mbddd n a contnuum solvnt wth a frquncy-dpndnt dlctrc constant Hs analytcal xprssons for solvnt-nducd vbratonal frquncy shfts hav bn usd xtnsvly and rfnd by othrs. 61,62 Thy nabl th rlatv contrbutons of solvnt polarty (ε ) and solvnt polarzablty at optcal frquncs (ε ) to b stmatd. Rcntly, ths approach has bn appld to wakly hydrogn-bondd cass Pulln's and Buckngham s drvatons ar closly rlatd, xcpt for th startng ponts n dfnng molcular Hamltonans and th stmaton of th dlctrc constants for dffrnt contrbutons n th xprssons for th solvnt-nducd vbratonal frquncy shfts. Howvr, whl th mcroscopc manng of th dffrnt constants n Buckngham s xprssons snotstraghtforward for polyatomc molculs, 63 Pulln s xprsson maks th xtnson to polyatomc molculs wth off-dagonal anharmoncts straghtforward. W thrfor apply Pulln s drvaton of th solvnt-nducd vbratonal frquncyshfts,andxtndtwththvandrzwan Hyns rlatonshp 48 to dscrb a tm-dpndnt racton fld nducd by th pont dpol altrd by lctronc xctaton Evn though w dscuss solvnt-nducd frquncy shfts of 1N and 2N n solvnts wthout xplct hydrogn bondng of th OH-group, ths approach can b xtndd to hydrogn bondng solvnts as wll, provdd that a propr xprsson for th vbratonal potntal of th OH-strtchng mods of hydrogn-bondd complxs can b dfnd. In th followng, w prsnt th analytcal xprssons for th tm-dpndnt solvnt-nducd vbratonal frquncy shft, followng th drvaton of Pulln 43,44 and th tm-dpndnt xtnson as dfnd by van dr Zwan and Hyns Mors Potntal. Th Mors vbratonal potntal n th gas phas of th molcular systm V (Q) canbwrttnasataylor xpanson along vbratonal coordnat Q as V ðq Þ¼D ð1 α Q Þ 2 ¼ 1 2 Q 2 þ 1 3 Q 3 þ ::: ð3þ whr D s th dssocaton nrgy of th th lctronc stat, and α =(V /2D ) 1/2. Not that for uncomplxd 1N or 2N, w assum that th anharmonc couplng btwn th OH-strtchng mod wth th othr normal mods (.., cubc forc constants V ) can b dscardd n th Taylor xpanson of q 3. For ths, w rly on th larg body of nformaton accumulatd wth ultrafast nfrard spctroscopy of vbratonal mods n lqud soluton, whr th vbratonal dphasng and vbratonal rlaxaton rats can b proprly xpland wth an anharmonc OH-strtchng mod coupld to a hat bath comprsng ovrdampd low-frquncy solvnt mods. 72,73 Th quadratc forc constant V and cubc forc constant V of th Mors potntal ar thn ¼ 2D α 2 ¼ 6D α 2 ð3aþ ð3bþ 3.2. Solvaton of Mors Potntal by th Onsagr Pont Dpol Modl. Th dlctrc rspons of th mdum surroundng th sphrcal Onsagr cavty (wth a radus a ) formd by th polar photoacd molcul rsults n a racton fld R (Q) thatntracts wth th molcul. Th solvaton nrgy s V s ðqþ ¼ 1 2 μ ðq ÞRðQ Þ ¼ V s þ V s Q þ 1 2 s Q 2 þ ::: ð4þ whr μ (Q) s th molcular dpol momnt, that s dpndnt on th nuclar coordnat Q. Usng a Taylor xpanson along th normal coordnat, ths bcoms μ ðq Þ¼μ þ μ Q þ μ Q 2 þ ::: ð4aþ whr μ s th prmannt dpol momnt of th solut, wth μ and μ bng th frst and scond drvatvs of th dpol momnt along th vbratonal coordnat Q, rspctvly. Th racton fld thn bcoms R ðq Þ¼f μ þ f μ Q þ f μ Q 2 þ ::: ð4bþ whr f and f ar th functons of th statc dlctrc constant ε and th optcal dlctrc constant ε, rspctvly. f ¼ 1 a 3 2ε 2 2ε þ 1 ¼ 1 a 3 F ð4cþ f ¼ 1 2ε 2 ¼ 1 a 3 2ε þ 2 a 3 F ð4dþ Th optcal dlctrc functon f s rlatd to th statc dlctrc functon f by f ¼ f þ f ðq Q Þ ð4þ whr Q* s th nw qulbrum bond lngth of th Mors potntal n soluton. From th quatons prsntd abov, th followng quantts can b radly dntfd: f or ¼ f f ð4fþ F ¼ 2ε 2 2ε þ 1 ð4gþ 2777 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

4 Th Journal of Physcal Chmstry A F ¼ 2ε 2 2ε þ 2 Substtutng qs 4a and 4b nto q 4, w obtan V s ðq Þ¼ 1 2 ðμ þ μ Q þ μ Q 2 þ :::Þðf μ ð4hþ þ f μ Q þ f μ Q 2 þ :::Þ ð5þ By groupng trms by ordr Q and comparng thm to th Taylor xpanson coffcnts, w fnd V s ¼ 1 2 ðf þ f Þμ 3 μ ð5aþ Accordng to q 4, at th qulbrum pont n soluton (Q = Q*), f = f,onfnds V s ¼ f μ 3 μ ð5bþ s Q ¼ Q ¼ ½ðf þ f Þμ 3 μ þ f μ 3 μ Š ð5cþ Th solvatd Mors potntal thn bcoms V sol ðq Þ¼V ðqþþv s ðqþ ¼ 1 2 Q 2 þ 1 3 Q 3 þ V s þ 1 2 s Q 2 þ ::: Th frst drvatv of V sol (Q) s þ V s Q V sol ðq Þ¼V s þ Q þ s Q þ 1 2 Q 2 þ ::: At th nw qulbrum pont V sol ðq Þj Q ¼ Q ¼ and thus, th nw qulbrum lngth Q*s V V s s Q þ s Q ¼ Q Th scond drvatv of V sol (Q) s Q ¼ Q ð6þ ð7þ ð8þ ð9þ solðq Þ¼V þ Q þ s þ ::: ð1þ By substtutng q 7 nto q 8, w obtan sol ðq Þ 2 ¼ 4 1 V s Q ¼ Q V s Q ¼ Q þ s ð1aþ A5 ð1bþ s 13 By substtutng qs 5a and 5b nto q 1b, w obtan ( " sol ¼ 1 1 f μ 3 μ μ 3 μ #) þ f ðμ 3 μ þ μ 3 μ Þ whr Δ ¼ 1 ¼ ð1 ΔÞ ð11aþ ð11þ " # f μ 3 μ μ 3 μ þ f ðμ 3 μ þ μ 3 μ Þ ð11bþ 3.3. Vbratonal Frquncy Shfts Du to Solvaton. W ar now abl to dfn th solvnt-nducd vbratonal frquncy shft as sffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff Δν ν ν ν s ð1 ΔÞ ν ¼ Δ=2 ð12þ whr Δν = ν ν s s th dffrnc btwn th vbratonal frquncy n soluton (ν s ) and n th gas phas (ν ). By substtutng q 11b nto q 12, w obtan Δv v ¼ f μ 2 3 μ μ 3 μ whr þ f 2 2 ¼ f or g μ þ f g ¼ μ ðμ 3 μ þ μ 3 μ Þ ð13þ μ 2 ½ðg þ μ Þμ þ μ 3 μ Š ð13aþ ð13bþ Substtutng qs 4c d and V = k =4π 2 mv 2 nto q 13, w fnd that Δν shows a lnar dpndnc on F F Δv ¼ 8π 2 mv μ 3 3 a μ μ 3 μ F þ 8π 2 mv 3 a ðμ 3 μ þ μ 3 μ Þ ð14þ Th slop of ths lnar rlatonshp btwn Δν and F s gvn by F S ¼ 8π 2 mv μ 3 3 a μ μ 3 μ ð14aþ and th ntrcpt s drvd to b F B ¼ 8π 2 mv 3 a ðμ 3 μ þ μ 3 μ Þ ð14bþ Formally, F s also solvnt-dpndnt, as th dlctrc constant at optcal frquncs s rlatd to th rfractv ndx through th rlatonshp ε = n 2. Howvr, th varaton of th rfractv 2778 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

5 Th Journal of Physcal Chmstry A Tabl 1. Dlctrc Constants and Rfractv Indcs for th Solvnts Usd n Ths Study solvnts ε (lt) a n (lt) a n (3337 cm 1 ) (.15 ε (3337 cm 1 ) n-hxan c-hxan C 2 Cl CHCl CH 2 Cl ,2-DCE a Valus takn from rf Vbratonal Frquncy Shfts Du to Elctronc Exctatons. For th OH-strtchng mod of 1N and 2N n th lctronc xctd stat, w hav to consdr th rol of solvnt rorganzaton (solvaton dynamcs) xpctd to tak plac on ultrafast tm scals. Ultrafast solvaton dynamcs of solut chromophors s a topc that has bn xtnsvly xplord durng th past svral dcads ,74 76 Elctronc xctaton of a solut mpls th rarrangmnt of lctronc charg dnsty wthn th solut chromophor. Bcaus of th solut solvnt couplng, th surroundng solvnt shlls rspond to ths lctronc xctaton wth an nstantanous componnt du to th lctronc hyprpolarzablty and nonnstantanous componnts du to nuclar dynamcs. A multtud of modls wth dffrnt dgrs of sophstcaton hav bn dvlopd to dscrb th tm-dpndnt solvnt rorganzaton. 28 W follow th stablshd van dr Zwan Hyns approach 48 to ncorporat a tm-dpndnt racton fld nto th xprssons for th tmdpndnt solvnt-nducd vbratonal frquncy shfts upon lctronc xctaton of a solut. R ðtþ ¼f μ ðqþ þf or μðtþ ð17þ whr μðtþ ¼μ g ð1 zðtþþ þ μ zðtþ ð17aþ Fgur 1. (a) Dpndnc of F, F, and F or on th statc dlctrc constant ε. (b) Dpndnc of th frquncy shft rato σ on th statc dlctrc constant ε. ndx n at optcal frquncs s rathr small. Ths s tru for both lctronc and vbratonal transtons, provdd solvnt rsonancs ar not clos to thos of th solut. In ordr to confrm our assumpton on ε, w hav masurd th group dlay of fmtoscond md-nfrard pulss through a flow cll wth a fxd thcknss flld wth th solvnts usd n ths study. As shown n Tabl 1, th solvnt dpndnc of n IR at 3 μm s mnor, and thus consdrng F to b constant s a vald approxmaton (s Fgur 1) Frquncy Shfts of th Solvatd Ground Stat. Snc th stady-stat xprsson by Pulln s applcabl for th OHstrtchng mod of 1N and 2N n th lctronc ground stat, w can, accordng to qs 13 and 14, dfn th followng: Δv g ¼ S g ¼ F 8π 2 mv g a g 3 1 8π 2 mv g a g 3 V μ g 3 μ g F g μ g 3 μ g þ 8π 2 mv g 3 a ðμ g 3 μ g þ μ g 3 μ g Þ g μ g 3 μ g g Vg g μ g 3 μ g ð15þ ð16þ In ths xprsson, th tm-dpndnt dpol momnt μ(t) taks nto account th fnt dlctrc rspons of th solvnt by a tm-dpndnt chang from μ g to μ, whr μ and μ g ar th prmannt dpol momnts n th lctronc xctd and ground stats, rspctvly. z(t) s th solvaton coordnat changng from z(t = ) = at th ntal solvnt confguraton of th chromophor n th S -stat, to z(t = ) = 1, whn th qulbrum solvnt confguraton for th chromophor n th S 1 -stat has bn rachd. Th followng solvaton corrlaton functon C(t) s connctd to th tm-dpndnt solvaton coordnat z(t): CðtÞ ¼ Δν s ðtþ Δν sðt ¼ Þ Δν s ðt ¼ ¼ 1 zðtþ Þ Δν sðt ¼ Þ ð18þ Rplacng μ (Q) n q 17 usng q 4a, w fnd RðtÞ ¼f ðμ 3 μ Q þ μ Q 2 þ :::Þ þf or μðtþ ð19þ By rplacng q 4b by q 19 and prformng a drvaton smlar to that n qs 5 13, w obtan th followng tm-dpndnt solvnt-dpndnt vbratonal frquncy shft: ΔvðtÞ v ¼ f ½ðg 2 þ μ Þμ þ μ 3 μ Š f or þ g 2 μðtþ ð2þ At long dlay tms, solvnt shll rorganzaton s fully stablshd,.., whn z(t = ) = 1, so w can smplfy usng μ(t) =μ gvng F Δv ¼ 8π 2 mv μ 3 3 a μ μ 3 μ þ F 8π 2 mv a 3 ðμ 3 μ þ μ 3 μ Þ ð21þ 2779 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

6 Th Journal of Physcal Chmstry A S ¼ 1 8π 2 mv a 3 μ 3 μ V μ 3 μ ð22þ 3.6. Rato of Vbratonal Frquncy Shfts: Exctd Stat/ Ground Stat. To summarz, th solvnt-dpndnt vbratonal frquncy shft of th OH-strtchng markr mod of 1N or 2N n lctronc stat can b approxmatd as a lnar functon of F wth a slop S govrnd by molcular paramtrs V, V, μ, μ,andμ as wll as th Onsagr cavty sz a. In th drvaton, th vctoral proprts of th molcular dpol momnt and ts drvatvs ar takn nto account. As th molcular paramtrs of th solut vbratonal potntal (V and V ) and solut dpol momnt (μ, μ, and μ ) n lctronc stat can b calculatd wth ab nto quantum chmcal mthods, and th Onsagr cavty sz a can b stmatd wthn Onsagr s racton fld thory, on can thn calculat th absolut solvnt-dpndnt vbratonal frquncy shfts by usng q 15 for th S -stat and qs 2 or 21 for th tm-dpndnt and long tm valus for th S 1 -stat. W wll compar th xprmntal valus obtand for th solvnt-dpndnt frquncy shfts for th OHstrtchng mods of 1N and 2N wth thortcal prdctons usng th abov-dfnd formalsm n scton 5. Hr, t s usful to compar xprmntal and thortcal valus for th rato of slops n th plot of Δν as a functon of F for 1N or 2N n th lctronc xctd stat to that n th ground stat. From qs 22 and 16, w drv S S g ¼ μ 3 μ V μ 3 μ V μ g 3 μ g g μ g 3 μ g g ν g ν 3 ð23þ whr th Onsagr cavty radus a can b drvd from th Onsagr solvaton nrgy V S as follows: VS ¼ μ 2 F ð23aþ a 3 2 In addton to that, th rlatv mportanc of nstantanous vs nonnstantanous contrbutons n th tm-dpndnt vbratonal frquncy shft n th lctronc xctd stat can b stmatd from th rato of th arly tm-dpndnt shft (t =)vsthlongtm shft (t = ) σ Δv s ðt ¼ Þ Δv sðt ¼ Þ Δv sðt ¼ Þ " # V ðf F Þ μ μ 3 ½μ g μ Š ¼ " # ð24þ V F μ μ 3 μ þ F ½μ 3 μ þ μ 3 μ Š 4. RESULTS 4.1. Natur of Elctronc Exctaton to th 1 L b -Stat. Th two lowst-lyng lctronc transtons for naphthaln wr dtrmndbyplattanddsgnatdas 1 L a and 1 L b (s Fgur 2). 51 Th transton dpol momnts of ths two lctronc xctatons ar polarzd prpndcularly to ach othr. Th 1 L a -transton dpol a g a Fgur 2. UV/vs lctronc absorpton spctra of naphthaln (N), 1-naphthol (1N), and 2-naphthol (2N) n n-hxan, showng th locaton of th 1 L a -and 1 L b -manfolds. momnt s orntd through th short-axs along th cntral C C bond connctng th two aromatc rngs, and th forbddn 1 L b - transton dpol ponts along th long through-bond axs. Th addton of an OH-group at th α-orβ-poston to form 1N or 2N braks th symmtry, thrby mxng th two lctronc stats wth a concomtant chang n rlatv nrgy spacng and n rlatv magntuds of transton dpol momnts. 77 In 1N, on obsrvs a larg spctral ovrlap btwn th two transtons. Th orgn absorpton transton to th S 1 -stat ( 1 L b ) s locatd at cm 1, whras th lctronc absorpton band of th S 2 -stat ( 1 L a )startsn th rgon around 33 2 cm 1. For 2N, th frst two lctronc xctd snglt stats ar clarly sparatd n nrgy. Th orgn absorpton of th S f S 1 (S f 1 L b ) transton of 2N s locatd at cm 1 n n-hxan, whras th scond S f S 2 (S f 1 L a ) lctronc transton s rachd at cm 1. W now prsnt rsults from th quantum chmcal calculatons of th lctronc ground and xctd stats of 1N and 2N. W hav to dstngush btwn two possbl stabl rotamr gomtrs wth dffrnt orntatons of th O H bond vctor rlatv to th aromatc rng, dnotd as cs- and trans-, rspctvly. Prvous calculatons hav shown that whl th natur of th lctronc transtons of naphthaln s consrvd for 1N, n 2N, sgnfcant mxng btwn th two stats occurs. 38 Our quantum chmcal calculatons of th lctronc ground and xctd stats of 1N and 2N support ths fndngs. Th 1 L b xctd stat obtand from our TD-DFT calculatons s dntfd by rfrrng to th orntaton of th lctronc transton momnts and th corrspondng oscllator strngths, as wll as th compost confguratons of th xctd stat wav functons. Th TD-DFT(B3LYP/TZVP) calculatons (s Tabl 2) show that for both cs- and trans-1n, th lctronc S f 1 L b transton dpol momnt s polarzd clos to th drcton of th long-axs of th naphthaln rng. For both cs- andtrans-2n, howvr, th S f 1 L b transton dpol momnt s polarzd slghtly tltd away from th short-axs of th naphthaln rng. In contrast, th S f 1 L a transton dpol momnt s always drctd along th short-axs of th naphthaln rng for any rotamr of both 1N and 2N. Th oscllator strngth of th S f 1 L b lctronc transton s much smallr than that of th S f 1 L a transton. Th calculatd orntaton of th lctronc transton dpol momnt and oscllator strngths ar summarzd n 278 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

7 Th Journal of Physcal Chmstry A Tabl 2. Transton Dpol Momnts of 1N and 2N, wth th Oscllator Strngth f, Calculatd by TD-DFT at th B3LYP/ TZVP Lvl Tabl 2. Ths fndngs ar consstnt wth xprmntal and thortcal studs rportd n th ltratur, 38,78,79 dspt a dscrpancy n calculatd ordrng of nrgy of th 1 L a -and 1 L b -stats. 52 In Tabl 3, w compar th lctronc confguratons of th HOMO 1(ψ H 1 ), HOMO (ψ H ), LUMO (ψ* L ), and LUMO +1(ψ* L+1 ) molcular orbtals of th cs- and trans-rotamrs of 1N and 2N as wll as thos of naphthaln. It appars that for both 1N and 2N, th 1 L a -stat s to a larg dgr domnatd by th ψ H ψ L * confguraton, whras th 1 L b -stat s composd of th antsymmtrc combnaton of th ψ H 1 ψ L * and ψ H ψ L+1 * confguratons. Ths obsrvatons ar consstnt wth numrcal studs rportd n th ltratur basd on calculatons at th H uckl or mprcal CI lvls. 38,78 In Tabl 4, w prsnt th calculatd chang n lctron dnsty for th cs- and trans-rotamrs of 1N and 2N upon lctronc xctaton to th 1 L b -stat. Th gnral fatur s that lctronc xctaton dos not lad to a larg chang n lctron dnsty on th O-atom of th proton donatng hydroxyl-group. Ths s n agrmnt wth prvous calculatons showng that th lctronc charg rdstrbuton s only of modrat sz n photoacd molculs and much largr n th conjugat photobas fulng argumnts of photobas drvn photoacdty. 23,25 Indd, our quantum chmcal rsults ar consstnt wth prvously rportd valus from AM1 calculatons on 2N. 24 A closr nspcton of th actual valus shows a markd dffrnc btwn 1N and 2N: for both cs- andtrans-1n, lctronc xctaton lads to a largr transfr of th lctron dnsty from th OH-group to th naphthaln rng than n 2N. Furthrmor, th OH-group appars to xhbt a largr lctron donatng capablty n cs-1n (+.72 charg dffrnc on th O-atom) than n th cas of trans-1n (+.32 on th O-atom). Ths can b ascrbd to th ψ H ψ L+1 *confguraton bcaus for ths confguraton, th lctron dnsty s dlocalzd on th OH-group n th HOMO stat, whl no such dlocalzaton xsts for th LUMO + 1 stat (s Tabl 3). Ths charg transfr ffct s rducd by contrbutons from th ψ H 1 ψ L * confguraton, whr th lctron s not dlocalzd on th OH-group n th HOMO 1 stat, but nstad gts dlocalzd onto th OH-group n th LUMO stat(stabl3). For both cs- and trans-2n, th dgr of charg transfr from th OH-group to th naphthaln rng systm s smallr than that for cs-1n. For cs-2n, thr s vn nglgbl lctron dnsty chang on th O-atom upon xctaton. Th much smallr amount of charg transfr from th OH-group to th naphthaln aromatc rngs s assocatd wth th lctron dstrbuton charactrstcs of th domnant lctronc confguratons (.., ψ H ψ L+1 * and ψ H 1 ψ L *). In ths ψ H ψ L+1 *orψ H 1 ψ L * confguratons, th lctron dnsty s dlocalzd btwn th OHgroup and th aromatc rng systm pror to lctronc transton (ψ H or ψ H 1 ) and rtans a largr dgr of dlocalzaton n th fnal stat (ψ L+1 *orψ L *). W can now dtrmn th molcular dpol momnt μ and ts frst drvatv μ and scond drvatv μ n th S - and 1 L b - stats for all rotamrs of 1N and 2N (s Tabl 5). For ths, t s ncssary that w consdr th vctoral proprts of μ, μ,and μ.whavdpctdthorntatonofμ, μ,andμ ( =S, 1 L b ) n Tabl 6. It follows that for cs-1n and trans-1n, th lctrcal dpol momnt s orntd along th long-axs n both lctronc stats, whras for cs-2n and trans-2n, th orntaton s along th short-axs. A comparson of th orntaton of our calculatd lctrcal dpol momnts and transton dpol momnts wth prvously rportd valus shows a satsfyng corrspondnc (s Tabl 7). trans-1n and both conformrs of 2N ar fully planar. Only cs-1n has a dpol momnt componnt n th z-drcton,.., orthogonal to th plan of th aromatc rng systm, ndcatng that th O H bond vctor s pontng out-ofplan. In th S -stat, th lctrcal dpol momnt s largr for cs-1n (1.46 D) than for trans-1n (1.27 D), but th stuaton s rvrsd n th 1 L b -stat bcaus for cs-1n, a larg dcras n dpol momnt occurs to a valu of.62 D, whras for trans-1n, t ncrass to 1.91 D. An ncras n th dpol momnt upon lctronc xctaton s supportd by th Lpprt Mataga analyss of th lctronc absorpton and msson spctra, whr w fnd a valu of μ μ g =.3 (.5 D (Fgur 3). Ths fndngs can b compard to thos rportd n th ltratur: usng th Gaussan 94 packag at th CIS/6-31(d,p) lvl, t was found that 1N (no spcfd rotamr structur) has a dpol momnt of 1.21 D n th S -stat and 2. D n th 1 L b -stat. 8 An vn smallr chang from 1.7 D n th S -stat to 2 D n th 1 L b -stat s calculatd wth INDO/S calculatons. 81 For 2N, th trans-conformr has th largr lctrcal dpol momnt n both S and 1 L b -stats, vn though t dcrass somwhat wth optcal xctaton, whras an ncras s calculatd for cs-2n. Th calculatd valus for cs-2n ar n clos corrspondnc to thos rsults obtand usng rotatonally rsolvd lctronc Stark-ffct spctroscopy. 79,82 Th orntaton of th frst and scond drvatvs of th lctrcal dpol momnt, μ and μ, appars to chang only slghtly upon lctronc xctaton for trans-1n, cs-2n, and trans-2n but vars mor for cs-1n. Mor mportantly, w not that n both lctronc stats, μ and μ ar 2781 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

8 Th Journal of Physcal Chmstry A Tabl 3. Elctronc Confguratons of th 1 L a - and 1 L b -Exctd Stats for 1N and 2N dfntly not drctd along th OH-bond vctor. Ths mans that dspt th fact that th natur of th OH-strtchng mod can b rgardd to b clos to that of a local mod, longaton along th OH-strtchng coordnat has a largr ffct on th lctronc charg dstrbuton n a drcton dffrnt from th OH-bond vctor Enrgy Dffrnc btwn th cs- and trans-rotamrs. For gas phas 1N and 2N, th dstncton btwn cs- and trans-rotamrs has bn wll stablshd. 79,82 86 Rcntly, t has bn shown that for 2N n th S -stat, th cs-rotamr s slghtly mor nrgtcally favorabl than th trans-conformr. 87,88 Ths ordr s nvrtd n th S 1 -stat, and rotatonal somrzaton s argud to tak plac whn 2N s xctd to th 1 L b -stat. W hav thrfor analyzd th nrgtcs of th cs- and trans-rotamrs of 1N and 2N. Furthrmor, w hav calculatd th gas phas nrgtcs, and w hav nvstgatd th rol of th dlctrc mdum on th rlatv nrgtcs of ths conformrs. Fgur 4a shows th nrgy dffrnc btwn th cs- and trans-rotamrs of 1N as a functon of th dlctrc functon F. Whl trans-1n s nrgtcally mor stabl than cs-1n n th S -stat, th nrgy dffrnc dfnd as ΔE = E cs E trans s postv and mor mportantly much largr than kt at room tmpratur (1kT =.593 kcal/mol at 295 K). Ths nrgy dffrnc ncrass wth ncrasng F, whch s quvalnt to an ncras n solvnt polarty quantfd by th statc dlctrc constant. Evn though ΔE 1N s clos to 1kT n th gas phas, th trans-rotamrs ar clarly favord n soluton. On avrag, ΔE 1N n th rang of F appld n ths study s qual to.82 kcal/mol for th 1 L b -stat and 1.5 kcal/mol for th S -stat. Assumng a Boltzmann dstrbuton xp( ΔE/kT), th populaton rato of cs-1n/trans-1n s.7:.93 n th S -stat, n accordanc wth a rportd valu obtand from an NMR study n CCl Ths rato changs to.2:.8 n th 1 L b -stat, provdd somr qulbraton s possbl. Fgur 4b shows th dpndnc of ΔE 2N as a functon of th dlctrc functon F for 2N. Our rsults show that n th S -stat of cs-2n s nrgtcally mor favorabl than trans-2n, although th nrgy dffrnc s 1kT for 2N n th gas phas (s Fgur 4b; F =).Upon lctronc xctaton, ΔE 2N dcrass to.6kt for 2N n th gas phas. Th nrgy dffrnc dmnshs whn dssolvng 2N n a dlctrc mdum, for both S -and 1 L b -stats,.., whn ncrasng F. Th avrag valu of.53 kcal/mol found for ΔE 2N for 2N n soluton, gvng a Boltzmann dstrbuton populaton rato cs-2n/trans- 2N qual to.71:.29, s agan n accordanc wth rportd valus from th NMR-study n CCl Upon lctronc xctaton, ths populaton rato changs to.63:.37, provdd qulbraton taks plac Exprmntal Frquncy Shfts n 1N and 2N. Th lctronc orgn absorpton of th S f 1 L b transton of gas phas 1N s locatd at cm 1 for cs-1n and at cm 1 for trans-1n. 9 A solvnt-nducd frquncy downshft of 449 cm 1 occurs whn dssolvng 1N n n-hxan. Ths downshft ncrass to 455 cm 1 n 1,2-dchlorothan (1,2-DCE). Fgur 5 shows th solvnt-dpndnt UV/vs lctronc absorpton and fluorscnc spctra of 1N n n-hxan and n 1,2-dchlorothan. Th solvntnducd Stoks shft ncrass from 254 to 363 cm 1, ndcatng an ncras n solut solvnt ntractons whngongfromnonpolar 2782 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

9 Th Journal of Physcal Chmstry A Tabl 4. Charg Flow Inducd by th S f 1 L b Exctaton of 1N and 2N a Th maxmal ngatv chang (.., ncrasng lctron dnsty) s rprsntd n rd, and th maxmal postv chang (.., dcrasng lctron dnsty) s rprsntd n grn. b Th ground stat ESP charg was obtand by th MP2/TZVP mthod, whl th xctd stat ESP charg was obtand by th TD-B3LYP/TZVP mthod. Tabl 5. Calculatd Valus of μ, μ, and μ for 1N and 2N S cs-1n trans-1n cs-2n trans-2n μ (D) (1.4425,.1685,.1648) ( ,.1657,.) (.2822, 1.5,.) (.5493, 1.594,.) μ (D 3 A 1 3 amu 1/2 ) (.4823,.887,.19) ( 1.552,.759,.) (.8472,.8772,.) ( 1.349,.4591,.) μ (D 3 A 2 3 amu 1 ) (.6569, 2.75,.1223) (1.6293, ,.) (2.277, ,.) (2.5638,.1233,.) 1 L b cs-1n trans-1n cs-2n trans-2n μ (D) (.5274,.2977,.1415) ( 1.969,.151,.15) (.1445, 1.219,.16) (.7536, ,.13) μ (D 3 A 1 3 amu 1/2 ) (.187,.9523,.174) ( ,.7639,.) ( 1.66,.9931,.) ( ,.3449,.2) μ (D 3 A 1 3 amu 1 ) (1.87, ,.3349) ( 1.848, ,.43) (2.264, ,.) (2.4719,.1586,.74) n-hxan (ε = 1.88) to wakly polar 1,2-dchlorothan (1,2-DCE; ε = 1.1). W hav slctd a numbr of alkans and halocarbon solvnts n th prsnt study to nvstgat th solvnt-nducd vbratonal frquncy shfts of th OH-strtchng mod n 1N and 2N. Snc a sgnfcant lftm shortnng was obsrvd n CHCl 3 and C 2 Cl 4, and knowng that CHCl 3 can form wak hydrogn bonds, 33,91,92 th occurrnc of spcfc ntractons, thr wth th OH-group or wth th aromatc π-molcular orbtals of 1N or 2N, ndd to b stmatd. W frst nvstgatd th stady-stat IR-actv fngrprnt band pattrns of 1N and 2N. Indd, whn spcfc ntractons ar prsnt such as wth DMSO, sgnfcant changs n both band pattrns and ntnsts occur. Howvr, byond mnor changs ascrbabl to th varyng solvnt polarts, th fngrprnt pattrns wr found to b th sam n all solvnts usd n ths study for both 1N and 2N (s Fgur 5). W thn chckd th transnt IR-rspons of th fngrprnt pattrns of 1N and 2N, whch wr also found to b smlar n frquncy postons and band cross-sctons for all solvnts usd n ths study. Although n 2N no dynamcs wr obsrvd up untl 5 ps, n 1N, sgnfcant qunchng n CHCl 3 and C 2 Cl 4 alrady occurs on ths tm scals. W thrfor masurd th dynamcs of th OH-strtchng mod n CHCl 3 to s f th vbraton was affctd by a possbl xcplx formaton. As shown n Fgur 5, ths s not th cas: qunchng and subsqunt partal blach rcovry s obsrvd, but ths affcts nthr th frquncy nor th band shap of th vbraton. W prformd on last tst n ordr to confrm that th qunchng mchansm dos not nvolv any drct ntracton wth th OH-bond. For ths, th transnt fngrprnt rgon of 1N complxd wth dmthylsulfoxd (DMSO) n C 2 Cl 4 was masurd. In such a systm, gvn th vry hgh complxaton constant of DMSO and 1N through th formaton of a mdum strong HB, no drct ntracton of th OH-group wth nonpolar C 2 Cl 4 can occur: th OH bond s ffctvly td-up. As th sam qunchng bhavor was obsrvd, w conclud that th qunchng ntracton wth th 2783 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

10 Th Journal of Physcal Chmstry A Tabl 6. Orntaton of μ, μ, and μ n 1N and 2N Tabl 7. Calculatd Angls (Absolut Valus, wth a Rang of 9 ) of Transton Dpol and Elctrcal Dpol Momnts Rlatv to th x-axs (Along th Long-Axs) calculatd angl of lctrcal dpol momnt (dg) xprmntal angl of lctrcal dpol momnt (dg) b calcd angl of transton dpol momnt (dg) xptl angl of transton dpol momnt (dg) a S 1 L b S 1 L b cs-1n trans-1n cs-2n trans-2n a From rf 79. b From rf 82. halocarbon solvnts occurs wth th aromatc systm. Ths rsult s furthr supportd by th fact that qunchng s also obsrvd n th parnt naphthaln molcul, whch dos not hav any OH bond. 53,54 Fgur 6a shows th stady-stat IR spctra of 1N dpctng th solvnt-dpndnt OH-strtchng transton. In a fashon smlar to that of 2N, 49 a largr frquncy downshft and concomtant ln broadnng ar obsrvd whn gong from nonpolar n-hxan to polar 1,2-DCE. Whn plottng th xprmntal ln wdth as a functon of frquncy poston (Fgur 6c), a lnar corrlaton rsults that can vn b xtrapolatd to th known valu for gas phas 1N. 83 Th transnt IR spctra masurd at 1 ps show ground stat blach sgnals and postv absorbanc changs at lowr frquncy valus than th OH-strtchng frquncy of 1N n th S -stat (Fgur 6b). A dcras of th OH-strtchng frquncy thus occurs upon lctronc xctaton of 1N, n a fashon smlar to that obsrvd for 2N. 49 A ln shap fttng routn was appld to dtrmn th solvnt-dpndnt frquncy shft and ln wdth of th OHstrtchng mod of 1N n th 1 L b -stat. As for th lctronc ground stat, an mprcal frquncy ln wdth corrlaton s obtand for th OH-strtchng mod of 1N n th lctroncally xctd stat (Fgur 6c). In contrast to 2N, howvr, no valu for gas phas 1N n th 1 L b -stat has bn rportd n th ltratur dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

11 Th Journal of Physcal Chmstry A Fgur 3. UV/vs absorpton and msson spctra of 1N n n-hxan and 1,2-dchlorothan (1,2-DCE). Th uppr rght nst shows th Lpprt Mataga plot of th Stoks shft btwn th lctronc absorpton and msson orgn transtons as a functon of F F = (2ε 2)/(2ε +1) (2ε 2)/(2ε + 1) from whch Δμ = μ μ g =.3 (.5 D can b drvd. Bcaus th lnar frquncy poston ln wdth corrlaton occurs for 2N n both lctronc ground and xctd stats, 49 w argu that w can xpct ths to also b th cas for 1N. W can thrfor xtrapolat our xprmntal data to prdct th OHstrtchng frquncy of gas phas 1N n th 1 L b -stat to b qual to 362 ( 1 cm 1. Fgur 7 shows th xprmntally masurd OH-strtchng frquncy shfts as a functon of F, for 1N and 2N, n th S and 1 L b stats. Evn though th ntrcpt turns out to b too small for both 1N and 2N and thus cannot accuratly b dtrmnd wth our currnt data st, w can drv th rato of th slop valus S /S g by a lnar ft to b qual to 1.13 (.5 for 1N and 1.23 (.5 for 2N. 5. DISCUSSION 5.1. Calculatd Molcular Paramtrs. Accordng to q 14a, th slop of th frquncy shfts vs F s govrnd by th followng molcular paramtrs: th lctrcal dpol momnt (μ ), th lctrcal dpol frst (μ ) and scond (μ ) drvatvs, th rato of cubc to quadratc forc constants ( / ), th harmonc vbratonal frquncy (ν ), th vbratonal rducd mass (m), and th Onsagr cavty radus (a ). W hav lstd th rlvant product trms n Tabl 8. It turns out that for both conformrs of 1N and 2N n both lctronc stats th ( )/( )μ 3 μ trm domnats th prdctd solvnt-nducd vbratonal frquncy shft. Whl for trans-1n, cs-2n, and trans-2n th μ 3 μ trm has postv valus, t s ngatv for cs- 1N. As a rsult, th calculatd slop S s ngatv for cs-1n,.., th solut solvnt ntracton lads to a OH-strtchng frquncy upshft for ths conformr. Th postv slop S for trans-1n, cs- 2N, and trans-2n mpls nstad a frquncy downshft for th OH-strtchng mod upon mbddng th solut n a dlctrc mdum. In all cass, w obsrv a largr absolut valu for th slop S n th 1 L b -stat than n th S -stat. Th ntrcpt B s calculatd to b on th ordr of a fw wavnumbrs for both csand trans-conformrs of 1N and 2N n th S -stat. Elctronc xctaton of th 2N conformrs dos not chang th valu of th Fgur 4. Enrgy dffrnc btwn th cs- and trans-rotamrs of 1N (a) and btwn th cs- and trans-rotamrs of 2N (b). ntrcpt sgnfcantly. Only for cs- and trans-1n n th 1 L b -stat s th ntrcpt calculatd to ncras to cm 1. Fnally, whras th rato of slops (S /S g ) appars to b smlar for cs-2n (1.41) and trans-2n (1.42), for trans-1n (1.61), t has a much smallr valu than that for cs-1n (2.71). Th Pulln van dr Zwan Hyns approach also nabls us to xplan why w only hav obsrvd a small tm-dpndnt solvnt-nducd vbratonal frquncy shft n th cas of th most polar solvnt usd,.., for 2N n 1,2-DCE. 49 Us of q 24 wth th paramtr valus gvn n Tabls 5 and 8 provds nsght nto ths. It follows that for alkan solvnts lk n-hxan and cyclohxan th rato btwn th tm-dpndnt shft and ovrall shft for th OH-strtchng mod of 1N or 2N ar clos to zro, bcaus F F = F or. Ths factor bcoms sgnfcant for polar solvnts, such as 1,2-DCE (s Fgur 1b). Avragng ovr th cs- and trans-rotamrs of 2N, w stmat a maxmum thortcal valu of 15%. Th lowr xprmntal valu of 5% may b du to th lmtd tmporal rsoluton of.2 ps n th xprmnts, whch may hav causd us to mss th arlst tmdpndnt rspons. 49 Mor mportantly, for 1N ths valu s xpctd to b 2 3 tms smallr than that for 2N and wll thus b blow th spctral rsoluton of our qupmnt. In addton, on can also prdct that ths rato wll b at most 2% vn n solvnts of hghr polarty such as DMSO. Howvr, ths s solly an acadmc dscusson, as n ths cas, hydrogn bondng wll lad to a chang of all th paramtrs Comparson btwn Exprmnt and Thory. Agood agrmnt btwn thory and xprmnt s found for th solvnt-dpndnt OH-strtchng frquncy shfts as a functon of F whn th prturbatv approach of Pulln s paramtrzd at th TD-DFT lvl of thory. As th prdctd valus for th ntrcpt ar smallr than th uncrtanty n th lnar fts n Fgur 7, w focus our analyss on th slops of th curvs. To proprly compar thory and xprmnts at room tmpratur, w prform a propr nsmbl avrag ovr possbl conformrs. W not only consdr th populaton rato of th cs- and transconformrs but also stmat a mnmal xchang rat btwn th 2785 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

12 Th Journal of Physcal Chmstry A Fgur 5. (a) Stady-stat FT-IR spctra of 1N n dffrnt solvnts, showng that only a spcfc hydrogn bond n a 1:1 complx of 1N wth DMSO-d 6 (dssolvd n C 2 Cl 4 ) sgnfcantly affcts th fngrprnt pattrn; (b) Transnt IR-spctrum of 1N n CDCl 3 showng th tm-dpndnt dynamcs of th OH-strtchng mod. Fgur 6. (a) Stady-stat IR spctra of 1N; (b) transnt IR spctra of 1N masurd at a 1 ps puls dlay; (c) corrlaton btwn th solvntdpndnt frquncy shft and transton bandwdth of 1N n th S (black squars) and 1 L b (rd dots) lctronc stats, ncludng rportd gas phas valus for 1N n th S -stat (blu squars) and th xtrapolatd valu n th 1 L b -stat for gas phas 1N (purpl dot). two conformrs. For 2N n th S -stat, t has bn rportd that th 1 85,88 OH-strtchng frquncy s locatd at 3652 cm or 3654 cm 1 84,93 for cs-2n and at 3661 cm 1 for trans-2n. 84,93 Th valu for 2N n th lctronc xctd 1 L b -stat (369 cm 1 ) rfrs to cs-2n, although, t has bn argud that cs f trans somrzaton occurs. 88 For 1N n th S -stat, valus of 3661 cm 1 for th cs-1n conformr and 3655 cm 1 for th trans-1n conformr hav bn rportd. 83 As a rsult, th cs- and trans-conformrs can only b dstngushd f spctral faturs can b rcordd wth a rsoluton bttr than th frquncy spacng of th OH-strtchng rsonancs of th cs- and transconformrs,.., 6 8 cm 1. In th xprmntal spctra of 1N and 2N n soluton, only on spctrally broadnd OH-strtchng band s found, both n th S and th 1 L b -stats. Sttng asd a lmtd spctral rsoluton for th transnt IR masurmnts and knowng that for th most polar solvnt usd n ths study (1,2-DCE) th ln broadnng s mor than 1 ordr of magntud largr than th OH-strtchng frquncy spacng of th cs- and trans-conformrs, on should, n prncpl, b abl to montor th two conformrs n n-hxan or cyclohxan wth th stady-stat FT-IR spctromtr whr th spctral ln wdth s 13 cm 1 (fwhm). Howvr, as th ln shaps of th OH-strtchng bands of 1N and 2N ar clos to fully Lorntzan, on can conclud that th xchang btwn th two conformrs s ultrafast. A coalscnc of th OH-strtchng bands of th two rotamrs can b calculatd to occur for xchang tms shortr than 2.5 ps. For 2N, th calculatd valu for th slop rato s almost qual for both conformrs. Our xprmntal valu s about 13% lss than th calculatd valu. Whras for 2N, w hav an nsmbl avrag of about qual amounts of cs- and trans-conformrs n soluton, ths s crtanly not th cas for 1N, whr n th S -stat th trans-conformr domnats. Th avrag populaton rato btwn cs-1n and trans-1n s.2:.8 n th 1 L b -stat and.7:.93 n th S -stat (scton 4.2). Thus, th slop for 1N aftr corrcton usng th Boltzmann dstrbuton of th cs- and trans-rotamrs s Ths s rmarkably clos to th xprmntally found valu of Th solvatochromc vbratonal frquncy shft upon xctaton s obsrvd to b dffrnt btwn 1N and 2N. From Fgur 7, w s that, n a partcular solvnt mdum, th frquncy shft ω g upon xctaton (.., S f 1 L b -transton) of 1N s smallr than that of 2N. Accordng to q 14, V g V g s ¼ S g F þ B g ð25aþ 2786 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

13 Th Journal of Physcal Chmstry A Fgur 7. Exprmntal frquncy shfts for th S - and 1 L b -stats of 1N (dots) and 2N (squars), rlatv to th frquncy of th S -stat of 1N (3658 cm 1 ), togthr wth sold and dashd lns obtand by (a) xprmntal fts, (b) prdctons accordng to Pulln s modl wth factors calculatd wth TD-DFT calculatons, and (c) prdctons accordng to th PCM modl n Gaussan 9 at th TD-DFT lvl wth th PCM solvnt. Tabl 8. Calculatd Paramtr Valus for 1N and 2N Govrnng th Solvnt-Inducd Vbratonal Frquncy Shfts trm cs-1n 1 L b cs-1n S trans-1n 1 L b trans-1n S cs-2n 1 L b cs-2n S trans-2n 1 L b trans-2n S μ 3 μ (D 2 A 2 amu 1 ) μ 3 μ (D 2 A 1 amu 1/2 ) V /V (A 1 amu 1/2 ) μ 3 μ (V )/(V )μ 3 μ [μ (V /V )μ ] 3 [μ g μ ] a (Å) v (cm 1 ) S (cm 1 ) a μ μ 3 μ (D 2 A 2 amu 1 ) μ + μ 3 μ B (cm 1 ) b S /S g a S = (1/8π 2 mv a 3 )(μ 3 μ (V )/(V )μ 3 μ ). b B =(F /8π 2 mv a 3 )(μ 3 μ + μ 3 μ ) s th ntrcpt, whr F.4. V V s ¼ S F þ B ð25bþ from whch w drv ω g ¼ V g s V s ¼ðV g V ÞþðS S g ÞF þðb B g Þ ð25cþ Hnc, ω g s dtrmnd by th frquncy shft upon xctaton n th gas phas (v g v ), th slop dffrnc (S S g ), and th ntrcpt dffrnc (B B g ) of th frquncy shfts btwn th lctronc xctd and ground stats upon solvaton. Hr, on can compar our fndngs usng th OH-strtchng mod as a local solvaton prob wth thos obtand wth UV/vs lctronc spctroscopy, 3,36,8 whr th photoacd solvnt ntracton s govrnd by th full solvaton shll ntractng wth th lctronc charg dstrbuton of th chromophor. In ths UV/vs lctronc spctroscopc studs, th smmprcal Kamlt Taft analyss was prformd on a largr st of solvnts, ncludng thos wth spcfc hydrogn bondng ntractons. It was found that for 2N th nonspcfc solut solvnt ntractons (as dscrbd by th coffcnt for th solvnt polarty/polarzablty paramtr π*) ar smallr than thos of 1N, and accordngly for 2N, smallr contrbutons to lctronc transton frquncy shfts rsult through ths componnt. Ths, howvr, s not what w obsrv whn w nspct th lctronc Stoks shft of 2N and 1N n our st of nonpolar/wakly polar solvnts. In contrast, w fnd that th magntud of th solvnt-nducd lctronc Stoks shft s fully consstnt wth th magntud of th solvnt-nducd OH-strtchng frquncy shft, namly, bng smallr for 1N than for 2N. Whras th magntud of th lctronc Stoks shft as a functon of (F F ) scals wth (μ μ g ) 2, as,.g., dfnd by th Lpprt Mataga quaton, 39,58,94 th dffrnc n solvntnducd OH-strtchng frquncy shfts n lctronc xctd and lctronc ground stat follows q 25c wth whch w can xplan th smallr solvnt-nducd ffcts on th OH-strtchng mod of 1N than thos of 2N. Ths s a consqunc of a smallr valu for th gas phas frquncy shft (v g v ) for 1N compard to 2787 dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,

14 Th Journal of Physcal Chmstry A Tabl 9. Calculatd and Exprmntal OH-Strtch Vbratonal Frquncs calcd frquncy (cm 1 ) a scald frquncy (cm 1 ) b calcd ω g (cm 1 ) for S f 1 L b transton xptl frquncy (cm 1 ) c xptl ω g (cm 1 ) for S f 1 L b transton c cs-1n, S d cs-1n, 1 L b d trans-1n, S trans-1n, 1 L b d cs-2n, S d cs-2n, 1 L b d trans-2n, S trans-2n, 1 L b d a Th S -stat was calculatd usng th MP2/TZVP mthod; th 1 L b -stat was calculatd wth th TD-B3LYP/TZVP mthod. b Scalng factor:.952. c Exprmntal valus of 1N and 2N n th gas phas wr takn from rfs and 93. d Avrag valu for cs- and trans-conformrs. that of 2N and valus wth oppost sgns for th slop dffrnc (S S g ) for cs-1n and trans-1n, whras (S S g ) has a postv valu for both cs-2n and trans-2n. For th comparson btwn th OH-strtchng frquncy shfts of 1N and 2N upon lctronc xctaton, th gas phas factor (v g v ) also plays a ky rol n dctatng th frquncy shfts obsrvd n soluton. Frquncy shfts upon lctronc xctaton n th gas phas ar causd by th charg rarrangmnt n 1N and 2N. Hnc, n th followng, w xplor th lctrostatc potntal (ESP) charg dffrnc du to th S f 1 L b -transton for 1N and 2N, for both th cs- andtransrotamrs. For th calculaton of th ESP charg, th MP2/ TZVP mthod was usd for lctronc ground stats, and th TD-B3LYP/TZVP mthod was usd for lctronc xctd stats. Th ratonalzaton for choosng th ab nto mthods was basd on th fact that th calculatd OH-strtchng vbratonal frquncs usng ths mthods for th ground and xctd stats of 1N and 2N show good consstncy wth th xprmntal vbratonal frquncs (s Tabl 9). Th comparson of xprmntal vbratonal frquncy shfts and th corrspondng shfts computd wth Pulln s modl shows mprovmnt ovr prdctons basd on th standard PCM tchnqus as mplmntd n Gaussan 9 at th sam lvl of TD-DFT thory. Ths s qut rmarkabl, consdrng th smplcty of Pulln s modl of dynamcal solvatochromc ffcts. Whn compard to mor standard tchnqus, Pulln s modl has th dsadvantag of smplfyng th lctrostatc dscrpton of th molcul to a pont dpol. Howvr, th racton fld n th polarzabl contnuum ncluds both statc and optcal rspons functons nducd by changs n th molcular pont dpol momnt assocatd wth vbratons and/or lctronc xctatons. It s thrfor natural to conclud that th dscrpton of solvatochromc ffcts basd on standard PCM modls would bnft from xtnsons of th mthods to nclud th optcal rspons of th solvnt du to vbronc or lctronc xctatons. 6. CONCLUSIONS W hav combnd ultrafast UV/md-nfrard pump prob spctroscopy and thortcal modlng of solvatochromc ffcts to nvstgat th OH-strtchng mod of 1-naphthol (1N) and 2-naphthol (2N) n th ground (S ) and frst xctd ( 1 L b ) stats n svral solvnts of modrat polarty, whr spcfc ntractons such as hydrogn bondng ar absnt. To undrstand th obsrvd solvnt-nducd vbratonal frquncy shfts n both lctronc stats, w hav appld th prturbatv tratmnt of Pulln, as rfnd wth th van dr Zwan Hyns rlatonshp to ncorporat th tm-dpndnt rspons of solvnt shlls upon th lctronc xctaton of th solut. To quantfy th dffrnt contrbutons n ths prturbatv approach, w hav prformd quantum chmcal TD-DFT calculatons to dtrmn th rol of th lctronc charg dstrbutons n th S -and 1 L b - stats of 1N, as rflctd by th molcular lctrcal dpol momnt and ts frst and scond drvatvs along th OHstrtchng coordnat, as wll as th dgr of anharmoncty of th molcular vbraton. Furthr rfnmnts of th approach may nclud th ncorporaton of solut polarzablty, as wll as xtnson to cass whr spcfc ntractons ar prsnt. Th nflunc of solut polarzablty on solvnt-nducd vbratonal frquncy shfts can asly b stmatd, provdd nformaton on molcular polarzablty n a partcular lctronc stat s avalabl. Accordng to Pulln, 43,44 on should thn rplac th rspctv f wth f/(1 fα) prsntnthdffrnt trms n th xprssons for th solvnt-nducd vbratonal frquncy shfts. A solut polarzablty α lads to an ncras of solut solvnt ntractons for th polar solvnts, wth concomtant larg vbratonal frquncy shfts. Usng avalabl polarzablty data on th parnt naphthaln molcul 95,96 and assumng smlar valus for th polarzablty for 1N and 2N n both S - and 1 L b -stats as thos of naphthaln, suggsts a 1 2% addtonal frquncy shft for th most polar solvnt usd n ths study. A natural choc to xplor th potntal applcablty of th approach dmonstratd hr wll b to nvstgat th solvntnducd frquncy shfts of OH-strtchng mods of photoacd bas complxs. Whl th prturbatv approach of th solut solvnt ntractons may b suffcnt for hydrogn-bondd OH-groups as wll, th mpact of dagonal and off-dagonal anharmoncts s xpctd to b mor pronouncd. Explorng ths aspct of Pulln s prturbatv approach wll b an ntrgung topc as th nxt tstng ground for undrstandng solvntnducd vbratonal frquncy shfts n hydrogn-bondd photoacd bas complxs. AUTHOR INFORMATION Corrspondng Author *E-mal: nbbrn@mb-brln.d (E.T.J.N.); vctor.batsta@yal. du (V.S.B.) dx.do.org/1.121/jp28426v J. Phys. Chm. A 212, 116,