Analysis of vibronic intensities in the phosphorescence spectrum of dimethylbenzaldehydes in durene

Chemtcal Phjstcs 58 (1984) 229-245 North-Holland. Amsterdam

229

ANALYSIS OF VIBRONIC INTENSITIES IN THE PHOSPHORESCENCE OF DIMEiTHYLBENZALDEHYDES IN DURENE

A. DESPRkS. Laborarowe

V. LEJEUNE,

de Phoroph>srque

rifolecularre

C. MIJOULE Laborarorrede Ph_wque

neorrque

G MARCONI IsrrruroFRA E del

4016

G. ORLANDI IsrrruroChmr.co

CNR

“G

Clamrclan’

E. MIGIRDICYAN du CNRS.

des Parrrcules.

Bologna.

SPECTRUM

\

Umcersrre

de Purrs -Sod

UmLersrre de PIcurdle,

9I-fO5 Orsu~.

80039 Amrens.

France

France

Iral)

dell Unrversrta

Bologna,

lrulr

and

W. SIEBRAND Dwrslon

and M.Z. ZGIERSKI

o/ Chemrag,

Narronal

Research

Councri 01 Canada

’ Ocra~~a. Canadu

Kl.4

OR6

Recrlvrd 17 Jnnumy 19S4

An attempt IS reported to evplam the mam mtenslty patterns m the phosphorescence spectra of 2.4-. 25 and 3.+dlmethylbenzaldehyde-lh, and -Id,. observed previously The analysis IS based on CNDO and MIND0 calculatrons of (transItIon) dipole moments, spm-orbtt couphngs, vlbromc couplmgs, state energtes, normal coordmates and vIbratIonal frequencies Where possible these quantltles are empnically checked and correctted. Adchtlonal InformatIon. especclally about the separation of the closely spaced T,(3~*) and T?(‘nn*) states, IS obtamed from phosphorescence excltatlon spectra reported here for all SIX Isomers The phosphorescence spectra consist of two components, an “alloucd” component of 3m* and a “forbidden” component of ‘na* symmetry It IS concluded that the allowed component IS partly Induced by the crystal field The forbidden component IS vlbromcally Induced by out-of-plane vrbrattons among which the aldehydtc CH(CD)-wag mode is the most active The observed mtenslty patterns for this componenr are ascribed to Interference between two mechamsms, one mvolvmg vlbroruc couphng between S, and S,(‘nn*) and spm-orbit couphng between S, and T, the other mvohlng vlbroruc couphng between T, and Tz and spm-orblt couphng between S,, and T2 Wlthm the groups of either Ih, or Id, Isomers.. the mam changes m the spectrum are shown to be due to the change III T, -T? energy separauon The changes observed upon deutenum substltutlon In the aldehyde group Involve. m addlhon to changes m the T,-T2 gap, changes m vlbroruc couphng due to normal-coordmate rmxmg All these spectral changes are reproduced by calculations based on a mixture of theorettcal and emptncal mput parameters denved from. or at least conststent wth. other observations. mcludmg excltatton spectra. dtpole moments and zero-field sphttrngs It IS concluded that the mechamsms underlymg these calculattons offer a satisfactory explanatton of the observed mtenstty patterns tn the phosphorescence spectra of dtmethylbenzaldehydes

’ Issued as NRCC No 23383

0301-0104/84/$03.00 Q Elsevier Science Pubhshers B.V. (North-Holland Physxs Publishmg Divrslon)

-1 Despres er al / Phosphorescence

230

1. Introduction

spectra

of DMB

separation between the coupled states. The treatment rlssumes that thts ratto. to be called the HT ratio. IS small, then the only observable effect of the

clectromc band systems However. the nature of thus transfer IS governed not only by the HT ratto. but also by the ratto of vtbrattonal and electronic energy separattons. If thts second r,.ttro. to be called the BO ratro. is also small. as usually assumed m HT theory. the transfer can be understood as an electromc phenomenon. formulated wtthm the BO approxtmatton. Hoiieever. tf thts second ratro IS not small. the BO approxtmatron break down. although first-order perturbatton theory may still be appropnate. namely wtth the expanston carned out on a vtbromc - rather than an electrontc - basrs If. on the other hand, the HT ratio IS not small. the perturbatron exp,mston does not converge. so that a matnx dtagonahzatton. as for perturbattons mvolvmg degenerate states. IS requu-cd [2 31 In thts paper we are concerned wth systems m vvhlch the BO ratlo IS not small. I e . systems In N htch the coupled electromc states dre sepdr‘tted by gyps of the order of a quantum of the tnductng mode or less This nnphes that the two electromc mnmfolds w11l overlap strongly If these mamfolds ‘ire coupled. the tndrvrdual levels wll show varytng ,tmounts of mtxtng. dependtng on the proxtmtty of appropriate levels of the other mamfold. If the couphng IS very weah (I e _ tf the HT ratto IS very small). this WIII give nse to an anomalous mtenstty dtstrtbutron and perhaps an occasional resonance interactton when two levels belongmg to different mamfolds ,.tre acctdentally very close and at least one of them carries mtenslty. If the couphng IS not iieak. level shifts wll accompany the mtensq redlstrlbutlon The resultmg spectrum wtll exhtbtt anomalous spacmgs as well as mtenstttes and hence WIII no longer show the chardctensttc regular spacings that permtt asstgnment by mspectton [3] The best way to Interpret such scrambled spectra is to unscramble them. I e.. to deternune how the spectra would have looked wthout the couplrng Such a procedure reduces two anomalous mamfolds to two “normal” mamfolds plus a couplmg. These normal mamfolds perrmt the usual analysts which gwes mformatton on the vibrattonal force fteld of the uncoupled states and, after the coupling IS rntroduced, on its dependence on thts coupling Such mformatton cannot be dtrectly

coupltng

extracted from the scrambled mantfolds m which

Our general understandmg of the electromc spectra of polyatomtc molecules IS based on a number of approximattons that give rrse to recogntzable spectral patterns Foremost amongst these IS the Born-Oppcnhetmer (BO) approwmatton vvhlch permits separation of electromc and wbrattonal mottons. thereby reducing the spectra to elcctrontc bands vvtth wbrattonal structure The Intensity dtstnbutton among the elcctromc bands IS governed by selectton rules which ccln be derived from the orbital symmett-v and spin multtphctt~ of the electronrc vvavefuncttons. In the stmplest porn--Ï ble case the bands clre classlfwl .IS either .rllo~ed. I e.. wrth tntenstty or forbtdden. I e. vvtthout Intensrty In thus sample case the vrbratronal rntensrty dtstnbutton vvrtthtn an allo\\cd band IS governed by the Fran&-Condon prlnclplc. I e. b> the change m vibrational force ftrld bctiveen the st,ttes

tn transttton The resultmg structure IS usually dominated b> progresstons of totall> symmetnc modes In practrcc. most polyatomrc molecules show 3prctrrt that dre not so stmplc Most forbtddcn transIttons cart-y mtenstty. although less than allowed ones. and m,my of them shon wbrattonJ structure In vvhtch non-totally symmetnc vtbrattons parttctpate promtnently. For multtphctty-allowed tr~nsrttons. these observattons rare rattomtlrzcd by Herrberg-Teller (HT) theory [I] m terms of vrbrontc mrwng betlveen electromc states Induced by a non-totally symmetrtc vtbratton of the proper symmetry As a result of this mtwtg. the forbidden transttton can borrow Intensity from an Alovved one: typrcallv. the borrowed rntensttv shows up m vtbromc bands rnvolvtng .t smglequantum wbratronal transttron of the non-totAly symmetnc “mducmg“ mode In Its traditlonal form. HT theory IS based on a first-order perturbatton treatment in vvhtch the e\panston parameter IS the ratto of two electromc energy terms. namely a couphng term. medIated lnductng mode. dnd the electromc energy

IS a transfer of mtenstty

by

betiieen

the

two

A. Despres er al / Phmphorescence spectra of DMB

electronic and vtbrational character IS thoroughly mtxed. This analysis obtains added slgmfzance m a senes of closely related molecules, where it may happen that the zeroth-order states remain essentrally the same, and only the coupling changes. The present paper deals wrth such a series of molecules, namely three lsomenc dlmethylbenzaldehydes. A pnon it appears tmprobable that the electromc structure of these molecules in their ground states or lower exctted states wrll strongly depend on the positton of the methyl groups. Nevertheless, tt has been observed [4] that there are large dtfferences between the phosphorescence spectra of the 2.4-. 2.5 and 3.4-rsomers. These spectra show strong activity of out-of-plane bending modes. IX., the type expected to mLx nn* and 7r7r* states If we label the tnplet states as T,, T,, etc. m order of Increasing energy, and use thts notation to mdlcate pure-spin electromc states. then T, IS a 3‘OTT*and Tz a 3n,* state [4]. Hence the actrvrty of out-of-plane bendmg modes in the phosphorescence spectrum indicates vrbromc mrxmg of these closely spaced states Labellmg the correspondmg smglet states as S,. S,, etc. S, bemg the ground state. we note that the spur-o,stt mtxmg of S and T states. whrch IS responstble for the phosphorescence intensrty. WI!! be mamly between WIT* and nrr* states [5], so that T,(%r*) will mrx predomrnantly with S,(‘nT*) and T,(“nq*) mainly with S,. S,, etc. Thus TX + S,, which can borrow intensity from strong S,,(n=*) --, &(717f*) transrtions, ~111 be a much stronger transttton than T, + S, whrch denves rntensrty from very weak S,( 71~~) + S,(mr*) transttions Hence it IS not surpnsmg that T, + S, borrows vtbrontc mtenstty from T1 + S,, vta out-of-plane modes, especrally smce T, and T, closer indeed than the are close m energy, frequency of some of the out-of-plane modes. It follows that the BO ratio IS not small for these couplmgs, so that the BO approxlmatron breaks down. Moreover, the presence of Irn*-nT* coupltng m the tnplet manifold tmphes that the same couphng will be present in the smglet mamfold. In other words S,(‘na*), from whrch T,(3~n*) denves tts Intensity via spin-orbit coupling, is itself coupled vrbrorucally to ‘no* states from whrch it derives

vrbromc mtenstty. plmg scheme

231

Hence

m addmon

to the cou-

we have the scheme sptn-orb11 T,

c,

s,

“bys”(lTT*)_

These two “mechantsms” of transferrmg mtensity from S,. n = 2. 3, etc., to T, may show Interference

161

Addtttonal schemes can be wntten down mvolvmg the ground state. e g.,

smce the phosphorescence acqwres intensity also If the ground state has a &T* component. As argued before [4], such mechamsms may show interference with the mechanisms that give a ‘TIT* component to T, In thts paper, we report detatled calculattons armed at analyzmg these mechamsms. so as to account for the “anomalous” phosphorescence spectra of the three drmethylbenzaldehydes (DMBs) reported earlrer (41 These calculatrons constst of (I) a CND0/2 calculatton of electromc eigenstates and ergenvalues; (II) a CNDO/S calculation of spur-orbit Integrals; (III) a MIND0/3 calculation of out-of-plane normal coordinates and normal-mode frequencies; (IV) a calculatron of vibromc couplmg Integrals, and (v) a (parttal) reconstructton of the observed phosphorescence spectra. At low temperatures these spectra consist of a great number of sharp bands representing transttrons startmg from the lowest level of the coupled tnplet mamfolds At higher temperatures a more Intense transttion from a thermally populated level takes over. The former level has 3~~*, the latter 3nT* character; thetr separation of the order of 100 cm - ’ vanes sharply among the three rsomers and among theta mono-deuterated counterparts All spectra show strong acttvtty of outof-plane modes, especially the aldehydic CH(CD)wag mode. Upon deuteratton of the aldehyde group

232

the activity

A

of thus mode

mcreases

Despres

er al

/

Phosphorescence

m two of the

ihree isomers. in terms of HT theory [I]. thus would be an anomalous

Isotope effect. To account for this anomalous effect and the strong vanattons in CH-wag acttvtty. tt has prevtously been assumed [4.6] that there are at least two pathways of rntensrty borrowmg which exhtbrt Interference Although an anomalous Isotope effect IS not tncompattble \\tth a smgle mechamsm [7]. the magnltudc of the anomaly cannot be explaIned In this way The exact nature of the mterfenng mecharusms has not been established unambtguously (-1.61 It IS \ery dlfflcult to extract such rnformatron from phosphorescence spectra which ortgtnate from one or at most two levels of the e\cttcd-state manrfold In thts paper me therefore report phosphorescence e\cttatton spectra covermg many states of the T,-T2 coupled mdrufolds together ~tth d thorough quantum-chemrcal study of the molecules under mvesttgatton

2. E\perimentAl

The phosphorescence

spectra of 2.4- 2.5 and

3.4-DMB and then CHO-deuterated ,.malogs hJ\e been reported and Jsstgned m an earher paper [4]. To the extent that the xwgnments affect the present \vorh. they stand. but correcttons hdve been made to the lntensltles reported sarhcr. ‘IS a result of the replacement of peah hetghts by peah areas A corrected hst. contatnmg the bands to be consrdcred m detail. IS given m table 1. In general the spectra correspond to a superposrtton of spectra from two different sites tn the durcne crystal In alI spectra. the orrgm (O-O). several members of the totally symmetrtc COstretch progressron. d strong aldehydtc CH-wag O-1 band and a Lveaker O-2 band. along wtth a CO-stretch/CH-wag combmatton band. can be unambtguously asstgned It follows that the spectra constst of two components. one wtth the symmetry properties of a TT* transttton. and the other vvrth that of an nc* transttton. The first. “allowed“ component conststs of the O-O band. a CO-stretch progresston and many other bands whrch we shall not consider exphcttly. The second component consrsts of a number of O-l (and perhaps O-3)

Table

specrra

of D UB

I

Obsened mtegrated Intenswes’), relatwe to the O-O ongm band ( = 100). of selected bands In the phosphorescence spectra of three d~methylbenAdeh~des In durene crys~sls Isomer

SIW

34-l/2,

I

34-Id,

II I

25-M, 2 j-Id, 2.1-l/r, 7-I-16,

II I II I II I II I II

CH(D)-uag 180 130 90 80 55 290 105 410 50

CO-stretch

CH(D)sCO

ZXCO

40 30

70 7.5

-

50 45 SO IO5 SO

50 20 25 110 4.5

35 5

95

20

(50) 05

(120) 55

(20) 75

40 15

(100)

(100)

(50)

-

” The r~1lal1~e err~)r IS titlmaled

IO be 20% for strong band>

Jnd Luger for ur&. and okerlappmg bands Numbers I” parsnthrsrb are conwdrred uncerwn Oml:rcd mtenbllws corwpond IO bands that could nor be measured rehably

out-of-plane transtttons and then combmattons \vrth totally symmetnc progresstons. we shall mJmly focus on the CH(CD)-wag mode and Its combmdtton wtth the CO-stretch progresston. Since these trtplet transtttons borrow then mtenstty from smglet transtttons, the energtes of the Sl(nz* )and S,,(nrr*).rr = 2.3 ,..., statesof DMBs. as well ds the frequenctes of the CO-stretchmg and the CH(CD)-waggmg modes in the S,(nn*) state are also relevant to the mvesttgatton These datd were obtarned from the phosphorescence excrtatton spectra of DMBs m durene at lo-20 K detected m spectral regtons correspondmg to the S, - Sl(nv*)O (3800-3300 A) and S, --, S(~T*) (2900-2500 A) transtttons. The spectra were recorded by scanrung the UV contmuum of a 150 W Osram-Xenon lamp through a THR 1500 Jobm-Yvon (1.5 m. i/12) spectrometer having an Inverse disperston of 2.6 A/mm For excttatton spectra corresponding to the !S,,+ Sl(nT*) transthon. the whole phosphorescence of the sample was detected through a GG 420 Schott falter, whrle for the S, + S_(TP*) transitton. it was necessary to morutor the most Intense phosphorescence bands (the ongm band or the vtbrontc bands correspondmg to the CH(CD)-waggtng or CO-stretching modes) through a Huet M25 monochromator (j/3)

A

with a Ah = 60-100

A bandwidth

Despres

er al

/

Phosphomscettce

spema

o/ DMB

233

The Integrated H3C

Intensity of the !3,,+ S, band system is estimated to be = 3% of that of the S, --, S, band system. The phosphorescence excitation spectra corresponding to the S, + S,(nn*) transitron of DMBs constst of sharp bands. They have been assigned by comparison with the analysis made by Goodman and Koyanagr [S] for benzaldehyde in polycrystallme methylcyclohexane at 4.2 K. Although the spectra corresponding to S, - S,(mr*) transrtions are broader than those correspondmg to S, --) S,(nT*) transitions. the ongin bands are sufficiently well resolved to determine the energies of the S2( VIT*) electronic states wrthm f 20 cm-‘. The sharp S, + S,(nn*) excitation spectra of DMBs present Important activrty of the CO stretclung mode around 1300 cm-’ in the S,(nn*) state. the correspondmg band showing the same polartzatron characteristics as the origin band In contrast, the vtbroruc bands correspondmg to the CH(CD)-waggrng modes have different polanzatron charactenstrcs Furthermore, these modes show a drastic decrease m frequency m going from the ground to the S,(nT*) state, as was already menttoned for the CH-wagging mode In benzaldehyde by Goodman and Koyanagi [8] and m the vapour absorptron of propynal by Lm and Moule [9]. The phosphorescence excitatron spectra correspondmg to the S, - T translttons of DMBs IR durene at lo-20 K were obtained by morutoring the most intense phosphorescence bands, while scannmg the emissron of a home-made dye laser pumped by a Lambda-Physik nitrogen laser. According to the wavelength region of interest, solutrons of PBBO (Exciton) were used for 2,4and 2,5-DMB-lh, and -Id,, and of BIBUQ (Lambda-Phystk) for 3,4-DMB-lh, and -Id, Stray light dunng the excrtatron pulse was excluded by means of a Boxcar integrator (PAR model 160). For 2.4 and 2,5-DMB-lh, and -Id,, where the phosphorescence spectra of guests m sttes I and II of durene crystal are well separated (24 and 32 cm-‘, respectrvely), it was possible to record single-site excitatron spectra from powdered samples by narrow-band observation (AX,, = 3 A) through the THR spectrometer. For 3,4-DMB-111, and -Id,, where the site separation is only 4-6

LO3 cm-l7

CHO

YC 3,‘-OMB-lh,

IN

OURENE-h,

7:17K

/ I

1 3900

I 3950

xtA1

LOO0

FIN 1 Phosphorescence excltntlon spectrum of 3 4DMB-lh, in SIWS 1 and 11 of durene-/I,, observed by momtonng the phosphorescence bands at 994 and 1000 cm-’ (CH wag) from the ongln

cm-‘. the excttatton spectra correspond to both sites. The laser-Induced S,-T phosphorescence evcnation spectra of 2,4- 2,5- and 3,4-DMB drs-

persed m durene-h,,

are shown m figs. 1-6, suni-

lar spectra were obtamed in durene-d,, crystals. The excitatron spectra of 2,4- and 2,5-DMB-lh, and 2,4.5- trrmethylbenzaldehyde-lh, (TMB) have been reported very recently by Wmkler and Hanson [lo]. These phosphorescence excrtatron spectra do not show nurror Image symmetry with respect to the correspondmg phosphorescence spectra For 2,4- and 2,5-DMB-l/z, and -Id,, the first excrta-

H3C H;C r28cm

D1:

coo

’

1 3.4 - DME

- Id,

IN

LIURENE-

h,

7zZOK

I

I 3900

I

f 3950

I vial

I LOO0

Fig 2 Phosphorescence excltallon spectrum of 3.4-DMB-Id, m sites I and II of durene-h,, observed by momronng the phosphorescence bands at 863 and 868 cm-’ (CD wag) from the ongm

CHO CH3 1 ’ 2 S-DMW-Ih, IN

2 .4-OMW -1 h, IN

DURENE-h,,

OURENE-hlL

T=5 K /

F:g 5 Phosphorescence exc1tatlon spectrum In SII~ I of durens-h,, obsened bj momtonng cence band at 1693 cm- ’ (CO srrerch) from 7

LO50

Mi’

f.100

Fig 3 Phosphorescence ewwlon spectra (I. bottom and II rop) of 2.5DXlB-l/r, m sites I and II of durene-h,, obsened b> momronng the phosphorescence band\ at 990 cm-’ (CH wag) from the ongmz

CD0

H3C xx 1: 2 5-DMW-Id,

130cm-

226 CH3 IN T-6-7

of 24DMB-lh, the phosphorathe ongm

DURENE-

tton band comctdes III wavelength to wtthm 1 A or less wtth the correspondtng phosphorescence ongm and IS therefore attrtbuted to the T,(%r71’;1*) state. For 3.4-DMB-I/I, and -ICI, where the T,-T, energy gap 1s larger. this band is nussmg To determme the T,-T, sap accurately, we must locate the T7 orrgm. In earher papers [4,10,11] this ongm was equated wtth the ftrst strong band in the T, regron that can be thermally populated and shows ‘nc* character. However, the phosphorescence ex-

hlL

K I

120 cm-’

T=6 K

L

I

1

LOO0

LO50

LlOO

hIA)

Fig 4 Phosphorescence ercltauon spectra (I bottom and II, top) of 2 5-DMB-lcl, m sws I .md II ol durcne-h,, observed by momroring the phosphorescence bands at S55 cm-’ (CD \bag) from the onglns

I

I

I

LOO0

LO50

Fig 6 Phosphorescence excltatlon spectrum m SIW I of durene-h,., obsened by momtonng cence band at 1688 cm-’ (CO stretch) from

at61 of t.rlDMB-Id, the phosphoresthe ongm

A

Desprk er al / Phasphocescencespectra of DMB

a larger relative uncertainty in the location of the T2. origin, especially since the bands in the excitation spectrum have different width. In 2,5-DMBlir,. the gap and level density are so small that the spectrum reduces to one strong peak w!uch therefore may be tdenttfled with the Tz ongin._ In table 2 we have collected the singlet and tnplet state energtes derived from the observed phosphorescence excttatton spectra. Also ltsted m t!us table are the CO-stretch and CH(D)-wag frequencies associated with these states. as they appear m the spectra. These results will be used as input parameters m our attempt to analyze the mtensltles of these modes m the phosphorescence spectra

citation spectra reported here indicate that this assignment should be modified. The- structure observed in the T, region of these spectra has no counterpart m the corresponding spectrum of benzaldehyde Itself [8.12], where the lowest triplet state is ‘nc* and not %r*. This spectrum has no strong bands between the O-O and 0-l(CO-stretch) peaks. The prominent structure observed in the T,-origin region of the DMBs must therefore be due to mixing of the T,-ongin level with resonant or near-resonant vtbrationa! levels of T, which. through this mixmg. acquire intensity originally belonging to the T, origin. To ftnd the unperturbed posItIon of this origin, we would have to decouple the two triplet states: however. this IS not an easy task smce the couplmg will be different for each mode. As an alternative, we can use the fact that virtually a!! intenstty in the unperturbed system ortgmates from the T,-ongm band. thts mlplies that this unperturbed or&n must be situated near the “centre of gravity” of the band system, since the couplmgs WI!! redlstrtbute the transItIon moment in a symmetric fashion. It follows that in 3.4-DMB as we!! as in TMB [IO], where the T,-T,

3. Mechanisms The structure of the phosphorescence spectrum cdn be expressed in terms of the transttlon dipole moment (GIMIP). where fLf IS the electnc dipole operator, IP) the “exact” phosphorescent state and IG) the mamfold of exact ground state levels populated m the emission process. These states WI!! be expressed m a basts set of pure-sptn Born-Oppenheimer states. labelled S,, S,. S,. . for the singlet and trlplet compoand T,, T,,... nents. respectively. Each state S, or T, represents a product of an electromc and vIbratIona! wavefunctlon. the latter being treated as a product of

gap IS large enough to give rise to an appreciable density of T, states near the unperturbed Tz origin,

this ongm can be located with good accuracy m the centre of a relatively broad-band system. Note that m general It will coincide with a valley and not with a peak m this structure In 2.4-DMB. where the T,-T, gap IS narrower and hence the density of near-resonant T, levels sparser. there IS

Table 2 Obsentd Qunntlty

E3’

G’co

uCH(CD)

stnglet and 1r1p1r1s131e enrrgws atd vtbrattonal State

Sl S2 T l-2

23.5

frequencies (m cm-‘)

of DMBs

m durene

Isomer 34-/I,

3.4-d,

2

WI,

2 5-,f,

2 4-/i,

2.44,

26952

26990 33350 24972 b’ 25500

26068 31240 24283 24360

26109 31240 24280 24410

26288 32670 24464 24570

26330 325SO 24455 24575

33380 24974 h’ 25450

s, h’

1701

1689

1688

1677

1693

1688

St

1332

1317

1318

1399

1317

1306

994 510

863 422

988 510

853 416

993 510

873 425

s, h’ S,

a’ Energy of thz O-O tmnsmor. relntwe to S,, h’ From the phosphorescence spectrum [4]

harmomc s, = rd-Il%l

*here

functions,

osc~iiator

T, = jl’;n,U” n

.)-

U”IS d vlbrdtionai

pnmd

symbol,

refer

formuid,

trdnsparcnt IS lnrdnt

\,hr.~t~oncil

iectzis

,a).

qudnturn

to trlplets

WC do IO he dcveioped, v~br~r~on~i part cxphcitiy

I ur I’

t tz (1)

number

and

In the formahsm

not

normally

in

order

However.

hst

the

to keep

the

a summation

to

imply

d summation

of

these st‘~tes. IX

differing by one quantum of an out-of-plane bendrng mode. and (Ii) a crystal-field mteraction term D wiuch mixes wbronic Ie\els of Tao rlectromc states differing by an eken number (including zero) of such quanta: Mg!=C

over

ober

all

C, should

be

KiN),,*

C[(

=

+

(MLK

),,*I

J’

+CC[(,~~KL),,+(K‘~IL),,] ’ J +CC[(LK12f),;,+(LnlAr),,~]-

rc.id d5 &!?I. _

’ H

(4)

J’

here

(KLW,,

= (W

(2)

+

~QIW(S,~K,,l~,)

x (~,lwL>&3,&,~.

( AIL./\’),,* = (s”lwv(w.JJ . ( I-M 1, = !~,,l~~,,~,,(~,I~~~~lj~O,~. (IlIt),

= :~,,I~~~lg,~s,I~~,‘,lr,}~l

z,,=(L,-fr,)

.mtl

x U,P + i\‘QlT,)G,&, ,.

( MKL. I,, = (S,lMIs,>(W

’

(3)

)I,‘,‘,! clcnotcs

the spin-orhtt

hlghcr-order

opt’r.ltor

termr

Here

H,,

IS

energy of st.1~ IS,) This vlbronlr elcp‘ukon method I\ v.~ld of the coupling\ are small comparal

10

iCVd\

II

~ncthod

cup.mwn much

the (vlbromc) sp.rclngs Cdlt bC reduced to the

I.lrgcr

of

LiSlldl

if the clectromc

th.ln the wbr~tton.ll

the coupled

level spacing-

IS

the

I.IIIY VIKC they Ic.I~ to closure

in the systcmb

1111\reduction

I< not

\.~lttl XIIICC vwt’

of the elccironlc

tion\ .krc 41n.ill th~~~cvtx-. wnit’ WIICC III pratlw

I’ .uitl 1 111(2)

c.m

I he tcrnix I\,$’ ,~li~wcd

truln III\OI~C

~o~npon~~~t

nlT* .\I.I~c\ of the

energy

reduction to nq*

contrIbute

srpar,iof eq

terms.

that S.~IIIC

c,m

(3)

over

~t.~tes [5] to the orbltJiy

of the phosphorescence

The nc\l-ll@rr-order prrturh.ltlons

gener~liy

the surnmdtlons

ht’ hnuted 111 (7)

I&Aled

couple

n~ult~pl~c~t~

nT* Two

specM:,:.

.md such

1Lrnis \\11l hc considcrcd(i) d ~ibronic couplmg taxi rcprcscntd hy an operdlor KQ = r,, KmQ,, \vhtch IIII\C\

vlbramc

Ic\cls

= (Sol0 -t-KQIS,)(S,/MIS,)

of NV

x

($1H,,JT,)Zo,G, -

( LA-M),;* = C%lfLl-WTl~ + /\‘QIT)

electronic

(L,VK),;*

= (~,t~.,~TXT,I~~~T,)

each trw

~iir~lcrcond~r.ilioli.

14 pnwhlc.

(/ML),,

,Z, ,.

electronic

level sp,lclng

OLL’T IIIC vthrcltwn.rl \t~tes of III.IINIO~J c.!n then be performed

WI~I~.~~IOI~~

clcctnw~

+ KQIS,)

x (s,lKlT,P,

C, IS the (vlhromc)

,md

-

ht.ltes

x (T,iD +

(5)

KQI’I, >-G/z,,

these. the terms (KLM), IP, (MLK )03~. (MKL),,. (KML),,. (LKAI), I . and (LMK), 1 refer to static dipole contnbutlons The terms proportIonal to D contribute to the orbltaiiy allowed component. those proportlonal to KQ to the forbidden component. In the foiiowmg sectlons. we consider each of these Integrals m d&ad, using both empirical and Of

theoretlcnl

approaches

to estimate

their

values.

In

separate into an electromc and d vlbratlonai factor. In prmclple, the electronlo Integrals can be evaluated by quantumchemxal calculations: the wbrational factor USU.dly assumes the form of an overlap integral general.

eJch

Integral

WIII

A

4. Eigenmhes

DesprCs et al

/

Phosphorescence

and eigenfunctions

The electronic eigenvalues and eigenfunctions of the DMB molecules have been calculated in the CNDO approximation. The carbonyl and CHOphenyl bond lengths were optimtzed for the SCF ground state (S,,) by a method, described elsewhere [ 131. whtch ytelds both the equrhbrmm bond length and the corresponding stretching frequencies. The parameters chosen for these computatrons were the origmal CND0/2 parameters 1241 which are adequate for changes of geometry. Such a conformatlonal analysis is necessary because some of the properties of the ground and excncd St&es depend on the geometry [15.16]. The verttcal transttton energies S, + S, and T, c T, were computed on the basts of the CNDO/S VO CI method of Del Bene and Jaffe [17]. extended to double excitations. The lowest 100 singly and doubly excited conflguratlons were Included m the CI calculations. the basis set used being the set of SCF ground state MOs. This descrlptlon also leads to a stralghtforward formulation of the spin-orbit couphng Integrals as matrix elements of the spm-orbit operator. The resultmg spm-orbit couphngs and their effect on the observed zerofield sphttmgs have been dlscussed elsewhere [ 18,293. The same formulauon was used to evaluate the static eiectnc dipole moments of S,. S,, T, and TZ. as well as the trdnsttlon dipole moments between S, and S,. T, and T,(TT*) and TZ and T,(na*) All these computations, based on symmetry-adapted pure-spin wavefunctions. were perfern-red with programs adapted for CDC and IBM computers In table 3 we list the calculated energies relative to S, for states relevant to the phosphorescence spectrum These calculations are carned out for a CO distance of I.24 A. the calculated ground-state equrhbnum distance. The calculated vertical en-

ergy differences agree reasonably well with the adiabatic energy differences listed in table 2 The latter values will be used m our calculations, eycept for higher excited states for which only calculated energres are avarlable The calculated spur-orbit Integrals are listed in table 4. Smce they yield an accurate reproductron of the zero-held splrttrngs 1161, they are expected to be suffrcrently

specrra

237

of DMB

Table 3 Calculated and observed (m pdrenlheses) energies (m cm-‘) electromc states relevant to thr phosphorescence spars

of of

_ DMBs State

S, s3

S, SS T, TZ T, TJ

Isomer 3.4-DMB

2,5-DMB

2.4-DMB

2703q26952) 40040 50360 52260

2675q26068) 4.0130 51240 =’ 51700

269Sq262SS) 39890 50400 52160

25230(24974) 27500(25450) 33440 33780

2495o(Z4253) 2495q24360) 32070 33640

25lSq24464) 25200(24570) 33370 33980

.I’ s, Slrllr

accurate for our purpose. In addition, second-order spin-orblt contnbutlons to the allowed T, + S, component were calculated. They gave nse to a transnlon dipole moment of the order of lo-” debye which IS too small to contrlbute slgmflcantly. The calculated permanent and transmon dipole moments for the states relevant to the phosphorescence spectrum are hsted m table 5. Recently Wmkler and Hanson [lo] have reported dlpoie differences for triplet levels of 2,5DMB, 2,4-DMB and TMB m durene crystals; the last molecule IS very smular to 3,4-DMB m Its spectroscopic properttes. In table 6, these differences Ap of T, and TZ relattve to S, are compared wtth calculated “zeroth-order” drfference drpole moments, denved

Table 4 Cd~hted

st31es

spm-orblt

couplmg

mtrgr.ds

(m cm-‘)

for DMBs

Isomer 3 4-DMB

2.5-DhlB

2.4-DhlB

S,, .T,

-5478

So T,

-1698 8 76

-5469 - 17 41 s 47

-5430 - 16 29 945

3 85 -939 -749 1302 - 12 32

3 85 -939 -678 1332” - 10 95

3 85 -9 39 -742 12 55

%.TI S,.T, S, .Td S3

T,

S.,.T, S, -T,

.’ S,.T?

-1081

A

13s

Tdds

Despres

er al

/

Phosphorescence

spectra

of DMff

5

C.dcularrd

(rransmon)

Sta.lrs

dlpolc moments

(III dshyc) for Ihe DhiB molecuk

AI, = 0 by symmrrry

Isomer 3 5-DhlB

so5, S, S, = T; T2 T, -T, S,, S S, S.. S, S, T, J-1 T, T, Tz TX

Z 4-DAlB

2 5-DMB

Iif,

M_

I 75 056 2 3s -025 0 94 -035 -0 I5 007 0 33

-

3 30

1 30 -369 0 33 -010 011 002 -005 -0 I’ -

“,

Sl

AI,

0 s9 -023

-330 - I 31 - 3 31 0 29 -007=1 011 006 -009 0 II

-0 17 1 09 -026 0 92 -035 -0 13 -007 0 34

1 06 -005

109”’ -035 -0 I6 0 20 -035

from the data of table 5 by means of the formula

-373 -172 -367 0 35 -001 011 0 10 -0 I7 -0 I3

integrals

The calculations

the sign tahen for Ap IS postttve for the T’;;* and negative for the na* state. ewept for the observed values of TMB \vhtch are equal rn stgn and magmtude for the two states. In agreement wtth Wmkler and Hanson [lo]. we ascrtbe thts to the mtxmg of the T, ortgm wtth a number of near-resonant T, levels. the high denstty of such levels rn TMB (and X4-DklB). N here the T,-T2 gap is relattvely large. wll reduce the LIP v~lus m the T,-ortgtn regton to v Aues close to that of T,. In 2.4- and 2.5DMB. vvhhere the T,-Tz separation. and thus the T, level denstty near the T, ortgm. IS much smaller, $.I tn thts rzgton is close to the value expected for nq* states The 1~ v,.tlues for the T, origm show some evtdence of crystal-fteld ml\lng (vtde tnfra).

‘if_

096

5. Vibrational

[~r(T,,)]‘=[~~f,(T,,)-M,(S,)]~

described

m sectlon

4 lead to

CO equtltbrtum distances oco = I 24 A tn S,. 1.31 i\ tn T, and 1 35 A m T?. wtth correspondmg frequencies wco = 1700 cm-’ in S, and T,. and 1530 cm- i In T, The values cakulated for Tz should also apply to S,. compartson with table 2 shows that tic0 n-t S, IS somewhat overesttmated. The vtbrational dtsplacements @co(S,)-~co(T,) and @co(S,)-~co(T,) can be compared wtth the tntenstty dtstrrbutron In the CO-stretch progresstons observed n-r T, ---, S, and T, + S, (or S, + S,) spectra. To thts end we elpress these displacements and the correspondtng frequency shifts m terms of dtmensionless parameters [20] BII

r,

=

[w,,,w,,,/(w,,,+~,,,)]“2(~,,,-~“,).

58,,, = ( a,,, -

W,r, )A

% + %, )

(3

The tntenstty ratto of the 1-O and O-O bands of a progression IS then given by

Tahlc 6

Cnlcularrd and ohse:ned [lOI (In parenthats) .i\rrJge prrmJnrnt dlpols moment\ Ap (In dsb>e) III T, and T2 relatl\e to S, for the DUB nrolc~uirs studwd .md L-l S-TRlB

I,, ,,(l-0)

I,, (0-O) r,

Iwmer

T,

T2

2 4DMB 2 5-DXIB 3 I-DXlB

0 I-1(07?) 0 I7 (0 S5) 071

-251 -117(-20)“’ -132

2 I 5-ThlB

studled

(11’)

(1 3

From

” ”

1 - l,;, ,, 1 + I,, ,,

(

Ill =

B,,

calculated

‘I2

i

&, values. one derives and Bc, 3o = B,, ,‘,, = 1.6. but the observed CO progresstons [4.12,21] yteld B co 10 = B CO20 = 1.2 and B,, ,so = 0.8. We accept these emptrtcJ values tn our calculattons; since B co

the

,;p

1so = 2.2

A

Desprec

et al

/

Phosphorescence

they are only rough estimates, we shall use them together with the simplifying assumption that frequency differences can be neglected The overlap integrals can then be written in the form [20] (u,, JO,, ,) = exp( - fB,‘,,)B,:

,,/(u1)“‘-

(9)

The resulting values for the states relevant to the present study are listed m table 7. For the aldehydic CH-wag mode, the calculatlons of section 4 yield w,-~(&,) = o,--(T,) = 1000 cm-’ and tiCH(T7)= 490 cm-‘. The latter value should also apply to S,. These values are m excellent agreement with the experimental values Wed m table 2. Theory and expenment both Indicate that the molecules remain planar m the states consldered here. so BCH ,,= 0 for all of them. The two relevant overlap integrals are then [20]

,,)‘?

&H NCH,) = (1- l&t

,,)I”-

(lo)

Their values are hsted m table 7 In addition. be integrals of the form [20]

there

(2

CH

,&H

,) = 2-1”&, ,,(l -&I

wll

(I,,

,I~CHi&W

,)

=

t2%W

,)-“‘(l

-

&

,,)“‘. (11)

arising from the KQ vlbromc coupling term. In the calculations to follow the factor (1 - la)‘/’ will be taken equal to unity, and the factor (2~~~ ,)-“’ WIII be absorbed in the expression for the vibromc coupling Integral Y, ,, = (4,

,I(~l~,,QnI/)l% ,)

= K, ,,/wJ,, ,Y = (1, ,IOl~W~Q,I/)Q,l~,, which will be expressed Table 7 VIbratIonal States

,)T

(12)

in cm-’

over1.1~ mtegrals

for DMBs calculated

spectra

oj DAfB

239

6. Vibronic coupling

To evaluate the vibronic couphng between the states contnbutmg to the phosphorescence spectra, a precise description of the normal coordmates and their effect on the state mixing is required. These more elaborate calculations, based on the MIND0/3 method. have been camed out only for benzaldehyde itself and its mono-deutero-lsomer. They are based on a program developed by Dewar and Ford [22] which follows the method introduced by Mclver and Kormomcki [23] First dertvattves of the energy with respect to carteslan coordmates were determmed by analytlcal methods and second denvatives by finite differences after the apphcatlon of small displacements ( = 0 005 A) The matnx of second denvatlves was used first to optimize the geometry and then to obtain the frequencies and normal modes by the standard GF method [24]. In these calculations. the SIX vibrational frequencies correspondmg lo translation and rotation, although different from zero, were always smaller than 30 cm-‘. The calculated and observed frequencies 1251 are compared m table 8: although the calculated frequencies show the well-known systematic devlatlons from the expenmental values such as the over-

estlmatlon agreement

of stretchmg IS satisfactory.

frequencies,

teal energy surfaces. To calculate the required vibromc couplmg integrals, CNDO/S calculations were carned out for geometnes dlffenng by a small drsplacement along a calculated normal coordinate. The calculated energes and transitron dipole strengths to the

on the basis of spectral observations

Integral

(OPko

UP),,

waco

top),,

OPkH

0 70

S&

= S,.T, = S,.T,

-059 -048

0 36 0 19

097 1

0 23 -

&.I-,

=-I-,.-i-,

096

005

1

S,.S,

OS5

0 27

the overall

In particular. the normal coordinates Illustrated m fig. 7 are expected to be reliable smce they do not ongmate from a flttmg procedure but from a realistic electromc hanultoman that should yield reasonably accurate poten-

A Desprex et (11 / Phosphorescence spectra of DMB

240

Table 8 Calculated and obsenrcd [15] (III parentheses) frequenaes cm-‘) of out-of-plane bendmg modes m benzaldehyde-l/z, -Id,

Table 9 Calculated smglct ad tnplet energla (In cm-‘) translIlon moments relauve 10 S, for bcnzllldehyde used m the \qbroruc couplmg ckulatlons

(in and

Mode =’

Dexnpt~on

B-ih,

B-id,

SliUtZ

Symmetry a)

E

16 [ o(CH)] 77 I1731 78 [S] 79 [17b] 3O[lOJ] 31 [:I]

ald H(D) wag CH bend CH bend CH bend CH bend CH bend Arletal bend sheletal bend

919 (1010)

SIO (860)

S,

3016.5

2x 10-J

869

(960)

871 h’

%

A”(n7’) A’(&)

9x

SSI 861 s15 708 598 a7

(978) (925) (514)

881 S67 h’ s14

s, S,

A’(L) A’(&)

38230 41050 52830

0046 103 104

(7%)

697

(688) (449)

594 438

(410) (145) (133)

3s’ 168 (215) 45 (105)

3’[-l]

33 [16b] 31[16aJ 35 [ w(CHO)]

sklcr~l

bend

CH(D)O NJg CH( D)O torsion

361~1 A’ in brsAxs

the nomuon

used

h’ Modes 17 and 29 m B-Id, [I731 and [17b]

ground

table were

3Y1 179

50 m ref

of modes

54280

18390 30165

-l-I

T? TX

4”(n-*) A’( B, 1

-&

A’(L,)

T5

A’(B,)

33715

334-10 35875

48

-63

-11

-16

C,H,CHO -2

‘-7

0

l-26 32

4

-2

- 16

-3 -4

-2

-I

II

C,H,CDO

I II

26

-i:

‘5

‘-26

Q36 Fig 7 CAulared

‘24 Q 26

Q35 artrsmn

d~~placemrnrs

of om-of-plmr

bendmg

of

belong; the MO coeffments \\ecre kept fmed and only the Cl coefficients were varted [26.27] The resulting couplings are expected to represent

state for the states Involved are Ilsted III 9 In these calculations. the atorruc orbltals kept centred at the nuclet to which they

-16

A’(k) A’( l-, )

IO_-’

,’ The notallons A’ ond A” denote the IUO represenratlons Ihe group C,. Ihe noldllon K-Ip.xcnlheses IS that of Pl~tt

[d[

xc hncar comhmaon

S,

f

modes

of benuldeh>de-lh,

md

-lrl,

A

Despr.

et al. / Phasphorescence spectra of DMB

241

Table 10 Calculated vlbromc couplmgs (In cm- ‘) for singlet and tnplet states of benzaldrhyde-lh, and -Id, Induced by out-of-plane bending modes hlode

States So.%

26-h

26-d 27-h 27-d

28-h 28-d 29-h 29-d 30-h 30-d

31-h 314 32-h 32-d 33-h 33-d 34-h 34-d

35-h 35-d 36-h 36-d

s,.s,

1737 776 -224 27 146 45

-5 70 -54 38 -24 25

656 35 -52 - 10s

-56 -97

-194 915 - 1034 1016 1967 - 1773 - 105 -112 - 2898 - 2579 3037 2915

215 - 207 -39 -42 18 -10 33 22 -122 127 -37 -38 138 143

s,.s3

s,.s,

- 173 - 495 -19 3 38 -2s

16 -51 1 -217 122 169 -66 -11 57 58 348 316

-130 -217 29 -21 30 ‘2 120 -63 -76 -38 201 - 238 -77 136 -135 -59 130 -133 528 478

-154 -169 - 14 6 33 28 94 -21 14 45 128 168 -93 145 -98 -44 57 -60 392 360

- 285 - 278

- 524 - 534

- 357 -340

109 - 14

adtnbattc

couphngs m a dtabattc basrs. the atomic orbttal followmg IS requtred tf the perturbation expanston 1s terminated after the ftrst term [26]

The calculated couphngs are reduced to thetr hnear components, the coupling parameter thus bemg the ftrst denvattve of the calculated couplings wtth respect to the normal-coordtnate amphtude.

The results for the integral (~]i!lH/aQ,,~) obtained in eV/A. are expressed tn terms of vibrontc matnx elements tn table 10. 7. Crystal-field

v, ,,. gtven by eq (12). and hsted

mking

In thts sectton we consider evtdence for the mixing of T, and T, by the crystal fteld. Such mtxing ~111 affect the allowed component of the phosphorescence spectrum. No attempt has been made to calculate crystal field effects quantumchemtcally, smce the structure of the trappmg sttes is not known wtth sufftctent accuracy. However, it

-I-, .T,

and

thus

lower

Tz

T3

52 100 -88 -56 -35 -32 -52

97 216 -206 -96 111 21 -41 42 I6 -146 - 148 -116 -113 215 219

than

the molecular

i-1

-L

-56 -8’ -51 -4 40 33 23

52 83 9s 110 152 -146 177 30 -8 -17 - 19 214 194 -129 - 121

symmetry

C,.

hence it ~111 induce mtxmg of nn* and np* states. This mtxmg w1l1 tend to be stronger, the smaller the T,-T2 gap; on this basts. one would expect the 2,4- and 2,5-isomers to show stronger mixrng than the 3&isomer. Tills is Indeed the case as mdtcated by the followmg observattons. (i) The phosphorescence excttatton spectra of the 2.4 and 2,5-isomers, tllustrated tn ftgs 3-6, show a T,(~‘rr*) ongm but the correspondmg 3.4 Isomer spectrum, illustrated tn ftgs. 1 and 2, does not. (II) The phosphorescence hfettme of the 2,4and 2.5-isomers IS about half that of the 3&isomer [4,11,2S].

(111) The CO-stretch progression. whtch IS usually more strongly developed for nn* than for WIT* transtttons, is longer m the phosphorescence spectra of 2,4- and 2,5-DMB than in the correspondmg 3.4DMB spectrum [4]. These observations mdtcate mixing of the T,

1

247

Despres

er al / Phosphorescence

origin (the phosphoresc:ng level) with the T2 band system and m particular wth the T, origin which iq energetically closer to T, than the other T2 bands. If the crystal-field mteractlons D,,2. = (T,IDIT,) IS much smaller than the T,-T, separation. only this Tz ongin needs to be rncluded. The observation that the T, ongm IS much weaker than the T2 ongm Indlcatrs that crystal-field ml\mg IS ,ndeed small compared to the T,-T, gap In all Isomers. e\en 2.5DMB-l/z, v.here thrs gap equals 75&j cm-’ In the phosphorescence ewtatlon spectrum of this molecule. the T,-ongm band hds = 5% of the Intensity of the T,-origin band. mdlcatlng a cnstal-field mterxtlon D,,, = 17 cm-‘. since (17/j5)2 = 0 05.In L4-DMB-lk,. where T, has roughly the same amount of ns* character as In the 25rsomer. this argument leads to a crystalfield mterxlwn of = 50 cm-’ Flnally. In the ?.-l+omer. T, appears to have nsgliglble nT* character

( =g 59).

leadIng

to an InteractIon

2 50 cm - ’

These numbers agree quJit,ltlvely \\lth the obsened ~Jurs of 1~ for T,. hstrd m table 6 The smJlrr \~lue of 2.3- and 2.5DMB rclJtl\e to 2.4.5TMB. ,md presum,lbly 3.4-DMB. might be due to a (negative) contnbutlon of T, Induced by the crystal field If the crjst.11 flrld 15 the only source of this dlfferencc. the observed Jp values lndlcnte =10% nz* character In T, of 7.4- and 2 5-DMB. In agreement \\lth the estimate gILon above. Houever. since the calculations rndlcate Jnothcr possible source for this difference. .ls mdlcated In table 6. this mtrrpret~tlon IS not umque. If similar crystal-fleld InteractIons apply to the slngkt manifold. I e. D,: ,( 50 cm-‘. most of the S,, - S, absorption wll be lntnnslc rather th,m crystaLfIeld Induced The Integrated Intcnslty of th1.s band amounts lo = 3% of the Integrated S,, --) S, nbsorptlon whrch our calculations predict to be = 20% of the S,, - S, absorption. In the calculatlons to tollo~~. \\e therefore tahr this S,, -+ S: ahsorptIon to exeed the S, - S, absorption by a 1;ILtor of 150 Thrs wll determine the lntcnslty of the lntnnslc part of the allowed component The crystaLfIeld

Induced

part

IS borrowed

mdwzctly

from S,-S, and several higher-energy transltlons of comparable strength For slmphclty we replace these contributions by a smgle contnbutlon tahen equal to twice the contnbutlon of S,-S,

specrra

of DMB

8. Calculations

We now combmc these estimates m an attempt to calculate the relative Intensities of a number of prominent bands m the DMB phosphorescence spectra. The bands selected for detailed study are the members of the CO-stretch progression. represent:ng the allo\\ed component, and the CH(CD)wag fundamental and CH(CD)-wdg + CO-stretch comblnatlon band reprcsentmg the forbldden (induced) component. The Integrated mtensltles of these bands are hsted in table 1. The allowed component IS governed by the matnx elements (2) together with the crystal-fwld Induced components (D-terms) of eq. (4). its vlbratlondl structure IS governed by the CO-stretch overlap Integrals hsted In table 7. The progrrsslon wll be modlfled by non-Condon effects 1291, due to spm-orbit and crystJ-field couplmgs fo states L\hose CO-stretch overlap mdtnx with T, or S, IS not dlagondl. The overJl mtenslty of the allowed component IS dewed from the mtenslty of the lending transItIons S, - S, and S, --, S,. whose rel~tw lntenslttes are assumed to differ by J LICtor of I50 (wde supra). This Intensity depends on the strength of the crystal-field werxtlon rcprrsented by the pxameter D,,,. The values denbed In sectlon 7 for this parameter from the phosphorescence exatatlon spectra are \wy crude. To produce rhe observed mtensltles 01 the Alowed components. slight ddJustnlents are necessary. The calculated mtensltws and the adjusted parameter Lalues are !lsted m table 11. Of the many contrlbutlons to the forbldden component. wntten In eq. (5) ds permutdtlons of (KLM ),,. SIXare clearly domtndnt They fall mto two groups a group A conslstmg of A, = =(LKAI),, and AI,=(LMK),.,. ( IMLK )“? . -i, and a group B conslstmg of B, = (hfKL),,_B, = (KLM),, . and B; = (KML),,. Group A Involves T,-T, wbromc and S,-T, spin-orbit couphng. and group B. S,-S, wbromc couphng and S,-T,spm-orblt couphng Both groups are unconventlonal m that they denve from permanent rather than transItton dipole moments; in addltlon. group B rnvolves coupling wrth the ground state which is often neglected. The two groups lead to matnx elements of different sign so that the correspond-

.-t Despres

et a.! /

Phosphorescence

ing mechanisms interfere destructively. As a result, the relatively small changes in T,-T, separation between the isomers can greatly alter the balance between the mechanisms A and B. Tlus ccnfums the earlier conclusion [4] that the strong vanatlons m CH- and CD-wag intensity must be due to the present analysis Identifies the two interference: interfenng mechamsms. To test this interpretation quantltatlvely, we calculate the relative mtenslties of the induced fundamentals m units

2 (ApfBp)kfap.

AM,=

u

=)

,“,

(13)

p=l

where p labels the permanent dipole moment used. viz p = 1 for S,,. 2 for T, and 3 for either S, or T, taken to have the same dipole moment The parameters used m this calculation are all taken from tables 2-10. except the T,-T, vibronlc coupling parameter VCH ,.z. which 1s adjusted. This parameter, along with V,, 01, has been calculated only for benzaldehyde and hence may be expected to show some variation m the three Isomers. Since the relative intensities to be calculated depend on the ratio of these two parameters, the fact that V,,, 0, IS kept constant implies that V,, I,lP must absorb

the

vanations

in

both

parameters.

The

other theoretical and empirical parameters used are of course also subJect to errors, so that VCH,,z, also has to account for these deviations. Our reason for choosing VCh ,,2, as the adjustable parameTable 11 Calcul~ed CO-stretch presented

A) Numbers

to the gap,

so that

the value

of

on the basis of a constant gap will be inaccurate. The present procedure allows us to Investigate this pomt. The calculated relative intensities of the forbidden component, together with the V,, 1,2, values used, are listed m table 11. They show reasonable agreement aqth experimental intensities. listed m parentheses. The anomalous deutenum effects are reproduced by the appropnate changes in vlbrational frequency. T,-T, gap and vibronic coupling Integrals.

Similarly,

the strong

lntenslty

changes

for 2,5-DMB between sites I and II are reproduced by a change of only the crystal-field parameter D I.‘* and agam the T,-T, gap. The calculated mtensltles of the T, origin bands for the SLXISOmers are compared by means of the numbers m brackets; these indicate tnat the ongin bands of 2.4- and 2.5-DMB are more Intense than the 3.4DMB ongm, a conclusion confumed quahtatlvely by the observed excitation spectra. Quantltatlvely. these results depend strongly on the chosen value for the crystal-field parameter D,.,. of the 2,4- and 2.5-isomers. Note that the values of 58 and 23 cm -’ are m good agreement wtth the estimates of 50 and 17 cm-’ In section 7. It follows that the

kH°CO

14 (-)

178(180)

83(70)

52 (50)

14 (-) 21 (35)

8wO) 59(55) 11q105

66(50)

61 (55)

2.5-d,

contnbute

VCH,e2e denved

0 CH&O

2.4-d,

2,5-h,

will

OCHh 52 wu

2,4-h,

2 S-d,

ter, taking Into account that the data do not Justifythe mtroductlon of more than one such parameter, IS that the adJusted value ~11 serve as an indication whether the perturbation approach is valid for T,-T2 coupling. In this case. it IS not immediately obvious that the couphng will be small compared to the (vtbrontc) energy gap. If not, the coupling

III Ihe preceding secuons (in parentheses)

65 62 57 55 57

2.5-h,

243

of DMB

and obsened (m parentheses) mtensltles. relatwe to the O-O ongm band ( = 100) of phosphorescence bands aitnbuted to and CH(CD)-wag modes of DMBs The last two columns compare the adjusted parameter values used wth the estimates

Site

3.4-h, V-d,

spectra

(SO) (80) (105) (-) (95)

20 (5) 17 (-) 25 6) 17 (40)

19 (15)

279(290)

276(410) 53(50) 66(65)

in square brackeis are relative to isomer 3.4-h,,

sue I ( = 1)

ICH

1CO

22(25) 99(45) 110(110) 239 (-) 19(20) 57(25)

‘CH

OCO

ID,,, I

1v,, 1’2’1

I11=’

58(50)

87( 154)

IO91

102( 169) 54(154) 6S( 169)

131

58( 50) 23(17) 23(17) 10 10 5q50)

PI

50(5O)

80( 169)

I2 51

1121 W61 1051

54(154) 68( 169) 71(154)

A

244

Despres

er al

/

Phosphorescence

theoretically and emplncally derived parameters. with some adJustmen& can account satisfactonly for the strong vanatlons m mtenslty dlstnbutlon observed for these isomenc molecules The parameter adJustments required to fit the observed mtensltles are very mmor for D,.,. but not for the \lbromc couplmg parameter Z’,, ,.2P. wbch IS reduced by as much as a factor of two m some cases Thts may mdlcate that the perturbatlon formulation used for these systems IS begmrung to break down The conclusion that the empincall! dcnvcd values of both D, 1 and 1/c- , 2 are smallest m absolute value for the 2.5Isomer. which has the narrolvrsl l-,--T, gap. points In the same

dlrectron

9. Discussion

This mvestlgntIon started \\ith the obsematlon that In DMBs the structure of the phosphorescence spectrum depends stronglj on the posItIon of the two methyl substltuents. A slmllar strong posItIon dependence was observed for the effect of dcutenum

substltutlon

m

the

aldehyde

group.

These effects are anomalous m that the methyl groups produce not much change In the lower elrctromc states of the molecules It wrls recogmzed earlter [4] that these observations can be traced back to the close proxlmlty of the lo\\ecst two tnplet states- the relatively small shifts of their energy caused by the methyl substltuents give nse to large relative changes m therr spacmgs. which In turn strongly Influence the:lr couphngs. Hence It was assumed that the m&n changes m the phosphorescence spectrum associated with reposItIonmg of the methyl substltuents can be understood m terms of changes In T,-T, mterdctlon caused by changes in the T,-T, energy gap. Ho\\crcr, It was

recognized that the observed intensltles and deutenum effects do not change monotomcally as rl function of th1.s gap. from ths It was Inferred that there IS Interference between t\\o mteractlon mechamsms. one of mhlch Imolves the T,-T2 mteractlon Speclflcaily. It wds argued that an mcrease m the T,-T, gap from the value m 2,4- and 2.5DMB to that m 3.4-DMB weakens the T,-T, mteractlon to the pomt where It loses its donu-

spectra

01 DMB

nance over the second interaction. tentatively associated wth coupling mvolving the ground state [4]. This mterpretatlon IS baslcally conflrmed by the present work. but \lth some slgmflcant modlflcatlons. A key element UI the analysis IS the observatlon of phosphorescence excitation spectra which mahes It possible to estimate the T,-T, gap with much better accuracy than before. Of comparable Importance are vibromc couphng Integrals. caiculated for benzaldehyde. which show the coupling betileen S,, and S, to be strong enough to provide a second mechamsm for mducmg phosphorescence spectra. These same calculations mdlcate that deuterdtion of the aldehyde group produces a substan11dl change In the normal coordmates of outof-plane bendmg modes. thereby rearrangmg the T, -T2 couphng amon, 0 these modes Thus changes the balance betbbeen the two mterfenng mechanisms for a given mode and helps to account for the unusual

deuterium

effects

on

the phosphores-

cence spectra The Interplay between Interference and normal-mode mlxmg leads to a number of mterestIng effects. Thus the sign of the deutenum effect on a given band depends on which of the two mterfermg mechamsms IS the larger for tbs band. In the absence of mode nuumg. large deutenum effects of elthcr sign would be compatible only with nearly elact cancellation of the two contnbutlons. This would Imply that the modes subject to large deutenum effects would be ueah. contrary to observation. On the other hand, the mode mlxmg explams at once why different modes are SubJect to different deutenum effects both In sign and magmtude m general. the reduction m the couplmg by one mode ~111 be compensated by an Increase m coupling by other modes. Thus IS conflrmed by the caiculatlons of sectlon 6 which preduct Increased actlvlty upon deuteration for several modes, notably modes 30 and 31 ( v,,,~ and v,~) Accordrngly. a number of bands rn 3,4-DMB mcrease their mtenslty upon deuteratlon (e.g. those assigned to vJ. uioJ and Y,~, i e., modes 32, 30 and 33/34 in ref. [4]), contrary to the behavlour of the CH-wag bands. Speclflcally, the band attnbuted to l’,O.l m the three Isomers is much stronger m the deuterated compounds, a behaviour predtcted for L’,,_ While tbs suggests to reassign the bands at-

A

DespGs

er al / Phosphorescence

tributed to uIoXas due to v,,. it should be realized that the posstbility of normal-coordinate rotatton upon electronic excitation may comphcate matters. In addition to providmg evtdence for mterference and deuterium Induced normal-mode mtxing, the spectra also conftrm that the crystal field leads to nr*--m* mixmg. This effect IS tllustrated by the difference m phosphorescence spectra observed when the same isomer IS trapped at drfferent sites in the durene

lattrce.

The apparent

in-

crease m intensity of the Induced component of 2,SDMB m sue II relative to site I by a factor of about ftve should be mostly due to a correspondmg reductron In the Intensity of the O-O band used as standard. This follows from the fact that most of the induced bands undergo a substanttal mcrease relative to the O-O band It IS readily reproduced by a reductton of the crystal fteld parameter

from 23 to 10 cm-‘. Fmally. we point out that the couplmgs and level shtfts that cause these comphcattons are small n-r an absolute sense, namely of the order of 100 cm-’ or less. wtth one exception: the couphng of S, and S, which IS of the order of 1000 cm-‘. The overall picture emerging for these systems IS thus unconventtonal: the ground-state coupling whtch IS usually neglected IS as effective as the coupling between two nearly degenerate states, usually considered to dominate the spectra. In a forthconung paper, we shall return to these couphngs m an effort to unravel the phosphorescence excrtatron spectra m the triplet region. References

[ 1] G Herzberg and E Teller. 2 Physlh Chem (Leipzig) 21 (1933) 410 [2] R L Fulron and M Goutsmum. J Chem Phys 35 (1961) 1059.41 (1964) 2280 [3] W H Henneker. A P Penner, W Slebrand and M Z Zgrerskl. J Chem Phys 69 (1978) 1884 [4] A Despres, V LeJeune. E Mlgudlcyan and W Slebrand Chem Phys 36 (1979) 41

spectra

of DMB

245

[5] MA El-Sayed, J Chem Phys 38 (1963) 2834 [6] W Slebrand and M Z Zglerskl. Chem Phys Letters 67 (1979)

I71

13

I &kan

and L Goodman.

Chrm

Phys Letters 64 (1979)

32 L Goodman

and hl Koyansgt. Mol Photochem 4 (1972) 369 [91 CT Lm and D C Moule. J. hfol Spectry. 37 (1971) 280 1101 i C. Wmhler and D M Hanson, J Chem Phys 78 (1983) 4536 A Despra E Mlgndlcyan and L Blanco. Chem Phys 14 IllI ISI

(1976)

11’1

229

L Goodman,

M Lamow and hl Koyanagt. Chem Phys 47(1980)329 1131 J Leclerq and J M Leclercq. Chrm Phys 22 (1977) 221 [14 J A Pople D P Sanrry .md G A Segal. J Chcm Phys 43 (1965) S129. J A Pople and G A !&gal. J Chem Phys 43 (1965) S136. D P. Sdntty and G A Segdl. J Chem Phys 47 (1967) 158 1151 C Mqoule and J hl Leclrrcq, J Chem Phys 70 (1979) 2560 C hfgoufr. Chum Phys Letters 80 (1981) 593. [W A Despres .md E Mlgndtcyan Chem Phys 50 (1978) 381 I171 J Del Brne and H H Jaffe. J Chem Phys 48 (1968) 1807 4050. 49 (1968) 1221. 50 (1969) 1126 1181 R L Elhs. R Squue and H H Jaffe J Chem Phys 55 (1971) 3499 I191 C h~lJoufe and P Yvan Chrm Phys Letters 43 (1976) 524 [ZO] C Mannrbach Physux 17 (1951) 1001 [21] J Olmsred and MA El-Sayed. J Mol Spectry 40 (1971) 71 [32] M J S Drcnrand G P Ford J Am Chcm Sot 99 (1977) 1685 1231 J W Mciver and A Kormomclu Chrm Phys Letters 10 (1971) 303, J Am Chrm Sot 94 (1972) 2625 [24] E B Wdson, J C. Deems and PC Cross Molecular wbratlons (McGrawHill. New York 1955) [25] R Zwanch. J Smolarek and L Goodman. J Mel Specwy 38 (1971) 336 [26] G Orlando. Chem Phys Letters 44 (1976) 277 1271 G Orlando and G Marcom, Chem Phys Letters 53 (1978) 61 [ZS] A Despres. V LeJeune and E Mlgudlcyan Chem. Phys 66 (1982) 57 [29] W Slebrand and M Z Zgerskl. Chem Phys 52 (1990) 321