Non-Condon effects in triplet-singlet spectra. The 3B1-1A1 system of NO2− in NaNO2 and NaHCO2

.. Ph,si& 96 (1985)109-124 North-HoUanb Amsterdam Ciitid

. .

:.

NON-CONDON EFFECI-S IN TRIPLET-SINGLET THE sB,~‘A, SYSTEii OF NO, IN NaNO, AND K.E

GOTBERG

Depanmauof

309‘.

~~ :

~..~_.

:-

SPECI’RAa Nai-ICO,

>-

and D.S. TINT1

Chmisrry.

Uniccrsity of CaIifmio.

Davis. Cdifomia

95626. USA

Received 26 November 19%X

Spin-level nsoIv&i spectra of the 3B,-?+, o;-&) transition of NO,- in neat NaNo1_ and in a NaHco, host ar < 4 k intensity cn\dopcs for the rotily synuneuic bending progression,indiur;ng a breakdown of the Condon with the 5 spin level of the 3a, state and +R_ approximation The non-Condon effeas are associated predo~dy Tbc I-csulUcan be reasonably inreqxeeredin wrms of an empirical linear dependof panicukrtr scvcre in Ntiq/;r;o~-. the uansition moment on the bending coordinate. bur the detailed origin of the effect is unclear-

shots- difkrcnr

1. Introduction The analysis of the intensity distribution in a totally symmetric progression based on an electronic origin proceeds in lowest order by assuming that the eiectronic- transition moment is independent of nuclear coordinates. whereupon the intensity distribution depends, aside from a frequency factor, onIy on Franck-Condon factors. Although the assumptions involved in this approach may be rather severe. observations of deviation from the simple theory (non-Condon effects) are not many for polyatomic systems and may result from additional assumptions in evaluating the FranckCondon factors. As fit indicated by Breiland and Harris [l]. non-Condon effects can be readily exposed in a triplet-singlet spectrum &hout explicit evaluation of the Franck-Condon factors by comparison of the intensity distributions in a given totalIy symmetric progression for -different active spin levels of the tripIet state. These distributions should be identical for aII active spin levels if non-Condon effects are absent. Different distributions indicate that non-Condon effects-are occurring for.at Ieast one of the active spin 1eveI.s.This conclusion does not require a comparison of. calculated Franck-Condon factors with absorption and emission spectra, as generally required for a singiet-singlet transition and applied by

Craig and Small [2]_ A model for such non-Condon effects has been considered in a series of papers by Siebrand and co-workers [3-51. They show that effects are generahy expected in a weak or formally (space or spin) forbidden transition since the coupling (vibronic or spin-orbit) which enhances the intensity is itself subject to. a Franck-Condon effect_ I Since the spin levels of a triplet state generally have different spin-orbit symmetries, thereby couphng to different singIet states, non-Condon effects exemplified by spinlevel dependent vibrational intensity distributions result. Recently we have shown that moderateIy different intensity distributions in a totally symmetric progression obtain in the spin-level resolved 3B,-rA, (T,-S,,) spectra of a NO; trap-in NaNOs doped with AgNOz [6J_The different distributions could be explained with a spin-level independent displacement parameter for the totally symmetric mode between the 3B, and ‘At states and generaliz& vibrational factors resulting from inchrsion of the linear term in an expansion of the transition moment in terms of the totally symmetric coordinate. The -magnitude of the non-Condon effects were qualitatively in, agreement with a low-order model of Siebrand and Zgierski [3], but firmconelusions regarding the spin level most ~effected could -not be r&ched: It was &o uncIear if ‘the

0301-0104/85/$0330 Q Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

_.

..

-

rather large Ag’ perturbation in the trap (73 was somebow responsible for the non-Condon behavior_ or if the efkts were intrinsic to the 3B,-1AA, transition of N‘ia_. We present herein the results of similar studies in neat NaNa_ and of NOT as a guest in a NaHCO, host ctystal. We fits; consider the theoretical framework used to expose and interpret the rest&s. taking an empirical approach based hugely on Craig and Small [2] and relating to a theor&& model of Siebrand and Zgierski [3]_ Experimental results are then presented which indicate that non-Condon effects also occur in the 3B,-‘A, spectra of Naz in NaNO, and NaHCa__ We extract from the data the spin-level dependent vibrational factors that govern the intensity distribution in a totally symmetric progression. and compare and discuss these in terms of the framework presented.

L

Theoretical

background

Tbe emission intensity in cncrgy per second from the 5 spin level of a triplet state with no vibrational excitation to the ground state with m quanta of a totally symmetric mode excited can be written

tbat the transition moment factors into an electronic term IMjO’l’ evaluated at a fxed nuclear position and a Fran&-Condon factor F, = [(m”p,)l*, so that

(4

i

According to eq_ (4)- the intensity distribution in the progression is independent of the triplet state spin level and given by pzFnr_ Hence, if an intensity change AZ, is induced by a population change .&Vi, say through some ODMR experiment, the ratios bZJZ_.,, will be constant and independent of the member of the totally symmetric progression monitored. On the contrary, if non-constant AZJZ,,, obtain, then the intensity distribution in the progression is dependent on the triplet state spin level; the approximations leading to eq. (4) must be invalidi and non-Condon effects occur_ Low-order corrections to the elementary theory can be incorporated by an expansion of the transition moment in terms of the coordinate Q associated with the totally symmetric mode which forms the progression_ Retaining only the towest-order correction term and explicitly noting that emission (em) is being considered, Miz = M,‘“‘(m”lO’y> -I- Mj*‘
(5)

Eq_ (3) now becomes where P, is the frequency of the emission transition: X-f_ is the radiative rate constant; lY_ is the population of r,; and t is a constant whi& accounts for the experimental details and units Expressing the radiative rate in terms of the magnitude of the transition moment leads to

whem additional fundamental constants have been inciuded in c. Summing over the three spin ievets, the total intensity in the cold phosphorescence transition terminating in m quanta of the totaliy symmetric mode is (3) The usual and simplest appro_&ation

assumes

(6)

i

where the G are generalized vibrational factors for cold emission from 5; and given by e

= [(m-!O’)

+f;-(m”~Q~O’)]2.

(72)

Symmetry restrictions wilf with f;- = Mi”/nri(“‘_ generally dictate different A from each TV.causing the vibrational factors to become spin-level dependent_ Hence, different intensity distributions in the totalfy symmetric progression of a phospborescence spectrum obtain from each active spin-level for which f,#O_ If k=O, eq. (6) reduces to (4) and non-Condon effects are absent. However, if A + 0. the spin-level dependent vibrational factors cause non-Condon effects to occur_ for a cold absorpEntirelysinr2armsultsoccur

tion spectrum from the zero-point-level of the ground state to the triplet state with m quanta of the totally symmetric mode excited_ Thc~corre-

sponding equations for ibsoqkion

_ AEDFF’TlON

-.

-.

(abs) folIow

[]’

-dD/tf?=LO _ 5 .1 _

-.~

.

OS

and spin-level dependent viirational factors also

@aI

-. _-

_ oc _ _

(=I

occur in absorption if fi # 0. We note that the intensity distributions in absorption and emission for the spin IeveI ?;-are given-by the corresponding vibrational factors, but from the relationship of the Einstein coefficients with different dependences on the respective frequency factors (I”” a /Fern and I* a pFabs)_ To evaluate eqs_ (7) we assume that the progression forming, totally symmetric mode is harmonic in both the ground and triplet states; and that these normai modes in the ground (Q”) and triplet (Q’) states are simply displaced, thereby neglecting any rotation in the transformation (Duschinsky effect) [S,9]. Application of the recursion relationship for Hermite polynomials then yields

-~.

D=3m0

directly from eq. (5) by substituting 0”. and m’ for jMzlr = ** and O’, respectively.~ Hence, ;nMi’o,2F:~ with Fmy=

..

EM’SSION

Q’OA??TA

Fig I_ CaIItated vibrational factors in absorption and emission for a harmonic progression with equal viirational frequencies but displaced equilibrium mIucs of the vibrational coordi: nate in the (~‘0 states_ As the parameter d deviates from zero. the linear dependence of the transition moment on tbc vibralional coordinate increases_AU graphs refer to the same vertical scale if the single absorption graph noted is increased by a factor of CUD.

Fzp = [(1+11_@‘)(O”lm’) +~(ti/2o”)‘/z(1”1m~)]~. where in the triplet state, for mode is Q’ = Q - Q’ with @ and o* =_Zrrv’ the harmonic ing the origin of coordinates (S) can be written e

(8b) example. the normal the equihbrium value frequency_ By choosat (p + Q”)/2. eqs_

= [ (1 -t- Sd,D/fi)
-f- di
‘. (94

in terms of

the dimensionless

parameters

6=

(,‘/““)1/2,

(&/j#r-(@

_

dL= Q”)

f;r(h/20’)‘/‘.

and

D =

*_

Illustrativecalculations of c and F,zp based on eqs- (9) and the recursion formulas of Henderson et al. [lo] are shown in fig_ 1 for the case 6 = 1 and D = 3.00, which roughly approximate ~the parameters for the 3BI-tA, transition of NO.._ Similar results for different values of the patameters have been given by Craig and. Small [2]. The non-Condon effects are characterized by di- which is varied from 0 to *(e/D!, corresponding to Mjt’(F - p> varying from 0 to *2Mj”‘_ The

* In ref_ [6] chc-origins were chosen at 3.

and @* in rht vibrational factors for emission and absorption. t-espectitiy_

_

112

KE

Gotbeq. DS

liii / Non-Con&n effkct.t

absorption (emission) envelope for d6 > 0 is identical to the emission (absorption) envelope for d, -CO_

Only the case di -C0 is given in rig_ 1. The results show the welLknown mirror symmetry in absorption and emission for cc’ = & if di = O_ However. if di + 0 such symmetry is lost, Depending on the reIative signs of D and di, for smalI di the progression is either lengthened in absorption and shortened in emission or the converse_ The distortions of the simple Franck-Condon enveIopes are smaII and comparable at first in both absorption and emission as jdil increases from zero_ However. as [dJ becomes large the distortion becomes quite significant and more evident in either absorption or emission_ This again depends on the sign of dtDl sinceit determines for which transition the factor multiplying the normal Franck-Condon term in eqs_ (9) becomes < l_ Moreover. for di + 0 the sum of the viiratiocal factors over the prcr gression are unequal in absorption and emission and do not sum to unity [2]_ The model cakulations and resulting conclusions apply equally to a triplet-singlet system for a particular spin Ievel or to a singlet-singIet system_ In the latter case- non-Condon effects must be recognized in the distortion of - a normaI Franck-Condon envefope or by comparison of the corresponding enMopes in absorption and emission spectra_ The former is difficult unless the effects are quite b=e_ Accordingly_ Craig and Small [2] used a comparison of the ‘A,-‘;\, (S,-!&) absorption and fluorescence spectra to identify non-Condon effects in phenanthrene. How-ever. as noted by them, anharmonic and Duschinsky effects may be important in such a comparison. In a triplet-singIet transition the identification of nonCondon effects is less subject to the problems noted since the di are spin-level dependent and cause differeut intensity distributions in a progression for the different active spin IeveIs_ This can be recogg in either the absorption or emission spectrum without knowing the normal FranckCondon distribution- Differences in the absorption and emission enveIopes associated with the same spin IeveI will also occur, but their interpretation requires evahzation of the vibrational factors with model poten&& and accompanying assumptions_ The foregoing results are based on an empirical

expansion of the transition moment, The latter can obtain in. a singlet-singIet transition whenever a totally symmetric mode effects vibronic perturbations in a Herzberg-Teller sense and also forms progressions due to a displacement of its origin on electronic excitation [2]_ Since in a triplet-singlet transition the transition moment arises from spin-orbit coupling. the corresponding view would have the spin-orbit interaction dependent on the totally symmetric coordinate (first-order spinvibronic mixing [ll]). Siebrand and Zgierski [3] take an alternate view and explicitly consider a totally symmetric progression in a triplet-singlet transition_ These authors assume spin-orbit coupling to occur only between the pure-spin, adiabatic components of the triplet state and a singIe excited singIet state tid obtain a low-order expression for the transition moment within the harmonic approximation for the totally symmetric mode_ Comparison uith their results indicates that in Iow-arder for smaI1 di

In eqs- (10). &fi is the transition moment between the ground state and the excited singlet state that spin-orbit couples by the (orbital) mattix element Li with the 5; spin level of the triplet state; AEi is the energy gap between the excited singlet and triplet states: and Bi is a displacement parameter for the totally symmetric mode between the triplet and perturbing singlet states. Hence, the Fmi depend not onIy on the vibrational properties of the ground and triplet states. but also on the vibrationai properties of the relevant singlet state from which the ri spin level gains activity_ Non-Condon effects are thereby anticipated in triplet-stiglet spectra whenever the potentials of the spin-orbit coupled states are appreciably different and their energy separation not too large_ A separation of the contributions of the spin levels to the totalIy symmetric progression, yieiding the F,+ is needed for a quantitative analysis. This deconvolution can be effected by various

techniques. For example, polarized spectra in absorption or emission or time-resolved spectra in emission can be used in favorab!e cases. However, ODhlR methods under conditions that spin-lattice relaxation processes are neghgibIe reIative to phosphorescence provide a particularly convenient approach The relevant parameters measured by ODMR methods are the relative radiative rates k,:-. After correction for the wavelength dependence of the optical detector and for the frequency factor, these yield relative values of ]iW/“‘]‘~_ The three data sets from the three spin levels can then be normal&d and fit to eq_ (9a) with a single displacement parameter D and three parameters di_ the latter characterizing any non-Condon effects associated with 4_ Commonly in ODMR studies the relative radiative rates are determined only for the electronic origin and implicitly assumed to be the same for vibronic bands involving just totally symmetric modes This assumption is indeed often used to assign bands in a phosphorescence spectrum to the involvement of symmetric or asymmetric modes However, if non-Condon effects are occurring, the relative radiative rates can vary among bands involving different totally symmetric modes Nonconstant ratios of the radiative rates for such bands were first noted by Breiland and Harris [I] in the phosphorescence of tetrachlorobenzene, but they did not attempt to fit their results to any model.

3. Jkperimentai Crystals of neat NaNO, were grown from aqueous solution by slow precipitation or from the melt

by Bridgman in NaHCO,

techniques. (5

05%

by

Doped mass)

crystals were

of NO;

grown

from

an aqueous solution of the corresponding

sodium salts_ The crystal space groups with the site symmetries for the anion in parentheses are Imm2 (Cz,.) and C2/c (C,) for NaNO, [12] and NaHCO,

[13]. respectively. The instrumentation

used to record conventional optical spectra and to obtain and anaIyze zero-field optically detected magnetic resonance (ODMR) spectra and transients have. been de-

scribed previously- [6]_ A Nz laser vvti used as. a puIsed optic& excitation source for phosphorescence decay measurements and in conjunc- .. tion ‘with a boxcar integrator to obtain time%solved phosphorescence .sRect&_ The phosl phorescenee, fluorescence, and ODhlR inten.siti& for different vibronic “lines” were integrated over the zero-phonon linewidths, either direc$y by

measurement

of the areas for optical

spectra

re-

corded with a spectrometer slit-width Iess than the linewidth or indir&tIy for optic&l spectra and .. ODMR signaIs by using a slit-width sufficiently greater than the Iinewidths_ Corrections for the spectrometer sensitivity and the frequency factor of the vibronic band were applied to obtain relative vibrational factors in emission_ Intensities in optical absorption spectra were determined as the product of the peak absorption coefficient (in relative units m-‘) and the full linewidth at half absorption (in units s- ’ ), and then corrected for the frequency factor to obtain relative vibrational factors in absorption-

4_ Results

?_1. Optica

spectra

Both the emission and absorption spectra associated with the 3B,-‘A, transition .were obtained for neat NaNO, at 4 K as a prerequisite to extracting the vibrational intensity distributions_ Since the spectra are generally well-known [14-161, we mainly summarize our measurements, focusing on some new observations_ The intensity distributions are presented later. Part of the normal (photostationary state with ‘B, + ‘A, excitations) emission spectrum of neat NaNO, is shown in fig 2 with the three progressions in the totahy symme:ric bending mode, D: = that constitute the phosphorescence 830 cm-‘. spectrum noted. As in the fluorescence spectrum [17,18], whose long wavelength tail is also partially seen in fig_ 2, v:’ progressions 3re seen in the phosphorescence spectrum based on the origin at p0 = 18960 cm-’ (vacuum) and on one quantumof the totally symmetric stretching mode. P;’ = 1330 cm”; with the latter progression of much lower

I

I

I

800

I

!

I

700

600

WAVELENGTH/nm

intensity_ However, in the phosphorescence spectrum an additional weak P$’ progression occurs based on one quantum of the asymmetric (b) stretching mode. P;’ = 1240 cm-‘. This latter progression has z3nintensity ti polyaystalline sampks slightIy greater than the progression based on v,, f P:_ Howexr, whereas portions of the former progressions have been prcviousiy reported [14,19], the lattex pi-ogre&on has not, since its maximum intensity oc&s in the previously unreported long wavelength tail of the phosphorescence emission_ AII three corresponding progrrons have been reported for the ‘B, +‘A1 absorption spectrum [24.16& We note that our samples of NaNQ_ +d not show the flue rescence lines assigned by Yamanaka et aI_ 118) to Na: perturbed by NO,impurity_ Since our phosphorescence measumments extend to longer wavelengths, we give -in table 1 a complete viironic analysis of the zero-phonon Lines_ The ground state vibrational cncrgies were fit to

are given in table 2, and show good agreement with previous determinations from emission spcctra [i4]. The mean error between the observed and

where l, m, aad n represent the quanta of P?, z$‘. and P;‘, zspectively, and xi; arc anharmonic correction ternls_ The extracted viirational constants

527-27 55139

18960 18131

0 829

5643 567.1 m-73 5912

177l6 17629 17304 16896

1244 1331 16% 2064

p; v;: 2-F m;i-1;

594-78 606.73 621.70 62535 638.67

xscl8 16477 16080 15987 15653

2152 2483 2880 2973 3307

r"+ Z I m" 3r," ry+zm,v;+2w; 4wg

655.07 659.13 674-W 69212 696.69 7lX61 733-441 738-71 75x90 779.85

15261 15167 14831 14444 14350 14010 13631 13533 13191 12819

3699 3793 4129 4516 4610 4950 5329 -5427 5769 6140

p-+3-" 3 1 ,;+3v,5r:' *;1"+41; q+4r; 6~; p;+5r," .;+51; -7-2" .r;+ir;

785.89 808.04 8324

1272X 12372 12010

6239 6588 6950

-r"t6r" I I 8~; r;+7*;

r;

--

.-

.’

-_

z-’

_Table2.

..

vibrational consall ‘A; s_tatesof N4_

_.-‘:ff

;

.

NaNa_

‘B,~.

-18960..

‘0 *z ~.

18058

.--0.6

‘1+x11 % r3+x33

-%z =2L +3

cakulated

NaHC02/h’0,-

644”

+2 ‘A,

~-‘

ts in an-’ for the excited ‘Bi and ground .from 3f$-k, spectra

:

1303 820.6. 1226. - 6.6 -0.85 -112

1330 829-7 1242 -6-i -077 -8-6

wavenumbers

_

for

based

the phosphorescence

on

I 600

I

: -- i7238 16832

60883 623.87 64.975 65696

16420 16024 15602 15217

1 829

:

I=6 1638 2034. 2436 2841

:

_P;

‘.-..

1

29:’

WAVELENGTH

/ nm

:--~.

v;‘;‘.r:

__,

3p; .~ ..:-p..+2p.,~

-r

3

660.76 675.99 693.81 698.12 71531

lsl30 14789 14409 14320 13976

2927 3269 3649 3736 4082

p”+29” 1 2 4vi’ _. u;S’t3x7:* .p..+3pT. _ 2 ~~.. &F

734.63 739.87 759.37 780.63

13608 13512 13165 12807

12706

4450 4544 4893 5251

5352

aq+4v; r”i4%-; 6;;.. v’3 + sv-: 2

v;+sv;

809.13 865-78

12356 11547

5702 6511

7V:’ 8P:’

786-81

-~

.-

sented. The weak phosphorescence of NaHCO> NO; at 4.2 K, tune-resolved from the overlapphrg and normally much more intense fhrorescence, is shown in part in fig. 3 *th its complete vibronic analysis presented in table 3. Two progressions in v$’ are evident in the time-resolved spectrum. The more intense progression, part of which was de: tected previously in the normal emission’[23]. is assigned as .v,,-mv;l built on the Origin at v0 = 18058 cm-r_ The weaker progressiorr~wbich~ was not detected in the normal phosphorescence,‘is.

‘

700

-.

-n-. -:_ ._-_

r3

3

the -vibrational constants is 5 1 cm-’ and witbin the measur*ment uncertainties_ Table 2 includes some of the corresponding vibrational consttts in the 3B, state of &NO, obtained from our measurements of the absorption spectrum_These constants also agree with previous determinations[14]. However_ the correlation with the observed wavenumbers is Fomewhatpoorer for the 3B, than the ‘A, sta;e_ The origins of the 3BI-xA, transition agree in absorption and emission, indicating that the emission occurs from the bulk crystal rather than traps. Other evidence indicates that these triplet excitons are mobile in NaNOz [20-223. The normal phosphorescesce of NO; -in a NaHCQ host has also been previously reported [23]_ However, due to its very low intensity, only a partial and tentative vibronic analysis was prelines

579.94 5939.5

I 800

,

..

assigned as q,-~;‘-m~~_ Table 3 also contains measurements for a third P;’ progression observed vveakly only in am-PMDR [24] action spectra (vide -. i&a) and assigned as &+Hw;‘_ The ground state vibrationd constants for Naz in NaHCO, were extracted from the data in tabie 3 and are included in table 2 The constants are in good agkement with available constants from anaIysis of the fluorescence spectrum of NaHCQJNQ; [23] = and yield the vibrational energies from the phosphorescence data to within meaSurrmcnt errors_ The constants are ako vety reasonabie relative to neat NaNa_. the major difference being an increased anharmonic constant x; in NaHCOJNq_ The anaIysis of the phosphorescence spectrum in neat NaNC& is unambiguous given the coincident origins for the 3B,-xA, transition in absorption and emission and the known ground state fundamentak from infrared and Raman data [25]_ The situation is Icss definite in NaHCOJNO;_ No other consistent assignment for the final states of the observed phosphorescence Lines appears possible, and only a single excited state seems to be invokd. However, the assignment of the initiai state in NaHCOJNa: as the zero point level of the sBr state remains an assumption, albeit reasonable We note that relative to neat NaNO, [M-X?] the ‘El, and 313, states are respectiveiy red-shifted by 325 and 902 cm-’ in NaHCa_. 937 and 811 cm-’ in KCI (261. and 1042 and 913 cm-’ in KI !26]. showing a larger 1B,-3B, energy splitting in NaHCa_ (7591 cm-‘) than in the other hosts ( t 700 cm- I)_ 4-L am-PMDR

16073~ MHz) [27] In NaNO, 12500; q-5, the ODMR line&apes appeared lorentzian, which has been explained in termsbf motional averaging of triplet excitons [20,21], ‘whereas fin NaHC0.J NOT the ODMR signakshowed evidence of r4N h_vperfine interactions_ In both systems the ODMR frequencies and lineshapes were independent of the phospho rescence line monitored_ However_ the relative ODMR signal intensities were not constant in either system within the main J$’ progression based on the origin_ Figs_ 3 and 5 .show for NaNOz and NaHCOJNO;. respectively, am-PMDR spectra for members of q,-m$’ for modulation of the rc-r_ and ~~-7~ transitions_ In both systems the q-r__ and rx-yW am-PMDR spectra show different envelopes for the P; progression_ Each ~~-2~ spectrum resembks its respective normal phosphorescence spectrum, and for NaHCOflO; its timeresolved spectrum which is included in frg_ 5. However. the 5-5 spectra are anomalous, being evident in NaNO, particularty at high moduIation Tr-7_.

2.86 C?t. IOOr,--cm

spectra and kinetic parameters

The &ree expected ODMR resonances were detected at the previousIy reported frequencies in NaNO, (r--r=, 2865; s-rr, 12241; ~~-7~. 15106 MHz) [21] and in NaHCOJNO; (T~-T=, 3573;

t 0

I I

I 2

I

3

I 4

I 5

I 6

f 7

I 8

Q'_'ANTA of am-PMDR qxctm of the q,-ms$’ pro@-cGon in N&a_ at 12 K with an optical detector _’ slit-width of = 05 IIIZ Fig 4. Comparison

::

.~

16.073 GHz 265 Hz-m

Fig 5. Compllrison

of time--htd

spectra of at 12 K with an

and am-P.MDR

the ro-mw;’ pmgrcssl ‘on in NaHCOJNO; opticaldcrmor slit-uidh of = 05 nm

frequencies. Discounting the electronic origin in NaNOz because of possible problems with self-absorption, the rX-s spectra have a ‘signal intensity minimum or a change in the sign of the signai around the middle of the envelopeIn NaHCOJN~ the minimum occurs where the normaI or time-resolved phosphorescence spectrum has its maximum signal Hence, AI,Jf,,, for the ~~-7; transition is not constant in.eitherNaNO?

or NaHCOJNOj-_ As discussed earlier, a dependence of A1,J1,,, on -viirationaI quanta within a totally asymmetric progression signals a breakdown of conventiond theory and the occurrence of non-Condon effects. Since the -variation in Al,/I, is. rather large, partktdarly in NaHCOJNO; .: the vibronic assignments were, presented in -some detail to em-

phkize that ‘the monitored progression is correctly assigned. Further, the optical resolution. (5 10 cm-‘) used in. comparing the nor@ amPMDR tqinimiz~ the possibiiity of

letns with unresolved site% -,The laker- $ .iqrgkj~ .I: elimikted in NaI-ICOJNO& by. thii 1si@c_ Site_ seen in t+e Iow-field ODMR study, [27],-and seems -. equahy remote for .the exciton-in NaN02._ Hen=we ‘conclude that non-C&don effects are._asscki- 1 ated with the vz coordinate inthe 3Br-‘A1- tranktion of NO;- in neat NaNO, tid in a;NaHCai

~. host. . To clarify the anomalous behavicr .of .bi,/i, requires a deconvoiution into the intensity distributions associated with e&h spin IeveI. of the triplet state. This Was effected in NaI-ICOJNO~by analysis of ODMR induced transients; -which yielded the kinetic parameters and the vibrational factors for tw0 of the spin-levels of the 3R, state However, problems occurred using these meth&ls in NaN4, causing us to turn to- the absorption. spectrum to obtain the vibrational factors (bide infra). The ODMR transients in NaNOz at 1.4 K were not consistent with three uncoupled. spin levels,_ each characterized -by an exponential decay. law_ For example, the recovery of the rX-s--MODOR 1281 transient monitoring any of the more-intense members of r+mv$ was not a simple difference of two exponential terms. Rather, three exponential components were required to fit the signal with rates (and signs for the pm-exponential faotors) of =1~10~s-‘(-+),~x10~s-r(--),-and1x10’ s- ’ (-)_ x lo3 S-’ and respectively, but the signal to noise realized in these cases did not allow firm conclusiors regarding the decay law_ Based mainly on the ?;-< MODOR data;.. we con&de that the lneasured rates are not simply depopulation rates ki of *be isolated spin leGelse-+ Perhaps himolecular decay processes (triplet-triplet annihilation) 1221 or spin-lattice rekxation processes [29] are significant for the exciton in NaNOz_ The ODMR results in NaHCOJNOFdid -not present the inconsistencies found in NaNO,. The total depopulation rates ki were determined moni-. toring members of ~o-mz$’ from the phosphor-es- -m cence decay following pulsed excitation and from the transients induced by pumping the r~-< and ?---7: transitions at photostationary state or during

= 2 x lo3 s-l,

.’

_.

-.

*he phospho fescence decay_ A consistent set -of rates was obtained with mean vahres at l-4 K for k, and k= of (I.36 A 0.1) X 10’ and (3.15 f 0-l) X lo3 s-l, respectiveIy_ These rates were not significantly different at 42 K, indicating that spin-lattice reIaxation pare effectively suppressed at -Z 4 K The rate k, was more difficult to determirieandonIytheIi&tk,>:lxlOS s-r could be established. due in part to the Iow signal to noise at the required bandwidth_ However, aI1 data were amsistent with this Iimit The rates k, and k_ were independent of the particuIar member of pO-mpF monitored The reIative radiative rates kf:, for r, and 5 were aho extracted from the ODLMR transients in NaHCOJN4_ For the main P$’ progression for m = l-7_ The kf6 were determined from anaIysis of LMODOR and fast-passage [303 transients at photostationary state using the ~~-5 and rx~V transitions with the ki taken as the mean values given above Within the experimentaI errors engendered by the weak phospho rescence intensity, the reIative ki:, determined by the various methods agreed_ However* we emphasize those determinations for which the better signai to noise wz achieved_ The latter obtained for k&, and k& in the r--r, MODOR signal. and the resulting ratios k:Jkz, are given in table 4_ For a series of measurements under constant conditions save for the wavehmgth setting of the opt&I detector the data also yieId the dependence of ki’ on the quanta m of vg, namety the Fmi. after correction

Fig 6- Cakdarcd (bar graphs)axxtobsa~zd (poinu) vibraLional facrors for the main r2 ptqmsion in abrarptionand em&ion for the +-IA, syzsm for SK in NaHC~__ The dam were obtained from ana!ysis of the r,-> MODOR vansialts (0); the ---‘I- fast-passage uansicms (1); and she timeresohd pbospho(A)_

for the detector sensitivity and the frequency factor_ The F,, and F,= so obtained are shown in fig_ 6. Good signal to noise for F,= was ah obtained from the ~-4~ fast-passage signah., and these results are inchided in fig 6. The F,, present a seemingIy normaI distribution, whereas the F,, are highly anomaloLls The k&, data can be directly compared with the time-resolved phosphorescence spectrum obtained at long times in the phospho rescence decay since k, -S k, or k,_ The endopes obtained from the k:, data and the long-time v,,-mvz intensities are compared in rig 6 and are essentiaIIy identical, as requinxL A veq simihu uncorrected distribution obtains for the am-PMDR spectrnm shown in fig 5 modulating the r--r, transition. since for the moduIation frequency used (< k,) the sigtd in-

and possible failure to achieve n&

tens&es are r&hly &qxxtio~ to k&,/ki_ A phosphckescence spectrum from just 5, required to directly check the k,‘, data; .couId not be_ obtained -from the- time-resoIved phosphorescence spectrum at short times since the populating rates at the N, _laser excitation wavelength favored T-_ However, the k& data could be indirectly checked against the intensity changes induced from resonance (with “saturation’~ of the 7,-r= frequency modulated microwave power) and satisfactory agreement was obtained. The rate constants associated with -rl- were not accurately determined as -a function of vibronic band because of the signa&t+noise limitations noted earlier. Instead, we concentrated on the ~-3~4’ band where the magnitude of the r--‘;-, signal is maximum. The rate k, and the ratio k:/k: were estimated for this band by analysis of the optical transient caused by switching on the microwave power at 1~ k;’ during the phosphorescence decay_ If the T---T~ transition is suddenly saturated at t = t’ ze k;l and saturation is maintained during the remainder of the decay, then the difference between the perturbed and unperturbed decays for t > t’ is given by

saturation. of.. Additional observations also in&- 1.cated ky w A-, or k,. For example, the~intekity of.“.the time-resolved phosphorescence spectrum for-:..{ t = k;‘- in a polycrystalline sample is greatly rei -. duced by application of a static magnetic field, as expeCted from Zeeman mixing .with a short-lived spin level. We note that k, B k= or k,-is 9 the expected ~result b-ased on the non-radiative contributions since only the rY spin level of the ‘B, state _ can directly spin-orbit couple with the ground state. No kinetic data were obtained monitoring the much weaker I$ progressions in NaHCOJNOg based on the false origins F~-u;’ and uo-$_ -Both progressions were detected in am-PMDR spectra and showed different sensitivities to the ODMR transition pumped_ The vo-v;‘-mv~ series was detected on1y in the ~~-5 am-PMDR spectrum, wherein an intensity increase was obscrvcd. The Y0-v”-mvF series showed an intensity decrease for 3 r--yy and no detectable change for T,-T__ However, the signals were not investigated in greater detail.

bl_=cN,Oexp(-k,t’)

Although the contributions of the individual spin levels to uo-mvT in the phosphorescence of NaNOz could not be extracted, comparable results were obtained for p. + mv: from polarized absorption spectra with E II~ and E III_ These yield the p. + mv$ envelopes associated with T= and Q respectively, for a 3B,-1A, transition_ The v$ progressions based on p0 + vi and vo+ v$ were too weak to obtain good intensity data. The extracted vibrational factors FzF and &$ for.v, + mv; are shown in fig. 7 and are slightly, but distinct3y, different. peaking at big&r quanta of v; for -, than ?;_ This difference. also evident in published spectra [16], is in qualitative agreement with the non-constant- AI-/I= data from the emission sp&rum.in that both indicate the occurrence of non-Condon effects in the 3B,-1A1 transition. The observed -polaization ratios are summarized in table 4. The expfkmental ~Fzp were fit IO a-harmonic Franc&-Ckindon distribution (& = 0) using the measured fundamental frequency for z$’ : (829

x {t(k:,+k_;,,,)

=p[-+f(k,+k,)(t-t?]

--k&,

-

exp[

-k,(t

t’)]}.

(12)

where 1%‘: is the population of T-- at t = 0. If tbe t-~-r transition is not saturated by the resonant microwave power, then the first term in braces becomes a sum of two exponential terms with rate constants and pre-expo nential .factors dependent on the degree of saturation- The important point in our case is that for near-saturation conditions one of these terms dominates and for this dominant term eq. (12) approximately applies. A signal which appears to be a difference of two exponentiaI decays as predicted by eq_ (12) is observed for pumping of the T--? transition at our maximum available power- Its anaIysis in ternk of eq- (12) with k, as given earlier yields k;;/k: 2 10. and ky B 1 X 10’ s~‘_~The~limitsresidt from the bandwidth of the detection system, -which may have caused some “clipping” of the fast component,

the transition

4-R Analyses

Gf vibrational

factors

Fig 7 also shows experimental vibrational factors in emission for v&mv;’ and-q+vj’-mv~‘; These data are from polycrystahine NaNa_ at 4-2 K and. therefore. represent uaverages.. over the active spin levels. The two emission progressions should nevertheless have identical intensity distributions in lowest order, whereas the results again show different enveIopes. The enveIope for P,,v;‘-mv: has a more nearIy normaI Franck-Condon distribution than that for vo-mvz; for which a minimum occurs near six quanta of ~2. The vibrationaI factors for vo-v;-mu; were also fit to a harmonic Franck-Condon distribution. using the fundamental frequency for ~5 (64.5 cm-‘) and a mean frequency for vg (823 cm-‘) and neglecting members with m < 3 since their intensities were uncertain due to overlap with underiying broader features *_ The fit. included in fig 7. yielded D = 337. which agrees with er ex-uacted from the absorption data The vibrauonal factors were &so detzmined for P~-Y;‘-~zP:’ and its envelope more cIoseIy resembled vo-mvz than vo-v~-mv~_ However. the errors involved were larger, due to the Iower intensity and greater linewidth. and the results are not included in fig 7_ The preceding results can be qualitatively interpreted in terms of the known active spin levels in :he 3B,-‘A, transition of NaN02 and a model for the non-Condon effects. Hochstrasser and Marchetti (141 concluded from optical Zeeman data that 7r is the predominandy active spin Ievel in bands of Q + P; + mvg while r= is most active for p0 -I- mvi_ The latter agrees with our own polarization measurements, and those of others

an-‘) and a mean frequency for P; (640 cm-‘). yielding or = 336 and 0, = 3-60 where the subscripts identify the spin Ievel and D >0 is assumed in accord with expectations [31f. The caIcuIated factors are induded in fig 7 and show reasonabIe agreement ~6th the experimental results_ However. since the required displacement parameters are different. we view the agreement as somewhat fortuitous and as indicating the difficulty of inferring non-Condon effects simply from distortions in an intensity distriiution from a Franck-condon enve.Iope

[15,16,20], which indicate’ for p. +-_mv$ that ]M~“‘]2/1it4~o’]’ = 2.0. Assuming that alI spin levels are populated in the photostationary state at 42 K, these sami relative activities should also be manifest in the phosphorescence spectrum. Hence, based on the latter expectations and the very similar D values for _v& + rnv; with E II z (T,.) and ro-v;-mr” I* rr does not appear to show non-Condon effects. This conclusion assumes the correctness of the Franck-Condon factors (harmonic approximation with neglect of Duschinsky rotation) and neglects any complicating effects caused by spin-orbit-vibronic interactions [3]. On the contrary, po-mv;’ arises from r,. and rz and its envelope is anomalous. Hence, the -averag& non-Condon effects appear to be associated more with T= than T, and to act to lengthen the main r$ progression in absorption and shorten the corresponding v’* a progression in emission from that expected for a harmonic Franck-Condon distribution with D = 3_4_A predominant perturbation of rz also agrees qualitatively with the more constant ?a1,,,/1,,, for the ~~-7,. transition than the T-~-T= transition_ We attempted to reconcile all of the available data for NaNO, with a model wherein non-Condon effects occur only for 3, taking D = I?._= 3.37 and d=-_L d-I_= dx = O_ We fit the Y,,+ mv: data for t_ to eq_ (9b) and the P,,-mr$ data (neglecting the origin because of possible self-absorption) to a sum of two equations of the form (9a). correspond ing to contributions from an unperturbed r,_ (and r-) and a perturbed r=_ Fair agreement, as shown in fig_ 7, obtained for d= = -0.47 with the “averaged” emission containing 7% 3. (and T=) and 93% T=_ The vibrational factors calculated for v,,-m$’ for pure 5 emission are also shown in fig. 7_ Comparison of the latter with the calculational results for T= in absorption shows the considerable distortion from umirror-symmetry~ caused by the non-Condon -effects. The parameters D and di characterizing the vibrational factors for NaNOa are summarized in table 5. In NaI-ICOJNO; the vibrational factors of ro-mv:’ were also anomalous for r-, as evident from %g 6. We interpreted these data also by assuming that non-Condon effects occur only for 3 and employing eq. (9~)~ For ~5 we used the

Table5

:

-’ progressionior

thk.!3B,-‘~,

T~tiOIl

Parameter

‘B,--‘AI 3B,--‘A1

D -. Dd,

q+ra NaNa: 278 =’ 337 - 0.47

oi NO;

.-I_

:

_

.,_

N~HCOJN
I -. : :

..

~. -__

a) Ref. 1321.

fundamental frequency (626 cm-‘) in the t Bt state [23] and for vy the mean frequency (814 cm-‘) in the ground state. From a fit of the t- data from the Z-~-S MODOR analyses and the time-resolved emission, D = 320 obtained_ The r, data from the T~-T-. MODOR and fast-passage signals could then be reasonably accommodated with D = 320 and dz = -0_95. The data point for s with m = 7 _&as neglected in the latter fit since its experimental uncertainty was significantly greater than the other data points. The caIculated factors are compared with the experimental factors in fig. 6 and the parameters summarized in table 5. Based on the calculated factors, in NaHCOJ NO; the members of v,-mug with m = l-6 constitute 24.6 and 42.7% of the total sum for the progression from 5 and T,, respectively. Using these values to correct the corresponding truncated sums of. the experimental data leads to the estimate JMj”‘jz/j~~~*)]’ = 8.2_ This does not significantly differ from the mean of the ratios given in table 5, which equals 62 for m = l-6 and 8.6 for m = l-7_ Assuming that non-Condon effects are absent for rrI the single determination k_t/& 110 for ve-3~; gtven earlier then abows the conclusion ]hfj”]’ = ]M_,!“)lz2 lO]M~*)]* for the 3B,-1A, transition of NO; in NaHC02, in qualitative agreement with neat NaNO,. The displacement par-ameters concluded for the transition of NOT in NaNa_ and 3B,-‘A, NaHC4 are roughly equal (337 and 320, respectively)_ Kokai and Azumi [32] obtained. D = 2.56 in NaNO? from a harmonic Franck-Condon an& ysis of vo-rnv; data. However, they only considered m < 4. for which our phosphorescence ~data also show a good lit to a harmonic Franck-Condon. distribution and yieId p = 2% .. Deviations from this distribution, and the inadequacy of &n:

ICE Gxbqg

122

D-S

limi / Snt-Condo

pie Franck-Condon factors, onIy become apparent in&ding data for m > 4. Moreover, D = 3-4 is required by the absorption data in NaNOa. In comparison the ‘Br-‘A1 transition of the trap in NaNwAg+ bas D = 3.0 [6]. SimiIar displacement parameters in NaNa_ and NaHCOJNw aIso obtain For the ‘Bt-‘A, transition_ Our measurement OF the main VT progression in the fIuo_ rescence spectrum of NaHCaflCXj; yielded au apparently unperturbed envelope ufrth D = 2-90. while D= 278 aas found by Kokai and Azumi [321 in NaNO,_ Hence, l Lhe implied geometry changes upon excitation are roughIy equal in the two hosts and somewhat Iaq~er to the 3B, than the ‘B, state. The latter conclusion disagrees with Kokai and Azuu& but agrees with tbeoreticai [33] and avaihable experimental (341 bond anghs in the ground k, and excited t3Br states of the isovalent system SO,_ Using mean values for D of 2.84 and 328 For the ‘B, and 3B, states of NO; and the relationship given in reF_ (61 leads to increases in the bond angle of 135” and 15-Y. respectively. From 116O [12] in the ground state The corresponding values in Sa_ are = 4O and 6-7” with a ground state angIe of 119” [33,34g In contrast to the similar D values, the parameters d= characterizing the non-Condon eFFects associated with the pz mode and T= differ by a factor of two in

NaNO,

(-0.47)

and NaHCOJN@~

( -O-955

Further, d= For either system is larger than [dJ For the trap in NaNO-,JAg* (= 02) [6]_

5. Izcussion In both NaNa_ and NaHCOJNO; the rest&s show that non-Condon effects are occurring for the 5 spin level in the 3B,-tA, transition of Nar_ The Fred0 minant view is that the ‘i-, activity arises from spin-orbit couphng between the 3B, (z$ + ) states [14,1S]. aItIlougb mixa)andiEL(+C--T ing of ‘AZ (+ + n) character into the ground ‘A, state may aIso be important [7.35]_ We begin by considering the non-Condon effects predicted For the preceding couplings by the theory of Siebrand and Zgierski (sz) [3] in lowest order as given by eqs- (1% assuming for SimpIidty a constant vibrational Frequency in aII relevant states For mixing

effkfs

between the ‘I$ and 3B, states_ this predicts dZ/D=(/io/~)[E(‘B2)--E(3B1)]-*. x [Q(N)

- ~(‘BI)]

x [@Bt)

- a(‘A,)]

-‘_

(134

Mixing of 3A2 into the ground state leads to d=/D

= (h/ti)[ x [i?(‘&)

x

[8(%,)

E(3A,)

- E(‘&)]

--I

- ~(‘AI)]

- Q(‘&)]

--I-

(=b)

Using data For the bond angle changes in SOa [33,34,36] to estimate the required bD. d=/D -z 0 is predicted For either mixing in agreement with the experimentaI results summarized in tabIe 5 However, the predicted magnitude of dJD For reasonabIe values of the remaining parameters cm-‘) is so-05 and (AE = 3oooO 1371, 0=700 much smaller than required by the experimental Fits_ The preceding comparison is valid oniy in low order_ Sz present a more accurate approach than their truncated expansion, from which cqs. (10) and (13) obtain, based on spin-orbit interaciion between vibronic states_ Considering just the spin-orbit coupling with the ‘& state, this yields

04) if onIy the single totally symmetric mode p2 is considered and any nuciear coordinate dependence of the spin-orbit operator is neglected. Using parameters in the range of those indicated above, the envelopes caIcuIated From evaIuation of the sum in eq_ (14) aLso did not agree with the experimental resuIts_ In particuiar, the calculated envelopes were smooth with only a single maximum For m” c 10. even when the -&veIopes became severely distorted at smaller AE From a normal Franck-CoEdon distribution For D = 3_- However, this conclusion could be modified if spin-orbit COUFdiIlg with both ‘g and 3Ar states were important in the 3B,-‘A, transition moment, or if the ‘I$ state in NW were asymmetrIcally distorted as

: ICE

Go&-~

D-S_- 7inti / Non - Codon

in SO, [36] or !X& [38] wherein the r&_ state is strongly bent with a doubleminimum potential along the pj(bz) coordinate. We did not caky out detailed calculations along either pf these lines since the required parameters can at best only be estimated_ However, it seems likely that both of -&e above possibilities would in fact occur in NO;-. The reasonable fits obtained based on eqs- (9) do suggest that some me&nism is operative which causes the transition moment to effectively depend linearly on the + coordinate, leading to destructive interference of allowed and induced components in v,-mu$’ from s_ As previously noted, this could arise from a dependence of *he spin-orbit

interaction on the totally symmetric bending mode, so that 1!4:‘) a <(~%o(~)/%?)o)A~-l-I-he

anomalous distributions for T_ -wouId thereby be interpreted in terms of direct spin-orbit and firstorder spin-(totally symmetric) vibronic interactions of comparable magnitudes. First-order spin-vibronic interactions are usually neglected relative to second-order spin-orbit-vibronic mixing for asymmetric nuclear motions This apparently stems from the conclusions reached by Albrecht [ll] for the ‘zr* state of benzene, for which the spin-orbit interactions are very small while the vibronic interactions are large_ In cases where the spin-orbit interactions are large, such as states, the neglect of first-order for 3na* spin-vibronic mixing may be unwarranted for either asymmetric or symmetric nuclear coordinates. This could be particularly true in a triatomic system wherein the wavefunctions may depend relatively strongly on geometry and the equilibrium geometries even within C& symmetry can range from strongly bent to near-linear among interacting states. However, we are very hesitant to ascribe the observed non-Condon behavior, and in particular the very large effects for > in NaHCOJNq, to simple spin-vibronic mixing since rough estimates do not yield a sufficiently large effect. We have considered other possible explanations for the anomalous intensity distributions, but these were largely eliminated. We we.-e most concerned with selective (i.e. polarized) absorption of the phosphorescence radiation_ For example, the emission from 5 should be y-polarized and as such

_- :

-. .. -.:&--

effkcts

could be selectively absorbed by the. 3+, e3b, transition of NO; before exiting the_ NaNC$ or NaHCQ k-ystal. The energies involved .areI not c .i&nsisten~ with &is idea_ Thi minimum the phosphorescence occurs at = 15000 cm:‘, placing ‘.. the 3Az state at = 4.15 eV above the ground stated and near its c&mated energy 1371. However; we do not beheve’such selective absorption .by ~excited states of NO; resp&sible, ba&d on ~&imates of their possibie concentrations_ Recorded spectra of neat NaHCa_ and NaN02 also -eliminated the possibility of absorption near 15000 cm-’ -by- impurity ground-state species. in summary, anomalous intensity distributions for the totally symmetric bending progression associated with T= are evident in the 3B,-*A, spectra of NO; in NaNOz and NaHC02. The effects are considerably larger than seen in the same transition for a perturbed NO; trap in NaNO, doped with AgN02 [6] and appear intrinsic to “unperturbed” NO; _ The results can be reasonably interpreted in terms of a linear dependence of the stolen transition moment on the totally symmetric coon&at& but the detailed mechanism causing this effective dependence is unclear. Anomalous low-resolution am-PlMDR spectra have also been reported for the 3B,-‘A, transition of POT in KC1 and explained in terms of overlap of Y,,-znz$’ from T,. and q,-z$‘-mv; from TV [39]_ Such an explanation cannot apply to our higher-resolution data in NO;, which suggests that an alternate explanation may also apply in POT. We are unware of comparable data for the same transition in other members of the isovalent series and in uarticular for

in

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16: m

[Si [9J

[IO]

[Xl]

WJL Hamckcr. W_ Siirand ami hfZ_ Zgiaski. C&ZL PfkyL Leltas 68 (1979) 5; ADqn&V_L+u.acEhfigirdiqru~ChfijoukG_ Mxcwi. G_ Orlamli ‘.V_ Sickand and M-2 Zgicrski aan Fs>% 8s (198-a) 229_ KE GocbuB spd DS Timi. ,Moi_ Pb>x_ to be published_ SE CIak ad DS Tkni. Charr Phjx_ Letters 60 (1979) 292 F- Dm&imky. Acta v USSR 7 (1937) 551. GJ. SmaB_ I Ckan Phys_ 54 (l97l) 3300; EV_ Dok~omr. LA_ IbfalEn and V.I. Man-ko. J_ MoL spauy_ 77 (1979) 178: G. OIbticb and I-L Kupka. Z Naturforscb- 38a (1983) 937_ JR Hendason RA_ Wti ht hfuramo to and D-C_ _ Robyoum. Tables of immxmic Fran&-Condon o\&ap integrals irk&u@ displacamot of nofmal ccxmiilutcs. lku&s Report S%f45SO7 (DOU&IS Airaxft Co_ Sama mmka. 1964). AC_ AIbrecbt. J. Cban Ph>x 33 (1960) 1%. 169; 38

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