Volume 3. number 5 CHEI\IICAL PHYSICS LETTERS May 1969

CHANGE OF STATIC ELECTRIC POLARIZABILITY UPON TRANSITION

INTO EXCITED MOLECULAR STATES

K. SEIBOLD, H. NAVANGUL and H. LABHART Phpikalisch-chemisckes Instifut de7 Uniuersitltt Ziirich, Switzerland

Received 17 March 1969

The change of the static electric polarizability upon transition to the first excited singlet-state of crocetindimethylester. bixinmethylester, lycopene and p-dimethylamino+-nitrostilbene has been de- termined from measurements of electric field induced spectral changes. The molecules were solved in liquids as well as in rigid organic glasses at low temperature_ Preliminary quantum-chemical cal- culations of the change of polarizability upon excitation are reported for crocetindimethylester.

1. INTRODUCTION

In a series of papers changes of dipole mo- ments upon electronic excitation have been de- termined either from solvatochromic shifts [L-6] or from the influence of an electric field on the absorption spectrum 17-141. In these investiga- tions the change of polarizability has usually been neglected and up to now only few workers dealt-with this latter property, either experi-

mentally or theoretically. Abe 1151 determined the change of polarizability upon excitation of p- nitrpaniline from solvent shifts, whereas one of the$resent authors in a previous study [16] on nonpolar polyenes evaluated electric field induc- ed spectral changes. The aim of the present paper is to consolidate and supplement the pre- vious results by investigating molecules imbed- ded in rigid organic glasses, as well as to com- pare the experimental data with the result of one of our more recent calculations on polarizability change in polyenes. Furthermore we show that the change in polarizability also can be observed for polar molecules when they are solved in rigid glasses.

2. DETERMINATION OF THE CHANGE OF WLAF2IZABILITY FROM THE INFLUENCE OF AN ELECTRIC FIELD

Solved molecules, having a permanent electric moment or an anisotropic polarizability are par- tially oriented when a static electric field is ap- plied. Thus the absorption of light polarized at an angle x with respect to the field direction de-

pends on the strength cf the field F acting on the molecule and on x.

Usually

L=_x_ 1 x -I 2.30F2

is defined, where D is the optical density and AI/I the relative change upon application of the electric field of light intensity passing through tL.e solution. In this paper the field F is apprord- mated by the Lorentz-field, i.e.

F= l DK + 2 F 1 a’

where EDK is the dielectric constant and pa the external field. As shown earlier 1181, this does not affect appreciably the results when compared to the same molecular properties drawn from an evnluation based on the cavity field, as long as there is no contr3ution from molecular orienta- tion to the dielectric constant of the solvent.

Our experimental setup [9] alloxvs for the di- rect measurement of AI/l. For an isolated ab- sorption band the following expression derived by Liptay [12] connects Lx with molecular properties:

where

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Volume 3. number 5 CHEMICAL PHYSICS LETTERS May 1969

+3 cos2x-1 30

3&m - 3) i-

kT -

B, -9 (1) *A,u

i- (3 cos2x-1) 3(m-pcc)(m-Ap)-(pAj~) kT

_.- - + $(A@,- As) - +(2R 0) - 3R(2)) e Al4 ;

I

CX = 5(A~r)~ + (3 cos2 x - 1){3(rn- Ap)2 - <a~)~] .

E is the molar decadic extinction ccofficient of the compound, m the unit vector in direiYon of the transition moment, h, k and T have the usual meaning. am is the polarizability in the direc- tion of the transition moment, d the mean polari- zability, ktig and ,~a the dipole moments in the ground state and excited state respectively, AF = pa - Pg, and similarly A(Ym and A@ stand for the change of om and E upon excitation. The vectors R(l) and @2) arise from the first order perturbation of the transition moment by the static electric field and the scalars S(l) and SC21 account for the second order pe- rbation.

The contributions to + from dipole moments and from polarizabilities may be separated by measurements at different temperatures. In rQ,id organic glasses (EPA at - lS6”C, decahydronaph- talene (decalin) at - 14O’C) the viscosity is so large [19] t-hat relaxation times for orientation are much longer than seconds. This yields arl- other possibility for eliminating effects e,f orien- tztion .

2.1. iVun>oZar moleclrles . + has been measured for .y = O”, 54.8’ and

90° for crocetinciimethylester and bixinmethyl- ester solved in decalin at room temperature and in the rigid state at - 140°C. Crocetindimethyl- ester has additionally been investigated at -20cC, Iycopene in 3-methylpentane at 25OC.

These molecules having no permanent elec- tric moments, the third term in equation (1) vanishes and LX must be porportional to {d lne/@/dG. As fig. 1 shows for crocetindi- methylester, this behavior is found experimen- tally. Irrespective of the temperature at which the measurements were taken, for a given angle

x all the straight lines coincide. This means that the anisotropy of the polarizability does not lead to a detectable orientation and that these mole- cules l ae really nonpolar. The same behavior is found at 25% when the molecules are solved in dioxane. The evaluation, the steps of which we shall describe in a forthcoming paper, yields the data compiled in table 1.

If these molecules are solved in EPA, in the rigid glass, effects are observed which only can be explained if a change in dipole moment 5s as-

Crocetindimethylester

in Llekaiin

I _-

-Zoo 0 D I

40 50

/ dlnV,-

\dB

+25* 0 v +

Fig. 1. Li= Lv 1 - - - measured under different r 2.3DFE

conditions. Crocetindimethylester in dekalin.

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Volume 3, number 5 CHEMICAL PHYSICS LETTERS

Table 1

May 1969

Change of static electric polarizability of crocetindimethylester, bixinmethylester and lycopene upon transition to the first excited singlet-state

Molecule Crocetindimethylester Rixinmethylester Lycopene

Solvent Dekalin EPA Dekalin EPA 3 -Methyl- pentatte EPA

Temperature +25oc -2ooc -14ooc -196’C +25OC -14ooc -196OC +2S°C -196OC

As X lO24 (cm3) 172*10 172*12 172*6 174*8 223*12 223*16 234*12 246*22 234 * 12

(Aa, - AB) X lO24 (cm3) 338 * 32 338 * 45 338 l 11 353*22 446*24 446-144 446*46 480 f 32 446546

$1) x 1010 -15*6 -15*6 -15*6 -18*6 -18*6 -1-eI-6

(Am2 X 1O36 (esu2) 15.8 *0.6 18.6+1.2 23.3”l.l

(3(m. Qq2 - (Ap)z) 33.3*2.6 43.3*3.8 46*3.2 X 1O36 (esu2)

sumed. Then the polarizability clange within OK- limits of error comes out to be the same as in nonpolar solvents. The values of Aa as well as the changes of the dipole moments determined in this matrix are equally included in table 1. Tentatively we explain this result by assuming that the chains of conjugated double bonds are polarized by association kth polar solvent mole- cules. The change of the induced moment upon transition to the excited state then should corre- spond to the increase of polarizability. Indeed, the change in dipole moment becomes larger the larger is the change in polarizability.

2.2. Polar molecules The preponderance of orientational effects in

liquid solutions makes it impossible to determine the change of polarizability. However, in rigid decalin at - 140°C and in EPA at - 196’C with fi-dimethyiamino-fi’-nitro-stilbene, effects are measured, which, when plotted in the form L;(/[(d ln E [ c,)/dc] against

[(d ;;/‘g)2 + (d’ge/‘U)], d ;;/c

lead to straight line representations of the type given in fig. 2 for EPA. From the fact that these

4

Fig--2- (d &/ii)/dJ measured with p-dimethylamino-p’-nitro-stilbene in EPA at - 196oC.

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Vohnne 3. number 5 CHEWCALPHYSICSLETTERS Nay 1969

Table 2 Change of moiecular properties of P-dimethylamt~ -b’-nitro-stilbene upon transition into the lowest excited singlet

state fro-n meearements fn rigid glasses. -

Solvent Dekalin-glass

(- 14OOC) EPA-glass

(- 196OC)

l$pj2 X 1O36 (esu2) 334*14 334 f 14

(mAp)2-~1036 (esu') 333 f 30 328 f 30

(lAZ+@l)*A,U) X1O24 (cm3) 234*70 285 *SO

(3A~-~l).A~~~lp(~).Ar) x lo24 (cm3) 755 *195 585 l 85

lines do not pass through the origin it may be concluded that there is a detectable change of polarizability. The values evaluated with help of equation (1) are given in table 2. We assume the change of mean polarizability to be one third of the change of polar&ability in direction of the transition moment. Furthermore J&j and lpt21 are known from measurements in benzene and di- oxane to be 4 X 10m6 esu and 8 X 10m6 esu respec- tively, whereby the approximate C2v symmetry has been used. In this way the change of mean polarizability of fi-dimethylamirio-fi’-nitro-stil- bene upon transition to the lowest excited sin let state is estimated to be (150* 50) X 1O-24 cm !! . ‘rhisexperimental valuefitswellwiththetheo-

retical value calculated bz Kuhn, and Schweig [22] who found Aar = 157 X lo- 4 cm”.

3. CALCULATION OF THE CHANGE OF POLAR- IZABILITY

For B - nf transitions we considered it as sufficient to evaluate the change in polarizability of the n-system. In order to avoid the tedious calculation of matrix elements between states represented as linear combinations of different configurations we adopted the method which Schweig 1203 used for ca&&itions of polariza- bilities. Thereby the dipole moment is calcu- lated which results, when the electric field is directly incorporated into the PIltonian. Thus the ionization potentials of the atomic or- bitals are modified according to their relative- position in the field. The po%ntial differences correspond to a field &rength of about lo6 V/cm. Then, on the one hand, the induced dipole mo- ments were large enough compared to rounding errors in the calculation, on the other hand they were still proportion,r; to the field strength, and thus not affected by hy.perpoIarizabilities. The SCF-PPP-program wa used was provided to give excited state dipole moments directly.

278

Table 3 Calculated values of Ir-polarizability of crocetindi- methylester. The parameters used were pczo = -2.80 eV, Bczc = -2.66 eV,- PC+ = -2.26 eV. The y-values

are the same +s in a former paper [Zl].

ml, x1024 cY22 Xl024 90 1% AZX~O~~

State (cm3) (cm3) (cm3)

SO 113.0 1.8 -14.3 52.2

Sl 26%.8 6.5 - 3.3

From a series of calculations on polyenes we give the results for crocetindimethylester which can be compared with experimental findings. The components of the polarizability tensor have been evaluated by applying thr? field, once in x- direction, once in y-direction. In every case x- and y-components of the dipole moment are in- duced. Transformation to principal axes leads to the values compiled in table 3 together with the angle 81x between the axis of largest polarizabil- ity and the x-axis.

The calculated change of polarizability is about 3 times smaller than the experimental one. This discrepancy is probably mainly due to the fact, that in our CalcuIations configurations doubly excited with respect to the ground state but singly excited with respect to the excited state are left out. We plan to deal with this problem further.

Cur thanks are due to CIBA Ltd., Basle, for supporting this work.

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Volume 3, number 5 CHEMICAL PHYSICS LETTERS May 1969

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