Vibronic Activity of the Totally Symmetric Vibrations of Naphthalene

In document Rotational and vibronic effects in molecular electronic spectra (Page 144-148)

7B3G NP-D8.K 825 8B3G NP 08 K 495 5B3G NP 08 K 1036 6B3G NP-D8.K

3.4.6 Vibronic Activity of the Totally Symmetric Vibrations of Naphthalene

In allowed transitions, vibronic mixing by totally symmetric vibrations is a demonstrated effect in, for example, azulene [Lacey,

9

McCoy and Ross 1973] and phenanthrene [Craig and Small 196Ä], but there is a need for a wider appreciation of its incidence.

Our vibronic calculations have accordingly been extended to the a modes of naphthalene, but some further theory is first required. The

8

exposition below, while embodying the methods formulated by Craig and Small, is concerned with vibronic effects on total intensities rather than with the intensities of individual progression members and the

argument follows a different course, resulting in a differently expressed conclusion, to that of Craig and Small.

We assume that the ground and excited electronic states have geometries related by a displacement 6 along a totally symmetric

coordinate Q. For such coordinates there is no obvious choice for the origin of 0, and so for definiteness we adopt the following definition. Let the electronic transition moment for the transition between the two

states be a = a(Q) — the same notation as in Sec. 3.1.3, though for simplicity we ignore state labels. We also write a.Q = a(Qfr) for the transition moment at the geometry of the upper state iind aQ = a(Qg) for - that at the geometry of the lower. Over the range of Q of practical interest ve assume that a varies linearly with Q, with slope

m 3 a 3a iq-j Qo 3qJ Qtf (3.4.1)

Now define the origin of Q as that of linearly extrapolated geometry for which a = 0. Fig. 3.4d illustrates this, and defines new coordinates

Q" = Q - Q Ö (3.4.2)

Q ’ = Q - Q o = Q - Qo ” 5 (3.4.3) where

6 = Q ’ - Q" . (3.4.4)

Fig. 3.4d: Transition moment a as a function of totally symmetric coordinates Q.

Note that since the sense of Q is arbitrary, we may always choose it such that the relative magnitude of the transition moments in the two equilibrium geometries is expressed through 6, which is positive if ctg >a", and negative if a' < a " . Also defined in the figure is the mean transition moment

a 0 = ^(aj+a'o') = m Q 0 , (3.4.5) where

Q0 « 3i(Qq - Qq) - = Q ’ -%<5 . (3.4.6) For transitions v ’ - On and O ’ ~ v" (primes are added to keep track of the origins of the. respective vibrational wavefunctions), the vibronic transition moments are respectively

<v'|a|0"> = m<v ’ IQ10" > - (3.4.7) ( v"I a I 0 T > - m(v"IQI 0 ’ ) . (3.4.8)

For coordinates Q, originating at the rest position of an harmonic oscillator

Q 10> = (2ß)”^|l> , (3.A.9)

where

3 = 47r2vy/h . (3.4.10)

So, using (3.4.7), the coordinate QM and in coordinate Q*, we get

(3.4.3) the

< v ’ | a | 0M ) - ct^v’ |0n )+ (23”)"’^ ra<v* |l"> (3.4.11) ( v"|a|0 1 ) = aj<v"|0'>+ (23’)"^ m<vn |l’> (3.4.12)

Squaring, summing over v ’ or v" as appropriate, effecting closure and noting that (0[0> = < 1 j1> = 1 and ( 0 11> = 0 gives the total intensities

(omitting constants) as

Iabs = (a,J)2 + m 2/2ß" (3.4.13) b l u e r = («5)2 + m z/2B’ • (3.4.14) These equations may be recast with the aid of (3.4.5) and (3.4.6), to yield

Iab° = («ü+ ^ 2 ö 2 + m 2 /23M) - ^ 0 (3.4.15) Ifluor = ( S o + W ö Z + H i ^ a ^ + m ö ä o • (3.4.15) For the present purpose we assume 3' - 3” - 3 (whence the term m6a0 , produces the interference) and introduce

a* = 2 2 :n 0 # = (23)“'1 m (3.4.17) zpt

I

Now aK , in a calculation, is the change of transition moment evaluated at a displacement 2

‘zpt from Qjj (or Q^) If/ 0 is the ratio of the first to the zeroth progression members in a Franck-Condon

progression. Where vibronic effects are suspected, the ratio should be determined (from a spectrum) using a progression built on a false origin

(where vibronic effects due to other modes enter only in second order).

Using (3.4.17) and (3.4.13), v/e obtain

"abs f luor a g j l + (X 1/0i* 1 ) ( k\ a*

— ~ (x

y2

I6 I U l/0;

a*

0

*

0

- (3.4.19)

Calculations on naphthalene are now given in Table 3.4f. The most active vibration is 5a^; the total induced intensity is 20% of the intrinsic intensity.

Table 3.4f

Vibronically induced transition moments (in /\) due to totally

symmetric vibrations, in naphthalene. The calculated

value of q q is 0.1185. Frequencies in cm""1 .

Mode

V calc

a

Vobs l«*lb 103x(a*)2 |a*/a0 |

1 3065 3058 0.0148 0.2193 0.1249 2 3041 3025 0.0045 0.0205 0.0382 3 1603 1579 0.0242 0.5856 0.2042 4 1468 1465 0.0124 0.1538 0.1046 5 1418 1380 0.0291 0.8491 0.2458 6 1160 1148 0.0047 0.0217 0.0393 7 1014 1021 0.0169 0.2856 0.1426 8 720 765 0.0172 0.2972 0.1454 9 484 514 0.0200 0.4000 0.1687 Total 2.8329 = 0.2016 c^'2 a From Kydd [1969], b a*= \a (2-hQzpc)-«(Q0)|.

Mode 5a also appears to he the most: active vibration in the 8

[Stockburger 1973] one finds I ^ ^ = 0 . 6 , from a p r o g r e s s i o n built on the strong false origin due to 8 b _ .

' ■ ' O

Since we do not know w h e t h e r 6 is posit i v e or negative (to do' so, it w o u l d be necessary to compare p r o g r e s s i o n lengths in absorption and emission, as illustrated by Craig and Small [1968]), we use odj for and from (3.4.19) find for the p r o g r e s s i o n in 5a built on the origin

8 abs f luor fluojr \ b s 1 .097 + 0 . 3 80 1.097 - 0.380 -1-1.48 .

We conclude that vibronic activity due to m ode 5a^ is likely to be d e t e ctable in naphthalene. Unfortunately, the observed span of the abso r p t i o n s p e ctrum is short (it is soon o v e rlaid by a stronger

transition) and most of the intensity derives from false origins. The

f l uorescence is clearer, but the origin is normally self absorbed and its intensity not easily measured. Hence naph t h a l e n e is not the molecule we w o u l d choose to p u rsue these issues.

In Sec. 3.5 we investigate another, much more spectacular case of vib r o n i c interaction by totally symmetric interactions, in azulene, but there it appears that <5~0, w h ence I ^ q = 0. The interesting

transition moment interference effects are therefore not significant in that case.

3.5 VIBRONIC COUPLING IN AZULENE

3.5,1 Introduction

This section treats two transitions in azulene. Most attention

is given to the 3500 X transition to the second excited state, assigned Aj -A i, wdierein most of the intensity derives from a particularly strong

i nteraction w i t h a still higher Aj state; the a^ m ode m a i n l y responsible has frequency 1580 cm 1 (ground state value) but there are undoubtedly other v i b r o n i c origins, notably one near 1050 cm” 1 .

Sec. 3.5.5 deals w i t h the Bj-eAj (M-polarized) transition at 7000

X,

w h i c h has v i b r o nically induced L - p o larized intensity, recently d o c u mented by Small and K u s serow [1974].

In treating the 3500 X system, we note that Lacey, McCoy and

Ross [1973] concluded that Franck-Condon active v ibrations were not

In document Rotational and vibronic effects in molecular electronic spectra (Page 144-148)