Inorganic Chemistry: Toward the 21st Century - American Chemical

8 Excited-State Electron Transfer THOMAS J. M E Y E R

Downloaded by COLUMBIA UNIV on April 14, 2013 | http://pubs.acs.org Publication Date: March 3, 1983 | doi: 10.1021/bk-1983-0211.ch008

The University of North Carolina, Department of Chemistry, Chapel Hill, NC 27514

Many of the features of electron transfer reactions involving excited states can be understood based on electron transfer theory. In other c o n t r i b u t i o n s i n t h i s symposium, a c l e a r case has been made f o r the p o s s i b l e value of molecular e x c i t e d s t a t e s as a b a s i s f o r s o l a r energy conversion processes. Amongst p o s s i b l e approaches i n using molecular e x c i t e d states i s the f o l l o w i n g s e quence of events: 1) O p t i c a l e x c i t a t i o n to give an e x c i t e d s t a t e . 2) E l e c t r o n t r a n s f e r quenching of the e x c i t e d s t a t e to give separated redox products. 3) U t i l i z a t i o n of the separated redox products as a b a s i s e i t h e r f o r a p h o t o v o l t a i c a p p l i c a t i o n where the stored chemical redox energy appears as a p h o t o p o t e n t i a l , or a photochemical a p p l i c a t i o n where the stored energy appears as high energy redox products. In order to i l l u s t r a t e the approach suggested above, i t i s of value to consider a s p e c i f i c case. V i s i b l e or near-UV e x c i t a t i o n of the complex Ru(bpy)3 + r e s u l t s i n e x c i t a t i o n and formation of the w e l l - c h a r a c t e r i z e d metal to l i g a n d charge t r a n s f e r (MLCT) exc i t e d s t a t e Ru(bpy>32+*. The consequences of o p t i c a l e x c i t a t i o n i n the Ru-bpy system i n terms of energetics are w e l l e s t a b l i s h e d , and are summarized i n eq. 1 i n a Latimer type diagram where the p o t e n t i a l s are versus the normal hydrogen e l e c t r o d e (NHE) and are 2

(1)

3

Ru(bpy) + 3

R

u

(b

p

y

)

2 3

+

-

1

·

2

6

Ru(bpy)

+ 3

+2. IV 2+* 3+ -0.84 Ru(bpy) " " Ru(bpy)3 w

3

>

u

+0.84

Ru(bpy)

+ 3

w r i t t e n as r e d u c t i o n p o t e n t i a l s (]L) . In the reduced form of the couple, R u ( b p y ) , the added e l e c t r o n i s i n a ir*(bpy) l e v e l and i n the o x i d i z e d form of the chromophore, Ru(bpy)3^ , the e l e c t r o n has been removed from a dïï l e v e l . +

3

+

0097-6156/83/0211-0157$06.00/0 © 1983 American Chemical Society In Inorganic Chemistry: Toward the 21st Century; Chisholm, M.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

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The redox p o t e n t i a l diagram i n eq. 1 i l l u s t r a t e s that the e f f e c t o f o p t i c a l e x c i t a t i o n i s to create an e x c i t e d s t a t e which has enhanced p r o p e r t i e s both as an oxidant and reductant, compared to the ground s t a t e . The r e s u l t s o f a number of experiments have i l l u s t r a t e d that i t i s p o s s i b l e f o r the e x c i t e d s t a t e to undergo e i t h e r o x i d a t i v e or r e d u c t i v e e l e c t r o n t r a n s f e r quenching (2). An example of o x i d a t i v e e l e c t r o n t r a n s f e r quenching i s shown i n eq. 2 where the oxidant i s the a l k y l pyridinium i o n , paraquat ( 3 ) . (2)

R

u

Ru(bpy)

(

b

2 + 3


(PQ

p

)

y

3

2 + ^ 2 +

* + PQ 2 +

R

u

(

b

p

y

)

3

2 + *

— Ru(bpy)

3 +

+ PQ

3

= CH -N^)-

+ + DMA

3

= Me NPh) 2

In the case of e i t h e r eq. 2 or eq. 3, even though e x c i t e d s t a t e energy has been converted i n t o stored chemical redox energy, the storage i s temporary because of back e l e c t r o n t r a n s f e r between the separated redox products, e.g., eq. 4. (4)

Ru(bpy)

3 + 3

+ PQ

+

— * Ru(bpy)

2 + 3

+ PQ

2 +

A major dilemma i n any approach to energy conversion processes based on e l e c t r o n t r a n s f e r r e a c t i o n s o f molecular e x c i t e d s t a t e s i s u t i l i z a t i o n o f the stored redox products before back e l e c t r o n t r a n s f e r can occur. The net quenching r e a c t i o n i n eq. 2, which leads to separated redox products capable of o x i d i z i n g and reducing water, r e l i e s on a s e r i e s of e l e c t r o n t r a n s f e r steps. The b a s i c theme of t h i s a c count i s e x c i t e d s t a t e and r e l a t e d e l e c t r o n t r a n s f e r events which occur i n such systems and the b a s i s that we have f o r understanding them both experimentally and t h e o r e t i c a l l y . In order to begin i t i s u s e f u l to consider Scheme 1, i n which the quenching r e a c t i o n i n eq. 2 i s considered i n k i n e t i c d e t a i l . In the scheme, the assumption i s made that the only important quenching event i s e l e c t r o n t r a n s f e r and that energy t r a n s f e r quenching i s n e g l i g i b l e . The s e r i e s o f e l e c t r o n t r a n s f e r events i n the scheme a r e i n i t i a t e d by o p t i c a l e x c i t a t i o n to give the exc i t e d s t a t e and the e l e c t r o n t r a n s f e r r e a c t i o n s which occur f o l -

In Inorganic Chemistry: Toward the 21st Century; Chisholm, M.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

8.

Excited-State

MEYER

Electron

159

Transfer

lowing e x c i t a t i o n are: 1) Excited s t a t e decay to the ground s t a t e occuring by a combination of r a d i a t i v e and nonradiative processes (1/τ i n Scheme 1). Nonradiative decay i s by a l i g a n d to metal 0

Scheme 1 RuB

2 + 3

*

+

P Q

2

+

^ RuB

HK RuB

^PQ %^ R u B ^ P Q ^ â 2

" .. D k

2 +

+ PQ

3

2 +

( b p y ) R u (bpy)2 (dïï^). 2) E l e c t r o n t r a n s f e r quenching (k^) . 3) Back e l e c t r o n t r a n s f e r to repopulate the excited s t a t e ( k _ ^ ) . 4) Back e l e c t r o n t r a n s f e r to give the ground s t a t e rather than the excited s t a t e (k2). In any photoredox a p p l i c a t i o n based on e l e c t r o n t r a n s f e r quenching, l i k e the one i n Scheme 1, the c r i t i c a l f a c t o r s determining device performance are the per photon e f f i c i e n c y with which the separated redox products appear, and the u t i l i z a t i o n of the separated redox products before back e l e c t r o n t r a n s f e r between them can occur. The separation e f f i c i e n c y i s determined i n l a r g e part by the s e r i e s of e l e c t r o n t r a n s f e r steps described above: 1) Quenching must occur before e x c i t e d s t a t e decay. 2) Following quenching, the e f f i c i e n c y of separation of the redox products shown by k _n i n Scheme 1 must be r a p i d compared to back e l e c t r o n t r a n s f e r to give the ground s t a t e , k2« Clearly i t i s essential to understand the f a c t o r s which c o n t r o l the r a t e constants f o r such e l e c t r o n t r a n s f e r events. 2+

f

E l e c t r o n Transfer

Theory

The f a c t o r s that determine the r a t e of e l e c t r o n t r a n s f e r between chemical s i t e s are the extent of e l e c t r o n i c coupling between e l e c t r o n donor and acceptor s i t e s and the extent of v i b r a t i o n a l trapping of the exchanging e l e c t r o n by both intramolecular and medium v i b r a t i o n s . V i b r a t i o n a l trapping i s a n a t u r a l consequence of the e f f e c t s of changes i n e l e c t r o n content on molecular s t r u c t u r e . The point i s i l l u s t r a t e d i n Figure 1 where a p l o t i s shown of pot e n t i a l energy versus a normal coordinate f o r the e l e c t r o n t r a n s f e r system, D,A -> D ,A". The p l o t i s f o r a trapping v i b r a t i o n assuming the harmonic o s c i l l a t o r approximation. In order f o r a v i b r a t i o n to be a trapping v i b r a t i o n , the displacement between the bottoms of the p o t e n t i a l w e l l s i n Figure 1, A Q , must be nonzero. In the c l a s s i c a l l i m i t , e l e c t r o n t r a n s f e r can only occur at the i n t e r s e c t i o n between the two p o t e n t i a l curves because i t i s only at that point that energy i s conserved before and a f t e r the e l e c t r o n t r a n s +

eq


INORGANIC C H E M I S T R Y : TOWARD T H E 21 ST C E N T U R Y


160


8.

Excited-State

MEYER

Electron

161

Transfer

f e r event. The c l a s s i c a l energy of a c t i v a t i o n w i l l be determined by the thermal energy needed to reach the i n t e r s e c t i o n region, f o r a l l of the normal v i b r a t i o n s which respond to the change i n e l e c ^ t r o n d i s t r i b u t i o n before and a f t e r e l e c t r o n t r a n s f e r occurs. As noted above, there are two c o n t r i b u t i o n s to v i b r a t i o n a l trapping, one from the intramolecular v i b r a t i o n s of the molecule, which are normally i n the frequency range 200-4000 cnT^ and the c o l l e c t i v e v i b r a t i o n s of the surrounding medium, which f o r a solvent are of low frequency and i n the range 1-10 cm"^. In f a c t , e l e c t r o n t r a n s f e r occurs at the microscopic l e v e l where quantum mechanics provides the necessary d e s c r i p t i o n of the phenomenon (5-13). In the quantum mechanical s o l u t i o n , associated w i t h the p o t e n t i a l curves i n Figure 1 are quantized energy l e v e l s , Downloaded by COLUMBIA UNIV on April 14, 2013 | http://pubs.acs.org Publication Date: March 3, 1983 | doi: 10.1021/bk-1983-0211.ch008

Ej

=

(VJ

+

1 / 2 ) ^ 0 ) . , where v^

and

ajj

=

2TTVJ

are

the

vibrational

quantum number ancl angular frequency f o r v i b r a t i o n j . The cor responding v i b r a t i o n a l wavefunctions are X-:. In the quantum mech a n i c a l p i c t u r e the advantage of thermal a c t i v a t i o n to the i n t e r s e c t i o n region i s enhanced v i b r a t i o n a l overlap between the v i b r a t i o n a l wavefunctions f o r the i n i t i a l (D,A) and f i n a l (D ,A~) s t a t e s . The importance of v i b r a t i o n a l overlap i s that where i t occurs the v i b r a t i o n a l c o n f i g u r a t i o n s of both s t a t e s are allowed and e l e c t r o n t r a n s f e r can occur. The presence of the e l e c t r o n acceptor s i t e adjacent to the donor s i t e creates an e l e c t r o n i c p e r t u r b a t i o n . A p p l i c a t i o n of time dependent p e r t u r b a t i o n theory to the system i n Figure 1 gives a general r e s u l t f o r the t r a n s i t i o n r a t e between the s t a t e s D,A and D ,A~. The r a t e constant i s the product of three terms: 1) 2πν /η where V i s the e l e c t r o n i c resonance energy a r i s i n g from the perturbation. 2) The v i b r a t i o n a l overlap term. 3) The density of s t a t e s i n the product v i b r a t i o n a l energy manifold. In the c l a s s i c a l l i m i t where the c o n d i t i o n -ftu) > k 2 , k _ , back e l e c t r o n t r a n s f e r to give the e x c i t e d s t a t e i s r a p i d , and eq. 10 a p p l i e s . D

(10)

RTlnk

1

q

= RTln(k

f

_ + k )K -D I A 0

A

AGI

In the equations, k (0) i s the h y p o t h e t i c a l quenching r a t e con stant when ΔΕ (=AG) = 0 and AG^ i s the f r e e energy change on quenching. Eqs. 9 and 10 make c l e a r p r e d i c t i o n s about the dependence of quenching r a t e constants on the f r e e energy change i n the quench ing step. One way of t e s t i n g the theory i s to observe the quench ing of the e x c i t e d s t a t e by a s e r i e s of r e l a t e d quenchers where the parameters k^(0), K^, and k _Q should remain s e n s i b l y constant and yet where the p o t e n t i a l s of the quenchers as oxidants or r e ductants can be v a r i e d s y s t e m a t i c a l l y . Such experiments have been c a r r i e d out, most notably with the MLCT e x c i t e d s t a t e , Ru(bpy)32+* (1). The experiments have u t i l i z e d both a s e r i e s of o x i d a t i v e nitroaromatic and a l k y l pyridinium quenchers, and a s e r i e s of r e ductive quenchers based on a n i l i n e d e r i v a t i v e s . From the data and known redox p o t e n t i a l s f o r the quenchers, p l o t s of RTlnk q vs. E ° f o r the quencher couple show regions of slope 1/2 and slope 1 as p r e d i c t e d by eq. 9 and 10. In f a c t , the t h e o r e t i c a l equations appear to account f o r the observed v a r i a t i o n of l n k ' ^ with E ° s a t i s f a c t o r i l y . Given the agreement with theory, i t follows that i f an e x c i t e d s t a t e i s thermally e q u i l i b r a t e d , i t can be viewed as a t y p i c a l chemical reagent with i t s own c h a r a c t e r i s t i c p r o p e r t i e s , and that those p r o p e r t i e s can be accounted f o r by using equations and t h e o r e t i c a l developments normally used f o r ground s t a t e reac tions. q


f

f

1

f

T r a n s i t i o n Between the Normal and Inverted Regions. In the pre vious s e c t i o n , e l e c t r o n t r a n s f e r events were considered i n the framework of a v a i l a b l e theory f o r the normal region where -ΔΕ < X. According to eq. 6, as -ΔΕ approaches X i n magnitude, E ·*• 0, and there i s no longer a v i b r a t i o n a l trapping b a r r i e r f o r the exchang ing électron. With a f u r t h e r increase i n -ΔΕ, -ΔΕ > X and as shown i n Figure 2, one p o t e n t i a l curve i s "embedded" w i t h i n the other. In t h i s , the i n v e r t e d region, the s i t u a t i o n i s q u i t e d i f ferent from that f o r an e l e c t r o n t r a n s f e r r e a c t i o n i n the normal region. In the normal region, the i n t e r s e c t i o n region occurs out side the p o t e n t i a l curves. In the quantum mechanical view, ther mal a c t i v a t i o n i s d e s i r e d i n order to reach regions near the i n t e r s e c t i o n region where v i b r a t i o n a l overlap i s maximized. In the i n v e r t e d region, the two p o t e n t i a l curves are w i t h i n each other and v i b r a t i o n a l overlap plays a more important r o l e . In a d d i t i o n , because of the embedded nature of the p o t e n t i a l curves, emission can occur i n the i n v e r t e d region. The r e l a t i o n s h i p between e l e c t r o n t r a n s f e r i n the normal and i n v e r t e d regions i s i l l u s t r a t e d i n Figure 3 f o r the case of quenching of R u i b p y ) ^ * * by a nitroaromatic quencher. E x c i t a t i o n a



164

INORGANIC C H E M I S T R Y : TOWARD T H E 21 ST C E N T U R Y

Ε

Figure 2. Energy-coordinate diagram for the "inverted region" where — Δ Ε > χ.

1

Q

Figure 3. Energy-coordinate diagram for quenching of Ru(bpy) ** (RuB **) by a nitroaromatic (A rN0 ). 2

3

2

3

2


8.

Excited-State

MEYER

Electron

165

Transfer

of an a s s o c i a t i o n complex between the ruthenium complex and the quencher, Ru(bpy)3 ,ArN0 , would lead to R u ( b p y ) 3 * i n close contact with the quencher. E x c i t e d s t a t e decay of t h i s s t a t e by nonradiative decay ( k ^ i n Figure 3) can occur as an e l e c t r o n t r a n s f e r process i n the i n v e r t e d region. E l e c t r o n t r a n s f e r quen ching and e x c i t e d s t a t e repopulation (k^ and are r e a c t i o n s i n the normal region. The quenching step can be viewed as an i n t e r conversion between intramolecular and intermolecular charge trans fer excited s t a t e s — ( b p y ) R i ( b p y ) * , A r N 0 — • ( b p y ) R u ( b p y ) , A r N 0 ~ . The f i n a l process to consider i n Figure 3 i s back e l e c t r o n t r a n s f e r to give the e x c i t e d s t a t e ( k ) — R u ( b p y > 3 ^ , ArN0 *~ — * Ru(bpy>3 ,ArN02. This i s a l s o a r e a c t i o n i n the i n v e r ted r e g i o n and can be viewed as nonradiative decay of an "outersphere , charge t r a n s f e r e x c i t e d s t a t e . 2+

2+

2

I I

2 +

2

i n

2

2

2+

2

+

2

2+

2


11

E l e c t r o n Transfer i n the Inverted Region. Decay of an e x c i t e d s t a t e and e l e c t r o n t r a n s f e r i n the i n v e r t e d region are conceptual l y the same process (14). As suggested by the p o t e n t i a l curves i n Figure 2, there a r e three l i m i t i n g pathways a v a i l a b l e f o r e x c i t e d s t a t e decay, but a l l three are subject to the l i m i t a t i o n s imposed by energy conservation. Decay can occur by emission, i n which case energy conservation i s met by the l o s s of an emitted photon. Decay could occur n o n r a d i a t i v e l y by thermal a c t i v a t i o n to the i n t e r s e c t i o n r e g i o n between p o t e n t i a l curves, which i s the pathway i n the c l a s s i c a l l i m i t . However, decay can a l s o occur from lowl y i n g v i b r a t i o n a l l e v e l s of the e x c i t e d s t a t e to high energy l e v e l s of the ground s t a t e (Figure 2). Because of energy conser v a t i o n , the e l e c t r o n i c energy l o s t i n the t r a n s i t i o n between s t a t e s , e.g., ( b p y ) R u ( b p y ) 2 * —> ( b p y ) R u ( b p y ) , must appear as v i b r a t i o n a l energy i n the product. A c r i t i c a l feature i n determining the r a t e of the t r a n s i t i o n i s the extent of v i b r a t i o n a l overlap between the v i b r a t i o n a l wavefunctions f o r the s t a t e s before and a f t e r e l e c t r o n t r a n s f e r . V i b r a t i o n a l overlap i s obviously of importance i n the i n v e r t e d region because of the n e s t i n g of the p o t e n t i a l curves as shown i n Figure 2, and i t s mag nitude i s i n f l u e n c e d by: 1) The v i b r a t i o n a l quantum spacing f o r the acceptor v i b r a t i o n or v i b r a t i o n s , "huty. As the v i b r a t i o n a l quantum number ν increases, the v i b r a t i o n a l amplitude increases near the p o t e n t i a l curve. For a high frequency v i b r a t i o n , the energy conservation c o n d i t i o n i s met f o r v i b r a t i o n s with lower ν values. 2) The extent of d i s t o r t i o n of the acceptor v i b r a t i o n i n the e x c i t e d s t a t e compared to the ground s t a t e , A Q . As A Q increases, v i b r a t i o n a l overlap i n c r e a s e s . 3) The energy gap be tween the ground and e x c i t e d s t a t e , ΔΕ. As ΔΕ decreases, energy conservation i s met f o r v i b r a t i o n a l l e v e l s of lower ν number where the amplitudes a r e greater toward the center of the p o t e n t i a l curve f o r the ground s t a t e . In the l i m i t that η ω » kfiT, the r a t e constant f o r nonradia t i v e decay i s simply the product of the square of the v i b r a t i o n a l overlap i n t e g r a l < X i i t i a l I X f i n a l * d an e l e c t r o n i c term f o r the Il:L

2+

I I

2 +

2

eq

Μ

a

n

n


eq

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INORGANIC C H E M I S T R Y : TOWARD THE

21 ST

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t r a n s i t i o n between s t a t e s . In the l i m i t that "huty >> kgT and assuming a r e l a t i v e l y small e x c i t e d s t a t e d i s t o r t i o n , the r a t e constant f o r nonradiative e x c i t e d s t a t e decay i s given by eq. 11 (11).

k

nr

C

=

1

\ < " Η ί φ Ε 1 - )

/

2

- Ρ - ν

χ

Ρ - ^

ΔΕ;

the i n t e r n a l energy change accompanying e x c i t e d s t a t e decay. ω = 2πν^; the angular frequency of the acceptor v i b r a t i o n or v i b r a t i o n s . S = -^Δ ; a measure of the d i s t o r t i o n of the acceptor v i b r a t i o n i n the e x c i t e d s t a t e . Δ i s the dimensionl e s s , f r a c t i o n a l displacement i n normal v i b r a t i o n M between the thermally e q u i l i b r a t e d e x c i t e d and ground states. I t i s r e l a t e d to A Q by = AQ^C^) / , where M i s the reduced mass f o r the v i b r a t i o n . Ύ = ln(|AE|/S nu) )-l C œ^; note below. Μ

2

M

Μ


Μ

1

2

eq

M

M

2

To f i r s t order, the t r a n s i t i o n between e x c i t e d and ground s t a t e i s forbidden because they are both s o l u t i o n s of the same molecular Hamiltonian and t h e i r wavefunctions are orthogonal. However, the t r a n s i t i o n can be induced by e x c i t i n g a promoting v i b r a t i o n or v i b r a t i o n s (ω^) which when a c t i v a t e d r e s u l t i n a change i n e l e c t r o n i c overlap between the e l e c t r o n donor and acceptor s i t e s . The magnitude of the v i b r a t i o n a l l y induced mixing of the states i s given by C.; the angular frequency of the promoting v i b r a t i o n i s ω^. When c o n t r i b u t i o n s from the low frequency, c o l l e c t i v e v i b r a t i o n s of the solvent are included, eq. 11 becomes eq. 12. In eq.

/TON

(12)

ι k

2

η / π l/2 _ = C ω. ( — — - — ) exp-S exp nr k 2hu)..E ' Μ Μ em N

N

γ E Y k Τ ο em_ ο Β , 2, exp + -—fcr—(γ +1) J ηω^. ηω-,τιω., ο M M M Γ

η

v

12 the assumption i s made that the experimentally observed emis s i o n energy at X , E , i s r e l a t e d to ΔΕ and X as i n eq. 13. m a x

(13)

e m

Q

Ε

~ ΙΔΕΙ - X em ο The assumption i s reasonable i n the l i m i t that the d i s t o r t i o n i n uty i s not too great i n the e x c i t e d s t a t e . When w r i t t e n i n l o g a r i t h m i c form and noting that the pre-exp o n e n t i a l and Y terms i n eq. 12 are only weakly dependent on E , eq. 12 can be w r i t t e n i n the form of the "energy gap law" (12a, 12b) as shown i n eq. 14. γ E bx (14) Ink = Ink = Ιηβ - ° + zr nr et ο ηω^ ηα^ 1

1

Q

e m

e m

2


8.

Excited-State

MEYER

Electron

C2m(—-!—)l/2 k 2ηω Ε M em

β = o k

b

= 4

167

Transfer

7

>χ

R

T

(

Y

2 +

°

1

)

M One way to t e s t the "energy gap law" and therefore the a p p l i c a t i o n of e l e c t r o n t r a n s f e r to the i n v e r t e d region i s by measuring r a d i a t i o n l e s s decay r a t e constants f o r a s e r i e s of c l o s e l y r e l a t e d excited states. An e s p e c i a l l y u s e f u l s e r i e s has turned out to be the complexes ( b p y ) 0 s L 4 or (phen)OsL4 + (L = py, RCN, 1/2 bpy, 1/2 phen, P R 3 . . . ) , a l l of which contain an MLCT (Os(dTr)-bpy(π*)) based chromophore. The range of ligands that can serve the r o l e of L i s l a r g e , and systematic changes i n L can cause r e l a t i v e l y l a r g e v a r i a t i o n s i n the emission energy. The primary o r i g i n of the v a r i a t i o n s i n E appears to be i n the backbonding a b i l i t i e s of L i n s t a b i l i z i n g the ground s t a t e by metal to l i g a n d backbond ing. In any case, f o r a s e r i e s of r e l a t e d chromophores i n a con stant solvent, the terms β , f i u ^ , and X i n eq. 14 are expected to remain s e n s i b l y constant and p l o t s of l n k ^ v s . E are expected to be l i n e a r . In a d d i t i o n , i n low temperature (77°K) emission measurements v i b r a t i o n a l s t r u c t u r e can be observed. From the energy spacings between the v i b r a t i o n a l components, *ηω^ ~ 13001400 cm~l f o r the acceptor v i b r a t i o n ( s ) . I t i s a l s o p o s s i b l e to c a l c u l a t e S ( = 1 A ) from the r e l a t i v e i n t e n s i t i e s of the v i b r a t i o n a l components (15).


2+

2

e m

0

Q

e m

2

M

m

2

Experimentally, E i s a v a i l a b l e from the emission spectrum and k from a combination of e x c i t e d s t a t e l i f e t i m e (τ ) and emission quantum y i e l d ( φ ) measurements as shown i n eq. 15. An e m

n r

0

Γ

(15)

— τ

= k ο

nr

+ k

r

k r + k r nr extended s e r i e s of osmium complexes i s a v a i l a b l e , and the r e s u l t s of experiments where both emission energies and k allow p l o t s of lnknj- to be made (16) . As the data show, the l i n e a r r e l a t i o n ship p r e d i c t e d by eq. 14 i s observed. I t i s even more s t r i k i n g that the slopes of the l i n e s of the p l o t s are a l s o i n agreement with eq. 14 although a d e t a i l e d a n a l y s i s of the data i s required. The s i m i l a r i t y i n slopes and v i b r a t i o n a l spacings i n low tempera ture emission spectra f o r the two s e r i e s show that the acceptor v i b r a t i o n s are r i n g - s t r e t c h i n g i n nature. The d i f f e r e n t i n i n t e r cepts f o r the two s e r i e s i s not s u r p r i s i n g . The i n t e r c e p t i n cludes the term C which i s dependent on the e l e c t r o n i c s t r u c t u r e of the chromophoric l i g a n d . Given the change i n e l e c t r o n i c _ d i s t r i b u t i o n between MLCT e x c i t e d and ground s t a t e s , e.g., ( b p y ) 0 s L 4 — * ( b p y ) 0 s L ^ , a second approach to t e s t i n g the energy gap law should be through k

n r

2

I I I

II


168

INORGANIC C H E M I S T R Y : TOWARD T H E

21ST

CENTURY

solvent v a r i a t i o n s . In the c l a s s i c a l d i e l e c t r i c continuum l i m i t , ΔΕ i s p r e d i c t e d to vary with the s t a t i c d i e l e c t r i c constant of the medium (Dg), as i n equation 16, and X with Dg and the o p t i c a l d i Q

e l e c t r i c constant D as i n eq. 17 (17). In eq. 16 and 17 μ and \if are the d i p o l e moments of the metal-ligand e l e c t r o n i c d i s t r i b u t i o n s before and a f t e r e l e c t r o n t r a n s f e r has occurred. In the


Qp

±

equations a i s the radius of a sphere enclosing the metal-ligand dipole. According to eq. 14, i f v a r i a t i o n s i n X are r e l a t i v e l y small through a s e r i e s of s o l v e n t s , p l o t s of l n k vs. E should be l i n e a r f o r a s i n g l e e x c i t e d s t a t e . I t has been shown that f o r a s e r i e s of polar organic s o l v e n t s , the p r e d i c t i o n i s borne out f o r s e v e r a l of the (phen)0sL^2+_type MLCT e x c i t e d s t a t e s , i n c l u d i n g O s ( p h e n ) 3 * (18). I t i s e s p e c i a l l y s t r i k i n g that the slopes of the p l o t s are the same w i t h i n experimental e r r o r as i n the e x p e r i ments described above where L was v a r i e d . However, f o r h y d r o x y l i c solvents such as methanol or water, s p e c i f i c solvent e f f e c t s e x i s t , the d i e l e c t r i c continuum r e s u l t i n eq. 17 i s no longer a p p l i c a b l e , and v a r i a t i o n s i n X are appre c i a b l e . Even so, eq. 14 s t i l l a p p l i e s i n that f o r a s e r i e s of e x c i t e d s t a t e s l i k e (bpyjOsL^+a, p l o t s of l n k vs. E remain l i n e a r and have the same slope as the p l o t s f o r polar organic s o l vents. The d i f f e r e n c e i s that the l i n e s are p a r a l l e l but o f f s e t , because the term appears i n the i n t e r c e p t and x i s non-negli g i b l e f o r the h y d r o x y l i c s o l v e n t s . Studies l i k e those mentioned here on the osmium complexes are more d i f f i c u l t f o r r e l a t e d complexes of ruthenium because of the i n t e r v e n t i o n of a l o w l y i n g , thermally populable d-d e x c i t e d s t a t e . However, i t i s p o s s i b l e to separate the two c o n t r i b u t i o n s to e x c i ted s t a t e decay by temperature dependent measurements. In the case of R u ( b p y ) 3 * , temperature dependent l i f e t i m e s t u d i e s have been c a r r i e d out i n a s e r i e s of s o l v e n t , and the r e s u l t s obtained f o r the v a r i a t i o n of k with E are i n agreement with those ob tained f o r the Os complexes (19). A c l o s e l y r e l a t e d t e s t of the energy gap law f o r Ru complexes has come from temperature dependent l i f e t i m e and emission measure ments f o r a s e r i e s of complexes of the type R u ( b p y ) 2 L 2 (L = py, substituted pyridines, pyrazine...). From the data, the v a r i a t i o n in l n k with E p r e d i c t e d by the energy gap law has been ob served and i t has been p o s s i b l e to observe the e f f e c t of changing the l i g a n d s L on the t r a n s i t i o n between the MLCT and dd states (20). The d i s c u s s i o n i n t h i s s e c t i o n has been o r i e n t e d toward the use of intramolecular r e a c t i o n s and e x c i t e d s t a t e decay to t e s t Q

n r

e m

2+

Q

n r

e m

Q

2+

n r

e m

2+

n r

e m


8.

MEYER

Excited-State

Electron

169

Transfer

e l e c t r o n t r a n s f e r theory i n the i n v e r t e d region. However, the same ideas should apply to intermolecular e l e c t r o n t r a n s f e r where e l e c t r o n hopping occurs between d i f f e r e n t chemical s i t e s , as long as the c o n d i t i o n s which d e f i n e the i n v e r t e d region are appropriate. One s t r i k i n g p r e d i c t i o n of the energy gap law and eq. 11 and 14 i s that i n the i n v e r t e d region, the e l e c t r o n t r a n s f e r r a t e constant ( k = k ) should decrease as the r e a c t i o n becomes more favorable ( l n k - Δ Ε ) . Some evidence has been obtained f o r a f a l l - o f f i n r a t e constants with i n c r e a s i n g -ΔΕ (or -AG) f o r i n t e r molecular r e a c t i o n s (21). Perhaps most notable i s the pulse r a d i o l y s i s data of B e i t z and M i l l e r (22). Nonetheless, the a p p l i c a b i l i ty of the energy gap law to intermolecular e l e c t r o n t r a n s f e r i n a d e t a i l e d way has yet to be proven. A p p l i c a t i o n of the energy gap law to the energy conversion mechanism i n Scheme 1 leads to a notable conclusion with regard to the e f f i c i e n c y f o r the appearance of separated redox products f o l lowing e l e c t r o n t r a n s f e r quenching. From the scheme, the separa t i o n e f f i c i e n c y , Φ ρ » i s given by eq. 18. D i f f u s i o n apart of the n r

e t

œ


n r

3β

k,

(18)

-D 's e p - k2+k'_ D

Y

D

f

quenching products once the quenching step has occurred ( k _ ) i s d i c t a t e d by such features as the charge types on the r e a c t a n t s , and the solvent p o l a r i t y and v i s c o s i t y . However, back e l e c t r o n t r a n s f e r to give the ground s t a t e ^2) i s an e l e c t r o n t r a n s f e r r e a c t i o n . According to the energy gap law, as the quenching step produces redox products where the energy stored becomes more and more favorable, -ΔΕ i n c r e a s i n g , k should decrease. One therefore reaches the s t r i k i n g conclusion that i n a properly designed system both the e f f i c i e n c y of separation of the redox products and the amount of energy stored should increase as the reduction p o t e n t i a l of the quencher approaches that of the e x c i t e d s t a t e (2b). D

2

Directed Electron Transfer. This account was begun by c o n s i d e r i n g the p o s s i b i l i t y of c r e a t i n g energy conversion schemes based on simple e l e c t r o n t r a n s f e r processes i n v o l v i n g e x c i t e d s t a t e s . One obvious extension i s to more complex systems where some of the de mands of an o v e r a l l conversion mechanism could be spread amongst d i f f e r e n t chemical s i t e s . In order to b u i l d more complex, coupled systems where l i g h t absorption and chemical redox events are sepa rated, i t i s necessary to understand and c o n t r o l the molecular c h a r a c t e r i s t i c s which can lead to d i r e c t e d , intramolecular e l e c t r o n or energy t r a n s f e r . What i s meant by d i r e c t e d e l e c t r o n t r a n s f e r i s that f o l l o w i n g o p t i c a l e x c i t a t i o n of a chromophore, the e x c i t e d e l e c t r o n or e l e c t r o n hole, or perhaps both, d r i f t away from the i n i t i a l chromophoric s i t e by intramolecular e l e c t r o n t r a n s f e r . I f the r a t e of recombination of the e x c i t e d e l e c t r o n e l e c t r o n hole p a i r i s s u f f i c i e n t l y slow, i t i s p o s s i b l e to e x t r a c t them from d i f f e r e n t parts of the molecular at a l a t e r time, before recombination can occur (23). As an example of such a system,


170

INORGANIC C H E M I S T R Y :

TOWARD

THE 21ST

CENTURY

+

consider the complex [ R u ( b p y ) ( N C ^ N - M e ) ] ^ + i n which there are both Ru(bpy) chromophoric s i t e s a n d a t t a c h e d , intramolecular e l e c t r o n acceptor pyridinium s i t e s . There i s a c l e a r s i m i l a r i t y between t h i s intramolecular redox complex and the r e a c t i o n i n Scheme 1 based on paraquat. In the complex, the b i m o l e c u l a r , intermolec u l a r quenching r e a c t i o n of Scheme 1 has been converted i n t o an intramolecular quenching r e a c t i o n . Experimentally, o p t i c a l exc i t a t i o n of the Ru-bpy chromophore i n a frozen s o l u t i o n at 77°K leads to e x c i t e d s t a t e decay by an emission which i n terms of emission energy, v i b r a t i o n a l s t r u c t u r e and l i f e t i m e c l o s e l y resemb l e s the emission from R u ( b p y ) 3 . However, at room temperature a s t r o n g l y r e d - s h i f t e d , weaker, s h o r t - l i v e d emission i s observed from the molecule (24). The most s t r a i g h t f o r w a r d i n t e r p r e t a t i o n of the sequence of events that occurs f o l l o w i n g e x c i t a t i o n at room temperature i s summarized i n Scheme 2. 2

2


2+

Scheme 2 CT

n

CT

+

(bpy) (bpy) ( L ) R u ^ l ® ^ - M e ]

2

(bpy)

JL

+hv

-hv

(L)Ru

+

*

4+

(NOHgk'-Me] *

1

(bpy) (L) R u

GS

1 1 1

4

2

1 1

+

(Ng> -Me) ]

4

+

At room temperature thermally a c t i v a t e d e l e c t r o n t r a n s f e r occurs from the bpy l i g a n d to the remote pyridinium s i t e followed by decay of the lower, pyridinium-based CT s t a t e . The e l e c t r o n t r a n s f e r step i s the intramolecular analog of the paraquat quenching of R u ( b p y ) * . A feature of i n t e r e s t i n the sequence of events o u t l i n e d i n Scheme 2 i s that f o l l o w i n g o p t i c a l e x c i t a t i o n , d i r e c t e d e l e c t r o n t r a n s f e r does occur away from the chromophoric s i t e to a remote ligand. In that sense, the e x c i t e d s t a t e acts as a molecular photodiode (23). With the proper molecular design i t may be poss i b l e to b u i l d systems where the e x c i t e d e l e c t r o n and/or e l e c t r o n hole cascade through a s e r i e s of redox l e v e l s l e a d i n g to the spat i a l separation of the e l e c t r o n - e l e c t r o n hole p a i r and slow back electron transfer. I t i s important to r e a l i z e that the observat i o n of d i r e c t e d e l e c t r o n t r a n s f e r i s subject to the " r u l e s of e l e c t r o n t r a n s f e r as described above. For the case of the p y r i dinium complex, n o n r a d i a t i v e decay from the i n i t i a l CT s t a t e . CT~, [(bpy)(b^y)(L)RuiII(N^)

Inorganic Chemistry: Toward the 21st Century - American Chemical

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