Solvent Reorganization Energetics and Dynamics in Charge-Transfer

16 Solvent Reorganization Energetics and Dynamics in Charge-Transfer Processes Downloaded by GEORGETOWN UNIV on August 20, 2015 | http://pubs.acs.org Publication Date: May 5, 1991 | doi: 10.1021/ba-1991-0228.ch016

of Transition Metal Complexes X u n Zhang, Mariusz Kozik, Norman Sutin, and Jay R. W i n k l e r

1

Chemistry Department, Brookhaven National Laboratory, Upton, N Y 11973

Time-resolved and steady-state luminescence measurements were used to probe the energetics and dynamics of solvation in two different transition metal complexes. The metal-to-ligand charge-transfer excited state of Ru(bpy) (CN) (bpy is bipyridine) was studied in a series of aliphatic alcohols, and the luminescent excited state of Mo Cl [P(CH ) ] was studied in aprotic organic solvents. The energetics of excited-state solvation were evaluated from the shapes and positions of the steady-state luminescence spectra recorded at low (~10 K) and room temperatures. The dynamics of excited-state solvation were probed by time-resolved emission spectroscopy. 2

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THE SOLVENT PLAYS A MAJOR ROLE IN GOVERNING the rates of transfer reactions i n solution ( I , 2). T h e solvent reorganization associated w i t h electron-transfer reactions i n polar solvents is often the major c o n t r i b u t o r to the total reorganization energy (X). I n recent years, questions have arisen r e g a r d i n g the i m p o r t a n c e of solvent reorganization d y n a m i c s i n c o n t r o l l i n g the rates of fast electron-transfer processes (3-11). M o d e l s that treat the solvent as a continuous d i e l e c t r i c m e d i u m are often u s e d to d e s c r i b e solvation energetics a n d d y n a m i c s , b u t the a p p l i c a b i l i t y of these m o d e l s to real c h e m i c a l systems r e m a i n s an o p e n q u e s t i o n . E l e c t r o n i c a b s o r p t i o n a n d e m i s s i o n spectroscopies are p o w e r f u l techniques for p r o b i n g the e n v i r o n ments o f m o l e c u l e s i n s o l u t i o n (12-22). T h e energies a n d shapes o f a b s o r p t i o n

CA 91125

Current address: Beckman Institute, California Institute of Technology, Pasadena, 0065-2393/91/0228-0247$06.00/0 © 1991 American Chemical Society

American Chemical Society Library 1155 16th SUHW.

In Electron Transfer in Inorganic, Organic, and Biological Systems; Bolton, J., et al.; Washington. D.C. 20036 Advances in Chemistry; American Chemical Society: Washington, DC, 1991.

electron-

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248

E T IN INORGANIC, ORGANIC, A N D BIOLOGICAL SYSTEMS

a n d e m i s s i o n profiles correlate w i t h solvent properties a n d e m p i r i c a l solvent parameters a n d p r o v i d e insight i n t o the energetics of solvation. T i m e - r e s o l v e d e m i s s i o n spectroscopy ( T R E S ) is an i m p o r t a n t t e c h n i q u e for e x a m i n i n g the d y n a m i c s of solvation of excited m o l e c u l e s , as w e l l as the solvent d y n a m i c s associated w i t h fast electron-transfer processes (23-55). T h e e q u i l i b r i u m positions of n u c l e i i n molecules generally shift as a c o n s e q u e n c e of e l e c t r o n i c excitation. S u c h a shift p r o d u c e s b r o a d spectral profiles a n d , i n some cases, v i b r a t i o n a l fine structure. I f o n l y solvent n u c l e i change t h e i r e q u i l i b r i u m positions, the e n e r g y of the steady-state a b s o r p t i o n or e m i s s i o n m a x i m u m d i r e c t l y reflects the difference i n p o s i t i o n a l o n g the solvent coordinate of the i n i t i a l a n d final states. S i m i l a r i n f o r m a t i o n is c o n t a i n e d i n the breadths of the bands. W h e n i n t e r n a l - m o d e distortions a c c o m p a n y e l e c t r o n i c excitation, it is m o r e difficult to extract i n f o r m a t i o n about the solvent configuration because the b a n d shape a n d p o s i t i o n also reflect i n t e r n a l - m o d e rearrangements. T o characterize the energetics of solvation of an excited m o l e c u l e , i n t e r n a l - m o d e c o n t r i b u t i o n s to the a b s o r p t i o n o r e m i s s i o n profiles m u s t b e factored out. O n c e the solvent c o n t r i b u t i o n to the b a n d shape has b e e n d e t e r m i n e d , the r e s u l t i n g solvent reorganization e n e r gies can be c o r r e l a t e d w i t h solvent d i e l e c t r i c properties. Because electrons m o v e m u c h faster than n u c l e i , a short laser p u l s e can b e u s e d to p r e p a r e a m o l e c u l e i n a n o n e q u i l i b r i u m solvation e n v i r o n m e n t . F o l l o w i n g excitation, the solvent w i l l rearrange to accommodate the n e w e l e c t r o n d i s t r i b u t i o n a n d g e o m e t r y of the excited m o l e c u l e . T h e p o s i t i o n a n d shape of the e m i s s i o n b a n d reflect, i n part, the solvation e n v i r o n m e n t ; therefore the t i m e e v o l u t i o n of the emission profile can b e u s e d to m o n i t o r the d y n a m i c s of the approach to e q u i l i b r i u m solvation. M o s t p r e v i o u s investigations of solvent reorganization d y n a m i c s have i n v o l v e d organic p r o b e m o l e c u l e s , especially laser dyes. T h e r e are, h o w e v e r , m a n y l u m i n e s c e n t m e t a l c o m p l e x e s that can serve as p r o b e molecules i n these e x p e r i m e n t s . O n e u n i q u e feature of metal complexes as c o m p a r e d to organic c h r o m o p h o r e s is t h e i r shape: the organic probes t e n d to be large flat m o l e c u l e s , b u t m e t a l complexes can b e a variety of shapes (e.g., flat, c y l i n d r i c a l , or spherical). R u t h e n i u m - b i p y r i d i n e complexes, for e x a m p l e , are r o u g h l y s p h e r i c a l a n d have l o n g - l i v e d (>100 ns) l u m i n e s c e n t chargetransfer excited states. T h e t i m e - r e s o l v e d e m i s s i o n spectra of one m e m b e r of this class of m o l e c u l e s , R u ( b p y ) ( C N ) (bpy is b i p y r i d i n e ) , have b e e n e x a m i n e d i n alcohols near the glass transition (39). W e e x t e n d e d this study to h i g h e r temperatures (-20 °C) a n d faster t i m e scales (>20 ps) i n a series of aliphatic alcohols. I n a d d i t i o n , w e p e r f o r m e d a band-shape analysis of the steady-state e m i s s i o n spectra of R u ( b p y ) ( C N ) i n alcohol solvents to c h a r acterize the energetics of solvent reorganization about the e x c i t e d m o l e c u l e . R u ( b p y ) ( C N ) suffers from two shortcomings for solvent d y n a m i c s ex2

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In Electron Transfer in Inorganic, Organic, and Biological Systems; Bolton, J., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1991.

16.

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Solvent Reorganization

249

Energetics and Dynamics

p e r i m e n t s : a l o w radiative rate constant (the l u m i n e s c e n t state is f o r m a l l y a triplet) a n d l o w s o l u b i l i t y i n aprotic solvents. W e therefore i n i t i a t e d T R E S studies of a second l u m i n e s c e n t m e t a l c o m p l e x , M o C l [ P ( C H ) 3 ] 4 . T h i s m o l e c u l e is soluble i n most organic solvents (except alcohols), a n d steadystate spectra suggest that its l u m i n e s c e n t state has a respectable d i p o l e m o m e n t (vide infra). F u r t h e r m o r e , the fact that the l u m i n e s c e n t e x c i t e d state is a singlet greatly facilitates T R E S studies o n p i c o s e c o n d t i m e scales. F o r these reasons w e e x a m i n e d the p i c o s e c o n d t i m e - r e s o l v e d e m i s s i o n spectra o f M o C l [ P ( C H ) ] 4 i n b e n z o n i t r i l e b e t w e e n 20 a n d - 3 2 °C. 2


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Experimental Details Materials. A l l solvents used in this study were H P L C grade. Methanol (MeOH), 1-propanol (PrOH), 1-butanol (BuOH), and absolute ethanol ( E t O H ) were refluxed over Na, distilled, and stored under A r over molecular sieves (3 À for M e O H , 4 Â for higher alcohols). Tetrahydrofuran (THF) was refluxed over Na-benzophenone, distilled, and stored under vacuum over Na-benzophenone. Hexanes (bp 68-69 °C) were refluxed over N a K alloy, distilled, and stored under vacuum over N a K . M e t h ylene chloride ( C H C 1 ) , chloroform (CHC1 ), and acetonitrile ( C H C N ) were refluxed over C a H , distilled, and stored under vacuum over molecular sieves (4 Â for C H C 1 and C H C 1 , 3 Â for C H C N ) . Ethyl acetate, diethyl ether, butanone, d i methyl sulfoxide ( D M S O ) , and benzonitrile were stored under vacuum over 4-Â molecular sieves. cis-Ru(bpy) (CN) was prepared and purified by published procedures (56, 57). Purity was determined by T L C on silica, developed with methanol. M o C l [ P ( C H ) ] was prepared according to a published procedure (58). Sample purity was evaluated by absorption spectroscopy. Samples for steady-state and time-resolved emission spectra were kept under vacuum in sealed fused-silica cuvettes. 2

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Data Collection. Steady-State Emission Spectra. Emission spectra were recorded on an instrument constructed at Brookhaven National Laboratory (59). Samples for low-temperature spectra were held under vacuum i n sealed 4-mm-o.d. fusedsilica tubes and mounted on the cold head of a closed-cycle refrigerator. Identical configurations were used for room-temperature and low-temperature spectra. Time-Resolved Emission Spectra. Picosecond time-resolved emission spectra were r e c o r d e d f o l l o w i n g e x c i t a t i o n w i t h a v e r t i c a l l y p o l a r i z e d 30-ps p u l s e ( M o C l [ P ( C H ) ] , 532 nm; Ru(bpy) (CN) , 355 nm) from a flashlamp-pumped, actively-passively mode-locked N d : Y A G laser. Emitted light passed through an analyzing polarizer, then was dispersed by a spectrograph and directed to the entrance slit of a streak camera. The instrument response time was 35-40 ps (59). Timeresolved emission spectra were recorded with the analyzing polarizer set to the "magic angle" (54.75° from vertical) (60). Time-resolved fluorescence depolarization measurements were performed without dispersion of the emission spectrum by using parallel (0°) and perpendicular (90°) orientations of the analyzing polarizer (61). 2

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4

250


Results Ru(bpy) (CN) . Steady-State Emission Spectra. T h e r o o m - t e m p e r ature a n d l o w - t e m p e r a t u r e e m i s s i o n spectra of R u ( b p y ) ( C N ) i n ethanol are s h o w n i n F i g u r e 1. A t r o o m t e m p e r a t u r e the emission profile is a b r o a d , a s y m m e t r i c b a n d . A t 12 Κ a progression i n a h i g h - e n e r g y v i b r a t i o n a l m o d e can b e r e s o l v e d . T h e l o w - t e m p e r a t u r e spectra w e r e fit to the m o d e l d e s c r i b e d b y eqs A 3 - A 6 (see A p p e n d i x ) , i n w h i c h a single q u a n t u m m o d e was i n c l u d e d , a n d the r e m a i n d e r of the i n t e r n a l - m o d e b r o a d e n i n g was t r e a t e d semiclassically (dashed l i n e s , F i g u r e 1). T h e frequency of the q u a n t u m m o d e for a l l of the alcohols, about 1300 c m , c o n t r i b u t e d —0.16 e V to the i n n e r s h e l l reorganization p a r a m e t e r (X ). T h e resonance R a m a n s p e c t r u m of s o l i d R u ( b p y ) ( C N ) exhibits, i n a d d i t i o n to a 1 3 1 7 - c m peak, intense features at 366, 663, 1024, 1172, 1485, 1557, a n d 1601 c m i n d i c a t i v e of distortions along these v i b r a t i o n a l coordinates i n the M L C T (metal-to-ligand chargetransfer) excited state (62). T h e > 1 4 0 0 - c m vibrations do not clearly c o n t r i b u t e to the l o w - t e m p e r a t u r e emission s p e c t r u m , a n d t h e i r c o n t r i b u t i o n s to \ have b e e n neglected. A s s u m i n g that the c o n t r i b u t i o n to the b a n d w i d t h f r o m solvent relaxation d u r i n g the l i f e t i m e of the excited state can be neglected at l o w t e m p e r a t u r e s , a n d that the r e m a i n i n g i n n e r - s h e l l distortions can b e r e p r e s e n t e d b y an 2

2

2

2


1

in

2

1

2

1

_ 1

in

600

600

600

800

λ, nm Figure 1. Emission spectra ofRu(bpy) (CN) in EtOH. Left: 12 K. Right: room temperature. Dashed lines are Franck-Condon fits to the spectra using one quantum mode. 2

2


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Z H A N G ET AL.



251

average v i b r a t i o n a l f r e q u e n c y of 600 c m " , the semiclassical i n n e r - s h e l l d i s t o r t i o n can b e calculated ( X ~ 0.05 eV, e q A5). T h i s calculation m a y b e c o m b i n e d w i t h the q u a n t u m - m o d e reorganization to p r o v i d e an estimate of X ~ 0.21 e V for the R u ( b p y ) ( C N ) M L C T e x c i t e d state. T h e solvent r e organization p a r a m e t e r ( X ) can be d e t e r m i n e d f r o m the b r e a d t h of the r o o m - t e m p e r a t u r e emission profiles b y u s i n g the i n n e r - s h e l l d i s t o r t i o n p a rameters o b t a i n e d f r o m the l o w - t e m p e r a t u r e spectra (eq A 5 ) . T h e r e s u l t i n g X values are 0.09 e V for M e O H , 0.11 e V for E t O H , 0.09 e V for P r O H , a n d 0.07 e V for B u O H . 1

i n j

i n

2

2

out


o u t

Time-Resolved Spectra. T h e l u m i n e s c e n c e l i f e t i m e of R u ( b p y ) ( C N ) is —400 ns i n alcohols at - 2 0 °C. I n the four alcohols s t u d i e d , solvent relaxation at this t e m p e r a t u r e was c o m p l e t e before there h a d b e e n any significant excited-state d e p o p u l a t i o n . T h e w a v e l e n g t h d e p e n d e n c e of the R u ( b p y ) ( C N ) l u m i n e s c e n c e decays i n B u O H (-20 °C) are s h o w n i n F i g u r e 2. T h e most s t r i k i n g aspect of these data is that the f o r m of the e m i s s i o n decay f u n c t i o n is w a v e l e n g t h - d e p e n d e n t . A t shorter wavelengths ( < 6 4 0 n m ) , a large i n i t i a l e m i s s i o n i n t e n s i t y r a p i d l y decays to a s m a l l e r , constant v a l u e (on the 2-ns t i m e scale). A t l o n g e r wavelengths (>680 n m ) , a r a p i d increase 2

2

2

Time, ne Figure 2 . Wavelength dependence of time-resolved emission profiles of Ru(bpy) (CN) in BuOH at -20 ° C . Left, lower to upper: 614, 631, and 648 nm. Right, upper to lower: 665, 682, and 699 nm. 2

2


2

252


i n e m i s s i o n i n t e n s i t y follows excitation. I n t e r m e d i a t e b e h a v i o r is f o u n d at w a v e l e n g t h s b e t w e e n these two extremes. T h i s b e h a v i o r is consistent w i t h an e m i s s i o n profile that shifts to the r e d f o l l o w i n g excitation. S i m i l a r b e h a v i o r was f o u n d for R u ( b p y ) ( C N ) i n M e O H , E t O H , a n d P r O H (at - 2 0 °C), t h o u g h 2

2

o n different t i m e scales. T o extract solvent relaxation d y n a m i c s f r o m the t i m e - r e s o l v e d e m i s s i o n decays, s m o o t h i n g was effected b y first fitting the s i n g l e - w a v e l e n g t h d e c a y k i n e t i c s to m u l t i e x p o n e n t i a l functions. A s u m of t h r e e e x p o n e n t i a l functions, c o n v o l u t e d w i t h the i n s t r u m e n t response f u n c t i o n , p r o v i d e d adequate fits to the data. T h e r e c o n s t r u c t e d t i m e - r e s o l v e d spectra g e n e r a t e d f r o m t h e


e x p o n e n t i a l decay parameters w e r e t h e n fit to s y m m e t r i c G a u s s i a n d i s t r i b u t i o n functions. T h e d y n a m i c s of solvent relaxation are g i v e n b y t h e c o r r e l a t i o n f u n c t i o n , C(t) (eq 1) (31-54)

c ( t ) c ( f )

_ - - - (vH)

( 1 ) ( 1 )

w h e r e (v(t)) is the m e a n v a l u e o f the spectral d i s t r i b u t i o n f u n c t i o n at t i m e t. B e c a u s e the t i m e - r e s o l v e d e m i s s i o n spectra of R u ( b p y ) ( C N ) w e r e fit to 2

2

s y m m e t r i c functions, (v(t)) is s i m p l y g i v e n b y the peak m a x i m a o f these spectra. T h e r e s u l t i n g C(t) functions are b i p h a s i c for R u ( b p y ) ( C N ) i n E t O H , 2

2

P r O H , a n d B u O H at - 2 0 °C. A single e x p o n e n t i a l f u n c t i o n describes

C(t)

i n M e O H at - 2 0 ° C , b u t i t is l i k e l y that faster c o m p o n e n t s are lost because of the l i m i t e d t i m e r e s o l u t i o n o f the T R E S apparatus. A p l o t o f C(t) R u ( b p y ) ( C N ) i n B u O H appears i n F i g u r e 3, a n d the C(t) e x p o n e n t i a l 2

for fitting

2

parameters appear i n T a b l e I. M o C1 2

4

[P(CH ) ] . 3

3

4

Steady-State Emission Spectra.

The binuclear

m e t a l c o m p l e x M o C l [ P ( C H ) 3 ] 4 fluoresces f r o m its l o w e s t - l y i n g e x c i t e d 2

4

3

singlet state (58). T h i s e x c i t e d state is d e s c r i b e d as a δ δ * m e t a l - l o c a l i z e d e x c i t e d state i n m o l e c u l a r o r b i t a l models (58, 63) a n d as a m e t a l - t o - m e t a l charge-transfer ( M M C T ) e x c i t e d state i n valence b o n d m o d e l s (64).

The

excited-state l i f e t i m e is ~ 1 4 0 ns. I n contrast to its a b s o r p t i o n s p e c t r u m , the e m i s s i o n s p e c t r u m o f M o C l [ P ( C H ) ] 4 at r o o m t e m p e r a t u r e i n f l u i d so 2

4

3

3

l u t i o n is v e r y sensitive to the solvent ( F i g u r e 4). T h e e m i s s i o n m a x i m a appear at l o w e r energies, a n d the b a n d w i d t h s increase w i t h i n c r e a s i n g solvent p o larity. The

reorganization energy

associated

w i t h the l u m i n e s c e n t

transi

t i o n was d e t e r m i n e d f r o m the r o o m - t e m p e r a t u r e e m i s s i o n s p e c t r a of M o C l [ P ( C H 3 ) 3 ] 4 . I f solvent r e o r i e n t a t i o n is t r e a t e d as a single classical 2

4

n u c l e a r coordinate d e s c r i b e d b y h a r m o n i c p o t e n t i a l surfaces w i t h e q u a l force constants i n the g r o u n d a n d e x c i t e d states, t h e n e v e r y v i b r o n i c l i n e i n the s p e c t r u m can b e r e p r e s e n t e d b y a G a u s s i a n l i n e shape. U n d e r these c i r cumstances, the first m o m e n t o f t h e total e m i s s i o n spectral d i s t r i b u t i o n


Z H A N G E T AL.


16.


Energetics and

Dynamics

253

Table I. Kinetic Parameters for Solvent Relaxation in the M L C T Excited State of Ru(bpy) (CN) 2

2

Solvent

Oil

MeOH EtOH PrOH BuOH

-—

.—

0.74

26

114

0.60

94

332

0.49

156

513

τ

2

34

NOTE: For biexponential relaxation functions, a is the coefficient of the exponential with decay time Τι, and (1 — OLI) is the coefficient of the exponential with decay time τ . Decay times are in pico seconds. x

2

f u n c t i o n i ( v ) (eq A3) w i l l d e p e n d l i n e a r l y u p o n X ab

the v - d e p e n d e n c e of spontaneous 3

e m i s s i o n , the

o u t

. A f t e r c o r r e c t i n g for

first

moments

o f the

M o C l [ P ( C H ) 3 ] 4 e m i s s i o n profiles w e r e d e t e r m i n e d b y n u m e r i c a l i n t e g r a 2

4

3

t i o n . T h e e m i s s i o n s p e c t r u m i n hexanes was chosen as a reference:

The

s p e c t r u m was a s s u m e d to arise solely f r o m i n t e r n a l - m o d e d i s t o r t i o n s , a n d t h e s o l v e n t r e o r g a n i z a t i o n e n e r g y w a s a s s u m e d to b e z e r o .

Because

M o C l [ P ( C H ) 3 ] 4 absorption spectra are not p a r t i c u l a r l y sensitive to the 2

4

3

solvent, h a l f the difference

between

first

moments

i n the s p e c t r u m

of

M o C l [ P ( C H ) 3 ] 4 i n hexanes a n d that i n a p o l a r solvent p r o v i d e s an estimate 2

4

3



254


20

15 ν,

10

cm"

3

1

Figure 4. Absorption (left) and emission (right) spectra of Mo~2Cl [P(CH3)3]4 in hexanes (dashed curve) and benzonitrile (solid curve) at room temperature. 4

for X

o u t

. T h e results of these calculations are set out i n T a b l e I I . C o n t i n u u m

m o d e l s p r e d i c t that the solvent reorganization p a r a m e t e r s h o u l d d e p e n d u p o n the d i e l e c t r i c f u n c t i o n F F

x

(eq 2) (65) 3(e

= 1

[4(€

s

-

€ )

. ,

op

+ l)(c

S

+1)]

op

K

Table Π. Solvent Reorganization Energies for Mo Cl [P(CH ) ]4 2

Solvent Hexanes Chloroform E t h y l ether E t h y l acetate Tetrahydrofuran Dichloromethane Benzonitrile Dimethyl sulfoxide Butanone Aeetonitrile

4

3

3

Fi

0.0 0.114 0.121 0.154 0.165 0.173 0.197 0.220 0.221 0.247

(eV) 0.0 0.024 0.011 0.017 0.018 0.032 0.027 0.032 0.024 0.042

NOTE: Energies are determined from steady-state emission spectra in aprotic solvents at 293 K. The solvent dielectric parameter F is defined in eq 2. Dielectric data are taken from ref. 67. L


)

16.

Z H A N G ET AL.

where € and € s

o p


Energetics and

255

Dynamics

are the static a n d o p t i c a l d i e l e c t r i c constants of the solvent,

r e s p e c t i v e l y . T h e m a g n i t u d e of X

o u t

for the M o C l [ P ( C H ) 3 ] 4 e x c i t e d state 2

4

3

generally increases w i t h the solvent d i e l e c t r i c p a r a m e t e r F

l 5

b u t the r e l a -

t i o n s h i p is not l i n e a r ( F i g u r e 5). T h e s o l i d l i n e i n F i g u r e 5 was c a l c u l a t e d b y u s i n g a m o d e l that treats the solute as a sphere of l o w i n t e r n a l d i e l e c t r i c constant (e

— 2.5) e m b e d d e d i n a continuous d i e l e c t r i c m e d i u m (66). A

int

p a r t i a l charge (0.4 electron) was assumed to transfer f r o m one m e t a l to the o t h e r (2.1 A) w i t h i n a sphere of 3.96-Â radius [the v a l u e o b t a i n e d f r o m an analysis of the rotational c o r r e l a t i o n t i m e of Mo Cl [P(CH3)3]4 i n b e n z o n i 2

4

t r i l e ; v i d e infra]. T h e d i p o l e m o m e n t c o r r e s p o n d i n g to this charge transfer


is 4 D . T h e p a r t i a l charge transfer is consistent w i t h the m i x e d character of the excited state. A l t h o u g h these parameters p r o v i d e a satisfactory fit to the data, it is i m p o r t a n t to r e m e m b e r that this t r e a t m e n t is based u p o n a d i e l e c t r i c c o n t i n u u m d e s c r i p t i o n of the solvent. T h e deviations f r o m the c a l c u l a t e d c u r v e can be the r e s u l t of specific s o l u t e - s o l v e n t interactions. Time-Resolved

Emission

Spectra.

N o spectral e v o l u t i o n was o b s e r v e d

i n the t i m e - r e s o l v e d e m i s s i o n spectra of M o C l [ P ( C H ) 3 ] 4 i n b e n z o n i t r i l e 2

4

3

b e t w e e n 20 a n d - 3 2 °C (the d e p r e s s e d f r e e z i n g p o i n t of the solutions was near - 3 5 °C). T h i s finding places an u p p e r l i m i t of —5 ps o n the solvation t i m e for b e n z o n i t r i l e at - 3 2 °C. T h o u g h solvent r e o r i e n t a t i o n d y n a m i c s w e r e b e y o n d the t i m e r e s o l u t i o n of the i n s t r u m e n t , the rotational d y n a m i c s of

1

0.05 ι

0.04

Figure 5. Solvent dielectric function (Fi) dependence of λ for Mo2Cl [P(CH )3]4Solid line was calculated from a single-sphere dielectric continuum model. Solvents are oxygen donors (o), nitriles (•), and chlorocarbons (a). ο ω ί

4

3


256

E T IN INORGANIC, ORGANIC, AND BIOLOGICAL SYSTEMS

M O C 1 [ P ( C H 3 ) ] 4 w e r e measurable. Solute rotational d y n a m i c s w e r e 2

4

3

t e r m i n e d i n the 2 0 to - 3 2 ° C t e m p e r a t u r e range b y t i m e - r e s o l v e d

de fluo

rescence d e p o l a r i z a t i o n ( 6 1 ) . T h e data for p a r a l l e l a n d p e r p e n d i c u l a r p o l a r izations (relative to v e r t i c a l excitation polarization) w e r e fit to e q A 7 ( F i g u r e 6 ) . T h e t u m b l i n g d y n a m i c s are adequately d e s c r i b e d b y a single e x p o n e n t i a l Γ

that is strongly t e m p e r a t u r e d e p e n d e n t .

The


rotational t i m e constant τ

0

1

2 Time, ns

Figure 6. Top: Time-resolved fluorescence depolarization kinetics for Mo2Cl [P(CH )3]4 in benzonitrile at -32 °C. Bottom: Rotational correlation function derived from Mo Cl [P(CH )3]4 depolarization kinetics. The dashed line is a fit to a single exponential decay function. 4

3

2

4

3


16.

Z H A N G ET AL.


257


m a g n i t u d e o f τ increases b y a factor o f 5.5 b e t w e e n 20 a n d - 3 2 °C [Γ (K), τ (ps): 293, 86; 273, 106; 258, 174; 248, 396; 241, 470]. T h e rotational correlation t i m e is e x p e c t e d to d e p e n d u p o n solvent viscosity, η, a c c o r d i n g to e q 3 (61) Γ

Γ

!

=

(3)

w h e r e k is the B o l t z m a n n constant, Γ is absolute t e m p e r a t u r e , a n d V is the effective v o l u m e of the solute m o l e c u l e . T a k i n g η = 1.34 c P at 20 °C (67) (interpolated value) gives a solute v o l u m e o f 260 Â , c o r r e s p o n d i n g to a sphere o f radius 3.96 Â. Plots of 1η(τ Γ) vs. T~ are not l i n e a r , perhaps o w i n g to the d e v i a t i o n from A r r h e n i u s b e h a v i o r of the solvent viscosity near the f r e e z i n g p o i n t . B


3

Γ

l

Discussion Ru(bpy) (CN) . C o n t i n u u m models are generally the first recourse for discussions o f solvation p r o p e r t i e s . A s was s h o w n i n F i g u r e 1, a d i e l e c t r i c c o n t i n u u m m o d e l adequately describes the breadths o f the R u ( b p y ) ( C N ) steady-state e m i s s i o n profiles. Specific solvation effects, especially h y d r o g e n b o n d i n g , can c o m p l i c a t e the analysis, b u t the general t r e n d appears to b e d e s c r i b e d b y b u l k solvent p r o p e r t i e s . T h e d y n a m i c s of m i c r o s c o p i c solvation can also b e d e s c r i b e d b y c o n t i n u u m models. I n a D e b y e - t y p e d i e l e c t r i c , the a p p r o a c h to e q u i l i b r i u m o f the d i e l e c t r i c p o l a r i z a t i o n f o l l o w i n g an i n s t a n taneous change i n the p e r m a n e n t d i p o l e m o m e n t o f a s p h e r i c a l solute is e x p o n e n t i a l , w i t h a t i m e constant T g i v e n b y e q 4 (3-11, 68, 69) 2

2

2

2

l

(4)

w h e r e T, the D e b y e t i m e , is the e x p o n e n t i a l t i m e constant for the a p p r o a c h to e q u i l i b r i u m p o l a r i z a t i o n f o l l o w i n g an instantaneous change i n the e x t e r n a l e l e c t r i c field (70-72). T h e h i g h - a n d l o w - f r e q u e n c y d i e l e c t r i c constants, €«, a n d e , r e s p e c t i v e l y , arise from the d i e l e c t r i c d i s p e r s i o n of the m e d i u m . A l c o h o l s are not s i m p l e D e b y e solvents a n d are r e p o r t e d to have t h r e e regions o f d i e l e c t r i c d i s p e r s i o n . T h e highest f r e q u e n c y c o m p o n e n t is a t t r i b u t e d to rotation of free h y d r o x y l groups, the m i d - r a n g e c o m p o n e n t to r e orientation of free alcohol m o l e c u l e s , a n d the l o w - f r e q u e n c y c o m p o n e n t to d i s r u p t i o n of h y d r o g e n b o n d s i n alcohol aggregates (Table III) (73). I n M e O H , E t O H , P r O H , a n d B u O H , the l o w - f r e q u e n c y process accounts for the major part o f the d i e l e c t r i c constant. T h e d e f i n i t i o n o f T for alcohols is also c o m p l i c a t e d . A different v a l u e of € 0 0 is associated w i t h each o f the t h r e e d

s

l


258


Table III. Dielectric Relaxation Properties of Aliphatic Alcohols Alcohol MeOH EtOH PrOH BuOH

— — 4 3.5

— — 34 50

154 632 1920 3145

43.2 31.4 27.4 23.6

23 98 274 486

6.40 4.85 3.92 3.65

NOTE: Relaxation times at 253 Κ are in picoseconds. Data are taken from ref. 73.

regions of d i e l e c t r i c d i s p e r s i o n . T h e s e values differ from the o p t i c a l d i e l e c t r i c constant € , w h i c h is e q u a l to the square of the refractive i n d e x of the


o p

m e d i u m a n d w h i c h is c o m m o n l y u s e d for e

œ

i n nonassociated solvents. T h e

significance of this c o m p l i c a t i o n is especially clear i n B u O H w h e r e , p e n d i n g u p o n the c h o i c e of e , œ

3.65; e

= 1.96). T h e T

o p

u s i n g the e , e ^ , a n d T 01

l 1

d 1

T

l

can v a r y b y almost a factor of 2 ( e

de=

œl

values i n T a b l e I I I w e r e calculated f r o m e q 4 b y

values i n ref. 45 ( e ^ refers to the lowest f r e q u e n c y

region of dielectric dispersion, T

D 1

> T

D 2

> T

D 3

).

I n l i g h t of the c o m p l e x d i e l e c t r i c relaxation b e h a v i o r of the m e d i u m , it is not s u r p r i s i n g that the solvent relaxation d y n a m i c s for the R u ( b p y ) ( C N ) 2

2

M L C T e x c i t e d state are b i p h a s i c i n alcohols. C o m p a r i s o n of the data i n Tables I a n d I I I reveals that the slower solvent relaxation t i m e (τ ) is i n fair 2

a c c o r d w i t h the l o w - f r e q u e n c y l o n g i t u d i n a l d i e l e c t r i c relaxation t i m e (T ) L1

for the four alcohols e x a m i n e d i n this w o r k . T h e c o n t r i b u t i o n s of the t w o relaxation t i m e s to t h e i r c o r r e s p o n d i n g relaxation functions, h o w e v e r , q u i t e different. A l t h o u g h the d i s p e r s i o n r e g i o n w i t h t i m e constant T

are cor

l 1

responds to the largest part of the d i e l e c t r i c constant i n these alcohols, T

2

represents less t h a n h a l f of the o b s e r v e d m i c r o s c o p i c solvation d y n a m i c s . T h e s e results are s i m i l a r to o t h e r reports of solvent relaxation about e x c i t e d c h r o m o p h o r e s i n alcohols (32, 3 3 , 36, 41, 42, 50, 53, 54). B i p h a s i c relaxation k i n e t i c s are t y p i c a l l y o b s e r v e d , a n d one relaxation t i m e is g e n e r a l l y c o m p a r a b l e to T

l 1

. I n some reports the slowest relaxation t i m e is l o n g e r t h a n

T , b u t faster c o m p o n e n t s are also o b s e r v e d . F e w of the systems u s e d thus l 1

far have b e e n free of p o t e n t i a l h y d r o g e n - b o n d i n g interactions. It is, t h e r e fore, difficult to assess the i m p o r t a n c e of this specific i n t e r a c t i o n , a n d m a n y aspects o f solvent relaxation d y n a m i c s i n alcohols r e m a i n u n r e s o l v e d . Mo Cl [P(CH3)3]4. 2

T h e steady-state e m i s s i o n spectra of

4

Mo Cl 2

4

[ P ( C H ) ] are strongly s o l v e n t - d e p e n d e n t , a n d the variations are i n g e n e r a l 3

3

4

agreement

with a dielectric continuum model.

A s i n the case

of

R u ( b p y ) ( C N ) , specific s o l u t e - s o l v e n t interactions are also l i k e l y to b e i m 2

2

portant i n M o C l [ P ( C H ) ] because the vacant axial sites at the two m e t a l 2

4

3

3

4

centers c o u l d b e o c c u p i e d b y strong d o n o r solvents. I n this r e g a r d , i t is s u r p r i s i n g that the absorption s p e c t r u m of M o C l [ P ( C H ) ] varies so l i t t l e 2

4

3

3

4

w i t h solvent; the shift i n a b s o r p t i o n m a x i m u m b e t w e e n hexanes a n d b e n -


16.

Z H A N G ET A L .


Energetics and

Dynamics

259

z o n i t r i l e is o n l y 60 c m " . I n contrast* the shift i n e m i s s i o n m a x i m u m b e t w e e n 1

these t w o solvents is 700 c m . T h e simplest explanation of these results is - 1

that d o n o r solvents interact m u c h m o r e strongly w i t h e l e c t r o n i c a l l y e x c i t e d M o C l [ P ( C H ) 3 ] 4 t h a n w i t h the ground-state 2

4

3

species.

T h e d i e l e c t r i c p r o p e r t i e s of b e n z o n i t r i l e are p r e s e n t e d i n T a b l e I V (74-76). U n l i k e alcohols, b e n z o n i t r i l e exhibits s i m p l e D e b y e relaxation p r o p erties, a l t h o u g h t h e r e is some u n c e r t a i n t y i n the m a g n i t u d e o f T . T h e c h o i c e d

between e

a n d €«, (2.24 a n d 3.80, respectively) adds e v e n m o r e u n c e r t a i n t y

o p

to t h e value of T . T h e D e b y e t i m e for b e n z o n i t r i l e has b e e n r e p o r t e d for l


temperatures between

15 a n d 40 °C (76), b u t data are not available for

t e m p e r a t u r e s as l o w as - 3 2 °C. A r o u g h estimate for the D e b y e t i m e of b e n z o n i t r i l e at this t e m p e r a t u r e can be o b t a i n e d f r o m the M o C l [ P ( C H 3 ) 3 ] 4 2

rotational c o r r e l a t i o n t i m e s . B o t h T

d

4

a n d τ are b e l i e v e d to d e p e n d a p p r o x Γ

i m a t e l y l i n e a r l y o n solvent viscosity (61,

70). A s s u m i n g that the

effective

solute v o l u m e r e m a i n s constant, a value of η = 6.0 c P can be e s t i m a t e d for b e n z o n i t r i l e at - 3 2 °C. G i v e n a r o o m - t e m p e r a t u r e D e b y e t i m e of 16 ps, T is e s t i m a t e d to b e 87 ps at - 3 2 °C. T h i s gives T

l

=

D

13 ps, p r o v i d e d that

€ o o / e remains a p p r o x i m a t e l y constant. O n the basis of these estimates of s

dielectric

relaxation

Mo Cl [P(CH ) ] 2

4

3

3

4

times,

the

time-resolved

emission

spectra

of

indicate that solvent relaxation t i m e about the e x c i t e d

m e t a l c o m p l e x is shorter t h a n or e q u a l to T . T h i s result differs f r o m s o m e l

o t h e r m e a s u r e m e n t s o f solvent relaxation i n n i t r i l e s , w h e r e o b s e r v e d relax ation times are 2 to 5 times l o n g e r than T , a l t h o u g h n o n e of the o b s e r v e d l

relaxation t i m e s e x c e e d 5 ps (32, 50, Caveats.

53).

A n a l y s e s of the t i m e - r e s o l v e d e m i s s i o n spectra a n d t h e i r

i n t e r p r e t a t i o n i n t e r m s of solvent r e o r i e n t a t i o n d y n a m i c s are c o m p l i c a t e d by

several factors.

I n the first instance,

both

the

Ru(bpy) (CN) 2

Table IV. Measured and Estimated Dielectric Properties of Benzonitrile Τ (Κ)

TjT_ 1.4

323

9

313

11

1.7

303

13

2.0

293

16,

283

18

241

87

38

2.4,

d

5.7

d

2.7 13

E

E

Relaxation times are in picoseconds. Data are taken from ref. 76. T was calculated according to eq 4 by using e = 25.2 and = 3.80. Data are taken from ref. 75. Data are taken from refs. 74 and 75. Estimate from fluorescence depolarization determination of solvent viscosity. The (depressed) freezing point of the solution was ~238 K. See text.

fl

fc C

d e

l

s


2

and

260

E T IN INORGANIC, O R G A N I C , A N D BIOLOGICAL SYSTEMS

MO C1 [P(CH3)3] 2

4

4

c o m p l e x e s w e r e e x c i t e d w i t h laser pulses significantly

above t h e origins o f the e m i s s i o n bands (—1.4 a n d 0 . 3 eV, respectively). T h i s excess e n e r g y is u l t i m a t e l y d e p o s i t e d i n t o t h e solvent, w h e r e i t leads to l o c a l h e a t i n g . T h e r e s u l t i n g t e m p e r a t u r e gradient c o u l d c o m p l i c a t e t h e solvent relaxation d y n a m i c s . F u r t h e r m o r e , i n R u ( b p y ) ( C N ) , t h e a b o v e - t h r e s h o l d 2

2

excitation w i l l l i k e l y p o p u l a t e t h e singlet M L C T state before t h e t r i p l e t . N o clear e v i d e n c e for singlet e m i s s i o n was f o u n d i n R u ( b p y ) ( C N ) , a 2

finding

2

that suggests that t h e i n t e r s y s t e m crossing t i m e is m u c h shorter t h a n t h e t i m e r e s o l u t i o n o f o u r T R E S apparatus. T h e p r e s e n c e o f s u c h

fluorescence,

h o w e v e r , c o u l d confuse t h e analysis o f t h e solvent relaxation d y n a m i c s .


T h e spectral m o d e l s d e s c r i b e d i n t h e A p p e n d i x also i n c l u d e a n u m b e r of assumptions. T h e most tenuous c o u l d b e t h e C o n d o n a p p r o x i m a t i o n , w h i c h states that t h e transition d i p o l e , a n d h e n c e the e l e c t r o n i c w a v e f u n c tions, are i n d e p e n d e n t o f a l l n u c l e a r coordinates, i n c l u d i n g those o f t h e solvent. T h i s m a y b e a p o o r a s s u m p t i o n ; t h e wave functions d e s c r i b i n g M L C T a n d M M C T e x c i t e d states c o u l d d e p e n d d i r e c t l y u p o n t h e solvent o r i e n t a t i o n because t h e e l e c t r i c field e x p e r i e n c e d b y t h e m o l e c u l e w i l l v a r y substantially w i t h solvent o r i e n t a t i o n . It is w e l l k n o w n f r o m Stark-effect spectroscopy that excited-state w a v e functions c a n b e significantly p e r t u r b e d b y e x t e r n a l e l e c t r i c fields (77). F l e m i n g a n d co-workers have p r o p o s e d a s i m i l a r e x p l a n a t i o n for t h e r a p i d

fluorescence

depolarization dynamics found

w i t h c o u m a r i n 1 5 3 i n a l c o h o l solvents (33). F i n a l l y , specific interactions b e t w e e n solute a n d solvent m a y vitiate any c o m p a r i s o n b e t w e e n solvation d y n a m i c s o f these e x c i t e d c h r o m o p h o r e s a n d b u l k solvent d i e l e c t r i c r e l a x ation p r o p e r t i e s . C l e a r l y , t h e systems to b e s t u d i e d m u s t b e selected w i t h care, a n d t h e observations i n t e r p r e t e d w i t h c a u t i o n .

Summary E x c i t a t i o n o f R u ( b p y ) ( C N ) i n a l c o h o l solvents to a t h e r m a l l y e q u i l i b r a t e d 2

2

M L C T e x c i t e d state r e q u i r e s , d e p e n d i n g u p o n t h e a l c o h o l , 0 . 0 7 - 0 . 1 1 e V o f solvent r e o r g a n i z a t i o n . A t - 2 0 ° C this solvent r e o r i e n t a t i o n p r o c e e d s o n a s u b n a n o s e c o n d t i m e scale a n d t h e f u n c t i o n d e s c r i b i n g solvent relaxation is biphasic. F o r m a t i o n of excited M o C l [ P ( C H ) ] 2

4

3

3

4

i n a p r o t i c p o l a r solvents

is a c c o m p a n i e d b y 0 . 0 1 - 0 . 0 4 e V o f solvent r e o r i e n t a t i o n energy. T h e d y n a m i c s o f this r e o r i e n t a t i o n i n b e n z o n i t r i l e are faster t h a n 5 p s , e v e n at t e m p e r a t u r e s as l o w as - 3 2 ° C . A t this t e m p e r a t u r e ,

fluorescence

depolar-

i z a t i o n m e a s u r e m e n t s suggest that t h e solvent viscosity increases to n e a r l y 5 t i m e s its r o o m - t e m p e r a t u r e v a l u e . F o r b o t h R u ( b p y ) ( C N ) i n alcohols a n d 2

2

M o C l [ P ( C H ) ] i n b e n z o n i t r i l e , solvent relaxation p r o c e e d s o n a t i m e scale 2

4

3

3

4

greater t h a n o r e q u a l to the l o n g i t u d i n a l d i e l e c t r i c relaxation t i m e .

Appendix: Data Analysis Steady-State Emission Spectra.

T h e conventional description of

radiative transitions p r e d i c t s that t h e total spontaneous e m i s s i o n p r o b a b i l i t y


16.

Z H A N G ET AL.



261

p e r u n i t t i m e , w, for a m o l e c u l e i n a c o n d e n s e d phase is g i v e n b y e q A l (78) 64 I T V ^^-Z (v)dv

to

(Al)

a b

i n w h i c h η is the refractive i n d e x a n d e is the d i e l e c t r i c constant of the m e d i u m , b o t h at f r e q u e n c y v; E

e

is the effective e l e c t r i c field at the c h r o m -

o p h o r e a n d Ε is the macroscopic e l e c t r i c field; c is the s p e e d o f l i g h t ; a n d i ( v ) is the e m i s s i o n p r o b a b i l i t y p e r u n i t f r e q u e n c y i n t e r v a l at f r e q u e n c y ν


ab

for t h e e l e c t r o n i c t r a n s i t i o n f r o m state a to state b. T h e f u n c t i o n I ( v ) is ab

given by eq A 2 = Av

Id?)

in which A v Ψ ; X Άτη

n

m

Σ

IM

I

a

b

I Ψύ

2

I

- £

hv)

-

b n

(A2)

indicates a B o l t z m a n n average over i n i t i a l v i b r a t i o n a l states

m

is a s u m o v e r a l l final states Y

b n

;M

a

b

is the d i p o l e transition operator;

δ is the D i r a c d e l t a f u n c t i o n ; a n d h is P l a n c k ' s constant.

Internal-mode

distortions can b e treated as h a r m o n i c oscillators b o t h q u a n t u m m e c h a n i c a l l y and semiclassically, a n d solvent r e o r i e n t a t i o n is g e n e r a l l y d e s c r i b e d c l a s s i cally. I n v o k i n g of the C o n d o n a p p r o x i m a t i o n leads to e q A 3

lab(v)

=

Solvent Reorganization Energetics and Dynamics in Charge-Transfer

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