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Idea Transcript


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ISFER ROTR N ENM ET AL. 1? FED 00 Tit-?@ 0 E r IS ELIECT

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OIC FiLE CA1

CV OFFICE OF NAVAL RESEARCH Contract N00014-86-K-0556 Technical Report No. 78

Solvent Relaxation in Thermal Electron-Transfer Reactions:

0

Some Comparisons with Real-Time Measurements of Solvation Dynamics

by

OWN-l!'

G. E. McManis and M. J. Weaver

tM

'LfCT

Prepared for Publication

FE2Q98

in

S

Chem. Phys. Lett.

¢Am

Purdue University Department of Chemistry West Lafayette, Indiana

1988

February 17,

Reproduction in whole, or United States Government.

This document has been distribution is unlimited. *

in part,

is

47907

permitted

approved for

public

for any

release

purpose

and

sale:

of the

its

%'

%1

SiCuRiTy CLASS,CATON OF

~I

PAGE~

REPORT DOCUMENTATION PAGE Ib RESIRiCTIVE

.a REPORT SCURITY CLASSIFICATION

MARK.INGS

Unclassified SECURITY CLASSIFICATION AUTHORITY

'a

DIS'RiBUTION/AVAiLABILiTY

3

for

_____________________________________Approved

2b

DEC LASSIF ICA TION

/

DOWNGRADING SCHEDULE

Report No.

6a

of

sale;

its

5 MONITORING ORGANIZATION REPORT NuMVBER(S)

78

NAME OF PERFORMING ORGANIZATION Purdue University Department

5c

OF REPORT release and

distribution is unlimited.

4 PERFORMING ORGANIZATION REPORT NUMBER(S) Technical

public

7a NAME OF MONITORING ORGANIZATION Division of Sponsored Programs

60 OFFICE SYMBOL (if applicable)

Purdue Research Foundation

Chemistry

ADDRESS (City, State, and ZIP Code) Purdue University

7b ADDRESS (City, State, and ZIP Code) Purdue University

Department of Chemistry 47907 West Lafayette, IN

West Lafayette, IN

Sa NAME OF FUNDING, SPONSORING ORGANiZATION Office of Naval Research

47907

9 PROCU.REMENT INSTRUMENT IDENTIFICATION N~jMBEIR

lOb OFFICE SYMBOL (if #PPl'cabwe)

10

6C ADDRE SS(City, State. and ZIP Code)

800 N. Quincy Street Arlington, VA 22217

SOURCE OF FUNDING NUMBERS PROJIECT NO

PROGRAM EMNTNO

1TASK

IACCESS

1wORK

jNT

NO

NO

I1I TITLE (include Security Classification)

i

Relaxation in Thermal Electron-Transfer/Reactions: Measurements of Solvation Dynamics/

SSolvent

Some Comparisons with Real-Time

PERSONAL AUTHOR(S)/ -J

G_ i 3a

F_ MrMnis ind M_ TYPE OF REPORT

J

Wpnypr 13b TIME COVERED TO

I

14 DATE OF REPORT (Year. Month.Dy),

PAGE COUNT

! 6 SUPPLEMENTARY NOTATION

FIELt)

19 ABSTRC

*The

*

GROUP

solvent relaxation, electron transfer, timefresolved fluorescence

SUB.GROUP

(Continue on rev'erse if necessary and identify by biock number)

role of solvent dielectric relaxation on the barrier-crossing dynamics for outersphere electron transfer (ET), as evaluated from the solvent-dependent kinetics of metallocene self-exchange reactions, is compared with recent real-time measurements of polar solvation dynamics obtained from time-dependent fluorescence Stokes shifts (TDFS) for suitable chargetransfer excited states. While the solvent-dependent kinetics obtained in some aprotic media are consistent with the TDFS measurements, the barrier-crossing dynamics in several associated and/or highly polar liquids are indicative of much faster relaxation than inferred from TDFS. The possible nature, and implications, of these rapid modes are discussed.

20 DISTR:SUTiON /AVAILABILITY OUNCLASSIFIEDIUNLIMITED 22a

or

OF ABSTRACT 0 SAME AS RPT

121 0

DTIC USERS

94 MAR

Unclassified 122b TELEPHONE (Include Ate Coe

NAME OF RESPONSIBLE INDIVIDUAL

DD FORM 1473.

ABSTRACT SECURITY CLASSIFICATION

S3AReiinmpb

All edition

sdit

al~tdSECURITY

are obsolete*~

'is~r

2

FFICE SYMBO0L

CLASSIFICATION OF THIS PAGEd

I

A KI,.

Solvent Relaxation in Thermal Electron-Transfer Reactions: Some Comparisons with Real-Time Measurements of Solvation Dynamics

George E. McManis and Michael J. Weaver Department of Chemistry Purdue University West Lafayette, Indiana

47907, U.S.A.

.1k

S+

,

to Chemical Physics Ltes Lette

pSubmitted

.

. . .. . . . . . .

.5,

.,s

U

S

r

,

+ +

+,.

t,

t*+.

ABSTRACT

The dynamics

from the solvent dielectric relaxation evaluated barrier-crossing (ET),onasthe transfer electron for outer-sphere role

.

of

solvent-dependent

kinetics

of

compared with recent real-time

metallocene

self-exchange

measurements

of polar solvation dynamics

reactions,

is

obtained from time-dependent fluorescence Stokes shifts (TDFS) for suitabl& charge-transfer

excited

states.

While

the

solvent-dependent

kinetics

obtained in some aprotic media are consistent with the TDFS measurements, the barrier-crossing dynamics in several

associated and/or highly polar

liquids are indicative of much faster relaxation than inferred from TDFS. The possible nature, and implications, of these rapid modes are discussed.

I

Although the important role of the solvent medium in determining the free-energy barrier, recognized, I recently

its

been

AG*,

influence

treated

characteristics distortions),

,

(such as

upon

the

By

processes

has

long been

barrier-crossing dynamics

has

only

and subsequently afforded detailed

utilizing

probe

reactions

having

suitable

a small barrier contribution from intramolecular

and by taking proper account of the variation in AG* with the

solvent, kinetic

data

for electron-exchange

approximate

information

frequency,

',

corresponding

electron-transfer

theoretically, 2

scrutiny. 3

experimental

for

upon

on

the

the

dependence

solvent

solvent-dependent

reactions can yield at

of

properties. 4

frequencies

the

least

barrier-crossing

Comparison

predicted

from

with

the

conventional

dielectric continuum treatments yields reasonable agreement in some cases,3 although some substantial deviations between the experimental and predicted frequencies have come to light. 3 d ,4 b~c Concurrent

with

(yet

independent

of)

these

activities,

real-time

measurements of the dynamics of dipolar solvation have been undertaken by utilizing time-dependent fluorescence Stokes shifts (TDFS) for chromophores forming suitable charge-transfer excited these

measurements

(> 10 ps) down

to

in some ca.

been

restricted

to

"8

While the majority of

relatively

recent studies have examined solvent

0. 2 ps.and

relaxation times, dielectric

have

states. 5

Comparisons

between

rs, and the longitudinal times,

continuum

model

indicate

that

long

timescales

relaxation times

the experimental

TDFS

rL, predicted from the

typically

rs

rL,

although

6 multiexponential decay behavior is commonly observed. -8

Prompted in part by these experimental studies, increasing attention is

being

~~,--Z

focused

on

the

manner

and

extent

to

which

solvent

relaxation

%.

%~%,P~~-

2 charge

attending

transfer may

picture. 6 d '9

continuum

from

differ

In

for

accounting

mechanisms

particular,

dielectric-

conventional

the

multiexponential relaxation have been identified,including the expectation that r > rL for solvent molecules nearby the solute as a consequence of diminished dipole interactions.6d,9 Given the current rapid evolution in both experimental and theoretical aspects of charge solvation dynamics, it is clearly of interest to compare these results and concepts with corresponding information on the dynamics In particular, there is a need to

of electron-transfer barrier crossing.

identify the components of the overall dielectric response having the most Such a comparison is considered

relevance to the barrier-crossing problem. here,,

utilizing

our

recent

data

on

metallocene self-exchange reactions. 4 c believe ,

that

its

significance

is

solvent-dependent kinetics

the

for

While necessarily preliminary, we heightened

by

the

emerging

new

perspectives of dynamical solvent effects in chemical reactivity.

Results and Discussion Unlike TDFS measurements of dielectric solvent relaxation, which are from

relatively directly

extracted evaluation

of

such

effects

in

the

time-dependent dynamics

of

Stokes

shifts,10

the

barrier

crossing

for

intermolecular electron transfer requires consideration of the influence of energetics

barrier

upon

the

observed

rate

constant,

kob.

A

useful

I formalism for this purpose is expressed as1 ,12

kob - K

where

K

is

the

equilibrium

9v

exp(-AG*/RT)

constant

for

(1)

forming

the

appropriate

I %5

3 internuclear geometry, and K., is the electronic transmission coefficient. We have recently employed this relation to extract solvent-dependent barrier-crossing frequencies, vP, from kob values obtained for metallocene self-exchange

reactions

technique.4c,13

These

using

the

reactions,

(Cp - cyclopentadienyl), pentamethyl-cyclopentadienyl),

proton

involving

nmr

line-broadening

cobalticenium-cobaltocene,

its decamethyl derivative, C' Co +/O

and

ferricenium-ferrocene,

several virtues for this purpose, as detailed earlier. 4

(C-

Cp2 Fe+/o,

have

These include the

presence of only small inner-shell (i.e. reactant intramolecular) barriers, small

or

negligible

work-term effects

upon

K.,

and

the

stability

and

0nonspecific solvation of the reactants in a variety of nonaqueous media.-[ The

estimation

of

absolute

Y.

values

for

such

electron-exchange

processes is hampered not only by uncertainties in Kp but, most critically, *P

in the AG* values. -*

However, relative v. values in different solvents can

be evaluated, at least approximately, since K

should be roughly constant

p

and there is good evidence be described

for

that the required solvent dependence of AG

self-exchange reactions by the

can

conventional dielectric

continuum formula 14 -..

&G:-

where

e

is

the

(e2 /4)(a-'

electronic

R')(,e-l

charge,

1)

(2)

a is the reactant radius,

R

internuclear distance (commonly presumed to equal 2a), and eop and

is

the are r

the optical and static dielectric constants, respectively.

*This 0

includes

measurements

of

optical

intervalence

transition

energies, Eop, in mixed-valence compounds, such as analogs of the metallocenes considered here, 15 in which the15 solvent-dependent E.p values ,16 vary approximately in accordance with Eq (2).

?-

4

%

The central issue here is the role of solvent dielectric relaxation in the

barrier-crossing

implies that ic.

frequency.

While

be

minor

solvent

for

the

present

This contribution, however, is

metallocene

systems

component of AG* is relatively small, ca 10%. then, we can time, r

sensitivity

= I (i.e. reaction adiabaticity is achieved), 17 w

influenced by reactant vibrations. to

the

simply regard

vn

since

the

of

may be likely

inner-shell

Under these circumstances,

to be related to

the

effective

relaxation

I by

(3)

n--i

The

vn

comparison

between

transfer barrier

such

solvent-dependent

crossing and

r*f

corresponding TDFS

values

for

relaxation

electron-

times,

TS'

forms the objective here. At least for a Debye fluid (i.e. that having a single relaxation time, dielectric

D)

terms

of

type 4 a,

continuum treatments

one-dimensional

of the barrier-crossing dynamics

overdamped motion 2 ab

lead

to

relations

in

of the

7

(4)%

a-Kr

(f/CS)r 0 , with e.

dielectric loss spectra, by rL

-

frequency" dielectric constant.

Although the proportionality constant K in

Eq

(4) depends

somewhat

on AG

being the

as well as on the shape of

"infinite

the barrier

top,2b this dependence is relatively mild so that usually K is within ca twofold

of

unity

for

weak-overlap

electron

circumstances, then, we expect that r~f

i

exchange.

Under

these

%]

can be equated approximately with

,%

"%.

5 7

*

A

related

treatment

for

solvents

exhibiting

multiple

dielectric

relaxation yields the conclusion that r.ff is influenced disproportionately by the

faster relaxation mode(s),

so

often-predominant "slow" relaxation.2 c Debye solvents we might anticipate

this

dependent

situation,

it

electron-transfer

rLI,

where rLI

is the

On the other hand, at least for > T

that r.f

as a result of short-

f,as noted above. 9 a

range solvent contributions to Given

r.ff <

that

is

instructive

results

in

to

the

examine

light

of

the the

solventcontinuum

predictions as a preface to comparison with corresponding TDFS data. I

summarizes

rate

constants

for

self

ke,

exchange,

for

Table

+/0 Cp2 Co,

Cp2Co /0, and Cp2 Fe+/*

in fifteen solvents, expressed as rate ratios with

respect

in

to

those

k. /k..(ref).

The

extracted

from

reference

solvent

data

refs.

the

solvent"

for

the

cobaltocene

and

18,

respectively.

4c

is

"reference

somewhat

arbitrary,

and

dimethylsulfoxide,

ferrocene

couples

are

Although the choice of

dimethylsulfoxide was

selected

since it displays Debye-like dielectric loss behavior 1 9 and TDFS relaxation kinetics. 6 a

Listed

these

probes

in each solvent, again quoted as ratios

value

in DMSO,

alongside

are

ff/* ff(ref).

The

the

corresponding

latter were

?*ff

estimates

to respect

for

to the

obtained from the

rate

ratios by using (cf. Eq. (1)]: [off/r~fa(ref)]-

where

the

AG03

[k.*/k. 1 (ref)] exp([AG*-

estimates

were

obtained

AG

from

(ref)]/RT )

Eq.

(2)

(see

(5)

Table

I

footnotes).

This procedure therefore assumes that Kp (and x* 2 ) are solvent

independent

(vide supra).

While the absolute k.

values in each solvent

are markedly different for the three probe reactions

.

,m_ .

. .. ...

.= ,.

r

.

.

m>

...

. K.

..

..

E.. B..

. .

*.,

.

.^

. *.

...

(apparently due to

_

,

6 electronic

coupling

effects

on K

,113),

the

rate

and

relaxation

time

ratios are largely similar in a given solvent.

e 140%

,.

Also listed in Table I are the corresponding longitudinal relaxation time ratios,

rL/TL(ref),

obtained from dielectric loss

data.

Comparison

between the corresponding rvff/r ff(ref) and TL/TL(ref) values reveals that while these ratios are in reasonable agreement (within ca. twofold of each

V.

other) in a number of solvents, some substantial discrepancies are present.

V

Most notably, the r f

values in methanol and ethanol are at least 50 fold This anomaly has been noted previously on

smaller than expected from r

the basis of related electrochemical exchange kinetics. 3 d '4 b similar discrepancies between the relative r

and r

Qualitatively

values are also seen

in Table I for propylene carbonate and especially N-methylformamide (NMF). The

TDFS

solvation

acetonitrile,

DMSO,

Castner et al. probe LDSthan

in

of four

nitrobenzene,

and

of

the solvents

methanol,

have

in

been

Table

I,

"

examined by

for timescales down to ca. 0.5 ps using the fluorescence

.6a

7 50

dynamics

DMSO

The

[i.e.

r.

value

rs/ts(ref)

in

acetonitrile

-

0.11,

in

is

about tenfold smaller

rough

accordance

with

the

corresponding rL ratio (Table I), even though rs is ca. 1.5-2 times rL 6a in good accordance with the corresponding r ff/r ff(ref)

This behavior is ratios in Table methanol,6a

I.

however,

corresponding r*f obtained

in

r ,/r

differ

significantly

data in Table I.

nitrobenzene,

smaller than r. with

The solvation dynamics observed in nitrobenzene and

with

the

=

solvent benzonitrile

2

predominant -

for nitrobenzene

(Table I).

that

expected

from

I

the

Biexponential relaxation behavior was

This yields rs/rs(ref)

ff(ref)

from

rs

value

being

4

fold

0.5 in this solvent, as compared and the

dielectrically

For methanol Castner et al.

similar

found that

*.-.* .4.4

~d'.

-

9

~,r..'-'

*~q~,%

1 .,%%%

*4*44

7 s/rs(ref)

1

relaxation

which

times

Indeed, the r

for

stands

in

marked

barrier-crossing,

contrast

to

the

r*ff/rff(ref)

corresponding

0.05

(Table I).

values are indicative of dielectric relaxation in methanol

that is at least as rapid as in acetonitrile, whereas the rs value in the latter solvent is around tenfold shorter than in the latter. 6a More striking differences between the barrier-crossing and real-time solvent relaxation behavior are exposed by examining some recent TDFS data obtained using %

Coumarin

153

the

multiexponential

decay

behavior was

values

were obtained in propylene

(N4P)

that

values.

are

These

markedly and

fluorescence probe. 6 b

(5-10

other

are

than

indicative

of

accordance with

the MSA

treatment

short-range relaxation time, with es.6b

6b-d

Although the

these measurements,

observed,

average

i

rs

(PC) and N-methylpropionamide

longer

7S/TLand the solvent dielectric constant, NMP under the conditions employed.

in

typically

carbonate

fold)

data

30 ps

to > ca.

restricted

laaintmsaewas and

as

Es'

the

corresponding

rL

a correlation between es = 75-300 in PC and

since

This behavior is qualitatively in

of Wolynes,9a which predicts

that

the

is longer than rL to an extent increasing

r.,

A difficulty, however, is

that the

likely concomitant changes

in c. and the solvent size can blur this prediction.

versus log

,

relative

to

DMSO as

The data

for

For comparison purposes, a plot of log (rff/L) r

r

and

listed

in

numbered

refer Table

1

the

relaxation times

I,

is

shown

according

to

the

in

Fig.

scheme

1.

in

Table

I.

are

seen

to

decrease

continuously

(and

solvents with progressively higher e. values.

,-p

'""51

In

those

.,.'iL-'i...%

%.%

q

-%

~%'

%

"%

in

each solvent contrast

- log es behavior noted in ref. 6b, the log (r/vL)

log (/ Fig.

to

where

roughly

to

is the

values in

linearly)

for

In particular, the solvents

'%

%

t%%

t"%

"-"%%°%

"•"%

","-

.

2-'•" S"..

.7-.

8 having the

highest dielectric constants,

respectively), yield also (.ff/%L)

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