Energetics and dynamics of solvent reorganization in charge-transfer excited states

23

Coordination Chemistry Reviews, 97 (1990) 23-34 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

ENERGETICS

AND IN

Mariusz

Kozik,

Chemistry

DYNAMICS

OF

SOLVENT

CHARGE-TRANSFER

Norman

Sutin,

Department,

EXCITED

and Jay

Brookhaven

REORGANIZATION STATES

R. Winkler

National

Laboratory,

Upton,

NY 11973

SUMMARY 2 metal-to-ligand charge-transfer The dynamics of salvation of the Ru(bpy)s(CN) excited state have been examined in a series of aliphatic alcohols. Steady-state emission spectra recorded at low temperature (N 10 K) and at room temperature were used to resolve internal-mode and solvent contributions to the emission bandshape. Time-resolved emission spectra were fit to a model that takes into account internal-mode distortions as well as time-dependent broadening and shifts in emission maxima. A single-exponential solvent relaxation function does not adequately describe the temporal development of the emission profile of Ru(bpy),(CN) 1 in alcohols. The evolution of the emission spectrum is clearly biphasic, and can be reasonably fit wit,h a biexponential function. The slower of the two relaxation times is comparable to the longest longitudinal relaxation time reported for the bulk solvent. ThPse slower components, however, rcprcsent less than half of the overall approach to equilibrium. Local heating due to above-threshold excitation, and local solvent relaxation arc two likely sources of the faster dynamics.

INTRODUCTION Electronic environment and emission parameters

profiles to provide

spectroscopic resolved

absorption

used to examine

If just

solvent

directly

the

and

initial

bands.

When

be correlated

insight the

dynamics

of microscopic

associated nuclei

states.

internal-mode

then the

their the

salvation

equilibrium

energy

difference

Similar

distortions

along

upon

the

electronic

0 1990 Elsevier Science Publishers B.V.

that

(refs.

solvent in the

Timeis being

as well as 2-8).

electronic

absorption

is contained

accompany

to study.

molecules,

processes

solvent

of fast laser

technique

of excited

steady-state

in position

information

amenable

positions

of the

the advent

powerful

excitation or emission

coordinate breadths

excitation,

the

of absorption

and empirical

With

are also

is a particularly

used to probe

and shapes

properties

with fast electron-transfer

change

reflects

solvent

of salvation.

of s&&ion

the dynamics

final

OolO-8546/90/$04.20

with

into the nature

have long been

Tl le energies

1).

(TRES)

in solution,

maximum

(ref.

spectroscopy

dynamics

of a molecule

spectroscopies

in solution

can

methods,

emission

the solvent

and emission

of molecules

of

of the

it becomes

24

more difficult to extract also reflects

information

internal-mode

contributions,

about the solvent configuration

rearrangements.

In an attempt

we have performed a Franck-Condon

low temperature

(z

10 K) steady-state

emission

since the bandshape

to factor-out

internal-mode

analysis of the room temperature spectra

of Ru(bpy),(CN)2

and

in alcohol

solvents. Because to prepare the solvent molcculc.

elect,rons

a molecule

move much faster

than nuclei,

in a nonequilibrium

will rearrange

salvation

to accommodate

a short laser pulse can be used

environment.

Following excitation,

the new permanent

dipole of the excited

Since the position and shape of the emission band reflect, in part, the salvation

environment, dynamics

the time evolution

of microscopic

emisswn spectra

of Ru(bpy),(CN)

the analysis of the steady-state its metal-to-ligand

of the emission

salvation.

profile can be used to monitor

We have examined 2 in alcohols at -20

emission spectra,

charge-transfer

(MLCT)

the picosecond

“C and, using information

evaluated

the dynamics

the

time-resolved from

of salvation

of

excited state.

METHODS Materials HPLC-grade and absolute

methanol

ethanol

over molecular

(MeOH),

(EtOH)

n-propanol

were refluxed

(n-PrOH),

and n-butanol

over Na, distilled,

sieves (3A for MeOH, 4A for higher alcohols).

prepared and purified according to published procedures

(n-BuOH),

and stored

under Ar

cis-Ru(bpy)l(CN)z

(refs. 9-10).

was

Purity was judged

by TLC on silica, developed with methanol. Data Collection Steady-state ment constructed temperature

emission

at Brookhaven

spectra

refrigerator.

and low-temperature

Time-resolved

emission

were recorded following excitation of a flashlamp-pumped, was dispersed

Laboratory

were recorded (ref.

respsonse

Identical

11).

Samples

tubes

configurations

on an instruon

were used for both

Picosecond

time-resolved

emission

with a 30.ps pulse from the third harmonic mode-locked

and directed

time was 3540

for low-

and mounted

spectra.

spectra.

actively/passively

by a spectrograph

The instrument

National

spectra

were held in sealed 4-mm OD fused-silica

the cold head of a closed-cycle room-temperature

Emission

spectra.

Nd:YAG

to the entrance

laser.

spectra (355 nm)

Emitted

slit of a streak

light

camera.

ps (ref. 11).

Data Analysis Steady-state

emission spectra.

unit time, w, is given by eq. 1 (ref. 12):

The total spont,aneous

emission probability

per

26

in which

n is the refractive

E, is the effective field;

c is the speed

interval

is given

and F is the dielectric

field at the chromophore

of light;

at frequency

z*(v)

index

electric

and lab(v)

constant,

is the emission

I, for the electronic

transition

both

and E is the probability

from state

at frequency

macroscopic per unit

a to state

11;

electric frequency

6. The

function

by eq. 2:

(2) in which Au,, final states

indicates

Internal-mode ically

a Boltzmann

@bn; Mob is the dipole distjortions

can he treated

and semiclassically,

Invoking

the

Condon

average

while

over initial

transition

leads

Qarn; C,

oscillators

reorientation

then

states

is a sum over all

and 6 is the Dirac

as harmonic

solvent

approximation

operator;

both

is generally

delta

function.

quantum

described

mechanclassically.

to eq. 3:

> in which is the squares

the

of the

by recursion that

repeated

wavefunction

vibrational

relations

the vibrational

is taken

product

to be Gaussian

and the classical

g(“,m,v) =

01

0’ = 4XsRT

-t 2)31jhwj)coth j

- [E(n, {

exP

C

Xrj +

j The

term

the

(ref.

h#

62

13),

(eqs.

4-6,

state

factors,

lineshape

from both

and xjP, j.

The

are given

and it has been

a and b. The

contributions

mode

modes

electronic

Franck-Condon

in states

broadening solvent

p of the

assumed function

the internal

ref. 14).

I

(4)

(5)

C(m, -

ni)ftwi

!

parameters

clude modes

treated

modes.

is the electronic

&a

i.e.,

polynomials

m) - As -

Xs is the reorganization

are the reorganization

quantum-mechanical state

w, is the same

and to contain

modes

E(n)m) = EOO-

imegrals,

for the Hermite frequency

over the

E in vibrational

overlap

semiclassical

u

extends

for mode

(3)

semiclassically, origin

parameter

for the classical

for the classical

internal

and the sum over i includes for the a-to-b

transition.

solvent

modes.

mode

The

and the Xlj

sums over j in-

the quantum-mechanical

26 Time-resolved the solvent

emission

configuration

pendence,

spectra.

Time-dependent

is a function

the spectral

lineshape

of time.

function

In order

can be recast

spectral

shifts arise because

to account according

for this

to eqs.

time

7-8

de-

(refs.

3,

15).

- [E(n,m)

- Xs(l - 2p(t))

- hv]*

(7)

o(tY

2XsRT(

IJ(~)~ = 4XsRT

The term

00’ is the breadth

vent coordinate

If quantum

coordina,te, modes

=

In this

described

(8)

distribution

the

peak

of excited

p(t) dcscribcs

and is the object

arc ignored,

by g(n, m, V, t) and that

qt)

of the energy

at t = 0. The function

along the solvent

generally

1

1 - p(t)Z) + f70”

2X.yRT + ou”

relaxation

by the correlation

along the solmolecules

of this study.

it can be seen that maximum

molecules

of the excited

the emission

will vary with

function

C(t)

time

band

as p(t).

given by eq. 9 (refs.

is described This

shift

b(t)) - Mw)) (40)) - Mm)) approximation

of quantum

modes

(9) the experimental

and broadening

evolut,‘on of the spectrum. then time-resolved

is

4-7).

function

C(t)

is equivalent

in g(n, m, V, t) produces

If internal-mode

distortion

to p(t).

Inclusion

a far more complex time-

parameters

are known, however,

spectra can be fit to eqs. 3-8 using an assumed form for p(t).

RESULTS Steady-state

emission

spectra.

The room-temperature

and low-temperature

emission spectra of Ru(bpy)t (CN) z in ethanol are shown in Figure 1. At room temperature the emission profile is a broad, asymmetric

band. At 12 Ii, a progression in a high

energy vibra$ional mode resolves. The spectra were fit to the model described by eqs. 36 in which a single quantum mode was included and the remainder of the internal-mode broadening was treated semiclassically approximate, temperature

(dashed lines, Figure 1). This model, though only

does provide an adequate spectra:

description

of the low-temperature

and room-

the difference between the two is included as a distortion

along

the classical solvent coordinate. The solvent reorganization

parameter

Xs can be determined

mum of the emission profile or from its breadth (eqs. 4-5).

from the peak maxi-

By neglecting the temperature

X, Figure Right: mode.

800

600

800

600

nm

1. Emission spectra of Ru(bpy)s(CN) s in EtOH. Left: 12 K. Dashed lines are Franck-Condon fits to the spectra

dependence of the semiclassical u* at the two temperatures. at the two temperatures the solvent reorganization

morn-temperature. using one quantum

modes, X.5 can be determined from the difference between Alternatively,

the difference in the maxima of g(n, nz, V)

should be equal to twice Xs. parameter

Continuum

should be proportional

models predict that

to the dielectric

function

Fr (eq. 10, ref. 16).

3(rs - cap) 4

= I4(es + l)(e,r

(10)

+ l)]

es and e,r are the static and optical dielectric constants of the solvent, respectively. plots in Figure 2 of Xs versus 4 of the emission profiles correlate peak-maxima

illustrate

reasonably

accounted

well with F,,

data show an inverse correlation.

discrepancy is some temperature-dependence

in n-BuOH

The most likely explanation

for in cq. 4. The values of XS determined

at -20

spectra.

but those determined

for this

from the band widths are upper

dependence of the semiclassical

The time-resolved

emission spectra

“C! are shown in Figure 3. The most striking

is that the form of the emission

from

of the peak maximum that is not explicitly

limits because of the neglect of the temperature Time-resolved

The

that the values determined from the breadths

decay function

modes.

of Ru(bpy)z(CN)z aspect of these data

is wavelength-dependent.

At shorter

wavelengths, a large initial emission intensity rapidly decays to a smaller, constant value (on the 2-ns timescale).

At longer wavelengths,

a rapid increase in emission intensity

28

150

I

I

r\

‘:

0

‘;; - 100

>

2 2 50 200

I

I

220

240

F,

(xl

260

0-?

Figure 2. Plots of apparent Xs versus the solvent dielectric function Fr. Values of Xs were determined from emission maxima (O), and from breadths of emission bands (0).

follows excitation

until a constant

value is attained.

at wavelengths between these two extremes.

Intermediate

sion profile that shifts to the red following excitation. Ru(bpy)r(CN)*

in MeOH, EtOH, and n-P&H,

As described above, the time-resolved correlation

function,

C(t).

wavelength time-decays to multiexponential spectra which are fit to Gaussian are decidedly nonexponential -20 “C.

likely that faster components apparatus.

The parameters

The correlation

functions.

2 in EtOH,

describes

C(t)

time-resolved

The resulting n-PrOH,

C(t) functions and n-BuOH

in MeOH at -20

arc lost because of the limited timc-resolution from the biexponential

It is possible,

only if no internal-mode therefore,

of the TRES

C(t) fits are collected in Table 1.

distortions

that the biphasic

accompany

C(t) decays arise from the complex

tion, p(l). We examined this point by fitting the Ru(bpy)z(CN)s to the low-temperature

emission spectra.

ble 1. Again, biexponential spectra.

along

the a-to-b tran-

spectral evolution set out in eqs. 3-8, rather than from a biphasic solvent relaxation spectra to cps. 3 -8, using the internal-mode

at

“C, but it is

function described by eq. 9 rigorously describes the relaxation

the solvent ,coordinate sition.

can be fit to the empirical

functions, then reconstructing

distribution

function

Similar behavior was found for

smoot,hing is effected by first fitting single-

for Ru(bpy)s(CN)

A single exponential

is found

with an emis-

though on different timescales.

emission spectra

Two-dimensional

behavior

This behavior is consistent

distortion

parameters

time-resolved

func-

emission

derived from the fits

The results of these fits are summarized in Ta-

decay functions are necessary to describe the time-resolved

The agreement between the peak-maximum

fits and the Franck-Condon

fits is

0

1

0

Time,

I ns

Figure 3. Wavelength dependence of time-resolved emission profiles of Ru(bpy)r(CN)r in n-BuOH at -20 “C. Left, lower to upper: 607, 620, 634, 648 nm. Right, upper to lower: 661, 675, 689, 699 nm.

reasonably

good. The major difference is that the time constant

process is substantially

smaller in the Fran&Condon

ancy could lie in the fact that in the Franck-Condon t = 0 spectrum float.

fits.

fits the position

are fixed, while in the peak-maximum

In any event, both fitting

procedures

for the faster relaxation

The source of this discrepand shape of the

fits the value of (v(0))

clearly indicate

biphasic

is free to

solvent relaxation

dynamics.

DISCUSSION Continuum erties.

models are generally the first recourse for discussions

As was shown in Figure 1, a dielectric

breadths of the Ru(bpy)r(CN)r

steady-state

continuum

of solvation prop-

model adequately

describes the

emission profiles, but not the emission max-

30 Table

1

Kinetic parameters

for solvent relaxation

in the MLCT

_

_

33

0.88

5

30

0.75

19

140

0.77

5

70

0.68

42

285

0.70

2

202

0.51

81

477

0.50

6

429

MeOH

EtOH

n-PrOH

n-BuOH

’ For biexponential decay time rt, and Decay times are in the peak-maximum

Table 2 Diclcctric

relaxation functions, C1 is the coefficient of the exponential with (1 - Cl) is the coefficient of the exponential with decay time r2. piccseconds. For each solvent, the upper set of parameters is from analysis and the lower set is from the Franck-Condon analysis.

rclsxation

properties

of aliphatic

Alcohol

TDo3

TD2

MeOH EtOH

_

-

_

n-PrOH

4

n-BuOH

3.5

a Relaxation

dielectric,

solcation

a time-constant

TL1

23

43.2

6.40

31.4

4.85

98

34

1920

27.4

3.92

274

50

3145

23.6

3.65

486

(refs. 4e, 6f, 23).

can be described

the approach

GO1

154

hydrogen-bonding,

to equilibrium

can complicate

by bulk solvent properties.

have also been described

neous change in the permanent

E01

632

times are in picoseconds

but the general trends

alcohols at 253 K.” 701

ima. Specific solvation effects, especially microscopic

excited state of Ru(bpy)r(CN)z.a

by continuum

of the dielectric

The dynamics

models.

polarization

dipole moment of a spherical

the analysis, of

In a Debye-type

following an insta-

solute is exponential,

with

TL given by eq. 11 (refs. 1720):

(11) where rD, the Debye-time, rium polarization

is the exponential

following an instantaneous

time-constant

for the approach

change in the external

electric

to equilibfield (refs.

31

21, 22).

The high and low frequency

dielectric

dispersion of the medium.

dielectric

Alcohols are not simple Debye solvents, dielectric

dispersion.

hydroxyl groups,

The highest frequency

the mid-range

and the low-frequency (Table 2, ref. 23).

component

n-PrOH,

also complicated.

constant.

for E, in nonassociated

solvents.

The significance

dispersion,

i.e., rnr > rn2 > 70s).

behavior of the alcohols it is not surprising Ru(bpy)s(CN)r

MLCT

excited

longitudinal

been examined. relaxation constant

MLCT

excited

is especially

In light of the complex dielectric Comparison

clear

relaxation

dynamics for the

of the data in Tables

time (7s) is in fair accord with the

time (rrr ) for the four alcohols that have

of the two relaxation

times to their corresponding

While the dispersion region with time

to the largest part of the dielectric

less than half of the observed microscopic

model.

E,,,, which is

from eq. 11 by using

that the solvent relaxation

dielectric relaxation

The most obvious explanation continuum

constant

refers to the lowest frequency region of

however, are quite different.

r~r corresponds

rr represents

with each of the three regions of

TL can vary by almost. a factor of two

state are biphasic.

The contributions

functions,

process

The definition of 7~ for alcohols is

of this complication

1 and 2 reveals that the slower solvent relaxation low-frequency

in alcohol a.ggregat,es

the low-frequency

The 7~~ values in Table 2 were calculated

~~1, and r~r values in reference 6f (c,r

dielectric

of free

index of the medium, and which is commonly used

in n-BuOH where, depending upon the choice of e,, (cm, = 3.65; t,r = 1.96).

to rotation

of free alcohol molecules,

These values differ from the optical dielectric

equal to the square of the refractive

the csr ,

to have three regions of

of hydrogen-bonds and n-BuOH,

A different value of E, is associated

dielectric dispersion.

and cc, arise from the

is attributed

to reorientation

to disruption

accounts for the major part of the dielectric

E,

and are reported component

component

In MeOH, EtOH,

constants,

constant

salvation

of the above data is a breakdown

Most of the solvent reorganization

associated

in these alcohols,

dynamics. of the dielectric

with formation

state is likely to be found in the first few salvation

of the

shells around the

solute (refs. 4g, 6e, 24). In this region near the solute, however, the solvent reorientation dynamics are least likely to resemble bulk solvent dynamics. ticularly

The problem could be par-

acute in alcohols where the solute will disrupt the hydrogen-bonded

found in the bulk.

A simple explanation

is that the faster decay times reflect relaxation slower times ‘arise from relaxation Similar explanations

aggregates

of the observed solvent relaxation of solvent nearer the solute,

of more distant,

bulk-like

in aprotic solvents (refs. 4-7).

sults with alcohols, however, observed relaxation The Debye time is reported

dynam-

Unlike the re-

times fall in the range rn > r,,bad > 7~.

to be a better measure of individual

times than r~, and is expected

while the

solvent.

have been proposed to explain the biphasic relaxation

ics found for several organic chromophores

dynamics

to be a better approximation

molecule reorientation

to the relaxation

of solvent molecules nesrer the solute (refs. 4g, 22). The obvious conclusion,

dynamics

then, is that

32 in these

aprotic

solvents,

molecules

nearby.

behavior.

Since

The

aggregation

solvent

molecules

t,o be extensively reorientation with

aggregated,

times,

r~s.

This

simple

pulses

explanation

significantly

is ultimately solvent

number states

above

relaxation

describing since

wit,h solvent state

the

wavefunctions

Fleming

electric

dynamics

found

known

to hydrogen-bond

action

need not be identical therefore,

would not be described

alcohol-molecule fair agreement

the electronic This

excited

by the

perturbed

groups

in the ground

(ref.

26),

and MLCT

also be contributing solvent

electric

excited

excited-

fields

(ref.

Protic

states.

25).

fluorescence A further

solvents

and the magnitude

to the observed

dielectric

substantially

(ref. 4~).

(CN),.

the

the solvent

that

rapid

solvents

of Ru(bpy)s

a

which

because

will vary

for the

153 in alochol

ligands

include

upon

spectroscopy

explanation

energy

are indcpcndent

directly

molecule

laser

complicate

also

assumption

by external

a similar

excess

approximation

wavefunctions,

Stark-effect

a number with

could

above

Condon

could depend

from

This

which

may be a poor

state

with coumarin

by bulk

band.

described

be the

with

were excited

models

might

solvent.

cyano

be tempered

s complexes

spectral

the cyanide

with

might

1 must

heating

and hence

proposed

involves

different

are not likely

1 reveals

to local

can be significantly

complication

the solvent

for their

the individual in Table

of the emission

field experienced

have

than

of the solute

leading

It is well-known

serious

dynamics,

resemble

in Table

tenuous

the MLCT

and coworkers

depolarization

The

most

including

orientation.

faster

responsible

vicinity

the Ru(bpy)s(CN)

dipole,

wavefunction orientation

might

of the data

The

coordinates,

is possibly

(M 1.4 eV) the origin

the transition

relax

of 7~s.

dynamics.

of all nuclear

the solute

to the rr values

into the solvent,

of assumptions. that

in alcohols

instance,

deposited

from

in the immediate

relaxation

values

In the first

farther

Comparison

the corresponding

of caveats.

the

molecules

are

of this inter-

Hygrogen-bonding

solvent

relaxation,

but

properties.

CONCLUSIONS Excitation excited tion.

requires,

At -20

the function these edge

of Ru(bpy)s(CN)s

state

“C this

in the

vicinity

in describing

of the

however,

solute.

proceeds

solvent

relaxation

The

models

must

therefore,

of solvent

major

nearer

in

to be

deficient

component

in agreement

component

molecules

to occur

solvent

slower

to ski,

up to the

describe

are likely The

is comparable faster,

is likely

accurately

dynamics.

and

used to describe

continuum

reorientat,ion

model

MLCT

reorganiza-

timescale

often

is a uniform

models,

relaxation

theories.

from

The

of the solvent

reorientation

equilibrated

eV of solvent

on a subnanosecond

solvent

a reliable

Continuum

of solvent

of continuum arises

most

to a thermally 0.08~0.12

is biphasic.

dielectric

however,

MLCT

probably

the

solvents

the alcohol,

relax&ion

Since

shells,

all aspects

the Ru(bpy)z(CN)s the predictions

that

solute.

few solvent

upon

reorientation

solvent

assume

of a spherical

the first

solvent

describing

dynamics

in alcohol

depending

of with

of the relaxation, the

solute,

rep-

33 resenting a breakdown studio

of the dielectric continuum

model.

We are continuing

TRES

of metal complexes in order to characterize further the parameters that comrol

the dynamics of solvent reorientation about electronically Acknowledgment.

excited solutes.

We thank Dr. Bruce Brunschwig for many helpful discussions,

and for his assistance in the preparation of this manuscript.

This research was carried

out at Brookhaven Nat,ional Lahoratory under Contract, DE-AC02-76CH60016

wit,h the

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