Spin Coupling and Electron Delocalization in ... - ACS Publications

Chapter 26

Spin Coupling and Electron Delocalization in Mixed-Valence Iron—Sulfur Clusters 1

2

Stephen F. Sontum , Louis Noodleman , and David A. Case

2

1

Department of Chemistry, Middlebury College, Middlebury, VT 05753 Department of Molecular Biology, Research Institute of Scripps Clinic, La Jolla, CA 92037

Downloaded by UNIV OF ROCHESTER on April 23, 2013 | http://pubs.acs.org Publication Date: June 8, 1989 | doi: 10.1021/bk-1989-0394.ch026

2

We extend our previous analysis of spin coupling in fully oxidized Fe clusters [L. Noodleman, D.A. Case and A. Aizman, J. Am. Chem. Soc. 1988, 110, 1001] to cases where one or two of the iron atoms is reduced. This requires a spin Hamiltonian that contains "resonance" delocalization terms in addition to the usual Heisenberg spin coupling. Energies from broken symmetry Χα scattered wave calculations have been f i t to simple spin Hamiltonians in order to gain a better understanding of the interactions between the metal ions in these clusters. We find that the Heisenberg coupling constants J are significantly smaller in the reduced than in the oxidized clusters, and that resonance parameters Β are negative, with typical values of | B | / J in the range 1.5 to 3.0. Complexation with Zn at one apex of a tetrahedron stabilizes the reduced forms of the Fe complexes, but has l i t t l e effect on the spin interactions. Prospects for the use of such an analysis in other transition metal complexes are discussed. 3

3

Many

metalloproteins

catalytic Examples various

tasks include

the

clusters

orientation

typically

oxidation

states,

mixed-valence simplest

of

dependence

the

highest

for

forms

Fe(II)

in

i n which

(1).

metal

synthetic

high-spin

or

cluster. clusters

oxidation

can interact

state),

of

e x t e n t on

ions

in

important

ways

and

Fe(II)

and

magnetic

vectors.

These

mixed-valence

from

ions.

"classical" Some o f

or

Fe(III)

qualitative

ions

theories (2),

it

the

This

is particularly

are

of

their

ground s p i n state

(which have

at

least

the

remains

"coupling constants,"

even

since

the

naturally-occurring

c o u p l i n g a r e w e l l known

of iron-sulfur

d electrons

strong

spin

low-spin metal

t o compute magnitudes

formal

hemerythrin,

exhibit

ion

related

complexes.

depends to an important

in

geometry,

and

metal

oxidase,

these

Although useful

a particular

transfer

transition

metal

high-spin

found

upon molecular

expected

"reduced" in

task

the

containing

antiferromagnetic

a difficult be

are

clusters,

bridged by s u l f i d e s origins

energy

a n d may d i f f e r

examples

iron-sulfur

A l l of

of

contain

complexes

electron

cytochrome

proteins.

i n which the state

relative

in

polynuclear

nitrogenases,

iron-sulfur

coupling,

involved

contain

to

true

for

one

iron

derealization

strongly with spin coupling

0097-6156/89/0394-0366$06.00/0 ο 1989 American Chemical Society

In The Challenge of d and f Electrons; Salahub, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

of

the

effects.

26. SONTUM ET AL. Considerable application sulfur

to

clusters.

Fe S 2

each

These

atom,


In

alignment

three-

often

subsystem with

is

sufficiently

spin

S

(1)

In isolated

clusters,

related,

resonance

(5).

parameter, i n

a

resonance

small,

states.

parallel

than

along

pioneered

extension

they

but

are

2

t h eresonance spin

(S'=h),

the resonance

o r dynamic sites

i s much sites

since

often

larger, and i s easier

when

the spins

no n e t change (A

h a s been

clusters

to

however,

i t

shift.

interaction

state

lead

case,

language,

dimers

2

distortions will

(S'=9/2)

iron

F o r these

most

Anderson and

i n t h e former

f o r Fe S

(6).)

factor,

perhaps

of

b y E q . (2)

a r e opposed,

lines

of this

spin iron

Girerd

S enters

cluster

component

J

in

detailed

given

by

i s

positive,

stabilizes

states of

represents

Later

cluster

S'=9/2. leads

studies

many

o f theproperties

to energies

we h a d b e e n s t u d y i n g

properties;

this

co-workers

came

a balance o f

ferredoxin, confirmed

i n a variety

iron

sulfur

physically

which

molecular

t h e subdimer

o f the reduced

showed c l e a r l y

that

a spin

that dimer

Hamiltonian

g i v e n i n E q . (2) c a n e x p l a i n In parallel

f o r many y e a r s

orbital

consistent

has been the total

Fe(II)/Fe(III)

of clusters.

clusters

Here

with

analysis

was a d e l o c a l i z e d have

clusters

(7).

along

from

analogous t o those

shown how b r o k e n - s y m m e t r y a

to three-iron

the Hamiltonian

motivation

i n D. gigas

of this

that

provide

theory

and their

into

Thei n i t i a l

with

to

dimer

static

t o "hop"between

the final

b y Munck,

S ' .

three

energies are

forces.

The

one

these

low S' , while

model

In a simple

i s involved

and Baerends

S ' , so that

spin

when

interactions

ways,

of the iron

predicted

areobtained.

are

system

sothat minor

Interaction

states

d-electron

opposing

can be

and electron

(2)

of

For theferomagnetic

the final

favoring

results

(J/2)S'(S'+Ι),

exchange"

equivalence

for

high

derealization

andthe proportionality variety

t h e "double

the strict

trapped valence

analysis

spin

couple to

(J/2)S'(S'+l)±B(S'+4)

derived

i s quite

Noodleman

a

spectroscopically

t h e dimer

Ε -

have

parallel sites

electron

so that

For theantiferromagnetic

exchange

however,

interactions

formula

Hasegawa

the

clusters,

and Fe(III)

conflicting

spin

from

delocalized

Fe(II)

and Fe(III)

seemingly

the Heisenberg

f o r the

two-iron

t h e two s i t e s

are strongly

associated

and 2

(J>0) and t h e c l u s t e r s

Fe(II)

make

spins

5/2

identifiable

that

c a n be

break

describe

2

magnitudes

transparently

that

iron

b y Gibson and

approximated as

Β i s a

splitting

i n the

to

2

and S

1

with

These

Ε -

(S'+h)

e

i s favored

to

models

application

S ' = 9 / 2 , and i n which

(4).

by just

closely

Here

S

l

by recognizing

derealization more

Here

i n which

strong

indistinguishable rationalized given

JS

andfour-iron

occurs,

few y e a r s

Hamiltonian

cluster.

character,

a

not

theclassic

a n d have

coupling

valence

i n the past

or spin Hamiltonian

H -

Fe(III)/Fe(II)

antiferromagnetic sites.

follow

clusters.

2

iron

mixed-valence trapped

coupling"

(3) o f t h e H e i s e n b e r g

describe

with

p r o g r e s s h a s b e e n made

o f "vector

co-workers

367

Spin Coupling and Electron Derealization

calculations

picture

included an alternate derivation

of

work,

(6,8)and had

many

can be used of

their

o f t h e (S'+H)

factor


368

THE C H A L L E N G E OF d AND f ELECTRONS

relating this

resonance e n e r g i e s t o c l u s t e r s p i n (6) .

a n a l y s i s t o t h e o x i d i z e d forms

linear

a n dc u b a n e - l i k e

forms o f t h e three reduced The

systems

.

(11)


the

of

to create

of three-iron

coupling problem

since

i t

crux

o f our computational

broken

metal

sites

symmetry have

compute a n d i n t e r p r e t , used.

cobalt

interest

because i t

approach a r i s e s

the

from

( i n which

broken

symmetry

the recognition

the

pure-spin

ground

three

S=5/2

extend for in

locations

We

Heisenberg

the

pure

We h a v e

spin

earlier

applied

H e n c e , we

computed

from

including

this

clusters

to the reduced and doubly

are

that are

parameters

states,

three-iron

t i m e we c o n s i d e r t h e e f f e c t s

assume

spins

andunderstand. to energies

methods

(which

states

anduse the resulting

as i n oxidized

the analysis

polynuclear

iron

state.

spins,

the f i r s t

to approximate

easy to

functional

wavefunctions

spin Hamiltonian of

equivalent

are relatively

density

"correct"

wavefunctions,

estimate

can be systems

stabilizes

otherwise

2

t o f i t a n (assumed)

four-iron

mixed-metal

eigenfunctions of S ) aregenerally multiconfiguration choose

to

a n dz i n c

Cluster.

especially i f local

c o n s i d e r a b l y more d i f f i c u l t

procedure to ( £ ) .

H e r e we

reduced species,

of electron

where

derealization

clusters. that

the true

together

electrostatic

can be

replaced

interactions

by

an

that

interaction

couple of the

type:

2

1 2

that

the off-diagonal

electron

derealization

discussed then

above.

consists

matrix

The essence of

choosing

eigenvalues this

important may

be We

we w i l l

basis

spin matrices,

for

first

state.

In

on each

a

three

where

Hamiltonian to

be

model

included,

andcomparing the r e s u l t i n g

i n order

to estimate

interpretations

the high site

three

iron spin

Β and J .

of

models

a l l

We f o r m

basis

three

configurations, in

a

configurations

worked

with

the

equivalent

Fe(II)/Fe(III)/Fe(III)

are aligned

(which must b e spin-down) We h a v e

cluster

reduced",

spin-up.

sites.

states

more c o m p l e x s p i n H a m i l t o n i a n

quantitative

d-electron three

states

c o n s i d e r o n l y the s i m p l e s t models t h a t have t h e

i n the "singly

d-electrons

connecting

be o f the form B(S'+H), as

data.

consider

sites

oxidation

will

of choosing a spin the

physical interactions; necessary

experimental metal

elements

t o t h e computed Χα e n e r g i e s

paper,

(3)

1

i s "allowed"

diagonalizing theresultant In

to the

H — J SiS +Ji3S 'S3+J23S2S3 and

of

certain

i s diamagnetic.

spin populations)

By c o n t r a s t ,

in

c l u s t e r s b u t does n o t a f f e c t t h e

wavefunctions

different

i nt h e

andi n aconitase

converted

novel

Symmetry A n a l y s i s f o r a T h r e e - I r o n

that

are

iron

sites

vinlandii)

shown t h a t

TheZn complex i s o f p a r t i c u l a r

Broken The

been

clusters,

3

a r e themselves

the active

c a n be r e a d i l y

of the fourth

more r e d u c e d forms

spin

for

a n d Azobacter

sites

both

states.

chosen f o r i l l u s t r a t i o n

andi t has recently

i n place .

these

extended

(with

we c o n s i d e r t h e r e d u c e d

and analogous ZnFe

as models

( f r o m D. gigas

Many

clusters,

we h a v e

interest

ferredoxins

used

iron clusters,

We r e c e n t l y

iron clusters

( 9 ) . ) Here

a n dd o u b l y - r e d u c e d o x i d a t i o n

considerable (10)

geometries

o f three

to reside

out the

parallel

five

fashion, say

by allowing i n turn

matrix

formal

the f i r s t the

final

on each o f the

elements


of the

26. SONTUM ET AL· Heisenberg

portion

delocalization Hence,

of

the Hamiltonian

terms

characterizes

we

resonance

assume matrix

and below,

between

each

the diagonal


5 for parallel

equivalent (65/4)J these

+

elements

clusters, symmetry

atoms

(which

equivalent

we

atoms

configurations, the

2

3

find

state,

we

J =

2

represents

(65/4)J

"a") the

dimers. -

5B'

five of

pair

d-electron.

Following

the

λ

opposite

Papaefthymiou

only between

t h e two i r o n s

x

lowest.

For

For the

are

to

that

both

three

basis of the

et

s t i l l

iron

of

possible locations

that

(7),

al.

we w i l l

adopt

resonance i n t e r a c t i o n

o f t h e same s p i n ,

pair

"b" .

is

Here

spin matrix i s :

Here

we

have

symmetry results the

allowed

state,

0

0

•(15/4)J

0

0

•(25/4)J

the

The

symmetry

from t h a t

case

are E

1

J ' s and B ' s c a n , thus,

differences

arising

from

state

value)

energies

are

then

Hamiltonian. various

orbital

-

the model

o f Β and J are given

the

broken the Χα

Eigenvalues f o r 3

=

-(15/4)J.

by comparing those

state

the

computed

and estimates

resulting used

in

+ 5B a n d E

with

approach,

(5)

spin state;

indeed happens.

-(25/4)J

the ground

from

(For the simple

values

2

formulas

(including made

>

parameter

i n the high

be e s t i m a t e d

these

b r o k e n symmetry m o l e c u l a r spin

delocalization

B, to d i f f e r

r e p o r t e d b e l o w show t h a t t h i s

broken

5B

(25/4)J 5B

energy

carry

out an approximate

spin

and i t s

parametrized

here,

i n R e f . 7.)

projection

energy from

spin spin

the eigenstates In

a

o f the pure

for

the language

o u r p r e v i o u s p a p e r s , we a r e u s i n g t h e H e i s e n b e r g H a m i l t o n i a n to

three

are E =

o f one o f t h e

spin

There

simplest delocalization hypothesis,

important

lies

Ε

corresponding to the three

give

(S'+^s)

degenerate).

d-electrons

"b".

energy

elements

We a r e a s s u m i n g

(doubly

and, hence

is

the system

The e i g e n v a l u e s

2

B'2.0

3 shows t h e m o l e c u l a r

orbitals

h a s some

the Fermi

corresponds to antiferromagnetic and a

observed irons is

S-2 Fe(II)

(11).

monomer,

are reduced to Fe(II) low-energy

electrons. there

yielding

net

for

and the other 55a').

This

Fe(II)/Fe(III)

spin

"a" iron 1

of

5/2,

remains

Fe(III) several

a r e now p o s s i b l e a c c e p t e r s low-lying

orbitals

"a" site

orbitals

o f many m o r e

the existence

as

However,

o f these

to the u combination o f the "b" pair

a r e now a d d i t i o n a l

this

i n which both o f the "b"

and the unique

and 37a") and on the u n i q u e , imply

57a'),

a

occupation,

features,

level

orbital

g

i n energy by 1,300 cm" ).

orbitals

In a d d i t i o n

the

parameters.

w i t h one e x t r a

coupling o f an S ' - 9 / 2

(An a l t e r n a t i v e

computed to be h i g h e r

other

(in orbital (in

the

knowledge

by the zinc i o n .

l o c a l i z e d on the " a " i r o n "b" pair

worth

of

special

d-orbitals near

is

much

electron

dimer

cubane-like It

f o r o u r l o w e s t - e n e r g y b r o k e n symmetry s t a t e , the

likewise

geometries

n o r d o we h a v e

of the iron

(for

since,

i s predicted

(7).

cluster,

over

we

the ground s t a t e

cluster

3

o f the f o r the

t h a n t h o s e shown i n t h e

o f J and Β t o changes i n s t r u c t u r a l

reduced

stabilization

delocalized

than

discussed below);

experimental

a r e n o t known,

As with

| B | / J a r e around 1.5

|B|/J to be l a r g e r

with a l l J ' s equal,

though,

doubly

of

the

the doubly Zn complex,

about the s e n s i t i v i t y The

for

combination. t o the geometry

the computed J ' s t o be t o o l a r g e ,

cluster,

remembering,

values

Computed magnitudes

except

we e x p e c t

three-iron

to be r e l a t e d

absolute

the true values of

Table, to

below the antisymmetric

o f Β appear

both

there

(38a" and 6 0 a ' ) . states

than

extra

(36a"),

(e.g.,

56a'

These

extra

i n our model

o f E q . (7) , a n d s u g g e s t t h a t more c o m p l i c a t e d s p i n H a m i l t o n i a n m o d e l s may

be necessary

to

Hence,

the estimate

rather

approximate;

much s m a l l e r The

nevertheless,

reported

that

gas often

electron (19).

species

correlation

the q u a l i t a t i v e use

include

than

effects

(9).

effects

of

the values

past

found

in

a

spin-dependent

generally

studies

a

approximation,

effects

(20),

on the reduced

exchange-correlation potentials

of

reliable.

exchange-correlation

account

states

to increase J over

Calculations

Χα

density

a better

high-spin

conclusion

should be

the c o r r e l a t i o n

give

was i n d e e d f o u n d i n o u r e a r l i e r

clusters

calculations.

and c a n be compared t o

local

Since correlation

more

the

interest

the

uniform

this

here

Within

parametrizations properties

orbital

f o r J i n the doubly reduced complex i s

which has h i s t o r i c a l

calculations.

spin

the molecular

1

J f o r the doubly reduced complex

results

function,

describe

o f 45 cm"

stabilize

one would

low

expect

reported here, and

of oxidized species

three-iron

using

improved

give

serious

are i n progress.

Conclusion The

calculations

present

here

among

c o n s i d e r a t i o n to the competing e f f e c t s delocalization

in

polynuclear

qualitative

features

to

experimental

a

describe particular

solely

support

mechanism

from a n a l y s i s

transition

the "double

spectra in

the

these

(7),

first

to

o f s p i n coupling and e l e c t r o n metal exchange"

although

we d o n o t

calculations--the

o f computed t o t a l

energies

clusters. model

put

The forth

postulate

results

for various

arise states.


26.

SONTUM E T A L .

-0.


80

-0.

Iron Β

Iron A

05k

-0.10

375

Spin Coupling and Electron Delocalization

α'

38

a"

57

α',

58%

85%

1

86%

39

α "_

36%

59

α*

25%

5b

α'

33%

37

a".

37%

58

α'

39%

38

α"

45%

15

CO

55 a'...! — 44%

cn 0) JO

>^ - 0 .

20

54

c LU

.22%

α ' 3 9 %

53

-0.

ο*.

.26%

25

Figure 3. As i n Figure 1, for the lowest energy broken symmetry state of the doubly-reduced ZnFe cluster. Valence o r b i t a l s are numbered within each symmetry and have been placed i n three columns depicting the location of their primary charge d i s t r i b u t i o n . V e r t i c a l bars indicate occupied o r b i t a l s . 3


376

THE CHALLENGE OF d AND f ELECTRONS

Even

though

general

the magnitudes

trends

qualitative elsewhere

information (21)

that

spin coupling i n Fe S 4

at the

first

sight

delocalization others

forward lines

(23).

of

Although there

wave m o d e l s , to

they

obtaining

ideas

Furthermore, computers)

are clear

for

a wide

range

can

a clear

to

relatively

that

incorporate

and

electron

a n d t h e method

i s being

to

t o ab

local

exchange

the method, initio

t h e scheme o u t l i n e d h e r e localized

are

interactions

the

models

shows

explain

results

and

the such

limitations

and

along

should enable

and d e l o c a l i z e d

adapted

muffin-tin

and one c a n

studies

t o b e made b e t w e e n s p i n H a m i l t o n i a n m o d e l s a n d p r a c t i c a l metal

Even

one o f u s ( L . N . ) these

offer

useful

exchange

are not essential

Thus,

too high,

c l u s t e r s , where t h e e x p e r i m e n t a l

of

(with faster

are often

to be r e l i a b l e .

useful:

extension

i n complex c l u s t e r s ,

(22).

approximations


+ 3

path

are l i k e l y

c a n be quite

A

physics

I

simple

perplexing.

straightforward

by

a

Χα and scattered

essential

o f J we p r e d i c t

seen i n Table

look

t h e same

connections calculations

polynuclear

transition

complexes.

Acknowledgments We t h a n k

E c k a r d Munck

Institutes

of Health

f o r many u s e f u l (GM39914)

discussions,

for financial

and The N a t i o n a l

support.

Literature Cited 1.

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