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Adiabatic potentials for a bridged three-site electron-transfer system
CHEMICAL
Volume 93. number 5
ADIABATIC POTENTIALS FOR A BRIDGED Leslie J. ROOT
I7 Dcccmbcr 1982
PHYSICS LL7TCRS
THREE-SITE
ELECTRON-TRANSFER
SYSTEM
and Mary Jo ONDRECHEN
Rccavcd 14 September 1982
Born-Oppcnhumcr polcnl~al surfaces for 3 brrdfrd thrcesw clcctron~transfer system .IIC c&ulrkd The adub&L polcr~l~alsdepend upon both the vibrarlonal sum and d~flcrcn~c coordmdlcs Along lhc wbrdllondl dlffcrcnw wordmllc, rhc ground+lJte surface has smplc-mmnnum form when the through.brrdgc elcctromc couplmp 15slrong. Jnd double-mmmrum form for weah Ihrough-bridge coupling The Romulus arc lompJrcd IO ~hosc prcvrcmslg rcporkd for IWO-SII~ mod&
I _ Introduction
mode are coupled
Through-bridge experimentally particular
electron
transfer
III a wide variety
has been studied
of systems
[I I. One
bridged mixed-valence species,
[(NH3)5Ru(pyr)Ru(NH,),lS* kw= w-me), W~WAIwas first reported by Creutz and Taube (21,
which
hasbeen the SubJect of mtense expenmental
belongs
theoretical
study
[3] and
according
Robm-Day [lo].
[ 121 class (I. II, or Ill)
A number
hnve been proposed,
[4-71.
to eq (4)
From models of the type expressed by eqs. (I)(4), one may obtam hneshapes for the mtervakncc absorption band [S,l 1J_The relative m.gmtude of theelectronic couphngparameter Pand the elcctromcwbrational coupling parameter A, dew-mines to of crltena
usuz~tly based on IWO-sltc models
Most previous theoretlcal descriptions of bridged electron-transfer systems hke the Creutz-Taube Ion
of this type [9,10,13,14]. A few treatments which Include
have been based on two-site
local states have been reported.
donor
and acceptor
The harmltonian H = &I + k,b
models,
m which
states are consIdered
only
[5,8-I
for such models may be wntten + %I,
H,,=E~& +er&
I ]. as
(1)
*
+fi(&+a;a,),
(3) (3)
(4) P and r stand for the local sites on Ihe left and
the right sides of the molecule,af and 11,are the creation and annihilation operators for the ith local electromc state. pi and q1 are the momentum and coordinate of the local vibrational mode on the ith site. On the ith site the local electromc state and vibrational
0 009-2614/82/0000-0000/S
02.75 0 1982 North-Holland
more than two
Linderbcrg
and Ratncr
of electron locahzatlon usmg a four-site model in which two s.ltcs encompass edch of Iwo locahzat~on regions wlthm the molecule [ I5 1
examined
the question
Kuznetsovand Ulstrup sttldled electron transfer
vii-t
intermediate states using a perturbative method [ 161 We have also exammed the role of the bridge state III a three-srte system with fired nuclear coordmates [17,18]. In the present paper, we report on a study of a three-site electron transfer system m wlucli the two tennim
are coupled via a smgle local bridge state. We
assume that the two termim where
the system
for delocahAon
sufficiently
so that duect
are separated
couphng
between
III space them IS
negligible. (This IS probably the case rn the CreulzTaube ion, for instance.)Couplingto the nuclear motion is taken to be of the polaron type a1 the two tcrmud. The features of the adlrbatrc (BomOppenheimer)
potential
surfaces
are examined,
and 421
the relationslup ofthese features to those of previously studled two-site models is discussed _
2. The model
mmi (states 1 and 3) are coupled Vana bridgmg state 2, and where the two tennmi are each coupled to a nuclear degree of freedom wltb a polaron-type cou-
pling Wewrotethe hantiltomanfor thussystemas L 91 = J(q7, +a,a, ta;u; tu+72) t SAfw’qf _
+p@
-r’13[cos(\0)
,
degree of freedom. We take the nuclear vibrations to be harmorttc, and neglect duect electronic coupling between states 1 and 3. It IS also assumed that couphng of the bndge state to the nuclear motion ISsmall
md can be neglected. Note that the local basisstales I, 2, and 3 are taken to be degenerate. Hence, the
(10)
-
-(A3Q3 t36f'AQ 9A3Qq") (245’+3A’q”+A’Q”)Y”
C
(3
of as a Hiickel
(9a) t fAQ, (9b) (9c)
=~(74J’+3Alq’+A”Q’)‘/‘,
+ ;nk&;
may be thought
- 3’Izsin(iB)]
E3(q, Q) = 2r1/3 cos(i 0) + ‘,dQ ,
r1/3
are the momenlumand coordlnaleof the rth nuclear
system
E&,Q)=
where
where uf and o1 are the creation and annihllatlon operators lor the tth fermton state, and wherep, and q,
present
coordmates Q and 4 are coupled to the electronic degrees of freedom. For fuced 4 and Q, the eigenvalues of eq. (8) are obtained as.
e =cos-1
+4&Q)
+47&,
1982
E~(q,Q)=-r1/3[cos(fO)+31/2nn(fe)]+f~Q,
Constder a three-stte system m which the two ter-
+PflJ 71
I7 Dcccmbcr
CHFMICAL PHYSICS LETTERS
Volume 93. number 5
Hence, the adiabatic (Born-Oppenheimer) are given by V,(q,8)=-r~~3[~0~(:0)+3~~~sin(~O)]
1 (11) .
potent& +;AQ
+;K(q’tQ’), V,(q,Q)=
(12)
-r’~3[~~~(fO) - 31/2sm(iO)]
+$AQ
t$(q’tQ’),
(13)
V3(q, Q) = 2r1/3 cost4 0) + f AQ + ;A’($ + Q’)
ally1
‘(14)
systemwith the two rermmi each coupled to a local
where K =Mu”.
vlbratlonal mode.
Note that the features of the three potential SWfaces depend upon the through-bridge electrontc couplmg parameterJ, the polaron coupling parameter A, and the vibratlonal force constant K. Thk ISdiscussed
Eq. (5) may be transformed Into the basis set I+, -, L?},where aI and ~1 are defied as 0T = 7-l/l(0; + 7-qa; f?y = _
+.;,
)
(64
-g,.
m sectlon 3.
(6b)
The nuclear coordinates are transformed mto a vlbrationd chfference coordinate
q and n sum coordinate
3. Features of the Born-Oppenheimer
potential
surfaces
Q
ri=91-43 Q=q1
7
(7a)
Ub)
f43.
Upon transformation of eq. (S), the electronic and electronic-nuclear terms become: Q,, = ?‘zJ(a:,oz +:A[-Q(a$,- _ _
ground-stateadiabaticpotentialsurfacefor a case with relatively weak electronic coupling (J = -0.01
+ u:u+, I)+&&
The most stnkmg dtfference between the adiabatic potentials for the present system and those for correspondmg two-nte models is that the potent& now depend on the vlbratlonal sum coordinate, as well as the difference coordinate. Fig. 1 showscontours of the
eV; A = 1.OeV/A; K = 10.0 eV/A’-).Note that the +a:~+)].
Note that m eq. (8), both the sum and difference
(8)
potential along the vlbratlonal difference coordmate q has double-mmimum form; thk is also true of the two-site case when J is relatively small. Unhke the
Volume 93. numbrr 5
CHEMICAL
J 3,75
PHYSICS LC-ITERS
IL;
I7 Dcczmbsr 198’
-0125
-I
0425
000 0
0
rig 1 Contours of the ground-state polenkd surface Tot the CBSCJ q -0 01 eV,A q I 00 CV/A. K = 10.00 cV/A~ Contours are show as functions of the vtbr,monal sum and dtfference coordtttatcs Q and q (m A) Innermost contour = -0 0.50 CV Contours tn tntcrvals of 0 008 eV.
I & 3 Contours of the &!roundsl.ttc powntul surtxc for the case J= -0 I cV. A = I 00 cV/A. K = IO 00 &‘/A’ Contours drc shown 3s fttncltons of the wbr~~tott~l sum end dtflcrcnrr coordmatcs Q and y (m I\) Innrrtuo\t Conlours m mtcrvk or0 008 rV
contour
= -0
48 rV
two-site case, the adiabatic potential IS now dependent on lhe sum coordmate Q PSwell. Along Q, the mtnimum
occurs at negatwe
dtsplacement,
stnce some
electron density IS taken away from the termmi and IS located on the bndge site. Fig. 2 shows all three adlabattc potentials as functtons of the difference coordlnate q in the plane Q = -0.096&for the same parameters as III fig. I. (Note that Q = -0.096 .A corresponds to the minurtum
DIFFERENCE
COORDINPTE
The three schabaltc potenltals (m cV) 3s a function of the vtbrallortal dtfferettce coordmate q (In A) for the cxc shown tn f& 1 and for the sum coordmatc Q fi\ed at -0 096 rtg.
2.
in the ground-scare
potenual
along the sum coordmate.) Contours of the ground-state potentlal surface for a case of relatively strong electromc couphng (J = -0.10 eV, A = I.OO eV/A,K = 10.0 eV/A2) arc shown tn fig. 3. The surface has single-mmimum form along the vlbrational sum coordinate Q: the minimum is located at negative displacement, as in the we&coupling lirmt (cf. fig. 1). However, the surface now exhlblts single-mmunum form along the difference coordinate q as well, wilh the minimum located at q =o.
A. 413
CHkXIICAL
V~~lumr.93. numbcr 5
4. Discussion
and conclusions
III Ihe presenI ground-sIJIc dIfercncc
three-site
adldbatw coordmafc
ed tar two-site lorm
model,
potenllal y show
models
the form
cnlployed
bridge
coupling
the same trends
(donor-bridge direct
no ground-state
The ground
Wtlun
couplmg
is
tlIe framework surface
of tnple-
and firstewted difference
Although
the functIon.d
poIenIIals
upon Ihe dIffcrence
some slgmficant
potcntIal
surfaces
coordmate
used
dependence
dlffcrences
el and the two-site
models
of the adIabatIc
coordmate between
IS the same,
the present
[eqs. (I)-(Gj;
40
electrow
dctcnnines
the
strength
of
mod-
ef-
couplmg between the two termmitl
local sratcs (2) The odmbatx sum coordmate
potent&
now depend
Q, whxh WIIIcontrIbute
upon the
to the hne-
shapes of the absorption (3) Naturally,
emerge
bands two exIted-state
from the present
potential
surfaces
+ B transItion a better
The present
.malogy
of the HO&e1
ally1 system
for the present
results demonstrate
Whwz.J
I3C
Dunlcr,
Chcm Sot DkonTrms (1977) 1171, R S Dngo, D N Clendnchson, R \I 100 (1978)
P
II ClIrIn dnd A P G1nsberg.J Am Chrm Sot 103 rcfcrenlcs Iherrm
IJI N S tlush,Chem. Phys IO (1975) 361 151 S B. Plepho, [: R Krausz and P N Schrlz, J Am Chcm Sot 100 (1978) 1996 I61 P N. SC~I.IIZ.S B Prep110and E R Kwusz, Chcm Phys Lctrcrs 55 (1978) 539
I71 J W Lauhcr. Inorg. Ctnm Acta 39 (1980) 119. 181 R L I ulron and ~I Couwrmul. J Chrm Phss -%I (1961) 2280
191 E M
Mudlnov
and \ A
F~rsov. Sovler
Phys
7 (1965) 435 (IO] M A Ratner. lnrcrn. J. Quantum Chem
[ 111 IC1 sot [I?]
Sohd
SI~IC
1-l (1978) 675.
Wang, P H SCIIAE and S B Plcpho, J Am Chem 101 (1979) ‘793
LI B Robm and P Day.Advan (1967) 247
lnorg Radiochem
IO
[ 131 N R Kcstncr. J Log.m and J Jorlner, 1. Phys Chcm
78 11976) 3.168.
potential surface m the present model IS no! the same type of inrervalence transItIon as ffl the two-site case. perhaps
AH
(1981) 3673..md
model.
(4) The transItIon from the ground to firstexctted
The AI
1086
3805.
emerge-
tk
(1973)
Phys 39 (1963)
Rirhmdn Jnd S L Kcsscl, 1. Am Chcm Sot UI
(I) TIIC local donor and acceptor sites need not be directly coupled In the present model, the throughfectwc
3988.95
and A H Maki, J. Chcm
I31 J K Be.rtrw. N S Ilush, P R Tay1or.C L Rns~on and
IS observed
vlbratwxnl
couplrn~I
Ill
778. A llann, AccounIsChcm. Rea 8 (1975) 264, II rIschcr,G ,\I Tom and tl. Taubc,J Am Clwm Sot 98 (1976) 551’ C. Creulz dnd lI Taube.J Am Chem Sot 91 (1969)
of
e g. the I’lepho-Kraw-SclIatz [S] model are consIstent wth the results of the present threeate model.
br+e
J C tlarrimdn
couphng used
the present
along illc
III
is lhe througl~-
donor-acceptor
model.)
mmunu~~~ form
References
It is important couplfflg param-
and acceptor-bridge)
zero In the present model,
report-
couplmgsmgle-nununum
in the present model
(The
Tlus work is supported in part by Grant No. RR07143, Department of He&h and Human Services
Double-mInImum
.md not the direct donor-acceptor
previously
for the
along the vIbrational
[5,9,lOj
for wcah cleclronic
17 Dcccmbcr 1982
Acknowledgement
form for strongelectromc couplmg. to note, however. thdt the electromc eterJ
PHYSICS LLTTCRS
Is
model.
how the features
of the ndlabatlc potential surfaces for a three-site model differ from those of a correspondmg wo-slte
model. Investigntion of the details of the electrontransfer propertIes and the absorption lineshdpes for bndged systems IS currently m progress.
[Id] [IS]
S tlrrma and .\I ken, Chem Phys 13 (1976) 447. J Lmdcrbcrg .md %I A Ratncr, J. Am Chcm Sot 103
[ 161
(1981) 3’65 A \I Kuznctsov md J. Uls~rup. J. Chem Phys 75 (1981) 20-17
[ 171 1IS]
LJ Root and XI J Ondrcchen, Chem. Phys Letters 88 (1982) 538. \I J Ondrcchcn and hl A Ratner, J Chem Phys. 66 (1977) 938
Volume 93. number 5
ADIABATIC POTENTIALS FOR A BRIDGED Leslie J. ROOT
I7 Dcccmbcr 1982
PHYSICS LL7TCRS
THREE-SITE
ELECTRON-TRANSFER
SYSTEM
and Mary Jo ONDRECHEN
Rccavcd 14 September 1982
Born-Oppcnhumcr polcnl~al surfaces for 3 brrdfrd thrcesw clcctron~transfer system .IIC c&ulrkd The adub&L polcr~l~alsdepend upon both the vibrarlonal sum and d~flcrcn~c coordmdlcs Along lhc wbrdllondl dlffcrcnw wordmllc, rhc ground+lJte surface has smplc-mmnnum form when the through.brrdgc elcctromc couplmp 15slrong. Jnd double-mmmrum form for weah Ihrough-bridge coupling The Romulus arc lompJrcd IO ~hosc prcvrcmslg rcporkd for IWO-SII~ mod&
I _ Introduction
mode are coupled
Through-bridge experimentally particular
electron
transfer
III a wide variety
has been studied
of systems
[I I. One
bridged mixed-valence species,
[(NH3)5Ru(pyr)Ru(NH,),lS* kw= w-me), W~WAIwas first reported by Creutz and Taube (21,
which
hasbeen the SubJect of mtense expenmental
belongs
theoretical
study
[3] and
according
Robm-Day [lo].
[ 121 class (I. II, or Ill)
A number
hnve been proposed,
[4-71.
to eq (4)
From models of the type expressed by eqs. (I)(4), one may obtam hneshapes for the mtervakncc absorption band [S,l 1J_The relative m.gmtude of theelectronic couphngparameter Pand the elcctromcwbrational coupling parameter A, dew-mines to of crltena
usuz~tly based on IWO-sltc models
Most previous theoretlcal descriptions of bridged electron-transfer systems hke the Creutz-Taube Ion
of this type [9,10,13,14]. A few treatments which Include
have been based on two-site
local states have been reported.
donor
and acceptor
The harmltonian H = &I + k,b
models,
m which
states are consIdered
only
[5,8-I
for such models may be wntten + %I,
H,,=E~& +er&
I ]. as
(1)
*
+fi(&+a;a,),
(3) (3)
(4) P and r stand for the local sites on Ihe left and
the right sides of the molecule,af and 11,are the creation and annihilation operators for the ith local electromc state. pi and q1 are the momentum and coordinate of the local vibrational mode on the ith site. On the ith site the local electromc state and vibrational
0 009-2614/82/0000-0000/S
02.75 0 1982 North-Holland
more than two
Linderbcrg
and Ratncr
of electron locahzatlon usmg a four-site model in which two s.ltcs encompass edch of Iwo locahzat~on regions wlthm the molecule [ I5 1
examined
the question
Kuznetsovand Ulstrup sttldled electron transfer
vii-t
intermediate states using a perturbative method [ 161 We have also exammed the role of the bridge state III a three-srte system with fired nuclear coordmates [17,18]. In the present paper, we report on a study of a three-site electron transfer system m wlucli the two tennim
are coupled via a smgle local bridge state. We
assume that the two termim where
the system
for delocahAon
sufficiently
so that duect
are separated
couphng
between
III space them IS
negligible. (This IS probably the case rn the CreulzTaube ion, for instance.)Couplingto the nuclear motion is taken to be of the polaron type a1 the two tcrmud. The features of the adlrbatrc (BomOppenheimer)
potential
surfaces
are examined,
and 421
the relationslup ofthese features to those of previously studled two-site models is discussed _
2. The model
mmi (states 1 and 3) are coupled Vana bridgmg state 2, and where the two tennmi are each coupled to a nuclear degree of freedom wltb a polaron-type cou-
pling Wewrotethe hantiltomanfor thussystemas L 91 = J(q7, +a,a, ta;u; tu+72) t SAfw’qf _
+p@
-r’13[cos(\0)
,
degree of freedom. We take the nuclear vibrations to be harmorttc, and neglect duect electronic coupling between states 1 and 3. It IS also assumed that couphng of the bndge state to the nuclear motion ISsmall
md can be neglected. Note that the local basisstales I, 2, and 3 are taken to be degenerate. Hence, the
(10)
-
-(A3Q3 t36f'AQ 9A3Qq") (245’+3A’q”+A’Q”)Y”
C
(3
of as a Hiickel
(9a) t fAQ, (9b) (9c)
=~(74J’+3Alq’+A”Q’)‘/‘,
+ ;nk&;
may be thought
- 3’Izsin(iB)]
E3(q, Q) = 2r1/3 cos(i 0) + ‘,dQ ,
r1/3
are the momenlumand coordlnaleof the rth nuclear
system
E&,Q)=
where
where uf and o1 are the creation and annihllatlon operators lor the tth fermton state, and wherep, and q,
present
coordmates Q and 4 are coupled to the electronic degrees of freedom. For fuced 4 and Q, the eigenvalues of eq. (8) are obtained as.
e =cos-1
+4&Q)
+47&,
1982
E~(q,Q)=-r1/3[cos(fO)+31/2nn(fe)]+f~Q,
Constder a three-stte system m which the two ter-
+PflJ 71
I7 Dcccmbcr
CHFMICAL PHYSICS LETTERS
Volume 93. number 5
Hence, the adiabatic (Born-Oppenheimer) are given by V,(q,8)=-r~~3[~0~(:0)+3~~~sin(~O)]
1 (11) .
potent& +;AQ
+;K(q’tQ’), V,(q,Q)=
(12)
-r’~3[~~~(fO) - 31/2sm(iO)]
+$AQ
t$(q’tQ’),
(13)
V3(q, Q) = 2r1/3 cost4 0) + f AQ + ;A’($ + Q’)
ally1
‘(14)
systemwith the two rermmi each coupled to a local
where K =Mu”.
vlbratlonal mode.
Note that the features of the three potential SWfaces depend upon the through-bridge electrontc couplmg parameterJ, the polaron coupling parameter A, and the vibratlonal force constant K. Thk ISdiscussed
Eq. (5) may be transformed Into the basis set I+, -, L?},where aI and ~1 are defied as 0T = 7-l/l(0; + 7-qa; f?y = _
+.;,
)
(64
-g,.
m sectlon 3.
(6b)
The nuclear coordinates are transformed mto a vlbrationd chfference coordinate
q and n sum coordinate
3. Features of the Born-Oppenheimer
potential
surfaces
Q
ri=91-43 Q=q1
7
(7a)
Ub)
f43.
Upon transformation of eq. (S), the electronic and electronic-nuclear terms become: Q,, = ?‘zJ(a:,oz +:A[-Q(a$,- _ _
ground-stateadiabaticpotentialsurfacefor a case with relatively weak electronic coupling (J = -0.01
+ u:u+, I)+&&
The most stnkmg dtfference between the adiabatic potentials for the present system and those for correspondmg two-nte models is that the potent& now depend on the vlbratlonal sum coordinate, as well as the difference coordinate. Fig. 1 showscontours of the
eV; A = 1.OeV/A; K = 10.0 eV/A’-).Note that the +a:~+)].
Note that m eq. (8), both the sum and difference
(8)
potential along the vlbratlonal difference coordmate q has double-mmimum form; thk is also true of the two-site case when J is relatively small. Unhke the
Volume 93. numbrr 5
CHEMICAL
J 3,75
PHYSICS LC-ITERS
IL;
I7 Dcczmbsr 198’
-0125
-I
0425
000 0
0
rig 1 Contours of the ground-state polenkd surface Tot the CBSCJ q -0 01 eV,A q I 00 CV/A. K = 10.00 cV/A~ Contours are show as functions of the vtbr,monal sum and dtfference coordtttatcs Q and q (m A) Innermost contour = -0 0.50 CV Contours tn tntcrvals of 0 008 eV.
I & 3 Contours of the &!roundsl.ttc powntul surtxc for the case J= -0 I cV. A = I 00 cV/A. K = IO 00 &‘/A’ Contours drc shown 3s fttncltons of the wbr~~tott~l sum end dtflcrcnrr coordmatcs Q and y (m I\) Innrrtuo\t Conlours m mtcrvk or0 008 rV
contour
= -0
48 rV
two-site case, the adiabatic potential IS now dependent on lhe sum coordmate Q PSwell. Along Q, the mtnimum
occurs at negatwe
dtsplacement,
stnce some
electron density IS taken away from the termmi and IS located on the bndge site. Fig. 2 shows all three adlabattc potentials as functtons of the difference coordlnate q in the plane Q = -0.096&for the same parameters as III fig. I. (Note that Q = -0.096 .A corresponds to the minurtum
DIFFERENCE
COORDINPTE
The three schabaltc potenltals (m cV) 3s a function of the vtbrallortal dtfferettce coordmate q (In A) for the cxc shown tn f& 1 and for the sum coordmatc Q fi\ed at -0 096 rtg.
2.
in the ground-scare
potenual
along the sum coordmate.) Contours of the ground-state potentlal surface for a case of relatively strong electromc couphng (J = -0.10 eV, A = I.OO eV/A,K = 10.0 eV/A2) arc shown tn fig. 3. The surface has single-mmimum form along the vlbrational sum coordinate Q: the minimum is located at negative displacement, as in the we&coupling lirmt (cf. fig. 1). However, the surface now exhlblts single-mmunum form along the difference coordinate q as well, wilh the minimum located at q =o.
A. 413
CHkXIICAL
V~~lumr.93. numbcr 5
4. Discussion
and conclusions
III Ihe presenI ground-sIJIc dIfercncc
three-site
adldbatw coordmafc
ed tar two-site lorm
model,
potenllal y show
models
the form
cnlployed
bridge
coupling
the same trends
(donor-bridge direct
no ground-state
The ground
Wtlun
couplmg
is
tlIe framework surface
of tnple-
and firstewted difference
Although
the functIon.d
poIenIIals
upon Ihe dIffcrence
some slgmficant
potcntIal
surfaces
coordmate
used
dependence
dlffcrences
el and the two-site
models
of the adIabatIc
coordmate between
IS the same,
the present
[eqs. (I)-(Gj;
40
electrow
dctcnnines
the
strength
of
mod-
ef-
couplmg between the two termmitl
local sratcs (2) The odmbatx sum coordmate
potent&
now depend
Q, whxh WIIIcontrIbute
upon the
to the hne-
shapes of the absorption (3) Naturally,
emerge
bands two exIted-state
from the present
potential
surfaces
+ B transItion a better
The present
.malogy
of the HO&e1
ally1 system
for the present
results demonstrate
Whwz.J
I3C
Dunlcr,
Chcm Sot DkonTrms (1977) 1171, R S Dngo, D N Clendnchson, R \I 100 (1978)
P
II ClIrIn dnd A P G1nsberg.J Am Chrm Sot 103 rcfcrenlcs Iherrm
IJI N S tlush,Chem. Phys IO (1975) 361 151 S B. Plepho, [: R Krausz and P N Schrlz, J Am Chcm Sot 100 (1978) 1996 I61 P N. SC~I.IIZ.S B Prep110and E R Kwusz, Chcm Phys Lctrcrs 55 (1978) 539
I71 J W Lauhcr. Inorg. Ctnm Acta 39 (1980) 119. 181 R L I ulron and ~I Couwrmul. J Chrm Phss -%I (1961) 2280
191 E M
Mudlnov
and \ A
F~rsov. Sovler
Phys
7 (1965) 435 (IO] M A Ratner. lnrcrn. J. Quantum Chem
[ 111 IC1 sot [I?]
Sohd
SI~IC
1-l (1978) 675.
Wang, P H SCIIAE and S B Plcpho, J Am Chem 101 (1979) ‘793
LI B Robm and P Day.Advan (1967) 247
lnorg Radiochem
IO
[ 131 N R Kcstncr. J Log.m and J Jorlner, 1. Phys Chcm
78 11976) 3.168.
potential surface m the present model IS no! the same type of inrervalence transItIon as ffl the two-site case. perhaps
AH
(1981) 3673..md
model.
(4) The transItIon from the ground to firstexctted
The AI
1086
3805.
emerge-
tk
(1973)
Phys 39 (1963)
Rirhmdn Jnd S L Kcsscl, 1. Am Chcm Sot UI
(I) TIIC local donor and acceptor sites need not be directly coupled In the present model, the throughfectwc
3988.95
and A H Maki, J. Chcm
I31 J K Be.rtrw. N S Ilush, P R Tay1or.C L Rns~on and
IS observed
vlbratwxnl
couplrn~I
Ill
778. A llann, AccounIsChcm. Rea 8 (1975) 264, II rIschcr,G ,\I Tom and tl. Taubc,J Am Clwm Sot 98 (1976) 551’ C. Creulz dnd lI Taube.J Am Chem Sot 91 (1969)
of
e g. the I’lepho-Kraw-SclIatz [S] model are consIstent wth the results of the present threeate model.
br+e
J C tlarrimdn
couphng used
the present
along illc
III
is lhe througl~-
donor-acceptor
model.)
mmunu~~~ form
References
It is important couplfflg param-
and acceptor-bridge)
zero In the present model,
report-
couplmgsmgle-nununum
in the present model
(The
Tlus work is supported in part by Grant No. RR07143, Department of He&h and Human Services
Double-mInImum
.md not the direct donor-acceptor
previously
for the
along the vIbrational
[5,9,lOj
for wcah cleclronic
17 Dcccmbcr 1982
Acknowledgement
form for strongelectromc couplmg. to note, however. thdt the electromc eterJ
PHYSICS LLTTCRS
Is
model.
how the features
of the ndlabatlc potential surfaces for a three-site model differ from those of a correspondmg wo-slte
model. Investigntion of the details of the electrontransfer propertIes and the absorption lineshdpes for bndged systems IS currently m progress.
[Id] [IS]
S tlrrma and .\I ken, Chem Phys 13 (1976) 447. J Lmdcrbcrg .md %I A Ratncr, J. Am Chcm Sot 103
[ 161
(1981) 3’65 A \I Kuznctsov md J. Uls~rup. J. Chem Phys 75 (1981) 20-17
[ 171 1IS]
LJ Root and XI J Ondrcchen, Chem. Phys Letters 88 (1982) 538. \I J Ondrcchcn and hl A Ratner, J Chem Phys. 66 (1977) 938