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Correlation of electronic charge transfer transitions and electrochemical potentials.
Volume 113, number 6
CORRELATION
CHEMEAL
OF ELECTRONiC
PHYSICS
28 December
LL’TTERS
1981
CHARGE TR.ANSFER TRANSITIONS
AND
ELECTROCHEMICALPOTENTIALS. THE B~PYRA~~NE(TETRACARBONYL)MOLYBDENUM(O)SYST~MINVARIOUSSOLVENTS &ifleS.DODSWORTH and A.B.P. LEVER Depurzmenr of ChenriFtry, York University. Dowttslfeien~,Toronto, Ontario, Canallo M3J 1P3 Received 34 August 1984;
in final form 9 October 1984
Usinga free-energydiagram. 3 relationship is drawn between an optical char~c transfer energy and the electroclmtliwl potentidsof tltcdonor and acceptor orbitais concerned. The charge tmnsfer spectroscopy and efectrochemirzil potentiafs of rhc title comphx wcrc studied in vxious solvents. A Linear correlation, with ncptive slope, was observed between the difference in osidstion nnd reduction potentih and an MLCT transition. Using, some additional solvenr data, a number of useful p.xamcters were derived in a fashion which woufd not be possible through consideration of either technique alone.
An electronic charge transfer transition involves excitation from ;f donor orbital in the ground state of a molecule, to an acceptor orbital in a Franck-Condon (non-equilibriunl} excited state of the molecule. III tfris paper we refer specifically to an IMLCT transition, From an orbital, Ghr ~ ~nair~ly on the metal. to an orbital, $L,primarily 011 Ihe ligand. However the treatment is quite general. An electrochemical study may, in appropriate cases, define the redox potentials of orbitais retrtted to those above. Thus we may observe the oxidation potential of rjr,r in the ground state of the compiex ML,l, and the reduction potential for adding an electron to tit_ to form the ground state of the reduced species ML,;. Previous authors [l--S] have demonstrated qualitative reIationships between optical charge transfer energies and electrochemicaI potentials but now we seek a more quantitative understanding in which quantities not derivable from either electronic spcctroscopy of electrochemistry alone. can bc obtained by a combined amdysis. In view of the salvation contributions to the paranleters obtained with each technique, a combined analysis is best approached within the framework of the collection and comparison of data in a range of solvents. The analysis which follows is based upon
theories
developed by Born 161, Onsager 171, Kirkwood [SJ. Lippcrt [9],Marcus [lO,ll]and Meyer [i2). Use of a free-energy cycle (fig. I) permits one to relate the various thermodynamic quantities (as defined in the legend to fig 1). measurable in the two cxperimental regimes. Thus the following equalities nx~p be written:
E op=u*+Xi
“X0-
(11
4E, = AEg f A(sol) , AEs = IzFAE(redoxf
=: [IzFAE’(redox)
(3
i- AAG, +x]
+Q
+ AAG, + Q
(3)
(see text below), and hence Eop = [Xi f tzFAE(redox)
+ xc, +
A(sol) ,
+ A&G, i- Q] W
where x0 + A(so1) is the total change in salvation free energy as earlier defined in eq. (13) of ref. [ 1 l] and eq. B2a of ref. [Y], andXj and x0 are the inner-sphere (vibrational) and outer-sphere (solvent, but also vibrational in nature) contribuiions to the reorganisation energy of the transition, respectively. Ncte that as a consequence of the Franck-Condon nature of the excited state, the transition energy Eop is a free 567
Volume
CHEMICAL
112. number 6
-BG
-_
2(!.!L)s
I%ig 1. I‘rcecnrrgy .md (ML-) A(;<
state.
(ML)g+
(ML*)?
energy
in htt
cqttiltbr~tcd 13q. (4).
Now
cncrgy
is dcfincd
that in the te\t A4G,
the cntroptcs cxctrcd
sutc
in which
the
the
function
satne
excited
involved
= ZAG,
- 4q
-
and nonbrackets
I> salvent
indcpcndcnt for a given n~o!eculc, provides tltc ttnporlant correlation between the two techniques. The complcs hIo(C0)4bpz(bpz= bipyrazinc) 1131 dt$ays J strong band, inter alid, attributed to d(Mo(O)) - rr* (bpz) MLCT.wltose crwgy,EoD.vztries
flm~ about 16000 to 20000 cm-’ depending upon tltc solvent ct~virontttet~t and shifting to bigher energy with ~ncrcasing solvent polarity (table 1; cf. the solv~rochrotnistn of the bipyridine analog [14]). Electrocitcmtcal data for LLrllngc ofsolventsare also shown tn table I. The reduction porcntial for tbc electrochemically rcvcrsiblc Mo(CO)4bpz/hlo(CO)qbpzcouple involves ~ddttion of an electron to GL (n* bpz) forming the rddtcdl bpL- bound to MO(O). This couple shifts to more postttvc potcttti~ls wttlt increasing polarity of the solvent. as the grouttd state radtcal anion becomes more solvent srabtliscd. 566
stale.
a&and
ifs the rcvcrsiblc
AEs is the solvent Jn
A(so1)
s
1984
-----_-
is tbc neutr.d species.
rcspectivcly.
minus the reduction
in transferring
[l l].
in square
potential
2 (XL)
(ML)
species
species being defined
4s the oxid,ttion
energy
of the ground are
quantities.
and mono-negative
to the equilibrated
Q IS the resotunce
-----_-_-------_--------
s
.tnd clcctrochemical
motto-positive
for thcsc respective
AE(rcdox)
cuitdtion
The quntity
2(:u_)
spectroscopic
excited,
free cncrgies
to J solvent.
AEg is the g.is phase hratrd
------_-__---_-_-_----_-
d~dgr.tm rekttn~
drc rltc solvation
28 December
LETTERS
= nFiE(redox)
are tllc cquihbrJtcd
the gac ph~c
PHYSICS
Similarly nork
to transfer
potential
and (ML*), (hIL3
AC,,AGf, Ad, and these solutes
of the ncLm1
phase excitation
energy
from
species.
to the equili-
electron from (ML_), to (ML?)g yielding = AC:-
AC,.
Oxidation occurs at the hlo(0) d manifold but is electrochemically irreversible, due to a following chemical reaction (ECi mechanism) [ 16.171. However the slow step of the following reaction appears to be tMo-CO bond breaking which is solvent independent. Thus the true thermodynamic potential will be more positive than recorded in table 1 by a solvent independent quantity, say x mV (probably 100
E OP = -1.04
M’(redox)
+ 33950
(cm-l)
_
This is an unexpected result appearing to contradict intuition in that as the potential difference between donor and acceptor orbital decreases, the optical transition energy increases_ Such an inverse correlation has not been previously reported_ An understan-
(3
Volume 112, number 6 Table 1 Llectrocl~emical Solvent
DhlF PC hleCN PY TIII‘ DCE DChl lzt, 0 CHC1s TCM pent “slls”
CHEMICAL
and spectroscopic
PHYSICS LEl-l-ERS
Xl December
1984
data”)
E(hlo(l)/hlo(O)) b)
E(bpz/bpz2
(CV)
(eV)
Af?(rcdox) (eV)
(cm-1 )
+ p bol)
AA&
E0p
x0
(cm-’ )
(cm-’ )
(cm-‘)
0.26 0.32
-1.42 -1.41
1.68 1.73
(13550) (14000)
19650 19550
3650 3550
3710 3260
0.28 0.76 0.30
-1.45 -1.52 -1.52
1.73 1.78
(14000) (14350)
19450 18900
3450 ‘900
3260 2310
0.34
-1.53
1.82 1.87
(14700) (15100)
18650 18150
2650 x50
2560 2160
1.90 c) 1.93 c) 1.98c) 2.07 c) 2.09 c) 2.14 e)
(15350) (15530) (15950) (16670) (16870) (17260)
17990 17790 17360 16610 16400 16000
1990 1790 1360 610 100 0
1910 1730 1310 590 390 0
a) All electrochemical potentials referenced against fcrrocene as internal reference (Fc+/Fc is at 0.16 eV versus SCE) [ 151. Potentials were recorded on Pt electrodes using cyclic voltammetry at scan rates of 100.50 and 20 mV/s. Confirmatory data acre obtained using differential pulse polarography. Dater arc averages of several esperiments. DhlJ- = dimcthylformamide, PC = propylene carbonate, PY = pyridine, THF = tetrahydrofumn, DCL = 1,2dichloroethane, DC11 = dichloromethane. TCM = tetrais cstrapolation using eq. (I 1). chloromethnne. pent = pentane, “ws” ~ b, The oxidation process is electrochemically irreversible. E p - El,b is compar.rble to that of the fcrrocene couple under the same conditions. Value quoted is:(Ep + Ep@. ')Calculated from eq_ (5) in text. MS + xi = 16000 cm-’ ; xi +s + Q = -1260 CIII-~.
ding of this phenomenon develops from further analysis below. The following expression [S] allows one to approximate the solvation free energy of a species as a power series: t1=-
AG,
= 0.5
c
n=o
(tz+ 1x2,1 baz+l
1
-d,
(II + l)D, +tz
>
where terms higher than II = 1 are ignored and the reader is referred to the earlier literature [6-l?] for detailed discussion of the conditions under which this expression is useful. D, is the static dielectric constant of the solvent, b is the radius of the solute. Q. =z2e2T 2nd Qr = ~2, where p is the dipole moment of the solute species. The term in zz = 0 disappears for uncharged species_ Using (6) the difference in salvation free energies of the uncharged and thermally equilibrated ground and excited states, A(so1) may be writ ten *(solj=AGs(ej-AGs(gj=~~, Following
earlier authors
(7) [S-l 2 1, the Franck-C&don
destabilisatiozl of the excited state. due to solvent interactions, may be written
(cr,-&)’ x0 =
b3
1 -Do,
1 -D,
c~Dop+l
where in (7) and (8) the ground and excited state dipole nlonlents are appropriately discriminated. and Do, is the optical dielectric cozrstant of the solvent (square of the refractive index). The total solvent dependence excluding non-polar contributions (very small [ Ii] ), eq. (4), is A&- = A(sol) + x0; suniming (7) and (8) yields (after evaluating the vector productsj [9,12] :
* 2-@4&0s bJ- II”) J - b3
1 -D, p_ X&+1
The angle 0 is that between the ground and excited state dipoles. The ground state dipole moment lies along the C2 axis with the negative end pointing towards the CO groups. Eq. (4) can now bc recast in the general form: 569
CHtSIIC4L
Volume 113. number 6
whcrefand f’ group the factors shown in cq. (9). In d forthcoming paper [ 161 we devclopcd this analysis with 73 solvents. Hc~c WC shall riwricl ourselves to LonsldcIulg G solvents of low polarity and low dieleclric ,XI~SLI~I whtcl~ might be expected to obey the diclectm ~onmuum model. The optlcal data thereof (rdhlc 1) obey ( IO) well according to (in cm-l) 9500
I: ~,,, =
C I - D,,,)/(7D,,
+ I)
- 7600 ( 1 - D,)/( ZD, •i- 1) + 16800
(1 t>
~111 :! Lorrel~tion cocl‘ficicnt oTO.988 and A standard dcvlarion of 65 (the lower set ol‘ six solvents shown in 1h1c 1 were used). and where the constant term, 16800 CW- 1 IS associated with Xi + AEg_ However 111~ &I& yield a l‘amly of solutlonswhich do not differ grmtly 111their correlation coefficients or standard dc\Gtlwis. indeed the solutton /= 0,f’ = -7 1 10, and IS not unre~sou~blc (correlaX, + AL’.. = 15 1 10 cm-~ II~II coekicient 0.97, standard deviation 169). This LiIrsr St~llIliOil is. however, uiconsistent with IllC CX~~~c~wm _m (9). The solution in (1 I) IS statistically the hc~,r. but dots 1101 difl‘er significmtly from many other
which flies hetwccn zero and 9500 m-1 I iuwxve~ /’ IS gcncrally found 111the range -(7000\ Imges rrom about 7000; cl11-1 anJ the constant 15OOC IO 17000 cm-t. At rim stage ol’ study WC note tlUt thz appoxzti sce~iis Justified hut tint iligllcr-qual-
~III!KIII~
rry.
dlrcctton
113 rhcg~ound cl111g of
ared
data .NC necessary.
101 I' rcquircs, conndermg eqs. I I ), tlial. III tlm systcui, tlic dipole ~nonient
clIa11pzs
111~
SIJIC
~~mc’ldtm~i For
tlic
state
Frock
by
polar
sliown put po5c
by
1 SO” in the
[1.15].
-Cowlon solvents.
cxcitcd
Tlusprovidcsan
dcstabllmtion
state
relative
undcrstm-
of the ex-
and 11e11cc of the ricgalive
111 (5). of miicating
how
thcsc data niay
he utihcd.
wc cl~oosc .I mcdmn v.duc of the COIK.LIII~ of 16000 cn- 1_ Note thdt in the gas ph.m, AAG, = 0. therefore X, + &*M’(rcdo\) f s + Q = 16000 cm-l _ Further, use oicq. (5) provides the value for nF4E’(redox) in the gas ~ILISC by imertion ofE,t, = 16000 cmM1. Knowing rll:“(rcdox) allows derwation of Xi +x + Q = - 1260 cm-t _This then leads to the evaluation: of AAG, /q_(3)]_ Use ot cq. (I) leads to cv,duation of 570
1984
A(so1) + X0_ These data arc also collected in table 1. The sun1 XI +x is necessarily positwe but Q, using an appropriate free-energy cycle, is estimated to he near -0.5 V [IS] _The “gas phase” optical energy is close to that observed in pentane, as might be anticipated. The procedure provides an interesting set of parmicters whose vA.~cs seems eminently reasonable. Further developrncnt on this and related syslen~ should provide the impetus to link the study of elcctrochemistry and optical spectroscopy and to seek evaluation ofothcr useful parameters. such as the selfcschangc energy, which may be derivable from a freeenergy cycle involving Q_ The merits and boundary conditions inherent in this analysis will he discussed in more detail in a future publication [ 16]_ We also currently seek emission data which should further defme some of the parameters derived. The authors and Engineering
are indebted to the Natural Research Council (Ottawa)
Sciences and tbc
Office of Naval Research (Washington) for financial support. cussions Walker.
We also gratefully acknowledge useful dlswith Prol‘essor T.J. Meyer and Professor 1-M.
References
III
311d more cxwnsivc The ncgJtivc k~iue
(S)-(
28 December
PHYSICS LET-l-fRS
Rudd, 1~. Caunder and H. Tube, J. Am. 90 (1968) 1187. B-I’. Sullivan and T.J. Meyer, Inors. Chem.
[ 11 P.C. I‘ord, F.P. ]7
]
Chcm. Sot. J.C. Curtis, 12 (1983)
224.
[ 31 A.B P. Lcvcr, Inorgnic
electronic spectroscopy, 2nd Id. (Ekcvier, Amsterddm, 1981). [4] A.B.P. Lever, S. Licoccia. P.C. Minor. B.S. Ramaswamy and S.R. Pickens, J. Am. Chcm. Sot. 103 (1981) 6600. [S] S. Goswami, R. Mukhcrjec and A. Chakravorty. Inor?. Chcm 22 (1983) 2825. 161 hl. Born. 2. Phys. 1 (1920) 45. [71 L. OnsAger, J. Am. Chcm. Sot. 58 (1936) 1486. 181 1-G. Kirkwood. J. Chcm. Phys. 2 (1934) 351. 191 C. Lippert. 2. Elektrochem. 61 (1957) 962. 1101 R.A. hlarcus, J. Chem. Phys. 39 (1963) 1734. illi R-4. Marcus. J. Chem. Phys. 43 (1965) 1261. 1121 EM. Sober, B-I’. Sullivan and T.J. Meyer, Inorg. Chem. 23 (1984)
2098.
R.J.
Crutchley and A.B.P. Lever, Inorg. Chem. 21 (1981) 2276. H. Saito, J. rujita and I(. S&o. Bull. Chem. Sot. iapdn 41 (1968) 663. R.R. Gage, CA. Kovdl and C.C. Lisensky, Inog. Chem. 19 (1980) 26.54. IX. D.
Dodsworth
and A.B.P.
Lever,
to be submitted.
Xllholova’, L. Pospisil, and A.A. VI&, Proceedings of the 13th International Conference on Coordination Chemistry, Boulder (1984); private communication.
CORRELATION
CHEMEAL
OF ELECTRONiC
PHYSICS
28 December
LL’TTERS
1981
CHARGE TR.ANSFER TRANSITIONS
AND
ELECTROCHEMICALPOTENTIALS. THE B~PYRA~~NE(TETRACARBONYL)MOLYBDENUM(O)SYST~MINVARIOUSSOLVENTS &ifleS.DODSWORTH and A.B.P. LEVER Depurzmenr of ChenriFtry, York University. Dowttslfeien~,Toronto, Ontario, Canallo M3J 1P3 Received 34 August 1984;
in final form 9 October 1984
Usinga free-energydiagram. 3 relationship is drawn between an optical char~c transfer energy and the electroclmtliwl potentidsof tltcdonor and acceptor orbitais concerned. The charge tmnsfer spectroscopy and efectrochemirzil potentiafs of rhc title comphx wcrc studied in vxious solvents. A Linear correlation, with ncptive slope, was observed between the difference in osidstion nnd reduction potentih and an MLCT transition. Using, some additional solvenr data, a number of useful p.xamcters were derived in a fashion which woufd not be possible through consideration of either technique alone.
An electronic charge transfer transition involves excitation from ;f donor orbital in the ground state of a molecule, to an acceptor orbital in a Franck-Condon (non-equilibriunl} excited state of the molecule. III tfris paper we refer specifically to an IMLCT transition, From an orbital, Ghr ~ ~nair~ly on the metal. to an orbital, $L,primarily 011 Ihe ligand. However the treatment is quite general. An electrochemical study may, in appropriate cases, define the redox potentials of orbitais retrtted to those above. Thus we may observe the oxidation potential of rjr,r in the ground state of the compiex ML,l, and the reduction potential for adding an electron to tit_ to form the ground state of the reduced species ML,;. Previous authors [l--S] have demonstrated qualitative reIationships between optical charge transfer energies and electrochemicaI potentials but now we seek a more quantitative understanding in which quantities not derivable from either electronic spcctroscopy of electrochemistry alone. can bc obtained by a combined amdysis. In view of the salvation contributions to the paranleters obtained with each technique, a combined analysis is best approached within the framework of the collection and comparison of data in a range of solvents. The analysis which follows is based upon
theories
developed by Born 161, Onsager 171, Kirkwood [SJ. Lippcrt [9],Marcus [lO,ll]and Meyer [i2). Use of a free-energy cycle (fig. I) permits one to relate the various thermodynamic quantities (as defined in the legend to fig 1). measurable in the two cxperimental regimes. Thus the following equalities nx~p be written:
E op=u*+Xi
“X0-
(11
4E, = AEg f A(sol) , AEs = IzFAE(redoxf
=: [IzFAE’(redox)
(3
i- AAG, +x]
+Q
+ AAG, + Q
(3)
(see text below), and hence Eop = [Xi f tzFAE(redox)
+ xc, +
A(sol) ,
+ A&G, i- Q] W
where x0 + A(so1) is the total change in salvation free energy as earlier defined in eq. (13) of ref. [ 1 l] and eq. B2a of ref. [Y], andXj and x0 are the inner-sphere (vibrational) and outer-sphere (solvent, but also vibrational in nature) contribuiions to the reorganisation energy of the transition, respectively. Ncte that as a consequence of the Franck-Condon nature of the excited state, the transition energy Eop is a free 567
Volume
CHEMICAL
112. number 6
-BG
-_
2(!.!L)s
I%ig 1. I‘rcecnrrgy .md (ML-) A(;<
state.
(ML)g+
(ML*)?
energy
in htt
cqttiltbr~tcd 13q. (4).
Now
cncrgy
is dcfincd
that in the te\t A4G,
the cntroptcs cxctrcd
sutc
in which
the
the
function
satne
excited
involved
= ZAG,
- 4q
-
and nonbrackets
I> salvent
indcpcndcnt for a given n~o!eculc, provides tltc ttnporlant correlation between the two techniques. The complcs hIo(C0)4bpz(bpz= bipyrazinc) 1131 dt$ays J strong band, inter alid, attributed to d(Mo(O)) - rr* (bpz) MLCT.wltose crwgy,EoD.vztries
flm~ about 16000 to 20000 cm-’ depending upon tltc solvent ct~virontttet~t and shifting to bigher energy with ~ncrcasing solvent polarity (table 1; cf. the solv~rochrotnistn of the bipyridine analog [14]). Electrocitcmtcal data for LLrllngc ofsolventsare also shown tn table I. The reduction porcntial for tbc electrochemically rcvcrsiblc Mo(CO)4bpz/hlo(CO)qbpzcouple involves ~ddttion of an electron to GL (n* bpz) forming the rddtcdl bpL- bound to MO(O). This couple shifts to more postttvc potcttti~ls wttlt increasing polarity of the solvent. as the grouttd state radtcal anion becomes more solvent srabtliscd. 566
stale.
a&and
ifs the rcvcrsiblc
AEs is the solvent Jn
A(so1)
s
1984
-----_-
is tbc neutr.d species.
rcspectivcly.
minus the reduction
in transferring
[l l].
in square
potential
2 (XL)
(ML)
species
species being defined
4s the oxid,ttion
energy
of the ground are
quantities.
and mono-negative
to the equilibrated
Q IS the resotunce
-----_-_-------_--------
s
.tnd clcctrochemical
motto-positive
for thcsc respective
AE(rcdox)
cuitdtion
The quntity
2(:u_)
spectroscopic
excited,
free cncrgies
to J solvent.
AEg is the g.is phase hratrd
------_-__---_-_-_----_-
d~dgr.tm rekttn~
drc rltc solvation
28 December
LETTERS
= nFiE(redox)
are tllc cquihbrJtcd
the gac ph~c
PHYSICS
Similarly nork
to transfer
potential
and (ML*), (hIL3
AC,,AGf, Ad, and these solutes
of the ncLm1
phase excitation
energy
from
species.
to the equili-
electron from (ML_), to (ML?)g yielding = AC:-
AC,.
Oxidation occurs at the hlo(0) d manifold but is electrochemically irreversible, due to a following chemical reaction (ECi mechanism) [ 16.171. However the slow step of the following reaction appears to be tMo-CO bond breaking which is solvent independent. Thus the true thermodynamic potential will be more positive than recorded in table 1 by a solvent independent quantity, say x mV (probably 100
E OP = -1.04
M’(redox)
+ 33950
(cm-l)
_
This is an unexpected result appearing to contradict intuition in that as the potential difference between donor and acceptor orbital decreases, the optical transition energy increases_ Such an inverse correlation has not been previously reported_ An understan-
(3
Volume 112, number 6 Table 1 Llectrocl~emical Solvent
DhlF PC hleCN PY TIII‘ DCE DChl lzt, 0 CHC1s TCM pent “slls”
CHEMICAL
and spectroscopic
PHYSICS LEl-l-ERS
Xl December
1984
data”)
E(hlo(l)/hlo(O)) b)
E(bpz/bpz2
(CV)
(eV)
Af?(rcdox) (eV)
(cm-1 )
+ p bol)
AA&
E0p
x0
(cm-’ )
(cm-’ )
(cm-‘)
0.26 0.32
-1.42 -1.41
1.68 1.73
(13550) (14000)
19650 19550
3650 3550
3710 3260
0.28 0.76 0.30
-1.45 -1.52 -1.52
1.73 1.78
(14000) (14350)
19450 18900
3450 ‘900
3260 2310
0.34
-1.53
1.82 1.87
(14700) (15100)
18650 18150
2650 x50
2560 2160
1.90 c) 1.93 c) 1.98c) 2.07 c) 2.09 c) 2.14 e)
(15350) (15530) (15950) (16670) (16870) (17260)
17990 17790 17360 16610 16400 16000
1990 1790 1360 610 100 0
1910 1730 1310 590 390 0
a) All electrochemical potentials referenced against fcrrocene as internal reference (Fc+/Fc is at 0.16 eV versus SCE) [ 151. Potentials were recorded on Pt electrodes using cyclic voltammetry at scan rates of 100.50 and 20 mV/s. Confirmatory data acre obtained using differential pulse polarography. Dater arc averages of several esperiments. DhlJ- = dimcthylformamide, PC = propylene carbonate, PY = pyridine, THF = tetrahydrofumn, DCL = 1,2dichloroethane, DC11 = dichloromethane. TCM = tetrais cstrapolation using eq. (I 1). chloromethnne. pent = pentane, “ws” ~ b, The oxidation process is electrochemically irreversible. E p - El,b is compar.rble to that of the fcrrocene couple under the same conditions. Value quoted is:(Ep + Ep@. ')Calculated from eq_ (5) in text. MS + xi = 16000 cm-’ ; xi +s + Q = -1260 CIII-~.
ding of this phenomenon develops from further analysis below. The following expression [S] allows one to approximate the solvation free energy of a species as a power series: t1=-
AG,
= 0.5
c
n=o
(tz+ 1x2,1 baz+l
1
-d,
(II + l)D, +tz
>
where terms higher than II = 1 are ignored and the reader is referred to the earlier literature [6-l?] for detailed discussion of the conditions under which this expression is useful. D, is the static dielectric constant of the solvent, b is the radius of the solute. Q. =z2e2T 2nd Qr = ~2, where p is the dipole moment of the solute species. The term in zz = 0 disappears for uncharged species_ Using (6) the difference in salvation free energies of the uncharged and thermally equilibrated ground and excited states, A(so1) may be writ ten *(solj=AGs(ej-AGs(gj=~~, Following
earlier authors
(7) [S-l 2 1, the Franck-C&don
destabilisatiozl of the excited state. due to solvent interactions, may be written
(cr,-&)’ x0 =
b3
1 -Do,
1 -D,
c~Dop+l
where in (7) and (8) the ground and excited state dipole nlonlents are appropriately discriminated. and Do, is the optical dielectric cozrstant of the solvent (square of the refractive index). The total solvent dependence excluding non-polar contributions (very small [ Ii] ), eq. (4), is A&- = A(sol) + x0; suniming (7) and (8) yields (after evaluating the vector productsj [9,12] :
* 2-@4&0s bJ- II”) J - b3
1 -D, p_ X&+1
The angle 0 is that between the ground and excited state dipoles. The ground state dipole moment lies along the C2 axis with the negative end pointing towards the CO groups. Eq. (4) can now bc recast in the general form: 569
CHtSIIC4L
Volume 113. number 6
whcrefand f’ group the factors shown in cq. (9). In d forthcoming paper [ 161 we devclopcd this analysis with 73 solvents. Hc~c WC shall riwricl ourselves to LonsldcIulg G solvents of low polarity and low dieleclric ,XI~SLI~I whtcl~ might be expected to obey the diclectm ~onmuum model. The optlcal data thereof (rdhlc 1) obey ( IO) well according to (in cm-l) 9500
I: ~,,, =
C I - D,,,)/(7D,,
+ I)
- 7600 ( 1 - D,)/( ZD, •i- 1) + 16800
(1 t>
~111 :! Lorrel~tion cocl‘ficicnt oTO.988 and A standard dcvlarion of 65 (the lower set ol‘ six solvents shown in 1h1c 1 were used). and where the constant term, 16800 CW- 1 IS associated with Xi + AEg_ However 111~ &I& yield a l‘amly of solutlonswhich do not differ grmtly 111their correlation coefficients or standard dc\Gtlwis. indeed the solutton /= 0,f’ = -7 1 10, and IS not unre~sou~blc (correlaX, + AL’.. = 15 1 10 cm-~ II~II coekicient 0.97, standard deviation 169). This LiIrsr St~llIliOil is. however, uiconsistent with IllC CX~~~c~wm _m (9). The solution in (1 I) IS statistically the hc~,r. but dots 1101 difl‘er significmtly from many other
which flies hetwccn zero and 9500 m-1 I iuwxve~ /’ IS gcncrally found 111the range -(7000\ Imges rrom about 7000; cl11-1 anJ the constant 15OOC IO 17000 cm-t. At rim stage ol’ study WC note tlUt thz appoxzti sce~iis Justified hut tint iligllcr-qual-
~III!KIII~
rry.
dlrcctton
113 rhcg~ound cl111g of
ared
data .NC necessary.
101 I' rcquircs, conndermg eqs. I I ), tlial. III tlm systcui, tlic dipole ~nonient
clIa11pzs
111~
SIJIC
~~mc’ldtm~i For
tlic
state
Frock
by
polar
sliown put po5c
by
1 SO” in the
[1.15].
-Cowlon solvents.
cxcitcd
Tlusprovidcsan
dcstabllmtion
state
relative
undcrstm-
of the ex-
and 11e11cc of the ricgalive
111 (5). of miicating
how
thcsc data niay
he utihcd.
wc cl~oosc .I mcdmn v.duc of the COIK.LIII~ of 16000 cn- 1_ Note thdt in the gas ph.m, AAG, = 0. therefore X, + &*M’(rcdo\) f s + Q = 16000 cm-l _ Further, use oicq. (5) provides the value for nF4E’(redox) in the gas ~ILISC by imertion ofE,t, = 16000 cmM1. Knowing rll:“(rcdox) allows derwation of Xi +x + Q = - 1260 cm-t _This then leads to the evaluation: of AAG, /q_(3)]_ Use ot cq. (I) leads to cv,duation of 570
1984
A(so1) + X0_ These data arc also collected in table 1. The sun1 XI +x is necessarily positwe but Q, using an appropriate free-energy cycle, is estimated to he near -0.5 V [IS] _The “gas phase” optical energy is close to that observed in pentane, as might be anticipated. The procedure provides an interesting set of parmicters whose vA.~cs seems eminently reasonable. Further developrncnt on this and related syslen~ should provide the impetus to link the study of elcctrochemistry and optical spectroscopy and to seek evaluation ofothcr useful parameters. such as the selfcschangc energy, which may be derivable from a freeenergy cycle involving Q_ The merits and boundary conditions inherent in this analysis will he discussed in more detail in a future publication [ 16]_ We also currently seek emission data which should further defme some of the parameters derived. The authors and Engineering
are indebted to the Natural Research Council (Ottawa)
Sciences and tbc
Office of Naval Research (Washington) for financial support. cussions Walker.
We also gratefully acknowledge useful dlswith Prol‘essor T.J. Meyer and Professor 1-M.
References
III
311d more cxwnsivc The ncgJtivc k~iue
(S)-(
28 December
PHYSICS LET-l-fRS
Rudd, 1~. Caunder and H. Tube, J. Am. 90 (1968) 1187. B-I’. Sullivan and T.J. Meyer, Inors. Chem.
[ 11 P.C. I‘ord, F.P. ]7
]
Chcm. Sot. J.C. Curtis, 12 (1983)
224.
[ 31 A.B P. Lcvcr, Inorgnic
electronic spectroscopy, 2nd Id. (Ekcvier, Amsterddm, 1981). [4] A.B.P. Lever, S. Licoccia. P.C. Minor. B.S. Ramaswamy and S.R. Pickens, J. Am. Chcm. Sot. 103 (1981) 6600. [S] S. Goswami, R. Mukhcrjec and A. Chakravorty. Inor?. Chcm 22 (1983) 2825. 161 hl. Born. 2. Phys. 1 (1920) 45. [71 L. OnsAger, J. Am. Chcm. Sot. 58 (1936) 1486. 181 1-G. Kirkwood. J. Chcm. Phys. 2 (1934) 351. 191 C. Lippert. 2. Elektrochem. 61 (1957) 962. 1101 R.A. hlarcus, J. Chem. Phys. 39 (1963) 1734. illi R-4. Marcus. J. Chem. Phys. 43 (1965) 1261. 1121 EM. Sober, B-I’. Sullivan and T.J. Meyer, Inorg. Chem. 23 (1984)
2098.
R.J.
Crutchley and A.B.P. Lever, Inorg. Chem. 21 (1981) 2276. H. Saito, J. rujita and I(. S&o. Bull. Chem. Sot. iapdn 41 (1968) 663. R.R. Gage, CA. Kovdl and C.C. Lisensky, Inog. Chem. 19 (1980) 26.54. IX. D.
Dodsworth
and A.B.P.
Lever,
to be submitted.
Xllholova’, L. Pospisil, and A.A. VI&, Proceedings of the 13th International Conference on Coordination Chemistry, Boulder (1984); private communication.