- Email: [email protected]
Intramolecular intervalence charge transfer in bimolecular mixed-valence complexes of metals
Volume 64. number 2
CHEMICAL PHYSICS LEFI-PERS
INTRAMOLECULAR IN BIMOLECULAR
INTERVALENCE MIXED-VALENCE
1 July 1379
CHARGE TRANSFER COMPLEXES
OF METALS
Ernst D. GEMIAN Imtitute of Electrochemi3try. The Academ_v ofSciences of the USSR. hfoscow V-71. USSR
Received 5 March 1979
The eilipsoidai cavity model of Kirkbood-Westheimer the cavity. Within this model the solvent reorgxdsation
is extended to the case u hen cknrges are loated nn)\%here in energies assocwted with intmniolecular charse transfer are ulco-
Wed and compxed with experimental data.
Binuclear mixed-valence complexes of AhlLIL(L)bl*BIL type often have unusual absorption bands in their electronic spectra [I-S] _ If metal-metal interactions are weak, the complexes are classified as trapped-valence compounds. In such complexes the corresponding absorption bands are in the near-infrared region, and they are assigned to intervalence-transfer transitions (IT) [l-5] _ The theory of such IT bands was developed by Hush [6] _According to ref_ [6] the energy of light-induced electron transfer in solution (Eop), and outer-sphere (Es) zrnd inner-sphere (Ejn) rearrangement terms are related by Eop = AGo + Es + Ei” where AGO is the free energy change in the reaction of intramolecular electron transfer between hl* and hl. The relation enables one_ in patt$ular, to make use of optical data for testing models developed for calculation of solvent reorganisation energies (Es) characterizing charge transfers. In accordance with most theoretical approaches [6--S] Es is calmdated as an integral over all space except the volume occupied by reActants Es = (C/8x)
j-@,
- D,)’
dF’ )
(la)
where C= l/e0 - l/es (E, and es are optical and static dielectric constants of solvent respectively), 0, and Df are dielectric displacements in medium created by the charge distrrbution in reactants and products_ It was recently shown [9] in terms of a different model used for description of the interaction between reactants and solvent that the reorganisation energy is Es = (C/Sir) S(~i
- ~,)2
d V,
where Ci and 8, are the electric fields created by reactants and products in vacua respectiveIy. The explicit form of Es depends on the particular model chosen for the approximation of the reactants. terms of the hlarcus metal spheres model [S] both the integral (la) and (lb) equals Es = Ce2(1/2Rt
+ l/ZR,
-
II'R) ,
(Lb) In
(2)
where R, and R, are the sphere radii, and R is distance between the sphere centres. Cannon [IO] has proposed an expression for Eiin terms of the ellipsoidal cavity model of Kirkwood-Westheimer (KW) [I l] which seems to be more suitabIe for the description of intramolecular electron transfer than hfarcus model_ The calculations of Es in terms of the KW model for a sphere-shaped cavity were carried out in refs. [ 12,13]_ In this paper the KW model is generalized to the case when charges are located anywhere m the ellipsoidal
295
Volume 64, number Z
CHEhlICAL PHYSICS LITi-TERS
I Juiy I979
cavity- The generalized KW model is used For calculations of
Es in terms of eqs_ (la) and (1 b). Results of these calculations are compared with experimental data for Iight-induced intramoiecular electron transfers in binuclear complexes of ruthenium_ - At this point we shaI1 represent a moIecule (or particIes in contact) in a solvent as an ellipsoidal cavity of dielectric constant Ein which is surrounded by ;t medium of dieIectric constant es_ In the cavity there are K point charges 2: (corresponding to effective charges on atoms in the precursor comples) whose values change to Z,f (in the successor complex) in the process of electron transfer. Using the generalised Neumann expansion [ 141 for I/lr - r-i-and the KW procedure [I I] one an show that the expressions for the electric potential created by the charges2: (2,‘) in the interior cavity, Gin _and outside the boundary eilipsoid. Gel, are given by
where G,‘: = 2(3-II + I)[(n - az)!/(/r + r&, F;;(a) = q;(QP,‘,“(x,) cos(nzy,& pa, A, and *a are proiate spkeroidaf coordinates of the charge 2,. P,‘f’ and Qz are associated Legendre poIynomials of first and second kinds. h defines the botmdary ellipsoid with semi-major and semi-minor axes A and B, -y = 1 form = 0 and 2 for ULf O- Eqs_ (3) and (3b) are reduced to the KW equations [I I 1 for the case when charges are on the major axis between the foci. Substitution of (3b) In eq_ (la) leads to
where R, is rhe interfomI distance and 4Z- =Zi - .ZL_ For the particuhr c-se when charge transfer takes ptace between two points symmetrically focated on the major axis betkxeen the foci ({pt. Xt = I. tiI = 0) and _ - 0): p1 = -pl > 0). and when ein < es we approximately obtain t&_X~ = I. ‘-r> &; = (&&,)
c
n=o
iI - (-I)‘*]” [(lkr + I)f(n + I)] Pz(JLl) ___ ___.___
Ip$+J’
[X0 - Q:,,($,)~Q:($,,>l
-
(5)
Now we shaI1 calculate Es in terms of eq_ (Ib). The electric field in vacua created by K charges Iocated in the amity equ& ticn = -grad ZE=t Z:f)e/lr - rJ_ Thus. the value 4& = &f - &i can be espressed as -grad Z$t rliS,e/Ir - r-I_ Substitution of 4& in eq. (lb) with use of the above-mentioned Neumann expansion and integration (in proIate spheroid31 coordinates) over aI1 space except the cavity volume leads to
64, number 2
Volume
CHEhlICAL
PHYSICS
LEl-l-IlRS
1 July 1979
Table 1
Tbeoreticai and experimental energies aj of optical transitions in binuclcar complexes hj Complex cj
A/B
d)
KW model
RZ e)
Esf>
Marcus model
EO’OP
Esgj
Es h)
E,i)
theory
ekperiment Qj
I CI(bpyjzRuWyzjRu(bpqj2CI
7.7/6-O
3.5
9.0
16 0
24.8
22.6
II Cl(bpyj~Ru(BPY)Ru(bpy_)2CI
9.85J6.3
5.65
I4 8
23.6
15.4
17.6
27.8 Jj
29.0
III CI(bpy)zRu(TEB)Ru(bpyj2CI
1 I-1/6.6
69
17.0
26.0
12.5
7.314.7
35
14.2
27.9
‘4.8
15.5 14.0
30 ojj
LV (NH3)5Ru(Pyzj
31.0 23.1 nj
34.1 kj
27.0
Ru(bpyj2CI
V (NH3jsRu(P~zjRuWH,j, VI (NH3j5Ru(BPY)Ru(NH3)s VII (Pyj(bpyjzRu(BPYj aj cj dj cj hj j) ej “j
Ru(bpyj2(P,j
7.Of3.5
35
24.3
37.6
74.8
24-0
9.2/4.0
5.65
30.7
41.0
15.4
19.0
12.4/6.8
5.65
9.9
15.7
ISA
14.0
22-o mj
18 22.6
In kcaI/mole. bj For CH3CN medium, 25°C. Pyz = 1.4-pyrazine. bpy = Z,Z’-bipyridyl. BPY = 4,4’-bipyridyl, TEB = trans-eth~lenebipyridyl. In A. value of semi-mmor ais B is taken as mean of characteristic distances For atom Ru along octahedron bonds. q R, equals halFoF the Ru-Ru distance. r) Czdcuhted using eq. (7)g) Calcuhted using eq- (5j, ‘in = 3. Calcuhted using eq. (7) For RI = Rz = RZ_ Ij Calculated using eq_ (2) For RI = Rz r AL’Calcuhted using Es from column 4 and E,” = 13 kcal/moIe. k) Crticulatedusing E:” = 1 ktimole from ref- [15]mj This vzdue 0f Eop is taken as LLconventional ofie. Experimental data From refs. [ I-5, IS I _ This value represents the difference betrteen Eop and AGo_
-
Es
=
(Ce2/Ro)
x COS[~Z(~~ For
tile case
F
PI
c c
rr=o m=O -
@]
’ 7(-n
+ I) ((22 - nz)!:(n
[Qz(h,)]'
of charge transfer
between
f nr)!]
[(II + IlAo - (IIpoints
tocated
3g
.I.$ nz,nz,P~~Or,i~~~~)P,:)IO-‘p)Pfl’Op)
nz + I)Q,!~IOO)/Q~~‘~~O)I -
(6)
on the major axis eq- (6) is reduced to
(7)
The equations obtained are used below for calcuIating Es and optical transition energies in complexes of as transfer To make crtlculations simpler the transition [MIII ___hl*Ir] + [hl*1I ___hl”‘] is considered of one charge between the points located on the ruthenium atoms (change in electron density on the ligands is not taken into account). Results of the calculation using eqs. (5) and (7) are given in fifth and fourth columns of table 1 respectively_ Es values calculated according to eq. (2) are given in columns 6 and 7_ The optical energies, for compIexes II and III were calculated with Es from column 4 and the value Ej” = 13 kcal/mole. The E lay&i value is obtained as the difference of Eop r;nd Es for complex I used as a conventional one on the sssumption that complexes I_ II and III with similar nonbridging ligands have similar Ejn_ For complex I the value of Ei” has been taken as 4 kcal/moIe according to ref. [IS] *_ Table 1 shows that the calculation of Es using eq_ (7) provides the best consistency with the experimental data, although for compiex V the obtained theoretical value of Es is unrealistic. Such discrepancy between theory and experiment for this complex is not unexpected_ It conforms to the idea [I] that in V valencies are to 3 great extent delocalised. It is also possible that for complex V the parameters A and B are not quite proper. Eq. (2) is not satisfactory for describing the relationship between Es ruthenium-
* In other cases theoreticzd evaluations
oFER
have not been carried out For Iack oFX-ray
data.
297
I July 1979
CHEMICAL PHYSICS JLETTERS
VoIume 64. number 2
Table 2 Solvent effect on lT ener_gy3 So:vent tfio
DMSO
CH3CN
DMF 20.9
&aop theory b)
‘3 3 __-
205
22
“ap
22.6
20.9
22 c)
experimental d)
b) Es is calculated using eq. (7). $ 3) Far complex I; in kaljmale. ZS”_ d) Ref. [2J_ c) This value of Eop is used as a conventional one-
and the geometry
of the molecules, especialiy for compIexes
C.&N%
(CH3)zCO
19.6
21.5
20.4 = 13 kcaiilmole-
I--III. Comparison
with experiment
of the theoretical
Es obtained according to the cavity model (eq. (7)) for different solvents (table 2) also seems to favour this modei.
References %lJ_ POWXS. R-W_ C&&an, DJ_ S&non and TJ_ Meyer, Inorg- Chem_ 15 (1976) 1457. [21 MIS. Pa\Qers,D_J. Salmon. R-X’_ C~ilahzn 2nd TJ. Meyer. J. Am. Chem. Sac. 98 (1976) 6731. [31 C_ Creutz and H. T;tube. J. Am. Chem. Sac. 95 (19f3) 1086. [4] G.hf. Tom, C. Cretitz and H. Tat&e, J. Am. Chem. Sac. 96 (1974) 7827. [5J MJ. Powers and TJ- Meyer, Inorg. Chem- 17 (1978) 17&S161 NS. Hush. EIectrachim. Actn I3 (1968) 1005;Progr- Inorg. Chem. 8 (1967) 391. (7 j R-R.. Dagonadze and A-hi. Kuznetsov, Progr. Surface Sci. 6 (1975) l_ [81 R_A_ Mwzus.J_ Chem_ Phys_ 24 (19%) 966. 19) R-R. Dogoonadze.Adl. Kuznetsov. MA_ Varot)ntsev and MC_ Zaqaraia. J- Electroan& Chem. 75 (1977) IlO] R-D. Cannon, Chem. Phys. Letters 49 (1977) 299. [I I 1 J-G- Kirk\\oodand F-H- Westheeimer.J. Chem. Fhys- 6 (1938) 506; [ll
F-H_ Westheimer atd J-G. Kirkwood, J. Chem. Phys_ 6 (1938) 516. [13-j ED- Germanand AAl_ Kuznetsov. B.dI_ Acad. Sci_ USSR (1978) 2817. (131 YJ- Kharbtz, Electrochemistry I2 (1976) 1886. 1141 J- Sister, Electronic structure of molecules (MeCraw-Hill. New York. 1963) zq~p-6. 115 J C- Creutz. lnorg- Chcm_ I7 (1978) 3723_
298
3 15.
CHEMICAL PHYSICS LEFI-PERS
INTRAMOLECULAR IN BIMOLECULAR
INTERVALENCE MIXED-VALENCE
1 July 1379
CHARGE TRANSFER COMPLEXES
OF METALS
Ernst D. GEMIAN Imtitute of Electrochemi3try. The Academ_v ofSciences of the USSR. hfoscow V-71. USSR
Received 5 March 1979
The eilipsoidai cavity model of Kirkbood-Westheimer the cavity. Within this model the solvent reorgxdsation
is extended to the case u hen cknrges are loated nn)\%here in energies assocwted with intmniolecular charse transfer are ulco-
Wed and compxed with experimental data.
Binuclear mixed-valence complexes of AhlLIL(L)bl*BIL type often have unusual absorption bands in their electronic spectra [I-S] _ If metal-metal interactions are weak, the complexes are classified as trapped-valence compounds. In such complexes the corresponding absorption bands are in the near-infrared region, and they are assigned to intervalence-transfer transitions (IT) [l-5] _ The theory of such IT bands was developed by Hush [6] _According to ref_ [6] the energy of light-induced electron transfer in solution (Eop), and outer-sphere (Es) zrnd inner-sphere (Ejn) rearrangement terms are related by Eop = AGo + Es + Ei” where AGO is the free energy change in the reaction of intramolecular electron transfer between hl* and hl. The relation enables one_ in patt$ular, to make use of optical data for testing models developed for calculation of solvent reorganisation energies (Es) characterizing charge transfers. In accordance with most theoretical approaches [6--S] Es is calmdated as an integral over all space except the volume occupied by reActants Es = (C/8x)
j-@,
- D,)’
dF’ )
(la)
where C= l/e0 - l/es (E, and es are optical and static dielectric constants of solvent respectively), 0, and Df are dielectric displacements in medium created by the charge distrrbution in reactants and products_ It was recently shown [9] in terms of a different model used for description of the interaction between reactants and solvent that the reorganisation energy is Es = (C/Sir) S(~i
- ~,)2
d V,
where Ci and 8, are the electric fields created by reactants and products in vacua respectiveIy. The explicit form of Es depends on the particular model chosen for the approximation of the reactants. terms of the hlarcus metal spheres model [S] both the integral (la) and (lb) equals Es = Ce2(1/2Rt
+ l/ZR,
-
II'R) ,
(Lb) In
(2)
where R, and R, are the sphere radii, and R is distance between the sphere centres. Cannon [IO] has proposed an expression for Eiin terms of the ellipsoidal cavity model of Kirkwood-Westheimer (KW) [I l] which seems to be more suitabIe for the description of intramolecular electron transfer than hfarcus model_ The calculations of Es in terms of the KW model for a sphere-shaped cavity were carried out in refs. [ 12,13]_ In this paper the KW model is generalized to the case when charges are located anywhere m the ellipsoidal
295
Volume 64, number Z
CHEhlICAL PHYSICS LITi-TERS
I Juiy I979
cavity- The generalized KW model is used For calculations of
Es in terms of eqs_ (la) and (1 b). Results of these calculations are compared with experimental data for Iight-induced intramoiecular electron transfers in binuclear complexes of ruthenium_ - At this point we shaI1 represent a moIecule (or particIes in contact) in a solvent as an ellipsoidal cavity of dielectric constant Ein which is surrounded by ;t medium of dieIectric constant es_ In the cavity there are K point charges 2: (corresponding to effective charges on atoms in the precursor comples) whose values change to Z,f (in the successor complex) in the process of electron transfer. Using the generalised Neumann expansion [ 141 for I/lr - r-i-and the KW procedure [I I] one an show that the expressions for the electric potential created by the charges2: (2,‘) in the interior cavity, Gin _and outside the boundary eilipsoid. Gel, are given by
where G,‘: = 2(3-II + I)[(n - az)!/(/r + r&, F;;(a) = q;(QP,‘,“(x,) cos(nzy,& pa, A, and *a are proiate spkeroidaf coordinates of the charge 2,. P,‘f’ and Qz are associated Legendre poIynomials of first and second kinds. h defines the botmdary ellipsoid with semi-major and semi-minor axes A and B, -y = 1 form = 0 and 2 for ULf O- Eqs_ (3) and (3b) are reduced to the KW equations [I I 1 for the case when charges are on the major axis between the foci. Substitution of (3b) In eq_ (la) leads to
where R, is rhe interfomI distance and 4Z- =Zi - .ZL_ For the particuhr c-se when charge transfer takes ptace between two points symmetrically focated on the major axis betkxeen the foci ({pt. Xt = I. tiI = 0) and _ - 0): p1 = -pl > 0). and when ein < es we approximately obtain t&_X~ = I. ‘-r> &; = (&&,)
c
n=o
iI - (-I)‘*]” [(lkr + I)f(n + I)] Pz(JLl) ___ ___.___
Ip$+J’
[X0 - Q:,,($,)~Q:($,,>l
-
(5)
Now we shaI1 calculate Es in terms of eq_ (Ib). The electric field in vacua created by K charges Iocated in the amity equ& ticn = -grad ZE=t Z:f)e/lr - rJ_ Thus. the value 4& = &f - &i can be espressed as -grad Z$t rliS,e/Ir - r-I_ Substitution of 4& in eq. (lb) with use of the above-mentioned Neumann expansion and integration (in proIate spheroid31 coordinates) over aI1 space except the cavity volume leads to
64, number 2
Volume
CHEhlICAL
PHYSICS
LEl-l-IlRS
1 July 1979
Table 1
Tbeoreticai and experimental energies aj of optical transitions in binuclcar complexes hj Complex cj
A/B
d)
KW model
RZ e)
Esf>
Marcus model
EO’OP
Esgj
Es h)
E,i)
theory
ekperiment Qj
I CI(bpyjzRuWyzjRu(bpqj2CI
7.7/6-O
3.5
9.0
16 0
24.8
22.6
II Cl(bpyj~Ru(BPY)Ru(bpy_)2CI
9.85J6.3
5.65
I4 8
23.6
15.4
17.6
27.8 Jj
29.0
III CI(bpy)zRu(TEB)Ru(bpyj2CI
1 I-1/6.6
69
17.0
26.0
12.5
7.314.7
35
14.2
27.9
‘4.8
15.5 14.0
30 ojj
LV (NH3)5Ru(Pyzj
31.0 23.1 nj
34.1 kj
27.0
Ru(bpyj2CI
V (NH3jsRu(P~zjRuWH,j, VI (NH3j5Ru(BPY)Ru(NH3)s VII (Pyj(bpyjzRu(BPYj aj cj dj cj hj j) ej “j
Ru(bpyj2(P,j
7.Of3.5
35
24.3
37.6
74.8
24-0
9.2/4.0
5.65
30.7
41.0
15.4
19.0
12.4/6.8
5.65
9.9
15.7
ISA
14.0
22-o mj
18 22.6
In kcaI/mole. bj For CH3CN medium, 25°C. Pyz = 1.4-pyrazine. bpy = Z,Z’-bipyridyl. BPY = 4,4’-bipyridyl, TEB = trans-eth~lenebipyridyl. In A. value of semi-mmor ais B is taken as mean of characteristic distances For atom Ru along octahedron bonds. q R, equals halFoF the Ru-Ru distance. r) Czdcuhted using eq. (7)g) Calcuhted using eq- (5j, ‘in = 3. Calcuhted using eq. (7) For RI = Rz = RZ_ Ij Calculated using eq_ (2) For RI = Rz r AL’Calcuhted using Es from column 4 and E,” = 13 kcal/moIe. k) Crticulatedusing E:” = 1 ktimole from ref- [15]mj This vzdue 0f Eop is taken as LLconventional ofie. Experimental data From refs. [ I-5, IS I _ This value represents the difference betrteen Eop and AGo_
-
Es
=
(Ce2/Ro)
x COS[~Z(~~ For
tile case
F
PI
c c
rr=o m=O -
@]
’ 7(-n
+ I) ((22 - nz)!:(n
[Qz(h,)]'
of charge transfer
between
f nr)!]
[(II + IlAo - (IIpoints
tocated
3g
.I.$ nz,nz,P~~Or,i~~~~)P,:)IO-‘p)Pfl’Op)
nz + I)Q,!~IOO)/Q~~‘~~O)I -
(6)
on the major axis eq- (6) is reduced to
(7)
The equations obtained are used below for calcuIating Es and optical transition energies in complexes of as transfer To make crtlculations simpler the transition [MIII ___hl*Ir] + [hl*1I ___hl”‘] is considered of one charge between the points located on the ruthenium atoms (change in electron density on the ligands is not taken into account). Results of the calculation using eqs. (5) and (7) are given in fifth and fourth columns of table 1 respectively_ Es values calculated according to eq. (2) are given in columns 6 and 7_ The optical energies, for compIexes II and III were calculated with Es from column 4 and the value Ej” = 13 kcal/mole. The E lay&i value is obtained as the difference of Eop r;nd Es for complex I used as a conventional one on the sssumption that complexes I_ II and III with similar nonbridging ligands have similar Ejn_ For complex I the value of Ei” has been taken as 4 kcal/moIe according to ref. [IS] *_ Table 1 shows that the calculation of Es using eq_ (7) provides the best consistency with the experimental data, although for compiex V the obtained theoretical value of Es is unrealistic. Such discrepancy between theory and experiment for this complex is not unexpected_ It conforms to the idea [I] that in V valencies are to 3 great extent delocalised. It is also possible that for complex V the parameters A and B are not quite proper. Eq. (2) is not satisfactory for describing the relationship between Es ruthenium-
* In other cases theoreticzd evaluations
oFER
have not been carried out For Iack oFX-ray
data.
297
I July 1979
CHEMICAL PHYSICS JLETTERS
VoIume 64. number 2
Table 2 Solvent effect on lT ener_gy3 So:vent tfio
DMSO
CH3CN
DMF 20.9
&aop theory b)
‘3 3 __-
205
22
“ap
22.6
20.9
22 c)
experimental d)
b) Es is calculated using eq. (7). $ 3) Far complex I; in kaljmale. ZS”_ d) Ref. [2J_ c) This value of Eop is used as a conventional one-
and the geometry
of the molecules, especialiy for compIexes
C.&N%
(CH3)zCO
19.6
21.5
20.4 = 13 kcaiilmole-
I--III. Comparison
with experiment
of the theoretical
Es obtained according to the cavity model (eq. (7)) for different solvents (table 2) also seems to favour this modei.
References %lJ_ POWXS. R-W_ C&&an, DJ_ S&non and TJ_ Meyer, Inorg- Chem_ 15 (1976) 1457. [21 MIS. Pa\Qers,D_J. Salmon. R-X’_ C~ilahzn 2nd TJ. Meyer. J. Am. Chem. Sac. 98 (1976) 6731. [31 C_ Creutz and H. T;tube. J. Am. Chem. Sac. 95 (19f3) 1086. [4] G.hf. Tom, C. Cretitz and H. Tat&e, J. Am. Chem. Sac. 96 (1974) 7827. [5J MJ. Powers and TJ- Meyer, Inorg. Chem- 17 (1978) 17&S161 NS. Hush. EIectrachim. Actn I3 (1968) 1005;Progr- Inorg. Chem. 8 (1967) 391. (7 j R-R.. Dagonadze and A-hi. Kuznetsov, Progr. Surface Sci. 6 (1975) l_ [81 R_A_ Mwzus.J_ Chem_ Phys_ 24 (19%) 966. 19) R-R. Dogoonadze.Adl. Kuznetsov. MA_ Varot)ntsev and MC_ Zaqaraia. J- Electroan& Chem. 75 (1977) IlO] R-D. Cannon, Chem. Phys. Letters 49 (1977) 299. [I I 1 J-G- Kirk\\oodand F-H- Westheeimer.J. Chem. Fhys- 6 (1938) 506; [ll
F-H_ Westheimer atd J-G. Kirkwood, J. Chem. Phys_ 6 (1938) 516. [13-j ED- Germanand AAl_ Kuznetsov. B.dI_ Acad. Sci_ USSR (1978) 2817. (131 YJ- Kharbtz, Electrochemistry I2 (1976) 1886. 1141 J- Sister, Electronic structure of molecules (MeCraw-Hill. New York. 1963) zq~p-6. 115 J C- Creutz. lnorg- Chcm_ I7 (1978) 3723_
298
3 15.