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A quantitative interpretation of the magnetic field effect on hyperfine-coupling-induced triplet fromation from radical ion pairs
Volume
CHEMICAL
96, ntrmbcr 1
25 March 1983
PHYSICS LETTERS
A QUANTITATIVE INTERPRETATION OF THE MAGNETIC FIELD EFFECT ON ~~ERFiNE~OUPLlNG-INDUCES A. WELLER, F. NOLTlNG
TRIPLET
FORMATION
FROM RARICAL
ION PAIRS
and H. STAERK
.~ta.~-Plonck-Znsrinrtfir Biophysikalische Ci~emie, Abteilung Spektroskopie, 03100 Grtingen. FederaI Republic of Germany Rccelred
29 December 1982
Lqcrimentaily determined Btt2 x-dues characterizing the magnetic field dependence of molecular triplet production from radiral ion pairs originating from photoinduced electron transfer are compared with semi-empirical values obtained xcordmg to B,,l(hfi) = 2& +Bg)/(B, + Bz) from the root-mean-square values for the hyperfine coupling of the two rddrcals, Bt dnd B2 _ The very good agreement is discussed.
i. introduction
It is well established (I -41 that radical pairs gener ated by electron-transfer fluorescence quenching in a sin&x electron spin state can recombine to form moIccuktr triplets as indicated by the simplified scheme: ‘(‘A-
+?D+)
kst(B’
+3(?A-+zD+)-+3A*
or3D*
_
The required spin rIlult~pi~city change occurs with the (time-dependent) rate constant k,(B) which is based on the Ilyperfine-coupling-induced coherent spin motion of the unpaired electron spins and can be modulated b> we& magnetic fields (B). This effect as described by the energy-level diagram in fig. 1 is based on the relative vatues of the hyperfine interaction energy. U‘tlfi. the Zeeman splitting of the radical pair and the exchange interaction energy.f. In order to be able to predict the expected magnetK tleld effect one needs to compare the strength of the hyperfine inreraction energy with the spacing between the S, dnd the T,, To, T_ levels. This has led to the predicrions. confirmed by calculations [1,3,4], that for a magnetic field strength close to zero the hyperfine interaction produces a realigntnent of the electron spins m the radical ion pair. so that the initial singlet electron spin alignment will assume ==70% triplet character after some lo-20 ns. For strong fields, however,
Fi_p. 1. Splitting of the T+, To, T_ energy levels of a doublet pair {‘A- + *D? (with overall triplet multiplicity) due to Zeeman interaction; also indicated is the singlet-triplet splitting by 2J due to (weak) exchan_ee interaction.
where the Zeeman splitting is much larger than AEbt+ the T+. T_ states cease to be coupled to So so that the initially prepared state So can only mix with the To state leading to an asymptotic equipartitioning between these states. Thus the triplet production is reduced to SO% at field strengths of a few hundred gauss. This ma~eti~-meld-dependent triplet production is characterized by the fidd strength BIlz at half saturation [cf. eq. (3)]_ It is the purpose of the present paper to derive a relation which quantitatively correlates the magnetic
0 COP-2614/83/O~O~OO~/S
03.00 0 1983 North-Ho&nd
Volume 96, number1
CHEMICALPHYSICSLETTERS
25 March 1983
field effect observed experimentally with the hyper-
fine interaction energy of the radical pair calculated on the basis of the isotropic hyperfme coupling constants nik which have been obtained from the ESR literature [S] or other references [6.7J.
’ ‘---I
I
I
Pyrene - dn + DCNB -dL
in MeCN
2. Experimental Relative triplet yields have been determined by measuring the intensity, IDF, of the delayed fluorescence which is brought about by triplet-triplet anuihilation. As long as most of the triplets disappear by processes other than triplet-triplet annihilation the relative tripIet yield is given by *#)I*~(O)
=
PD&W~D&BI 1’2 -
Pyrene+ DCNB tn MeCN
(2)
The apparatus, a phosphoroscope-type spectrometer with a pulsed laser as the excitation source, has been described [8 ] . Full advantage of the signal-averaging capabilities of digital devices has been taken, employing a mini-computer (LSI 1 l/2) with interfaces (DT 2764, DATA Translation; DRV 11 C, MDB) which control all functions of the instrument and perform the signal averaging. The compounds of purest quality commercially available were purified by zone refining (pyrene, DCNB) or vacuum distillation (DMA, DMT). PyrenedIO and DMAdI1 @98% D, Merck, Sharp and Dohme) were used without further purification. DMDMA, DCNBJ,, p-F-DMA andp-F-DMA-ds were synthesized in this laboratory and finally checked by IR, NMR and/or chromatography for their purity. Methanol (Merck spectrograde) was used without further purification. Acetonitrile was dried over P4010 followed by rectification. All amines and solvents were stored under nitrogen until use. The samples containing ~2 X 10m4 Mpyrene (-d& and 1 X 10-3 M quencher were degassed by 5-6 freeze-pump-thaw cycles. During the measurements the temperature of the solutions was kept at 19OC. 3. Results and discussion The relative pyrene triplet yield as a function of the magnetic field strength is shown in fig. 2 for systems withp-dicyanobenzene (DCNB) and N,N-
I Pyrene+DMT
..
I
In MeCN
i
i I I
-7
---
i 0
Magnetic
100
I -!
--
200
,
1 t
< 650
Field Strength B/Gauss
Fig_ 2. Magnetic field dependence of the pyrene triplet yield in acetonitrile as derived from delayed fluorescence measurements: pyrene-d&p-dicyanobenzene+, 81~ = 8 G; pyreneJ p-dicyanobenzene, B,, = 17 G; pyrene/N, N-dimethyl-ptoluidine, B,,, = 59 G (cf. table 1).
diiethyl-ptoluidine (DhlT) as pyrene fluorescence quenchers in acetonitrile. For these systems the relative triplet yield decreases with increasing magnetic field strength, gradually reaching a saturation value +@)&-(0) above 200 G. The BI J2 value which is 25
Volume 96. number 1
CHEMICAL
PHYSICS
25 March 1983
LETTERS
defined according to
and Bz, of the two radicais, weighted
@,W,
B =+(B1 + B2)
/?I = ; P’T(O) - Q~r(m)l
is the arithmetic
varies between S and 59 G. Additional systems which have been investigated in methanol and acetonitrile are listed in table I. The
AEu
Bt I2 values which can be obtained with an accuracy of rk 1 G are increasing from top to bottom. It should
It has been shown that the dominant magnetic in-
tcraction in organic doublet molecules is the hyperfins interaction between the nuclear spinsIX and the unpaired electron spin in each radical which is governed b> the isotropic hyperfine coupling constants Q and c.m conveniently be described [4] by the root-
Bi =
value
(ck L&rA-(ik
l/2
+1j
)
(5) mean of the two values, one obtains
=%B1
+ ?I?2
B; +Bf = 23, +B2 - @)
~~ = fi/Bi
.
(7)
which is characteristic of the hyperfine-couplinginduced electron spin motion in each radical and varies between 1.5 ns for the p-F-DMA radical cation
On the basis of an expected correlation between the HI ,z value and the root-mean-square values. Bt TJblC 1 fi, ,1 and root-mxn-squdrc \aiue~.Bj = I’kL7$IkU~++‘)]~‘2. Ikmor-.lccepior (1)
-
-
_~___
(3
.~_~~~~~._~_~~__~__
_.~ p) rcned, p> rcnr-di, 1’) re11L’ pyrenc p) rcnc pyrsncd, pprcne pyrrned, pj rcnc pyrenc-,-d,
0 o
o 0 o
p>rene pyrcnc pyremxIl I))‘reae pywne4, pyreneilj J’ \lco11. l’Vl)V k’)Ci q
systcn1~)
o o o --.-.-
DCNB& DCNB DCNLkfJ DCNB DMAx/Il r
DMAiil , p-l--IMA+ p-I--DMA+ DMDhlA DM DhlA DMA DhlT DMA p-r-DhlA DblT p-1--DhlA
where
This relation implies that both radicals contribute independently to the change in the overall spin multiplicity of the radical pair. Their values, B, and Bz, as obtained according to eq_ (4) with the aid of the relevant Qilr values are listed in table 1 and lead to the Bl,,(hfi) values given in the last column of table l_ The plot ofBt,,(exp) against Bl,Z(hfi) in fig. 3 gives a straight line going through the origin with a slope of unity and clearly confirms the reliability of eq. (6). In addition this seems to indicate that the time available for electron spin realignment in the radical pair is long compared to the transition time
bc poinred our rhat although according to theory the hyperflnc interaction is independent of solvent parameters. such as viscosity or polarity, this does not necessarily apply lo AEi,fi.
msan-square
= Bl,,(hfi)
by Bill,
eq. (4). of the hyperfiie B1 lzk-\~) in hi&N
s 9 18 16 34 33 4s 51 52 55 58 59 59 67 60 74 _-
8 9 16 17 34 35 49 45 51 55 60 59 63 66 62 72
(in G)
B2
B:+B; 2BI +B2
3.7 4.6 3.7 4.6 17.6 17.6 26.4 26.4 29.6
6.4 7.7 16.8 16.8 29.4 31.7 43.9 48.9 49.6
2.3
29.6
55.3
9.1
32.5 34.5 32.5 37.4 34.5 37.4
54.8 58.4 61.0 63.7 65.0 70.7
Bl
in MeOH
interaction
-2.5 1.5 10.1 10.1 9.1 2.3 9.1 ‘3 9:1
9.1 2.3 9.1 2.3 2.3
-m~~hsool; McCN. acetonitrile; DCNB,p-dicyanobenzene; DhlA. N,Ndimethylaniliie;p-F-DhlA,p-fluorodimethylani~e; -1. 3.5Qilllcrho*y-N,N-dilncrhykniline; DhlT. N.N-dimethyl-p-toluidine. (6)
b)
CHEMICAL
Volume 96, number 1
PHYSICS LETTERS
Acknowledgement We thank B. Frederichs for technical assistance and Dr_ W. Kiihule and his co-workers for preparing and purifying many of the substances. This work has been supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich SFB 93 “Photochemistry with lasers”_
R. SchuIten. H. Staerk, A. Weller, H--J. Werner and B. Nickel, 2. Physik. Chem. NF lOl(1976) 371. K-J. Werner, IL Schulten and A. Weller, J. Chem. Phys. 68 (1978) 2419. Fig 3. Experimental B,,
values, Btm(esp),
interaction
plotted against values Bln(hfi) = 2(&
theoretical
hyperfine
+Bf)j(81
+ B2) according to table 1.
and 25 ns for the pyrene-dIo radical anion. Further measurements to check this with other A/D combinations iuclu~ng ffuo~oated compound with particularly strong hyperfrne coupling constants and in other solvents are in progress.
A. Weller, 2. Physik. Chem. NF 130 11982) 129. K_ Schuulten and P-G. Wolynes, J, Chem. Phys. 68 (1978) 3292. 1.C. Lewisand L-S. Singer. J- Chem. Phys. 43 (1965) 2712; G-J. Hoytink, J. Townsend and S.I. Weissman, J. Chem. Phys. 34 (1961) 507; B.M. Latta and R.W. Taft, J. Am. Chem. Sot. 89 (1967) 5172; 1-E. Bloor, B-R. Gison and DJ). Shillady, J. Phys. Chem.
711196?7) %238; J.R. Bdton. A. Carrington and A.D. McLacMan. Mol. Phys. 5 (1962) 31; E-T. Seo. R-F_ Nelson, J-hi. Fritscfl. L-S. Marcoux, D.W. Leedy and R.N. Adams, J. Am. Chem. Sot. 86 (1966) 3498. A. Canington and A.D. McLachlau, Introduction to magnetic resonance (Harper and Row. London, 19671. F. NoIting and A. Weller, unpubiished +esoIts. F. Nolting and A. Weller, Chem. Phys. Letters 88 (1982) 523.
27
CHEMICAL
96, ntrmbcr 1
25 March 1983
PHYSICS LETTERS
A QUANTITATIVE INTERPRETATION OF THE MAGNETIC FIELD EFFECT ON ~~ERFiNE~OUPLlNG-INDUCES A. WELLER, F. NOLTlNG
TRIPLET
FORMATION
FROM RARICAL
ION PAIRS
and H. STAERK
.~ta.~-Plonck-Znsrinrtfir Biophysikalische Ci~emie, Abteilung Spektroskopie, 03100 Grtingen. FederaI Republic of Germany Rccelred
29 December 1982
Lqcrimentaily determined Btt2 x-dues characterizing the magnetic field dependence of molecular triplet production from radiral ion pairs originating from photoinduced electron transfer are compared with semi-empirical values obtained xcordmg to B,,l(hfi) = 2& +Bg)/(B, + Bz) from the root-mean-square values for the hyperfine coupling of the two rddrcals, Bt dnd B2 _ The very good agreement is discussed.
i. introduction
It is well established (I -41 that radical pairs gener ated by electron-transfer fluorescence quenching in a sin&x electron spin state can recombine to form moIccuktr triplets as indicated by the simplified scheme: ‘(‘A-
+?D+)
kst(B’
+3(?A-+zD+)-+3A*
or3D*
_
The required spin rIlult~pi~city change occurs with the (time-dependent) rate constant k,(B) which is based on the Ilyperfine-coupling-induced coherent spin motion of the unpaired electron spins and can be modulated b> we& magnetic fields (B). This effect as described by the energy-level diagram in fig. 1 is based on the relative vatues of the hyperfine interaction energy. U‘tlfi. the Zeeman splitting of the radical pair and the exchange interaction energy.f. In order to be able to predict the expected magnetK tleld effect one needs to compare the strength of the hyperfine inreraction energy with the spacing between the S, dnd the T,, To, T_ levels. This has led to the predicrions. confirmed by calculations [1,3,4], that for a magnetic field strength close to zero the hyperfine interaction produces a realigntnent of the electron spins m the radical ion pair. so that the initial singlet electron spin alignment will assume ==70% triplet character after some lo-20 ns. For strong fields, however,
Fi_p. 1. Splitting of the T+, To, T_ energy levels of a doublet pair {‘A- + *D? (with overall triplet multiplicity) due to Zeeman interaction; also indicated is the singlet-triplet splitting by 2J due to (weak) exchan_ee interaction.
where the Zeeman splitting is much larger than AEbt+ the T+. T_ states cease to be coupled to So so that the initially prepared state So can only mix with the To state leading to an asymptotic equipartitioning between these states. Thus the triplet production is reduced to SO% at field strengths of a few hundred gauss. This ma~eti~-meld-dependent triplet production is characterized by the fidd strength BIlz at half saturation [cf. eq. (3)]_ It is the purpose of the present paper to derive a relation which quantitatively correlates the magnetic
0 COP-2614/83/O~O~OO~/S
03.00 0 1983 North-Ho&nd
Volume 96, number1
CHEMICALPHYSICSLETTERS
25 March 1983
field effect observed experimentally with the hyper-
fine interaction energy of the radical pair calculated on the basis of the isotropic hyperfme coupling constants nik which have been obtained from the ESR literature [S] or other references [6.7J.
’ ‘---I
I
I
Pyrene - dn + DCNB -dL
in MeCN
2. Experimental Relative triplet yields have been determined by measuring the intensity, IDF, of the delayed fluorescence which is brought about by triplet-triplet anuihilation. As long as most of the triplets disappear by processes other than triplet-triplet annihilation the relative tripIet yield is given by *#)I*~(O)
=
PD&W~D&BI 1’2 -
Pyrene+ DCNB tn MeCN
(2)
The apparatus, a phosphoroscope-type spectrometer with a pulsed laser as the excitation source, has been described [8 ] . Full advantage of the signal-averaging capabilities of digital devices has been taken, employing a mini-computer (LSI 1 l/2) with interfaces (DT 2764, DATA Translation; DRV 11 C, MDB) which control all functions of the instrument and perform the signal averaging. The compounds of purest quality commercially available were purified by zone refining (pyrene, DCNB) or vacuum distillation (DMA, DMT). PyrenedIO and DMAdI1 @98% D, Merck, Sharp and Dohme) were used without further purification. DMDMA, DCNBJ,, p-F-DMA andp-F-DMA-ds were synthesized in this laboratory and finally checked by IR, NMR and/or chromatography for their purity. Methanol (Merck spectrograde) was used without further purification. Acetonitrile was dried over P4010 followed by rectification. All amines and solvents were stored under nitrogen until use. The samples containing ~2 X 10m4 Mpyrene (-d& and 1 X 10-3 M quencher were degassed by 5-6 freeze-pump-thaw cycles. During the measurements the temperature of the solutions was kept at 19OC. 3. Results and discussion The relative pyrene triplet yield as a function of the magnetic field strength is shown in fig. 2 for systems withp-dicyanobenzene (DCNB) and N,N-
I Pyrene+DMT
..
I
In MeCN
i
i I I
-7
---
i 0
Magnetic
100
I -!
--
200
,
1 t
< 650
Field Strength B/Gauss
Fig_ 2. Magnetic field dependence of the pyrene triplet yield in acetonitrile as derived from delayed fluorescence measurements: pyrene-d&p-dicyanobenzene+, 81~ = 8 G; pyreneJ p-dicyanobenzene, B,, = 17 G; pyrene/N, N-dimethyl-ptoluidine, B,,, = 59 G (cf. table 1).
diiethyl-ptoluidine (DhlT) as pyrene fluorescence quenchers in acetonitrile. For these systems the relative triplet yield decreases with increasing magnetic field strength, gradually reaching a saturation value +@)&-(0) above 200 G. The BI J2 value which is 25
Volume 96. number 1
CHEMICAL
PHYSICS
25 March 1983
LETTERS
defined according to
and Bz, of the two radicais, weighted
@,W,
B =+(B1 + B2)
/?I = ; P’T(O) - Q~r(m)l
is the arithmetic
varies between S and 59 G. Additional systems which have been investigated in methanol and acetonitrile are listed in table I. The
AEu
Bt I2 values which can be obtained with an accuracy of rk 1 G are increasing from top to bottom. It should
It has been shown that the dominant magnetic in-
tcraction in organic doublet molecules is the hyperfins interaction between the nuclear spinsIX and the unpaired electron spin in each radical which is governed b> the isotropic hyperfine coupling constants Q and c.m conveniently be described [4] by the root-
Bi =
value
(ck L&rA-(ik
l/2
+1j
)
(5) mean of the two values, one obtains
=%B1
+ ?I?2
B; +Bf = 23, +B2 - @)
~~ = fi/Bi
.
(7)
which is characteristic of the hyperfine-couplinginduced electron spin motion in each radical and varies between 1.5 ns for the p-F-DMA radical cation
On the basis of an expected correlation between the HI ,z value and the root-mean-square values. Bt TJblC 1 fi, ,1 and root-mxn-squdrc \aiue~.Bj = I’kL7$IkU~++‘)]~‘2. Ikmor-.lccepior (1)
-
-
_~___
(3
.~_~~~~~._~_~~__~__
_.~ p) rcned, p> rcnr-di, 1’) re11L’ pyrenc p) rcnc pyrsncd, pprcne pyrrned, pj rcnc pyrenc-,-d,
0 o
o 0 o
p>rene pyrcnc pyremxIl I))‘reae pywne4, pyreneilj J’ \lco11. l’Vl)V k’)Ci q
systcn1~)
o o o --.-.-
DCNB& DCNB DCNLkfJ DCNB DMAx/Il r
DMAiil , p-l--IMA+ p-I--DMA+ DMDhlA DM DhlA DMA DhlT DMA p-r-DhlA DblT p-1--DhlA
where
This relation implies that both radicals contribute independently to the change in the overall spin multiplicity of the radical pair. Their values, B, and Bz, as obtained according to eq_ (4) with the aid of the relevant Qilr values are listed in table 1 and lead to the Bl,,(hfi) values given in the last column of table l_ The plot ofBt,,(exp) against Bl,Z(hfi) in fig. 3 gives a straight line going through the origin with a slope of unity and clearly confirms the reliability of eq. (6). In addition this seems to indicate that the time available for electron spin realignment in the radical pair is long compared to the transition time
bc poinred our rhat although according to theory the hyperflnc interaction is independent of solvent parameters. such as viscosity or polarity, this does not necessarily apply lo AEi,fi.
msan-square
= Bl,,(hfi)
by Bill,
eq. (4). of the hyperfiie B1 lzk-\~) in hi&N
s 9 18 16 34 33 4s 51 52 55 58 59 59 67 60 74 _-
8 9 16 17 34 35 49 45 51 55 60 59 63 66 62 72
(in G)
B2
B:+B; 2BI +B2
3.7 4.6 3.7 4.6 17.6 17.6 26.4 26.4 29.6
6.4 7.7 16.8 16.8 29.4 31.7 43.9 48.9 49.6
2.3
29.6
55.3
9.1
32.5 34.5 32.5 37.4 34.5 37.4
54.8 58.4 61.0 63.7 65.0 70.7
Bl
in MeOH
interaction
-2.5 1.5 10.1 10.1 9.1 2.3 9.1 ‘3 9:1
9.1 2.3 9.1 2.3 2.3
-m~~hsool; McCN. acetonitrile; DCNB,p-dicyanobenzene; DhlA. N,Ndimethylaniliie;p-F-DhlA,p-fluorodimethylani~e; -1. 3.5Qilllcrho*y-N,N-dilncrhykniline; DhlT. N.N-dimethyl-p-toluidine. (6)
b)
CHEMICAL
Volume 96, number 1
PHYSICS LETTERS
Acknowledgement We thank B. Frederichs for technical assistance and Dr_ W. Kiihule and his co-workers for preparing and purifying many of the substances. This work has been supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich SFB 93 “Photochemistry with lasers”_
R. SchuIten. H. Staerk, A. Weller, H--J. Werner and B. Nickel, 2. Physik. Chem. NF lOl(1976) 371. K-J. Werner, IL Schulten and A. Weller, J. Chem. Phys. 68 (1978) 2419. Fig 3. Experimental B,,
values, Btm(esp),
interaction
plotted against values Bln(hfi) = 2(&
theoretical
hyperfine
+Bf)j(81
+ B2) according to table 1.
and 25 ns for the pyrene-dIo radical anion. Further measurements to check this with other A/D combinations iuclu~ng ffuo~oated compound with particularly strong hyperfrne coupling constants and in other solvents are in progress.
A. Weller, 2. Physik. Chem. NF 130 11982) 129. K_ Schuulten and P-G. Wolynes, J, Chem. Phys. 68 (1978) 3292. 1.C. Lewisand L-S. Singer. J- Chem. Phys. 43 (1965) 2712; G-J. Hoytink, J. Townsend and S.I. Weissman, J. Chem. Phys. 34 (1961) 507; B.M. Latta and R.W. Taft, J. Am. Chem. Sot. 89 (1967) 5172; 1-E. Bloor, B-R. Gison and DJ). Shillady, J. Phys. Chem.
711196?7) %238; J.R. Bdton. A. Carrington and A.D. McLacMan. Mol. Phys. 5 (1962) 31; E-T. Seo. R-F_ Nelson, J-hi. Fritscfl. L-S. Marcoux, D.W. Leedy and R.N. Adams, J. Am. Chem. Sot. 86 (1966) 3498. A. Canington and A.D. McLachlau, Introduction to magnetic resonance (Harper and Row. London, 19671. F. NoIting and A. Weller, unpubiished +esoIts. F. Nolting and A. Weller, Chem. Phys. Letters 88 (1982) 523.
27