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Optically detected multiple-quantum transitions in photoexcited molecular triplet states in zero external magnetic field
Volume 17, number 1
1 November 1972
CHEMICAL PHYSICS LETTERS
OPTICALLY DETECTED MULTIPLE-QUANTUM TRANSITIONS IN PHOTOEXCITED MOLECULAR TRIPLET STATES IN ZERO EXTERNAL MAGNETIC FIELD * Albert Department
of Physics,
L. SHAIN and Mark SHARNOFF Universit>* of Dclaruarr,
Received
hlultiplequantum. micro\%zwdriven are observed and classified.
transitions
I9 71 I,
US/Z
22 June 1972
betwax
1. Introduction
~Vcwark. Delaware
zero-field
spin sublevels of a photoexcited
triplet state
photoescited triplet species in zero estcrr~al magtrefic We first observed such transitions during our early work on the cyclopentanone triplet [ 1 1j and, in seeking to understand their unusually narrow lines, have gone on to investigate them in several other systcms. We report results here for cyclopcntnnone and for quinoxaline.
jkid.
hialtiple-quantum transitions, arising from the simultarheous absorption of two or more quanta of electromagnetic radiation, were first observed over twenty years ago in a number of atomic and molecular kam electric resonance experiments [ 1,21, were subsequently found magnetically in optical pumping cxperiments 131,and have in recent years become commonplace in laser-induced multiphoton optical absorption [4] _ in conventional magnetic resonance esperiments carried out at high magnetic fields, double quantum transitions have been found in the NMR of liquids [ 51 and in the EPR of both transition metal complexes [6] and free radicals [7]. De Groot and van der Waals [8] reported a double-quantum transition in the EPR of the photoexcited triplet state of naphthalene, and Clements and Shamoff [9] have recently observed such a transition in the optically detected EPR of pyrazine. A double-quantum transition also appears to be responsible for the g= 2 resonance observed in the escitation-modulated experiments of Levanon and Weissman [ lo] . The purpose of this communication is to report the observation of magnetically-induced double- and trip!equantum transitions between the spin sublevels of * Research supported
by National Science Foundation Grant GF-295 19 and by US Army Research Office (Durham) Grant DA-ARO-D-31-124-71686.
2. Experimental The resonances are detected optically in the usual way. The experimental set-up is that described earlier [ 1 l] , supplemented by an Ej'HLabs Model 5 I 1 travelling wave tube (TWT) amplifier. The saturated output (1 to 1.5 W, depending upon frequency) of the TWT was transmitted via a calibrated vnriablc attenuator to the rigid coaxial line and slow-wave helix wound around the sample. The helix and sample were immersed in liquid helium. The transition frequencies were measured with a Hewlett-Packard Model 540.4 Transfer Oscillator and Model 524B Frequewy Counter. Single- (SQT), double- (DQT), and triple- (TQT) quantum transitions could be easily observed with the help of the TWT amplifier. We also attempted to observe the DQT and TQT by using the 20 mW output of our Polarad Model R Sweep Generator without amplification and found this power level generally insufficient to saturate the multiple-rluantum transitions.
95
Voiume
17, number
1
1 November
CHEMICAL PHYSICS LETTERS
1972
3. Results and discussion The signature of a multiple-quantum transition is !he dependence of its transition probability upon the intensity of the driving source. The transition probability for an SQT increases linearly, for a DQT increases with the square and for the TQT increases with the cube, of the driving intensity. In the present experiments the optical signals resuIt from partial saturation of microwave transitions (I?_] and, in the region of mild to moderate saturation, the logarithmic plot of signal amplitude versus microwave power would be expected to yield a straight line whose slope gives the order of the transition. This is clearly shown, in the case of cyclopcntanone X-traps, by the data of fig. 1. In the case of the ordinac4, or SQT transition, the region of moderate saturation appears at the extreme right ; as the microwave power level is raised further, the degree of saturation can no longer increase proportionally, and the plot curves over towards a horizontal asymptote. In the case of the DQT and TQT, the power available from our TWT is appnrentIy not sufficient to produce hard saturation, and the plots remain linez to the highest power Ievels. The very clear correlation of the slope, s, with the observed transition frequency, 3396 IMHz, is proof that the transitions arc not single-quantum transitions induced hy harmonics generated in the Polarad or TWT units, but are true multiple absorptions of quanta carried at the fundamental frequency. The secand interesting kature of our DQT and TQT signals is the diminution of linewidth with increasing order of the transition. A few years after the first observations of multipbe-quantum transitions, this narrowing was explained from theoretical considerations ( I3- 151 but these theories were concerned with transitions whose breadths were lifetime-limited (i.e., with komogcneously broadened lines). A simple extension of the theory to the case of inhomogeneously broadened lines can bc made and leads to ihe predictio n that, whatever the order of
the transition, the e value. v/Cv, observed in the limit of mild saturation will be independent of the order of the transition. This is seen from table I to be the case for our cyclopentanone SQT, DQT, and TQT. The 3397 MHz transition is known, from our studies [ 161 of transient response to pulsed microwave irradiation of cyclopentanone, to be inhomogeneously broadened. 96
ATTENUATION,db/lO
Fig. 1. Logarithmic
plot of relative signal amplitude wrsus microwave power for cyclopentanone X-traps af 42°K. The microwave power at 0 dB is different for each transition. The amplitude of each transition is normalized to its value at 0 dB attenuation. SQT (01, DQT (a), and TQT (0) represent the D-./El singlequantum, the double-quantum and the triplequantum transitions, respectively, and s measures the slopes of the linear portions of their power dependence.
Resonance
Table 1 frequencies and linewidths”) for cyclopentanone X-traps and cyclopcnt~none in /I-hexanc x-traps
ri-hexane
Transition frequency + 2 MHz
linewidth k 0.2 MHz
frequewy + 2 MHz
linewidth c 0.2 MHz
D- lkl DQT
3397 1697
4.4 2.2
3397 1698
24.0 8.0
TQT
1133
1.6
1133
8.5
a) Full width at half masimum.
The results, while mimicking those already observed in homogeneously optical pumping
broadened transitions studied by methods 131, thus differ from the
latter in this important rc:pect. In order to test our prediciions ;dmewhat more carefully, we studied the DQT corresponding to the D + El transition in the quinoxaline-durene system. The triplet state of quinoxaline has resolvable hyperfine structure [ 171 in zero external field, and we expected that the hyperfke splittings would collapse, with increasing transition order, to the same degree as the component linewidths. This proved to be the case,
as shown in fig. 2. DQ’f’s and TQT’s can be obskved sufficiently easily,
Volume 17, numbcr 1
1 November
CHEMICAL PHYSICS LETTERS
1972
-rules that are inherently different from those governing the corresponding single-quantum transi. tions. In the case of the zero fiefd, msgneticalfy driven transitions discussed in the present note? the magnetic quad~poIe-like transition moment* of any DQT must lie in the plane perpendicular to the rnagnetic dipole transition moment of the SQT u:curring at twice the DQT’s frequency. This property may prove useful in studying the relative orientatiolls of triplet mofecules in monocrystalline samples. seIectisn
-I
(a) (b)
4-f-J
\ lb-
i\
‘-
r The non-vanishing Fig. 2. Opticaily detected d~ub~e~u3ntunI transition corresponding to the L) + I&l trnnsirion at 3641 MHz, in the quinoxaline-durenc system, at 4.2”K, using phase scnsitivc detection at a modulation frequency of 160 Hz. Spectrum (a) obtained with maximum Sain of the TWT ampfifier. The “forbidden” hypcrfine satellites are shown on each side of the major nlIowed component at 1820 hfHz. Spectrum (b) obtained
output
under
TWT amplifier
conditions
in which
the power
is insufficient to saturate the “forbidden” components. Its linewidth at half-height is 0.7 MHz.
in MODOR experiments employing high-level microthat they may sometimes be mistaken for artifacts or signals from impurities. Indeed, it was the ap pearance of such an “‘impurity” in our first cycloperttanone samples that Ied us to the present investigation. Evidently, not every anomalous sisal need be thus ctassified. At a gross level of description, saturation of a DQT or TQT may be considered to redistribute the populations of the states connected in just the same fashion as does saturation of an ordinary SQT. Thus, we have observed that the intensity of the weak cyclopcntanone MODOR signal at 5022 MHz can be enhanced by simultaneousty pumping the DQT at 1698 MHz with intense cw microwaves. The m~imum cnhancemcnt we obtained in this \vay was not greatly different from that which we observed when cw pumping the intense single-quantum transition [18,19] at 3397 hlilz. At a subtler IeveI, however, it is to be remarked that muitiple-quantum transitions must obey waves,
the operator
component
of the mnfrh
ciemrnt
of
g&.
References V. Hughes and L. Gracbner, Phys. Rev. 79 (1950) 314. P. Kusch, Phys. Rev. 93 (1954) 1022. A. Kosffer, I. Opt. Sot. Am. 47 (1957) 460. W. Kaiser and C.G. Garrett, Phys. Rev. Letters 7 (1961) 229. [Sl W. Anderson, Phys. Rev. 104 (1956) 850. 161 J.W. Orton. P. Auzins and J. Wrtz, Phys. Rev. Letters
fl f [2I j3{ [4]
4 (1960)
128.
[7] hf. Katayama, Phys. Rev. 126 (1962) 1440. [S] M.S. de Groot and J.H. vnn der Weals, Pflysica 26 (1963) II%. 191 R. Clements and hi. Slwnoff, Chem. Phps. J&ttcrs 7 (1970) 4. f1Ol H. Levanon and S.I. Weissman, 3. Am. Cltem. Sot. 93 (1971) 4309. 1111 A.L. Shain, W.T. Chinng and XI. Sharnoff, Chcm. Phys. Letters 16 (1972) 206. r121 Xl. Sharnoff, J. Chem. Phys. 46 (1967) 3263. 1131 H. Salwcn, Phys. Rev. 99 (1955) 1274. [I41 51. Hack, Pbys. Rev. 10-I (1956) 84. [I51 S. Yatsiv, Phys. Rev. 113 (1959) 1.522. 1161 A.L. Shain and hf. Sfwnoff, Chcm. Phys. Luttcrs 16 (1972) SO>. 1171 J. Schmidt and J.H. van dcr Waals, Chem. Phys. Letters 3 (1969) 546. 1181 T. Kuan, D.S. Tinti 2nd M.A. El-Swrd, Chem. Phys. Zetters 4 (1970) 507. [I91 I.Y. Chan and J. Schmidt, Symp. Faraday Sac. 3 (1969) 156.
97
1 November 1972
CHEMICAL PHYSICS LETTERS
OPTICALLY DETECTED MULTIPLE-QUANTUM TRANSITIONS IN PHOTOEXCITED MOLECULAR TRIPLET STATES IN ZERO EXTERNAL MAGNETIC FIELD * Albert Department
of Physics,
L. SHAIN and Mark SHARNOFF Universit>* of Dclaruarr,
Received
hlultiplequantum. micro\%zwdriven are observed and classified.
transitions
I9 71 I,
US/Z
22 June 1972
betwax
1. Introduction
~Vcwark. Delaware
zero-field
spin sublevels of a photoexcited
triplet state
photoescited triplet species in zero estcrr~al magtrefic We first observed such transitions during our early work on the cyclopentanone triplet [ 1 1j and, in seeking to understand their unusually narrow lines, have gone on to investigate them in several other systcms. We report results here for cyclopcntnnone and for quinoxaline.
jkid.
hialtiple-quantum transitions, arising from the simultarheous absorption of two or more quanta of electromagnetic radiation, were first observed over twenty years ago in a number of atomic and molecular kam electric resonance experiments [ 1,21, were subsequently found magnetically in optical pumping cxperiments 131,and have in recent years become commonplace in laser-induced multiphoton optical absorption [4] _ in conventional magnetic resonance esperiments carried out at high magnetic fields, double quantum transitions have been found in the NMR of liquids [ 51 and in the EPR of both transition metal complexes [6] and free radicals [7]. De Groot and van der Waals [8] reported a double-quantum transition in the EPR of the photoexcited triplet state of naphthalene, and Clements and Shamoff [9] have recently observed such a transition in the optically detected EPR of pyrazine. A double-quantum transition also appears to be responsible for the g= 2 resonance observed in the escitation-modulated experiments of Levanon and Weissman [ lo] . The purpose of this communication is to report the observation of magnetically-induced double- and trip!equantum transitions between the spin sublevels of * Research supported
by National Science Foundation Grant GF-295 19 and by US Army Research Office (Durham) Grant DA-ARO-D-31-124-71686.
2. Experimental The resonances are detected optically in the usual way. The experimental set-up is that described earlier [ 1 l] , supplemented by an Ej'HLabs Model 5 I 1 travelling wave tube (TWT) amplifier. The saturated output (1 to 1.5 W, depending upon frequency) of the TWT was transmitted via a calibrated vnriablc attenuator to the rigid coaxial line and slow-wave helix wound around the sample. The helix and sample were immersed in liquid helium. The transition frequencies were measured with a Hewlett-Packard Model 540.4 Transfer Oscillator and Model 524B Frequewy Counter. Single- (SQT), double- (DQT), and triple- (TQT) quantum transitions could be easily observed with the help of the TWT amplifier. We also attempted to observe the DQT and TQT by using the 20 mW output of our Polarad Model R Sweep Generator without amplification and found this power level generally insufficient to saturate the multiple-rluantum transitions.
95
Voiume
17, number
1
1 November
CHEMICAL PHYSICS LETTERS
1972
3. Results and discussion The signature of a multiple-quantum transition is !he dependence of its transition probability upon the intensity of the driving source. The transition probability for an SQT increases linearly, for a DQT increases with the square and for the TQT increases with the cube, of the driving intensity. In the present experiments the optical signals resuIt from partial saturation of microwave transitions (I?_] and, in the region of mild to moderate saturation, the logarithmic plot of signal amplitude versus microwave power would be expected to yield a straight line whose slope gives the order of the transition. This is clearly shown, in the case of cyclopcntanone X-traps, by the data of fig. 1. In the case of the ordinac4, or SQT transition, the region of moderate saturation appears at the extreme right ; as the microwave power level is raised further, the degree of saturation can no longer increase proportionally, and the plot curves over towards a horizontal asymptote. In the case of the DQT and TQT, the power available from our TWT is appnrentIy not sufficient to produce hard saturation, and the plots remain linez to the highest power Ievels. The very clear correlation of the slope, s, with the observed transition frequency, 3396 IMHz, is proof that the transitions arc not single-quantum transitions induced hy harmonics generated in the Polarad or TWT units, but are true multiple absorptions of quanta carried at the fundamental frequency. The secand interesting kature of our DQT and TQT signals is the diminution of linewidth with increasing order of the transition. A few years after the first observations of multipbe-quantum transitions, this narrowing was explained from theoretical considerations ( I3- 151 but these theories were concerned with transitions whose breadths were lifetime-limited (i.e., with komogcneously broadened lines). A simple extension of the theory to the case of inhomogeneously broadened lines can bc made and leads to ihe predictio n that, whatever the order of
the transition, the e value. v/Cv, observed in the limit of mild saturation will be independent of the order of the transition. This is seen from table I to be the case for our cyclopentanone SQT, DQT, and TQT. The 3397 MHz transition is known, from our studies [ 161 of transient response to pulsed microwave irradiation of cyclopentanone, to be inhomogeneously broadened. 96
ATTENUATION,db/lO
Fig. 1. Logarithmic
plot of relative signal amplitude wrsus microwave power for cyclopentanone X-traps af 42°K. The microwave power at 0 dB is different for each transition. The amplitude of each transition is normalized to its value at 0 dB attenuation. SQT (01, DQT (a), and TQT (0) represent the D-./El singlequantum, the double-quantum and the triplequantum transitions, respectively, and s measures the slopes of the linear portions of their power dependence.
Resonance
Table 1 frequencies and linewidths”) for cyclopentanone X-traps and cyclopcnt~none in /I-hexanc x-traps
ri-hexane
Transition frequency + 2 MHz
linewidth k 0.2 MHz
frequewy + 2 MHz
linewidth c 0.2 MHz
D- lkl DQT
3397 1697
4.4 2.2
3397 1698
24.0 8.0
TQT
1133
1.6
1133
8.5
a) Full width at half masimum.
The results, while mimicking those already observed in homogeneously optical pumping
broadened transitions studied by methods 131, thus differ from the
latter in this important rc:pect. In order to test our prediciions ;dmewhat more carefully, we studied the DQT corresponding to the D + El transition in the quinoxaline-durene system. The triplet state of quinoxaline has resolvable hyperfine structure [ 171 in zero external field, and we expected that the hyperfke splittings would collapse, with increasing transition order, to the same degree as the component linewidths. This proved to be the case,
as shown in fig. 2. DQ’f’s and TQT’s can be obskved sufficiently easily,
Volume 17, numbcr 1
1 November
CHEMICAL PHYSICS LETTERS
1972
-rules that are inherently different from those governing the corresponding single-quantum transi. tions. In the case of the zero fiefd, msgneticalfy driven transitions discussed in the present note? the magnetic quad~poIe-like transition moment* of any DQT must lie in the plane perpendicular to the rnagnetic dipole transition moment of the SQT u:curring at twice the DQT’s frequency. This property may prove useful in studying the relative orientatiolls of triplet mofecules in monocrystalline samples. seIectisn
-I
(a) (b)
4-f-J
\ lb-
i\
‘-
r The non-vanishing Fig. 2. Opticaily detected d~ub~e~u3ntunI transition corresponding to the L) + I&l trnnsirion at 3641 MHz, in the quinoxaline-durenc system, at 4.2”K, using phase scnsitivc detection at a modulation frequency of 160 Hz. Spectrum (a) obtained with maximum Sain of the TWT ampfifier. The “forbidden” hypcrfine satellites are shown on each side of the major nlIowed component at 1820 hfHz. Spectrum (b) obtained
output
under
TWT amplifier
conditions
in which
the power
is insufficient to saturate the “forbidden” components. Its linewidth at half-height is 0.7 MHz.
in MODOR experiments employing high-level microthat they may sometimes be mistaken for artifacts or signals from impurities. Indeed, it was the ap pearance of such an “‘impurity” in our first cycloperttanone samples that Ied us to the present investigation. Evidently, not every anomalous sisal need be thus ctassified. At a gross level of description, saturation of a DQT or TQT may be considered to redistribute the populations of the states connected in just the same fashion as does saturation of an ordinary SQT. Thus, we have observed that the intensity of the weak cyclopcntanone MODOR signal at 5022 MHz can be enhanced by simultaneousty pumping the DQT at 1698 MHz with intense cw microwaves. The m~imum cnhancemcnt we obtained in this \vay was not greatly different from that which we observed when cw pumping the intense single-quantum transition [18,19] at 3397 hlilz. At a subtler IeveI, however, it is to be remarked that muitiple-quantum transitions must obey waves,
the operator
component
of the mnfrh
ciemrnt
of
g&.
References V. Hughes and L. Gracbner, Phys. Rev. 79 (1950) 314. P. Kusch, Phys. Rev. 93 (1954) 1022. A. Kosffer, I. Opt. Sot. Am. 47 (1957) 460. W. Kaiser and C.G. Garrett, Phys. Rev. Letters 7 (1961) 229. [Sl W. Anderson, Phys. Rev. 104 (1956) 850. 161 J.W. Orton. P. Auzins and J. Wrtz, Phys. Rev. Letters
fl f [2I j3{ [4]
4 (1960)
128.
[7] hf. Katayama, Phys. Rev. 126 (1962) 1440. [S] M.S. de Groot and J.H. vnn der Weals, Pflysica 26 (1963) II%. 191 R. Clements and hi. Slwnoff, Chem. Phps. J&ttcrs 7 (1970) 4. f1Ol H. Levanon and S.I. Weissman, 3. Am. Cltem. Sot. 93 (1971) 4309. 1111 A.L. Shain, W.T. Chinng and XI. Sharnoff, Chcm. Phys. Letters 16 (1972) 206. r121 Xl. Sharnoff, J. Chem. Phys. 46 (1967) 3263. 1131 H. Salwcn, Phys. Rev. 99 (1955) 1274. [I41 51. Hack, Pbys. Rev. 10-I (1956) 84. [I51 S. Yatsiv, Phys. Rev. 113 (1959) 1.522. 1161 A.L. Shain and hf. Sfwnoff, Chcm. Phys. Luttcrs 16 (1972) SO>. 1171 J. Schmidt and J.H. van dcr Waals, Chem. Phys. Letters 3 (1969) 546. 1181 T. Kuan, D.S. Tinti 2nd M.A. El-Swrd, Chem. Phys. Zetters 4 (1970) 507. [I91 I.Y. Chan and J. Schmidt, Symp. Faraday Sac. 3 (1969) 156.
97