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Mechanism of photodissociation of polyatomic molecules through the polarized fluorescence of fragments
Journal
of
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 4081409 (1997) 569-572
Mechanism of photodissociation of polyatomic molecules through the polarized fluorescence of fragments A.P. Blokhin, Institute of Molecular
M.F. Gelin, S.A. Polubisok,
V.A. Tolkachev,
A.A. Blokhin
and Atomic Physics, Academy of Sciences of Belarus, Skaryna pr. 70, Minsk 220072. Belarus
Received 26 August 1996; accepted 6
September 1996
Abstract To describe the polarized fluorescence of polyatomic photoproducts, a new model, based on the assumption of free rotation of products after photofragmentation, is proposed and checked against preliminary experimental data. 0 1997 Elsevier Science B.V. Kqwords:
Photodissociation; Polyatomic molecules; Polarized fluorescence
1. Introduction Optical excitation depends upon the orientations of absorption dipole moments and creates anisotropy in the ensemble of parent molecules. This anisotropy is mediated by photodissociation and eventually maps into the ensemble of photoproducts. The incipient photoproducts ‘remember’ both the initial optical pumping and the photofragmentation dynamics. Observation of the polarized emission of the photoproducts allows one to obtain valuable information about the detailed mechanism of photofragmentation
[Il. To describe this process theoretically, a wide variety of different approaches has been suggested, extending from ab initio calculations to simple physical models. Photodissociation of triatomics is conventionally investigated within the framework of the so-called impulsive models [2-61. It is assumed that the diatomic fragment suffers instantaneous torque during the rupture of the chemical bonds, rotates in the plane of the parent molecule, and that the triatomic
angular momentum can be neglected as compared to the diatomic one. When both parent and product molecules are large polyatomic ones, the picture of photofragmentation is hardly consistent with the previous case. A polyatomic molecule can be roughly regarded as a reservoir of vibrations. The energy transmitted to a polyatomic fragment due to photodissociation is therefore more likely to be redistributed among its vibrations than to contribute to additional angular momentum. One can expect that the torques arising in the course of the cleavage of the chemical bonds play a relatively minor role because the molecules are massive particles. It is therefore reasonable to examine the opposite situation, where forces and torques due to the rupture of chemical bonds are small and photoproducts fly off almost freely. We have developed the corresponding free recoil model and employed it to calculate the photofragment fluorescence polarization [7-lo]. The assumptions of this model have been tested by observations of the polarized fluorescence of
0022-2860/97/S] 7.00 0 I997 Elsevier Science B.V. All rights reserved PII SOO22-2860(96)09524-5
570
A.P. Blokhin et ul./Joumal
of Molecular
fragments produced through photodissociation large aromatic molecules [7,8].
2. Dissociative
of
kernels
We consider the photofragmentation dynamics in the reaction A + hv - B + C under the following assumptions (see [2-6,8-lo] for the pertinent discussion): the process is governed by classical mechanics; molecules A, B, C are regarded as rigid tops; excited parent molecules fall apart instantaneously and have no time to rotate during photodissociation. In order to cast the assumptions into a suitable mathematical form, it is convenient to adopt a description of the photofragmentation dynamics in terms of dissociation kernels (see, e.g., [ 111). We restrict ourselves to studying rotational parent-product correlations. Let us introduce rotational phase space variables for parent molecules and fragments: angular momenta and Euler angles, ri =ij @ ni (i = A, B, C). The entire effect of the photodissociation will then be contained in the dissociation kernel T(IIa, I’c]I’J. This kernel is the conditional probability density that just after the photofragmentation the product i has phase space variables ri provided that the parent molecule A possesses rA just before the photofragmentation. Further, if one implies that the parent molecules are distributed according to p(rJ, then the probability density to find the fragments near the points I’a, I’c in the phase space is drB,
rC)=
drAm&,
Structure 4OW409 (1997)
569-572
to invoke the laws of conservation of angular momentum and energy. These laws enable one to determine uniquely the angular momentum and partitioning of energy [7]. After some mathematics [7], one can arrive at the free recoil result: 5, = G&,
(4)
in which the elements given by
of the matrix G are explicitly
Gab=Ia,a
a, b=x,
F&)/l&t,;
Y, Z.
(5)
Here Ia and I, are the angular momentum vectors in the main axes of inertia of the molecules B and A, are the corresponding moments of I,,, and IA,b inertia, Fab(E) is the rotation matrix from the frame of the main axes of inertia of B to that of A, and ,” are the pertinent Euler angles. Therefore, the product angular momentum ja is expressed linearly through IA. Starting from Eq. (3), that of the parent mOkC&? one can write: T(Ya IIA)=S(J’a - GYA)
(6)
By assuming an initial Boltzmann parent molecules P(jA)=(2rkT)-3’2
distribution
of the
(zA,x~A,v~A,~)-“2 exp( -J,2/2kT10] (7)
(repeated Latin indexes a, b, c,... are to be summed over x, y, z) and using definition (l), one finally obtains:
rCirA)drA)?
s
dra drcT(ra,
&]I?,)
= 1.
(1)
J
Let B be the photofragment of interest. Then all the pertinent information is contained in the reduced kernel
The photofragmentation process thus gives rise to a Gaussian but evidently non-Boltzmann distribution of products.
3. Polarized
T(rBlrA) = drcT(ru,
&@A).
s
The impulsive character allows one to write: T(ra ]r,) =&@a -nA)T(&
of photoproducts
The probability of absorption and/or emission light in the oscillator model is proportional to
of the photofragmentation I&,).
emission
(2)
(3)
By further assuming that the only origin of the product molecule rotation is that of the parent one, it is natural
Ui(Qi, t)-3(Zizi(t))2 x o~,(Q,,)o~,(ni(t))o,2,(n,).
=
l +2m
of
k_,
(9)
A.P.
Blokhin
ofMoleculrrr
rt ul.Nourd
Here D&(Q) is an element of the Wigner rotation matrix, Euler angles &, specify orientation of the light polarization vectors Zi in the laboratory frame, !J, are Euler angles of the transition dipole moments p, in the molecular frame, and angles Q,(r) determine the relative orientation of these vectors at the time t. When polyatomic fragments are in ground electronic states after photodissociation, an additional laser pulse at t,, is required to excite their fluorescence. Therefore the intensity of the polarized emission of these photoproducts is ~e,,-(~ah~(~A,tahs)~ex(~B,~ex)~rrn(~B~~ern)
x
wB
k&c&4.rR
(10)
Here the subscripts ‘abs’, ‘ex’ and ‘em’ denote, respectively, absorption of the dissociative quantum, subsequent excitation and emission. The averaging procedure in Eq. (10) naturally gives rise to the following expressions:
W ec,,, - 1+ 2/5(3(&h,e’,x)’
-
+2/5((3%hs&n)2
-
+2/~3(~~~~~2
Here
1 )cZ(i&hw
I)cZ(/%hs>
- 1) c2(iL,
+
8/35[3(3(~~,,,~~,,)(~~h~~~~)(~~~~~~)
-
(i?&,,)2
x
C.i(liahs,
CA%,,
-(igc,,)’
i&
ikx,
tt,
b)
and
rd>
&x
i&m
td,
fm
ii,,
-
fd)
-?d)
0, rcnl -I,,) -(zzihs&x)2
1) - I]
+
/%I,
&TX
rd,
r,,
-rd,
WL,
tern-r,,)
,G,,
iC
(l
TV,
f2,
l)
t3)
twofold and threefold orientational correlation functions. These functions are quite complicated and are explicitly determined in [9]. We assume that the first quantum is absorbed at fahr = 0 and dissociation takes place at time rd; this enables one to take into account the predissociation effect. By using Eq. (1 l), one can straightforwardly calculate the polarization degree of photoproduct emission are
~=(~,~~lI-~~~,,,~)l(~r,,,,ll+
WC&,.)
in the case of the standard orthogonal experiment.
geometry of the
4. Results and discussion We have developed
a
FORTRAN
program that allows
Structure
408/409
(1997)
569-572
571
one to calculate fluorescence anisotropy in the most general case of asymmetric top parent and product molecules and also for arbitrary time intervals tab,, td, t,, and r,,. Recently the program was modified to take into account the effect of dissociative torques. When the time-integrated polarized fluorescence is must be time averaged. The optically measured, WcJ,,,, induced anisotropy of transition dipoles under collision-free conditions settles down after a few oscillations to an asymptotic stationary value on the time scale of the molecular rotation period -fl, normally a few ps. This is a direct consequence of angular momentum conservation under free molecular rotation, and is well known from investigations of the time evolution of fluorescence anisotropy decay of isolated polyatomic molecules [ 12,131. In our case this decay occurs after absorption of two quanta, practically just at tab, and t,,. Since t,, - t;lh, and the contribution of the nont - t,x > m, sF:tionary part of the anisotropy is very small and can be neglected. For the same reason, the particular shape of the nanosecond laser pulses is of minor importance. Of course, the time interval f,, - td in Eq. (1 1) is unknown. However, it is also logical to assume that I,, - td >> fl on the time scale of the molecular rotation period. Therefore, the determination of the photoproduct polarization degree reduces to the calculation of asymptotic values of correlation functions in Eq. (11) [9]. The assumptions of the free recoil model have been tested by polarization experiments carried out in our laboratory. Polarized emission of polyatomic photoproducts was observed. The fragments were produced through the photodissociation of his@-aminophenyl) disulphide (a) and bis@-acetylaminophenyl)disulphide (b) into two equal parts. In case (a), theoretical (7.3%) and experimental (7.4%) values of the fluorescence polarization degree are in excellent agreement [7,8]. The preliminary experimental polarization degree for molecule (b) is 12%. The free recoil model predicts P = 8.9% (when ,iiahh is directed along the S-S bond, as is assumed in the case of reaction (a)) and P = 16% (when &,, lies along the axis of the smallest moment of inertia of the parent molecule). The angle between the S-S bond and the axis of the smallest moment of inertia is approximately 60”. Thus theory and experiment can be brought into coincidence by presuming that the
512
A.P. Blokhin et al./Journal
of Molecular
angle between the axis of the smallest moment of inertia and jiabs is about 40”. This assumption looks not unreasonable, but further experimental and theoretical investigations are certainly required.
References [I] P.L. Houston, .I. Phys. Chem., 91 (1987) 5388. [2] G.A. Chamberlain and J.P. Simons, J. Chem. Sot., Faraday Trans., 12 (1975) 2043. [3] M.T. Macpherson, J.P. Simons and R.N. Zare, Mol. Phys., 38 (1979)2049. [4] G.W. Loge and R.N. Zare, Mol. Phys., 43 (1981) 1419. [5] T. Nagata, T. Kondow, K. Kuchitsu, G.W. Loge and R.N. Zare, Mol. Phys., 50 (1983) 49.
Structure 408/409
(1997) 569-572
[6] T. Nagata, T. Kondow and R.N. Zare, Mol. Phys., 70 (1990) 1159. [7] V.A. Povedailo, A.P. Blokhin, M.F. Gelin and V.A. Tolkachev, Opt. i Spektr., 73 (1992) 547. [8] A.P. Blokhin and M.F. Gelin, Opt. i Spektr., 74 (1993) 279; ibid., 272. [9] A.P. Blokhin and M.F. Gelin, Opt. i Spektr.. 77 (1994) 41; ibid., 222. [lo] A.P. Blokhin and M.F. Gelin, Opt. i Spektr., 80 (1996) 228. [I I] A.F. Wagner and E.K. Parks, J. Chem. Phys., 65 (1976) 4343. [12] A.B. Myers, P.L. Holt, M.A. Pereira and R.M. Hochstrasser, Chem. Phys. Lett., 130 (1986) 265. [13] N.A. Borisevich, E.V. Khoroshilov, I.V. Kryukov, P.G. Kryukov, A.V. Sharkov, A.P. Blokhin and G.B. Tolstorozhev, Chem. Phys. Lett., 191 (1992) 225.
of
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 4081409 (1997) 569-572
Mechanism of photodissociation of polyatomic molecules through the polarized fluorescence of fragments A.P. Blokhin, Institute of Molecular
M.F. Gelin, S.A. Polubisok,
V.A. Tolkachev,
A.A. Blokhin
and Atomic Physics, Academy of Sciences of Belarus, Skaryna pr. 70, Minsk 220072. Belarus
Received 26 August 1996; accepted 6
September 1996
Abstract To describe the polarized fluorescence of polyatomic photoproducts, a new model, based on the assumption of free rotation of products after photofragmentation, is proposed and checked against preliminary experimental data. 0 1997 Elsevier Science B.V. Kqwords:
Photodissociation; Polyatomic molecules; Polarized fluorescence
1. Introduction Optical excitation depends upon the orientations of absorption dipole moments and creates anisotropy in the ensemble of parent molecules. This anisotropy is mediated by photodissociation and eventually maps into the ensemble of photoproducts. The incipient photoproducts ‘remember’ both the initial optical pumping and the photofragmentation dynamics. Observation of the polarized emission of the photoproducts allows one to obtain valuable information about the detailed mechanism of photofragmentation
[Il. To describe this process theoretically, a wide variety of different approaches has been suggested, extending from ab initio calculations to simple physical models. Photodissociation of triatomics is conventionally investigated within the framework of the so-called impulsive models [2-61. It is assumed that the diatomic fragment suffers instantaneous torque during the rupture of the chemical bonds, rotates in the plane of the parent molecule, and that the triatomic
angular momentum can be neglected as compared to the diatomic one. When both parent and product molecules are large polyatomic ones, the picture of photofragmentation is hardly consistent with the previous case. A polyatomic molecule can be roughly regarded as a reservoir of vibrations. The energy transmitted to a polyatomic fragment due to photodissociation is therefore more likely to be redistributed among its vibrations than to contribute to additional angular momentum. One can expect that the torques arising in the course of the cleavage of the chemical bonds play a relatively minor role because the molecules are massive particles. It is therefore reasonable to examine the opposite situation, where forces and torques due to the rupture of chemical bonds are small and photoproducts fly off almost freely. We have developed the corresponding free recoil model and employed it to calculate the photofragment fluorescence polarization [7-lo]. The assumptions of this model have been tested by observations of the polarized fluorescence of
0022-2860/97/S] 7.00 0 I997 Elsevier Science B.V. All rights reserved PII SOO22-2860(96)09524-5
570
A.P. Blokhin et ul./Joumal
of Molecular
fragments produced through photodissociation large aromatic molecules [7,8].
2. Dissociative
of
kernels
We consider the photofragmentation dynamics in the reaction A + hv - B + C under the following assumptions (see [2-6,8-lo] for the pertinent discussion): the process is governed by classical mechanics; molecules A, B, C are regarded as rigid tops; excited parent molecules fall apart instantaneously and have no time to rotate during photodissociation. In order to cast the assumptions into a suitable mathematical form, it is convenient to adopt a description of the photofragmentation dynamics in terms of dissociation kernels (see, e.g., [ 111). We restrict ourselves to studying rotational parent-product correlations. Let us introduce rotational phase space variables for parent molecules and fragments: angular momenta and Euler angles, ri =ij @ ni (i = A, B, C). The entire effect of the photodissociation will then be contained in the dissociation kernel T(IIa, I’c]I’J. This kernel is the conditional probability density that just after the photofragmentation the product i has phase space variables ri provided that the parent molecule A possesses rA just before the photofragmentation. Further, if one implies that the parent molecules are distributed according to p(rJ, then the probability density to find the fragments near the points I’a, I’c in the phase space is drB,
rC)=
drAm&,
Structure 4OW409 (1997)
569-572
to invoke the laws of conservation of angular momentum and energy. These laws enable one to determine uniquely the angular momentum and partitioning of energy [7]. After some mathematics [7], one can arrive at the free recoil result: 5, = G&,
(4)
in which the elements given by
of the matrix G are explicitly
Gab=Ia,a
a, b=x,
F&)/l&t,;
Y, Z.
(5)
Here Ia and I, are the angular momentum vectors in the main axes of inertia of the molecules B and A, are the corresponding moments of I,,, and IA,b inertia, Fab(E) is the rotation matrix from the frame of the main axes of inertia of B to that of A, and ,” are the pertinent Euler angles. Therefore, the product angular momentum ja is expressed linearly through IA. Starting from Eq. (3), that of the parent mOkC&? one can write: T(Ya IIA)=S(J’a - GYA)
(6)
By assuming an initial Boltzmann parent molecules P(jA)=(2rkT)-3’2
distribution
of the
(zA,x~A,v~A,~)-“2 exp( -J,2/2kT10] (7)
(repeated Latin indexes a, b, c,... are to be summed over x, y, z) and using definition (l), one finally obtains:
rCirA)drA)?
s
dra drcT(ra,
&]I?,)
= 1.
(1)
J
Let B be the photofragment of interest. Then all the pertinent information is contained in the reduced kernel
The photofragmentation process thus gives rise to a Gaussian but evidently non-Boltzmann distribution of products.
3. Polarized
T(rBlrA) = drcT(ru,
&@A).
s
The impulsive character allows one to write: T(ra ]r,) =&@a -nA)T(&
of photoproducts
The probability of absorption and/or emission light in the oscillator model is proportional to
of the photofragmentation I&,).
emission
(2)
(3)
By further assuming that the only origin of the product molecule rotation is that of the parent one, it is natural
Ui(Qi, t)-3(Zizi(t))2 x o~,(Q,,)o~,(ni(t))o,2,(n,).
=
l +2m
of
k_,
(9)
A.P.
Blokhin
ofMoleculrrr
rt ul.Nourd
Here D&(Q) is an element of the Wigner rotation matrix, Euler angles &, specify orientation of the light polarization vectors Zi in the laboratory frame, !J, are Euler angles of the transition dipole moments p, in the molecular frame, and angles Q,(r) determine the relative orientation of these vectors at the time t. When polyatomic fragments are in ground electronic states after photodissociation, an additional laser pulse at t,, is required to excite their fluorescence. Therefore the intensity of the polarized emission of these photoproducts is ~e,,-(~ah~(~A,tahs)~ex(~B,~ex)~rrn(~B~~ern)
x
wB
k&c&4.rR
(10)
Here the subscripts ‘abs’, ‘ex’ and ‘em’ denote, respectively, absorption of the dissociative quantum, subsequent excitation and emission. The averaging procedure in Eq. (10) naturally gives rise to the following expressions:
W ec,,, - 1+ 2/5(3(&h,e’,x)’
-
+2/5((3%hs&n)2
-
+2/~3(~~~~~2
Here
1 )cZ(i&hw
I)cZ(/%hs>
- 1) c2(iL,
+
8/35[3(3(~~,,,~~,,)(~~h~~~~)(~~~~~~)
-
(i?&,,)2
x
C.i(liahs,
CA%,,
-(igc,,)’
i&
ikx,
tt,
b)
and
rd>
&x
i&m
td,
fm
ii,,
-
fd)
-?d)
0, rcnl -I,,) -(zzihs&x)2
1) - I]
+
/%I,
&TX
rd,
r,,
-rd,
WL,
tern-r,,)
,G,,
iC
(l
TV,
f2,
l)
t3)
twofold and threefold orientational correlation functions. These functions are quite complicated and are explicitly determined in [9]. We assume that the first quantum is absorbed at fahr = 0 and dissociation takes place at time rd; this enables one to take into account the predissociation effect. By using Eq. (1 l), one can straightforwardly calculate the polarization degree of photoproduct emission are
~=(~,~~lI-~~~,,,~)l(~r,,,,ll+
WC&,.)
in the case of the standard orthogonal experiment.
geometry of the
4. Results and discussion We have developed
a
FORTRAN
program that allows
Structure
408/409
(1997)
569-572
571
one to calculate fluorescence anisotropy in the most general case of asymmetric top parent and product molecules and also for arbitrary time intervals tab,, td, t,, and r,,. Recently the program was modified to take into account the effect of dissociative torques. When the time-integrated polarized fluorescence is must be time averaged. The optically measured, WcJ,,,, induced anisotropy of transition dipoles under collision-free conditions settles down after a few oscillations to an asymptotic stationary value on the time scale of the molecular rotation period -fl, normally a few ps. This is a direct consequence of angular momentum conservation under free molecular rotation, and is well known from investigations of the time evolution of fluorescence anisotropy decay of isolated polyatomic molecules [ 12,131. In our case this decay occurs after absorption of two quanta, practically just at tab, and t,,. Since t,, - t;lh, and the contribution of the nont - t,x > m, sF:tionary part of the anisotropy is very small and can be neglected. For the same reason, the particular shape of the nanosecond laser pulses is of minor importance. Of course, the time interval f,, - td in Eq. (1 1) is unknown. However, it is also logical to assume that I,, - td >> fl on the time scale of the molecular rotation period. Therefore, the determination of the photoproduct polarization degree reduces to the calculation of asymptotic values of correlation functions in Eq. (11) [9]. The assumptions of the free recoil model have been tested by polarization experiments carried out in our laboratory. Polarized emission of polyatomic photoproducts was observed. The fragments were produced through the photodissociation of his@-aminophenyl) disulphide (a) and bis@-acetylaminophenyl)disulphide (b) into two equal parts. In case (a), theoretical (7.3%) and experimental (7.4%) values of the fluorescence polarization degree are in excellent agreement [7,8]. The preliminary experimental polarization degree for molecule (b) is 12%. The free recoil model predicts P = 8.9% (when ,iiahh is directed along the S-S bond, as is assumed in the case of reaction (a)) and P = 16% (when &,, lies along the axis of the smallest moment of inertia of the parent molecule). The angle between the S-S bond and the axis of the smallest moment of inertia is approximately 60”. Thus theory and experiment can be brought into coincidence by presuming that the
512
A.P. Blokhin et al./Journal
of Molecular
angle between the axis of the smallest moment of inertia and jiabs is about 40”. This assumption looks not unreasonable, but further experimental and theoretical investigations are certainly required.
References [I] P.L. Houston, .I. Phys. Chem., 91 (1987) 5388. [2] G.A. Chamberlain and J.P. Simons, J. Chem. Sot., Faraday Trans., 12 (1975) 2043. [3] M.T. Macpherson, J.P. Simons and R.N. Zare, Mol. Phys., 38 (1979)2049. [4] G.W. Loge and R.N. Zare, Mol. Phys., 43 (1981) 1419. [5] T. Nagata, T. Kondow, K. Kuchitsu, G.W. Loge and R.N. Zare, Mol. Phys., 50 (1983) 49.
Structure 408/409
(1997) 569-572
[6] T. Nagata, T. Kondow and R.N. Zare, Mol. Phys., 70 (1990) 1159. [7] V.A. Povedailo, A.P. Blokhin, M.F. Gelin and V.A. Tolkachev, Opt. i Spektr., 73 (1992) 547. [8] A.P. Blokhin and M.F. Gelin, Opt. i Spektr., 74 (1993) 279; ibid., 272. [9] A.P. Blokhin and M.F. Gelin, Opt. i Spektr.. 77 (1994) 41; ibid., 222. [lo] A.P. Blokhin and M.F. Gelin, Opt. i Spektr., 80 (1996) 228. [I I] A.F. Wagner and E.K. Parks, J. Chem. Phys., 65 (1976) 4343. [12] A.B. Myers, P.L. Holt, M.A. Pereira and R.M. Hochstrasser, Chem. Phys. Lett., 130 (1986) 265. [13] N.A. Borisevich, E.V. Khoroshilov, I.V. Kryukov, P.G. Kryukov, A.V. Sharkov, A.P. Blokhin and G.B. Tolstorozhev, Chem. Phys. Lett., 191 (1992) 225.