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On the theory of band shapes of circular dichroism and circular polarization of luminescence spectra for weakly asymmetric molecules
Volume
22, number
CHEMICAL
2
ON THE THEORY AND CIRCULAR
PHYSICS
OF BAND SHAPES OF CIRCULAR POLARlZATION
FOR WEAKLY
1 October
1973
DICHROISM
OF LUMINESCENCE
ASYMMETRIC
M.D. FRANK-KAMENETSKII Department
LETTERS
SPECTRA
MOLECULES
and A.V. LUKASHIN
of Biology, Institute of Atomic Energy, Moscow, USSR
Revised
Received 25 February manuscript received
1973 5 July 1973
The intensity distribution iv vibronic spectra of circular dichroism and circular polarization of luminescence is calculated within the framewotk of the adiabatic approximation. In both cases the spectra are characterized by three terms. Two of them lead to band shapes quite similar to the band shapes of absorption (luminescence) while the third defines quite different intensity distributions. The third term gives rather different contributions to absorption and luminescence, which leads to a breakdown of the mirror symmetry of the absorption and luminescence spectra.
In the last years a number of investigations of fine structure of circular dichroism (CD) spectra have appeared. It has become clear that in some cases the shape of the CD spectrum for isolated electronic bands can essentially differ from the absorption band shape due to electronic-vibrational interaction effects. Moffitt and Moskowitz [I] were the first to poit out this fact. More recently this question was considered theoretically by Weigang [2], Caldwell [3], Lin [4], and experimentally in refs. [5-71. We have subjected this question to detailed theoretical analysis in our previous paper [8] for the case of a weakly asymmetric molecule in the framework of the strong adiabatic approximation. The symmetry properties of a symmetric molecule located in a weak asymmetric field have been taken into account. It has been shown ‘that in this case band shapes of the CD spectrum for an isolated electronic band are described by the following expression: ~Q;‘Ba+~Caya
a
a
c
i
Here R(o) is the rotatory
qvl->
.
power which is connected
with the transition between two electronic states (alO is the frequency of the pure electronic transition). Summation over u means the summation over all normal modes which are asymmetric with respect to inversion and reflection in a plane. Q(O) is the displacement of the equilibrium position of the nuclei along a given normal coordinate in the ground electronic state under the action of the asymmetric field. yi = AQi(Mini/2A)l12, w h ere Mi and Ri are the mass and frequency for a given mode i, and AQi is the change in equilibrium position, which takes place due to the electronic excitation. WV represents the normalized transition probability between two electronic states where the combination of vibrational quantum numbers takes on the values V = {vl, v2,..., Vi,... }.So W,~(O- ~10 --Ci RiVi) represents the shape of the absorption band conjugated with the CD band under consideration (for details see ref. [8]). The expressions for A, B, and C, in terms of the matrix elements of magnetic and electric dipole moments are given in ref. [8]. The three terms in brackets in formula (1) correspond to three sources of asymmetry arising from the action of an external field. The first one corresponds to asymmetry of electronic motion and coincides with a well known expression for induced optical activity
Volume
22, number
2
CHEMICAL
PHYSICS
Condon et al. [9]. The second term corresponds to asymmetric configuration of nuclei in the ground electronic state and the third one corresponds to the different asymmetry of the configuration of the nuclei in the ground and excited electronic states. The first and the second terms in expression (1) give band shapes much like the band shape of ordinary absorption, but the third term gives a different fine structure in the CD spectrum. After some value of v~, the expression for the rotatory power originating from this term changes its sign. The summation over all v, (throughout the entire band) of this term gives zero. It must be emphasized that the estimations carried out in ref. [8] show that all three terms have the same order of magnitude and there are no reasons to suppose noticeable difference in their values in general. The third term can lead to essential distortion of the CD spectrum up to the change of sign inside the isolated electronic band. In spite of the fact that our basic qualitative conclusion is similar to Weigang’s [2], there,are some important differences in the obtained results (see for details ref. [S]). In the last years, the first experimental investigation of circular polarization of luminescence for chiral molecules was begun [lo]. Performing calculations quite similar to those of ref. [8], the circular polarization of the luminescence spectrum can be shown to be described by the following equation: obtained
by
LETTERS
A’+zB’Qil’)a [
cC;ya a
References [I] W. Moffitt and A. Moskowitz, [ 21 [ 31 [4] [5]
[7] [S]
,
(2) [9]
where Q(‘).is the displacement of the nuclear equilibrium positions along a given normal coordinate in the excited electronic state under the action of the ex-
292
1973
ternal asymmetric field. The values of A’, Bi and Ci differ from A, Ba and C, by indexes transposition for magnetic and electronic matrix elements. Expression (2) differs essentially from eq. (1) due to the change in sign of the third term. This may lead to a breakdown of the mirror symmetry for the circular dichroism spectrum and circular polarization of the luminescence spectrum while the ordinary absorption and luminescence spectra for the same molecule may possess the mirror symmetry. The mirror symmetry can take place only if Cl, = C, = 0 for all u. Unfortunately, so far there are no unambiguous experimental pieces of evidence of the theoretically predicted difference between CD and absorption spectra. The interpretation of experimental data is difficult due to the presence in solution of different conformers of a given molecule in most cases. We hope that parallel study of CD spectra and circular polarization of luminescence spectra and their analysis with the aid of expressions (1) and (2) will help to clarify this problem.
[6]
R’(w)=
1 October
[lo]
J. Chem. Phys. 30 (1959) 648. O.E. Weigang, J. Chrm. Phys. 43 (1965) 3609. D.J. Caldwell, J. Chem. Phys. 51 (1969) 984. S.H. Lin, J. Chem. Phys. 55 (1971) 3546. E.H. Strickland, J. Horwitz and C. Billups, Biochemistry 8 (1969) 3205. J. Horwitz, E.H. Strickland and C. Billups, J. Am. Chem. Sot. 92 (1970) 2119. R.T. Klingbiel and H. Eyring, J. Phys. Chem. 74 (1970) 4543. M.D.. Frank-Kamenetskii and A.V. Lukashin, Opt. i Spektroskopiya 30 (1971) 1092 (in Russian). E.U. Condon, W. Altar and H. Eyring, J. Chem. Phys. 5 (1937) 753. C.A. Emeis and L.J. Oosterhoff, Chem. Phys. Letters 1 (1967) 129.
22, number
CHEMICAL
2
ON THE THEORY AND CIRCULAR
PHYSICS
OF BAND SHAPES OF CIRCULAR POLARlZATION
FOR WEAKLY
1 October
1973
DICHROISM
OF LUMINESCENCE
ASYMMETRIC
M.D. FRANK-KAMENETSKII Department
LETTERS
SPECTRA
MOLECULES
and A.V. LUKASHIN
of Biology, Institute of Atomic Energy, Moscow, USSR
Revised
Received 25 February manuscript received
1973 5 July 1973
The intensity distribution iv vibronic spectra of circular dichroism and circular polarization of luminescence is calculated within the framewotk of the adiabatic approximation. In both cases the spectra are characterized by three terms. Two of them lead to band shapes quite similar to the band shapes of absorption (luminescence) while the third defines quite different intensity distributions. The third term gives rather different contributions to absorption and luminescence, which leads to a breakdown of the mirror symmetry of the absorption and luminescence spectra.
In the last years a number of investigations of fine structure of circular dichroism (CD) spectra have appeared. It has become clear that in some cases the shape of the CD spectrum for isolated electronic bands can essentially differ from the absorption band shape due to electronic-vibrational interaction effects. Moffitt and Moskowitz [I] were the first to poit out this fact. More recently this question was considered theoretically by Weigang [2], Caldwell [3], Lin [4], and experimentally in refs. [5-71. We have subjected this question to detailed theoretical analysis in our previous paper [8] for the case of a weakly asymmetric molecule in the framework of the strong adiabatic approximation. The symmetry properties of a symmetric molecule located in a weak asymmetric field have been taken into account. It has been shown ‘that in this case band shapes of the CD spectrum for an isolated electronic band are described by the following expression: ~Q;‘Ba+~Caya
a
a
c
i
Here R(o) is the rotatory
qvl->
.
power which is connected
with the transition between two electronic states (alO is the frequency of the pure electronic transition). Summation over u means the summation over all normal modes which are asymmetric with respect to inversion and reflection in a plane. Q(O) is the displacement of the equilibrium position of the nuclei along a given normal coordinate in the ground electronic state under the action of the asymmetric field. yi = AQi(Mini/2A)l12, w h ere Mi and Ri are the mass and frequency for a given mode i, and AQi is the change in equilibrium position, which takes place due to the electronic excitation. WV represents the normalized transition probability between two electronic states where the combination of vibrational quantum numbers takes on the values V = {vl, v2,..., Vi,... }.So W,~(O- ~10 --Ci RiVi) represents the shape of the absorption band conjugated with the CD band under consideration (for details see ref. [8]). The expressions for A, B, and C, in terms of the matrix elements of magnetic and electric dipole moments are given in ref. [8]. The three terms in brackets in formula (1) correspond to three sources of asymmetry arising from the action of an external field. The first one corresponds to asymmetry of electronic motion and coincides with a well known expression for induced optical activity
Volume
22, number
2
CHEMICAL
PHYSICS
Condon et al. [9]. The second term corresponds to asymmetric configuration of nuclei in the ground electronic state and the third one corresponds to the different asymmetry of the configuration of the nuclei in the ground and excited electronic states. The first and the second terms in expression (1) give band shapes much like the band shape of ordinary absorption, but the third term gives a different fine structure in the CD spectrum. After some value of v~, the expression for the rotatory power originating from this term changes its sign. The summation over all v, (throughout the entire band) of this term gives zero. It must be emphasized that the estimations carried out in ref. [8] show that all three terms have the same order of magnitude and there are no reasons to suppose noticeable difference in their values in general. The third term can lead to essential distortion of the CD spectrum up to the change of sign inside the isolated electronic band. In spite of the fact that our basic qualitative conclusion is similar to Weigang’s [2], there,are some important differences in the obtained results (see for details ref. [S]). In the last years, the first experimental investigation of circular polarization of luminescence for chiral molecules was begun [lo]. Performing calculations quite similar to those of ref. [8], the circular polarization of the luminescence spectrum can be shown to be described by the following equation: obtained
by
LETTERS
A’+zB’Qil’)a [
cC;ya a
References [I] W. Moffitt and A. Moskowitz, [ 21 [ 31 [4] [5]
[7] [S]
,
(2) [9]
where Q(‘).is the displacement of the nuclear equilibrium positions along a given normal coordinate in the excited electronic state under the action of the ex-
292
1973
ternal asymmetric field. The values of A’, Bi and Ci differ from A, Ba and C, by indexes transposition for magnetic and electronic matrix elements. Expression (2) differs essentially from eq. (1) due to the change in sign of the third term. This may lead to a breakdown of the mirror symmetry for the circular dichroism spectrum and circular polarization of the luminescence spectrum while the ordinary absorption and luminescence spectra for the same molecule may possess the mirror symmetry. The mirror symmetry can take place only if Cl, = C, = 0 for all u. Unfortunately, so far there are no unambiguous experimental pieces of evidence of the theoretically predicted difference between CD and absorption spectra. The interpretation of experimental data is difficult due to the presence in solution of different conformers of a given molecule in most cases. We hope that parallel study of CD spectra and circular polarization of luminescence spectra and their analysis with the aid of expressions (1) and (2) will help to clarify this problem.
[6]
R’(w)=
1 October
[lo]
J. Chem. Phys. 30 (1959) 648. O.E. Weigang, J. Chrm. Phys. 43 (1965) 3609. D.J. Caldwell, J. Chem. Phys. 51 (1969) 984. S.H. Lin, J. Chem. Phys. 55 (1971) 3546. E.H. Strickland, J. Horwitz and C. Billups, Biochemistry 8 (1969) 3205. J. Horwitz, E.H. Strickland and C. Billups, J. Am. Chem. Sot. 92 (1970) 2119. R.T. Klingbiel and H. Eyring, J. Phys. Chem. 74 (1970) 4543. M.D.. Frank-Kamenetskii and A.V. Lukashin, Opt. i Spektroskopiya 30 (1971) 1092 (in Russian). E.U. Condon, W. Altar and H. Eyring, J. Chem. Phys. 5 (1937) 753. C.A. Emeis and L.J. Oosterhoff, Chem. Phys. Letters 1 (1967) 129.