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8.1 Introduction

- Linear magneto-optical phenomena, such as the Faraday effect, have been connected with antisymmetric matter tensors for a long time.
- There were only a few examples of the scattering of light through antisymmetric tensors that were of interest.

- Spiro and Strekas found that antisymmetric scattering dominated the resonance Raman spectrum of many metalloporphyrins.
- Antisymmetric scattering has been observed in a number of oddelectron transition metal complexes.

- The strontium didped into the yttrium aluminium garnet.
- There are many other examples of antisymmetric scattering.

- When an achiral sample is placed in a magnetic field parallel to the incident light beam, there may be a small difference in the scattered intensity of the incident light.
- The antiparallel arrangement reverses the signs of these observables.
- Section 3.5.5 shows that the magnetic Rayleigh and Raman optical activity begins in cross terms between the polarizability, or transition polarizability, and the same tensor perturbed to first order in the static magnetic field.
- The two topics are discussed together in this chapter since antisymmetric scattering is important in magnetic and Raman optical activity.
- We will see that magnetic Rayleigh and Raman optical activity can provide a sensitive test for antisymmetric scattering, as well as being used to determine electronic ground-state zeman splittings and how these change when a molecule is in an excited state.
- The phenomenon of magnetic resonance Raman optical activity was first observed in the 1970s and was explored in a number of systems in the early 1980s.
- The subject has been stagnant since reports of magnetic Raman optical activity in antiferromagnetic crystals of FeF2 were reported.
- Many novel applications to studies of metal complexes, biological molecules and magnetic solids may be contemplated, if the account in this chapter reignites interest in magnetic Raman optical activity.

- Section 2.8.1 shows the symmetry of the Hamiltonian with respect to time reversal.

- Ground-state degeneracy is required for scattering from systems in their ground states.
- This can be electron spin degeneracy or orbital degeneracy, separately or together.
- If the Coriolis force acting on the electrons is taken into account, antisymmetric scattering can be generated by the degeneracy of the rotational states of a molecule in a nondegenerate electronic state.
- Antisymmetric Rayleigh scattering can only be generated from excited vibrational states.

- It is not necessary for modes that do not span an antisymmetric irreducible representation to have electronic degeneracy in their initial state.

- The problem is that the complex operator determining the spatial symmetry aspects of any antisymmetric scattering is anti-Hermitian and time odd.

- This was added to the case of resonance scattering.
- In the present chapter, we use a lot of these relations.

- When a molecule is in a degenerate electronic state, time reversal and spatial symmetry arguments are combined in the generalized matrix element selection rule to elaborate the possibilities for antisymmetric scattering.

- The double group refers to the irreducible representations for odd-electron systems.

- If the zeroth-order Herzberg-Teller approximation is not invoked, there are other possibilities for which explicit mechanisms can be developed.

- Gener alized symmetry selection rules are superfluous because electronic degeneracy is no longer required.
- The generalized symmetry selection rules can only be valid in the absence of external magnetic fields.

- This can be understood by using the Plazcek approximation, which is valid for scattering at transparent wavelengths.
- The antisymmetric scattering is expected to be weak.

- refrin gent scattering phenomena can't be contributed to by the antisymmetric tensors discussed in this chapter.
- The sum of all the scattering transitions between the components of the Kramers degenerate set of states is zero.
- An external influence is needed to lift the degeneracy.
- Without external fields, antisymmetric Rayleigh and Raman scattering is possible.

- When the incident Frequency is in the vicinity of an electronic absorption Frequency of the atom or molecule, both antisymmetric scattering and magnetic Rayleigh and Raman optical activity can be observed.
- The resonance enhancement can be shown by the scattered intensities.
- We need to cast the transition tensors into a form that can be used for resonance scattering.

- Placzek's polarizability theory considers the dependence of the ground state electronic polarizability on the normal coordinates of vibration, and vibronic theories take detailed account of thecoupling It depends on a formal sum over all excited states and so is not applicable to the resonance situation.
- The Herzberg-Teller approximation provides a framework for a discussion of the symmetry aspects of resonance Raman scattering, but it is not a quantitative theory.

- The method for perturbed polar izabilities to the transition polarizabilities perturbed to first order is given in Section 2.7.
- If the excited electronic states are nondegenerate, this is satisfactory.

- The degenerate case will not be developed explicitly here because we are concerned with the symmetry aspects of the problem, and it turns out that the correct relative values of the transition components can be obtained from an essentially 'nondegenerate' development.

- The tran sition polarizabilities have explicit symmetric and antisymmetric parts.

- The upper and lower superscripts belong to the upper and lower signs.
- The term "terms" was introduced by Albrecht.

- tensors do not contribute to Rayleigh scattering.
- The real symmetric parts of the real tensors survive in nondegenerate systems if the initial and final electronic states are not degenerated.

- There are two conditions for resonance enhancement.

- A different formalism is required for quantitative considerations, but apart from the additional restrictions imposed by the generalized selection rule, the symmetry aspects are the same.

- It is possible to describe Rayleigh scattering, both transparent and resonance, and resonance Raman scattering in totally symmetric modes of vibration with the use of -tensors.

- These expressions are now applied to some simple examples in which the incident Frequency coincides with a transition Frequency to an excited spin-orbit state that is well resolved from other spin-orbit states.
- If the spin-orbit states are not resolved, a treatment similar to that used in the Faraday effect can be applied, with the spin-orbit interaction replacing the magnetic field.
- The terms are obtained.
- The details of the spin-orbit mechanism are referred to by Norby Svendsen.

- Although antisymmetric Rayleigh scattering is very small away from resonance because of contributions with opposite signs from other electronic transitions, it is finite and only tends to zero at very high and very low frequencies.
- On the other hand, antisymmetric Raman scattering in totally symmetric modes of vibration decreases more rapidly away from an excitation band envelope because of cancellation from other electronic transitions and the fact that the space of the wavefunctions associated with the excited electronic state can be invoked.

- The simplest case of an antisymmetric tensor can be found in atomic sodium vapour.
- The essential features of this case were discussed by Placzek.
- The antisymmetric scattering is generated at resonance with one or other of the components of the yellow doublet through both diagonal and off-diagonal transitions.

- The matrix elements of the cartesian components of the electric dipole moment operator between the atomic states are worked out using the results.

- The electric dipole is allowed in the transitions shown.

- The function shows two peaks if the transitions are well resolved.

- The scattered intensity is provided by the antisymmetric tensors.

- For simplicity, we will give just the values for exact resonance with one or other of the components of the doublet.

- The two resonances can be compared directly with the same factors.

- The description of iridium is similar to that of Fe(CN)3.

- The spin-orbit splitting is large and must be included explicitly.

- The calculation of the transition polarizability components proceeds along sim ilar lines to the Na case, but now we use the results from Harnung's version of the Wigner-Eckart theorem for the finite molecular double groups.

- There are two functions of the detailed orbital configurations generating the states.

- We refer to Hamaguchi, Stein, Brown and Spiro for alternative methods of calculation.

- vibroniccoupling is required for both resonance and nonresonance Raman scattering.

- In the two cases of nondegenerate initial states, the application of the antisymmetric tensors is different.

- If the initial electronic state is nondegenerate, the symmetry species of the mode of vibration must be the same as the antisymmetric component.
- These expressions are now applied to the scattering of nondegenerate ground electronic states in porphyrins, which have an even number of electrons.
- We refer to Hamaguchi (1977) for a detailed application to iridium (IV) hexahalides because the application to non totally symmetric modes in molecules with degenerate ground electronic states is too complicated to show here.

- There are examples of antisymmetric resonance Raman scattering through vibronic coupling provided by porphyrins.
- The electronic states and transitions responsible for the visible and near ultraviolet absorptions are described in Section 6.3.1.

- It can now be seen that a fundamental criterion for antisymmetric scattering is that the 0-1 and0-0 vibronic transitions are well resolved.

- There is no requirement for degeneracy in any of the molecular states in order to be nonzero.
- The general review of interference effects in resonance Raman scattering was given by Mortensen and Hassing.

- In a similar fashion, 2 modes can be calculated.

- Since the molecule has an even number of electrons and no magnetic field, we have taken a real representation of the wavefunctions.

- Section 8.5.4 of magnetic resonance Raman optical activity in porphyrins is calculated using this.

- The degeneracy is lifted in the presence of a magnetic field.

- The two vibrations are sum marized.

- Although these do not generate antisymmetric scattering, they are required for magnetic resonance Raman optical activity calculations.
- The dominant contribution is made by thetensors in.
- The relative values are found using both real and complex basis sets.

- L is given at transparent frequencies.
- Circular intensity difference components can be deduced from the parameters.

- For off-diagonal scattering transitions, it is best to work directly from (8.6.1).
- Magnetic Rayleigh and Raman optical activity in off-diagonal scattering transitions can be used to probe the ground state Zeeman splitting.

- Magnetic optical activity has not yet been observed in transparent Raman scattering.
- Magnetic fields don't have a big effect on the vibrational states.
- Magnetic circular dichroism is caused by the weaker direct effects of magnetic fields.

- We can apply the tensor components calculated explicitly in Section 8.4.2 if we use the resonance raytracing example.
- For the circular intensity differences associated with 90* scattering transitions between pure magnetic quantum states, the tensor components are replaced directly into.

- The magnetic optical activity effects can be understood from simple considerations.

- The values for the two lines will be the same.

- Half the separation of the lines could be measured as value.
- The possibility of 'Rayleigh electron paramagnetic resonance' is provided by off-diagonal Rayleigh scattering.
- There is a positive and a negative value on the higher and lower frequencies.

- The change is effected by an antisymmetric scattering tensor operator which is associated with the same selection rules as a magnetic dipole operator.
- A transition between atomic spin states can be effected by an operator with no apparent spin operator, but two spatial electric dipole moment operators.
- The scattering pathway connecting different initial and final spin states is provided by the intermediate resonant state, which is a resolved spin-orbit state.

- The possibility of 'Raman electron paramagnetic resonance' is caused by off-diagnonal scattering.

- The frequencies will be the average of the ground state and the molecule in the final excited state, which is slightly different, but it suits our purpose here to assume that they are the same.

- The recording was made in the author's laboratory.
- The intensities are not defined, but they are significant.

- The smaller couplets are due to overtone and combination modes.

- It is assumed that this is positive in both atoms and Molecules.

- The value is for the ground state of NpF.

- The theoretical value of IrCl2 should be negative.

- The transitions between the two levels are especially interesting.

- The U(C8H8)2 molecule is a part of the COT complex.

- In a positive magnetic field, a positive lower-frequency component and a negative higher component can be seen in the depolarized magnetic resonance Raman optical activity couplet in the 641.0 nm visible absorption band.

- The ground level is more valuable than the first excited level.

- There is a very weak band at 675 cm-1 in the resonance Raman spectrum of Uranocene.
- The 675 cm-1 band was confidently assigned to a combination of the 466 cm-1 electronic Raman transition and the totally because of the weak magnetic Raman optical activity couplet with the same sign as that of the absorption band.

- Since neutral porphyrins have nondegenerate ground states, we must use the magnetically perturbed development.
- Section 3.5.5 gives the machinery for this development.

- The magnetic analogues of (2.7.8), which take account of the finite lifetimes of the excited states, should be used in the region of an isolated absorption band, but the calculation becomes very complicated.

- The required terms are included in the parameters.

- The corresponding transition polarizability components are given for the 0-1 and0-0 vibronic resonances.

- The same magnitudes are obtained for the 0-1 resonance.

- Table 8.2 summarizes the results.
- The predictions have been confirmed by the measurement of the magnetic resonance-Raman optical activity spectrum of ferrocytochrome c. There is a magnetic circular dichroism spectrum with 6 Fe(II) metalloprotein.
- Each vibronic peak is associated with a curve like that.

- Adapted from Klein and Sutherland.

- The recording was made in the author's laboratory.
- The intensities are not defined, but they are significant.

- P'ezolet, Nafie, Peticolas, and Nestor and Spiro were taken from the resonance Raman bands.

- The absolute sign of a band depends on the symmetry species of the corresponding normal mode of vibration and the position of the wavelength relative to the vibronic peaks.
- The small deviations from perfect reflection symmetry on reversing the magnetic field direction may be the result of natural Raman optical activity.

- The results confirm that the vibronic theory of resonance Raman scattering in porphyrins and the theory of the associated magnetic Raman optical activity give a crucial role in the case of antisymmetric scattering.

- S. F. Mason has a book.

- Berova, N., Nakanishi, K. and Woody are authors.

- There is a scattering of light.

- B. Pullman's book, p. 1.

- Oeuvres de Pierre Curie.

- N. Berova, K. Nakanishi and R. W. Woody are authors.

- M.J. and R. E. were authors.

- R. G. Woolley wrote a book.

- The book was written by Griffiths, p. 745.

- P. G. Mezey has a book.

- N. Berova, K. Nakanishi and R. W. Woody are authors.

- N. Berova, K. Nakanishi and R. W. Woody are authors.

- W. J. Lough and I. W.

- F. Ciardelli and P.

- N. Berova, K. Nakanishi and R. W. Woody are authors.

- N. Berova, K. Nakanishi and R. W. Woody are authors.

- Cover Page

- About the book

- Title: MOLECULAR LIGHT SCATTERING AND OPTICAL ACTIVITY

- ISBN 0521813417

- Contents (with page links) 1 A historical review of optical activity phenomena 2 Molecules in electric and magnetic fields 3 Molecular scattering of polarized light 4 Symmetry and optical activity 5 Natural electronic optical activity 6 Magnetic electronic optical activity 7 Natural vibrational optical activity 8 Antisymmetric scattering and magnetic Raman optical activity

- Preface to the first edition

- Preface to the second edition

- Symbols

- 1 A historical review of optical activity phenomena 1.1 Introduction 1.2 Natural optical rotation and circular dichroism 1.3 Magnetic optical rotation and circular dichroism 1.4 Light scattering from optically active molecules 1.5 Vibrational optical activity 1.6 X-ray optical activity 1.7 Magnetochiral phenomena 1.8 The Kerr and Cotton-Mouton effects 1.9 Symmetry and optical activity

- 2 Molecules in electric and magnetic fields 2.1 Introduction 2.2 Electromagnetic waves 2.3 Polarized light 2.4 Electric and magnetic multipole moments 2.5 The energy of charges and currents in electric and magnetic fields 2.6 Molecules in electric and magnetic fields 2.7 A molecule in a radiation field in the presence of other perturbations 2.8 Molecular transition tensors

- 3 Molecular scattering of polarized light 3.1 Introduction 3.2 Molecular scattering of light 3.3 Radiation by induced oscillating molecular multipole moments 3.4 Polarization phenomena in transmitted light 3.5 Polarization phenomena in Rayleigh and Raman scattered light

- 4 Symmetry and optical activity 4.1 Introduction 4.2 Cartesian tensors 4.3 Inversion symmetry in quantummechanics 4.4 The symmetry classification of molecular property tensors 4.5 Permutation symmetry and chirality

- 5 Natural electronic optical activity 5.1 Introduction 5.2 General aspects of natural optical rotation and circular dichroism 5.3 The generation of natural optical activity within molecules 5.4 Illustrative examples 5.5 Vibrational structure in circular dichroism spectra

- 6 Magnetic electronic optical activity 6.1 Introduction 6.2 General aspects of magnetic optical rotation and circular dichroism 6.3 Illustrative examples 6.4 Magnetochiral birefringence and dichroism

- 7 Natural vibrational optical activity 7.1 Introduction 7.2 Natural vibrational optical rotation and circular dichroism 7.3 Natural vibrational Raman optical activity 7.4 The bond dipole and bond polarizability models applied to simple chiral structures 7.5 Coupling models 7.6 Raman optical activity of biomolecules

- 8 Antisymmetric scattering and magnetic Raman optical activity 8.1 Introduction 8.2 Symmetry considerations 8.3 A vibronic development of the vibrational Raman transition tensors 8.4 Antisymmetric scattering 8.5 Magnetic Rayleigh and Raman optical activity

- References

- Index (with page links) A B C D E F G H I J K L M N,O P Q R S T U V W,X,Y,Z

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