Placzek

B) THE MICROSCOPIC HYPERPOLARIZABILITY IN TERMS OF THE LINEAR POLARIZABILITY THE KRAMERS-HEISENBERG EQUATION AND PLACZEK LINEAR POLARIZABILITY THEORY OF THE RAMAN EFFECT... 

Lee S Y 1983 Placzek-type polarizability tensors for Raman and resonance Raman scattering J. Chem. Phys. 78 723-34... 

J. Szatkowski, E. Placzek-Popko, B. Bieg, A. Hajdusianek, and S. Kuzmiuski, 17th International Seminar on Suface Phjsics, Kudowa, Poland, 1995. 

Eberlein-Konig B, Placzek M, Pryzbilla B (1998) Protective effect against sunburn of combined systemic ascorbic acid (vitamin C) and d-alpha-tocopherol (vitamin E). J Am Acad Dermatol 38 45-48... 

Rueff F, Placzek M, Przybilla B Mastocytosis and 44 Hymenoptera venom allergy. Curr Opin Allergy Clin Immunol 2006 6 284-288. 

Jan Vredeman de Vries, Perspectiva, Leiden Henricus Hondius, 1604 (New York Golumhia University Press Dover, 1968), introduction hy Adolf K. Placzek. 

McCallum SE, Parameswaran N, Bordia T, Fan H, McIntosh JM, Quik M (2006) Differential regulation of mesolimbic alpha 3/alpha 6 beta 2 and alpha 4 beta 2 nicotinic acetylchohne receptor sites, function after long-term oral nicotine to monkeys. J Pharmacol Exp Ther318 381-388 McKay BE, Placzek AN, Dani JA (2007) Regulation of synaptic transmission and plasticity by neuronal nicotinic acetylchohne receptors. Biochem Pharmacol 74 1120-1133 Mena-Segovia J, Winn P, Bolam JP (2008) Chohnergic modulation of midbrain dopaminergic systems. Brain Res Rev 58 265-271... 

The derivation of S(q, co) is available in various textbooks [20-22], In this chapter, only the final expression is presented and its significance is discussed. The well-known Landau-Placzek formula for the dynamic structure factor is given by... 

These results apply specifically to Rayleigh, or elastic, scattering. For Raman, or inelastic, scattering the same basic CID expressions apply but with the molecular property tensors replaced by corresponding vibrational Raman transition tensors between the initial and final vibrational states nv and rn . In this way a s are replaced by (mv aap(Q) nv), where aQ/3(<3) s are effective polarizability and optical activity operators that depend parametrically on the normal vibrational coordinates Q such that, within the Placzek polarizability theory of the Raman effect [23], ROA intensity depends on products such as (daaf3 / dQ)0 dG af3 / dQ) and (daaf3 / dQ)0 eajS dAlSf / dQ)0. 

The tensors which enter theoretical expressions are transition tensors 7, for a transition between an initial state i and a final state /. The Placzek polarizability theory for vibrational Raman scattering [56], which we use here, is valid in the far from resonance limit, i and / are then vibrational states. If we assume that they differ for normal mode p, then the transition tensors can be written as... 

The separation into a vibrational and an electronic part is implied by the Placzek polarizability theory. The further analysis of vibrational motions has in the past typically been accomplished by calculating the vibrational energy distribution in valence coordinates. For the large-scale skeletal motions often important in ROA, and for relating Raman and ROA scattering cross-sections to the vibrational motions of structural parts of an entity, a different approach is needed. 

G. Placzek, Rayleigh-Streuung und Raman Effekt, in Handbuck der Radiologic , E. Maux (ed)., Akademische Verlagsgesellschaft, Leipzig, 1934 p. 205. 

The authors thank Mr. G. Z. Whitten and Mr. D. W. Placzek for their helpful assistance with some of the calculations. 

Murry RL, Fourkas JT, Keyes T. Nonresonant intramolecular spectroscopy beyond the Placzek approximation. I. Third-order spectroscopy. J Chem Phys 1998 109 2814-2825. 

As mentioned above, the basic theory of the Raman effect was developed before its discovery. However, at this time numerical calculations of the intensity of Raman lines were impossible, because these require information on all eigenstates of a scattering system. Placzek (1934) introduced a semi-classical approach in the form of his polarizability theory. This provided a basis for many other theoretical and experimental studies. Physicists and chemists worldwide realized the importance of the Raman effect as a tool for qualitative and quantitative analysis and for the detennination of structure. 

Placzek s theory (1934) which treats molecules as quantum objects and electromagnetic fields classically, satisfactorily describes the Raman effect on the condition that the exciting frequency differs considerably from the frequencies of electronic as well as of vibrational transitions. 

As already pointed out, this description of the Raman effect is based on the polarizability theory (Placzek, 1934) which is valid in a good approximation if the exciting frequency is much higher than the frequency of the vibrational transition // , but lower than the frequency of the transition to the electronic excited state If, on the other hand, is approaching then resonances occur which considerably enhance the intensities of the Raman lines, i.e., the resonance Raman effect. This effect and its applications are described in Sec. 6.1 and also in Secs. 4.2 and 4.8. 

The term on the right-hand side of this equation represents the microscopic parameters of the sample. According to Placzek s theory (1934), this expression should be independent of the frequency of the exciting radiation. In the absence of a resonance or pre-resonance Raman effect, it would be equal for all exciting lines. The term on the left-hand side normalizes the observed Raman intensity by including the P factor. These values have the dimension cm - sr. ... 

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