Optical spectroscopy theory

A diagrannnatic approach that can unify the theory underlymg these many spectroscopies is presented. The most complete theoretical treatment is achieved by applying statistical quantum mechanics in the fonn of the time evolution of the light/matter density operator. (It is recoimnended that anyone interested in advanced study of this topic should familiarize themselves with density operator fonnalism [8, 9, 10, H and f2]. Most books on nonlinear optics [13,14, f5,16 and 17] and nonlinear optical spectroscopy [18,19] treat this in much detail.) Once the density operator is known at any time and position within a material, its matrix in the eigenstate basis set of the constituents (usually molecules) can be detennined. The ensemble averaged electrical polarization, P, is then obtained—tlie centrepiece of all spectroscopies based on the electric component of the EM field. 

K. E. Peiponen, E. M. Vertiainen, and T, Asakura, Dispersion, Complex Analysis and Optical Spectroscopy. (Classical theory), Springer-Verlag, Berlin, 1999,... 

The first theoretical attempts in the field of time-resolved X-ray diffraction were entirely empirical. More precise theoretical work appeared only in the late 1990s and is due to Wilson et al. [13-16]. However, this theoretical work still remained preliminary. A really satisfactory approach must be statistical. In fact, macroscopic transport coefficients like diffusion constant or chemical rate constant break down at ultrashort time scales. Even the notion of a molecule becomes ambiguous at which interatomic distance can the atoms A and B of a molecule A-B be considered to be free Another element of consideration is that the electric field of the laser pump is strong, and that its interaction with matter is nonlinear. What is needed is thus a statistical theory reminiscent of those from time-resolved optical spectroscopy. A theory of this sort was elaborated by Bratos and co-workers and was published over the last few years [17-19]. 

Ohta, K., M. Yang, and G. R. Fleming. 2001. Ultrafast exciton dynamics of J-aggregates in room temperature solution studied by third-order nonlinear optical spectroscopy and numerical simulations based on exciton theory. J. Chem. Phys. 115 7609-7621. 

It is not the purpose of the present chapter to deal with all of the aspects related to this impressive capability. Rather, we will try to give some basic concepts, so that a nonspecialist in group theory is able to calibrate its potentiality and to apply it to simple problems in optical spectroscopy. 

The discovery of the rare earth elements provide a long history of almost two hundred years of trial and error in the claims of element discovery starting before the time of Dalton s theory of the atom and determination of atomic weight values, Mendeleev s periodic table, the advent of optical spectroscopy, Bohr s theory of the electronic structure of atoms and Moseley s x-ray detection method for atomic number determination. The fact that the similarity in the chemical properties of the rare earth elements make them especially difficult to chemically isolate led to a situation where many mixtures of elements were being mistaken for elemental species. As a result, atomic weight values were not nearly as useful because the lack of separation meant that additional elements would still be present within an oxide and lead to inaccurate atomic weight values. Very pure rare earth samples did not become a reality until the mid twentieth century. 

Note The acronyms used here are OSPED (optical spectroscopy in a pulsed electrical discharge), FAMS (flowing afterglow mass spectrometry), SIFT (selected ion flow tube), TRAPI (time-resolved atmospheric pressure ionization mass spectrometry), PHPMS (pulsed high-pressure ionization mass spectrometry), ICRMS (ion cyclotron resonance mass spectrometry), and ADO (averaged dipole orientation collision rate theory). 

M = (Mx,My,M ) is the dipole moment of the system. Moreover, the indices i, j designate the Cartesian components x, y, z of these vectors, ()q realizes an averaging over all possible realizations of the optical field E, and () realizes an averaging over the states of the nonperturbed liquid sample. Two three-time correlation functions are present in Eq. (4) the correlation function of E(t) and the correlation function of the variables/(q, t), M(t). Such objects are typical for statistical mechanisms of systems out of equilibrium, and they are well known in time-resolved optical spectroscopy [4]. The above expression for A5 (q, t) is an exact second-order perturbation theory result. 

A series of episodes in the historical development of our view of chemical atoms are presented. Emphasis is placed on the key observations that drove chemists and physicists to conclude that atoms were real objects and to envision their stracture and properties. The kinetic theory of gases and measmements of gas transport yielded good estimates for atomic size. The discovery of the electrorr, proton and neutron strongly irtfluenced discttssion of the constitution of atoms. The observation of a massive, dertse nucleus by alpha particle scattering and the measrrrement of the nuclear charge resrrlted in an enduring model of the nuclear atom. The role of optical spectroscopy in the development of a theory of electronic stracture is presented. The actors in this story were often well rewarded for their efforts to see the atoms. 

Spectroscopic methods can yield the required understanding of the complexes. Especially optical spectroscopy provides very detailed information about electronic and vibronic structures, in particular, when highly resolved spectra are available. However, without the development of suitable models, which are usually based on perturbation theory, group theory, and recently also on ab-initio calculations, a thorough understanding of the complexes is very difficult to achieve. In this volume and in a subsequent one some leading researchers will show that such a detailed description of... 

The deuteron, being the simplest compound nucleus, provides an important testing ground for theories of nuclear few body systems which predict the deuteron structure radius. Traditionally, this radius has been determined from accelerator-based electron scattering data. In an optical spectroscopy experiment in 1993, a new value for the deuteron structure radius with significant deviation from the previously adopted value was found [31]. 

Trimers and larger clusters involving open-shell monomers with spatially degenerate ground states are experimentally investigated by high-resolution optical spectroscopies and by photoelectron spectroscopy. On the theory side Chalasinski... 

The solid state properties of the linear chain compounds are substantially determined by the electronic structure of the molecular [Pt(CN)4]2 units. An ab initio calculation of the electronic structure of the [Pt(CN)4]2 complex including all 132 electrons or at least the 48 valence electrons does not exist as yet. Concerning the optical spectroscopy, however, mainly the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals are of interest. Thus, the number of electrons and states, which have to be considered, is restricted drastically compared to the full problem. The method usually applied to the approximative determination of the relevant states and their electronic structures is the molecular-orbital ligand field theory mostly using empirical fitting data50,31). 

This chapter concerns the energetics of charge-transfer (CT) reactions. We will not discuss subjects dealing with nuclear dynamical effects on CT kinetics. " The more specialized topic of employing the liquid-state theories to calculate the solvation component of the reorganization parameters is not considered here. We concentrate instead on the general procedure of the statistical mechanical analysis of the activation barrier to CT, as well as on its connection to optical spectroscopy. Since the very beginning of ET research, steady-state optical spectroscopy has been the major source of reliable information about the activation barrier and preexponential factor for the ET rate. The main focus in this chapter is therefore on the connection between the statistical analysis of the reaction activation barrier to the steady-state optical band shape. 

The CT/ET free energy surface is the central concept in the theory of CT/ ET reactions. The surface s main purpose is to reduce the many-body problem of a localized electron in a condensed-phase environment to a few collective reaction coordinates affecting the electronic energy levels. This idea is based on the Born-Oppenheimer (BO) separation " of the electronic and nuclear time scales, which in turn makes the nuclear dynamics responsible for fluctuations of electronic energy levels (Eigure 1). The choice of a particular collective mode is dictated by the problem considered. One reaction coordinate stands out above all others, however, and is the energy gap between the two CT states as probed by optical spectroscopy (i.e., an experimental observable). 

The electromagnetic field enhancement provided by nanostructure plasmonics is the key factor to manipulate the quantum efficiency. However, as it is illustrated in the unified theory of enhancement, since both the radiative and non-radiative rates of the molecular systems are affected by proximity of the nanostructure, the tuning has to be done on a case by case basis. In addition, there are factors due to molecule-metal interactions and molecular orientation at the surface causing effects that are much more molecule dependent and as are much more difficult to predict. Given the fact that fluorescence cross sections are the one of the highest in optical spectroscopy the analytical horizon of SEF or MEF is enormous, in particular in the expanding field of nano-bio science. 

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