Spectral theoretical model

Reilly P D and Skinner J L 1995 Spectral diffusion of individual pentacene molecules in p-terphenyl crystal theoretical model and analysis of experimental data J. Phys. Chem 102 1540-52... 

Skinner J L 1997 Theoretical models for the spectral dynamics of individual molecules in solids Single Molecule Optical Detection, Imaging and Spectroscopy ed T Basche, W E Moerner, M Orrit and U P Wild (Weinheim VCFI)... 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

Artificial neural networks are now widely used in science. Not only are they able to learn by inspection of data rather than having to be told what to do, but they can construct a suitable relationship between input data and the target responses without any need for a theoretical model with which to work. For example, they are able to assess absorption spectra without knowing about the underlying line shape of a spectral feature, unlike many conventional methods. 

Equations (1-3) are widely used for protein dynamics analysis from relaxation measurements. The primary goals here are (A) to measure the spectral densities J(co) and, most important, (B) to translate them into an adequate picture of protein dynamics. The latter goal requires adequate theoretical models of motion that could be obtained from comparison with molecular dynamics simulations (see for example Ref. [23]). However, accurate analysis of experimental data is an essential prerequisite for such a comparison. 

In this section we describe some of the theoretical models that have been applied to the interpretation of VOA spectra, with an aim toward understanding the link between the spectral features and the molecular stereochemistry. The application of the models is included in the discussion of individual molecules in Sect. IV. 

The method of fs DFWM spectroscopy and our theoretical model for the spectral simulation is discussed in our second contribution in this volume. The experimental setup has been detailed in a former publication [5], Here, we would like to highlight some special features of this technique with emphasis on the possibility to obtain, besides the rotational constants, centrifugal distortion constants (CDs) and information on the polarizability tensor (PT). 

Summarizing, it is demonstrated that the developed model correctly reproduces the general trends in various experimentally measured responses, which include cuts of time- and frequency-gated spectra at particular frequencies, peak-shifts of the fluorescence spectra, and integral signals. Moreover, the relative shapes and intensities of the spectral cuts at different frequencies are correctly reproduced. For a more complete and quantitative description of the experimental data, the theoretical model has to be augmented by including additional system and/or solvation modes. 

Theoretical models of correlation functions and line shapes have been proposed which satisfy the principle of detailed balance [35, 36, 41, 232]. These profiles, along with a number of extensions that were later added [69, 295, 47, 48], describe the known profiles well. Especially the BC and K0 functions, Eqs. 5.105 and 5.108, model multipole- and overlap-induced lines of the rototranslational bands closely. These three-parameter functions are simple analytical expressions that are readily computable, even on computers of small capacity (pocket calculators) the parameters can be computed from the lowest three spectral moments, see Chapter 5. 

The instrument observes the radiance emitted by the atmosphere at different values of the spectral frequency and the limb-viewing angle. The dependence of the spectra on the unknown profiles is not linear. A theoretical model, called forward model, simulates the observations through a set of parameters, i.e. the atmospheric profiles that have to be retrieved. The inversion method consists in the search for the set of values of the parameters that produce the best simulation of the observations. 

Lacking a detailed theoretical model of how the enhancement of the absorption process should be treated in relation to the energy band diagram, the enhancement will be treated as a multiplier to the underlying dipole-molecular absorption in the spectral region of enhancement. This multiplication factor can be quite large relative to one. 

The measurement of vibrational optical activity (VOA) lacks some of the severe disadvantages mentioned. Vibrational spectral bands are less likely to overlap and can be measured using two complementary techniques namely infrared and Raman spectroscopy. They can be measured as well in the crystalline as in the liquid or gaseous state, and the techniques are applicable to solutions while nearly reaching (complemented with the appropriate theoretical models) the accurateness of the X-ray method. VOA has drawbacks too the effects are quite small and tend to be obscured by artifacts. They are about 10 times weaker than the optical rotatory dispersion (ORD) and the circular dichroism (CD) in the UV-VIS range. However, this apparent disadvantage is more and more relieved by instrumental advances. 

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