Evaluation of derivative spectra

In this article, the mathematical and experimental methods for generation and evaluation of derivative spectra are discussed. 

Figure 4-35. Evaluation of derivative spectra, a) Peak-peak ratio b) side-peak-side ratio (the ratio of the minimum peak B is negative, the ratio of the peak maximum E positive) c) side-side ratio (gives a measure for resolution of superposed peaks) (schematic drawings).

The approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

The second dimeric base, (—)-pennsylpavoline (179), was shown to correspond to C-l-demethylpennsylpavine. Specifically, its NMR spectrum was devoid of the 8 3.71 singlet which represents the C-1 methoxyl absorption in (—)-pennsylpavine (178). Evaluation of CD spectra of these novel dimers and comparison with those of the aporphine (+)-A -methyllaurotetanine and the pavine (—)-platycerine led to the assignment of the absolute configurations as depicted in expressions 178 and 179. These dimers are probably derived biosynthetically from the aporphine-benzylisoquinoline dimers, (-)-pennsylvanine and (-)-pennsylvanamine, which were found in the same plant (7,173). 

Therefore, the emitting species M and M L can in principle be identified from a decomposition of the total emission spectrum, and thus TRES experiments are mainly based on the evaluation of emission spectra rather than luminescence decays. However, a detailed analysis of the decays allows one to derive important information that cannot be obtained through the emission spectra, as will be explained below. In the frame of model 2, it is easily shown that the expressions of the relative contributions of the two species to the global emission spectrum contain only one unknown parameter, Afapp, while the equivalent expressions under the frame of model 1 are much more complex. This raises the question as to whether model 2 can be considered a reasonable approximation of the more complex scheme 1. This issue can be discussed qualitatively on the basis of three distinct cases of model 1, depending on the importance of photochemical reactions. 

Lastly, modern analytical instruments are almost always interfaced with personal computers to provide sophisticated system control and the storage, treatment (for example the performance of Fourier transforms or calculations of derivative spectra) and reporting of data. Such systems can also evaluate the results statistically, and compare the analytical results with data libraries in order to match spectral and other information. All these facilities are now available from low-cost computers operating at high speeds. Also important is the use of intelligent instruments, which incorporate automatic set-up and fault diagnosis and can perform optimization processes (see Chapter 7). 

State-of-the-art for data evaluation of complex depth profile is the use of factor analysis. The acquired data can be compiled in a two-dimensional data matrix in a manner that the n intensity values N(E) or, in the derivative mode dN( )/d , respectively, of a spectrum recorded in the ith of a total of m sputter cycles are written in the ith column of the data matrix D. For the purpose of factor analysis, it now becomes necessary that the (n X m)-dimensional data matrix D can be expressed as a product of two matrices, i. e. the (n x k)-dimensional spectrum matrix R and the (k x m)-dimensional concentration matrix C, in which R in k columns contains the spectra of k components, and C in k rows contains the concentrations of the respective m sputter cycles, i. e. ... 

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

In their fundamental paper on curve resolution of two-component systems, Lawton and Sylvestre [7] studied a data matrix of spectra recorded during the elution of two constituents. One can decide either to estimate the pure spectra (and derive from them the concentration profiles) or the pure elution profiles (and derive from them the spectra) by factor analysis. Curve resolution, as developed by Lawton and Sylvestre, is based on the evaluation of the scores in the PC-space. Because the scores of the spectra in the PC-space defined by the wavelengths have a clearer structure (e.g. a line or a curve) than the scores of the elution profiles in the PC-space defined by the elution times, curve resolution usually estimates pure spectra. Thereafter, the pure elution profiles are estimated from the estimated pure spectra. Because no information on the specific order of the spectra is used, curve resolution is also applicable when the sequence of the spectra is not in a specific order. 

Vibrational spectroscopy is of utmost importance in many areas of chemical research and the application of electronic structure methods for the calculation of harmonic frequencies has been of great value for the interpretation of complex experimental spectra. Numerous unusual molecules have been identified by comparison of computed and observed frequencies. Another standard use of harmonic frequencies in first principles computations is the derivation of thermochemical and kinetic data by statistical thermodynamics for which the frequencies are an important ingredient (see, e. g., Hehre et al. 1986). The theoretical evaluation of harmonic vibrational frequencies is efficiently done in modem programs by evaluation of analytic second derivatives of the total energy with respect to cartesian coordinates (see, e. g., Johnson and Frisch, 1994, for the corresponding DFT implementation and Stratman etal., 1997, for further developments). Alternatively, if the second derivatives are not available analytically, they are obtained by numerical differentiation of analytic first derivatives (i. e., by evaluating gradient differences obtained after finite displacements of atomic coordinates). In the past two decades, most of these calculations have been carried... 

Evaluation of trends in /pp coupling constants in solid-state 31P NMR spectra of P-phospholyl-NHPs allowed one to establish an inverse relation between the magnitude ofM and P-P bond distances [45], The distance dependence of. /pp is in line with the dominance of the Fermi contact contribution, and is presumably also of importance for other diphosphine derivatives. At the same time, large deviations between lJvv in solid-state and solution spectra of individual compounds and a temperature dependence of lJ77 in solution were also detected (Fig. 1) both effects... 

Various chiral derivatizing agents have been reported for the determination of enantiomer compositions. One example is determining the enantiomeric purity of alcohols using 31P NMR.28 As shown in Scheme 1-8, reagent 20 can be readily prepared and conveniently stored in tetrahydrofuran (THF) for long periods. This compound shows excellent activity toward primary, secondary, and tertiary alcohols. To evaluate the utility of compound 20 for determining enantiomer composition, some racemic alcohols were chosen and allowed to react with 20. The diastereomeric pairs of derivative 21 exhibit clear differences in their 31P NMR spectra, and the enantiomer composition of a compound can then be easily measured (Scheme 1-8). 

The FT-IR technique using reflection-absorption ( RA ) and transmission spectra to quantitatively evaluate the molecular orientation in LB films is outlined. Its application to some LB films are demonstrated. In particular, the temperature dependence of the structure and molecular orientation in alternate LB films consisting of a phenylpyrazine-containing long-chain fatty acid and deuterated stearic acid (and of their barium salts) are described in relation to its pyroelectricity. Pyroelectricity of noncentrosymmetric LB films of phenylpyrazine derivatives itself is represented, too. Raman techniques applicable to structure evaluation of pyroelectric LB films are also described. 

As in the case of the MM2 force field, parameterization of MM3 for amines was based mainly on experimental data with occasional references to ab initio calculations, mainly to evaluate relative conformational energies and derive appropriate torsional parameters. As mentioned above, one notable difference between the two force fields is the removal of lp on sp3 nitrogens from MM3. This simplifies the treatment of vibrational spectra and allows for a realistic treatment of nitrogen inversion which could not be handled by MM2. As usual with MM3, parameterization was aimed at reproducing a variety of molecular properties such as structure, steric energy, dipole moments, moments of inertia, heat of formation and vibrational spectra. A complete list of MM3 parameters for amines is provided in Reference 6. 

There are two necessary and related preconditions which must be satisfied for complex mixture analysis by pattern recognition to be successful. First, we must obtain an adequate data base of FTIR spectra from which we can derive the spectral patterns we need to recognize. Second, we must demonstrate that there Is a suitable measure or metric of similarity between the spectra. It Is these two conditions which were evaluated by the work presented here. Pattern recognition techniques were most suitable for the evaluation. 

The case study of the tetranuclear manganese complex presented above and the specific examples of structure/spectroscopy correlations have established the validity of the proposed methods and set the stage for more ambitious applications. The first such application has been the recent evaluation of several structural models of the OEC in the S2 state ( 1 3) of the Kok cycle (107). Twelve structural models were considered, 10 of which were based on Mn405Ca core topologies derived by polarized EXAFS spectra. Figure 19 shows one of the models included in the set. 

---