Figure 1
Input and output for SVD-based MLS by means of Spectram toolbox. (a) Spectral data set A(x, c) generated from two independent chemical transitions with the control variable c. In practice x can be any energy equivalent common in spectroscopy (wavenumber, frequency, wavelength). The inset shows the change in spectral intensities. Random error was added to the generated data. (b) Application of Spectram box results in two matrices F and D which describe the original data by A = DFT. F contains in its columns the transitions in c determined by the model functions (f1 and f2). The obtained parameters pi_j may be physical quantities, when physical models are chosen over pure empirical descriptions. D contains in its columns the individual difference spectra Di for each chemical compound.
Table 1
Examples for applications of control variable c dependent transitions that may be studied by SVD-based MLS using Spectram. T: temperature, t: time.
| Control variable | Transition model function | Quantifiable model parameters |
|---|---|---|
| pH | Henderson Hasselbach equation | acid dissociation constant pKa |
| T | van’t Hoff equation | standard enthalpy change ΔH° |
| t | rate law, qualitative description by exponential decay | rate constants k, half life t ½ |
| any c | qualitative description for instance by sigmoidal | position of transition in c |
Table 2
Process steps for the SVD-based MLS decomposition and the supporting functions and programs provided by the Spectram box.
| Process Step | Spectram box function or command | |
|---|---|---|
| I | Prepare data | |
| II | SVD and rank determination | RankFinder(…) |
| III | Construct transition model | simple_model(…), model_fun, vecpar(…) |
| IV | MLS recombination | recombfit(…) |
| V | Assess results | eval_model(…), matres(…), plotmatres(…) |
| VI | Repeat from II (optional) |