# First and second derivatives of UV/Vis spectra using the Savitsky-Golay method

Three spectra have been obtained, A consisting of pure compound 1, B of a mixture and C of pure compound 2. The data, together with wavelengths, normalised to a constant intensity of 1 are presented below.

wavelength A B C
220 0.891 1.000 1.000
224 1.000 0.973 0.865
228 0.893 0.838 0.727
232 0.592 0.575 0.534
236 0.225 0.288 0.347
240 0.108 0.217 0.322
244 0.100 0.244 0.370
248 0.113 0.267 0.398
252 0.132 0.262 0.376
256 0.158 0.244 0.324
260 0.204 0.251 0.306
264 0.258 0.311 0.357
268 0.334 0.414 0.466
272 0.422 0.536 0.595
276 0.520 0.659 0.721
280 0.621 0.762 0.814
284 0.711 0.831 0.854
288 0.786 0.852 0.834
292 0.830 0.829 0.763
296 0.838 0.777 0.674
300 0.808 0.710 0.589
304 0.725 0.636 0.529
308 0.606 0.551 0.480
312 0.477 0.461 0.433
316 0.342 0.359 0.372
320 0.207 0.248 0.295
324 0.113 0.161 0.226
328 0.072 0.107 0.170
332 0.058 0.070 0.122
336 0.053 0.044 0.082
340 0.051 0.026 0.056
344 0.051 0.016 0.041
348 0.051 0.010 0.033

#### Questions

1. Produce and superimpose the graphs of the raw spectra. Comment.

2. Calculate the 5 point Savitsky Golay quadratic first and second derivative of A. Plot the graphs, and interpret them; compare both first and second derivatives and discuss the appearance in terms of the number and positions of the peaks.

3. Repeat this for spectrum C. Why is the pattern more complex? Interpret the graphs.

4. Calculate the 5 point Savitsky Golay quadratic second derivatives of all three spectra (note two of these graphs have already been generated) and superimpose the resultant graphs. Repeat for the 7 point derivatives. Which graph is clearer, 5- or 7-point derivatives? Interpret the results for spectrum B. Do the derivatives show it is clearly a mixture? Comment on the appearance of the region between 270 and 310 nm, and compare to the original spectra.