Optimal spectral resolution for solids and liquids using FT and other infrared spectrometers: how much resolution do you really need?

In this study we investigate the possibility of using spectral resolutions for infrared measurements of solids and liquids that are not powers of two, e.g. are not at 1, 2, 4, 8, or 16 cm^-1 resolution. In almost all reported literature of the last fifty years the resolution used to record a Fourier transform infrared spectrum has been a power of two. This stems from the fact that 1) the Cooley-Tukey algorithm used to compute such a transform was constructed to use only powers of two and was also driven by 2) the fact that the computing horsepower required to compute the Fourier transform increases as Nlog₂(N), where N is the number of points in the interferogram (spectrum). For typical spectra, however, the CPU time is no longer a consideration. Our study is based on both liquid and solid spectra, all of which were recorded at 2 cm^-1 resolution. There were a total of 70 solids spectra representing 2,472 spectral peaks and 61 liquids spectra (1,765 spectral peaks), each peak inspected for being singlet / multiplet in nature. Of the 1,765 liquid bands examined, only 27 have widths less than 5 cm^-1. Of the 2,472 solid bands examined, only 39 peaks have widths less than 5 cm^-1. For liquids, the mean peak width is 24.7 cm^-1 but the median peak width is 13.7 cm^-1, and, similarly, for solids, the mean peak width is 22.2 cm^{- 1}, but the median peak width is 11.2 cm^-1. In both cases, solids and liquids, a skewed peak width distribution was observed, the peak of the distribution representing narrower bands in the 7 to 9 cm^-1 FWHM range but displaying a long tail to the very broad bands, with some displaying spectral widths of 100 cm^-1 or more. Because one of the most important criteria for successful instrumental design in IR spectroscopy is the spectral resolution, the data were further analyzed showing that a value to resolve 95% of all bands is 5.7 cm^-1 for liquids and 5.3 cm^-1 for solids; such a resolution would capture the native linewidth (no instrumental broadening) of 95% of all the solids and liquid bands, respectively. Based on the present results we suggest that, when accounting only for intrinsic linewidths an optimized resolution of 6.0 cm^-1 will capture 91% of all condensed-phase bands for IR detection of chemical, mineral, and biological materials.