Relationship between selectivity and average resolution in comprehensive two-dimensional separations with spectroscopic detection

The average value of the multivariate selectivity (SEL) of randomly positioned peaks in a multi-component separation is shown to equal the average fraction of peaks that are singlets, as predicted by statistical-overlap theory (SOT). This equality is the basis for proposing a useful metric, specifically the average minimum resolution of nearest-neighbor peaks, for the performance of comprehensive two-dimensional (2D) separations. Furthermore this metric was computed both without ancillary spectroscopic information and with the assistance of such help, specifically multi-wavelength UV-vis spectra, acquired during the separation. Separations are simulated with randomly positioned peaks over wide ranges of total number of peaks, first- and second-dimension peak capacity, dimensionless first-dimension sampling time, and spectral diversity. The specific version of the general multivariate selectivity concept that is used here - identified as SEL - gives the relative precision of quantification when using the PARAFAC (parallel factor analysis) method, a popular curve resolution algorithm. The SEL values of all peaks were calculated, averaged, and compared to the predictions of SOT. In the absence of auxiliary spectral data, the SEL-based average minimum resolution required to separate two peaks in a 2D separation is 0.256, compared to resolution of 0.5 if no chemometric assistance is available. This was found to be valid over a wide range of conditions and is essentially independent of peak crowding. With the assistance of the spectral data, the requisite minimum resolution substantially improves, that is, it decreases, especially when peak crowding is severe. The requisite minimum resolution decreases even further, up to a limit, as the spectral diversity is increased. In contrast, the SEL-based average under-sampling correction factor is virtually independent of the presence of the additional spectral data, and additionally is about the same as calculated with SOT from the average number of maxima in closely analogous simulations. The use of selectivity greatly increases the fraction of peaks that are singlets, relative to the number of singlet maxima, especially when spectral assistance is added. The insensitivity of the under-sampling correction factor to either the use of selectivity or added spectral data simplifies optimization of the corrected peak capacity in on-line comprehensive 2D separations.