Error bounds on goodness of fit indicators in vibrational circular dichroism spectroscopy

Prior information is very useful in selecting the right and accurate models for particular experimental tasks. This is the same case in vibrational circular dichroism analysis where few alternatives to the correct model are available. In choosing the best alternative model, researchers have employed various methods. For instance, researchers have assigned absolute configuration to a stereoisomer with a spectrum that is consistent with the experimental data. This can be is, however, a complicated process, especially in cases involving more than one stereocenters and occurrence of more conformations, where computations are more demanding, or in case of low concentrations leading to spectra with low signal-to-noise ratio. Alternatively, a combination of several techniques and software has been employed to handle vibrational circular dichroism spectra with non-trivial situations. As such, robust goodness-of-fit indicators have been identified as a powerful tool. Unlike the mean square error, they are less biased by outliers and guarantee accurate results.

To this note, a group of Università di Salerno scientists: Professor Guglielmo Monaco, Dr. Giovanni Procida, Dr. Antonia Di Mola, and Professor Antonio Massa together with Prof. Wouter Herrebout from the University of Antwerp used the bootstrap method to estimate the error bound on five different goodness-of-fit indicators for potential use in vibrational spectroscopy analysis. The indicators were specifically employed to assess and select the suitable and best stereochemical model from possible stereoisomer alternatives. The work is currently published in the research journal Chemical Physics Letters.

In brief, the research team applied the bootstrap method together with the model-averaging method. First, the methods were tested on a 3-chloro-1-butyne of known absolute configuration and then adopted to assign the unknown absolute configuration of synthesized 3-methyl-3-nitromethyl-isoindolinone. The selection criterion was based on comparison with mean square errors taking into consideration the error-normalized dimensionless values. A total of five different goodness-of-fit indicators were applied with and without using the model-averaging method.

Results showed that the stereoisomer turned out to have the known absolute configuration as indicated by the obtained error bounds on the goodness-of-fit indicators. The correctness of the assignment of the absolute configuration could be validated through inspection. For all the utilized goodness-of-fit indicators, the difference between the two models was observed to be significant since the bootstrap estimate for standard deviation of the difference of the goodness-of-fit indicators was lower than its corresponding mean. All the goodness-of-fit indicators were capable of selecting the correct absolute configuration. For the unknown configuration a similar agreement between all goodness-of-fit indicators was observed. Furthermore, restricting the analysis to the few intense peaks whose frequencies were computed accurately, also led to same best model. As such, the difference of goodness-of-fit indicator and its corresponding error is a key tool in indicating the correctness of the absolute configuration.

In a nutshell, the Italian study employed goodness-of-fit indicators, together with error bounds obtained by the bootstrap method, to determine the stereochemical model which best matches the experimental vibrational circular dichroism spectrum. The method was applied to a known case as well as for the assignment of an unknown absolute configuration. The study provides useful insights that will be of great help in vibrational circular dichroism spectroscopy analysis in key fields like pharmaceutical industries.