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The idea of covariance mapping is based on a relatively straightforward statistical treatment of TOF data.816 Additional standard tools such as confidence interval and hypothesis testing could be readily supplemented with such statistical analyses.9 The interpretation technique similar to the peak sign analysis of a synchronous 2D spectrum was proposed by Berardi et al.10 In this case, however, two separate covariance maps, one comprising only positive peaks and the other with negative peaks, are created to differentiate the association and anti-association occurring between pairs of TOF spectrum points. Theoretical models for 2D covariance mapping were discussed by Bruce et al. for contour features, calculation based on energy and momentum conservation, and Monte Carlo simulation of correlation between first and second arrival ions.11 Cornag-gia showed 2D correlation coefficient maps based on the TOF mass spectra of Coulomb explosion and gave some discussion on the interpretation of the shape of correlation peaks.12
With all the activities along the covariance mapping concept in TOF mass spectrometry community, it is curious to note there is an apparent lack of interest in the use of asynchronous correlation. The information obtained in TOF
Extension of 2D Correlation Analysis to Other Fields
experiments can be potentially enriched by employing asynchronous correlation analysis, as there are many occasions where sequential events take place in such measurements. Cross et al., for example, considered the distinction of synchronously correlated direct double ionization reaction versus sequential stepwise ionization.13 Card et al. showed the existence of two separate ionization pathways by using positive and negative covariance maps, representing respectively a concerted reaction and a different competitive reaction process.1415 Interestingly, these authors do specifically cite the classic paper of generalized 2D correlation,18 but no asynchronous correlation analysis has been attempted so far in their work.
The use of generalized 2D correlation analysis in mass spectrometry applications is still surprisingly limited, but some promising attempts have recently been made. For example, Okumura et al. reported the 2D correlation analysis applied to a set of mass spectra obtained from the thermal desorption spectroscopy (TDS) study.19 In TDS mass spectrometry, a small amount of gas evolved from a sample material upon heating is analyzed. Mass spectra obtained from a TDS experiment, however, usually contain peaks observed in a very wide range, and each peak is often composed of several fragments with the same mass number that are derived from different species. 2D correlation analysis is then utilized effectively to sort out such complex spectral information.
In 2D TDS mass spectrometry, mass peaks that have significant changes could be readily picked up and the relationship between fragments are examined by the presence of 2D correlation peaks. In the study of Okumura et al.,19 thermal degradation products of a mixture of polyvinylchloride (PVC) and dioctylphtha-late (DOP) in ultrahigh vacuum was studied. The 2D TDS mass spectra clearly indicated that the desorption of PVC and degradation of DOP have multiple stages. More volatile DOP desorped before PVC, as expected. The desorption process of benzene occurred at a temperature slightly below that for dehydrochlorination of PVC. The formation of naphthalene occurred at a temperature just above the release of benzene. It was pointed out that the identification of the detailed sequential order of the desorption process was difficult without the help of 2D correlation, even if the characteristic fragments of the mixture components were known prior to the experiment.
15.4 OTHER UNUSUAL APPLICATIONS OF 2D CORRELATION ANALYSIS
The potential application of generalized 2D correlation is not limited to techniques found in analytical chemistry. The concept is so flexible that it can be readily applied to problems in many other scientific disciplines. An interesting example is the application of 2D correlation in computational chemistry, where correlation maps are constructed from a series of calculated data.
For example, Erman and coworkers employed the basic idea of generalized 2D correlation in the area of statistical mechanics.20 A molecular dynamics calculation of polymer chains was effectively combined with 2D correlation to showcase
Return to 2D NMR Spectroscopy
synchronously and asynchronously correlated segmental dynamics of polymeric molecules. Lee and Shin used a 2D correlation method for molecular dynamics simulation of temperature-dependent peptide unfolding of P-heparin.2122 In their study, essential dynamics (ED) analysis was used for atomic fluctuations in an MD trajectory in conjunction with generalized 2D correlation. Different folding mechanisms, e.g., hydrogen-bond-centric and hydrophobic-centric modes, were successfully analyzed by the 2D correlation spectra.