submitted papers Two-Dimensional Correlation Analysis and Waterfall Plots for Detecting Positional Fluctuations of Spectral Changes SOO RYEON RYU, ISAO NODA, CHANG-HEE LEE, PHIL HO LEE, HYONSEOK HWANG, and YOUNG MEE JUNG* Department of Chemistry, and Institute for Molecular Science and Fusion Technology, Kangwon National University, Chunchon 200-701, Korea (S.R.R., C.-H.L., P.H.L., H.H., Y.M.J.); and The Procter & Gamble Company, West Chester, Ohio 45069 (I.N.) In this study, we demonstrate the potentials and pitfalls of using various waterfall plots, such as conventional waterfall plots, two-dimensional (2D) gradient maps, moving window two-dimensional analysis (MW2D), perturbation-correlation moving window two-dimensional analysis (PCMW2D), and moving window principal component analysis two- dimensional correlation analysis (MWPCA2D), in the detection of the existence of band position shifts. Waterfall plots of the simulated spectral datasets are compared with conventional 2D correlation spectra. Different waterfall plots give different features in differentiating the behaviors of frequency shift versus two overlapped bands. Two-dimensional correla- tion spectra clearly show the very characteristic cluster pattern for both band position shifts and two overlapped bands. The vivid pattern differences are readily detectable in various waterfalls plots. Various types of waterfall plots of temperature-dependent infrared (IR) spectra of ethylene glycol, which does not have the actual band shift but only two overlapped bands, and of Fourier transform infrared (FT-IR) spectra of 2 wt% acetone in a mixed solvent of CHCl 3 /CCl 4 demonstrate that waterfall plots are not able to unambiguously detect the difference between real band shift and two overlapped bands. Thus, the presence or lack of the asynchronous 2D butterfly pattern seems like the most effective diagnostic tool for band shift detection. Index Headings: Frequency shifts; Waterfall plots; Two-dimensional correlation spectroscopy; 2D-COS; 2D gradient mapping; Moving window 2D correlation analysis; MW2D; Moving window principal component analysis 2D correlation analysis; MWPCA2D. INTRODUCTION A positional fluctuation of spectral bands can potentially cause serious problems in spectral analysis. It is very difficult to detect peak shift, especially when peaks are overlapped with those of other contributions. The reliable detection of position- shifting bands, therefore, is of importance in spectral analysis. For two-dimensional (2D) correlation spectroscopy, which is a well-established analytical technique providing considerable utility and benefit in various spectroscopic studies, 1–6 under- standing of the peak shift becomes especially important. For multivariate calibration, 7–10 the presence of a peak that is changing in position can become a major source of problems. Such a spectral response is fundamentally nonlinear, not obeying the linear Beer–Lambert law. This will force the calibration model to incorporate a large number of factors, leading to unstable over-fitting. If one can identify the region of peak-position shift prior to calibration-model building, such over-fitting can be avoided by masking the contribution of the shifting peak to the model. Methods for detection of peak- position shift have been reported, 11–17 but they do not provide a satisfying solution to the problem. We have recently investigated the nature of so-called positional or frequency fluctuations of spectral features. 18 Simple application of principal component analysis (PCA) to spectral data clearly showed the difference between the true frequency shift of a single band and apparent peak-maximum shift caused by relative intensity changes of overlapped adjacent bands. The spectral dataset containing a real band-frequency shift requires substantially more principal components (PCs) than normal PCA situations to adequately capture the detailed intensity variations arising from the nonlinear effect. This is because the shifting peak cannot be described as a simple linear combination of other peaks located at different frequencies. In contrast, an apparent positional shift of the peak maximum due to the relative intensity changes of overlapped bands requires only a few significant PCs. It was found that PCA is a surprisingly sensitive tool to distinguish the two possible mechanisms of peak-maximum shift. So-called band frequency shift phenomena in many cases are in fact the result of overlapped peaks, which are changing in relative intensity instead of in frequency position. It turned out that this feature cannot be adequately analyzed by any of the commonly used waterfall plots. Many different types of waterfall plots, such as conventional waterfall plots, deriva- tives, 19,20 the moving window 2D correlation method (MW2D), 21 and perturbation correlation moving window 2D analysis (PCMW2D), 22 can be used for detection of apparent positional fluctuation of spectral changes. These waterfall plots generate a slanted continuous ridge even when two overlapped peaks are changing the intensities. This plots strongly give the appearance of shifting band position, even more so than the usual stacked display of spectra. Thus, it may not be appropriate to use waterfall plots to determine the existence of band shifts. Received 2 September 2010; accepted 3 January 2011. * Author to whom correspondence should be addressed: ymjung@ kangwon.ac.kr. DOI: 10.1366/10-06114 Volume 65, Number 4, 2011 APPLIED SPECTROSCOPY 359 0003-7028/11/6504-0359$2.00/0 Ó 2011 Society for Applied Spectroscopy