A Demonstration of Principal Component Analysis for EPR Spectroscopy: Identifying Pure Component Spectra from Complex Spectra Oliver Steinbock,* Bettina Neumann, † Brant Cage, Jack Saltiel, Stefan C. Mu 1 ller, † and Nar S. Dalal* Department of Chemistry, Florida State University, Tallahassee, Florida 32306-3006 The application of principal component analysis (PCA) with self-modeling (SM) is extended to electron paramag- netic resonance (EPR) spectroscopy. Our approach develops a novel constraint in the SM procedure. This constraint relies on the mirror symmetry around the EPR peak position, a condition that is well satisfied by most paramagnetic compounds at the usual EPR measurement frequencies (9 -10 GHz, the X-band). Examples consid- ered are two- and three-component systems consisting of aqueous solutions of paramagnetic ions that exhibit distinct but overlapping spectra: Cu 2 + (single peak), Mn 2 + (sextet), and VO 2 + (octet). The results show that the PCA technique is capable of reproducing the correct number of components and reconstructing spectra in good agree- ment with control measurements. Other spectroscopy areas to which the symmetric peak constraint should be applicable include NMR, NQR, and ICR. A frequent problem in electron paramagnetic resonance (EPR) spectroscopy is the partial or complete overlap of signals from different paramagnetic species. 1 Consequently, the characteriza- tion, identification, and analysis of mixed EPR spectra is often difficult. Examples of this dilemma cover nearly the entire range of EPR applications, such as kinetic investigations of free radicals originating from chemical reactions 2 or radiolysis 3 and the analyti- cal characterization 4 of the composition of paramagnetic inorganic, organic, and biological samples. 5 Related analyses 6 are sometimes even further complicated by the lack of information on the total number of paramagnetic species that result in a complex EPR signal and/ or difficulties in obtaining the relevant pure substances that would allow the application of standard least-squares fitting procedures. One possible approach to help solve this problem is the use of higher frequencies and therefore higher magnetic fields. 7 High magnetic fields increase the separation of pure EPR signals, since the absorption maxima at H 0 shift according to the compound-specific g-values as expressed in where h is Planck’s constant, ν denotes the microwave (or infrared) frequencies, and  is the Bohr magneton. Although high-field EPR spectrometers ( ν > 100-400 GHz) are currently under development in some laboratories, 8 it is doubtful that these spectrometers will become standard analytical tools. We therefore see a need for improvements of analytical methodologies in the field of EPR spectroscopy. Intriguing possibilities are opened by a technique known as principal component analysis (PCA), 9-11 which has found many applications in the field of optical spectroscopy. PCA has been used for the analysis of UV/ visible and fluorescence data, 12,13 and its usefulness has also been demonstrated for liquid chromatog- raphy 14 and time-resolved infrared (FT-IR) spectroscopy. 15 PCA has been applied to NMR spectroscopy. 16 In particular, Kvalheim 17 demonstrated that PCA is helpful in the assignment of the various peaks of a complex NMR spectrum, such as that from crude oil. PCA techniques were shown to be helpful in improving the quantitation of peak intensities in standard NMR as well as in NMR imaging. 18 To our knowledge, however, there has been no report of any application of PCA to EPR spectroscopy. In this context, we note that there are significant differences in the appearance and parameterization of NMR and EPR spectra. Whereas NMR spectra are recorded in the absorption mode, EPR peaks are measured in the derivative mode. Moreover, NMR spectra consist of many multiplets, each one representing a specific group of nuclei. In EPR, on the other hand, each peak arises from interaction of the unpaired electron with the whole paramagnetic entity. Thus the line shapes and routine analysis procedures differ for NMR and EPR spectroscopies. It follows † Max-Planck-Institut fu ¨ r molekulare Physiologie, Rheinlanddamm 201, D-44147 Dortmund, Germany, and Otto-von-Guericke Universita ¨ t, Institut fu ¨ r Experimen- telle Physik, Universita ¨ tsplatz 2, D-39016 Magdeburg, Germany. (1) (a) Barker, B. E.; Fox, M. E. Chem. Soc. Rev. 1980 , 9, 143-84. (b) Ayscough, P. B. Electron Spin Resonance in Chemistry; Methuen: London, 1967. (2) Neumann, B.; Steinbock, O.; Mu ¨ ller, S. C.; Dalal, N. S. J. Phys. Chem. 1996 , 100, 12342-8. (3) Box, H. C. Radiation Effects: ESR and ENDOR Analysis; Academic Press: New York, 1977. (4) Dalal, N. S.; Suryan, M. M.; Seehra, M. S. Anal. Chem. 1981 , 53, 938-40. (5) Marsh, D. In Biological Magnetic Resonance; Berliner, L. J., Reuben, J., Eds.; Plenum Press: New York, 1989; Vol. 8, Chapter 5. (6) Evans, J. C.; Morgan, P. H. Anal. Chim. Acta 1981 , 133, 329-38. (7) Brunel, L. C. Appl. Magn. Reson. 1992 , 3, 83-97. (8) Cage, B.; Hassan, A. K.; Pardi, L.; Krzystek, J.; Brunel, L. C.; Dalal, N. S. J. Magn. Reson. 1997 , 124, 495-8. (9) Beebe, K. R.; Kowalski, B. R. Anal. Chem. 1987 , 59, 1007A-10A, 1012A, 1014A-7A. (10) Sharaf, M. A.; Illman, D. L.; Kowalski, B. R. Chemometrics; Wiley: New York, 1986. (11) Malinowski, E. R.; Howery, D. G. Factor Analysis in Chemistry; Wiley: New York, 1980. (12) Sun, Y.-P.; Sears, D. F.; Saltiel, J. Anal. Chem. 1987 , 59, 2515-9. (13) Saltiel, J.; Sears, D. F.; Choi, Y.-O.; Sun Y.-P.; Eaker, D. W. J. Phys. Chem. 1994 , 98, 35-46. (14) Vandeginste, B.; Essers, R.; Bosman, T.; Reijnen, J.; Kateman, G. Anal. Chem. 1985 , 57, 971-85. (15) Hessling, B.; Souvignier, G.; Gerwert, K. Colloq. INSERM 1992 , 221, 155- 8. Hessling, B.; Souvignier, G.; Gerwert, K. Biophys. J. 1993 , 65, 1929-41. (16) Chemometrics Review, Fundamental Review Issue, Anal. Chem. 1996 , 68, 21R-61R. (17) Kvalheim, O. M.; Aksnes, D. W.; Brekke, T., Eide, M. O.; Sletten, E. Anal. Chem. 1985 , 57, 2858-64. (18) Stoyanova, R.; Kuesel, A. C.; Brown, T. R. J. Magn. Reson., Ser. A 1995 , 115, 265-9. hν ) gH 0 (1) Anal. Chem. 1997, 69, 3708-3713 3708 Analytical Chemistry, Vol. 69, No. 18, September 15, 1997 S0003-2700(97)00308-9 CCC: $14.00 © 1997 American Chemical Society