Anal. Chem. 1007, 59, 2567-2569 2507

Automatic Peak-Unfolding Routine for Low-Mass Detection in Fourier Transform Mass Spectrometry

Robert B. Cody,* James A. Kinsinger,’ and Seth D. Goodman Nicolet Analytical Instruments, Madison, Wisconsin 5371 1

An automatic peak-unfolding routine has been developed for Fourier transform mass spectrometry, based upon the use of a look-up table. The routine allows the use of a reduced digitizer rate to increase resolution without sacrificing low- mass information. The routine is demonstrated for electron impact (EI) spectra of a variety of compounds, including m e with lsobark multlplets, which were correctly identified by the unfolding procedure. I n addition, the routine may be used to detect low-mass ions at a high magnetlc field strength, without requiring a faster digitizer rate. This Is 11- lustrated by obtaining an E1 mass spectrum of methane, using a digttization rate of 5.3 YHz, at a magnetic field strength of 3 1. The lowmass iookvp table is also found to be a useful complement to elemental composition calculations for iden- tifying ions based upon their measured masses.

Fourier transform mass spectrometry (FTMS), also referred to as “Fourier transform ion cyclotron resonance spectrometry” (1,2), is dependent upon mathematical manipulation of di- gitized analog signals. In order to accurately measure the frequencies present in an analog signal comprised of several frequency components, the digitizer must be operated a t a rate that is greater than twice the highest frequency contained in the signal. This m i n i u m rate is referred to as the “Nyquist rate”.

If the digitizer is operated at a rate which is less than the Nyquist rate, the higher frequency components will appear at a lower frequency than the true value. Such peaks are referred to as “folded-back” peaks, and the phenomenon is often referred to as “aliasing”.

In FTMS, an ion with a resonant frequency, f , greater than half the sampling frequency, f , , will appear at an apparent frequency, f a p p , according to the relation

(1) where n is an integer (0, 1, 2...) that satisfies the condition

f a p p = If - nfsl

0 5 f,,, 5 f , / 2 Folded-back peaks are normally avoided in FTMS by exciting only ions having frequencies less than half the digitizer rate, using a filter to remove the high-frequency components before detection, or by ejecting low-mass ions so that their frequencies are not contained in the ion signal.

However, it is often desirable to operate the digitizer at a reduced rate, in order to detect the ion transient signal for a longer time, thus obtaining higher resolution. In this case, it may also be desirable to preserve information about low masses. By deliberate excitation of ions having frequencies greater than half the digitization rate, lower masses will be present in the spectrum as aliased peaks. If an aliased peak can be identified, relation 1 can be used to calculate the true mass of the ion, and the ion can be ‘unfolded”, or placed in its proper position in the mass spectrum. This is similar to methods that have previously been applied to Fourier

*Present address: Masstron, Inc., Boulder, CO.

transform visible spectroscopy (3). In a recent paper (4) , we described the use of aliasing to

determine the elemental compositions of low-mass peaks in Fourier transform mass spectrometry. Aliased peaks were identified by their “unusual” mass defects and their true frequency (true mass) calculated. We suggested that this might provide a method for reducing the digitization rate without losing low-mass information. In addition, it was suggested that this might form the basis for detecting lower mass at higher magnetic field strengths, without requiring an excessively high digitization rate.

In order to develop a more general method for low-mass detection, it is necessary to find a reliable method for rec- ognizing aliased peaks. Several possibilities might be pro- posed. If the digitization rate, f , , is changed slightly, relation 1 shows that the apparent frequency of an aliased peak will be changed, while the measured frequencies of unaliased peaks will remain constant. In addition, the phase of the aliased peak will be changed, as is observed in Fourier transform nuclear magnetic resonance (5). While this is a reliable me- thod for detecting aliasing, it requires that several spectra be acquired at different digitization rates. This is not always practical if only a short time is available for the measurement (as in GC/MS).

The ”suspicious mass defect” approach, as employed in the previous paper, cannot be considered to be reliable for a general purpose method, since aliased peaks may occur at frequencies very close to the true frequencies of other ions in the mass spectrum, and it is difficult to define a criterion for “suspicious masses”. Furthermore, it is possible for low masses to appear at apparent frequencies that correspond to very high masses, and these might be overlooked if the op- erator is looking for suspicious masses within the normal mass range for E1 spectra.

A much more convenient and reliable method for identi- fying aliased peaks involves the use of a low-mass look-up table. Because only a limited number of elemental compo- sitions exist for low-mass fragments and small molecular ions in electron impact spectra, it is possible to create such a table. A starting point for the construction of such a table may be found in ref 6. This is a compilation of common low-mass fragments in electron impact spectra of organic compounds. For this work, it was also necessary to add the elemental compositions of low molecular weight compounds in ref 7 and to include significant isotope peaks for ions in the table, since ref 6 only lists fragments containing abundant isotopes.

With a table of low-mass ions available, it is possible to calculate the apparent frequency for each mass in the table, and then check to see whether that frequency is present in the spectrum. This will be reliable, provided sufficient res- olution is available to distinguish the aliased frequencies from peaks having true frequencies close in value. Fortunately, FTMS is capable of very high resolution and mass accuracy, suggesting that this approach might be practical.

In this paper, we describe the application of an automatic peak-unfolding routine based upon a low-mass look-up table. The method is shown to be capable of recognizing and cor- rectly identifying aliased low-mass peaks for a variety of

0003-2700/87/0359-2567$01.50/0 0 1987 American Chemical Society

2568 ANALYTICAL CHEMISTRY, VOL. 59, NO. 21, NOVEMBER 1, 1987

4 2 I

- _ - - 1 - 1 I 4 - - -a

Y _ L

V A S S I\ 4 V J

Flgure 1. (a) E1 mass spectrum (bar graph form) of cyclohexanone taken at a digitization rate equal to the high exchation limit of 2 MHz, before applying the unfolding algorithm. (b) Result of applying the unfolding algorithm to the spectrum given in part a. (c) E1 mass spectrum of cyclohexanone taken at a digitization rate of 4 MHz, with excitation to 2 MHz.

compounds. Isobaric multiplets are properly handled by the routine, and we show that it is possible to detect peaks having frequencies that cannot be otherwise detected at the maximum digitization rate available.

EXPERIMENTAL SECTION All experiments were conducted with a Nicolet FTMS-2000

dual-cell (8, 9) Fourier transform mass spectrometer having a 12-bit 5.3-MHz (maximum rate) digitizer and a 3-T supercon- ducting magnet. The low-mass look-up table was constructed as described in the introduction. The program to handle the au- tomatic unfolding algorithm was written in FORTRAN 77, and installed as a command in the FTMS operating system.

Best results were obtained for electron impact spectra with at least 64K data points acquired, and one zero fill employed to increase the number of points per peak. AU spectra were obtained by using direct mode (wide mass range) data acquisition. A calibration table was constructed by using seven ions in the mass spectrum of perfluorotributylamine. This calibration was suf- ficiently stable to allow reliable identifkation of folded-back peaks for several days without requiring an internal calibration com- pound for the electron impact spectra.

Swept-frequency (chirp) excitation from 0 Hz to an upper limit of 6 MHz was available without hardware modification to the system. The high-frequency limit of 6 MHz is sufficient to permit excitation of ions down to -8 amu at a magnetic field of 3 T, well below the mass of which is a meaningful lower mass limit for organic mass spectrometry.

RESULTS AND DISCUSSION Application of the Unfolding Algorithm to Several

Test Cases. Figure l a shows a mass spectrum of cyclo- hexanone collected at a digitization rate of 2 MHz, with ex- citation up to a high-frequency limit of 2 MHz. In this case, ions between 1 and 2 MHz fold back into the spectrum, as is evident from the absence of peaks below 50 amu. The automatic unfolding algorithm was applied to this spectrum by calculating the aliased frequency for each ion in the look-up table and checking for the presence of a peak at the corre- sponding frequency in the spectrum. If a peak occurred at

, , ! , , ! 1 , I j , 1 1 . I ,, , I " ' 1 " ' I d - 320 M A S S I N 4 2 0 3 M J 3::

Figure 2. (a) E1 mass spectrum of methyl stearate taken at a digi- tization rate equal to the high excitation frequency of 2 MHz. (b) Result of applying the Unfolding algorithm to the spectrum given in part a.

Figure 3. El mass spectrum of Impure methane, taken at a digitizer rate of 5.3 MHz and excltatlon up to 6 MHz.

Table I. Methyl Stearate Fragment Ions Identified by the Automatic Unfolding Program

composition massn composition massn

C2H2+ 26.0156 C3H3+ 39.0235 C2H3+ 27.0235 C3H4+ 40.0313 NZ+ 28.0610* C3HSC 41.0391 CZH4+ 28.0313* C2H20+ 42.0105* CHO+ 29.0027* C3H6+ 42.0469* CZH5+ 29.0391* CzH30+ 43.0184* CH30+ 31.0184 C3H7+ 43.0547* C3H+ 37.0078 C2H50+ 45.0340 C3H2+ 38.0156

"Numbers with an asterisk are those of resolved and correctly identified peaks having isobaric interferences.

the expected frequency within a tolerance of 0.01 amu, the folded-back peak was considered to be present. Each time a folded-back peak was identified, its true frequency was calculated by using relation 1, and the peak was replaced at its true position in the spectrum. The result is shown in Figure Ib. This may be compared with the spectrum (Figure IC) obtained by using a digitization rate of 4 MHz, a t which rate the low-mass peaks appear at their true frequency.

A mass spectrum of methyl stearate taken at a digitizer rate of 2 MHz and with excitation up to 2 MHz is shown in Figure 2a. The result of applying the automatic peak unfolding routine is given in Figure 2b. Table I lists ions that were identified in the folded methyl stearate spectrum by the au- tomatic unfolding algorithm. Isobaric doublets that were resolved and correctly identified are marked with asterisks in the table.

Figure 3 shows a mass spectrum of impure methane taken with a digitizer rate of 5.3 MHz, which normally corresponds to a low-mass limit of 18 amu at a magnetic field strength of

ANALYTICAL CHEMISTRY, VOL. 59, NO. 21, NOVEMBER 1, 1987 2569

Table 11. Conflicts between Folded-Back Peaks and Spectral Peaks with Excitation up to the Digitizer Rate of 2 MHz

folded true apparent conflicting true difference, ion mass mass ion mass amu

H35Cl+ 35.977 64.969 SOZH' 64.970 0.0013 40Ar+ 39.962 55.0531 CaH,+ 55.055 0.0016

3 T. The 14N+ and l60+ peaks are due to impurities in the gas and are separated from the isobaric CH2+ and CH4+ peaks. A trace of water is evident at m/z 18.010.

Ambiguous Assignments. In order to determine the minimum resolution required to assure that there would be no ambiguity in assignment for folded-back peaks, a program was written to calculate the apparent frequencies for all ions in the table at a specified digitization rate and compare those apparent frequencies with the resonant frequencies of other ions within the table. If the mass difference between any apparent frequency and any true frequency fell below a specified tolerance, that pair was printed out. After the entire table had been examined, the smallest mass difference found was printed out. This permitted us to examine various com- binations of digitization rate and resolution, and determine the viability of our approach.

Consider the case where the highest excitation frequency is equal to a digitization rate of 2 MHz. In this case, all ions having frequencies from 1 to 2 MHz will fold back into the spectrum. If we choose a mass tolerance of 0.01 amu, only two conflicts were found where the folded-back peak could not be unambiguously assigned. These two pairs are given in Table 11. All other ions in the table are resolved. Of these two pairs, the H35Cl+ might be assigned by noting whether or not an H37Cl+ peak is also present in the spectrum at the expected isotope ratio. Other considerations must be devised to resolve the remaining pair. For example, a C4H7+ peak might not be expected to occur in isolation without a 4% carbon-13 peak, and neighboring C4H6+, etc.

Other combinations of digitization rate and excitation were found to give varying numbers (ranging from 2 to 20) of folded-back peaks that could not be reliably identified by the look-up table approach, assuming reasonable numbers of data points (up to 256K), and typical resolution values (10-20000). However, it appears that methods could be devised (based on the presence of isotopes at expected ratios, for example) to verify the assignment for typical digitization rates and exci- tation frequencies. The number of ambiguous assignments is expected to increase as the digitization rate is lowered, since the number of ionic possibilities increases with mass. Hence, caution should be exercised in selecting conditions.

A mass tolerance of 0.01 amu was found to be generally useful for distinguishing aliased peaks having true masses below -50 amu (at a magnetic field of 3 T). Under normal conditions (Le. with the superconducting magnet operating at 3 T and source pressures below Torr), mass accuracy is sufficiently stable to provide accurate identification of these ions for long periods of time without need for recalibration.

Evaluation of the Algorithm. The automatic unfolding algorithm has proven useful for detecting masses below 18 amu without having to increase the digitizer rate or decrease the magnetic field. Given excitation to 6 MHz, it should be possible to detect ions down to m/z 8, although detection of m/z 12 is a useful lower mass for organic mass spectrometry. Detection of even lower masses is posible by this method; detection of helium would require excitation a t 11.6 MHz, while detection of hydrogen would require an excitation at 46.3 MHz.

As magnetic field strength is increased, the method should prove even more useful. At a magnetic field strength of 7 T,

a 6-MHz excitation corresponds to a lower mass limit of 18.03 amu, eauivalent to the mass of NHd+.

The algorithm has proven most iseful for detection at a reduced digitization rate without loss of low-mass information. Reducing the digitization rate permits observation of the signal for a longer period of time without increasing the number of data points. This increases the resolution obtained, without increasing the time required to process a larger number of data points. This may be of consequence for experiments where time is important, such as for GC-FTMS.

The low-mass look-up table may be used to determine the elemental composition of small fragment ions in E1 spectra (even without applying the unfolding algorithm). This is somewhat faster than conventional elemental composition calculations and is much less likely to produce chemically unreasonable compositions.

The algorithm is subject to several important limitations. Presently, the low-mass look-up table only contains masses for ions in E1 spectra of organic compounds and some common inorganic ions that might be encountered in organic mass spectrometry.

Noise can be folded back into the spectrum whenever the digitizer is operated at a rate less than the Nyquist rate re- quired to sample up to the frequency corresponding to the noise equivalent bandwidth (IO). Therefore a disadvantage of this method is that the signal-to-noise ratio will be reduced slightly, depending on the digitizer rate selected. Assuming a single-pole amplitude noise spectrum, then the increase in noise will be approximately (2fB/f,)1/2 where fB is the noise equivalent bandwidth (or 1.57 times the corner frequency, assuming single-pole rolloff) and f, is the sampling frequency. Despite the increased noise, the unfolding procedure may be justified by the additional low-mass information and the decreased computing time resulting from the use of a smaller data set. The mass range of the low-mass look up table limits the application of the automatic peak unfolding algorithm to bandwidths where the increase in noise is normally tolerable.

In order to reliably separate folded-back peaks from isobaric interferences, spectra should be obtained with sufficient resolution and mass accuracy to correctly identify masses that are 0.01 amu apart. This presents no additional difficulty for normal operation, due to the inherent mass scale stability and high resolution of FTMS.

A small number of ions cannot be unequivocally assigned on the basis of mass alone, without increasing the resolution requirement beyond the practical level. Other criteria (such as the presence of isotope peaks for chlorine-containing ions) must be applied to identify these masses.

At present, identification has only been shown to be reliable for peaks that are folded-back once, i.e. that have frequencies between 'Iz and 1 times the digitization rate. Nevertheless, there is no theoretical reason why the method should not be applicable to ions with frequencies outside this range.

LITERATURE CITED (1) Laude, D. A., Jr.; Johlman, C. L.; Brown, R. S.; Weii, D. A,; Wilkins, C.

L. Mass Spectrom. Rev. 1986, 5 , 107-166. (2) Gross, M. L.; Rempel, D. L. Science 1964, 226, 261-268. (3) Horlick, G.; Hall, R. H.; Yuen, W. K. I n Fourier Transform Infrared

Spectroscopy; B a s h L. J., Ed.; Academic: New York, 1982. (4) Cody, R. B.; Kinsinger, J. A. Anal. Chem. 1986, 58, 670-671. (5) Cooper, J. W. I n Transform Techniques in Chemistry; Griffiths, P. R..

Ed.; Plenum: New York, 1978; p 74. (6) McLafferty, F. W.; Venkataraghavan, R . Mass Spectral Correlations,

2nd ed.; Amerlcan Chemical Society: Washington, DC, 1982. (7) The WileylNBS Mass Spectral Database; Wiley: New York. (8) U.S. Patent ApplicBtlon. serial no. 610502. (9) Cody, R . B.; Kinslnger, J. A,; Ghaderi, S.; Amster, I. J.; McLafferty, F.

W.; Brown, C. E. Anal. Chim. Acta 1985, 178, 43-66. (10) Stremler, F. G. Introduction to Communication Systems ; Addison-

Wesley: Reading, MA, 1977; pp 168-169.

RECEIVED for review February 24,1987. Accepted July 2,1987.