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Anal. Chem. 1988, 60, 341-344
High-Resolution Multiple-Ion Simultaneous Monitoring by Means of Multiple-Foldover Fourier Transform Ion Cyclotron Resonance Mass Spectrometry Mingda Wang and Alan G. Marshall*’ Department of Chemistry, T h e Ohio State University, 120 West 18th Avenue, Columbus, Ohio 43210
reference frequency now appears a t zero frequency and the largest observed frequency arises from input signals, which differ by about fh.,, from the reference frequency. Because the desired (initially high) ICR frequency has been converted to a relatively low frequency, it can be sampled a t a lower digitizing rate for a longer time, to produce a narrow-range spectrum with higher analog and digital resolution. Ordinarily in Fourier transform spectrometry, the timedomain sampling frequency, vsamplhg, is chosen to be at least twice as large as any signal frequency, v ~ in order , to satisfy the Nyquist limit (eq 1)(5,6). A discrete Fourier transform
I n Fourier transform ion Cyclotron resonance (FTIICR) ma86 spectrometry, uttrahlgh m a s resolution requires a long tlmedomain data acquisnlon period, whereas coverage of a wide mass range requires a rapid time-domain sampling rate. A hlgh-resolution wide-range FT/ICR mass spectrum thus requires a very large data set (>1 Mword). However, when the true lonlc mass-to-charge ( m / r) values are known but the reiatlve abundances of ions of different m / r are not (as In muttiple-ion monitoring), then tlmedomaln sampling at a frequency well below the Nyquist ilmit can “fold over” the ICR slgnais from ions of widely separated m / r values into a single narrow-band (and thus high-resolution) spectrum. For example, we have produced a single m a s spectrum of an eiectron-ionized mixture of resplratory gases (H20, N,, O,, Cot, N,O) at a resolution sufficient to resolve CO (from N,) and N,O (from CO,) without heterodynlng, by direct sampling at a rate leadlng to more than 1000 foldovers. Other applications are discussed.
In all forms of discrete spectrometry, digital resolution is limited by the maximum size of the data set (e.g., 1 Kword to 1 Mword or so). Thus, even when an experimental spectrum is available at high analog resolution, that analog resolution can generally be approached only by narrowing the spectral frequency range so that the final discrete spectrum provides several data points per analog line width (measured at, say half-maximum peak height). One must therefore usually choose conditions which lead either to a narrow-range high-resolution spectrum or to a wide-range low-resolution spectrum. For example, in Fourier transform ion cyclotron resonance (FT/ICR) mass spectrometry, ultrahigh mass resolution (1100OOO) requires a time-domain data acquisition period of >1 s (1). However, since ion cyclotron frequency varies inversely with ionic mass-to-charge ratio, the frequency-domain bandwidth corresponding to a wide range of ionic mass-to-charge ratios (e.g., 60 < m / z < 2000) is 1-3 MHz at magnetic field strengths of 3-7 T (2). Thus,a directly detected ultrahigh-resolution FT/ICR wide-range mass spectrum (see Figure l a ) would require a data set (and the fast buffer memory in which to store it) of several megawords. Therefore, high-resolution FT/ICR mass spectra are generally acquired in heterodyne mode (3,4),as shown in Figure lb. In the heterodyne experiment, the amplified (but not yet digitized) ICR signal is mixed (i.e., effectively multiplied by) a reference sinusoid of nearly the same frequency. The mixer produces output signals at the s u m and difference frequencies of the ICR and reference input signals. The sum frequency can be removed by passing the mixer output through a lowpass filter whose upper frequency limit is ~ l ~to leave ~ - only ~ the difference frequency. The net effect of the mixer/filter process is to leave a band of frequency signals in which the Also Department of Biochemistry. 0003-2700/88/0360-0341$01.50/0
Vsampling
,
2
2Vsignal
(1)
of such a time-domain discrete data set will then yield a frequency-domain spectrum in which each signal appears at its correct frequency within the range, 0 Iv , Ivsmpk/2. ~ ~ ~ However, if v,,pliw < 2vsignd, so that the signal frequency exceeds the Nyquist limit, then the spectral signal still appears (with different phase but correct magnitude) within the same range, 0 5 vsignd Ivsampling/2, but with lower apparent frequency (see Theory). In other words, foldover can confuse the identification of signal spectral peak frequency, but foldover conserves the correct peak magnitude. Obviously, when the signal frequencies are unknown (e.g., ions of unknown m / z in FT/ICR), then foldover is a complication to be avoided, since the true signal frequency of a peak (and thus the ionic m / z in FT/ICR) could otherwise be assigned to any of several values, depending upon the number of foldovers. In such cases, either broad-band direct-mode (Figure la) or narrow-band heterodyne-mode detection (Figure Ib) are preferred. However, if the freqency of a signal is known but its magnitude is not, then the spectral peak magnitude can be determined at higher digital resolution (and thus at higher precision (7)) from a folded-over spectrum than from a wide-range spectrum which satisfies the Nyquist criterion. For example, atomic emission l i e s occur at precisely known frequencies, which are observable in the Fourier transform spectrum obtained by passing the signals through a Michelson interferometer. However, the frequencies of elements commonly detected by atomic emission (e.g., alkali metals) are widely separated, and a wide-band FT optical spectrum offers relatively poor digital resolution. Since the precision with which any spectral peak magnitude can be determined is proportional to the square root of the number of data points per line width (3,intentional undersampling of the emission interferogram offers a spectrum with enhanced digital resolution (and thus increased peak height precision) compared to a wide-band spectrum. Horlick et al. (8)have demonstrated up to 8-fold increase in digital resolution by multiple foldover for FT optical emission spectra of alkali metals. Similarly, the precision with which the center frequency of a peak can be determined is also proportional to the square root of the number of data points per line width (7).Thus, a high-frequency peak whose approximate frequency is known can be observed at higher resolution in a narrow-band foldover 0 1988 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 4, FEBRUARY 15, 1988 DIRECT,
FOLDOVER
NO F O L D O V E R
4 EXCITE
A
EXCITE
j. f DETECT
J
3 SIGNAL
t-7,
In this paper, we show that multiple foldover (up to 1000 or more) can be uniquely useful for FT/ICR applications requiring the determination, at high resolution in a single spectrum, the precise relative numbers of ions of known (but widely separated) m / z , as in multiple ion monitoring.
DIRECT,
HETERODYNE
4 DETECT
A EXCITE
Y
t DETECT
1 + SIGNAL
t
FILTER
+
j
SIGNAL
THEORY If any form of Fourier transform spectrometry, the Nyquist criterion requires that a sinusoidal signal be sampled a t least twice per cycle in order that its apparent frequency (after discrete Fourier transformation) be its true frequency (5, 6). If the sampling frequency, v , ~ =, analog-to-digital ~ ~ ~ ~ ~ conversion rate, is less than the true frequency, then the apparent frequency will be "folded over" or "aliased" into the displayed frequency range from zero to the bandwidth. The apparent frequency is related to the true frequency according to eq 2 and 3. The bandwidth is the highest frequency which will
If
=n
then
"apparent
and
"apparent
-
+ x, n = 0, 1, 2, 3, ...;
-- nvsampling+
- ( n + 1)"sampling
"truer
05
X:
0 Ix I 1.0 (2) 5 0.5
(34
- "true, 0.5 < x 5 1 (3b)
in which v Figwe 1. Three FT/ICR detection modes. Left: Direct mode without foldover. Signals are excited from zero to the bandwidth limit of the detector, digitized directly at high speed (without prior analog filtering),
and Fourier transformed. Direct mode without foklover is suitable for producing wide-range mass spectra at relatively low mass resolution, in which all ICR spectral peaks appear at their correct frequencies. Middle: Heterodyne mode. The response to a narrow-band excitation is muhiplied by a reference sinusoid, and the resulting difference frequencies are extracted by a low-pass filter before timedomain sampling and Fourier transformation. Heterodyne mode is suitable for generating ultrahigh-resolution mass spectra over a single narrow mass range. Right: Direct mode whh foldover. Frequencies outside the excited range are removed by a band-pass filter prior to direct lowspeed time-domain digitization and Fourier transformation. This mode, when combined with multiple selective excitation (see Figure 2), can provide multipleion monitoring (at high precision in peak position and magnitude) of ions of two or more widely separated m / z values, but the true ICR frequency of each ion must be approximately known in advance in order to identify its position in the folded-over mass spectrum (see text). spectrum than by wide-band detection which satisfies the Nyquist limit. Cody and Kinsinger (9) have exploited this feature to enhance mass resolution in FT/ICR, by deliberate undersampling by a factor of two, to fold peaks into the observed FT/ICR mass spectrum. A third obvious application for foldover is to detect signals whose frequencies are higher than that of the highest available analog-to-digital converter. For example, Cody et al. (10) employed a single foldover to detect and identify ions whose mass is too low (and whose ICR frequency is thus too high) to satisfy the Nyquist limit (e.g., observation of CH4+with a digitizer whose maximum sampling rate (5.5 MHz) is well below twice the 2.88-MHz ICR frequency of CH4+ at 3 T). That feature should prove especially useful for FT/ICR mass spectra a t higher magnetic field strength (e.g., 7 T). When, as in the examples of ref 9 and 10, only a single foldover is involved, a recently demonstrated alternative is to double to effective sampling rate by interleaving two time-domain digitized transient signals, one of which is delayed with respect to the other by half of one sampling period (11). The method of ref 11 can be used to eliminate aliasing arising from a few (say, 1-3 foldovers), but is not practical when a large number of foldovers (say, 1 4 ) are involved, and/or for single-shot experiments (e.g., laser desorption FT/ICR).
,
, =~ sampling ~ ~ ~ frequency ~ ~ = 2.(bandwidth)
(4)
be correctly represented after Fourier transformation of the discrete time-domain data set, vapparent is the apparent frequency of the folded-over peak, and 2n is the number of foldovers. Thus, the first foldover occurs when (n+ x ) > 0.5, the second when (n + x ) > 1, and so on. In this paper, we will demonstrate spectra folded over by more than 1000 times (e.g., n = 536).
EXPERIMENTAL SECTION FT/ICR spectra were produced with a Nicolet FTMS-1000 instrument operating at a magnetic field strength of 3.001 T. The various experimental modes are illustrated in Figure 1. For the multiple-foldover experiments, the amplified time-domain analog signal was band-pass filtered through a Krohn-Hite Model 3202 dual-channel adjustable bandwidth analog filter (fourth-order Butterworth, with 24 dB/octave rolloff) before proceeding to the analog-to-digitalconverter. In each case, ions were produced by electron ionization (electron beam of 100-ms duration and 130-nA emission current, biased at -90 V with respect to a 1-in. rectangular ICR trapped-ion cell. Sample pressure was 1.4-1.5 X Torr, measured by a Granville-Phillips convectron ionization gauge located at the same distance as the ICR cell from the cryopump. Radio frequency excitation/detection parameters for the various experiments are listed below. In each case, 200-250 transients were coadded before Fourier transformation. (a) N2and CO. In the normal heterodyne experiment (shown schematically in the middle column of Figure l),N2+and CO+ ions trapped by an electric field of 0.2 V/cm were excited by a fast frequency sweep from 1.644 to 1.646 MHz in 0.125 ms. The time-domain signal was mixed with the output of a reference oscillator at 1.646 MHz, low-pass filtered to a bandwidth of about 3 kHz, and digitized at 3066 points/s for 0.668 s to give a 2 Kword time-domain data set. In the corresponding foldover experiment (rightmost column of Figure l), the signal produced by the same excitation was band-pass fdtered such that only the band of frequencies spanning N2+and CO+ reached the digitizer. The band-pass filter width, continuously adjustable from 20 Hz to 2 MHz, was set to about 1.7 kHz, to match the bandwidth of the analog-to-digitalconverter (1.533 kHz). Digitization was the same as for the heterodyne experiment. (b) N2and Ar. In a foldover experiment, N2+and Ar+ were excited by two successive narrow-band frequency sweeps: from 1.644 to 1.646 MHz in 0.0944 ms for N2+,and from 1.152 to 1.153 MHz in 0.060 ms for Ar+. A band-pass filter was set to pass without attentuation only the frequencies spanning the range
ANALYTICAL CHEMISTRY, VOL. 60, NO. 4, FEBRUARY 15, 1988 RELATIVE EXCITATION MAGNITUDE
FOLDOVER
li
/ I '
FREOUENCY(MHz)
15
13
1 1
09
07
0 5
FREQUENCY(KHz1
DETECTION
HETERODYNE
HIGH PASS FILTER
I co+
ATTENUATION ( d b )
H20t
-40 0 90
343
135
180
2 25
2 70
FREQUENCY(MHz)
Figure 2. Excltatiin and detection bandwidths for foldover experiment designed to provide high-resolution simultaneous monitoring of Ions of six different masses, four of which are widely separated. Dlrect lowfrequency sampling provides a higkresolution f o w v e r FT/ICR mass spectrum (see Figure 5).
between the ICR frequencies of Nz+and ,'rA namely 1.1-1.7 MHz between 3 dB points of the filter. The signal was digitized at 3066 pointsjs for 0.668 s to give 2K time-domain data points. (c) HzO, Nz,CO, Oz, COz, and NzO. In this foldover experiment, the ICR signals from six molecular ions were excited by four successive narrow-band frequency sweeps: from 1.431 from 0.990 to 1.050 MHz in to 1.441 MHz in 0.250 ms for 02+, 0.600 ms for NzO+and COz+,single-frequency excited at 2.559 MHz for 0.105 ms for HzO+,and 1.644-1.646 MHz as before for N2+and CO' (Figure 2, top). Because of the wide signal bandwidth, a high-pass filter with low-frequency cutoff of about 1.0 MHz (Figure 2, bottom) was used in place of a band-pass filter, and the signal was then analog-to-digital converted at 59 260 pointsjs for 0.276 s to give 16K time-domain data points. The results of these experiments will now be discussed.
RESULTS AND DISCUSSION Foldover vs Narrow-BandHeterodyne FT/ICR CO+ and Nz'. The foldover method (Figure 3,top) is compared to conventional heterodyne detection (Figure 3, bottom) for an electron-ionized mixture of CO and Nz. For the same analog-to-digital conversion bandwidth (1.533kHz), the mass resolution obtained by either method is essentially the same (-450000: 1, measured at half-maximum magnitude-mode peak height), even though the ICR signals in the foldover experiment are folded back more than 1000 times (n = 536 in eq 2). Mass accuracy (-0.2 ppm) and signal-to-noise ratio for both CO+ and N2+for the foldover experiment are comparable to those for the heterodyne experiment at the same digitizer bandwidth. Foldover for Two Ions of Widely Separated m / z : Nz+ and Ar+. The ion cyclotron frequencies of Ar+ and Nz+differ by about 50 kHz a t a magnetic field strength of 3 T. Thus, heterodyne simultaneous detection of both ions would require a digitizer rate 2100 kHz, with a concomitant limitation on digital mass accuracy of 15 ppm for a 2 Kword frequencydomain discrete spectrum. However, low-frequency digitization (1.533-kHzdigitizer bandwidth) of the ICR signals from a bandwidth spanning a frequency range between the ICR frequencies of Ar+ and Nz+yields a high-resolution FT/ICR mass spectrum with mass accuracy of 0.2-1.0 ppm for a frequency-domain data set of only 2K points, as shown in Figure 4. Although noise at frequencies intermediate between the ICR frequencies of Nz+ and Ar+ is folded into the detected bandwidth, the signal-to-noise ratio in the final foldover spectrum is still satisfactory.
-
2a 012
2 a 020
2a 028
M A S ?(a mu) Flgure 3. Comparison of conventional heterodyne (bottom)and foldover (top) FTlICR mass spectra of an electron-ionized mixture of Torr, produced as carbon monoxide and nitrogen at 1.4 X shown schematically In Figure 1 (middle and rightmost columns, respectively). Although the top spectrum represents 1072 foldovers for N,+ and 1073 for CO', the foldover spectral mass resolution (450000:1), mass accuracy (-0.2 pprn), and signal-to-noise ratio are comparable to those obtained with the usual heterodyne method.
-
FOLDOVER
+
-1
1.5
Nz+ %A
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03
01
FREQUENCY(KHz)
High-resolution foldover FT/ICR mass spectrum of electron-ionized nitrogen and argon at -1.5 X lo-' Torr, produced as shown schematically in Figure 1 (rightmost column). The frequency scale for this spectrum Is the same as that for Figure 3. Although the actual mass difference between N,+ and Ar' is 12 amu. mutiple foldover places both ICR peaks in a single narrow-band spectrum. The foldover spectral mass resolution (450000:1 for N,+ and 329000:1 for Ar', respectively) and mass accuracy (0.2 and 1 ppm for N+ , and Ar', respectively) are comparable to those obtained for separate heterodyne narrow-band experiments on N,+ or Ar' alone. Flgure 4.
-
Multiple Ion Monitoring by Foldover FT/ICR: HzO+, CO', N2+,02',NzO', and COz'. Although mass spectrometry is becoming increasingly popular for monitoring of inspired and respired air during surgical operations (12),the typical mass spectrometer configuration is either a quadrupole (e.g., Centronic, Inc., Mountainside, NJ) or a MattauchHenog with multiple detectors (Masstron, Inc., Boulder, CO), both of which can readily cover the necessary mass range from about 18 (molecular ion of water) to about 44 (molecular ion of COz), but which are limited to at best 1 amu resolving power. Unfortunately, much higher mass resolution (>3000)is required to distinguish either of two isotopic pairs of potentially vital importance: poisonous carbon monoxide ( m / z
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VOL. 60,NO. 4, FEBRUARY 15, 1988
CHEMISTRY,
ANALYTICAL
isotope peak of M+ for both the reference and unknown bases, particularly when the difference in basicity is large and the (M + H)+ abundance is small compared to that of the carbon-13 isotope of M’.
FOLDOVER N20-
21
17
19
15
13
11
3
FREQUENCY(KHZ) Figure 5. Higkresolutiin foldover FT/ICR mass spectrum of a mixture of respiratory gases with carbon monoxide and nitrous oxide general anesthetic. Although the detected ions span a mass range of -26 amu, all six molecular ions are observed simultaneously, at mass resolution sufficient to distinguish CO+ from N,+ at nominal mass 28, and N,O+ from C02+ at nominal mass 44. The number of foldovers differs for different ions.
27.9944 for CO+) vs molecular nitrogen (m/z28.0056 for N2+), and carbon dioxide ( m / z 43.9893) vs nitrous oxide general anesthetic ( m / z 44.0005 for N20+). Because nitrous oxide (N20)is such a common general anesthetic (13), it would be especially useful to be able to monitor N20+independently of COz+by mass spectrometry (rather than by background subtraction, as a t present), while simultaneously monitoring the other gaseous species of interst. Figure 5 clearly shows that multiple-foldover FT/ICR can provide rapidly ( 1s) a mass spectrum in which H20+,CO’, N2+,02+, NzO+,and COP+can be monitored simultaneously, with resolution sufficient to distinguish N20 from C02 and CO from N2 It is worth noting that the digitizer bandwidth in this example happened to give a spectrum in which the peaks are correctly ordered from low mass to high mass-in general, foldover will not leave the peaks in their correct relative order. Other Applications. The previous examples show that multiple-foldover FT/ICR offers high-resolution multiple-ion monitoring of ions of widely different m / z in a single mass spectrum (Figures 4 and 5). Another general class of applications is to distinguish natural abundance carbon-13 isotope peaks from protonated species (e.g., 12CxHy+l+from 13C12C,-,H,+) in determinations of gas-phase ion/molecule reaction rate constants and equilibrium constants. For example, in a gas-phase basicity experiment, the unknown and reference bases may differ widely in mass, but it is nevertheless desirable to be able to resolve (M + H)+ from the carbon-13 N
CONCLUSIONS In summary, the multiple-foldover FT/ICR technique provides the first method for combining high mass resolution and wide mass range in a single mass spectrum. The method is particularly well-suited for monitoring ions of widely separated (known) mass and unknown relative abundance. As in any high-resolution mass spectrometric experiment, one should first perform a broad-band experiment, in order to identify the species to be monitored, and only then design the foldover conditions to monitor ions of specified m / z values. Although random noise will be folded into the observed spectrum, “chemical” noise from other species can be eliminated by selective excitation, either by successive single-frequency or frequency-sweep irradiation or (preferably) by means of stored-waveform (14-1 7) simultaneous excitation. Registry No. HzO, 7732-18-5; Nz, 7727-37-9; 02,7782-44-7; COP, 124-38-9; NzO, 10024-97-2;CO, 630-08-0. LITERATURE CITED (1) Marshall, A. G.; Comisarow, M. B.; Parisod, G. J. Chem. Phys. 1979, 77, 4434-4444. (2) Marshall, A. G. Acc. Chem. Res. 1985, 18, 316-322. (3) Comisarow, M. B.; Marshall, A. G. Chem. Phys. Letf. 1974, 2 5 , 282-283. (4) Cornisarow, M. B. Fourier. Hadamard, and Hilbert Transorms in Chemistry; Marshall, A. G., Ed.; Plenum: New York, 1982; pp 125-146. (5) Lathi, B. P. Communications Systems; Wlley: New York, 1968; p 89. (6) Marshall, A. G. Physical Methods ln Modern Chemical Analysis; Kuwana, T., Ed.; Academic: New York, 1983; Vol. 3, pp 57-135. (7) Chen, L.; Marshall, A. G. Chemom. Intell. Lab. Syst. 1986, 7 , 51-58. (8) Horlick, G.; Hall, R. H.; Yuen, W. K. Fourier Transform Infrared Spectroscopy;Ferraro, J. R., Basile, L. J., Eds.; American Chemical Society: Washington, DC, 1982; Vol. 3 pp 37-81. (9) Cody, R. B.; Kinslnger, J. A. Anal. Chem. 1088, 58,670-671. ( I O ) Cody, R. B.; Kinslnger. J. A,; Goodman, S. D. Anal. Chem. 1987, 59, 2567-2569. (11) Verdun, F. R.; Ricca, T. L.; Marshall, A. G. Appi. Spectrosc., in press. (12) Sodal, I. G. Low Flow snd Closed System Anesthesia; Aldrete, J. A., Ed.; Grune de Straton: New York, 1979; pp 167-182. (13) Lawler, P. G. General Anaesthesia, 4th ed.; Gray, T. G., Ed.; Butterworth: London. 1980. on 1006-1008. rr ----(14) Marshal(-A:G.’; Wang, T.-C. L.; Rlcca. T. L. J. Am. Chem. S O ~ . 1985. 107. 7893-7897. (15) Wang, T.-C. L.; Ricca, T. L.;Marshall, A. G. Anal. Chem. 1988, 58. 2935-2940. (16) Chen, L.; Wang, T . 4 . L.; Rlcca, T. L.; Marshall, A. G. Anal. Chem. 1987, 59,449-505. (17) Chen, L.; Marshall, A. G. Rapid Commun. Mass Spectrom. 1987, 7 , 39-42.
RECEIVED for review July 13,1987. Accepted October 15,1987. This work was supported by grants (to A.G.M.) from the U S . Public Health Service (N.I.H. GM-31683), the National Science Foundation (CHE-8617244), and The Ohio State University.
