J. Phys. Chem. 1992, 96, 9696-9703
9696
one referee for some interesting suggestions and to Professor Mark Ratner for useful comments. One of us (A.B.) gratefully acknowledges a fellowship provided by Ministerio de EducaciBn y Ciencia of Spain. Registry No. HCN, 74-90-8.
References and Notes (1) McDonald, J. D. Annu. Reu. Phys. Chem. 1979, 30, 29. (2) Smalley, R. E. J . Phys. Chem. 1982, 86, 3504. (3) Crim, F. F. Annu. Reu. Phys. Chem. 1984, 35, 657. (4) Miller, R. E. J . Phys. Chem. 1986, 90, 3301. (5) Hamilton, C. E.; Kinsey, J. L.; Field, R. W. Annu. Reu. Phys. Chem. 1986, 37, 493. (6) Quack, M. Annu. Reu. Phys. Chem. 1990, 41, 839. (7) Khundkar. L. R.: Zewail. A. H. Annu. Rev. Phvs. Chem. 1990.41. 15. (8) Carney, 6.D.;Sprandel; L. L.; Kern, C. W. Adu. Chem. Phis. 1978, 37, 305. (9) Tennyson, J. Comput. Phys. Rep. 1986, 4 , 1 . (10) Johnson, B. R.; Reinhardt, W. P. J . Chem. Phys. 1986, 85, 4538. (11) Ezra, G. S.; Martens, C. C.; Fried, E. L. J . Phys. Chem. 1987, 91, 3721. (12) Smith, B. S.;Shirts, R. B. J . Chem. Phys. 1968, 89, 2948. (13) Gerber, R. B.; Ratner, M. A. Adu. Chem. Phys. 1988, 70, 97. (14) Comput. Phys. Commun. 1988, 51. Thematic issue on molecular vibrations. (15) Bacic, Z.; Light, J. C. Annu. Reu. Phys. Chem. 1989, 40, 469. (16) Handy, N. C. In?. Rev. Phys. Chem. 1989, 8, 275. (17) Halonen, L. J . Phys. Chem. 1989, 93, 3386. (18) Sibert, E. L. Int. Rev. Phys. Chem. 1990, 9, 1 . (19) Wallace, R. Chem. Phys. 1975, 11, 189. (20) Wallace, R. Chem. Phys. 1982, 71, 173. (21) Wallace, R. Chem. Phys. 1983, 76, 421. (22) Thompson, T. C.; Truhlar, D.G.J. Chem. Phys. 1982, 77, 3031. (23) Lefebvre, R. Int. J . Quantum Chem. 1983, 23, 543. (24) Moiseyev, N . Chem. Phys. Lett. 1983, 98, 233. (25) Stefanski, K.; Taylor, H. S.Phys. Rev. 1985, A31, 2810.
(26) Bacic, Z.; Gerber, R. B.; Ratner, M. A. J . Phys. Chem. 1986, 90, 3606. (27) Horn, T. R.; Gerber, R. B.; Ratner, M. A. J . Chem. Phys. 1989,91, 1813.
(28) Bowman, J. M.; Ziifiiga, J.; Wierzbicki, A. J . Chem. Phys. 1989, 90, 2708. (29) Ziifiiga, J.; Bastida, A.; Requena, A.; Hidalgo, A. J . Phys. Chem., 1991, 95, 2292. (30) Hildalgo, A.; Ziifiiga, J.; Frances, J. M.; Bastida, A.; Requena, A. Int. J . Quantum Chem. 1991, 40,685. (31) Colbert, D. T.; Sibert, E. L. J . Chem. Phys. 1989, 91, 350. (32) Hutson, J. M.; Jain, S. J . Chem. Phys. 1989, 91, 4197. (33) Fleming, P. R.; Hutchinson, J. S. J . Chem. Phys. 1989, 90, 1735. (34) Gazdy, B.; Bowman, J. M. Chem. Phys. Lett. 1990, 175,435. (35) Gazdy, B.; Bowman, J. M. J . Chem. Phys. 1989, 91, 4615. (36) Gazdy, B.; Bowman, J. M. J . Chem. Phys. 1991, 95, 6309. (37) Bowman, J. M. Acc. Chem. Res. 1986, 19, 202. (38) Gerber, R. B.; Ratner, M. A. J . Phys. Chem. 1988, 92, 3252. (39) McCoy, A. B.; Sibert, E. L. J. Chem. Phys. 1991, 95, 3476. (40) Bastida, A.; ZBfiiga, J.; Molina, A. M.; Requena, A. Int. J . Quantum Chem. 1992, 42, 475. Zfifiiga, A,; Bastida, A.; Requena, A. J . Phys. Chem. 1992, 96,4341. (41) Christoffel, K. M.; Bowman, J. M. Chem. Phys. Lett. 1982, 85, 220. (42) Murrell, J. N.; Carter, S.; Halonen, L. 0.J . Mol. Spectrosc. 1982, 93, 307. (43) Bacic, Z.; Light, J. C. J . Chem. Phys. 1987,815, 3065. (44) Chang, B. H.; Secrest, D. J . Chem. Phys. 1991, 94, 1196. (45) Bentley, J. A.; Brunet, J. P.; Wyatt, R. E.; Friesner, R. A.; Leforestier, C. Chem. Phvs. Lett. 1989. 161. 393. (46) Brunkt, J. P.; Friesner, R. A.; Wyatt, R. E.; Leforestier, C. Chem. Phys. Lett. 1988, 153, 425. (47) Dunn, K. M.; Boggs, J. E.;Pulay, P. J . Chem. Phys. 1986,85, 5833. (48) Szalav. V. J . Chem. Phvs. 1990. 92. 3633. (49) Bacic; Z. J. Chem. PhG. 1991,95, 3456. (50) Leforestier, C. J . Chem. Phys. 1991, 94, 6388. (51) Moieseyev, N. Chem. Phys. Lett. 1985, 119, 388. (52) Hylleraas, E. A.; Undheim, B. 2.Phys. 1930,65,769. MacDonald, J. K. L. Phys. Reu. 1933, 43, 830.
Hadamard Transform Imaging Spectrometer for Time- and Energy-Resolved Photofragmentation Spectroscopy J. A. Smith, J. Winkel, N. C. Cotts,+ A. J. Stace, School of Molecular Sciences, University of Sussex, Brighton BNl 9QJ, U.K.
and B. J. Whitaker* School of Chemistry, University of Leeds, Leeds LS2 9JT, U.K.(Received: March 23, 1992)
A novel design for a time-of-flight mass spectrometer capable of imaging/detecting neutral species is described. The device uses a microchannel plate (MCP) detector and phosphor screen optically coupled to a photomultiplier tube by means of a fiber optic bundle through the vacuum chamber wall. The use of specially constructed Hadamard masks placed between the back of the optic fiber bundle and the photomultiplier tube allows positional information across the plane of the MCP detector to be extracted. Velocity- and energy-resolved photodissociation spectra of neutral photofragments can be obtained. This is illustrated for the case of the 532-nm photodissociation spectra of Ar2+and Ar3+.
Introduction Techniques capable of the direct imaging of reaction product velocity distributions have been developed recently.'-' Hitherto the velocity distribution has been determined by photoionizing the appropriate product species and accelerating the resultant ions onto an imaging detector using a pulsed electric field. The image is then a two-dimensional projection of the three-dimensional velocity distribution. This paper describes a new technique for recording the distributions, which has the advantage of temporal as well as spatial resolution. The experiment we describe also differs from previously reported photofragment imaging experim e ~ ~ t sinl -that ~ neutral product species are detected directly, and 'Resent address, Department of Chemistry, University of California, Santa Barbara, CA 93106.
only a single element detector is used. The basis of the method is the Hadamard transform. The use of Hadamard transform (HT) techniques to improve the performance of spectrometers and imaging devices has been described by a number of authors (see refs 8-12 for detailed reviews). In principle, HT instruments have a factor 2l/* signal-to-noise (S/N) advantage over interferometric spectrometers whose operation is based on the Fourier transform.* The HT formalism can also accommodate multiplexing schemes in which pseudorandom sequencesare employed to modulate data streams.13 These latter techniques have been applied in molecular beam scattering experiments to enhance t h r ~ u g h p u t ' ~and J ~to improve the temporal resolution obtainable from synchrotron sources.16 Hadamard sequences have also been used to improve efficiency in tandem Fourier transform mass ~pectrometry,'~ and weighing
0022-3654/92/2096-9696$03.00/00 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9697
Hadamard Transform Imaging Spectrometer TABLE I: The S,,Matrix" 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1
0 0 1 0
0 1 0 0
1 0 0 1
0 0 1 1
0 1 1 0
1 1 0 1
1 0 1 0
0 1 0 1
1 0 1 1
0 1 1 1
1 1 1 1
1 1 1 0
1 1 0 0
1 0 0 0
0 1 1 0 1 0 1 1 1 1 0
1 1 0 1 0 1 1 1 1 0 0
1 0 1 0 1 1 1 1 0 0 0
0 1 0 1 1 1 1 0 0 0 1
1 0 1 1 1 1 0 0 0 1 0
0 1 1 1 1 0 0 0 1 0 0
1 1 1 1 0 0 0 1 0 0 1
1 1 1 0 0 0 1 0 0 1 1
1 1 0 0 0 1 0 0 1 1 0
1 0 0 0 1 0 0 1 1 0 1
0 0 0 1 0 0 1 1 0 1 0
0 0 1 0 0 1 1 0 1 0 1
0 1 0 0 1 1 0 1 0 1 1
1 0 0 1 1 0 1 0 1 1 1
"The matrix is generated using a maximal length shift-register sequence obtained from the primitive polynomial of degree 4, x4 + x + 1. The shift register generates an infinite sequence which satifies the recurrence relation, si+4 = s,+, +2 si, where +2 signifies addition mod 2, and i = 0, 1, ..., . designs based on Hadamard matrices have been proposed to improve the precision of collisional cross-section measurements.'* The idea behind these applications is to gain a multiplex (FellgettIg)advantage compared with sequential data acquisition. Thus Hadamard transform methods are similar to those employing the Fourier transform but have certain computational advantages in that the fast Hadamard transform algorithm will run about 8-10 times faster than the fast Fourier transform on the same number of data points.I0 The concept of a 2D imaging device using only a single element detector was proposed by Gottlieb.20 Since then a number of such instruments have been designed, many in the field of high-energy astronomical imagers (X-and y-ray telescope^).^ Harwit and co-workers2'*22 in particular have developed a number of instruments which combined Hadamard masks for spatial resolution with a dispersive element to achieve spectrometric imaging, mainly in the infrared. More recently, the approach has been applied to photoaco~stic,~~ photothermal d e f l e c t i ~ nand , ~ ~RamanZ5imaging. In spatially modulated instruments, the object is imaged onto a 2D mask. The mask is a spatial pattern of elements that either transmit or block the incident signal. If the mask consists of n X m such elements, then by measuring the intensity passing through n X m independent such masks successively placed at the focal plane it is possible to reconstruct the object image. The important question in designing an instrument of this sort is clearly that of deciding on the optimum mask design so as to maximize the S/Nratio. It turns out that the most suitable masks are those generated from a Simplex matrix (see Appendix), the idea being to maximize the signal while at the same time masking each of the picture elements in turn with as few combinations as possible. For the masks described in the Appendix each one transmits approximately 50% of the incident light if uniformly illuminated. In practice, the intensity in each picture element (pixel) of the image will not, in general, be the same, and so the total intensity transmitted through a given mask will vary according to the shape. The intensity of each pixel is recovered by making a matrix transformation on the series.of measured transmitted intensities. The required transformation is described in detail in the Appendix. It is
where J, i s an n X n matrix of 1's and s,, is the transpose of the matrix describing which elements in each of the masks are open and which are closed. An example of this matrix, S15,is shown in Table I. The resolution of the recovered image is obviously dictated by the number of masking elements. In the present example this will not be very great; however, a number of realistic imaging applications using the technique have been reported in the literaturees The advantage of the HT method over a simple raster scan, in
which a single element mask would be scanned over the input image, is that by multiplexing the measurements a better S/N ratio can be obtained in the recovered image. The number of independent measurements needed for both methods is the same but because in the HT method the pixels are measured in groups rather than one at a time a Fellget advantage is obtained, leading to an improvement of order (t1/4)'/~ in the S/N ratio. In the instrument described below we show how particles resulting from the photodissociation of an ion cluster can be imaged using only a singleelement detector. The basic apparatus for these types of experiment consists of a mass spectrometer which feeds a time-of-flight (TOF) device mass and kinetic energy resolved ions. At the entrance to the TOF tube the ion beam is then crossed with the output of a laser whose frequency is such as to excite the ion to an unbound state. The measurement consists of determining the velocity vector of the photofragments, or, more crudely, in determining the kinetic energy of the fragments along a given direction. This information can then be used to determine the time scale of the photodissociation and also the symmetry of the photoexcited state.26 The angular distribution of the photofragments has been considered by a number of author^.^'-^^ Typically, the angular distribution of the photofragments is characterized by the laboratory frame anisotropy parameter, 8, in the equation I ( @ )a ( 4 ~ ) - [' 1 + @P~(COS e)]
(2)
where P2(x) is the second-order Legendre polynomiial and 6 is the recoil velocity relative to the polarization vector of the photolysis laser. The anisotropy parameter is given by29
(3) where T is the decay time of the unbound state, w is the rotational frequency of the parent state, and x is the angle between the parent transition dipole moment and the recoil velocity vector of the fragment. The value of 0 will lie between two extremes. For the instantaneous dissociation (T = 0) of a diatomic molecule, its value is -1 for dissociation perpendicular to the transition dipole, p, or 2 for dissociation parallel to p. In general, since the dissociation takes place on a finite time scale and since in the dissociation of a polyatomic species the recoil velocity can have some angle which is neither parallel nor perpendicular to the transition dipole, the measured 8 will fall between the two extremes. If the initial state of the ion cluster, before the photolysis laser pulse, is not welldefined, as is the case in the general experiment described above, then we expect to see a range of energies in the kinetic energy release spectrum even for complete dissociation into structureless fragments. However, provided that the decay time, T , of the excited state is less than the rotational period, w , we, nevertheless, expect to observe an anisotropy in the fragment recoil velocity with respect to the polarization vector of the photolyzing light. Therefore, if we arrange the polarization vector of the photolysis laser to lie along the direction of the ion beam, and if the bound-free transition dipole is parallel to it, we will see a range in the arrival times of the photofragment particles at a detector placed downstream of the intersection point of the laser and the ion beam. The range of arrival times will correspond to the range of directions and speeds in the recoil velocities of the fragments. It is possible to configure the detection system such that both temporal and spatial resolution can be achieved. With the polarization of the laser arranged so that the fragments fly perpendicular to the direction of the parent ion beam, spatial resolution is achieved by replacing the single detector above by a set of detectors. In this paper we consider the case where each detector in such a set takes the form of an annular strip. This could be done, for example, by using a set of resistive anodes placed behind a microchannel plate (MCP). Our approach, which is described in more detail below, has been to place masks between a MCP/scintillation detector and a photomultiplier. If the outer radius squared of an individual detector is proportional to total radius of the scintillation screen divided by the number of detectors,
Smith et al.
9698 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 slngle Focusstng Det j c tor
HV feed-through -I 8ooV
Photomulhplier lube
Fibre-ophc bundle
DlffuslOn/ PUmD
w
nlcrochannel
Figure 2. Schematic of the mask and phototube arrangement.
Figure 1. Schematic of the apparatus. The dissociation laser enters the port close to the ion focus at the exit of the electric sector analyzer ( S A ) in a field-free region (FFR)of the instrument. Ionic species are deflected by a charged plate in the time-of-flight tube. The phosphor screen and masks are positioned behind the microchannel plates at the end of the flight tube.
the detectors form a set of “bins” that are linear in the transverse kinetic energy of the photofragments. This is because the distance across the plane of the detector traveled by a fragment from time of dissociation to the time of detection will be proportional to the (transverse) fragment velocity. The kinetic energy resolution is adjusted, by altering the initial forward velocity of the parent ion beam and/or the length of the flight tube, so that the fastest moving photofragments fall in the outermost ring. Greater resolution can be realized in one or more of three ways: lower accelerating voltage, longer flight tube, increased number of detectors. In the Appendix (eq 25) we show that by multiplexing the measurements using a Simplex matrix the S/N ratio can be improved by a factor of -8 over the experiment in which the ions falling in each detector bin are simply measured sequentially. This is an important consideration in cluster ion dissociation experiments since the parent ion flux is typically -lo9 ion s-l and the laser pulse duration is typically lo-* s (Q-switched Nd:YAG laser) which means that even for a quantum yield of 1 at most only 10 photofragments can be produced per laser pulse. Indeed in some of our previous experiment~~’.~~ we have worked with counting rates lower than 1 ion s-l.
-
Experimental Section The basic experimental setup has been described elsewhere.33 Briefly, a combined supersonic nozzle and high-resolution doublefocusing mass spectrometer is used to prepare mass and kinetic energy resolved ion clusters. A schematic of the apparatus is shown in Figure 1. Ion clusters transmitted by the electrostatic sector pass through a pair of 3 mm diameter collimating holes separated by about 30 mm into a time-of-flight apparatus ca. 2 m long. The length of the flight time can be fine tuned by adjusting the ion acceleratingvoltage. At the entrance to the flight tube the ion beam is intersected by the output from a frequency-doubled Nd:YAG laser (Spectron SL401). A typical pulse energy at 532 nm is 60 mJ in a 10-15-11s time profile. Downstream from the laser ion beam interaction zone, an off-axis electrode, charged to a potential of -1.5 kV, is used to deflect any ionic photofragments and undissociated parent ions. The neutral photofragments continue to travel down the flight tube with a laboratory frame centersf-mass velocity equal to that of the parent ion cluster beam. At the end of the flight tube the neutrals strike the surface of a chevron-style microchannel plate (MCP) detector (Instrument Technology Ltd.). Since the neutrals have a laboratory frame kinetic energy similar in magnitude to that of the parent ion beam (3-8 keV) they are sufficiently energetic to excite the MCP and emit secondary electrons. Behind each point where
Figure 3. Hadamard masks for kinetic energy release measurements. Each ring of each mask is filled or not according to the elements of the rows of S15(Table I). The radius of each ring in a mask scales as i’I2R, where R is the radius of the MCP detector and i is the number of the ring element. Thus, when printed on acetate and placed over the phosphor screen each mask consists of IS rings whose widths scale as the kinetic energy release as measured across the face of the phosphor.
a neutral strikes the detector, the amplified electrons are accelerated onto the end of a fiber-optic bundle, which is coated with a fast phosphor (P47,80 ns response). The bundle is fed through a flange to the exterior of the vacuum chamber where the signal, now a 2D image, can be detected optically. By maintaining the pressure in the flight tube to UHV conditions Torr) collisional ionization of the background gas can be avoided and, as a result, the background noise level is extremely low. The gain produced by the MCP chevron is about 8 X lo6 under typical operating conditions (-800 V between front and back surfaces of each plate). In previously reported photofragment imaging experiments’-’ the spatial distribution of the fragments was obtained by directly recording the image on the fiber-optic screen. This is done using a gated image-intensified electronic camera. There are, however, some disadvantages to this approach. One is cost. At a more fundamental level the method cannot be used easily for timeresolved measurements. Although the camera can be gated to capture an image at a particular time delay from the dissociating laser pulse, it is not possible to obtain a time sequence of images because of the readout time of the camera chip. For chargecoupled devices (CCD’s) this can mean an order of several mi-
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9699
Hadamard Transform Imaging Spectrometer """
I
I
0'
I
I
18.4
'
I
I
I
I
I
18.6
18.8
19
19.2
I
19.4
(cp)
"e
Figure 4. Distribution of arrival times of neutral argon atoms following the 532-nm photolysis of At2+ in the entrance of the TOF device. The laser polarization vector was parallel to the ion beam velocity vector, and the ion source voltage was 6 kV. 180
I
I
I
I
160
I
A+: BT at 6kV
: 20
18.4
18.6
18.8 . *(CUI
19.2
19
Figure 5. As in Figure 4, but with the laser polarization vector perpendicular to the ion beam velocity vector.
c"ds dead time. Of course this problem could be overcome by scanning the intensifier gate in time on sequential laser shots; however, we would like to propose an alternative method which, although of rather limited spatial resolution, can provide temporal information on the nanosecond time scale, and in which the camera can be replaced by a simple photomultiplier tube.
1-1 I-[
m
m m m m
=
28 25 - 28 22 - 25 20 - 22 18 - 20 15 - 18 12 - 15 10 - 12
ABOVE
8
-
10 5- 8
2 BELOW
In our experiment the image is obtained by measuring the light intensity passing through a mask placed directly over the phosphor screen. An expanded diagram of this part of the experimental apparatus is shown in Figure 2. The light is then detected by a photomultiplier tube (EM1 9816B),and the output sent, via a fast preamplifier (EGBtG model VT120), to a multichannel scalar (SRS Model 430) which is triggered from the photolysis pulse by means of a photodiode. So far we have constructed the masks to be linear in energy space, but masks that are linear in velocity space could also be constructed. In the current experiment all the rings have the same area in energy space. So given a detector of radius R to be divided up into 15 "bins" the outer radius of the ith mask element is given by
r, = (i/15)'i2R
(4)
In a mask which resolves velocity, the widths of all the elements would be the same. The 15 energy masks used in the experiments are shown in Figure 3;each consists of 15 rings which for the ith mask are filled, or not, according to the elements of the ith row of SIS(see Table I). This was done using a drawing package (MacDraw) on a microcomputer. The resultant image file was then printed onto an acetate sheet using a laser printer. Each acetate mask is placed, in sequence as determined by Sls,over the phosphor screen of the channel plate/scintillation detector. The energy resolution could be improved, in principle, by increasing the number of masking elements. However, the size of the mask elements in relation to the diameter of the parent ion beam is about 1:1 with the current experimental configuration. That is, the area of ion beam spot observed on the phosphor roughly matches the area of central mask element so that increasing the number of mask elements would be ineffective because of the divergence of the parent ions. Further improvement to the resolution of the instrument will necessitate improvement of the ion-focusing at the exit of the ESA to produce a collimated ion beam. This will also improve the throughput.
Results and Discussion Figure 4 shows a typical photofragment timeof-flight spectnrm for the 532-nm photolysis of Ar2+recorded by the multichannel scalar. The accumulated signal for 32 500 laser shots is shown
n v) 50Q)
E .I-
-
-
-
25-
-
5 2
I
I, 2.5
5.0
7.5
10.0
12.5
15.0
Energy (mask units) Figure 6. Timeresolved kinetic energy release spectrum for argon atoms following 532-nm photofragmentation of Ar2+. The laser polarization was as in Figure 5 (i.e., perpendicular). The abscissa represents the energy bin (see text) and the ordinate the time axis. At early times the maximum particle flux appears in the low-energy bins. As time goes on the flux moves out to higher energies and an a hole appears in the center of the image. At still longer times the flux moves back toward the center of the image. The contours are the total number of counts recorded.
9700 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992
2600 -
3000
2OOoh8nb 1600
-
7 /7.1 600
022.6
w
'
1
1
I
22.8
23
23.2
23.4
Time (14
1 J
23.6
Figure 7. As in Figure 4, but for ATj+.
in the figure. At a repetition rate of 10 Hz this requires about 50 min. The time digitization is 5 ns and is slightly smaller than what the experimental parameters, in particular the phosphor decay time, would warrant. In this spectrum the polarization of the laser lies parallel to the parent ion beam velocity vector and perpendicular to the channel plate detector face. The arrival time distribution shows that this is a parallel transition, with the neutral fragments being scattered both forwards and backwards along the direction of the parent ion beam, Le., along the laser polarization vector. The parent and photofragment ions are not detected because of the deflection plate upstream. The kinetic energy release spectrum of the neutral Ar atoms is similar to that previously observed for the ionic ph~tofragment,~~ although the resolution and S/N ratio are better.35 Figure 5 shows the time-of-flight spectrum accumulated for 32500 laser shots and worded through one of the S-matrix masks with the laser polarization parallel to the channel plates (perpendicular to the ion beam). Now only a single peak is observed because the fragments are predominantly recoiling perpendicular to the parent beam velocity vector as a result of the parallel nature of the transition moment. Figure 6 shows the result of performing the reconstruction algorithm (eq 1) on 15 TOF spectra, one for each mask. This is done on each time "bin" in the time-of-flight spectra in turn
0 ABOVE 50' 45 - 50 0 40 - 45 36-40
= = m m =
32 - 36 27 - 32 22 - 27 I8 - 22 14-18 9 - 14 4- 9 BELOW 4
Smith et al. to obtain time series of kinetic energy release spectra. The anisotropy of the photofragments is clearly observed. Across the image are a series of kinetic energy release spectra recorded for different arrival times (down the image). The ion count in each energy-time bin is color coded according to the scale in the figure. Although the discrete time and energy bins have been smeared by the contouring algorithm, certain features are apparent. A "fringe- pattern running vertically through the figure (energy bins 4,8, and 12 seem to show anomalously low ion counts) is probably due to inaccuracies in the mask register. This leads to image "ghbsting"? The resolution is also limited by the finite diameter of the parent ion beam. In future experiments we plan to improve the resolution by the use of more rigid masks and improved ion optics. The physical interpretation of Figure 6 is as follows. At time zero (arbitrary origin) the neutral particles (Ar atoms) resulting from the laser-induced dissociation of ArZ+have not yet reached the detector, and the flux recorded in all the energy bins is close to zero. At around 20 ns from the time origin the fastest-moving particles arrive at the detector. The maximum flux for these particles appears in the low-energy bins. As time goes on, the flux moves out to higher energies and a hole appears in the center of the image, because the particle flux at this point (40 ns) has a velocity vector almost parallel to the plane of the detector as a result of the correlation between the plane of polarization of the dissociating laser and photofragment velocity. The kinetic energy release spectrum at this point in time should be similar to that obtained with a single detector and the polarization vector parallel to the parent ion beam (Figure 4), although the resolution should be better. Therefore, there should be a low particle flux in the low-energy bins, as observed in Figure 6 around 40 ns from the time origin. At still longer times the flux moves back toward the center line, until finally around 75 ns from the time origin even the slowest moving neutral photofragments have been detected. The figure only shows the modulus of the energy distribution because each mask is radially symmetric; i.e., the current implementation of the experiment does not distinguish which sector the particle strikes the detector. The greatest resolution is achieved at the midpoint of the arrival times, since at that time the fragment velocities are all perpendicular to the flight direction. At shorter
25
I
I
I
I
2.5
I
I
I
5.0
7.5
10.0
12.5
15.0
Energy (mask units)
Figure 8. As in Figure 6, but for Ar,+. The figure shows a low-energy dissociationchannel, in which the fragmentsappear to be isotropically scattered, and a higher energy dissociation channel, in which the photofragments are anisotropically scattered.
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9701
Hadamard Transform Imaging Spectrometer
cR
because of the isotropically scattered low kinetic energy neutrals that are ejected when Ar3+is photolyzed. It is interesting to note, however, that the anisotropy of the fast moving neutrals appears to be greater than in the case of Ar2+. This can be understood if Ar3+is a quasilinear species in which an Ar2+ chromophore, with the charge predominantly in the center of the chain, dissociates to produce both fast and slow photofragments.
Conclusion We have demonstrated a novel application of the Hadamard transform technique to measure the kinetic energy release spectra of neutral species following photolysis of ion clusters. The technique allows us to capture the temporal profile of the entire photodissociation scattering pattern. We have demonstrated the technique in a study of the 532-nm dissociation of Ar2+and Ar3+. There are significant differences in the patterns obtained for Ar2+ and Ar3+. The observed energy releases and spatial distributions are in agreement with previous studies33obtained by measuring arrival time distributions. The technique offers the potential for improved signal-to-noise because of a multiplex advantage over previous neutral TOF experiment^^^ which have employed sequential data acquisition. The resolution of the experiment reported above is, however, limited by problems assoCiated with mask register and by poor ion optics. We hope to overcome these problems in future experiments. O m
Figure 9. (a) A 15-pixel image of a white cross against a black background. (b) The first mask of the series generated from the S15Simplex matrix, as discussed in the text and the Appendix. (c) The image transmitted through the mask shown in Figure 9b; only 30 fthe white picture elements of Figure 9a are visible through the mask. (d-q) The remaining 14 masks generated from S15.When these are sequentially laid over the image and the visible pixels counted the result is the vector (eq 21) as discussed in the text. (s) A matrix operation on the measured quantities (eq 24) can be used to recover the original image in Figure 9a.
and longer times the kinetic energy release gives rise to velocity components parallel to the flight direction. At the center of the Ymage” the maximum flux falls in energy bins 6 and 7. This corresponds to a kinetic energy release of 1.2 eV. The value of the kinetic energy release is in agreement with that obtained from the TOF spectrum with the laser polarized along the ion beam velocity vector and a single detector (Figure 4). We arrive at the last result by noting that in the single detector TOF experiment the kinetic release, T,for the process
Mi+ + hv
+
Mz++ M3
(5)
expressed in terms of the flight time of the fragments is35
Acknowledgment. J.A.S. and N.G.G. would like to thank the Science and Engineering Research Council for the award of research studentships. The authors would also like to thank the SERC, the Royal Society, and the Paul Instrument Fund for financial assistance toward the development of the experiment. Acknowledgment is also made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. The authors are also extremely grateful to the referees for pointing out problems with the organization of a previous version of this paper. Appendix This appendix is devoted to a discussion of the general design of an HT experiment, and although all the details can be found elsewhere (see in particular ref 8) it is included for the benefit of those readers new to the technique. The ideas behind the HT were first developed in theories of the statistics of mea~urement.~~ In matrix notation one can represent a measurement by
m=Wo+e (7) where m is a column vector representing the measured quantities, mi, and likewise o represents the unknowns, oi,and e the uncertainties, ei. The matrix W, with elements wij, is called the design matrix. So, for example, if the measurements are made one by one, W is simply the identity matrix, I. From (7) we see that if the measurements were perfect (i.e. {ei)= 0 V i ) then o = W-’m
where Af is the difference in flight time between the fast and slow (forward and backward) peaks, L is the length of the flight tube, and Eo is the initial kinetic energy of the ion cluster. Figure 7 shows the distribution of arrival times for neutral species, presumably Ar atoms, following the photofragmentation of Ar3+with the laser polarized along the ion beam direction. The bimodal speed distribution evident in the figure has also been observed in the ionic dissociation channels (Ar+ and Ar2+)and has been attributed to the effects of intracluster collision/charge exchange dynamics on the excited-state repulsive surface of a quasilinear molecular ion.26 The time-resolved kinetic energy release spectrum for 532-nm photolysis of Ar3+obtained by taking the HT of the TOF spectra recorded through the masks is shown in Figure 8. The general form of the spectrum is in agreement with our previous results for the photofragmentation of this ion.35 The hole that was apparent in the case of Arz+ is now absent
(8)
but in any real experiment e # 0, and the best one can do is to obtain an estimate, p, of 0. In order to choose the optimum weighmg scheme so as to obtain the “best” estimate we make some assumptions about the errors. Assume that {ei)are random and unbiased, with variance d.Also assume that the detector response is linear, i.e. ei is independent of mi, and that the errors in different measurements are independent of one another, i.e. It is usual to seek an estimate, p, which is also unbiased, although there are arguments in favor of seeking a biased estimate.* On maximum entropy grounds we assume that p is a linear function of the measurements: p = Am (10) Substituting (7) into (10) we have p = A(Wo + e) (11)
9702 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992
which implies, on substituting (1 1) into (8), that (p) = AWo (12) given that (e) = 0. Since we seek an unbiased estimate (( p) = 0 ) we have AW-I (13) which implies p = W-'m
(14)
provided W-' exists. Ideally we would like to chose a design matrix which minimizes (ei)V i but this is usually not possible. One possibility is to choose the matrix W so as to minimize the value of the average mean square error, in which case W is called A-optimal. Now from eqs 7 and 12 it follows that pi
- oi = C1 w i f j
(15)
and therefore that the average mean error, e, is given by
Smith et al. a black background. Overlaying this image with the mask shown in Figure 9b to obtain the situation shown in Figure 9c only 50% of the cross is visible. Say that the total intensity transmitted through the mask is 3 units corresponding to the three white picture elements that are visible through the mask. When the 14 other masks shown in Figure 9 d q are sequentially overlaid, the sequence of measured intensities will be
bl = (3, 3, 5 , 3, 4, 4, 4, 3,6, 4, 3, 5, 2, 3, 41
(21) If q is the vector representing the separate measurements and o that representing the unknowns, then m = Sno
(22)
and o can be recovered by
2 o = S,,% = -(25, n+l
- Jn)m
where J, is an n X n matrix of 1's. Applying eq 23 to the set of measurements m we obtain the values
(0,1, 0,1, 1, 1, 0, 1, 0,0, 1, 0,0, 1, 01 (24) which describes the pixel values of the crass section in Figure 9a. The recovered image is shown in Figure 9s (the pixels are numbered from 1 to 15 left to right starting at the top left corner). Of course this example is extremely artificial and in general neither will the mask elements fit neatly over the structure in the original object nor will the input be a binary image, and as a consequence the image recovery will not be perfect. It is, however, possible to create spatial imaging masks of this type, and we have carried out some preliminary experiments of this kind. The basic idea here has been discussed in the Introduction. In these preliminary experiments we used the masks shown in Figure 9, and the spatial resolution was therefore extremely crude. However, we believe that experiments using a mask based on the S2ssmatrix would be feasible, particularly if an electrooptic mask was used for the encoding. The advantage of the method over a simple raster scan, in which a single-element mask would be scanned over the input image, is that by multiplexing the measurements a better S/N ratio can be obtained in the recovered image. The improvement in the variance is less for Simplex based masks than for Hadamard designs. One finds (0)=
=
-n Tr (6'W)-' U2
where %' denotes the transpose of W. Another possibility is to chose a W that maximizes IWl. This is equivalent to minimizing the general variance of the errors: u216'W-Il
(19)
Such a design is called D-optimal. One can shows that in the case of systems where the objects can be measured against one another, as in a chemical balance, that the best design schemes (in both the A and D senses) are given by Hadamard matries, H. A Hadamard matrix of order n is an n X n matrix with the property that the scalar product of any two distinct rows is 0. Thus H, must satisfy Ha = HH = n1 (20) The elements of H are f l , and n = 2 or, 0 mod 4, and hence Tr = 1 and e = u2/n. Thus, by choosing a Hadamard weighing design the variance in the measurements can be reduced by a factor of n. In many optical applications it is difficult to measure one intensity against another; either something is measured or it is not. It is possible to show that in this circumstance the best design scheme (at least D optimally) is given by a Simplex or S matrix.8 This matrix is obtained from a Hadamard matrix of order n + 1 by first "normalizing" Hn+l,that is to say permuting rows and columns so that the first column is made up of +l's, then deleting the first row and column, and finally replacing all the +l's with 0's and the -1's with +l's in the rest of the matrix. The rows of an S matrix are pseudorandom sequences containing an odd number of elements. There are three known constructions for S matrices. The most useful of these are derived from the maximal length shift-register sequence? since in this case there is an efficient transform algorithm similar to the CooleyTukey FFT algorithm for recovering the data. The method produces cyclic sequences of length n = 2" - 1, where m E N > 0. The sequence is obtained from a binary primitive polynomial of degree m. This primitive polynomial generates an infinite sequence so, sI,s2, ..., si, ... with period 2" - '1. Recipes for generating sequences up to n = 1 048 575 (or m = 20) are given by Hanvit and Sloane.8 The elements of the first period are taken as the first row of the S matrix. The next n - 1 rows of S are generated by left circulartly permuting the elements of the previous row. An example of an S matrix is given in Table I. To illustrate the method consider the very simple example shown in Figure 9. Figure 9a shows the image of a white cross against
e = 4nu2/(n
4u2/n
~ 2 :
+
for large n
(25)
(26)
However, the advantage is that S-matrix-based experiments are simpler to construct.
References and Notes (1) Chandler, D. W.; Houston, P. L. J . Chem. Phys. 1987, 87, 1445.
(2) Chandler, D. W.; Janssen, M. H. M.; Stoke, S.;Strickland, R. N.; Thoman, J. W.; Parker, D. H. J . Phys. Chem. 1990, 94,4839. (3) Thoman, J. W.; Chandler, D. W.; Parker, D. H.; Janssen, M. H. N . Laser Chem. 1988, 9, 27. (4) Baldwin, D. P.; Buntine, M. A.; Chandler, D. W. J. Chem. Phys. 1990, 93. - ,6578. -- ( 5 ) Suzuki, T.; Hradil, V. P.; Hewitt, S.A.; Houston, P. L.; Whitaker, B. J. Chem. Phys. Lett. 1991, 187, 257. (6) Buntine, M. A.; Baldwin, D. P.; a r e , R. N.; Chandler, D. W. J . Chem. Phys. 1991, 94,4672. (7) Suits, A. G.; Bontuyan, L. S.;Houston, P. L.; Whitaker, B. J. J. Chem. Phys. 1992, 96, 8618. (8) Harwit, M.; Sloane, N. J. A. Hadamard Transform Oprics; Academic Press: New York, 1979. (9) Carob, E.; Stephen, J. B.; Di Cocco, G.; Natalucci, L.; Spizzichino, A. Space Sci. Reo. 1987, 45, 349. (10) Treado, P. J.; Morns, M. D. Spectrochim. Acta Reo. 1990, 13, 355. (1 1) Griffiths, P. R., Ed. Transform Techniques in Chemistry; Plenum: New York, 1978. (12) Marshall, A. G.,Ed. Fourier, Hadamard andffilbert Transforms in Chemistry; Plenum: New York, 1978. (13) Hirshcy, V. L.; Aldridge, J. P. Reo. Sci. Instrum. 1971, 42, 381. (14) Secrest, D.; Meyer, H. D. Ber. Max-Plank-Inst.Stromungsforsch. 1972, 137.
(15) Comsa, G.; David, R.; Schumacher, B. J. Reo. Sci. Instrum. 1981,
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Vibrational Transition Probabilities in the B-X and B’-X Systems of the SiCl Radical Scott Singleton,+Kenneth G. McKendrick,* Department of Chemistry, The Uniuersity of Edinburgh, Edinburgh EH9 355, U.K.
Richard A. Copeland, and Jay B. Jeffries* Molecular Physics Laboratory, SRI International, Menlo Park, California 94025 (Receiued: May 14, 1992) Vibrational transition probabilities have been measured for the B2Z+(u’=0_3)“2~(~’’=Ck10) and B’2A(u’=0,1)-X211(u”=0_2) systems of SiCl. Individual vibronic levels of the excited states were prepared by laser excitation of ground-state Sic1 formed in a discharge-flow system, and the resultant emission was dispersed and recorded. Independent measurements made in two laboratories were in very satisfactory agreement. The extensive results for the B-X system were compared with Franck-Condon factors derived from Rydberg-Klein-Rees potentials, allowing the form of the electronic transition dipole moment function to be assessed. It was found that the electronic transition probability for the B-X system is relatively slowly varying with internuclear distance, consistent with previous conclusions on the electronic configurations of the states involved. The more limited data on the strongly diagonal Bf-X system were not readily reproduced from the accepted form of the potentials and the anticipated electronic transition dipole moment.
I. Introduction Quantitative spectroscopic information is valuable from at least two perspectives. It provides fundamental insight into the electronic and geometric structure of molecules, and it is also esscntial in the applied use of spectroscopy for the monitoring of concentrations of particular species. In this paper, we report experimentally-determined vibronic transition probabilities for the BZZ+-X211and B’2A-X211 systems of the Sic1 radical, which has been the subject of recent interest in the context of dry etching and deposition of silicon materials in the semiconductor industry.’-3 In addition to presenting this potentially useful information, we consider what these results reveal about the electronic character of the states involved. The Sic1 radical was first detected spectroscopically in 1914 by Jevons,4 who observed structure in the ultraviolet emission from the products of the reaction of S i c 4 vapor with active nitrogen. Subsequent early studies5v6revealed that many of the bands in the 200-300-nm region could be assigned to transitions involving a doublet state with a splitting of -200 cm-l. It was concluded that the ground state had 211 symmetry.’ Following further investigation?-” the first rotationally resolved spectraI2J3established conclusively the 211,2Z+, and 211 character of the X, B, and C states, respectively. Some outstanding difficulties remained over the assignment of the bands in the 280-nm r e g i ~ n but, , ~ after varied speculations?J1J4 higher resolution spectra established the presence of an additional Bf2Astate.IsJ6 In an extensive series of investigation~,”-~’ Bredohl and co-workers have characterized systematically the rotational structures of the A-, B-, Bf-, C-, D-,E-, *Towhom correspondence should be addressed. ‘Current address: Port Sunlight Laboratory, Unilever Research, Merseyside L63 3JW. U.K. 0022-3654/92/2096-9703$03.00/0
and F-X electronic transitions, improving on earlier work.’z’sJ6.~ Good agreement was found with the molecular constants for the X 2 n state derived from microwave measurement^.^^ More recently, the very high resolution Lamb dip measurements of Meijer et a1.25J6on the E X system have confirmed the values of constants deduced by Bredohl’s groupI8and also provided hyperfie splittings and the excited-state natural lifetime. A further recent has shown that Sic1 may be observed by resonance-enhanced multiphoton ionization through the C-, D-,and E-X systems. The potential curves for the known, lower, bound states of SiC1, derived by the well-established Rydberg-Klein-Rees (RKR) p r o c e d ~ r e ~from ~ - ~ ~the published molecular constants,’s~’7-2’~2s.27~3’~32 are shown in Figure 1. The excited states of interest in this study are the near-degenerate B22+and B’2A pair, around 35 OOO cm-1 above the X211ground state. As can be seen from this figure, the equilibrium internuclear separation (re = 2.036 A)Iss2’of the B’2A state is very similar to that of the ground state (re= 2.058 A),18*21325 whereas that of the B22+state is a little shorter (re= 1.971 A).’892s It is therefore to be expected that the B’ZA-X211 system will be strongly diagonal, with predominant Au = 0 vibronic transitions, in contrast to the B22+-X211 system which will exhibit longer progressions in vibration in emission (or absorption) from a given vibronic level. In this paper, we present experimental measurements of the fluorescence spectra emitted from single vibronic levels in the B2Z+ and Br2Astates to various vibrational levels of the X211ground state. The excited-state levels were prepared by selective laser excitation of ground-state radicals generated in a microwave discharge-flow system. The vibrational levels spanned were u’ = 0-3 in the B22+state, emitting to uf’ = 0-10 in the X211state, and uf = 0 and 1 in the B’2A state, emitting to u” = 0, 1, and 2 in the X211 state, respectively. The measurements were made independently in two laboratories (at Edinburgh University and 0 1992 American Chemical Society
