J. Phys. Chem. 1981, 85, 2599-2607
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FEATURE ARTICLE Laser Magnetic Resonance Spectroscopy P. B. Davles Department of phvsicai Chemistry, University of Cambridge, Cambridge CB2 lEP, United Kingdom, and Max-Planck-Institut fur Striimungsforschung,3400 CGttingen, West Germany (Received: May 8, 198 1)
Laser magnetic resonance spectroscopy is a powerful new technique for studying the rotational, vibrationrotational, or electronic spectra of free radicals, using fixed-frequency infrared lasers. This article describes the basic features of the experiment and the structural information derived from analyzing the measured Zeeman patterns. High resolution and sensitivity are important characteristics of laser magnetic resonance. In several cases species hitherto undetected by other high-resolution spectroscopic techniques have been identified by laser magnetic resonance and their basic structural features elucidated. In addition to purely spectroscopy measurements applications in chemical kinetics and laboratory astrophysics are also described briefly.
Introduction Laser magnetic resonance (LMR) has proved to be one of the most fruitful of the new techniques developed during the last decade for high-resolution spectroscopy of free radicals and other transient paramagnetic species. The development of LMR for free-radical spectroscopy followed a period in which relatively few new spectra had been discovered by the methods available in the microwave and far-infrared spectral regions. Although gas-phase electron paramagnetic resonance (EPR), and later microwave spectroscopy, had been successfully employed to obtain spectra of several free radicals and atoms the more labile species eluded detection. These included molecules like CH of fundamental interest to spectroscopists, radioastronomers, and combustion scientists. In EPR fixed-frequency microwave transitions are induced between magnetic sublevels of a paramagnetic atom or molecule in a resonant cavity. In 1968 Evenson and his colleagues’ demonstrated in a pioneering experiment that an analagous effect was feasible using a fixed-frequency far-infrared laser instead of a microwave source. The obvious similarities between the experiments led to the description “Laser Electron Paramagnetic Resonance Spectroscopy”, a title subsequently shortened to “Laser Magnetic Resonance Spectroscopy” or LMR. Initial experiments were performed on the stable paraNO,3and NO; all of which have near magnetic gases 02,2 spectral coincidences with far-infrared gas discharge laser frequencies. A striking demonstration of the inherent sensitivity of the new technique followed in 1971 with detection of a spectrum of CHS5 The enhanced sensitivity over microwave methods is expected from the frequency dependence of the absorption coefficient in addition to other factors, and the multitude of subsequent discoveries by far-infrared LMR have confirmed the prediction. Several years later LMR was extended to the mid-infrared (1)K. M. Evenson, H. P. Broida, J. S. Wells, R. J. Mahler, and M. Mizushima, Phys. Rev.Lett., 21, 1038 (1968). (2) K. M. Evenson and M. Mizushima, Phys. Rev.A, 6,2197 (1972). (3) M. Mizushima, K. M. Evenson, and J. S. Wells, Phys. Reo.A, 5, 2276 (1972). (4)R. F. Curl, K. M. Evenson, and J. S. Wells, J. Chem. Phys., 56, 5143 (1972). (5)K.M.Evenson, H. E. Radford, and J. M. Moran, Appl. Phys. Lett., 18,426 (1971). 0022-3654/81/2085-2599$01.25/0
by using C06 and C02’ lasers with similar success. The analagous technique of laser electric resonance or Stark spectroscopy has been developed concurrently but while LMR is suited for studying paramagnetic species the Stark experiment is better adapted for stable molecules.
Principle and Spectral Features (i) The LMR Experiment. The energy level diagram in Figure 1 shows the origin of the LMR transitions schematically. In a magnetic field of variable intensity B the of two rotational degeneracy of the magnetic sublevels, MJ, states J’and J” is lifted by the Zeeman effect. The rotational states involved may belong to different vibrational states. The flied-frequency laser is indicated schematically at the left of Figure 1and is close to coincidence with the frequency of the zero-field transition. Either far-infrared (A 28 900 pm) or mid-infrared (CO and C 0 2 lasers) have been used in LMR. At suitable values of the field transitions allowed by the dipole selection rules AJ = 1, AM, = 0,hl come into coincidence with the laser frequency, provided the Zeeman shift in the two levels connected by the transition are different, yielding the rotational or vibration-rotational LMR spectrum indicated by the vertical arrows in Figure 1. The much lower frequency (microwave) EPR transitions are also indicated. As we shall see in the examples cited later the Zeeman effect and LMR patterns are often much more complicated. However, LMR spectra with many components are often useful in characterizing the zero-field transition, i.e., they are an aid in assigning the latter. For the more complicated spectra a new nomenclature has been suggested with spectra described as Zeeman P, Q, R branches Zp, Z,, ZR, by analogy with conventional spectroscopy, in which AMJ = +1, 0, -1. Apart from the obvious requirement that the atom or molecule must be paramagnetic, several other features of LMR which define the feasibility of the experiment should be emphasized. The closeness of laser and transition frequencies is also important. Even for the magnetic field intensities available from large conventional electromag-
- -
(6)S.M. Freund, J. T. Hougen, and W. J. Lafferty, Can.J. Phys., 53, 1929 (1975). (7)H.J. Zieger, F. A. Blum, and K. W. Nill, J. Chen. Phys., 59,3968 (1973).
0 1981 American Chemical Society
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The Journal of Physical Chemistty, Vol. 85, No. 18, 1981
Rotational Energy
1
Mr /5/2
I
6
7
2
1
Magnetic Field Intensity, B
Flgure 1. Schematic energy level diagram showing the origin of LMR and EPR transitions. The mismatch, Av, of transition and laser frequencies Is much less than vlaW and the Zeeman shift is only a few percent, or less, of the transition energy. Only AM, = -1 LMR transitions are shown.
nets (up to -20 kG or 2 T) the strongest “tuning” transitions are not Zeeman shifted by more than 2 cm-l and in many cases the shift can be a factor of ten times smaller. Since the first-order Zeeman effect is varying approximately as 1/J(J+ 1)in simple diatomic radicals it is the lowest rotational transitions which have the maximum tuning range and are therefore more amenable to study. However, far-infrared laser frequencies are relatively large compared with the lower rotational transition frequencies of most molecules so LMR is better suited to studying hydrides which have large rotational constants. Nevertheless, progress is being made in extending the operating wavelengths toward the millimeter wavelength region facilitating studies of molecules with smaller rotational constants. In the mid-infrared CO and C02lasers provide a more uniform distribution of frequencies compared with the far-infrared lasers. In particular by using different isotopic forms of C02a dense spectrum of lines is available between 880 and 1100 cm-’. (ii)Line Widths,Resolution,and Accuracy. Line widths in LMR are determined by Doppler or pressure broadening, or by contributions from both. Below pressures of about 0.5 torr line widths for far-infrared transitions are Doppler broadened with pressure broadening becoming dominant above several torr. For example, the Doppler width for OH around 120 pm is -7.5 MHz at 298 K. In the mid-infrared, due to the linear frequency dependence of Doppler line widths, the lines are much wider. However, this apparent loss of resolution is offset by extensive use of saturation (Lamb dip) spectroscopy leading to subDoppler line widths. It is usual to describe experimental line widths in units of magnetic field intensity. These can be converted to frequency widths by using the rate of tuning of the transition expressed by the effective g factor: av/aB
cc
geff
where geffis determined by the g factors and magnetic quantum numbers of the upper and lower states, respectively: geff= g‘M/ - g“M/
Davies
It is therefore possible to obtain large experimental line widths for narrow frequency widths if geffis small (50.1). In most cases line widths in far-infrared LMR are sufficiently small without saturation spectroscopy to resolve some or all hyperfine structure. Full-widths at half-maxima are typically between 2 and 10 G (0.2 and 1 mT). Resolution is not quite as high as traditional microwave spectroscopy. In the mid-infrared at 10 pm the powerful COz lasers facilitate saturation spectroscopy and experimental line widths as narrow as 5 G are again observable. Accuracy of LMR measurements is determined by several factors including absolute field and frequency values, and laser stability. Magnetic field intensities can be measured with NMR probes to better than 1G for narrow lines and laser frequencies are known to better than 1MHz in the far-infrared and 3 MHz for CO and C02lasers. A small additional uncertainty of 5 MHz appears for C02 lasers associated with laser frequency instability. Overall, experimental errors of -10 MHz are expected in the mid-infrared and somewhat smaller values in the far-infrared. (iii)Spectroscopic Results. A variety of transitions can be studied by LMR. The most common in the far-infrared are the allowed rotational transitions directly analagous to those in the microwave while in the infrared most of the spectra arise from vibration-rotation changes. In addition, in both spectral regions it is possible to detect LMR spectra originating from electronic fine structure transitions; these usually have only weak magnetic dipole intensity but LMR is sufficiently sensitive for their detection. Several atoms have fine structure spacings lying in the infrared and their magnetic dipole LMR spectra have been measured and analyzed. Lastly, with the intrinsically high resolution of LMR many free-radicalspectra show resolved hyperfine patterns leading to important information about electronic structure. In general LMR yields a wide variety of parameters with up to MHz accuracy. Although this is somewhat lower than microwave spectroscopy it is not restricted to rotational transitions but includes vibrational, fine structure (spin-rotation, spin-orbit), and hyperfine effects. A pertinent question often raised about LMR is whether analysis is possible without prior spectroscopic information from other techniques. However, there are several striking examples in which LMR has provided the first structural details of a free radical in the gas phase, e.g., OF, HOz, and CH30. Several examples of the types of transition that can be studied and the information available from spectral analysis are given later in the section on spectra.
Experimental Section (i)Infrared Lasers. The discharge lasers wed in the first far-infrared LMR spectrometers gave relatively few lines and only a few near coincidences. These lasers were superseeded by optically pumped lasers which depend on the coincidence of a COz pump line and a molecular absorption at around 9.4 or 10.6 pm. There are now a large number of molecules which behave as active media in far-infrared lasers by absorbing on a vibration-rotation transition at one or more C02 laser frequencies and re-emitting on a rotational transition as a far-infrared laser. Continuing discoveries of new lasing molecules are providing a rapidly increasing coverage of the far-infrared region. Although an exact frequency measurement is required for analysis of the LMR spectra, measurement of the laser frequency during the LMR experiment itself is unnecessary. (Accurate frequency measurement is made by “beating” the laser against the harmonic of a klystron or other microwave oscillator and measuring the beat fre-
The Journal of Physical Chemistry, Vol. 85,No. 18, 1981 2601
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FAR 'YFRARED LASER C I V ' T V
1 5m
r
Figure 2. Basic features of a far-infrared LMR spectrometer operatlng between 40 and 900 fim, optically pumped by a Ilne-tunable carbon dioxlde laser.
quency.) All that is required during the experiment is identification of the laser line by wavelength measurement. Similarly in the mid-infrared the precise laser frequencies have been measured separately and can be used reliably by identifying the line, e.g., with a spectrum analyzer, and setting the laser to the center of its gain profile. (ii)Far-Infrared LMR Spectrometer. In their original experiment Evenson et al.' used an absorption cell external to the laser cavity. It was shown subsequentlys that the intracavity arrangement, now used universally in far-infrared LMR and many mid-infrared studies, is much more sensitive. A quantitative account of the enhanced sensitivity of intracavity absorption has been discussed at length elsewhereg in more specialized reviews. In terms of the minimum detectable loss (i-e.,absorption) it is estimated to be lo3times more sensitive than extracavity absorption. A schematic diagram of a far-infrared LMR spectrometer is shown in Figure 2 with transverse optical pumping by a line tunable CW C 0 2 laser. The pump radiation is multiply reflected between two gold-coated flats parallel to the far-infrared laser axis. Longitudinal pumping in which the pump radiation is introduced along the laser axis through a hole in one of the far-infrared laser mirrors has also been employed. Although this arrangement corresponds to a more efficient overlap of the C02 beam and far-infrared low-order transverse laser modes, and therefore more efficient optical pumping, it has the disadvantage that C 0 2 radiation is focussed along the axis of the farinfrared laser. The cavity is divided by a thin (- 10 pm) polypropylene beam splitter set at Brewster's angle which is easily ruptured by quite low C02 laser powers in the longitudinal arrangement. Recent designs therefore favor transverse pumping. The intracavity beam splitter is an essential part of the spectrometer. First, it determines the polarization of the laser with respect to the magnetic field. When the electric vector of the laser lies perpendicular to the magnetic field AMJ = fl (a) electric dipole transitions are induced; the AMJ = 0 (dtransitions appear with parallel polarization. Secondly, the beam splitter serves to separate the gain medium from the sample section and, since different vacuum and flow conditions are required, these two sections of the spectrometer are pumped separately. The optically pumped section requires good background vacuum for lasing to occur and can often be made to lase "sealed-off" if this condition is met. In contrast the sample section is usually part of a fast flow system requiring high (8) J. S. Wells and K. M. Evenson, Reu. Sei. Instrum., 41,226 (1970). (9) K. M. Evenson, R. J. Saykally, D. A. Jennings, R. F. Curl, and J. M. Brown in "Chemical and Biochemical Applications of Lasers", Vol. V, C. Bradley Moore, Ed., Academic Press, New York, 1980, p 95.
pumping speeds. The large majority of radicals studied so far by LMR have been generated by atom-molecule reactions in the gas phase, using well established discharge-flow techniques or by pumping the products of a microwave discharge rapidly into the sample region of the spectrometer. Less frequently, radicals have been generated by heterogeneous reactions between atoms and solid deposits on the wall of the spectrometer (e.g., hydrogen atoms have been found to react with elemental sulfur to produce SH(X211)radicals'O). A novel experiment using an electric discharge maintained inside both the cavity and magnetic field region was recently employed as a radical and ion source by Saykally and Evenson'l with considerable success. Three methods have been employed for coupling out a small fraction of the laser power for detection. Early experiments used the small levels of reflected power from the beam splitter.2 However, as the membrane is very thin it is susceptible to drum-head vibrations if there are pressure fluctuations and these are accentuated as the beam splitter ages. The alternative methods are hole coupling (Figure 2) through one of the far-infrared laser mirrors or by a variable coupler inserted into the far-infrared laser ~ a v i t y . ~ (iii)Detection and Sensitivity. The first far-infrared LMR spectra were recorded by using Golay cells. These have the advantage of room temperature operation and are easy to use but their response is slow and only low modulation frequencies in the range of tens of Herz can be used. The more sensitive helium-cooled Ge bolometer has a NEP (noise equivalent power) approaching the quantum noise limit and also has a much faster response than the Golay cell. With the Ge detectors source noise from laser instability, etc. is usually larger than detector noise and since the former decreases with increasing frequency there is a major gain in sensitivity with the faster detectors by operating at much higher modulation frequencies. Although fractional absorption of laser power as high as 0.1 has been observed', in most cases the absorption is much smaller and the signa1:noise ratio is improved by molecular modulation. This is achieved by applying a small ac magnetic field of up to 50 G using a pair of coils mounted in approximately Helmholtz configuration on the magnet pole caps (Figure 2). The modulated signal is then passed to a phase-sensitive detector and appears in first derivative form as in EPR. The effective sample volume defined by the modulating field, homogeneous region of the magnet, and laser mode diameter will vary with different laser lines and between instruments. With a conventional electromagnet effective sample volumes are in the range 2-20 cm3. A practical measure of sensitivity can be obtained by calibrating the spectrometer against known concentrations of radicals. For example, it has been foundg that quite weak O2 lines at 699.5 pm (methanol laser) give a signa1:noise (S:N) ratio -3OOO:l at 1 torr pressure. This corresponds to a sensitivity of 2 X 1013/cm3(S:N = 1:1, 1s time constant). This figure will, of course, depend on the strength of the transition and several other factors; nevertheless, it gives a useful practical estimate of sensitivity for magnetic dipole transitions. The limiting sensitivity for a transient radical like OH is of more importance in the search for new spectra, and has been mea(10) P. B. Davies, B. J. Handy, E. K. Murray Lloyd, and D. K. Russell, Mol. Phys., 36, 1005 (1978). (11) R. J. Saykally and K. M. Evenson, Phys. Rev. Lett., 43, 515 (1979).
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suedg as loe cm". The figure is close to that calculated from the minimum detected power loss. The sensitivity estimated for mid-infrared LMR is about ten times less. In either case LMR offers a distinct improvement in sensitivity over the earlier microwave (EPR) techniques. (iu) Experimental Details and Future Developments in Far-Infrared LMR. In the far-infrared LMR experiment the laser line of interest is first identified by measuring the distance between successive longitudinal modes. At these long wavelengths this is relatively easy to accomplish by mounting one laser mirror on a fine micrometer. Passive stabilization of the cavity length is accomplished by a combination of quartz (or thermostated aluminum) and invar rods. Any tendency for the C02pump laser to drift from coincidence with infrared absorption in the gain medium can be offset by feedback of the farinfrared output onto a piezoelectric drive on one of the C02 laser optical elements. These techniques enable the laser frequency to be stabilized to 1 MHz. When more than one far-infrared line is oscillating, changing the cavity length by several millimeters is usually sufficient to distinguish different wavelengths. Higher order transverse modes are usually suppressed with an intracavity iris. These modes are only likely to occur for the shorter wavelength lasers as the beam waist radius, wo, is wavelength dependent (0: All2) and longer wavelength lines have correspondingly larger diffraction losses. The latter factor is an important criterion in the design of suitable Fabry-Perot-type resonators for far-infrared lasers. For the longest wavelength lines, the laser tube should have the widest diameter possible with the limit set by the gap between the magnet pole faces. This in turn determines the size of the magnet required to generate as large a field as possible while maintaining maximum homogeneity over a gap of 60 mm or more. Recent experiments" with superconducting solenoids promise to extend the field range as well as maintaining maximum geometrical size. In addition the incoporation of the more compact waveguide structures which can lase to X 2 mm is an important goal for future spectrometer designs.
Davies
N
'E 6
-
-
I
i
-
-
Spectra. Examples and Results (i)Atoms. Although originally developed for molecular spectroscopy LMR in the far- and mid-infrared is sufficiently sensitive to detect paramagnetic atoms. These spectra originate from transitions between Zeeman components of electronic fine structure states and have magnetic dipole intensity only. The far-infrared LMR transitions in the 3PJground term of the oxygen atom serve as a convenient example. The first spectra were measured in 1977 by using lasers in CH30D and CH3NH2near 146 pm and are due to transitions between 3P1and 3P0substates.12 The frequencies of the lasers are accurately known and the Zeeman shifts are readily calculated with the aid of the high-precision g factors measured by EPR.13 The fine structure spacing can then be evaluated with much greater accuracy than previously possible from optical spectroscopy. This is an example where large Zeeman shifts occur: the g factor of 3P1M j = f l states is -1.5 while the 3P0state is nonmagnetic. Later14 the 3P2-3P1 spectrum near 63.1 pm was detected and measured by using a 13CH30Hlaser line. LMR and X-band microwave transitions are depicted in the energy level diagram in (12)P. B. Davies, B. J. Handy, E. K. Murray Lloyd, and D. R. Smith, J. Chem. Phys., 68,1135 (1978). (13) H.E. Radford and V. W. Hughes, Phys. Rev., 114,1274(1959). (14) R. J. Saykally and K. M. Evenson, J. Chem. Phys., 71, 1564
(1979).
I
-2
631ym lii
t
0
1
-
2
5 10 15 Magnetic Field Intensity IkG)
Flgure 3. Assignment of the far-infrared LMR transitions in the ground state of the oxygen atom. The six EPR transitions within the sP, and 3P, components are also shown.
Figure 3. The LMR spectra yield the following fine structure intervals: 3P0-3P1 68.716 4g4 cm-l
3P1-3P2 158.302 98, cm-' The fine structure spacing in the 'PJ 0 atom shows a small isotope effect which is measurable by LMR.12 When a sample containing 25% lSO2in lSO2is used to generate 0 atoms, transitions from both isotopic forms have been measured at 145.7 pm. The small shift in the spectrum, 5 G, leads to a value of the 3P1-3P0spacing which is 3.5 X cm-' greater in l80that in leg. (ii)Diatomics. Examples of diatomic free radicals in 38,211, and IA states studied by LMR are numerous. (A spectrum from a molecule in a 311 state has also been reported.) An interesting feature of these spectra is the variety of Zeeman patterns which are possible. In general 211 and lA molecules have essentially linear Zeeman effects and relatively simple spectra. The Zeeman effect in 38 states is usually nonliner and leads to complex spectral patterns which are more difficult to assign and analyze than the 211 and l A spectra. Some examples of the spectra from 32,211, and lA species are given below. ( a ) 211. T h e Ground States of OH and OF. The classic example of a 211 free radical is the OH molecule in its ground electronic state. The lower rotational levels of both Q = 1 / 2 and 3/2 substates are shown in Figure 4. Rotational transitions within the 2111/2 and 2113/2 manifolds are strongly allowed (electric dipole) and several have been observed by LMR.15 In addition, much weaker transitions between the Q fine structure states, which are forbidden for a strictly Hund's case (a) molecule by the AQ = 0 selection rule, have been observed. For example,16Figure 5 shows spectra of the 2r1112,J = 1 / 2 2113/2, J = 3/2 transition for OH in vibrational levels from u = 1-3 produced in the reaction H + O3 = OH + 0%In this case the zero-field spacing changes very little with vibrational
-
(15) J. S. Geiger, D. R. Smith, and J. D. Bonnett, Chem. Phys. Lett., 70,600 (1980). (16)P.B. Davies, W. Hack, A. W. Preps, and F. Temps, Chem.Phys. Lett., 64,94 (1979).
The Journal of Physical Chetnistty, Vol. 85, No. 18, 198 1 2603
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TABLE 11: Molecular Parameters (cm-') of the Ground State of FW parameterd
L
J
-
*O
91 2
A0
BO
1112-
B.
Rotational __3
D'
712
h re, A
- 512 312
2 l-h2
Flgure 4. Rotational energy levels of the 211112,3/2 ground state of OH and asslgnment of some of the observed far-Infrared LMR transitions. The A doubling of each level is much smaller than depicted but can be resolved in the LMR spectra.
n
n vz3
n
I
._
Magnetic field intensity
(kG)
Flgure 5. Far-infrared LMR spectrum of vlbrationally excited OH recorded with the 78.4-pm H,O discharge laser and electric vector of the laser perpendicular to the magnetic fleld. A spectrum of v = 0 OH appears at hlgher fields. (Reprlnted with permission from ref 18. Copyright 1979 Chem. Phys. Lett.)
TABLE I: Fine Structure Spacings (cm-') for v = 0-3 OH from LMRa
zn3,1,J = 312W.... J = '1, .A,*?
v=0
v = l
F,e(l)-F2e(l) 126.2936 126.886 F,f(l)-F,Al) 126.3951 126.984 a Uncertainty 6 0.002 cm".
previous values
1033.4812 ( 2 ) -177.3 (56) 1.05282 (19) 1.03934 (19) 3.9 (3.3)'X 10-6 0.02322 (59) 1.35789 (25)
1201,b 1028.7c -18@ 1.104b
1.321,b1.337b
Uncertainties in the LMR results are given in parentheses and are 3 standard deviation in units of the last digits. Calculated values (data taken from ref 17). Argon matrix spectroscopy (data taken from ref 17). v 0 denotes band origin;A, is the spin-orbit coupling; Bo,B, are rotational constants; D is the centrifugal distortion; h is the I9F hyperfine constant.
112
9732
LMR"
v=2
v=3
127.481 127.577
128.071 128.164
quantum number and spectra of different vibrational states appear conveniently close together with the same laser line. Using the precisely measured g factors and frequency of the H 2 0 laser line at 78.4 pm the spectra yielded the first direct measurement of this fine structure spacing (Table I). This is a further example of how EPR measurements of the g factors have provided complementary information for analyzing LMR spectra. Although the long wavelength limit of the latest far-infrared spectrometers is now nearly 1 mm, for rotational transitions far-infrared LMR is still best suited for studying hydrides. For "heavier" diatomics mid-infrared LMR is less limited in this sense as it depends primarily on the vibrational rather than rotation 1 spacings. In principle when a vibrational band lies i 9 o the wavelength region
covered by the fairly dense spectrum of CO or C 0 2laser lines there are good possibilities for detecting many vibration-rotation transitions. For example, the FO radical has not yet been detected by far-infrared LMR; its lowest rotational transition lies at 2.1 cm-'. In contrast several low J transitions in P, Q, R branches of its fundamental band have been detected by 10-pm LMR.17 FO is an important example of a free radical first detected spectroscopically in the gas phase by LMR. Although there was prior evidence for its existence from mass spectroscopy, structural details were limited to information from infrared spectroscopy in the condensed phase and from ab initio calculations. (The former gave a useful indication of the position of the band origin.) Table I1 compares the molecular parameters derived from LMR by McKellar17with earlier data, and is an impressive example of how the technique has extended our knowledge of the structure of this free radical. ( b ) ?Z, NH, and Its Isotopes. An interesting consequence of using a versatile and sensitive detection technique like LMR is that certain atom-molecule reactions have been found to be copious new sources of several radicals. The most striking example so far is the reaction of fluorine atoms with methane which generates C, CH, CF, CHz, and C2H. Another example is the reaction F NH, which yields NH and NH2,the former in ground and vibrationally excited states. The 32ground state of NH can be described by Hund's coupling case (b) in which the spin S and rotation N couple to give a resultant J. The three J fine structure states associated with each N are relatively close in energy compared with the rotational spacing and many transitions allowed by the selection rules AN = +1, AJ = 0, fl fall in the far-infrared. In general, the Zeeman effect for NH is nonlinear for field intensities up to 15 kG. At low fields, where Nand S are strongly coupled, the Zeeman levels can be labeled by the magnetic components of the total angular momentum, M,, while at higher field intensities N a n d S are uncoupled and eventually M N and Ms are more accurate quantum numbers. These effects can be seen in the energy level diagram in Figure 6 for NH and based on the work of Wayne and Radford18 on the far-infrared LMR of 14NH(u = 0 and l),15NH (u = 0), and 14ND(u = 0 and 11,all species obtained with isotopes in natural abundance. Among the wealth of information derived from the far-infrared LMR spectra are rotational and fine structure parameters for all the isotopic variants and vibrational states given above. These confiim and extend the accuracy of previous optical measurements; numerical comparisons
+
(17)A. R.W. McKellar, Can. J . Phys., 57,2106 (1979). (18)F. D.Wayne and H. E. Radford, Mol. Phys., 32, 1407 (1976).
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Davies
MJ
E-: 1 0
0
-2
U
d
0
1
1’ ’ Figure 6. Lowest rotational levels of a ‘2 radical, NH, in a magnetic field.
500 Gauss
Flgure 8. Far-infrared LMR spectra of PH In ground 32-(0)and metastable ‘A (0)states recorded near 11 kG with the 118.6-pm line of the water vapor laser. The four-line hyperfine structure expected from the phosphorus (I = 1/2) and proton nuclear spins is easily discernlbie In the 32-state. The large splitting of -500 G in the ’A spectrum is due to “P hyperfine: the much smaller proton Splitting is not resolved and appears as a silght dlstortion near line center.
For higher accuracy smaller second-order terms must be included due to the mixing from other rotational levels by the applied field. The most widely studied spectrum of l A P H corresponds to the rotational transition J = 4 5, near 118.6 pm, for which gJ = 0.2 and 0.1333, respectively. Although the Zeeman shifts are quite small an extensive spectrum has been measured and yields B0(lA) = 8.4392925 (46) cm-’. The IA hyperfine patterns are characterized by a large (-500 G) doublet spacing from the 31PI = 1/2 nucleus and a much smaller proton splitting which is often only partly resolved (Figure 8). Like the Zeeman term the hyperfine energy is essentially first order and, in a representation in which J and I are uncoupled, is given by
-
8016
I
‘
8116 GAUSS
I
Figure 7. Resolved nine-line hyperflne pattern in a far-infrared LMR transition in v = 0, ND(X38-). (Reprinted with permission from ref 18. Copyright 1976 Mol. Phys.)
can be found in Table 6 of ref 18. Of equal importance is the highly original information from the hyperfine structurela which is completely resolved in many of the spectra as shown in Figure 7 for a transition in ND. The nine-line pattern arises from a triplet splitting from the 14NI = 1 nucleus and a further triplet from the deuterium nucleur spin. An analysis of these LMR patterns permits a direct test of ab initio calculations.l8 (c) IA. The Metastable “a” State of PH. A convenient source for generating phosphorus radicals is the reaction of gaseous hydrogen atoms with powdered red phosphorus inside the spectrometer absorption cell, as close to the detection volume as possible. In this chemical system far-infrared LMR spectra from PH and PH2 have been observed with the same laser line.lS PH is formed in the ground 3Z and metastable alA states by mechanisms which remain open to speculation. Although both states have similar rotational constants the spectra are well separated at the resolution of far-infrared LMR. In addition, the different electronic fine structures lead to quite different Zeeman patterns and the spectra are further uniquely identified by their different hyperfine splittings as shown in the example in Figure 8. The Zeeman effect in the alA state is represented with reasonable accuracy by a fiist-order formula which for each J is
(19)P.B.Davies, D. K. Russell, and B. A. Thrush, Chem. Phys. Lett., 36, 280 (1975).
whf = aHgJMIHMJ + a&JMfMJ For either nucleus ar = 2 g m m (ry3) A where rI is the distance from the nucleus in question to the unpaired electron averaged over the orbital density. Since the other factors are known constants it is straightforward to obtain the important quantity (rf3) from the LMR hyperfine structure. The value for the phosphorus nucleus is (rp-3) = (24.0 f 1.2) X loz4cm-3 which is essentially the same as in the atom and in the 32 state of PH, also deduced from LMR.20 It has therefore been shown by analyzing the LMR spectra that the unpaired electrons in 32and IA states are essentially located in a 3p atomic orbital on phosphorus. (iii) Triatomics. Chemical knowledge about one species in particular, HOz, has been greatly enhanced by LMR with respect to both its structure and reactivity. Before its discovery by LMR the radical had been postulated as an important intermediate in flames and combustion systems but had only been detected by mass spectrometry which gave no structural information. In 1974, Radford, Evenson, and Howardz1published the first far-infrared LMR spectra of the zA” ground vibronic state. In addition to spectroscopic evidence for its existence they showed by chemical tests and isotopic substitution that under discharge-flow conditions the species is a constituent of many
(20)P.B.Davies, D. K. Russell, D. R. Smith, and B. A. Thrush, Can. J.Phys., 57, 522 (1979). (21)H.E. Radford, K. M. Evenson, and C. J. Howard, J . Chem. Phys., 60,3178 (1974).
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TABLE 111: Rotational, Distortion, and Spin-Splitting Parameters for HO, from Far-Infrared LMRZ3(cm-' p DK = 0.0041 ( 3 ) A = 20.358 ( 3 ) DNK= 0.00012 ( 1 ) B = 1.1179 (5) DN = 0.0000042 (8) C = 1.0567 ( 5 ) eaa=-l.630 (8)
OHI
Jc
OnI
a One standard deviation given in parentheses. E = is the principal component of the spin-rotation tensor.
chemical systems containing hydrogen and oxygen. Preliminary analysis of the extensive Zeeman branches was straightforward for this near prolate top ( ( B C)/2 = 1 cm-', A 20 cm-') and the rotational energy levels were calculated from the conventional symmetric top formula. The interaction between the single unpaired electron and the rotational motion in H 0 2 results in a doubling of each rotational level and rotational transitions are allowed from either spin substate. This permits determination of rotational parameters, the spin splitting, and components of the spin-rotation tensor from LMR spectra. Several other important triatomic radicals also have unpaired electrons in orbitally nondegenerate states, e.g., NH2(X2Bl),and Hougenn has developed general methods for assignment and analysis of their LMR spectra. The molecular energy levels of a spin doublet in a magnetic field are given approximately by the eigenvalues of a simple 2 X 2 matrix and the associated LMR patterns depend on the relative magnitude of laser frequency and rotational spacing (including the two spin substates of the rotational levels involved). It is then possible to classify the patterns as Zeeman, P, Q, and R branches in which AMJ = -1, 0, or +1. Further details are given in ref 22. Several of the HOz spectra conform to the predictions of Hougen's approach. However, it is often the case that more than one rotational transition is present on a single laser line as illustrated in Figure 9 for the spectrum with the 118.6-pm H20 laser lineB which contains six and twelve branches in the parallel and perpendicular polarizations, respectively. Nevertheless, Hougen et al.23were able to analyze and assign most of the spectra of H 0 2 obtained with several laser lines between 50 and 150 cm-'. The range of quantum numbers represented in these spectra is substantial (45 N I 19; 1 I K, I 4)and the data were used in a leasbsquares fit to an asymmetric rotor program to derive rotational, distortion, and spin-rotation parameters for HO, for the first time (Table 111). Based on this analysis the frequencies of several microwave transitions were predicted, with uncertainties of f1.5 GHz, and subsequently detected.24 This was a very satisfactory confirmation of the assignment of the complicated LMR patterns and the relatively simple model used to analyze the results. H 0 2 also has infrared active fundamentals and Johns, McKellar, and Riggin25have detected many vibrationrotation LMR spectra in the v3 0-0 stretching mode at 1097 cm-' (9.1 pm) using C1602and C1*02lasers. The spectra cover a range of rotational levels with 1 5 N I 7, 0 I K, I 4 and combined with the ground-state parameters yield data on the u3 = 1 rotational and fine structure parameters as well as the band origin. As an example of the accuracy achieved the band origin vo = 1097.6262 cm-' with
-
+
(22) J. T. Hougen, J. Mol. Spectrosc., 54, 447 (1975). (23) J. T. Hougen, H. E. Radford, K. M. Evenson, and C. J. Howard, J. Mol. Spectrosc., 56, 210 (1975). (24) Y. Beers and C. J. Howard, J. Chem. Phys., 63, 4212 (1975); S. Saito, J.Mol. Spectrosc., 65, 229 (1977). (25) J. W.C. Johns, A. R. W. McKellar, and M. Riggin, J. Chem. Phys., 68, 3957 (1978).
r 0
I
I
I
20
10 kG
1
0
lo
I
1
?"
I
1
I
20
Figure 8. Far-infrared LMR spectrum of Hopin parallel (n)and perpendicular (a) polarization with the 118.6-pm line of the water vapor laser. (Reprinted with permissionfrom ref 23. Copyright 1975 J. Mol. Spectrosc.)
a standard deviation of 2 X cm-'. (iu) Polyatomics. CH30 and CH2OH. These two species are the largest free radicals so far detected by LMR and the partial or complete analysis of their spectra achieved recently is highly promising for extension to other large molecules. Methoxy, CH30, is a symmetric top free radical, an unusual species not previously detected in the gas phase until its discovery by LMR. It is produced in the reaction of F atoms with methanol, or by the pyrolysis of dimethyl peroxide, and its far-infrared LMR spectra are characterized by two- or four-line hyperfine patterns characteristic of three equivalent protons, Le., where the effective total nuclear spin is 312 or 112 depending on the symmetry of the rotational eigenfunctions. In their initial experiments Radford and RussellB confiied the existence of CHBOby chemical and isotopic substitution tests and later2' analyzed spectra at eighteen far-infrared wavelengths establishing that the ground electronic state had 2Esymmetry. As well as rotational motion the molecule exhibits Jahn-Teller distortion and spin-orbit and spinrotation coupling leading to a complicated molecular Hamiltonian. One of the many interesting features of this important LMR study is the similarity of the experimentally derived parameters to earlier theoretical calculations. The latter predicted rotational constants of A = 5.35 cm-', B = 0.93 cm-l compared with A = 5.3280 (22) cm-' and B = 0.93177 (51) cm-' from LMR. The electronic structure from theory located the unpaired electron in a largely 2p atomic orbital on the oxygen atom. This implied that the spin-orbit coupling constant should be similar to its value in OH (-139.2 cm-') and this was confirmed experimentally (26) H. E. Radford and D. K. Russell, J. Chem. Phys., 66,2222 (1977). (27) D. K. Russell and H. E. Radford, J. Chem. Phys., 72,2750 (1980).
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The Journal of Physical Chemistry, Vol. 85, No. 18, 1981
TABLE IV: Free Radicals Detected by LMR Including Metastable Paramagnetic Excited States He, C. 0 . C1, HE CH, “,.OH, PH, SH, SeH, HBr’ CO, NO, 0,,N F , FO, CF, C10, SO, S,, NSe, SeO, BrO HO,, HCO, NH,, C,H, CH,, PH,, NF,, NO,, ClSO, FSO, HSO, ClO,, NCO CH-F. CH.
CH;O; C H ~ O H
by the LMR result: -142.8 cm-l. Finally, it is reasonable to postulate that the 10-gm LMR spectrum of CHBO should also be accessible to add to our knowledge of this interesting species. Very recently Radford, Evenson, and JenningsB have identified the LMR spectrum of the isomer of CH30, namely hydroxymethyl, CH20H,produced in the reaction of chlorine atoms with methanol. The identification was based on chemical behavior and on comparison of hyperfine structure with that of the radical in solid and liquid phases. It seems appropriate to end this section with a tabulation of all the paramagnetic species so far discovered by LMR (without distinguishing the spectral region in which they were found or their symmetry). Recent Experimental Developments and Applications (i) Molecular Ion Spectroscopy. Early in the development of LMR it was apparent that its high sensitivity made it a potentially fruitful technique for detecting molecular ions. Paramagnetic species like OH’, NH+, and HC1+have accurately known molecular parameters derived from their electronic emission spectra and in some cases conveniently tabulated rotational term values. However, considerable experimental problems were envisaged with introducing charged molecules into the magnetic field regions of LMR spectrometers. For example, with conventional electromagnets the discharge-flow system used to generate paramagnetic species is positioned perpendicular to the field, and ions formed in this geometrical arrangement would be rapidly deflected to the reactor walls. In an elegant experiment Saykally and Evensonl’ overcame this problem by using a superconducting solenoid to provide the magnetic field and introduced the ions along the solenoid axis (also the axis of the far-infrared laser cavity) by generating them in situ with a dc glow discharge. Additional advantages accrue from this arrangement. First, the sample region defined by the magnetic field region and modulation coils is considerably longer than in a conventional electromagnet. Secondly, superconducting solenoids can generate much higher field intensities than conventional electromagnets over the same air gap. Using this new spectrometer Saykally and Evenson were able to produce and detect far-infrared LMR spectra of HBr+ ions by discharging 1% HBr in He at total pressures 1torr. The experiment is analagous to that of Woods and his co-workers; they measured microwave absorption spectra of ions, e.g., HCO+, in similar discharges. The striking success with this new design suggests the method should be applicable to other molecular ions. (ii)Laboratory Astrophysics. Far-infrared LMR holds considerable promise as a laboratory technique to aid astronomy, in a similar manner to microwave spectroscopy. Several of the free radicals of interest to astrophysicists have eluded detection in laboratory microwave spectrom-
-
eters, CH being the best known example. Hence, the observation of its LMR spectrum at 118.6 pm6 was a particularly important discovery. Although LMR does not directly measure the A doubling transitions of interest to radioastronomers, analysis of several additional far-infrared LMR spectra of CH by Hougen et a1.29led to predictions of several transitions of this type in lower rotational levels, with sufficient accuracy for radioastronomy searches, Although the 10-cm (3.3-GHz) spectrum of the lowest rotational state (J = 1/21 of CH was detected independently in the interstellar medium, predicted A doubling frequencies for the higher rotational levels should be useful for future searches. The prediction of line positions for far-infrared astronomy is a second recent application in astrophysics. Carbon, one of the most abundant cosmic elements, is believed to exist in significant amounts in the interstellar medium as neutral atoms. As the nuclear spin of the most abundant 12Cisotope is zero the ground electronic state has no hyperfine spectra that can be detected by radioastronomy. However, fine structure transitions within the 3PJground multiplet for both I2C and 13Catoms have been measured by LMR30 enabling the astronomical detection of far-infrared emission of 12C atoms from several interstellar s0urces.3~ Two other species of importance in the interstellar clouds, CzH9and CH2,32have also been studied by far-infrared LMR. The latter has not yet been detected in astronomical sources and LMR spectroscopy leading to accurate line positions should help to reduce the search problem. (iii) Reaction Kinetics. Shortly after the initial spectroscopic discoveries with LMR it was realized that such a sensitive technique had considerable potential in free radical kinetics, particularly for those species like HOz which were not easy to detect by other methods. This has now been realized in several laboratories using both optically pumped and discharge excited lasers in the far-infrared. In the most sophisticated experiment combined LMR and EPR detection has been employed utilizing the same magnet.33 The most important single consideration for successful application to kinetics is linearity of the signal with concentration and this has been established for NO2 and other species over three orders of magnitude change in concentration.M All experimentaI systems use a variable injector discharge flow systemMorthogonal to the laser and as both laser and reactor tubes are open to each other the effect of diffusion of active species out of the flow tube must be carefully considered. In addition, power saturation, modulation broadening, and other instrumental factors are also important. Relative concentrations are straightforward to measure from the peak-to-peak amplitude of the first-derivative absorption signals, providing the line width remains constant in a particular kinetic “run”. Absolute concentrations are much more difficult to measure and are based on calibration against other paramagnetic species present in known concentrations. The transition moment, integrated intensity, g factors, and area under the absorption line scaled for instrumental effects must be taken into account (29)J. T.Hougen, J. A. Mucha, D. A. Jennings, and K. M. Evenson, J.Mol. Spectrosc., 72,463 (1978). (30)R. J. Saykally and K. M. Evenson, Astrophys. J. Lett., 238,107 (1980). (31)T. G. P h i b s , P. J. Huaains, T. B. H. Kuiper, and R. E. Miller, Astrophys. J. L e t t , 238,103 (i380). (32)J. A. Mucha, K. M. Evenson, D. A. Jennings, G. B. Ellison, and C. J. Howard, Chem. Phys. Lett., 66,244 (1979). (33)W. Hack, A.W. Preuss, F. Temps, HTGg. Wagner, and K. Hoyermann, Int. J. Cfiem. Kinet., 12,851 (1980). (34)C. J. Howard and K. M. Evenson, J. Chem. Phys., 61,1943(1974). ~~
(28)H.E. Radford, K. M. Evenson, and D. A. Jennings, Chem. Phys. Lett., 78,589 (1981).
J. Phys. Chem. 1981, 85, 2607-2611
to relate the concentrations to each other absolutely. Accumulated uncertainties are therefore in excess of 10% even for examples where the molecular dipole moment (i-e., transition moment) is known with reasonable accuracy from microwave spectroscopy. Fortunately the determination of radical concentrations from LMR follows similar procedures developed over a decade ago for kinetic applications of gas-phase EPR and, although laborious, the determination of line shapes and areas is well understood. Reactions of the important atmospheric species HOP have been particularly well studied by far-infrared LMR. The technique is advantageous for HOPkinetics due to its high sensitivity, lo9cm-3for the ground state, and capacity to detect related species such as OH simultaneously. For example, the reaction HOP + NO = OH NO2 has now been studied by LMR in three laboratories33$35936 with good agreement for the rate constant and with measurements by other techniques. The temperature dependence of this reaction has also been measured36 by incorporating a heated flow reactor before the LMR detection region, again in an analagous fashion to earlier experiments using EPR. The majority of the kinetic results obtained so far have used the discharge laser sources but as the optically pumped lasers are developed for kinetics a much wider variety of radical reactions should be amenable to study. Pioneering results on the chemistry of the methoxy radical are an indication of future kinetic research with these
+
(35)C. J. Howard, J. Chem. Phys., 71, 2352 (1979). (36)J. P. Burrows, D. I. Cliff, G. W. Harris, B. A. Thrush, and J. P. T. Wilkinson, h o c . R. SOC.London, Ser. A, 368, 463 (1979).
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lasers.37 Finally, it is interesting to note that all the kinetic applications so far have used far-infrared lasers and there appears to be no fundamental reason why mid-infrared spectrometers cannot be converted for kinetic studies also. Conclusion The rapid and successful development of LMR is now manifested by the many instruments in use in more than a dozen laboratories throughout the world. The continuing discoveries of new laser lines in the far-infrared provides an almost continuous frequency coverage in the region and it is reasonable to postulate that "tuning" transitions from one laser line to the next across the 100-1000-~mregion should be possible in the near future. This is fortunate as in the far-infrared there are no narrow-band tunable laser sources for spectroscopy at zero field, and LMR is presently the only technique available for spectroscopy of free radicals in this region. Although discoveries of new laser lines in the mid-infrared have not been forthcoming there are alternative tunable sources, particularly the semiconductor diode laser, to cover this region for highresolution free-radical spectroscopy. Acknowledgment. I express my gratitude to many colleagues in North America and Europe for extensive correspondence and discussions on LMR over the past five years. This work has been generously supported at Cambridge by the Science Research Council and the Royal Society, and in Gottingen by the Max Planck Gesellschaft. (37)H. E.Radford, Chem. Phys. Lett., 71,195 (1980).
ARTICLES Flexible d Bask Sets for Sc through Cu Anthony
K. Rappe, Terry A.
Smedley,+ and Wllliam A. Goddard, 111"
Arthur Amos Noyes Laboratory of Chemical Physlcs, t Calltornla Instltute of Technolcgy, Pasadena, Calliornla 9 1125 (Received: September IO, 1980: In Flnal Form: May 27, 1981)
A prescription is presented and implemented for Sc through Cu that leads to practical-sized Gaussian d basis seb capable of accurate descriptions of the srndn-'"states of the atom. Optimized Gaussian basis seta containing . four, five, and six primitives are given along with recommended double zeta, double zeta, and triple zeta contraction schemes, respectively. It is suggested that these basis sets be used for calculationson large, medium, and small transition metal complexes, respectively.
Introduction In molecular calculations involving transition metals, it is important to retain the smallest number of d basis functions consistent with accurate descriptions of the d orbitals of the atoms and molecules. The reasons are that integral calculations for d functions are costly and also that tITT Rayonier, Inc., Grays Harbor Division, Hoquiam, WA 98550. * Contribution No. 6304.
each additional set of d primitives normally leads to six additional Cartesian Gaussians for SCF calculations. Based on atomic calculations, it has been concluded that five sets of d primitive Gaussians [denoted as (5d)l are required to accurately describe the shape of the atomic d orbitals. [For some applications a properly determined (4d) basis wiU be adequate.] For example, the total energy of the d10 state of Ni drops by 5.99,5.74,1.57, and 0.14 eV upon going from three d's to four d's to five d's to six d's to seven ds, respectively. Of special concern in variational 0 1981 American Chemical Society
