(1702) Greene, F. D., Pazos, J. F., ibid., 34,2269-74 (1969). (1703) Bindra, A. P., Elix, J. A., Tetrahedron. 25.3789-94 (1969). (1704) C'leophax, J. Gerc,' S. C., Hilde sheim, J., Sepulchre, A. M., Guthrie, R. D., Smith, C. W., J . Chem. SOC.C, 1970,1385-90. (1705) Achesun, R. M., Tully, W. R., ( l$~fj, p l l117-21. e, R. E., White, E., Tetrahedron Lett., No. 22, 1871-4 (1970). (1707) Henhenson, F. M., Bauer, L., J. Org. Chem., 34,660-4 (1969). (1708) Lund, H., Feoktistov, L. G., Acta Chem. S c a d , 23,3482-92 (1969). (1709) Koerner Von Gustorf, E., White, D. V., Kim, B., Hess, D., Leitich, J., J . Org. Chem., 35,1155-65 (1970). (1710) Sasaki, T., Kanematsu, K.,
Kakehi, A,, Ichikawa, I., Hayakawa,
K.. ibid.. DD 426-33. (171i) Nekow, S., Shapiro, R., ibid., 34, 2011-13 (1969). (1712) Keana, J. F. W., Mason, F. P., ibid.. 3 5 , 8 3 8 4 0 (1970). (1713)'Potts, I(.T., Armbruster, R., ibid., pp 1965-8 (1970). (1714) Roesky, H. W., Beyer, H., Chem. Ber., 102,2588-94 (1969). (1715) Clemens, D. F., Caspar, M. L.,
Rosenthal, D., Peluso, R., Znorg. Chem., 9.960-3 - - - - 119701. (1716) Potts, K. T., Surapaneni, C. R., J. Heterocycl. Chem., 7,1019-27 (1970). (1717) Swanson. J. S., Btuckv. " . G. D.. ilSy$,~p 667-9. ee. F.T.. VO~DD. G. ?., ibid., pp. ' 41&1-18fi970l ' (1719) Paudler, W. W., Cornrich, S. J., ibid., 419-21. (1720) Sataty, I., ibid. 431-2. (1721) Le B r i , M. +., Bull. SOC.Chim. FT., 1970,2277-83. 11722) Jacauier. R.. Petrus, C., Petrus, F., ' Valentin,.M.. ;bid..,pp 2672-8. (1723) GlemrLe;, D., Von Halasz, S. P., Znorg. Nucl. Chem., 5,393-8 (1969). (1724) Mauser, H., Bokrana, H., Z. Naturforsch., 248,477-81 (1969). 11725) Borer. W. Z.. Cohn. K.. Anal. ' Chim. Acta:. 47.35&7 (1969). ' (1726) Roesk;, H. W.,' Aniew. Chem., Znt. Ed. Engl., 8,510 (1969). (1727) Beger, J., J . Prakt. Chem., 311, 746-59 (1909). (1728) Gregory R., Haszeldine, R. N., Tipping, A. k., J . Chem. SOC.C, 1970, 1750-8. (1729) Lmdner, E., Kunae, U., Chem. Ber., 102,3347-56 (1969). (1730) Freear J., Tipping, A. E., J. - I
\ - - . - I .
\ - -
- I
Chem.Soc.d,l969,1848-54.
(1731) L,o, E. S., Readio, J. D., Isewon, H., J.Org. C h a . , 35,2051-3 (1970). (1732) Druce, P. M., Ki? ston, B. M.,
Lappert, M. F., Smdina. T. R.. Srhktava, R. C.., 4. C h G . SOC.A;
1969,2106-10. (1733) Foester, R., Cohn, K., Znorg. C h a . . 9. 1571-2 11970;. (1734) Fldres, A. %L.,Darment, B., J. Phys. C h a . , 73,2203-8 (1969). (1735) Mitchell, R. W., Sondheirner, F., Tetrahedron,26,2141-50 (1'370). (1736) Roesky, H. W., Grim&, L. F., C h a . Ber., 102,2319-29 (1969). (1737) Smith, J. R., Malik, Z. A., J. C h a . SOC.B, 1970,617-23. (1738) Catlin, J. C., Synder, H. R., J . Org. Chem., 34,1664-8 (1969). (1739) Eisenbraun, E. J., Bansal, R. C., Hertsler, D. V., Duncan, W. P. Flanagan, P. W. K., Hamming, M. 6., ibid., 35,1265-71 (1970). (1740) Wilt, J. W., Chenier, P. J., ibid., DD 1562-70. (l?&) Sauer, D. T., Shreeve, J. M., Znorg. Nucl. Chem., 6,501-6 (1970). (1742) Beeby, P. J., Sternhell, S., A u t . J. Chem. 23,1005-14 (1970). (1743) House, H. O., Campbell, W. J., Gall, M., J. Org. Chem., 35, 1815-19 (1970).
Microwave Spectroscopy leRoy H. Scharpen, Scientific Instruments Division, Hewlett-Packard Company, Palo Alto, Calif. 94304 Victor W. laurie, Depurtment of Chemistry, Princeton University, Princeton, N.1. 08540
E
XPLOITATION OF m E MICROWAVE REGION of the electromagnetic
spectrum was made possible by the development of devices and techniques during World War I1 for generating, detecting, and manipulating very short wave radiation. Several new areas of spectroscopy were made possible, but the term microwave spectroscopy is generally applied to the study of the absorption spectra of molecular gases at low pressures. It is this subject which is under consideration here. Microwave spectroscopy has proved to be a powerful tool for studying a variety of fundamental molecular properties and it has remained an active and growing research discipline. Unlike most other forms of spectroscopy, however, it has not yet been assimilated into the general practice of chemistry but rather has remained almost exclusively the domain of specialists in the tmhnique. The emphasis now, however, appears to be changing. Lide (23) summarized the current stage in the development of microwave spectroscopy with the statement "microwave spectroscopy has passed from an early phase in which the primary emphasis was on developing techniques for measuring and analyzing spectra into a more mature phase where it is useful in attacking a wide variety of 378R
chemical problems." That a more general interest in the technique is now developing is also illustrated by the fact that several laboratories are beginning to devote part or all of their research effort to exploring anslytical applications; other groups have added a microwave spectroscopy capability to complement programs previously restricted to other spectral regions. Also commercial spectrometers are now available which are much more amenable to routine use than those constructed and used by microwave research groups in the past. It is perhaps appropriate then that the first review of microwave spectroscopy in this series should appear at this time. This review is not intended t o be a complete survey of recent microwave research. Rather it emphasizes those aspects of microwave spectroscopy which bear on analytical applications and should serve to introduce the technique to those interested mainly in analysis. Inclu-ded are sections which summarize the theoretical and experimental factors which must be considered when assessing analytical uses of the technique. Current trends in the main body of microwave spectroscopy research are sufficiently well summarized in reviews authored by Flygare
ANALYTICAL CHEMISTRY, VOL. 44,NO. 5, APRIL 1972
(7), Morino and Hirota (28), and Rudolph (SI) in three of the last five volumes of the Annual Rewiew of Physical Chemistry. Wilson (44) and Lide (23)discussed in a general way the kinds of chemical information that can be obtained from detailed analyses of microwave spectra. Laurie (26) summarized work on the special topic of internal molecular motions and molecular conformations, a particularly fruitful area of investigation. Earlier reviews emphasizing the potential of the technique for chemical analysis were authored by Hughes (IQ), Dailey (4), Millen (27), Goldstein (9), and Lide (24,661 * BOOKS, BIBLIOGRAPHIES, AND DATA COMPILATIONS
Though now outdated in certain areas, the book by Townes and Schawlow (3Q) remains a very useful reference. More recent books are by Sugden and Kenney (36), Wollrab (46), and Gordy and Cook (IO). Wollrab provides an excellent bibliography through 1965. Starck (37) provided a summary of molecular constants obtained from microwave data. Her bibliography (38) arranged conveniently by molecule now is available
covering literature references through 1970. A five-volume series from the National Bureau of Standards, NBS, Monograph 70, is available. Volumes 111-V are particularly useful since them contain microwave absorption frequencies tabulated both by molecule and in order of increasing frequency for all molecules. These contain only those frequencies reported in the literature, however, and are therefore not complete. Work to develop a more complete catalog of frequencies is in progress (41). Compilations of absorption frequencies are particularly important for analytical applications. Figure 1 . Trace of the I = 2-3 line of OCS taken on a Hewlett-Packard 8460A. The peak frequency is 36,488.80 MHz. Pressure was less than 1 mTorr
BASIC CONSIDERATIONS
The microwave spectra of most molecules consists of rotational transitions with various fine structure effects superimposed. The physical process leading to absorption is generally a coupling of the electric vector of the incident microwave radiation with the permanent dipole moment of the rotating molecule. The width of rotational energy levels and thus of the absorptions is determined primarily by collision processes. At the sample pressures normally employed (10-100 mTorr), the width of an absorption associated with a transition between two rotational levels is quite small, being on the order of 0.5 MHz or less. If the resolution is defined as the peak absorption frequency divided by the absorption full width at half-maximum intensity, typical resolution is ~ 5 0 , O o Oand values as high as ~500,000are possible with an ordinary spectrometer as illustrated in Figure 1. With special techniques, even higher resolution is possible. The intensity of an absorption is determined primarily by the magnitude of the permanent dipole moment of the molecule and the number of molecules in the lower energy state of the transition. The pattern of absorption frequencies i a sensitive function of the exact molecular structure and isotopic composition of a molecule. These considerations delineate qualitatively the limits of microwave spectroscopy: (1) The sample compound must have a vapor pressure of the order of 10 mTorr a t some accessible operating temperature (2) Integrated spectral intensity is proportional to the square of the electric dipole moment (3) Spectral intensity depends on the number of molecules in a specific rotation-vibration state and thus decreases with increasing molecular size because of the distribution of molecules among an increasing number of thermally available states. For many analytical purposes, both qualitative and quantitative, microwave
spectral measurements can be treated empirically using measurements on pure materials as a calibration. However, the usefulness of the technique is enhanced by an understanding of some of the basic theory. The next subsections outline some of the fundamental elements of the theory which amplify the qualitative statements given above. To describe the gross features of the microwave spectrum of most molecules, i t is sufficient to regard a molecule as consisting of point mmses with fixed interatomic distances. This model of a rigid rotor serves to point out many of the advantages, unique capabilities, and disadvantages inherent in microwave spectroscopy. For many molecules, the model is in fact sufficient to reproduce the microwave spectrum of a given vibrational state with an accuracy of the order of one part in lo6108. ROTATIONAL ENERGIES
The molecular parameters determining the rotational energies of a rigid rotor are the moments of inertia. These depend on the masses mi of the nuclei and their coordinates (xi, yi, and 2,) in the principal inertial axis system of the molecule : where I,, is the moment of inertia about the x-axis and permutation of x, y, and z yield expressions for I,, and Is*. Algorithms published by Thompson (40) and Hilderbrandt (16) facilitate calculation of moments of inertia when moleculsr structures are given in terms of bond lengths and angles. Expressions for rotational energies are most often given in t.erms of rotational constants A , B , and C, which are inversely proportional to moments of inertia, the proportionality constant being h / 8 r 2 where h is Planck’s constant. By convention, the rotational constants are identified with the prin-
cipal axes in such a way that A 7 B > C and are normally given in MHz. As far as calculation of rigid-rotor energies is concerned, any molecule can be placed in one of four classes. If A = B = C, the molecule is a spherical top. Since the molecular dipole moment vanishes for this class, it is not of interest in microwave spectroscopy. If the molecule is linear, then A >> B = C. Only electrons contribute to A and excitation of rotation about the molecular axis can be considered an electronic transition falling outside the microwave region. If a molecule has a threefold or higher axis of symmetry, then two of the rotational constants are equal and it is termed a symmetric top. It is called a prolate if A > B = C and oblate if A = B > C. If none of the three rotational constants are the same, then the molecule is termed an asymmetric top. It should be noted that a molecule may have considerable symmetry and still fall into the category of asymmetric top because of the lack of threefold or higher symmetry. An example is ethylene. Rotational energies for a rigid linear molecule are given by: EJ = hBJ(J 1) (2) where J takes on the values 0, 1, 2, 3 . . . , The total angular momentum of the molecule is quantized and has the value J h / 2 r . The selection rules for interaction of a polar molecule with microwave radiation are AJ = il. For absorption where J J 1, the rotational energy change is:
+
-
+
+
AE = 2hB(J 1) (3) which corresponds to an absorption frequency: V J = 2B(J f 1) (4) For rigid symmetric-top molecules, the energy for the prolate case is:
EJK = hBJ(J 4- 1)
+ h(A
- B)K2
ANALYTICAL CHEMISTRY, VOL. 44, NO. 5, APRIL 1972
(5)
379R
and for the oblate case is:
EJK = hBJ(J
+ 1) + h(C
- B)K*
(6)
where K is the quantum number for the component of angular momentum about the symmetry axis and J 1 K 2 - J . Selection rules are AJ = 0, *l, and AK = 0. Except when inversion doubling such as in ammonia is present, only &T = +1 transitions will be important. Since K remains constant, transition frequencies have the same form as for linear molecules. Thus, the spectrum of a rigid linear or symmetric-top molecule consists of transitions forming an equally spaced series of absorption lines with a spacing 2B. For asymmetric tops, there remain 2 J 1 energy levels for each value of J which become the degenerate K-states in the limiting symmetric-rotor case. The sublevels are most often labeled J K - l ~where I K-, and K1 are, respectively, the values of K in the prolate or oblate symmetric-rotor limit. The asymmetry of the molecule is most often expressed in terms of the asymmetry parameter:
+
which ranges from K = - 1 for a prolate rotor to K = +1 for an oblate rotor. The energy can be expressed as a function of a reduced (dimensionless) energy E ( K )
E(JL1K1)= h(A
2
J(J
+ 1) +
Values of E ( K )have been tabulated, but generally rigid-rotor calculations for asymmetric tops are done using computers. A number of microwave spectroscopy groups use versions of a program written by Beaudet (1) and Kneubeuhl, Gaeumann, and Guenthard (11) describe a program used in their laboratories. The selection rules for J for an asymmetric top are A J = 0, *l. The dipole moment can have a component along any of the three principal axes which leads to three types of transitions called a-type, b-type, and C-type, according to the dipole moment component responsible for the transition. The selection rules on K-, and K1 depend upon the transition type. Spectra for asymmetric tops can appear quite complex although assignment of observed lines to particular energy levels is now considered routine. I n the special case for which the asymmetry parameter is near a symmetric-top limit, a bunching of transitions near the frequencies expected for a true sym380R
ANALYTICAL CHEMISTRY, VOL.
Table 1. Rotational Constants for Conformers of n-Propyl Fluorides trana gauche 14,503.69 A 26,986.73 B 3,748.32 5,085.71
C
4,299.28 3,509.88 Units are MHz. Data from E. Hirota, J . Chem. Phys., 42,2071 (1962).
metric top will occur. The “band spectra” discussed below result when spectra of such compounds are observed under low-mlution. Because of their direct dependence on momenta of inertia, microwave absorption frequencies are sensitive to the exact details of molecular structure and isotopic composition. From Equation 1, it is apparent that the change produced by isotopic labeling of a compound will depend not only on the mass change but also upon the geometrical location of the atom exchanged. Except for atoms near the center of mass, an isotopic substitution will produce a change in the microwave spectrum considerably in excess of the resolution available. Thus isotope shifts can be accurately determined with no ambiguity concerning the location of the labeled atom. The moments of inertia and, consequently, the spectra are also very sensitive to molecular conformation m illustrated in Table I, where rotational constants for the trans and gauche forms of n-propyl fluoride are given. The microwave spectra of the two conformen are quite different from one another and are readily assigned to the appropriate conformer. This is another illustration of the high specificity of microwave spectroscopy. Because of this specificity, a small number of microwave absorption frequencies is generally sufficient to uniquely characterize a molecule even in a complex mixture. ABSORPTION LINE INTENSITIES AND SHAPES
In the microwave region, absorption coefficients 7 are sufficiently small that the power absorbed can be expressed as:
AP
= YLS
where P is the incident microwave power. L, is the effective absorption path length related to the physical length by Le = L(X,/X) where A, and A are, respectively, the radiation path length in the absorption cell and free space. The absorption coefficient for a transition between two levels iand j is defined by: Y =
W v ’ N Fifiij’ 1 b k T Av
44, NO. 5,
1
+ (v - V ~ ) ~ / A V ’
APRIL 1972
where c is the speed of light, k is Boltzmann’s constant, T is the temperature in OK, v is the microwave frequency, N is the number of molecules of, the absorbing species per cm*, vo is Che peak absorption frequency, pij is the dipole moment matrix element connecting the i and j levels, Fi is the fraction of molecules in the lower level of the transition, and A v is the absorption line half-width at half-maximum intensity. The magnitude of Fi depends on both the rotational and vibrational partition functions since transitions involving molecules in excited vibrational states will generally be resolved. The rotational factor in Fi will be of major importance in determining relative intensities to be expected for different molecules since i t is directly proportional to (ABC)lI*. The derivation of Equation 9 assumes that the microwave power density is sufficiently low that power saturation effects are not important. The De& intensity coefficient is then just:
Above a critical prwure, intermolecular collisions will produce the dominant contribution to A v . Above this pressure, both N and Av are proportional to pressure and -yo will be constant. It is apparent then that both Av and yo must be memured to determine the partial pressure p of a constituent molecule. This relationship can be expressed : p = gYo Av (12) where g is a temperature dependent constant for a particular transition. Determination of g can be done empirically by measuring r0 and Av using a pure sample at a known pressure. Harrington (11, 13) recently developed a different approach to microwave line intensities and showed that measurements at v0 alone are sufficient to determine a partial pressure. He defined an intensity coefficient:
r 9 =
= 99
(134
Y ~ / K ~ ~ (13b) ~
where Q is a function of the reduced (dimensionless) parameter 2 = K P and K is a power saturation coefficient. The parameter 7 is a function of molecular parameters only and is directly proportional to the partial pressure. The parameter (p approaches zero a t very low and very high incident microwave power and has a maximum value at some intermediate power level. The maximum value of 9 has the same value for every transition. The value of r at the peak absorption frequency when +c. is a maximum is, therefore, directly proportional to the partial
ntm _----_ .
Ze.
~
,>,
I
29 ',
