Molecular Paramagnetic Resonance of Gas-Phase Nitric Oxide James W. Whittaker Carnegie Mellon University, 4400 Fifth Avenue, Pittsburgh, PA 15213 A successful undergraduate laboratory experiment should both stimulate insight and educate young chemists in the methods and concepts of current research. The first requirement can be addressed by aiming for a simple and direct relation between results, analysis, and interpretation in the experimental design. The second requirement, the relevance to current research, is becoming increasingly difficult to realize because of the cost and training needed to operate modern research instrumentation. Magnetic resonance snectroscoov is one area where i t is Dossible to introduce advanced E&cepts and powerful techniques with relatively accessible instrumentation. makine it oarticularlv attractive for a physical chemistry lab. The fmfiiarity of t i e concepts of magnetic resonance is an additional advantage. Students are exposed t o the elementary concepts of nuclear magnetic resonance in the context of organic structural analysis, and these concepts are reinforced in physical chemistry lectures where problems of spin operators and wave functions are often introduced as a quantum mechanical paradigm. A number of interesting laboratory experiments relating to NMR have already been reported ( 1 , 2 ) ,but electron paramagnetic resonance (EPR)' is much less commonly considered. even thoueh i t is an essential tool in characterization of inorganic comaexes and organic free radicals (4, 5). The EPR studv of the eas ohase ~aramaeneticresonance of nitric oxide outlked berow is techkcally accessible for upper level undergraduates yet can give significant insight into the connection hetween spectroscopy, structure, and dynamics, complementing traditional experiments such as determination of the rovibrational structure constants of HCI and DCl in a molecular spectroscopy laboratory. Background Nitric oxide (NO) is a 15-electron diatomic molecule having a (lo)2(20)2(3u)2(40)2(1u)4(5u)2(2u)1ground state configuration (6). Pauli pairing among the odd number of electrons leads to a single unpaired electronic spin in the neutral molecule associated with a singly occupied T-bonding valence molecular orbital. As a result, nitric oxide is a paramaenetic eas with a s ~ i ndoublet (S = %) mound state exh&itinguan effective permanent m&neticdipole moment of 1.86 bohr maenetons a t room t e m ~ e r a t u r e(7). (Dioxveen, .- . with one more eiectron, is a ground Gate triplet.) By convention, molecular electronic states are labelled by a manyelectron molecular term symbol, 2t+'A~, which can be derived for a diatomic molecule by defining the component of orbital angular momentum along the internuclear axis (A), the electronic spin (2), and the total angular momentum (J), which is composed vectorially from orbital, spin, and rotational parts. Excellent discussions of angular momentum theory relating to molecular spectroscopy are available (8,9), so only an abbreviated presentation will bemade here.
'
A discussion of the relative merits of the terms EPR (electron paramagnetic resonance) and ESR (electron spin resonance) has recently been opened with the view of establishing a standard usage. See for example ref 3.
Figure 1. Vector coupling model for the NO molecule.
The internuclear axis is the quantization axis for orbital angular momentum in a diatomic molecule, as illustrated in Figure 1. A, the projection along this axis, can take all values from -L to +L in integer steps, the value being represented by a capital Greekletter in the series 2 , II, A,. . .for 1 ~ =1 0, 1, 2,. ..paralleling the sequence S, P , D,. . . familiar from the assignment of atomic spectral terms. (For a single aelectron, L = 1, so A = -1.0, +I). Spin-orbit coupling ties the electronic spin to the internuclear axis as well with projection 2. Rotational angular momentum ( R ) associated with the end-over-end tumbling of the molecule is on the other hand required to lie perpendicular to the internuclear axis and therefore perpendicular to A and 2. In the Hund's case (A) scheme, appropriate for a molecule like NO with moderate spin orbit coupling and relatively small atomic masses, L and S are tied to the internuclear axis with projecti0ns.A and 2 forming a resultant fl, the projection of the total angular momentum on the internuclear axis. The total angular momentum is formed by the vector sum J = L S R. The electronic ground state of NO can thus be systematically labelled by the term syrnbol2IIlizei2with the ambiguity in Jreflecting the fact that, even in the absence of a rotational contribution. J can be comoosed to eive either '/" or 3/7 bv vector addition of orbital and spin angular momenra. f a c k of these nerves as the origin for rotational ladders. Experi-
+ +
Volume 68
Number 5
May 1991
421
mentally, the J = %state is found t o lie lowest, with the J = 3/2 level approximately 120 cm-' higher in energy (11). The molecular magnetic moment of NO is associated with the total angular momentum of the molecule, with contrihutions from electronic spin and orhital angular momenta, as well as rotational angular momentum of the end-over-end motion of the molecule, as illustrated in the vector coupling diagram (Fig. 1).The magnetic moment leads to important spectroscopic consequences relating to magnetic field perturbation (Zeeman effect). A maenetic field couoline . with the permanent molecular magnetic moment splits degenerate levels. the maanitude of the solittina beinw ~ r o ~ o r t i o n a l to the projection-of the magnetic moment z i n g t h e field direction. In thevector coupling model of the diatomic molecule, we can evaluate the Zeeman interaction from the eigenvalues of the Zeeman Hamiltonian 3f = FJH where @.I is the molecular magnetic moment arising from the comhined spin and orbital moments and H is the magnetic field strength. The total angular momentum, J , is quantized alougthe direction of the magnetic field, H, giving projectionsM~.The component of the molecular magnetic moment FJ along the total angular momentum J m u s t he evaluated to obtain the magnitude of the Zeeman interaction. Working backward through the vector coupling formulas to compose the J in terms of elementary components, we evaluate the projection of J on H, the projection of Q on J, and the magnitude of the maenetic dioole moment due to orbital and snin comDo(The romtional contribution to the magnetic nents. .l 2. moment is relatively small.and so is nealected here ill,).) We can evaluate these terms geometricall$
-
+
This gives the magnitude of the magnetic field perturbation as
where B is the electronic bohr magneton (4.669 X low5cm-'/ gauss). The term in curly brackets arising from the vector coupling of molecular angular momenta is traditionally , "spectroscopic splitting fador" associated known as g ~the with paramagnetic resonance transitions between levels split by the Zeeman interaction (10, 11). Eq 3 contains the information that the splitting of molecular energy levels is proportional to MJ and to the magnetic field strength. We are now in a position to evaluate g~ for the NO ground state. There are two Q values to consider relating to the two electronic states 211112 and 2113/2, each arising from a different
422
Journal of Chemical Education
combination of A and 2. Inserting the appropriate values and identifying the term in curly brackets with g~ in eq 2 gives g~ = 0 for 211~12 (where A and 2 combine with opposite signs) and& = 4/5 for 211312. This indicates that2111i2does not split under magnetic field interactions, andsoonly the J = state is important in the magnetic resonance experiment. Further calculation indicates that the g~for the first rotationally excited state of the J = 31%manifold is so small that the resonance field H,, defined below is out of range of a typical EPR spectrometer. We will therefore focus on the lowest level of the 211312 manifold for the remainder of the discussion. The Effectlve Harnlltonlan and the Soectrurn
It is convenient to analyze paramagnetic resonance spectra in terms of an effective Hamiltonian for a J encompassing all angular momentum components in the state of interest, avoiding an explicit analysis outside of this state. The effective ~ a h i l t o n f a ngiving the energies of the components of a molecular state takes the form: 3f = s,,
+ 3f& + 3fhf
= gJBHJ,
+ D(J:
+
- % J ( J + I)) AJZZ
(3)
Here D represents an empirical "zero field splitting" parameter that reflects a perturbation that partly removes the MJ degeneracies in the absence of an applied magnetic field, A is the electron-nuclear hwerfine couoline .. ' .. constant. and we neglect quadrupolar coupling with the I = 1 nitrogen nucleus, which is iust below the level of resolution of this e x ~ e r i ment. We can use this effective Hamiltonian to defind the state of NO and interpret the fine structure of the 211312 spectra. First we will need to evaluate the eigenvalues of this effective Hamiltonian within the IJ, MJ, I, MI) basis set, which can be abbreviated as lMJ, MI). We can set up the Hamiltonian matrix between the 12 components of the basis set, using foresight t o order them in the most convenient fashion (table). The diagonal matrix elements give the Zeeman energies of the 12 components of the '11312, state in an applied magnetic field. There are no off-diagonal matrix elements so the A, 2, J remain good quantum numbers under the magnetic field perturbation. Transitions will be allowed between levels between which MJ differs by f1 (conservation of angular momentum for absorption ofa photon carrying 1unit of angular momentum) when the nuclear quantum number does not change (AM, = 0). These transitions among J levels are associated with a magnetic dipole transition moment, and are classified as magnetic dipole transitions. The AMJ = i 1 , O selection rule active for magnetic dipole transitions restricts the number of allowed transitions to nine. All nine transitions can be resolved in the spectrum (Fig. 2), permitting an experimental evaluation of the spectroscopic parameters g ~ D, . and A from the data.
Figure 2. X-harm magnetic resonance spectrum of NO. Experimental paramaters: mlcrawave frequency. 9.60 GHz: microwave power. 2.0 mW; center field.8850 G: scan range. 335 G modulation amplitude. 5.0 G; receiver gain. 8 X lo5:temperature. 298 K. The spectrum shown is the result of a 10-scan accumulation.
- -
-
T h e intensities of t h e 31% 'Iz, 1' 2 -%, and -% -% transitions have been calculated t o he in t h e ratio 3:4:3 (11) leading t o a n assignment of t h e major splitting in the spectrum a s arising from t h e zero field perturbation D, with the smaller triplet splittings resulting from electron-nuclear hyperfine coupling with t h e I = 1I4N nucleus. Experimental Procedure and Analysis The instrumentation requirements for this experiment are similar to those for other EPR experiments, and virtually any commercial X-band EPR spectrometer with magnetic field range up to 1 tesla will be appropriate. We have used a Bruker ER300 EPR spectrometer with a standard TEm cavity, modifying a l-em quartz NMR tube by attaching a vacuum stopcock to the top to construct the sample cell. The sample is prepared by several cycles of evacuation and backfilling with NO gas (Matheson), taking care to avoid contact with the nitric oxide. (Corrosive. Poison.) Atmospheric gases leaking into the sample cell will lead to the appearance of brown nitrogen oxides, which interfere in the experiment. The gas handling required for preparation of the sample is most conveniently performed on a vacuum manifold, taking adequate precautions in venting the gas from the vacuum system. No EPR signal for NO will be ohs&ed-at atmospheric pressure, but at roughing pump pressures (approximately 10-2-1 torr) the signal is sufficiently sharp to he observed. The disappearance of the signal at higher pressures is
the result of collisional hroadening, which is largely avoided by reducing the pressure to the point where the collision frequency is Less than the microwave frequency (approximately the reciprocal of the time required for a spectroscopic transition at a well defined energy hased on the uncertainty principle, approximately s at microwave frequencies.) The nine-line spectrum is recorded with sufficient resolution in the field axis to define the resonance fields, and the magnetic field and microwave frequency should be calibrated if gaussmeter and frequency counters are available. The experimental resonance fields can he read from the chart paper, measuring at the crossing points of the derivative EPR spectrum. From the resonance condition AE = hv,and the transition energies obtained by subtracting the Zeeman energies for states for which selection rules allow a spectroscopic transition, a table of resonance fields can he drawn up for the nine allowed transitions in terms of the parameters gj, D, and A, for example:
AE = h" = gJ@H,, + 20 + A
-
1) Ill2, 1) transition, etc. In all there are nine for t h e equations in three unknowns, making the problem overdetermined, and the set of simultaneous equations is then solved for the spectroscopic parameters. Conclusion Electron paramagnetic resonance can provide a n effective approach for teaching experimental methods of molecular spectroscopy. T h e approach is not limited t o free radicals or inorganic complexes in solution studies and can be used t o a deeper understanding of magnetic resonance re& niaues in a framework suitable for the advanced undergraduate laboratory. Literature Clted
1. Shoemaker, D. P.; Garland. C. W.: Steinfeld, d. I.; Niblcr, 3. W. Expa~imenlai n Physical Chemistry, 4th ed.; McGrsw-Hill: New York, 1981. 2. Roper, G. C. J. Chem. Edue. 1985.62.889. 3. Belford. L. R.EPR Soe. Newsletter 1989.1. 4. Eastman, M.P. J. Chem. Educ. 1982.59,677. 5. Moore, R.:DiMsgno.S.G.;Yaon, H. W. J. Chem. Educ. 1986.53.818. H. B.Molaculor Orbital Theory;Benjamin-Cummings: R e d ing. ~~.'1964. 7. Bitter. F.Pmc. N e t . Acod. Sci. US. 1929,15,632. 8. Zare, R. N. Angular Momentum: Undersfonding Spatial Asperfa in Chemistry and Physics: Wiley: New Y ~ r k 1988. . s Henhere. G. Molecular Socctro ond Moleculoi Sfruetun I. Spacrro of Diotomrc 6. Ballhausen. C.J.:Grsv.
Nominations Sought for Magnetic Resonance Award Nominations are now being sought for the 1992 Eastern Analytical Symposium (EAS) Award far Outstanding Achievements in Magnetic Resonance. The award consists of a plaque, which will be presented at a special award symposium arranged in recognition of the recipient. The Award will be presented at the 1992 EAS in Somerset, NJ ,in November 1992. Establiqhed in 1990, this award is designed to recognize an individual who has made significant contributions to the field of nuclear magnetic resonance. A nomination letter describing the nominee, including specific accomplishments, should be submitted along with a biographical sketch by August 1, 1990. Send all materials to Chairman, EAS Awards Committee, Eastern Analytical Symposium Inc., P.O. Box 633, Mantchanin, DE 19710-0633.
Volume 68
Number 5
May 1991
423
