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The rotational resonance Raman spectrum of nitrogen dioxide and the determination of electronic state symmetry from resonance Raman selection rules
JOURNAL
OF MOLECULAR
SPECTROSCOPY
50, 403-412 (1974)
The Rotational Resonance Raman Spectrum of Nitrogen Dioxide and the Determination of Electronic State Symmetry from Resonance Raman Selection Rules GEORGE
R. BIRD
AND MICHAEL
J. MARSDEN
wrigkt and Rieman Laboratories, Scl~ool of Chemistry, Rutgers ~:niversity, The State University qf Neze’ Jersey, Nem Brunszlick, Neut Jersey 08903
The pure rotational Raman spectrum of nitrogen dioxide has been observed and shown to be consistent with existing determinations of molecular parameters. Upon observation at 600 Torr pressure and 0.4 cm-’ resolution a well-defined rotational spectrum is obtained. This spectrum is overlaid with a number of fluorescence lines. The fluorescence lines are separated from the Raman spectrum by a comparison of Stokes and anti-Stokes branches of the rotational spectrum. Out of seven strong fluorescence lines seen with 5145 A excitation, five probably are identifiable with vibration-rotation fluorescence progressions observed by Abe. The most striking feature of these observations is the potential use of the resonance Raman effect for the analysis of complicated electronic spectra. When this rotational spectrum is observed with excitation by 5309 A or 5145 .k excitation, the Raman spectrum follows a-axis selection rules and the Q-branches are in the noise level or barely out of it. However, at 4880 ,% the AK = 2 Q-branches become a major feature of a spectrum, indicating that an appreciable part of the absorption at this wavelength is occurring through the operation of b- or c-axis selection rules. These findings are consistent with present notions of a *Bx excited state dominating absorption at longer wavelengths, while at shorter wavelengths a zBI excited state becomes important. Given a tunable laser, one could map the relative importance of these two possible selection rules for NO2 without any theoretical analysis more sophisticated than that presented in this paper. A simplified statement of the selection rules for resonance rotational Raman spectra of asymmetric tops has been developed in the course of this investigation. No attempt has been made to refine the rotational parameters of NO2 since all of the lines seen areunresolved multiplets. Our data should be regarded as a search spectrum preliminary to investigation on a high resolution instrument.
The advent of laser excited Raman spectroscopy has generated wide interest in resonance-excited observations. Individual molecular vibrations may or may not show the characteristics of resonance excitation (strong excitation and long progressions of overtones) if the vibration is or is not strongly coupled to the electronic transition in the region of excitation (1). In the condensed phase, Raman transitions tend to be narrower than fluorescence emission at ordinary temperatures (Z), and it is thus quite easy to separate the overlapping Raman and fluorescence spectra, provided, of course, that the fluorescence output does not simply overpower the Raman spectrum. The separation of fluorescence and Raman spectra for a polyatomic molecule in the gas phase is complicated by the narrowness of both kinds of emission lines. Even a 403 Copyright All rights
0
1974
by Academic
of reproduction
Press.
in any form
Inc. reserved.
404
BIRD AND MARSDEN
relatively simple molecule such as NOs has an exceedingly complex array of absorption lines (3), and may emit a rather complicated multiline fluorescence spectrum. Here the separation is accomplished by observing at relatively high gas pressure to maximize fluorescence quenching (4) and by observing with several closely spaced excitation frequencies. Under these conditions, the Raman shiJts from the frequency of excitation are conserved, while the fluorescence lines hold their absolute frequencies but vary grossly in intensity from one excitation frequency to another. Ideally, one would like to use a continuously tuneable laser and seek a relatively dead spot in the fluorescence excitation spectrum, but the separation of fluorescence and Raman spectra can be accomplished with as few as two or three fixed laser lines. Using these methods of high pressure and multiple excitation, we have obtained the vibrational resonance Raman spectrum of NOz in the gas phase (5) at total pressures of 200 to 600 Torr. With 514.5 nm excitation the strongest feature is a progression in ~2, the bending vibration. This feature is repeated with 488 nm excitation, and other features are seen which should be dismissed as fluorescence according to the test stated above, except that these features fall exactly where one would expect the symmetrical stretching vibration ZQ and the overtones and combinations of the two symmetrical vibrations. Lacking for a time a third strong laser line in the vicinity, we were at a disadvantage until the situation was clarified by observation of the rotational spectrum of NOz under these same conditions. The resonance rotational Raman spectrum of NO2 turns out to be both simple and highly informative with respect to the several excited electronic states of the molecule. The rotational Raman spectrum of a small molecule like NOa is especially simple to separate from any interfering fluorescence lines. The Stokes (red-shifted) and antiStokes branches are identical in location (s) and differ only by a thermal population factor in intensity. Thus, any gross difference between the Stokes and anti-Stokes branches may be attributed to fluorescence. Further, the rotational spectrum is highly redundant, with many more absorption frequencies than adjustable molecular constants, and in the case of NO? the ground state molecular constants are known from microwave (6) and high resolution infrared (7,8) results to very high accuracy. We could easily have neglected to observe the rotational Raman spectrum on the grounds that it would contain no new information. Happily, we did observe the spectrum with these two excitation lines, and discovered a source of information on the excited states of NOe. The rotational Raman spectrum of NOz is expected to fall in the region of 250 cm-r on both sides of the exciting line. This spectrum was observed on a Cary-Varian model 82 Raman spectrograph with nominal resolution of 0.4 to 0.5 cm-‘. The sample was at 600 Torr total pressure, and thus contains more N20.t than N02. However, the dimer has no absorption bands in the region of excitation, so the resonance Raman spectrum of the monomer completely dominates these observations. Any dimer present does serve the useful function of an added fluorescence quencher for the monomer. A COherent Radiation argon laser provided powers of 600 mW at 5145 A, and 900 mW at 4880 A, but the transfer optics of the Cary spectrograph delivered only 220 mw and 158 mW, respectively to the sample interaction space. With the 5309 A krypton line, 58 mW of power was delivered to the sample. The exciting radiation is almost totally absorbed in about 1 cm of path, so no attempt was made to use multipass excitation optics. The gas cell with Brewster windows was carefully mounted off-center so that
RESONANCE
Equation
KXMAS
SPECTRUM
405
OI: X02
I
E(N,K)
=
(y, N(N+l + (A-y
&,b;)
)(Kz,+
“=I
the region
of intense
irradiation
at the bottom
aperture of the monochromator-photometer. and recorded with 50 set time constant scale,
respectively
at 5145 A and 4880 A. Under
and observation, chromator and
the photometer
system
was spot-calibrated
the frequency
shifts
against
are certainly
at this level of resolution
Lines. Some
of the sharper
of the attenuated an upper width
limit
lines
of about
The calculation has been discussed
accurate
are actually
are actually exhibit
in relation
at medium-high levels from
levels
resolution
lines
(half-width
The monoin the
in all cases,
and symmetrical.
to
superimposed
to the direct Thus
region,
probably
All of the lines
of nonexactly
scattering.
observation
the results
at half-height)
set only
on the
line
mixture.
of a nearly
symmetric
in the Raman
parameters
of excitation
stability.
laser
comparable
to the high resolution
microwave
argon
multiplets
widths
monomer-dimer
conditions
gratifying
to 0.2 cm-’
lines are sharp
5 X 1W4 cm-‘/Torr
of the energy
extreme
with
laser line, as seen in Rayleigh
of iXOr in this particular
of energ!-
these
behaved
with the acceptance
were scanned at 0.01 cm-‘/see of 100 and 50 counts/set full
all the known
0.1 cm-’ in those cases where individual observed
of the cell coincided
The spectra and sensitivities
prolate
far-infrared spectrum,
can be adapted
top such
spectrum
as NO2
(7). Since we
the earlier
to the present
calculation spectra
by
nothing more than a shift of selection rules. The molecular parameters used in calculating the energy levels are given in Table 1, and Eq. (1) gives the basis for the calculation of energy levels. Note that the term A - (R + C)/2 dominates the energy equation, and will also dominate the pattern of the rotation spectrum if the limiting prolate symmetric quantum
number
KI is allowed
which is a very good quantum complete (J. Kl,
to change number
in the observed
transitions.
for NO?, will be simply. specified
selection rules are given, the notation K+l) will be used. Since NO, has a pair
of King, of identical,
Hereafter,
K 1,
as K, and where
Hainer, and C’ross (9) zero-spin nuclei, onI>
levels with K-1 + K+l = even are permitted to exist in the ?A 1 ground state. Also, since the molecule has an unpaired electron spin, the usual J quantum number becomes IV, and J is reserved for the total angular momentum of nuclear framework plus spin. Tn fact, no magnetic splittings have been observed in this Raman spectrum, but splittings are predicted to become observable with only a modest improvement in resolution. The selection rules for rotational Raman spectra have been explored by Placzck
BIRD
406
AND MARSDEN
and Teller (10). In the special case of resonance Raman effect involving virtual excitation to a single excited electronic state, the selection rules take on the same mathematical form as the selection rules for the successive processes of absorption and fluorescence to and from the excited electronic state (II). Since the selection rules are wellknown for absorption and emission, the Raman selection rules take on the same simplicity. The spectra reported here are a good example of this principle. Consider first the ‘Bz (u-axis polarized transition from 2A1 ground state) excited state, analyzed in part by Abe and co-workers (12). The dipole selection rules to this state are AN = f 1,O and AK = 0, and of course identical rules operate on the fluorescence transition back to the ground state. Thus, the overall Raman selection rules for the pure rotational spectrum are AN = f 2, f 1, 0 and AK = 0. The absence of any change in K greatly simplifies the spectrum and compresses it into a smaller region some 80 cm-’ on each side of the exciting line. These same selection rules will operate for vibration-rotation transitions involving fundamentals, overtones, and combinations of the symmetrical vibrations ~1 and v2 and for excitations to even multiples of the antisymmetric stretching vibration vs (13). The rotational Raman spectrum and the vibrational spectra obtained with 514.5 nm excitation are thus a good example of the operation of this set of selection rules. There is also a fragmentary analysis of an electronic state of 2B~ symmetry (14), and the dipole selection rules for absorption to this state (c-axis polarized transition) are AN = f 1,0 and AK = f 1. The allowable changes in N are as before, but two successive dipole transitions allow K to change by AK = f 2,0 but not by f 1. Thus, TABLE
NO*: IAN = 2, AK_,
KZ
a)
3 f-t 5 4-6 11* 12
(?)
5-7
ROTATIONAL
= 0, Tabulated
Frequency
*esilgment N + Pi+*
(all
PURE
II
Shift*
05.8 cd' 07.6~ 09.3 10.02 10.9-
RAM&N from
SPECTRUM 514.5
"m
Excitation
Fluorescence
SF ASF
AR/(~N
+ 6)
0.425 0.4227
11.a5 12.7
14.3 16.1
17 -
19
18 +* 20 * 21 22 23 24 25 26 *+ 27 /+ 28 <+ 29 30 4 31 -+ 32 33 ++
20 21 22 23 24 25 26 27 *a 29 30 31 3.2 33 34 35
19
36.2 37.95 39.8 41.3 43.15 44.7 46.55 4a.b 50.3s 51.5; 53.35 54.8, 56.75 58.1,
0. LZO? 0.4217 0.4234 0.4214 0.423u 0.4217 0.4232 IO.4215 0.4233 0.4225 0.4234 0.4219 0.4235 0.4214
RESONANCE
RAMAN
SPECTRUM
01; NO*
407
in the rotational Raman effect, these c-axis selection rules include all of the transitions having &V = f 2, f 1,0 and AK = f 2,0. The subset of new transitions with AIV = 0 and AK = f 2 will form especially strong and conspicuous clusters or Q-branches in the case of NOZ. The AK = 2 Q-branches are clearly observable in the spectrum obtained with 488 nm excitation, but are lost in the instrumental noise level when 5145 A escitation is employed. The Q-branches are just above noise level but very weak when 5309 A excitation is employed. Clearly the absorption spectrum of NO:! in the neighborhood of 5145 A is dominated by the 2Bg excited state, while the 2B~ state plays at least a significant role in the absorption spectrum near 488 nm. Thus we see that the resonance rotational Raman spectrum can be used as a symmetry indicator to sort out the statesymmetries involved in the electronic absorption band. This sorting process appears to be limited to distinguishing a-axis transitions from either b-axis or c-axis transitions’ 1The inability to distinguish b- and c-axis transitions results from the fact that k’,, is a very poor quantum number for NO*, so that b-axis dipole rules allow AK +I = i 1 and 13 almost equally, while c-axis rules allowAK+I = 0, 2 with almost equal facility. Since the Raman effect is a two-photon process, it is possible to accomplish AK,.1 = 0, 2, 4 and AK-1 = 0, 2 with either b-axis or c-axis selection rules.
408
BIRD
AND
MARSDEN
NO2 RESONANCE RAMAN SPECTRUM PLUS FLUORESCENCE LINES STOKES SPECTRUM ANTISTOKES SPECTRUM - - -514.5 NM
DISPLACEMENT
CM-’
EXCITATION
’
FIG. 1. The Raman Spectrum of NO* taken at 600 Torr pressure with two wavelengths of excitation. Spectra have been folded about the exciting frequency to superimpose the Stokes and anti-Stokes spectra so that fluorescence lines (F) may be detected by difference. Note that two different sensitivities were used in running the two spectra, so there are corresponding breaks in the sensitivity coordinate. The upper two spectra represent almost exclusively transitions with AN = 2 and AK-1 = 0 as excited through an electronic state of 2Bz symmetry (*A, u2B2 is u-axis polarized.) Except for differences in resolution and the obvious fluorescence lines the two spectra are substantially identical. The lower two curves are simply the continuation to larger shifts of the top two spectra. Here we note the striking difference in the intensity of Q-branch lines with AK = 2. These lines are absent with 5145 A excitation and The Q-branch lines are excited through an electronic present and quite strong with 4880 A excitation. virtual state connected to the 2A 1 ground state by a b-axis or c-axis transition (presumably 2A~ +-+2B~, c-axis polarized).
in the case of a nearly prolate molecule.
A mixture of b- and c-transitions
separated by much more subtle observations case presents just the sort of differentiation
could only be
on intensities. Fortunately NO2 as a test which can be accomplished, that of a- vs
b- or c-axis transitions. The two sets of Stokes and anti-Stokes spectra are shown in Fig. 1. The spectra have been folded about the laser line to illustrate the differentiation and extraction of fluorescence peaks. The measured shifts and families of dominant transitions are listed in Table
2. Some detailed
examples
of individual
unresolved
clusters are shown in Figs.
RESONANCE
RAMAN
+-1_
SPECTRUM
OF NO%
409
_ _Jl_
37 DISPLACEMENT
CM -’
e
PIG. 2. Figure 2 is the calculated spectrum showing the effect of finite molecular asymmetry on the individual S-branch lines. The effect of asymmetry is relatively small in the S-branch since all transitions connect states of the same parity. However, the even members of the S-branch have two strong lines shifted to high frequency and one low for a net bias to high frequency, while the odd members of the S-branch have a single strong component shifted to low frequency for a net bias to low frequency. This asymmexy shift will explain the net staggered bias of lines which may be seen in Table 2. The intensities are here calculated in the symmetric top approximation for a-axis selection rules. Magnetic effects are relatively unimportant in the 0- and S-branches, so no magnetic splittings have heen introduced here.
410
BIRD
AND
0
No,
I
CALCULATED SPECTRUM:
2
RAMAN 4K_,=O
:: 2
2 lu 2 9 bi
IL
MARSDEN
4
)
4.5 c l6 =21”2mp21 1 185
7 2 , 2j2 19.0 DISPLACEMENT
+&
WO~lZ
1
N=22++23 I
CM’~’
FIG. 3. Figure 3 gives a comparison of the S- and R-branches whether any of the R-branch lines have been seen in the present which fall between S-branch lines do contribute to a filling-in R-branch transitions connect states of opposite parity, so the For example, the transition 222.20 + 232.22 is shifted almost into transition 221,2t - 23r,t3 is shifted completely off the graph. ignored since they do not make a major contribution.
I 20.0
in the Raman spectrum. It is doubtful observations, but the R-branch members of the gaps between S-branch lines. The asymmetry shifts are very large indeed. the next lower R-branch cluster and the Here again, magnetic effects have been
2, 3, and 4. The fluorescence lines are listed in Table 3, along with partial identification following Abe’s recent results (IZb). The agreement between calculated spectra (Figs. 2, 3, 4) and observations (Fig. 1, Table 2) is highly satisfactory, but does not now permit derivation of new molecular parameters, since clusters of lines are observed in all cases. The point of greatest importance is the gross variation of the ratio of intensities between the Q-branches (AK = 2, b or c selection rules) and the 0, S-branches (AJ = f 2, AK = 0, a- or b- or c-axis).
NO2 AN=0
K$
=4*6
FIG. 4. Figure 4 shows a full detail of one of the Q-branches. The subbranch originating at 6- is composed from those transitions for which J = N - 3, whereas the branch originating with 6+ is composed of those having J = N + 3. The branch with J = N + ) is slightly more intense than the branch with J = N - $. The separating of these two branches is entirely a magnetic effect and should be observable with slightly higher resolution than is available on our present instrument. This type of transition represents about the largest magnetic effects which occur in the NO2 spectrum for lines of reasonable intensity. The intensities of the components here have been calculated using the symmetric top approximation with b- or c-axis selection rules.
RESONANCE
RAMAN
SPECTRUM
OF NO?
411
The Q-branch lines are essentially silent at 5309 A and 5145 A excitation, but rise to 30% of the S-branch intensity at 4880 A. We have here a point-by-point probe of the rising intensity of the 2.4I --f 2B~ absorption system, obtained without any of the complexity of attempting a direct solution of the electronic absorption spectrum. This is, as far as we know, the first time that rotational Kaman selection rules have been used to sort electronic states of an asymmetric top. The method is simple and direct, but one wishes for a tunable laser to explore finer details and to look for local oscillations in this ratio as the excitation frequency passes through vibrational subbands of the overall electronic transitions. The success of this sorting method is facilitated by the order-of-magnitude difference between (A - (B + C)/2) = 7.579 crt-’ and (I? + C)/2 = 0.422 cm-‘. This difference throws the Q-branch lines into a region free from interference by any other features, and lends a high sensitivity to the observation of Q-lines. However, the method appears to be general, provided only that a partial resolution of the rotational spectrum of the candidate molecule must be accomplished with the apparatus at hand. Note added in proof. Since submission of this manuscript, the measurements of intensities and intensity ratios have been extended to the Krypton 6471 X line. With this line, the AK = 2 Q-branches were lost in the noise level for a ratio (Table IV, bottom line) less than .Ol.
ACKNOWLEDGMENTS The spectrograph and lasers employed in this work were purchased jointly by the National Science I:oundation (under grant GP 28053) and by Rutgers University. The actual investigation was supported by the Rutgers Research Council. We gratefully acknowledge the help of Professor Joseph San Filippo in securing the spectrum and the help of Dr. Elizabeth Anderson Bond in purifying the NOI sample. RECEIVED:
July
23, 1973 REI;ERENCES
1. E. D. SCHMI~ AND B. BROSA, J. Chem. Phys. 58, 637 (1973). 2. JOSEPH BEHRINGER, “Raman Spectroscopy: Theory and Practice” (H. A. Szymanski, Plenum Press, New York, 1967. 3. J, N. I'ITTS,JK., J, H. SHAKP, AND S. I. CHAN,~. Chem. Phys. 39, 238 (1963).
Ed.), Chap. 6,
412
BIRD
AND
MARSDEN
4. F. E. BLACET, T. C. HALL, AND P. A. T,EIGHTON,J. dmer. Ckem. Sot. 84, 4011 (1962). 5. J. J. MARSDEN AND G. R. BIRD, J. Chem. Phys., 59, 2766 (1973). 6. (a) G. R. BIRD, J. C. BAIRD, A. W. JACHE, J. A. HODGESON,R. F. CURL, JR., A. C. KUNI~LE, J. W. BRANSFORD,J. RASTRUP-ANDERSEN,AND J. ROSENTHAL,J. Ckem. Pkys. 40, 3378 (1964). (b) R. M. LEES, R. F. CURL, JR., AND J. G. BAKER, J. Chem. Phys. 45, 2037 (1966). 7. G. R. BIRD, G. R. HUNT, A. H. GEBBIE, AND N. W. B. STONE, J. Mol. Spectrosc. 33, 244 (1970). 8. (a) E. T. ARAKAWA AND A. H. NIELSEN, J. Mol. Spectrosc. 2,413 (1958). (b) M. D. OLMANAND C. D. HAUSE, J. Mol. Spectrosc. 26, 241 (1968). 9. G. W. KING, R. M. HAINER, AND P. C. CKOSS, J. Chem. Pkys. 11, 27 (1943). 10. G. PLACZEKAND E. TELLER, 2. Physik 81, 209 (1933). II. Ref. (2), p. 214 and eq. 33. 12. (a) K. ABE, I;. MYEXS, T. K. MCCUHHIN, AND S. R. POLO, J. Mol. Spectrosc. 38, 552 (1971). (b) K. ABE, private communication. 13. G. HERZBERG, “Infrared and Raman Spectra (of Polyatomic Molecules),” Van Nostrand Co., New York, 1945. (See especially p. 106, pp. 113-4, 24&264.) II. A. E. DOUGLAS AND K. P. HUBER, Can. J. Phys. 43, 74 (1965). 15. (a) P. C. CROSS, R. M. HAINER, AND G. W. KING, J. Chem. Phys. 12, 210 (1944). (b) D. R. LIDE J. Chem. Phys. 20, 1761 (1952).
OF MOLECULAR
SPECTROSCOPY
50, 403-412 (1974)
The Rotational Resonance Raman Spectrum of Nitrogen Dioxide and the Determination of Electronic State Symmetry from Resonance Raman Selection Rules GEORGE
R. BIRD
AND MICHAEL
J. MARSDEN
wrigkt and Rieman Laboratories, Scl~ool of Chemistry, Rutgers ~:niversity, The State University qf Neze’ Jersey, Nem Brunszlick, Neut Jersey 08903
The pure rotational Raman spectrum of nitrogen dioxide has been observed and shown to be consistent with existing determinations of molecular parameters. Upon observation at 600 Torr pressure and 0.4 cm-’ resolution a well-defined rotational spectrum is obtained. This spectrum is overlaid with a number of fluorescence lines. The fluorescence lines are separated from the Raman spectrum by a comparison of Stokes and anti-Stokes branches of the rotational spectrum. Out of seven strong fluorescence lines seen with 5145 A excitation, five probably are identifiable with vibration-rotation fluorescence progressions observed by Abe. The most striking feature of these observations is the potential use of the resonance Raman effect for the analysis of complicated electronic spectra. When this rotational spectrum is observed with excitation by 5309 A or 5145 .k excitation, the Raman spectrum follows a-axis selection rules and the Q-branches are in the noise level or barely out of it. However, at 4880 ,% the AK = 2 Q-branches become a major feature of a spectrum, indicating that an appreciable part of the absorption at this wavelength is occurring through the operation of b- or c-axis selection rules. These findings are consistent with present notions of a *Bx excited state dominating absorption at longer wavelengths, while at shorter wavelengths a zBI excited state becomes important. Given a tunable laser, one could map the relative importance of these two possible selection rules for NO2 without any theoretical analysis more sophisticated than that presented in this paper. A simplified statement of the selection rules for resonance rotational Raman spectra of asymmetric tops has been developed in the course of this investigation. No attempt has been made to refine the rotational parameters of NO2 since all of the lines seen areunresolved multiplets. Our data should be regarded as a search spectrum preliminary to investigation on a high resolution instrument.
The advent of laser excited Raman spectroscopy has generated wide interest in resonance-excited observations. Individual molecular vibrations may or may not show the characteristics of resonance excitation (strong excitation and long progressions of overtones) if the vibration is or is not strongly coupled to the electronic transition in the region of excitation (1). In the condensed phase, Raman transitions tend to be narrower than fluorescence emission at ordinary temperatures (Z), and it is thus quite easy to separate the overlapping Raman and fluorescence spectra, provided, of course, that the fluorescence output does not simply overpower the Raman spectrum. The separation of fluorescence and Raman spectra for a polyatomic molecule in the gas phase is complicated by the narrowness of both kinds of emission lines. Even a 403 Copyright All rights
0
1974
by Academic
of reproduction
Press.
in any form
Inc. reserved.
404
BIRD AND MARSDEN
relatively simple molecule such as NOs has an exceedingly complex array of absorption lines (3), and may emit a rather complicated multiline fluorescence spectrum. Here the separation is accomplished by observing at relatively high gas pressure to maximize fluorescence quenching (4) and by observing with several closely spaced excitation frequencies. Under these conditions, the Raman shiJts from the frequency of excitation are conserved, while the fluorescence lines hold their absolute frequencies but vary grossly in intensity from one excitation frequency to another. Ideally, one would like to use a continuously tuneable laser and seek a relatively dead spot in the fluorescence excitation spectrum, but the separation of fluorescence and Raman spectra can be accomplished with as few as two or three fixed laser lines. Using these methods of high pressure and multiple excitation, we have obtained the vibrational resonance Raman spectrum of NOz in the gas phase (5) at total pressures of 200 to 600 Torr. With 514.5 nm excitation the strongest feature is a progression in ~2, the bending vibration. This feature is repeated with 488 nm excitation, and other features are seen which should be dismissed as fluorescence according to the test stated above, except that these features fall exactly where one would expect the symmetrical stretching vibration ZQ and the overtones and combinations of the two symmetrical vibrations. Lacking for a time a third strong laser line in the vicinity, we were at a disadvantage until the situation was clarified by observation of the rotational spectrum of NOz under these same conditions. The resonance rotational Raman spectrum of NO2 turns out to be both simple and highly informative with respect to the several excited electronic states of the molecule. The rotational Raman spectrum of a small molecule like NOa is especially simple to separate from any interfering fluorescence lines. The Stokes (red-shifted) and antiStokes branches are identical in location (s) and differ only by a thermal population factor in intensity. Thus, any gross difference between the Stokes and anti-Stokes branches may be attributed to fluorescence. Further, the rotational spectrum is highly redundant, with many more absorption frequencies than adjustable molecular constants, and in the case of NO? the ground state molecular constants are known from microwave (6) and high resolution infrared (7,8) results to very high accuracy. We could easily have neglected to observe the rotational Raman spectrum on the grounds that it would contain no new information. Happily, we did observe the spectrum with these two excitation lines, and discovered a source of information on the excited states of NOe. The rotational Raman spectrum of NOz is expected to fall in the region of 250 cm-r on both sides of the exciting line. This spectrum was observed on a Cary-Varian model 82 Raman spectrograph with nominal resolution of 0.4 to 0.5 cm-‘. The sample was at 600 Torr total pressure, and thus contains more N20.t than N02. However, the dimer has no absorption bands in the region of excitation, so the resonance Raman spectrum of the monomer completely dominates these observations. Any dimer present does serve the useful function of an added fluorescence quencher for the monomer. A COherent Radiation argon laser provided powers of 600 mW at 5145 A, and 900 mW at 4880 A, but the transfer optics of the Cary spectrograph delivered only 220 mw and 158 mW, respectively to the sample interaction space. With the 5309 A krypton line, 58 mW of power was delivered to the sample. The exciting radiation is almost totally absorbed in about 1 cm of path, so no attempt was made to use multipass excitation optics. The gas cell with Brewster windows was carefully mounted off-center so that
RESONANCE
Equation
KXMAS
SPECTRUM
405
OI: X02
I
E(N,K)
=
(y, N(N+l + (A-y
&,b;)
)(Kz,+
“=I
the region
of intense
irradiation
at the bottom
aperture of the monochromator-photometer. and recorded with 50 set time constant scale,
respectively
at 5145 A and 4880 A. Under
and observation, chromator and
the photometer
system
was spot-calibrated
the frequency
shifts
against
are certainly
at this level of resolution
Lines. Some
of the sharper
of the attenuated an upper width
limit
lines
of about
The calculation has been discussed
accurate
are actually
are actually exhibit
in relation
at medium-high levels from
levels
resolution
lines
(half-width
The monoin the
in all cases,
and symmetrical.
to
superimposed
to the direct Thus
region,
probably
All of the lines
of nonexactly
scattering.
observation
the results
at half-height)
set only
on the
line
mixture.
of a nearly
symmetric
in the Raman
parameters
of excitation
stability.
laser
comparable
to the high resolution
microwave
argon
multiplets
widths
monomer-dimer
conditions
gratifying
to 0.2 cm-’
lines are sharp
5 X 1W4 cm-‘/Torr
of the energy
extreme
with
laser line, as seen in Rayleigh
of iXOr in this particular
of energ!-
these
behaved
with the acceptance
were scanned at 0.01 cm-‘/see of 100 and 50 counts/set full
all the known
0.1 cm-’ in those cases where individual observed
of the cell coincided
The spectra and sensitivities
prolate
far-infrared spectrum,
can be adapted
top such
spectrum
as NO2
(7). Since we
the earlier
to the present
calculation spectra
by
nothing more than a shift of selection rules. The molecular parameters used in calculating the energy levels are given in Table 1, and Eq. (1) gives the basis for the calculation of energy levels. Note that the term A - (R + C)/2 dominates the energy equation, and will also dominate the pattern of the rotation spectrum if the limiting prolate symmetric quantum
number
KI is allowed
which is a very good quantum complete (J. Kl,
to change number
in the observed
transitions.
for NO?, will be simply. specified
selection rules are given, the notation K+l) will be used. Since NO, has a pair
of King, of identical,
Hereafter,
K 1,
as K, and where
Hainer, and C’ross (9) zero-spin nuclei, onI>
levels with K-1 + K+l = even are permitted to exist in the ?A 1 ground state. Also, since the molecule has an unpaired electron spin, the usual J quantum number becomes IV, and J is reserved for the total angular momentum of nuclear framework plus spin. Tn fact, no magnetic splittings have been observed in this Raman spectrum, but splittings are predicted to become observable with only a modest improvement in resolution. The selection rules for rotational Raman spectra have been explored by Placzck
BIRD
406
AND MARSDEN
and Teller (10). In the special case of resonance Raman effect involving virtual excitation to a single excited electronic state, the selection rules take on the same mathematical form as the selection rules for the successive processes of absorption and fluorescence to and from the excited electronic state (II). Since the selection rules are wellknown for absorption and emission, the Raman selection rules take on the same simplicity. The spectra reported here are a good example of this principle. Consider first the ‘Bz (u-axis polarized transition from 2A1 ground state) excited state, analyzed in part by Abe and co-workers (12). The dipole selection rules to this state are AN = f 1,O and AK = 0, and of course identical rules operate on the fluorescence transition back to the ground state. Thus, the overall Raman selection rules for the pure rotational spectrum are AN = f 2, f 1, 0 and AK = 0. The absence of any change in K greatly simplifies the spectrum and compresses it into a smaller region some 80 cm-’ on each side of the exciting line. These same selection rules will operate for vibration-rotation transitions involving fundamentals, overtones, and combinations of the symmetrical vibrations ~1 and v2 and for excitations to even multiples of the antisymmetric stretching vibration vs (13). The rotational Raman spectrum and the vibrational spectra obtained with 514.5 nm excitation are thus a good example of the operation of this set of selection rules. There is also a fragmentary analysis of an electronic state of 2B~ symmetry (14), and the dipole selection rules for absorption to this state (c-axis polarized transition) are AN = f 1,0 and AK = f 1. The allowable changes in N are as before, but two successive dipole transitions allow K to change by AK = f 2,0 but not by f 1. Thus, TABLE
NO*: IAN = 2, AK_,
KZ
a)
3 f-t 5 4-6 11* 12
(?)
5-7
ROTATIONAL
= 0, Tabulated
Frequency
*esilgment N + Pi+*
(all
PURE
II
Shift*
05.8 cd' 07.6~ 09.3 10.02 10.9-
RAM&N from
SPECTRUM 514.5
"m
Excitation
Fluorescence
SF ASF
AR/(~N
+ 6)
0.425 0.4227
11.a5 12.7
14.3 16.1
17 -
19
18 +* 20 * 21 22 23 24 25 26 *+ 27 /+ 28 <+ 29 30 4 31 -+ 32 33 ++
20 21 22 23 24 25 26 27 *a 29 30 31 3.2 33 34 35
19
36.2 37.95 39.8 41.3 43.15 44.7 46.55 4a.b 50.3s 51.5; 53.35 54.8, 56.75 58.1,
0. LZO? 0.4217 0.4234 0.4214 0.423u 0.4217 0.4232 IO.4215 0.4233 0.4225 0.4234 0.4219 0.4235 0.4214
RESONANCE
RAMAN
SPECTRUM
01; NO*
407
in the rotational Raman effect, these c-axis selection rules include all of the transitions having &V = f 2, f 1,0 and AK = f 2,0. The subset of new transitions with AIV = 0 and AK = f 2 will form especially strong and conspicuous clusters or Q-branches in the case of NOZ. The AK = 2 Q-branches are clearly observable in the spectrum obtained with 488 nm excitation, but are lost in the instrumental noise level when 5145 A escitation is employed. The Q-branches are just above noise level but very weak when 5309 A excitation is employed. Clearly the absorption spectrum of NO:! in the neighborhood of 5145 A is dominated by the 2Bg excited state, while the 2B~ state plays at least a significant role in the absorption spectrum near 488 nm. Thus we see that the resonance rotational Raman spectrum can be used as a symmetry indicator to sort out the statesymmetries involved in the electronic absorption band. This sorting process appears to be limited to distinguishing a-axis transitions from either b-axis or c-axis transitions’ 1The inability to distinguish b- and c-axis transitions results from the fact that k’,, is a very poor quantum number for NO*, so that b-axis dipole rules allow AK +I = i 1 and 13 almost equally, while c-axis rules allowAK+I = 0, 2 with almost equal facility. Since the Raman effect is a two-photon process, it is possible to accomplish AK,.1 = 0, 2, 4 and AK-1 = 0, 2 with either b-axis or c-axis selection rules.
408
BIRD
AND
MARSDEN
NO2 RESONANCE RAMAN SPECTRUM PLUS FLUORESCENCE LINES STOKES SPECTRUM ANTISTOKES SPECTRUM - - -514.5 NM
DISPLACEMENT
CM-’
EXCITATION
’
FIG. 1. The Raman Spectrum of NO* taken at 600 Torr pressure with two wavelengths of excitation. Spectra have been folded about the exciting frequency to superimpose the Stokes and anti-Stokes spectra so that fluorescence lines (F) may be detected by difference. Note that two different sensitivities were used in running the two spectra, so there are corresponding breaks in the sensitivity coordinate. The upper two spectra represent almost exclusively transitions with AN = 2 and AK-1 = 0 as excited through an electronic state of 2Bz symmetry (*A, u2B2 is u-axis polarized.) Except for differences in resolution and the obvious fluorescence lines the two spectra are substantially identical. The lower two curves are simply the continuation to larger shifts of the top two spectra. Here we note the striking difference in the intensity of Q-branch lines with AK = 2. These lines are absent with 5145 A excitation and The Q-branch lines are excited through an electronic present and quite strong with 4880 A excitation. virtual state connected to the 2A 1 ground state by a b-axis or c-axis transition (presumably 2A~ +-+2B~, c-axis polarized).
in the case of a nearly prolate molecule.
A mixture of b- and c-transitions
separated by much more subtle observations case presents just the sort of differentiation
could only be
on intensities. Fortunately NO2 as a test which can be accomplished, that of a- vs
b- or c-axis transitions. The two sets of Stokes and anti-Stokes spectra are shown in Fig. 1. The spectra have been folded about the laser line to illustrate the differentiation and extraction of fluorescence peaks. The measured shifts and families of dominant transitions are listed in Table
2. Some detailed
examples
of individual
unresolved
clusters are shown in Figs.
RESONANCE
RAMAN
+-1_
SPECTRUM
OF NO%
409
_ _Jl_
37 DISPLACEMENT
CM -’
e
PIG. 2. Figure 2 is the calculated spectrum showing the effect of finite molecular asymmetry on the individual S-branch lines. The effect of asymmetry is relatively small in the S-branch since all transitions connect states of the same parity. However, the even members of the S-branch have two strong lines shifted to high frequency and one low for a net bias to high frequency, while the odd members of the S-branch have a single strong component shifted to low frequency for a net bias to low frequency. This asymmexy shift will explain the net staggered bias of lines which may be seen in Table 2. The intensities are here calculated in the symmetric top approximation for a-axis selection rules. Magnetic effects are relatively unimportant in the 0- and S-branches, so no magnetic splittings have heen introduced here.
410
BIRD
AND
0
No,
I
CALCULATED SPECTRUM:
2
RAMAN 4K_,=O
:: 2
2 lu 2 9 bi
IL
MARSDEN
4
)
4.5 c l6 =21”2mp21 1 185
7 2 , 2j2 19.0 DISPLACEMENT
+&
WO~lZ
1
N=22++23 I
CM’~’
FIG. 3. Figure 3 gives a comparison of the S- and R-branches whether any of the R-branch lines have been seen in the present which fall between S-branch lines do contribute to a filling-in R-branch transitions connect states of opposite parity, so the For example, the transition 222.20 + 232.22 is shifted almost into transition 221,2t - 23r,t3 is shifted completely off the graph. ignored since they do not make a major contribution.
I 20.0
in the Raman spectrum. It is doubtful observations, but the R-branch members of the gaps between S-branch lines. The asymmetry shifts are very large indeed. the next lower R-branch cluster and the Here again, magnetic effects have been
2, 3, and 4. The fluorescence lines are listed in Table 3, along with partial identification following Abe’s recent results (IZb). The agreement between calculated spectra (Figs. 2, 3, 4) and observations (Fig. 1, Table 2) is highly satisfactory, but does not now permit derivation of new molecular parameters, since clusters of lines are observed in all cases. The point of greatest importance is the gross variation of the ratio of intensities between the Q-branches (AK = 2, b or c selection rules) and the 0, S-branches (AJ = f 2, AK = 0, a- or b- or c-axis).
NO2 AN=0
K$
=4*6
FIG. 4. Figure 4 shows a full detail of one of the Q-branches. The subbranch originating at 6- is composed from those transitions for which J = N - 3, whereas the branch originating with 6+ is composed of those having J = N + 3. The branch with J = N + ) is slightly more intense than the branch with J = N - $. The separating of these two branches is entirely a magnetic effect and should be observable with slightly higher resolution than is available on our present instrument. This type of transition represents about the largest magnetic effects which occur in the NO2 spectrum for lines of reasonable intensity. The intensities of the components here have been calculated using the symmetric top approximation with b- or c-axis selection rules.
RESONANCE
RAMAN
SPECTRUM
OF NO?
411
The Q-branch lines are essentially silent at 5309 A and 5145 A excitation, but rise to 30% of the S-branch intensity at 4880 A. We have here a point-by-point probe of the rising intensity of the 2.4I --f 2B~ absorption system, obtained without any of the complexity of attempting a direct solution of the electronic absorption spectrum. This is, as far as we know, the first time that rotational Kaman selection rules have been used to sort electronic states of an asymmetric top. The method is simple and direct, but one wishes for a tunable laser to explore finer details and to look for local oscillations in this ratio as the excitation frequency passes through vibrational subbands of the overall electronic transitions. The success of this sorting method is facilitated by the order-of-magnitude difference between (A - (B + C)/2) = 7.579 crt-’ and (I? + C)/2 = 0.422 cm-‘. This difference throws the Q-branch lines into a region free from interference by any other features, and lends a high sensitivity to the observation of Q-lines. However, the method appears to be general, provided only that a partial resolution of the rotational spectrum of the candidate molecule must be accomplished with the apparatus at hand. Note added in proof. Since submission of this manuscript, the measurements of intensities and intensity ratios have been extended to the Krypton 6471 X line. With this line, the AK = 2 Q-branches were lost in the noise level for a ratio (Table IV, bottom line) less than .Ol.
ACKNOWLEDGMENTS The spectrograph and lasers employed in this work were purchased jointly by the National Science I:oundation (under grant GP 28053) and by Rutgers University. The actual investigation was supported by the Rutgers Research Council. We gratefully acknowledge the help of Professor Joseph San Filippo in securing the spectrum and the help of Dr. Elizabeth Anderson Bond in purifying the NOI sample. RECEIVED:
July
23, 1973 REI;ERENCES
1. E. D. SCHMI~ AND B. BROSA, J. Chem. Phys. 58, 637 (1973). 2. JOSEPH BEHRINGER, “Raman Spectroscopy: Theory and Practice” (H. A. Szymanski, Plenum Press, New York, 1967. 3. J, N. I'ITTS,JK., J, H. SHAKP, AND S. I. CHAN,~. Chem. Phys. 39, 238 (1963).
Ed.), Chap. 6,
412
BIRD
AND
MARSDEN
4. F. E. BLACET, T. C. HALL, AND P. A. T,EIGHTON,J. dmer. Ckem. Sot. 84, 4011 (1962). 5. J. J. MARSDEN AND G. R. BIRD, J. Chem. Phys., 59, 2766 (1973). 6. (a) G. R. BIRD, J. C. BAIRD, A. W. JACHE, J. A. HODGESON,R. F. CURL, JR., A. C. KUNI~LE, J. W. BRANSFORD,J. RASTRUP-ANDERSEN,AND J. ROSENTHAL,J. Ckem. Pkys. 40, 3378 (1964). (b) R. M. LEES, R. F. CURL, JR., AND J. G. BAKER, J. Chem. Phys. 45, 2037 (1966). 7. G. R. BIRD, G. R. HUNT, A. H. GEBBIE, AND N. W. B. STONE, J. Mol. Spectrosc. 33, 244 (1970). 8. (a) E. T. ARAKAWA AND A. H. NIELSEN, J. Mol. Spectrosc. 2,413 (1958). (b) M. D. OLMANAND C. D. HAUSE, J. Mol. Spectrosc. 26, 241 (1968). 9. G. W. KING, R. M. HAINER, AND P. C. CKOSS, J. Chem. Pkys. 11, 27 (1943). 10. G. PLACZEKAND E. TELLER, 2. Physik 81, 209 (1933). II. Ref. (2), p. 214 and eq. 33. 12. (a) K. ABE, I;. MYEXS, T. K. MCCUHHIN, AND S. R. POLO, J. Mol. Spectrosc. 38, 552 (1971). (b) K. ABE, private communication. 13. G. HERZBERG, “Infrared and Raman Spectra (of Polyatomic Molecules),” Van Nostrand Co., New York, 1945. (See especially p. 106, pp. 113-4, 24&264.) II. A. E. DOUGLAS AND K. P. HUBER, Can. J. Phys. 43, 74 (1965). 15. (a) P. C. CROSS, R. M. HAINER, AND G. W. KING, J. Chem. Phys. 12, 210 (1944). (b) D. R. LIDE J. Chem. Phys. 20, 1761 (1952).