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The EPR and LMR spectra of the DO2 radical: Determination of ground-state parameters
JOURNAL
OF
MOLECULAR
SPECTROSCOPY
84,
179- 1% (1980)
The EPR and LMR Spectra of the DO2 Radical: of Ground-State Parameters C. Department
E. BARNES’
of Chemistry,
AND
The University,
Determination
J. M. BROWN Southampton
SO9 5NH,
England
AND
H. E. RADFORD Center for Astrophysics,
Harvard College 60 Garden Street,
Observatory Cambridge,
and Smithsonian Astrophysical Massachusetts 02138
Obsen*atory.
The detection of lines in both the gas phase EPR spectrum at 9 GHz and the far-infrared LMR spectrum of the DO, radical is reported. The measurements are fitted with an appropriate Hamiltonian and several parameters for the molecule in the @A” state are determined. The majority of the transitions in the EPR spectrum are K-type doubling transitions and involve the a-component of the electric dipole moment. However the observation of one b-type transition (505-4,4) permits the determination of the off-diagonal component of the spin-rotation tensor, cob. and an estimate of the relative magnitudes of the a- and b-components of the dipole moment. A combination of the parameters for HO, with those for DO, leads to a better understanding of the properties of the molecule. In particular, the r0 molecular geometry has been determined more reliably than previously to be r&OH) = 0.9774 A, r,(OO) = 1.3339 A, iHO = 104.15”. 1. INTRODUCTION
The hydroperoxyl radical, HOz, is of importance in both atmospheric and combustion chemistry. It has now been thoroughly studied in its ground state with a variety of spectroscopic techniques. In particular, the detection and analysis (I, 2) of its laser magnetic resonance (LMR) spectrum at far infrared wavelengths has proved to be a most significant study. Not only did it serve to characterize the spin-rotational energy levels of the_%2A”state but it has also provided a method by which the rates of reactions involving the radical could be measured (3,4). The spectroscopy of the deuteriated species, DOB, is much less well explored. The lo1-OoOtransition observed by Beers and Howard (5) is the only rotational transition to be detected so far. Although the main features of the infrared spectrum have been characterized by matrix isolation studies (6, 7), only the v2 (bending) vibration has been studied in detail, by McKellar (8) using the LMR technique. Finally, the electronic emission spectrum, A2A’-g2A”, has also been studied (9, ZO), but at fairly modest resolution. * Present address: England.
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180
BARNES,
BROWN,
AND RADFORD
In this paper, we report the detection and assignment of lines in the EPR and LMR spectra of DOz, recorded at about 9 GHz and at far-infrared wavelengths, respectively. Both spectra are rich in data and the analysis provides a definitive set of rotational, spin-rotational, and Zeeman parameters, for the molecule in its ground state. In particular, a complete determination of the four parameters in the reduced spin-rotation Hamiltonian (II) has been effected. The combination of the parameters for DO2 from the present work with those for HO, obtained in earlier studies (2,12,13) permits the determination of quantities not accessible to a study with a single isotope. The most obvious example is the molecular geometry which is determined here with much greater reliability than previously (5,10). It is also possible that the components of the full spin-rotation tensor (11) may be separable from our results. 2. EXPERIMENTAL
DETAILS
(i) The EPR Spectrum
The apparatus used to record the EPR spectrum of DO, at Southampton has been described in our earlier work on HO, (13). The radical was generated by the reaction of the products of a microwave discharge through CF, with D,O, and DHO, at a total pressure of about 0.7 Torr. It is presumed that the active ingredient in the discharge products is the F atom. The same reaction was used in the earlier study of DO, by Beers and Howard (5) and we have followed their procedure for the preparation of the deuteriated peroxide. The main impurities in the sample were D20, HzO, and H,O,; weak lines from the EPR spectra of OD, OH, and 0, were recorded in our work. The measurements of the lines in the EPR spectrum of DO, are given in Table I; we estimate the accuracy to be 1 G. Nearly all these measurements were made with an operating frequency of 8970 MHz. The three exceptions involve the lines from the 2,,-2,, transition which occur at sufficiently low fields for this frequency that they could not be measured with our proton NMR fluxmeter. The lines were therefore shifted to higher field by use of a microwave cavity resonant at 9270 MHz. Portions of the EPR spectrum of DO2 are shown in Figs. 1 and 2. The signal-to-noise ratios were quite high (about 25:l for the strongest lines with a 1-set time constant). Indeed the spectrum was stronger than the corresponding EPR spectrum of HO, but this difference is largely attributable to the fact that the 2H hyperflne structure was not resolved in the present work whereas the proton hyperfine structure was for HO,. (ii) The Far-Infrared
LMR Spectrum
The far-infrared LMR spectrum of DOz was recorded in Cambridge with the spectrometer described in Ref. (14). The radiation source was an optically pumped submillimeter gas laser. The radical was generated in a discharge/flow system by reacting fully deuteriated methanol, CD,OD, with the products of a 2450-MHz discharge through CF,. The signal was enhanced by the addition of 0, to the reaction mixture. The total pressure in the reaction region was about 0.5 Tort-.
8970.28 8970.34
I+1
1+1
8970.03
8970.30
I+1
2+2
8970.34
1+1
8970.14
8970.34
2+2
8970.11
I+1
I+1
8970.01
8970.14
l-+1
2+2
8970.20
1+1
8970.20
8970.20
I+1
2+2
8970.24
I+1
8970.30
9270.13
2+2
8970.24
9270.13
2+2
I+1
9270.13
2+2
2+1
8970.36 8969.91
2+1
8970.28
2+2
8970.21
vo/mz
I+1
MJ
I+1
Fi
b
in Tables 1'~ and
1946.5
1504.2
2187.3
1349.7
10937.8
10158.0
9836.2
10299.6
10176.2
9768.6
9741.6
1662.2
1480.2
1323.6
1190.8
1075.4
881.2
951.4
1021.5
10700.6
8827.6
7337.9
4625.0
Observed Bo/g.W
V
.
1947.6
1504.9
2187.6
1349.6
10937.5
10159.4
9637.2
10299.3
10177.3
9769.1
9742.2
1663.1
1479.9
1324.1
1190.2
1074.4
882.8
952.5
1022.7
10696.0
8829.2
7338.7
4624.8
Calculated Be/gauss
-1.1
-0.7
-0.3
0.1
0.3
-1.4
-1.0
0.3
-1.1
-0.5
-0.6
-0.9
0.3
-0.5
0.6
1.0
-1.6
-1.1
-1.2
4.6
-1.6
-0.8
0.2
ObsCalc
0.86
1.37
0.77
1.95
-0.83
1.81
1.75
1.56
1.54
1.37
1.36
0.34
0.42
0.52
0.65
0.81
0.60
0.51
0.44
0.18
-0.47
2.17
1.79
av/aB MHz/&ss
0.033
0.015
0.069
0.060
0.030
0.014
0.015
0.040
0.041
0.133
0.134
0.054
0.083
0.089
0.074
0.044
0.051
0.066
0.048
0.248
0.180
0.080
0.115
Relative lntensityb
The relative intensity does not include the Boltzmann factor. The dipole moment components are taken as unity.
aFlux density calculated using the parameters
505+414
so5'414
505'4L4
505+414
423+422
423f422
422t423
322c321
321f322
*21**20
*20+*21
211+212 2 11+*12
*11+*12
*11+*12 2 llf212
*11f212 2 11+*12 2 llC212
llo"ll
lllC110
lllfl10
'ldlll
ac
N KK
I
Observed Transitions in the EPR Spectrum of DO,
TABLE
182
BARNES, BROWN, AND RADFORD
I
I
9700
I
9900
9800
Flux density/gauss (b)
I
I
7300
I
7400 flux density/gauss
7500
FIG. 1. Part of the EPR spectrum of the DO* radical, recorded at 8970 MHz with a time constant of I sec. In (a), the doublet arises from the 2,,-2,,, MJ = 2’/2 +- I’/2 transitions and gives a direct measurement of the K-type doubling. In (b), the single line is the transition I,,-l,,,, M,, = 1% +- l/2. The weak triplet to higher field arises from the.! = II/i, n = 1% spectrum of the OD radical which is present in small amounts. Note that the deuteron hyperfine splitting is not resolved in the present work.
The LMR also for HOz be attributed examples of assignments
spectrum of DO2 is very extensive in the far-infrared region, as it is (2). The laser lines associated with transitions which could definitely to DO, are given in Table II; this list is not exhaustive. Two the spectra are shown in Figs. 3 and 4. Detailed quantum number have not been made for all the observed spectra. The assignments a
I
1300
b
a
b
I
I
I400
I500
Flux density/gauss Part of the EPR spectrum of the DO, radical, recorded of 1 sec. The lines marked a arise from the K-doubling transition b are from the b-type transition, &-4,,, F2 +- FP. Measurement transitions permits the determination of the relative magnitudes electric dipole moment of DO, (see Section 4). FIG.
2.
at 8970 MHz with a time constant 2,,-2,,, F, + F, and those marked of the relative intensities of these of the a- and b-components of the
183
SPECTRA OF THE DO* RADICAL TABLE II The Far-Infrared
Wavelength/urn
LMR Spectrum of the DO* Radical
Laser Gas
163 193
Q130H N2H4
229
CH30D
Frequency/GHz=
Rotational assignments
1838.8393 1554.0760
132,ll - 121.12
234
N2H4
1281.6258
295
CH30D
1016.8972b
302 311
HCOOH N2H4
991.7778 963.7314
315 330
CH3NH2 CH30D
952.1850
332
N2H4
903.8894
386 394
CH2CHc1 HCOOH
776.8471 761.6065
433
HCOOH
692.9505
469
CH30H
639.1846
513
HCOOH
584.3869
lo29 - "l,lO
'28 - '19
726 - 717
625 - %6
1139 -
717 -
122,lO
606
616 - 505 515
422 - 515 -
404
'Unless otherwise indicated, the frequency measurements are taken from Radfotd et a2 (2.3). bMeasured by Blaney et a2 (24).
that have been made are shown in Table II, with full details of the measurements and quantum numbers in Table III. The resonance flux densities were measured with a Hall probe which in turn was calibrated with a proton NMR fluxmeter. The precision of measurement is estimated to be 5 G. 163pm II polarization CT)
--+-++I--I+ I--++ I 0
I
I
I
I
1
2
4
6
8
IO
Fluxdenslty/kgouss
FIG. 3. Part of the far-infrared LMR spectrum of the DO* radical. The transition involved is 13,,,,12,,,,. The lines marked with asterisks are due to the HO* radical, which was also present in small amounts.
184
BARNES, BROWN, AND RADFORD 469
qn
J_ polaruatlon
I
I
0
I
I
2
4
6
Flux density/k
I
8
(a)
I IO
gauss
FIG. 4. Part of the far-infrared LMR spectrum of the DO, radical, recorded with a rapid scan and a lOO-msec output time constant. The rotational transitions involved are 6,,-5,, and 422-5,3. It can be seen that it is not easy to pick out members of the Zeeman branches and apply Hougen’s method of analysis (see text and Fig. 5).
3. ANALYSIS
(i) The EPR Spectrum
The lines observed in the EPR spectrum of DO, are given in Table I. The spectrum is richer than the corresponding spectrum of HO, (23) because the spin-rotation splittings are smaller, being comparable to the microwave quantum. Thus transitions between spin components are observed as well as those within a spin component. The lines were assigned on the basis of trial calculations, the strong transitions involving low N and K, values (Ilo- l,, and 2,,-2,,) being identified first. The tuning rate, Wr3B,,, could be estimated from the experimental linewidth. Possible assignments were therefore rejected unless they satisfied the expectations of calculated values for the tuning rate and relative intensity. These values are also given in Table I. The majority of the assignments were made to u-type, K doubling transitions but four lines at low field involved b-type transitions (&,-4&. Such transitions are rather unusual in EPR work; indeed this is the first time that they have been recorded in the literature. Two of the lines are shown in Fig. 2, marked b. The lines marked a involve a-type transitions (211-212). The proximity of these transitions has allowed us to make quite reliable measurements of their relative intensities. These measurements give information on the relative magnitudes of the a- and b-components of the electric dipole moment (see Section 4). (ii) The LMR Spectrum
LMR spectra of free radicals often display a regular pattern of lines that vary smoothly in intensity and spacing. An example from the spectrum of DO, is shown
SPECTRA
OF THE DO2 RADICAL
185
in Fig. 3. Hougen (15) has named these progressions Zeeman branches and suggested a simple procedure for the assignment of MJ quantum number in such branches. The method involves the trial of several different M.,numberings for a branch; the correct numbering is indicated by a minimum in the standard deviation of fit of the resonance flux densities to an appropriate formula. We used this method in the early stages of the analysis of the LMR spectrum of DO, but did not find it totally satisfactory. It was successful in identifying the correct M.,numbering of some branches, including that shown in Fig. 3. However in other cases it failed, either because it was not possible to pick out the members of the branch or because the fit of the resonances did not give a minimum standard deviation, irrespective of the different Mrnumberings attempted. This result is rather disappointing, particularly in view of the remarkable success of the method in the analysis of the LMR spectrum of HO2 (2). Spin-rotation splittings that are large relative to the Zeeman interaction are required if the method is to work; the spin-rotation splittings for DO2 are roughly half the corresponding intervals for HO,. We therefore adopted an alternative approach to the analysis of the LMR spectrum of DO*. First a zero-field calculation was performed with the best available molecular parameters (5,lO) in order to establish near coincidences between the molecular transition and the laser frequency. Zeeman patterns for the various
2-o 5-5 -s/2 -712 912
N 3
-'I2 7/Z -3R
\ p2
5/2 "L
-l/2 l/2 312 3R l/2 -l/2 5r2-3R 7/2_5n 912 -7/Z
-2.0
llfx* -11n
FI- 5
h-5 -4.0 0
. 2.5
5-O
75
100
Flux denslty/kga"ss
FIG. 5. A diagram showing the variation of the AMJ = 0 transition frequencies for the rotational transition 6,6-505 of D02, as a function of the applied magnetic field. The M., values for the individual transitions are marked on the right-hand side. The intersection of the horizontal line marked yLwith the transition frequencies generates the observed spectrum at 639.185 GHz (see Table III). Note the interleaving of the F, c F, and F, + F, branches.
186
BARNES, BROWN, AND RADFORD TABLE III Assignments for the LMR Spectrum of the DO, Radical 513p vL = 584.3869 GHz 515-404 parallel spectrum MJ" Be/G
Fi 2+2
Fi
MJ'
I+1
-1.0 2055 -3; -31 -0.7 1223 -21 -21 -0.2 913 -1i -14 -1.0 754 659 -1.8 I -f -3.5 600 Ii ’ -2.3 21 :i 562 -1.5 544 31 31 perpendicular spectrum 2614 -31 -1.2 -21 -2; -1; 1481 -1.3 1075 -1.7 -14 -1 872 -0.9 -t ; 756 -1.2 _:; : 1020 -1.8 -2, 703 -1.8 -1; -21 -1.9 655 -2.9 577 -f -'? -1 -2.4 525 1: 1 493 -4.5 2& II
I+1
(O-C)
/MHZ 2+2
I
2; 31 4; -2; -1;
I 2
1 1; 2; 31
l-+1
469p vL = 639.1846 GHz
2+2
I+1
2+2
2+1 I+1
2+2
422-515 parallel spectrum 7085 21
-0.7
2+2
616-5o5 parallel spectrum 5966 5.6 21 21 3364 4.0 31 31 2318 4.3 41 41 4537 -0.5 11 2930 3.0 1I 14 2176 5.5 21 21 1735 5.0 31 31 6.9 1451 41 41 1251 5.C 51 51 perpendicular spectrum 4899 4.9 21 11 3009 4.1 31 2t 2152 3.5 41 31 1666 -0.2 51 41 3896 -1.6 -1 1 2634 2.7 1 4.2 :1 lh 1999 1617 4.9 31 21 1364 6.7 41 31 1184 7.9 51 41 4.2 3311 11 21
I+1
21
315~ vL = 952.1850 GHz
2+2
-I(
-21
625-616 parallel spectrum 3224 -1)
-21
3954
0.0 -1.1
315~ (continued) MJ,' BO/G (0-C)/MHZ Mel' -31 -3; 5372 -1.6 -4; -41 9281 2.8 perpendicular spectrum -3; -41 3984 -1.3 -21 -31 3092 -0.4 -1; -21 2594 -0.1 _; -1i 2279 0.3 I 11 _;2 2065 1914 -1.6 0.1 1) 21 3; -1; -i
2 I :i 31 41
1811 1746 1713 5109 4034 3415 3031 2785 2634 2566
-1.5 -0.2 -2.1 -0.8 0.3 -1.0 -0.5 0.6 0.5 1.1
726-717 parallel spectrum 2i 21 4599 1.1 31 31 4072 3.1 4: 41 3688 1.1 51 51 3402 0.9 61 61 3196 1.9 61 61 7765 1.5 perpendicular spectrum li -1 4795 5697 2.5 1.5 :;I
li21
3719 4171
2.7 3.5
34: I
31
4479 3379
3.3 3.1
12
41 21
5974
3.0
432~ uL = 692.9505 GHz
z-+1 -1t -1
2+1
717-606 parallel spectrum -11 211 -7.3 -t 385 282 -3.1 -5.1
1I 1I 524 -1.4 21 21 701 -2.6 31 31 913 -2.3 41 41 1167 -1.9 51 51 1476 -1.4 perpendicular spectrum -11 -21 185 -8.3 -t 1I 21 31 41 51 61
-11 -1 14, 21 2", 51
243 328 456 619 827 1079 1393 1790
-0.4 -5.3 -2.2 0.9 -0.7 0.4 -1.6 -0.1
187
SPECTRA OF THE DO, RADICAL TABLE III-Continued 302~
vT
= 991.7778
GHz
386~
L
Fi
‘28-‘19 parallel MJ”
I+1
spectrum
MOT ’ -1
I
(continued)
MJ"
Be/G
-1
2362
I
Co-c)/MHz 3.4
Be/G
(o-C)MHZ
1i
If
2115 2226
1.1 1.8
2;
3113
-4.2
21
2t
2026
0.2
31
3;
3552
-5.1
31
3;
1954
-0.1
41
41
4051
-4.3
4;
41
1901
-1.8
5;
51
4619
-2.2
6;
6;
5271
-4.3
7;
:;
“J
’
21
’
8;
II
-4;
-51
2307
8.3
1.7
-3;
-4;
2097
6-S
6888
1.0
-2;
-3)
1936
4.8
-1;
-21
1807
3.7
-1;
1701
3.2
_;1
1546 1615
0.6 2.3
1;
1483
1.0
10
_f
1: /
speLrum
1I
5548
0.1
4796
-0.5
4240
-1.0
41
41
3812
51
5;
3478
-0.7
61
61
3210
-0.9
7;
7;
2995
-3.5
81
8;
2819
-2.0
91
91
2682
-5.2
6$
6$
12007
1.3
71
;‘1’
8292
2.4
6248
2.2
9t
4950
2.5
81 91
perpendicular
v.
=
1838.8393
GHz
L
132,11-121,12 parallel 1+1
2+2
spectrum
9;
9;
8899
1.9
10;
104
6771
1.9
11;
11:
5399
1.8
-2;
-21
9525
0.3
-1; -f
-1; -1
spectrum
7593
2I
0.0
6336
-0.8
5461
-0.4
0.1
14
4811
-1.4
7323
0.3
2;
4316
-1.1
5982
0.0
3;
3924
-1.5
4;
3607
-2.5
-0.4 0.0
3941
-0.4
0.2
3564
-1.1
zi
I
3136 3351
I
2955 2805
1.1
2677
0.0
-0.1 -0.8
3264
-2.5
:a
3019
-1.0
9;
2820
-1.2
10;
2572
0.4
2658
-3.4
11;
2489
3.1
9436
1.1
7385
1.1
91
81
7936
1.2
6096
1.0
104
91
6236
1.7
5212
1.5
121
11;
4245
4574
0.5
-1;
-21
6780
-0.3
-1)
5741
-0.9
-0.1
4092 3715
perpendicular I+1
2+2
-1
2.0
3419
2.1
3185
-0.8
10435
I
1;
-t
I
spectrum
1.9
4440 4979
-1.7 -1.5
63
31 1;
3382 4007
-0.4 -1.8
I
2.3
7554
2.5
51
4;
3149
-0.3
5856
2.6
6;
5?
2954
-0.1
4733
3.5
71
6;
2791
1.9
9262
0.1
81
71
2650
0.6
6728 =
163~
9521
5079
v,
2;
0.2
4429
386~
1+1
spectrum
6017
1029-101 parallel
perpendicular
776.8471
-0.2 GHz
113,9-122,10 parallel spectrum -31
-3;
3042
9.8
-21
-21
2755
6.7
-11
-11
2536
4.5
91
81
2532
1.1
104
91
2432
0.3
11;
104
2350
-0.2
121 -1
111 1
2289 7046
5.6 -0.3
I 11 21
14 21 31
5995 5238 4664
-0.9 -0.6 -1.3
31
4f
4216
-2.4
188
BARNES,
BROWN,
AND RADFORD
possibilities were then computed with programs described in our earlier work (13) and compared with the experimental observations. It was particularly helpful to plot the various transition frequencies as functions of field; an example of this display is given in Fig. 5 for the transition 6,,-5,,. An observed spectrum is defined by a horizontal line drawn across the graph. The main uncertainty in the assignment at this stage is in the mismatch between the laser and molecular frequencies. It can be accommodated simply by moving the horizontal line up or down until the predicted Zeeman pattern matches the experimental one. Note the interleaving of the Zeeman branches for the two transitions F, + F, and F2 - F, in Fig. 5. This behavior is quite typical and provides one reason why it was often difficult to pick out the Zeeman branches reliably by inspection. As assignments were made, the molecular parameters were progressively refined as described in the next section. This helped to remove uncertainties in the subsequent assignments for other laser lines. The results of the analysis are given in Table III. It may be seen from Table II that the spectra for several laser lines remain unassigned. In some cases the laser frequency has not yet been measured. For the others, we have done no more than determine the zero-field rotational transitions that are in near-coincidence with the laser frequency. The correct assignments require the prediction of detailed Zeeman patterns for all these possibilities. This is straightforward but laborious and we do not consider the extra information that would be gained justifies the effort involved. (iii) Determination
of Molecular
Parameters
The data listed in Tables I and III were fitted by a least-squares procedure to an appropriate Hamiltonian in order to determine the molecular parameters for DO* in its ground state. The Hamiltonian was the same as that used in the earlier work on HOz (13) with the exception of the spin-rotation Hamiltonian which was here taken in its reduced form, as formulated by Brown and Sears (1Z). Because the inertial properties of DO, are close to the prolate limit (K = -0.98149), we have used the S-reduced forms of the various centrifugal distortion corrections (II, 16). This facilitates comparison with the parameters for HO2 (13). The Zeeman Hamiltonian contained contributions from the electron spin and molecular rotational magnetic moments (17). Curl’s relationship (18) was used to estimate the anisotropic corrections to the electron spin g-factor in the preliminary fits. We consider the EPR data in Table I to be of higher precision than the LMR data in Table III. Accordingly, the former were weighted 25 times more heavily than the latter in a fit to the experimental frequencies. We included the two spin components of the lo1-OoOtransition measured by Beers and Howard (5) in the fit, also with a relative weight of 25. Various combinations of parameters were varied in an attempt to obtain an optimum fit. We were guided in this by the overall quality of the fit, the determinability of individual parameters and by a comparison with the corresponding parameters for HO,. The final results are given in Tables I and III and indicate that a satisfactory quality of fit was obtained. The parameters determined in this fit are given in Tables IV (zero-field parameters) and V (Zeeman parameters), with their standard deviations. Although the present work repre-
189
SPECTRA OF THE DO, RADICAL TABLE IV Molecular Parameters of DO2 in the .%*A” State in Megahertz Parametera
Present
Work
Other
Studies
334748(120)=
A
335602.94(78jb
B
31654.47(12)
31652.4(24Jd
C
28814.92(11)
28813.1(23)d 0.186(36jd
0.104705)
DN
1.65(24)d
2.511(22)
DNK
38.39(21)
a9.ge -0.6e
lo2
% dl
-0.758(76)
lo2
d2
-0.180(27)
IO4
hl
0.296(57)
-27152.5(68)d
-27145.8(26)
E aa
-393.3(41jd
-392.03(31)
‘bb
6.10(21)
LINKS + Due
0.154(82)
parameters
fit. b
not
listed
The spin-rotation
The numbers
were constrained parameters
in parentheses
least-squares ’
6.90(44)d
8.91(70)
%”
a All
7.a=
300(34)
,E&E’cbo,
fit,
in units
Value
determined
by Tuckett
d Value
determined
by McKellar
e Value
estimated
from
represent of
the
et a2
to zero
are defined
one standard last
quoted
in the least-squares
in ref.
(II).
deviation
decimal
of
the
place.
(JO).
(8).
the corresponding
quantity
for
H02.
sents a significant improvement in the determination of the molecular parameters for DO, it should be appreciated that the parameters determined by McKellar (8) in his fit of the 10-p LMR spectrum are remarkably reliable; his values are also given in Table IV for comparison. It is instructive to compare the values of the parameters for DO, determined in the present work with the corresponding values for HOe (13). Roughly speaking, the A-value for DO, is half that for HOz whereas the B- and C-values are comparable (A = 610.274 GHz, B = 33.5138 GHz, C = 31.6717 GHz for HOz). Indeed, the difference (B - C) is larger for DO2 than for HO2 (2.83% GHz as compared with 1.8422 GHz). It is therefore reasonable that DK is much larger for HO, (123.62 MHz) whereas DN (0.115 MHz) is about the same size. Furthermore both
190
BARNES,
BROWN,
AND RADFORD
TABLE
V
Zeeman Parameters for DO, in the ,%J2AsState Parameter
Present
aa %
9s
bb cc
gs lo2
g,”
IO3 9,
bb
lo4 9,“”
Theory
2.04235(20)a
2.04276b
2.00788(32)
2 .00851b
2.00048(32)
2.00243b
-0.5310(84)
-0.600’
-0.142
-0.087’
(58)
-O.OIC
-0.63(58)
a The numbers in parentheses least-squares
work
fit,
represent
in units
b Calculated
from Curl’s
’ Electronic
contribution
of
relationship only
one standard
the last (M),
quoted using
to the rotational
deviation
decimal
of
the
place.
gS = 2.00232. g-factors.
d, and d, are slightly smaller for HO2 (-0.70 x lo-’ and -0.81 x 10e3 MHz, respectively), However, we do not feel confident that the quartic sextic centrifugal distortion parameters are completely reliable, certainly not to the extent suggested by their individual standard deviations. They could be determined better by analyzing more of the LMR spectrum but we do not feel that the effort involved is justified since our main concern has been to measure the rotational constants and the spin-rotation constants reliably. 4. DISCUSSION
The EPR and LMR spectra of the DO2 radical were analyzed in order to determine the major molecular parameters for the molecule in its ground state. Although these numbers are of some interest in their own right, they are most informative when considered in conjunction with the parameters for HOz. It is then possible to characterize features of the geometric and electronic structure of the molecule that are not accessible from a study of a single isotopic species. (i) The Molecular Geometry It is well known that, because of the planarity condition, the rotational constants of at least two isotopic modifications of a triatomic molecule are required in order to determine its geometric structure. In the present case, the parameters
SPECTRA
OF THE DO, RADICAL
191
are available for the molecule in the zero-point vibrational state only so that at best we can determine the r. structure. In this situation, it is preferable to determine the structure from the A and B rotational constants because they are unaffected by the vibrational Coriolis coupling which is exclusively about the c axis. An additional complication arises because the rotational constants determined by fitting experimental data to a Hamiltonian are contaminated by centrifugal distortion effects. Watson (26) has shown that, for a treatment of centrifugal distortion truncated at the quartic level, there are eight determinable combinations of parameters in the Hamiltonian. They are: B3, = B, - 2T,,,
LBX= B, - 2T,,, T SE9
T fZ5
T l/Y,
B3, = B, - Tsu,
TI = T,, + T,.r + Tx,
and T2 = BJ,,
+ &L,
(1)
+ BJ,,,
using Watson’s notation. The relationship between these combinations and the parameters determined in the least-squares fit to a reduced Hamiltonian depend on the reduction used. For the S-reduction, the relationship is (16): B3, = B$? + 2DN + DNK + 2d, + 4d2, 93 II = Bcs’ 3/ + 2DN + D NK
-
2d, + 4d2,
93 z = Bcs’ z + 2DN + 6d 2, T,,
= -DN + 2d, + 2dz,
T,, = -DN - 2d, + 2d2, T,, = -D,+r - DNK - DK, T, = -3DN - DNK - 6d2, T2 = -(B,
+ i,
+ B,)DN - ; (B,
+ B,)DNK - (B,
- B,)d,
- 6Bzdz.
(2)
For the IF representation used in the present work, the fitted parameters A, B, and C correspond to BLs’, BY’, and Bf’, respectively. It is desirable to express the results of a fit of experimental data in terms of the determinable combinations ( SX, BV, 9$, etc.) defined by Watson, because they are independent of the reduction employed. However, it is the parameters B,, B,, and B, that are required for the geometry calculation and Eqs. (1) and (2) show that they are not directly determinable from experiment. The parameters are indeterminate to the extent of TV,, T,,, or Tzyr that is, by quantities approximately equal to DNK in magnitude (about 3 MHz). It can be seen from Eqs. (2) that DNK also makes the major contribution to .9&, $$)I, and aA, in their calculation from A, B, and C and it is by no means clear which of these two sets of parameters is closer to the required set, Bx, B,, and B,. We have arbitrarily used the parameters from the S-reduced Hamiltonian (A and B) in the present calculation.
BARNES,
192
BROWN,
AND RADFORD
The three geometric parameters were determined from a best fit of the four experimental data (A and B for HO, and DO*) with a weighted least-squares program. Kuchitsu (19) has shown that the effects of zero-point vibrational averaging can to some extent be accounted for by making a small contraction in the O-H bond length and a reduction in the HO0 angle on deuteriation. We found that the quality of the fits for HOz were quite insensitive to the latter. However, the reduction in bond length effected a marked improvement, the optimum value of r,(OH) - r,,(OD) being 0.0036 A, in exact agreement with the value suggested by Kuchitsu from his study of H,O. This can be seen in Table VI where the results of various fits have been collected; fit (2) where the contraction has been introduced is of significantly better quality than fit (1) where r,(OH) is the same for both isotopic species. In fits (1) and (2), the four data were assigned equal weights because, as estimates of B, and B,, they are all uncertain to the same extent (-ONK). Fortunately the actual choice of weights does not seem to be too critical. This can be seen from fit (3) in Table VI where each datum was weighted inversely as the square of its experimental uncertainty; the geometric parameters are very similar to those obtained in fit (2). One major difficulty in the determination of a reliable geometry for HOz is that the O-H bond length and HO0 angle are highly correlated (correlation coefficient = 0.996). This is a function of the inertial properties of the molecule and is unavoidable if the source of geometric information is restricted to HO2 and DO*. The present determination is more reliable than the previous ones (5, 6, IO), mainly because of the use of better values for the rotational constants of DO,. We consider the geometry from fit (2), namely, r,(OH) = 0.9974 A,
r,(OO) = 1.3339 A,
LHOO = 104.15”,
to be the best (i.e., closest to the re structure). For this fit, the differences between the observed and calculated values for the rotational constants are all less than 3 MHz or 10m4cm-l. We were not able to reproduce the results of Tuckett et al. (10) exactly with our program. Fit (4) in Table VI shows the geometry obtained from a fit of the rotational constants that they used while fit (5) is simply a calculation of rotational constants using their published geometry. The two sets of numbers do not agree very well. Dr. Tuckett informs us that the discrepancy is due to the use of a different conversion factor in his calculation. (ii) The Spin -Rotation
Interaction
It has been shown (II) that, for a molecule of C, symmetry in a doublet state, it is not possible to determine more than four spin-rotation parameters from experimental measurements, even though there are five nonzero components of the spin-rotation tensor permitted by symmetry (E,,, ebb, .fcc, l&,, and eba). All four parameters for DO2 have been well determined in this work (see Table IV). The off-diagonal component (e,b + Ebu)is determined largely from the observation of the transition 5,,-4,, in the EPR spectrum; the levels &, J = 4% and q13,
1.33387
1.33382
1.32899
1.3291
0.97752
0.98931
0.9754
(2)
(3)
(4)
(5)
104.02
106.19
104.16
104.15
107.31°
LHOO
20.4141
20.3572
20.3564
20.3565
Ho2
1.12612
1.12062
1.11790
1.11785
-1 1.1217Ocm
B
of the HO, Radical
-1 20.3568cm
A
of the r,, Structure
11.1451
11.1657
il.1948
11.1945
-1 11.1941cm
A
Do2
1.06360
1.05351
1.05595
1.05593
-1 1.05183cm
B
Also h/8n2c = 16.8576 a.m.h. g“~r,,-~.
-1 -1 A = 20.35656cm , B = 1.1179Olcm and for DC2
-1 A = 11.19451cm ,
B = 1.055879cm-1.
Fit with constants weighted equally and s(OH) = r(OD). Fit with constants weighted equally and r(OH) - r(OD) = 0.0036 8 Fit with constants weighted by l/o* and r(OH) - r(OD) = 0.0036 2 Fit with A and B constants determined by Tuckett et at (101, A = 11.167c~n-~and B = 1.0562cm-' and r(OH) = r(OD). Calculation of constants for geometry quoted by Tuckett et at 110).
Note that for HO2
(1) (2) (3) (4) (5)
The geometries were determined by fitting the A and B rotational contents of HO2 and IN2 as follows:
1.32650 8
0.99654 i?
0.97743
(1)
ro(OO)
ro(OH)
Calculations
TABLE VI
194
BARNES, BROWN, AND RADFORD
J = 4% lie close together for DO, and are shifted by about 4 MHz due to this term in the Hamiltonian. The interpretation of the spin-rotation parameters for HO* has been discussed at some length in a previous paper (13). We see no reason to change the conclusions reached there after the present study of DOZ. In principle, the availability of the spin-rotation parameters for DO, permits the separation of the parameters e&, and lba and the full determination of the spin-rotation tensor components. A detailed study of the isotopic dependence of the spin-rotation interaction is in progress (20). However, the consistency between the results for HO* and DO* can be appreciated from the following simplified argument. The data from the microwave, EPR and LMR spectra of HO, were fitted (13) by imposing the constraint cab/A = lba/B in the spin-rotation Hamiltonian. The VaheS obtained were ] cab1 = 1891 MHz and lebal = 103.8 MHz. Subsequently Brown and Sears (II) introduced an equivalent but preferable form of the spin-rotation Hamiltonian in which the effective parameters iab and iba are equal; this is the form we have used in the present work. Retaining the first form of the reduced Hamiltonian for the moment, we can estimate the parameters e& and E& for DO, by scaling in the ratio of the appropriate rotational COnStantS (e.g.,&, = E&t*/A). Using the values from Ref. (13) and Table IV, we obtain the magnitudes e$, = 1040 MHz and E$ = 98.0 MHz. The equations that relate the parameters in the two reductions (II) can then be used to give an estimated Vahe for )iab + iba1 of 353 MHz which is in good agreement with the experimental value of 300 5 34 MHz. (iii) The Orientation of the Electric Dipole Moment It has been mentioned that some transitions induced by the b-component of the electric dipole moment were detected in the EPR spectrum of DOz, in addition to the a-type transitions more usually associated with this technique. An example of an observed spectrum showing both types of transition is shown in Fig. 2. The two transitions of each type were recorded under the same experimental conditions and their relative intensities provide an estimate of the magnitudes of the dipole moment components involved. Halbach (21) has shown that the first moment of a magnetic resonance signal is proportional to the integrated intensity, regardless of modulation amplitude or frequency. As the modulation amplitude was constant in our experiments, the ratio of the first moments is equal to the ratio of the integrated intensities. We have thus been able to compare the intensities of pairs of lines in Fig. 2 for four independent scans from estimates of the first moments. These results were compared with the values calculated by a computer program,2 suitably modified by the Boltzmann factor, to give (,.&/,-‘b ( = 0.85 t 0.10. * The effects of mixing of basis states with K, = 0 and K, = 1 by terms in the spin-rotation Hamiltonian were included in this calculation. They were very small, changing the intensities by a few parts in a thousand only.
SPECTRA
195
OF THE DO* RADICAL
In other words, the dipole moment makes an angle of 49.5” with the a inertial axis for DOZ. The reliability of this result is limited by such effects as the possible saturation of the transitions by the microwave field. However it has important implications for kinetic studies of the HO* radical by LMR spectroscopy (3, 4). Such studies require a knowledge of pb in order to relate the concentrations of different reactants to their measured signal strengths whereas it is pu, which can be measured reliably from the Stark effect on the microwave spectrum (22). (iv) The Zeeman Parameters The Zeeman parameters obtained from the fit of the EPR and LMR spectra are collected in Table V. This is the first time that a full determination of all three electron spin and three rotational g-factors has been achieved for this type of molecule, a result which is attributable to the large number of lines in the EPR spectrum. The electron spin g-factors can be compared with the predictions of Curl’s relationship (18), which are also given in Table V. One has come to expect the relationship to be very reliable for light molecules and this indeed is the case. The rotational Zeeman interaction also makes significant contributions to the observed flux densities, particularly the g? component. The electronic contributions to the rotational g-factors can be estimated from the equation (13)
where 5 is an atomic spin-orbit be seen to be quite reliable.
coupling parameter.
This relationship
can also
ACKNOWLEDGMENTS It is a pleasure to thank Dr. Trevor Sears for his help in the development of the computer programs used in this work. We are also grateful to the Science Research Council for the purchase of equipment and the support of C.E.B. RECEIVED:
January
18,
1980
REFERENCES 1. H. E. RADFORD, K. M. EVENSON, AND C. J. HOWARD, /. Chem. Phys. 60, 3178-3183 (1974). 2. J. T. HOLJGEN, H. E. RADFORD, K. M. EVENSON, AND C. J. HOWARD, J. Mol. Spectrosc. 56, 210-228 (1975). 3. C. J. HOWARD, 1. Chem. Phys. 67, 5258-5263 (1977). 4. J. P. BURROWS, G. W. HARRIS, AND B. A. THRUSH, Nature 267, 233-234 (1977). 5. Y. BEERS AND C. J. HOWARD, .I. Chem. Phys. 64, 1541-1543 (1976). 6. M. E. JACOX AND D. E. MILLIGAN, J. MO/. Spectrosc. 42, 495-513 (1972). 7. D. W. SMITH AND L. ANDREWS, J. Chem. Phys. 60, 81-85 (1974). 8. A. R. W. MCKELLAR, J. Chem. Phys. 71, 81-88 (1979). 9. K. H. BECKER. E. H. FINK, P. LANGEN, AND U. SCHURATH, J. Chem. Phys. 60, 46234625 (1974). IO. R. P. TUCKETT, P. A. FREEDMAN, AND W. J. JONES, Mol. Phys. 37, 403-408 (1979). II. J. M. BROWN AND T. J. SEARS, J. Mol. Spectrosc. 75, Ill-133 (1979). 12. S. SAITO, J. Mol. Spectrosc. 65, 229-238 (1977).
196
BARNES, BROWN, AND RADFORD
13. C. E.
BARNES, J. M. BROWN, A. CARRINGTON, I. PINKSTONE, T. J. SEARS, AND P. J. THISTLE-
THWAITE, J. Mol. Specrrosc.
72, 86- 101 (1978). 14. F. D. WAYNE AND H. E. RADFORD, Mol. Phys. 32, 1407-1422 (1976). 15. J. T. HOUGEN, J. Mol. Spectrosc. 54, 447-471 (1975). 16. J. K. G. WATSON, Aspects of quartic and sextic centrifugal effects on rotational energy levels, in “Vibrational Spectra and Structure” (J. R. Durjg, Ed.), Vol. 6, Elsevier, Amsterdam, 1977. 17. I. C. BOWATER, J. M. BROWN, AND A. CARRINGTON, Proc. Roy. Sot. Ser. A 333, 265-288 (1973). 18. R. F. CURL, JR., Mol. Phys. 9, 585-597 (1965). 29. K. KUCHITSU, .I. Chem. Phys. 44, 906-911 (1966). 20. J. M. BROWN, T. J. SEARS, AND J. K. G. WATSON, Mol. Phys. 41, 173-182 (1980). 21. K. HALBACH, Phys. Rev. 119, 1230-1233 (1960). 22. S. SAITO, private communication. 23. H. E. RADFORD, F. R. PETERSEN,D. A. JENNINGS,AND J. A. MUCHA, IEEE .I. Quant. Electron. QE-13, 92-94 (1977). 24. T. G. BLANEY, D. J. E. KNIGHT, AND E. MURRAY-LLOYD, Opt. Comm. 25, 176-178 (1978).
OF
MOLECULAR
SPECTROSCOPY
84,
179- 1% (1980)
The EPR and LMR Spectra of the DO2 Radical: of Ground-State Parameters C. Department
E. BARNES’
of Chemistry,
AND
The University,
Determination
J. M. BROWN Southampton
SO9 5NH,
England
AND
H. E. RADFORD Center for Astrophysics,
Harvard College 60 Garden Street,
Observatory Cambridge,
and Smithsonian Astrophysical Massachusetts 02138
Obsen*atory.
The detection of lines in both the gas phase EPR spectrum at 9 GHz and the far-infrared LMR spectrum of the DO, radical is reported. The measurements are fitted with an appropriate Hamiltonian and several parameters for the molecule in the @A” state are determined. The majority of the transitions in the EPR spectrum are K-type doubling transitions and involve the a-component of the electric dipole moment. However the observation of one b-type transition (505-4,4) permits the determination of the off-diagonal component of the spin-rotation tensor, cob. and an estimate of the relative magnitudes of the a- and b-components of the dipole moment. A combination of the parameters for HO, with those for DO, leads to a better understanding of the properties of the molecule. In particular, the r0 molecular geometry has been determined more reliably than previously to be r&OH) = 0.9774 A, r,(OO) = 1.3339 A, iHO = 104.15”. 1. INTRODUCTION
The hydroperoxyl radical, HOz, is of importance in both atmospheric and combustion chemistry. It has now been thoroughly studied in its ground state with a variety of spectroscopic techniques. In particular, the detection and analysis (I, 2) of its laser magnetic resonance (LMR) spectrum at far infrared wavelengths has proved to be a most significant study. Not only did it serve to characterize the spin-rotational energy levels of the_%2A”state but it has also provided a method by which the rates of reactions involving the radical could be measured (3,4). The spectroscopy of the deuteriated species, DOB, is much less well explored. The lo1-OoOtransition observed by Beers and Howard (5) is the only rotational transition to be detected so far. Although the main features of the infrared spectrum have been characterized by matrix isolation studies (6, 7), only the v2 (bending) vibration has been studied in detail, by McKellar (8) using the LMR technique. Finally, the electronic emission spectrum, A2A’-g2A”, has also been studied (9, ZO), but at fairly modest resolution. * Present address: England.
CEGB, Computing
Branch, Bankside House, Sumner Street,
179
0022-2852/80/l Copyright All rights
London SEl.
10179-18$02.00/O
B 1980 by Academic of reproduction
Press.
Inc.
in any form reserved.
180
BARNES,
BROWN,
AND RADFORD
In this paper, we report the detection and assignment of lines in the EPR and LMR spectra of DOz, recorded at about 9 GHz and at far-infrared wavelengths, respectively. Both spectra are rich in data and the analysis provides a definitive set of rotational, spin-rotational, and Zeeman parameters, for the molecule in its ground state. In particular, a complete determination of the four parameters in the reduced spin-rotation Hamiltonian (II) has been effected. The combination of the parameters for DO2 from the present work with those for HO, obtained in earlier studies (2,12,13) permits the determination of quantities not accessible to a study with a single isotope. The most obvious example is the molecular geometry which is determined here with much greater reliability than previously (5,10). It is also possible that the components of the full spin-rotation tensor (11) may be separable from our results. 2. EXPERIMENTAL
DETAILS
(i) The EPR Spectrum
The apparatus used to record the EPR spectrum of DO, at Southampton has been described in our earlier work on HO, (13). The radical was generated by the reaction of the products of a microwave discharge through CF, with D,O, and DHO, at a total pressure of about 0.7 Torr. It is presumed that the active ingredient in the discharge products is the F atom. The same reaction was used in the earlier study of DO, by Beers and Howard (5) and we have followed their procedure for the preparation of the deuteriated peroxide. The main impurities in the sample were D20, HzO, and H,O,; weak lines from the EPR spectra of OD, OH, and 0, were recorded in our work. The measurements of the lines in the EPR spectrum of DO, are given in Table I; we estimate the accuracy to be 1 G. Nearly all these measurements were made with an operating frequency of 8970 MHz. The three exceptions involve the lines from the 2,,-2,, transition which occur at sufficiently low fields for this frequency that they could not be measured with our proton NMR fluxmeter. The lines were therefore shifted to higher field by use of a microwave cavity resonant at 9270 MHz. Portions of the EPR spectrum of DO2 are shown in Figs. 1 and 2. The signal-to-noise ratios were quite high (about 25:l for the strongest lines with a 1-set time constant). Indeed the spectrum was stronger than the corresponding EPR spectrum of HO, but this difference is largely attributable to the fact that the 2H hyperflne structure was not resolved in the present work whereas the proton hyperfine structure was for HO,. (ii) The Far-Infrared
LMR Spectrum
The far-infrared LMR spectrum of DOz was recorded in Cambridge with the spectrometer described in Ref. (14). The radiation source was an optically pumped submillimeter gas laser. The radical was generated in a discharge/flow system by reacting fully deuteriated methanol, CD,OD, with the products of a 2450-MHz discharge through CF,. The signal was enhanced by the addition of 0, to the reaction mixture. The total pressure in the reaction region was about 0.5 Tort-.
8970.28 8970.34
I+1
1+1
8970.03
8970.30
I+1
2+2
8970.34
1+1
8970.14
8970.34
2+2
8970.11
I+1
I+1
8970.01
8970.14
l-+1
2+2
8970.20
1+1
8970.20
8970.20
I+1
2+2
8970.24
I+1
8970.30
9270.13
2+2
8970.24
9270.13
2+2
I+1
9270.13
2+2
2+1
8970.36 8969.91
2+1
8970.28
2+2
8970.21
vo/mz
I+1
MJ
I+1
Fi
b
in Tables 1'~ and
1946.5
1504.2
2187.3
1349.7
10937.8
10158.0
9836.2
10299.6
10176.2
9768.6
9741.6
1662.2
1480.2
1323.6
1190.8
1075.4
881.2
951.4
1021.5
10700.6
8827.6
7337.9
4625.0
Observed Bo/g.W
V
.
1947.6
1504.9
2187.6
1349.6
10937.5
10159.4
9637.2
10299.3
10177.3
9769.1
9742.2
1663.1
1479.9
1324.1
1190.2
1074.4
882.8
952.5
1022.7
10696.0
8829.2
7338.7
4624.8
Calculated Be/gauss
-1.1
-0.7
-0.3
0.1
0.3
-1.4
-1.0
0.3
-1.1
-0.5
-0.6
-0.9
0.3
-0.5
0.6
1.0
-1.6
-1.1
-1.2
4.6
-1.6
-0.8
0.2
ObsCalc
0.86
1.37
0.77
1.95
-0.83
1.81
1.75
1.56
1.54
1.37
1.36
0.34
0.42
0.52
0.65
0.81
0.60
0.51
0.44
0.18
-0.47
2.17
1.79
av/aB MHz/&ss
0.033
0.015
0.069
0.060
0.030
0.014
0.015
0.040
0.041
0.133
0.134
0.054
0.083
0.089
0.074
0.044
0.051
0.066
0.048
0.248
0.180
0.080
0.115
Relative lntensityb
The relative intensity does not include the Boltzmann factor. The dipole moment components are taken as unity.
aFlux density calculated using the parameters
505+414
so5'414
505'4L4
505+414
423+422
423f422
422t423
322c321
321f322
*21**20
*20+*21
211+212 2 11+*12
*11+*12
*11+*12 2 llf212
*11f212 2 11+*12 2 llC212
llo"ll
lllC110
lllfl10
'ldlll
ac
N KK
I
Observed Transitions in the EPR Spectrum of DO,
TABLE
182
BARNES, BROWN, AND RADFORD
I
I
9700
I
9900
9800
Flux density/gauss (b)
I
I
7300
I
7400 flux density/gauss
7500
FIG. 1. Part of the EPR spectrum of the DO* radical, recorded at 8970 MHz with a time constant of I sec. In (a), the doublet arises from the 2,,-2,,, MJ = 2’/2 +- I’/2 transitions and gives a direct measurement of the K-type doubling. In (b), the single line is the transition I,,-l,,,, M,, = 1% +- l/2. The weak triplet to higher field arises from the.! = II/i, n = 1% spectrum of the OD radical which is present in small amounts. Note that the deuteron hyperfine splitting is not resolved in the present work.
The LMR also for HOz be attributed examples of assignments
spectrum of DO2 is very extensive in the far-infrared region, as it is (2). The laser lines associated with transitions which could definitely to DO, are given in Table II; this list is not exhaustive. Two the spectra are shown in Figs. 3 and 4. Detailed quantum number have not been made for all the observed spectra. The assignments a
I
1300
b
a
b
I
I
I400
I500
Flux density/gauss Part of the EPR spectrum of the DO, radical, recorded of 1 sec. The lines marked a arise from the K-doubling transition b are from the b-type transition, &-4,,, F2 +- FP. Measurement transitions permits the determination of the relative magnitudes electric dipole moment of DO, (see Section 4). FIG.
2.
at 8970 MHz with a time constant 2,,-2,,, F, + F, and those marked of the relative intensities of these of the a- and b-components of the
183
SPECTRA OF THE DO* RADICAL TABLE II The Far-Infrared
Wavelength/urn
LMR Spectrum of the DO* Radical
Laser Gas
163 193
Q130H N2H4
229
CH30D
Frequency/GHz=
Rotational assignments
1838.8393 1554.0760
132,ll - 121.12
234
N2H4
1281.6258
295
CH30D
1016.8972b
302 311
HCOOH N2H4
991.7778 963.7314
315 330
CH3NH2 CH30D
952.1850
332
N2H4
903.8894
386 394
CH2CHc1 HCOOH
776.8471 761.6065
433
HCOOH
692.9505
469
CH30H
639.1846
513
HCOOH
584.3869
lo29 - "l,lO
'28 - '19
726 - 717
625 - %6
1139 -
717 -
122,lO
606
616 - 505 515
422 - 515 -
404
'Unless otherwise indicated, the frequency measurements are taken from Radfotd et a2 (2.3). bMeasured by Blaney et a2 (24).
that have been made are shown in Table II, with full details of the measurements and quantum numbers in Table III. The resonance flux densities were measured with a Hall probe which in turn was calibrated with a proton NMR fluxmeter. The precision of measurement is estimated to be 5 G. 163pm II polarization CT)
--+-++I--I+ I--++ I 0
I
I
I
I
1
2
4
6
8
IO
Fluxdenslty/kgouss
FIG. 3. Part of the far-infrared LMR spectrum of the DO* radical. The transition involved is 13,,,,12,,,,. The lines marked with asterisks are due to the HO* radical, which was also present in small amounts.
184
BARNES, BROWN, AND RADFORD 469
qn
J_ polaruatlon
I
I
0
I
I
2
4
6
Flux density/k
I
8
(a)
I IO
gauss
FIG. 4. Part of the far-infrared LMR spectrum of the DO, radical, recorded with a rapid scan and a lOO-msec output time constant. The rotational transitions involved are 6,,-5,, and 422-5,3. It can be seen that it is not easy to pick out members of the Zeeman branches and apply Hougen’s method of analysis (see text and Fig. 5).
3. ANALYSIS
(i) The EPR Spectrum
The lines observed in the EPR spectrum of DO, are given in Table I. The spectrum is richer than the corresponding spectrum of HO, (23) because the spin-rotation splittings are smaller, being comparable to the microwave quantum. Thus transitions between spin components are observed as well as those within a spin component. The lines were assigned on the basis of trial calculations, the strong transitions involving low N and K, values (Ilo- l,, and 2,,-2,,) being identified first. The tuning rate, Wr3B,,, could be estimated from the experimental linewidth. Possible assignments were therefore rejected unless they satisfied the expectations of calculated values for the tuning rate and relative intensity. These values are also given in Table I. The majority of the assignments were made to u-type, K doubling transitions but four lines at low field involved b-type transitions (&,-4&. Such transitions are rather unusual in EPR work; indeed this is the first time that they have been recorded in the literature. Two of the lines are shown in Fig. 2, marked b. The lines marked a involve a-type transitions (211-212). The proximity of these transitions has allowed us to make quite reliable measurements of their relative intensities. These measurements give information on the relative magnitudes of the a- and b-components of the electric dipole moment (see Section 4). (ii) The LMR Spectrum
LMR spectra of free radicals often display a regular pattern of lines that vary smoothly in intensity and spacing. An example from the spectrum of DO, is shown
SPECTRA
OF THE DO2 RADICAL
185
in Fig. 3. Hougen (15) has named these progressions Zeeman branches and suggested a simple procedure for the assignment of MJ quantum number in such branches. The method involves the trial of several different M.,numberings for a branch; the correct numbering is indicated by a minimum in the standard deviation of fit of the resonance flux densities to an appropriate formula. We used this method in the early stages of the analysis of the LMR spectrum of DO, but did not find it totally satisfactory. It was successful in identifying the correct M.,numbering of some branches, including that shown in Fig. 3. However in other cases it failed, either because it was not possible to pick out the members of the branch or because the fit of the resonances did not give a minimum standard deviation, irrespective of the different Mrnumberings attempted. This result is rather disappointing, particularly in view of the remarkable success of the method in the analysis of the LMR spectrum of HO2 (2). Spin-rotation splittings that are large relative to the Zeeman interaction are required if the method is to work; the spin-rotation splittings for DO2 are roughly half the corresponding intervals for HO,. We therefore adopted an alternative approach to the analysis of the LMR spectrum of DO*. First a zero-field calculation was performed with the best available molecular parameters (5,lO) in order to establish near coincidences between the molecular transition and the laser frequency. Zeeman patterns for the various
2-o 5-5 -s/2 -712 912
N 3
-'I2 7/Z -3R
\ p2
5/2 "L
-l/2 l/2 312 3R l/2 -l/2 5r2-3R 7/2_5n 912 -7/Z
-2.0
llfx* -11n
FI- 5
h-5 -4.0 0
. 2.5
5-O
75
100
Flux denslty/kga"ss
FIG. 5. A diagram showing the variation of the AMJ = 0 transition frequencies for the rotational transition 6,6-505 of D02, as a function of the applied magnetic field. The M., values for the individual transitions are marked on the right-hand side. The intersection of the horizontal line marked yLwith the transition frequencies generates the observed spectrum at 639.185 GHz (see Table III). Note the interleaving of the F, c F, and F, + F, branches.
186
BARNES, BROWN, AND RADFORD TABLE III Assignments for the LMR Spectrum of the DO, Radical 513p vL = 584.3869 GHz 515-404 parallel spectrum MJ" Be/G
Fi 2+2
Fi
MJ'
I+1
-1.0 2055 -3; -31 -0.7 1223 -21 -21 -0.2 913 -1i -14 -1.0 754 659 -1.8 I -f -3.5 600 Ii ’ -2.3 21 :i 562 -1.5 544 31 31 perpendicular spectrum 2614 -31 -1.2 -21 -2; -1; 1481 -1.3 1075 -1.7 -14 -1 872 -0.9 -t ; 756 -1.2 _:; : 1020 -1.8 -2, 703 -1.8 -1; -21 -1.9 655 -2.9 577 -f -'? -1 -2.4 525 1: 1 493 -4.5 2& II
I+1
(O-C)
/MHZ 2+2
I
2; 31 4; -2; -1;
I 2
1 1; 2; 31
l-+1
469p vL = 639.1846 GHz
2+2
I+1
2+2
2+1 I+1
2+2
422-515 parallel spectrum 7085 21
-0.7
2+2
616-5o5 parallel spectrum 5966 5.6 21 21 3364 4.0 31 31 2318 4.3 41 41 4537 -0.5 11 2930 3.0 1I 14 2176 5.5 21 21 1735 5.0 31 31 6.9 1451 41 41 1251 5.C 51 51 perpendicular spectrum 4899 4.9 21 11 3009 4.1 31 2t 2152 3.5 41 31 1666 -0.2 51 41 3896 -1.6 -1 1 2634 2.7 1 4.2 :1 lh 1999 1617 4.9 31 21 1364 6.7 41 31 1184 7.9 51 41 4.2 3311 11 21
I+1
21
315~ vL = 952.1850 GHz
2+2
-I(
-21
625-616 parallel spectrum 3224 -1)
-21
3954
0.0 -1.1
315~ (continued) MJ,' BO/G (0-C)/MHZ Mel' -31 -3; 5372 -1.6 -4; -41 9281 2.8 perpendicular spectrum -3; -41 3984 -1.3 -21 -31 3092 -0.4 -1; -21 2594 -0.1 _; -1i 2279 0.3 I 11 _;2 2065 1914 -1.6 0.1 1) 21 3; -1; -i
2 I :i 31 41
1811 1746 1713 5109 4034 3415 3031 2785 2634 2566
-1.5 -0.2 -2.1 -0.8 0.3 -1.0 -0.5 0.6 0.5 1.1
726-717 parallel spectrum 2i 21 4599 1.1 31 31 4072 3.1 4: 41 3688 1.1 51 51 3402 0.9 61 61 3196 1.9 61 61 7765 1.5 perpendicular spectrum li -1 4795 5697 2.5 1.5 :;I
li21
3719 4171
2.7 3.5
34: I
31
4479 3379
3.3 3.1
12
41 21
5974
3.0
432~ uL = 692.9505 GHz
z-+1 -1t -1
2+1
717-606 parallel spectrum -11 211 -7.3 -t 385 282 -3.1 -5.1
1I 1I 524 -1.4 21 21 701 -2.6 31 31 913 -2.3 41 41 1167 -1.9 51 51 1476 -1.4 perpendicular spectrum -11 -21 185 -8.3 -t 1I 21 31 41 51 61
-11 -1 14, 21 2", 51
243 328 456 619 827 1079 1393 1790
-0.4 -5.3 -2.2 0.9 -0.7 0.4 -1.6 -0.1
187
SPECTRA OF THE DO, RADICAL TABLE III-Continued 302~
vT
= 991.7778
GHz
386~
L
Fi
‘28-‘19 parallel MJ”
I+1
spectrum
MOT ’ -1
I
(continued)
MJ"
Be/G
-1
2362
I
Co-c)/MHz 3.4
Be/G
(o-C)MHZ
1i
If
2115 2226
1.1 1.8
2;
3113
-4.2
21
2t
2026
0.2
31
3;
3552
-5.1
31
3;
1954
-0.1
41
41
4051
-4.3
4;
41
1901
-1.8
5;
51
4619
-2.2
6;
6;
5271
-4.3
7;
:;
“J
’
21
’
8;
II
-4;
-51
2307
8.3
1.7
-3;
-4;
2097
6-S
6888
1.0
-2;
-3)
1936
4.8
-1;
-21
1807
3.7
-1;
1701
3.2
_;1
1546 1615
0.6 2.3
1;
1483
1.0
10
_f
1: /
speLrum
1I
5548
0.1
4796
-0.5
4240
-1.0
41
41
3812
51
5;
3478
-0.7
61
61
3210
-0.9
7;
7;
2995
-3.5
81
8;
2819
-2.0
91
91
2682
-5.2
6$
6$
12007
1.3
71
;‘1’
8292
2.4
6248
2.2
9t
4950
2.5
81 91
perpendicular
v.
=
1838.8393
GHz
L
132,11-121,12 parallel 1+1
2+2
spectrum
9;
9;
8899
1.9
10;
104
6771
1.9
11;
11:
5399
1.8
-2;
-21
9525
0.3
-1; -f
-1; -1
spectrum
7593
2I
0.0
6336
-0.8
5461
-0.4
0.1
14
4811
-1.4
7323
0.3
2;
4316
-1.1
5982
0.0
3;
3924
-1.5
4;
3607
-2.5
-0.4 0.0
3941
-0.4
0.2
3564
-1.1
zi
I
3136 3351
I
2955 2805
1.1
2677
0.0
-0.1 -0.8
3264
-2.5
:a
3019
-1.0
9;
2820
-1.2
10;
2572
0.4
2658
-3.4
11;
2489
3.1
9436
1.1
7385
1.1
91
81
7936
1.2
6096
1.0
104
91
6236
1.7
5212
1.5
121
11;
4245
4574
0.5
-1;
-21
6780
-0.3
-1)
5741
-0.9
-0.1
4092 3715
perpendicular I+1
2+2
-1
2.0
3419
2.1
3185
-0.8
10435
I
1;
-t
I
spectrum
1.9
4440 4979
-1.7 -1.5
63
31 1;
3382 4007
-0.4 -1.8
I
2.3
7554
2.5
51
4;
3149
-0.3
5856
2.6
6;
5?
2954
-0.1
4733
3.5
71
6;
2791
1.9
9262
0.1
81
71
2650
0.6
6728 =
163~
9521
5079
v,
2;
0.2
4429
386~
1+1
spectrum
6017
1029-101 parallel
perpendicular
776.8471
-0.2 GHz
113,9-122,10 parallel spectrum -31
-3;
3042
9.8
-21
-21
2755
6.7
-11
-11
2536
4.5
91
81
2532
1.1
104
91
2432
0.3
11;
104
2350
-0.2
121 -1
111 1
2289 7046
5.6 -0.3
I 11 21
14 21 31
5995 5238 4664
-0.9 -0.6 -1.3
31
4f
4216
-2.4
188
BARNES,
BROWN,
AND RADFORD
possibilities were then computed with programs described in our earlier work (13) and compared with the experimental observations. It was particularly helpful to plot the various transition frequencies as functions of field; an example of this display is given in Fig. 5 for the transition 6,,-5,,. An observed spectrum is defined by a horizontal line drawn across the graph. The main uncertainty in the assignment at this stage is in the mismatch between the laser and molecular frequencies. It can be accommodated simply by moving the horizontal line up or down until the predicted Zeeman pattern matches the experimental one. Note the interleaving of the Zeeman branches for the two transitions F, + F, and F2 - F, in Fig. 5. This behavior is quite typical and provides one reason why it was often difficult to pick out the Zeeman branches reliably by inspection. As assignments were made, the molecular parameters were progressively refined as described in the next section. This helped to remove uncertainties in the subsequent assignments for other laser lines. The results of the analysis are given in Table III. It may be seen from Table II that the spectra for several laser lines remain unassigned. In some cases the laser frequency has not yet been measured. For the others, we have done no more than determine the zero-field rotational transitions that are in near-coincidence with the laser frequency. The correct assignments require the prediction of detailed Zeeman patterns for all these possibilities. This is straightforward but laborious and we do not consider the extra information that would be gained justifies the effort involved. (iii) Determination
of Molecular
Parameters
The data listed in Tables I and III were fitted by a least-squares procedure to an appropriate Hamiltonian in order to determine the molecular parameters for DO* in its ground state. The Hamiltonian was the same as that used in the earlier work on HOz (13) with the exception of the spin-rotation Hamiltonian which was here taken in its reduced form, as formulated by Brown and Sears (1Z). Because the inertial properties of DO, are close to the prolate limit (K = -0.98149), we have used the S-reduced forms of the various centrifugal distortion corrections (II, 16). This facilitates comparison with the parameters for HO2 (13). The Zeeman Hamiltonian contained contributions from the electron spin and molecular rotational magnetic moments (17). Curl’s relationship (18) was used to estimate the anisotropic corrections to the electron spin g-factor in the preliminary fits. We consider the EPR data in Table I to be of higher precision than the LMR data in Table III. Accordingly, the former were weighted 25 times more heavily than the latter in a fit to the experimental frequencies. We included the two spin components of the lo1-OoOtransition measured by Beers and Howard (5) in the fit, also with a relative weight of 25. Various combinations of parameters were varied in an attempt to obtain an optimum fit. We were guided in this by the overall quality of the fit, the determinability of individual parameters and by a comparison with the corresponding parameters for HO,. The final results are given in Tables I and III and indicate that a satisfactory quality of fit was obtained. The parameters determined in this fit are given in Tables IV (zero-field parameters) and V (Zeeman parameters), with their standard deviations. Although the present work repre-
189
SPECTRA OF THE DO, RADICAL TABLE IV Molecular Parameters of DO2 in the .%*A” State in Megahertz Parametera
Present
Work
Other
Studies
334748(120)=
A
335602.94(78jb
B
31654.47(12)
31652.4(24Jd
C
28814.92(11)
28813.1(23)d 0.186(36jd
0.104705)
DN
1.65(24)d
2.511(22)
DNK
38.39(21)
a9.ge -0.6e
lo2
% dl
-0.758(76)
lo2
d2
-0.180(27)
IO4
hl
0.296(57)
-27152.5(68)d
-27145.8(26)
E aa
-393.3(41jd
-392.03(31)
‘bb
6.10(21)
LINKS + Due
0.154(82)
parameters
fit. b
not
listed
The spin-rotation
The numbers
were constrained parameters
in parentheses
least-squares ’
6.90(44)d
8.91(70)
%”
a All
7.a=
300(34)
,E&E’cbo,
fit,
in units
Value
determined
by Tuckett
d Value
determined
by McKellar
e Value
estimated
from
represent of
the
et a2
to zero
are defined
one standard last
quoted
in the least-squares
in ref.
(II).
deviation
decimal
of
the
place.
(JO).
(8).
the corresponding
quantity
for
H02.
sents a significant improvement in the determination of the molecular parameters for DO, it should be appreciated that the parameters determined by McKellar (8) in his fit of the 10-p LMR spectrum are remarkably reliable; his values are also given in Table IV for comparison. It is instructive to compare the values of the parameters for DO, determined in the present work with the corresponding values for HOe (13). Roughly speaking, the A-value for DO, is half that for HOz whereas the B- and C-values are comparable (A = 610.274 GHz, B = 33.5138 GHz, C = 31.6717 GHz for HOz). Indeed, the difference (B - C) is larger for DO2 than for HO2 (2.83% GHz as compared with 1.8422 GHz). It is therefore reasonable that DK is much larger for HO, (123.62 MHz) whereas DN (0.115 MHz) is about the same size. Furthermore both
190
BARNES,
BROWN,
AND RADFORD
TABLE
V
Zeeman Parameters for DO, in the ,%J2AsState Parameter
Present
aa %
9s
bb cc
gs lo2
g,”
IO3 9,
bb
lo4 9,“”
Theory
2.04235(20)a
2.04276b
2.00788(32)
2 .00851b
2.00048(32)
2.00243b
-0.5310(84)
-0.600’
-0.142
-0.087’
(58)
-O.OIC
-0.63(58)
a The numbers in parentheses least-squares
work
fit,
represent
in units
b Calculated
from Curl’s
’ Electronic
contribution
of
relationship only
one standard
the last (M),
quoted using
to the rotational
deviation
decimal
of
the
place.
gS = 2.00232. g-factors.
d, and d, are slightly smaller for HO2 (-0.70 x lo-’ and -0.81 x 10e3 MHz, respectively), However, we do not feel confident that the quartic sextic centrifugal distortion parameters are completely reliable, certainly not to the extent suggested by their individual standard deviations. They could be determined better by analyzing more of the LMR spectrum but we do not feel that the effort involved is justified since our main concern has been to measure the rotational constants and the spin-rotation constants reliably. 4. DISCUSSION
The EPR and LMR spectra of the DO2 radical were analyzed in order to determine the major molecular parameters for the molecule in its ground state. Although these numbers are of some interest in their own right, they are most informative when considered in conjunction with the parameters for HOz. It is then possible to characterize features of the geometric and electronic structure of the molecule that are not accessible from a study of a single isotopic species. (i) The Molecular Geometry It is well known that, because of the planarity condition, the rotational constants of at least two isotopic modifications of a triatomic molecule are required in order to determine its geometric structure. In the present case, the parameters
SPECTRA
OF THE DO, RADICAL
191
are available for the molecule in the zero-point vibrational state only so that at best we can determine the r. structure. In this situation, it is preferable to determine the structure from the A and B rotational constants because they are unaffected by the vibrational Coriolis coupling which is exclusively about the c axis. An additional complication arises because the rotational constants determined by fitting experimental data to a Hamiltonian are contaminated by centrifugal distortion effects. Watson (26) has shown that, for a treatment of centrifugal distortion truncated at the quartic level, there are eight determinable combinations of parameters in the Hamiltonian. They are: B3, = B, - 2T,,,
LBX= B, - 2T,,, T SE9
T fZ5
T l/Y,
B3, = B, - Tsu,
TI = T,, + T,.r + Tx,
and T2 = BJ,,
+ &L,
(1)
+ BJ,,,
using Watson’s notation. The relationship between these combinations and the parameters determined in the least-squares fit to a reduced Hamiltonian depend on the reduction used. For the S-reduction, the relationship is (16): B3, = B$? + 2DN + DNK + 2d, + 4d2, 93 II = Bcs’ 3/ + 2DN + D NK
-
2d, + 4d2,
93 z = Bcs’ z + 2DN + 6d 2, T,,
= -DN + 2d, + 2dz,
T,, = -DN - 2d, + 2d2, T,, = -D,+r - DNK - DK, T, = -3DN - DNK - 6d2, T2 = -(B,
+ i,
+ B,)DN - ; (B,
+ B,)DNK - (B,
- B,)d,
- 6Bzdz.
(2)
For the IF representation used in the present work, the fitted parameters A, B, and C correspond to BLs’, BY’, and Bf’, respectively. It is desirable to express the results of a fit of experimental data in terms of the determinable combinations ( SX, BV, 9$, etc.) defined by Watson, because they are independent of the reduction employed. However, it is the parameters B,, B,, and B, that are required for the geometry calculation and Eqs. (1) and (2) show that they are not directly determinable from experiment. The parameters are indeterminate to the extent of TV,, T,,, or Tzyr that is, by quantities approximately equal to DNK in magnitude (about 3 MHz). It can be seen from Eqs. (2) that DNK also makes the major contribution to .9&, $$)I, and aA, in their calculation from A, B, and C and it is by no means clear which of these two sets of parameters is closer to the required set, Bx, B,, and B,. We have arbitrarily used the parameters from the S-reduced Hamiltonian (A and B) in the present calculation.
BARNES,
192
BROWN,
AND RADFORD
The three geometric parameters were determined from a best fit of the four experimental data (A and B for HO, and DO*) with a weighted least-squares program. Kuchitsu (19) has shown that the effects of zero-point vibrational averaging can to some extent be accounted for by making a small contraction in the O-H bond length and a reduction in the HO0 angle on deuteriation. We found that the quality of the fits for HOz were quite insensitive to the latter. However, the reduction in bond length effected a marked improvement, the optimum value of r,(OH) - r,,(OD) being 0.0036 A, in exact agreement with the value suggested by Kuchitsu from his study of H,O. This can be seen in Table VI where the results of various fits have been collected; fit (2) where the contraction has been introduced is of significantly better quality than fit (1) where r,(OH) is the same for both isotopic species. In fits (1) and (2), the four data were assigned equal weights because, as estimates of B, and B,, they are all uncertain to the same extent (-ONK). Fortunately the actual choice of weights does not seem to be too critical. This can be seen from fit (3) in Table VI where each datum was weighted inversely as the square of its experimental uncertainty; the geometric parameters are very similar to those obtained in fit (2). One major difficulty in the determination of a reliable geometry for HOz is that the O-H bond length and HO0 angle are highly correlated (correlation coefficient = 0.996). This is a function of the inertial properties of the molecule and is unavoidable if the source of geometric information is restricted to HO2 and DO*. The present determination is more reliable than the previous ones (5, 6, IO), mainly because of the use of better values for the rotational constants of DO,. We consider the geometry from fit (2), namely, r,(OH) = 0.9974 A,
r,(OO) = 1.3339 A,
LHOO = 104.15”,
to be the best (i.e., closest to the re structure). For this fit, the differences between the observed and calculated values for the rotational constants are all less than 3 MHz or 10m4cm-l. We were not able to reproduce the results of Tuckett et al. (10) exactly with our program. Fit (4) in Table VI shows the geometry obtained from a fit of the rotational constants that they used while fit (5) is simply a calculation of rotational constants using their published geometry. The two sets of numbers do not agree very well. Dr. Tuckett informs us that the discrepancy is due to the use of a different conversion factor in his calculation. (ii) The Spin -Rotation
Interaction
It has been shown (II) that, for a molecule of C, symmetry in a doublet state, it is not possible to determine more than four spin-rotation parameters from experimental measurements, even though there are five nonzero components of the spin-rotation tensor permitted by symmetry (E,,, ebb, .fcc, l&,, and eba). All four parameters for DO2 have been well determined in this work (see Table IV). The off-diagonal component (e,b + Ebu)is determined largely from the observation of the transition 5,,-4,, in the EPR spectrum; the levels &, J = 4% and q13,
1.33387
1.33382
1.32899
1.3291
0.97752
0.98931
0.9754
(2)
(3)
(4)
(5)
104.02
106.19
104.16
104.15
107.31°
LHOO
20.4141
20.3572
20.3564
20.3565
Ho2
1.12612
1.12062
1.11790
1.11785
-1 1.1217Ocm
B
of the HO, Radical
-1 20.3568cm
A
of the r,, Structure
11.1451
11.1657
il.1948
11.1945
-1 11.1941cm
A
Do2
1.06360
1.05351
1.05595
1.05593
-1 1.05183cm
B
Also h/8n2c = 16.8576 a.m.h. g“~r,,-~.
-1 -1 A = 20.35656cm , B = 1.1179Olcm and for DC2
-1 A = 11.19451cm ,
B = 1.055879cm-1.
Fit with constants weighted equally and s(OH) = r(OD). Fit with constants weighted equally and r(OH) - r(OD) = 0.0036 8 Fit with constants weighted by l/o* and r(OH) - r(OD) = 0.0036 2 Fit with A and B constants determined by Tuckett et at (101, A = 11.167c~n-~and B = 1.0562cm-' and r(OH) = r(OD). Calculation of constants for geometry quoted by Tuckett et at 110).
Note that for HO2
(1) (2) (3) (4) (5)
The geometries were determined by fitting the A and B rotational contents of HO2 and IN2 as follows:
1.32650 8
0.99654 i?
0.97743
(1)
ro(OO)
ro(OH)
Calculations
TABLE VI
194
BARNES, BROWN, AND RADFORD
J = 4% lie close together for DO, and are shifted by about 4 MHz due to this term in the Hamiltonian. The interpretation of the spin-rotation parameters for HO* has been discussed at some length in a previous paper (13). We see no reason to change the conclusions reached there after the present study of DOZ. In principle, the availability of the spin-rotation parameters for DO, permits the separation of the parameters e&, and lba and the full determination of the spin-rotation tensor components. A detailed study of the isotopic dependence of the spin-rotation interaction is in progress (20). However, the consistency between the results for HO* and DO* can be appreciated from the following simplified argument. The data from the microwave, EPR and LMR spectra of HO, were fitted (13) by imposing the constraint cab/A = lba/B in the spin-rotation Hamiltonian. The VaheS obtained were ] cab1 = 1891 MHz and lebal = 103.8 MHz. Subsequently Brown and Sears (II) introduced an equivalent but preferable form of the spin-rotation Hamiltonian in which the effective parameters iab and iba are equal; this is the form we have used in the present work. Retaining the first form of the reduced Hamiltonian for the moment, we can estimate the parameters e& and E& for DO, by scaling in the ratio of the appropriate rotational COnStantS (e.g.,&, = E&t*/A). Using the values from Ref. (13) and Table IV, we obtain the magnitudes e$, = 1040 MHz and E$ = 98.0 MHz. The equations that relate the parameters in the two reductions (II) can then be used to give an estimated Vahe for )iab + iba1 of 353 MHz which is in good agreement with the experimental value of 300 5 34 MHz. (iii) The Orientation of the Electric Dipole Moment It has been mentioned that some transitions induced by the b-component of the electric dipole moment were detected in the EPR spectrum of DOz, in addition to the a-type transitions more usually associated with this technique. An example of an observed spectrum showing both types of transition is shown in Fig. 2. The two transitions of each type were recorded under the same experimental conditions and their relative intensities provide an estimate of the magnitudes of the dipole moment components involved. Halbach (21) has shown that the first moment of a magnetic resonance signal is proportional to the integrated intensity, regardless of modulation amplitude or frequency. As the modulation amplitude was constant in our experiments, the ratio of the first moments is equal to the ratio of the integrated intensities. We have thus been able to compare the intensities of pairs of lines in Fig. 2 for four independent scans from estimates of the first moments. These results were compared with the values calculated by a computer program,2 suitably modified by the Boltzmann factor, to give (,.&/,-‘b ( = 0.85 t 0.10. * The effects of mixing of basis states with K, = 0 and K, = 1 by terms in the spin-rotation Hamiltonian were included in this calculation. They were very small, changing the intensities by a few parts in a thousand only.
SPECTRA
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OF THE DO* RADICAL
In other words, the dipole moment makes an angle of 49.5” with the a inertial axis for DOZ. The reliability of this result is limited by such effects as the possible saturation of the transitions by the microwave field. However it has important implications for kinetic studies of the HO* radical by LMR spectroscopy (3, 4). Such studies require a knowledge of pb in order to relate the concentrations of different reactants to their measured signal strengths whereas it is pu, which can be measured reliably from the Stark effect on the microwave spectrum (22). (iv) The Zeeman Parameters The Zeeman parameters obtained from the fit of the EPR and LMR spectra are collected in Table V. This is the first time that a full determination of all three electron spin and three rotational g-factors has been achieved for this type of molecule, a result which is attributable to the large number of lines in the EPR spectrum. The electron spin g-factors can be compared with the predictions of Curl’s relationship (18), which are also given in Table V. One has come to expect the relationship to be very reliable for light molecules and this indeed is the case. The rotational Zeeman interaction also makes significant contributions to the observed flux densities, particularly the g? component. The electronic contributions to the rotational g-factors can be estimated from the equation (13)
where 5 is an atomic spin-orbit be seen to be quite reliable.
coupling parameter.
This relationship
can also
ACKNOWLEDGMENTS It is a pleasure to thank Dr. Trevor Sears for his help in the development of the computer programs used in this work. We are also grateful to the Science Research Council for the purchase of equipment and the support of C.E.B. RECEIVED:
January
18,
1980
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