- Email: [email protected]
ESR spectra of the OD radical in the 2Π32 , J = 32 state, v = 0–5 levels
ESR Spectra of the OD Radical in the ‘rq, I = 3 State, v = O-5 Levels >l. H. RASHID, K. I’. LEE, AKD I*;. \:. I,. TX. SASTKY
‘I’hc paramagnetic resonance absorption spectrum of the OD radical in the exited villrational levels up to z = 5 of the ground *II<, J = 4 state has been observed at X-band frcquencies. The theory of the Zeeman effect of a paramagnetic W state of a light diatomic molecule has been aTplied to analyze the spectrum. The &doubling frequencies, the molecular r factors. coeliicients of the second order Zeeman effect, and the hyperline interaction constant?; wcrc determined for each of the vibrational levels. The experimental results agree reasonaM well with the values calculated from (a) optical data and (b) ab initio data. The experimental determinations are still much hetter than theoretical calculations.
ISTRODUCTION Electron paramagnetic resonance measurements provide a convenient tool for studies of gaseous molecules or free radicals having unpaired electrons. The free hydroryl radicals OH and OD have a 211 ground state which is paramagnetic. Radford (I) lirst used this technique to observe transitions betJveen Zeeman components of a few rotational levels of the hydrosyl radicals produced by an electric discharge in low-pressure. \vater vapor. Later Clough et al. (3) and Lee et al. (4, 5) could populate the excited vibrational levels of OH by reacting H with ozone and independently observed paramagnetic resonance in vibrationally exited OH. We have now extended the study to 01) radicals in several low vibrational states of the !%;, J = 3 electronic state.
The 01) radical was prepared by the reaction of ozone \vith atomic deuterium produced by a microwave discharge of Dr. The two gases were conveyed in separate quartz tubes through a g-in. port to the EPR cavity and were mixed inside the cavity. Tht product and the residual gases were pumped out through a similar third port via liquid nitrogen cold traps by an Alcatel vacuum pump (pumping speed -1000 litersi’min). The total gas pressure (not true pressure) measured at the outlet of the cavity by ~1 Pirani gauge was maintained between 0.035 and 0.050 Torr. The magnetic field was provided by a 9-in. electromagnet. The field strength leas measured by a proton NMR probe placed by the side of the cavity. The field values were corrected for the difference in field strengths at the center of the cavity and at the site of the NMR probe. This method might have introduced a relatively large systematic error (-0.5 G), but relative line positions could be estimated with an accuracy of 0.2 G. 199
A-Lkrultlit~g lCrequcncics, Cocllicicr~ts of the Secontl Order %ccmatr Elfecl, anrl
Hyperiine Structure Constants for ?I$, J = 3 State of OD 21
0
1 2 3 4 5
VA(MHz)
VA(MHz)
(exd
(Cal+
VA(MHz) (talc) b
310.15 ziz0.10 292.28 f 0.22 274.30 i 0.14 256.64 i 0.12 238.80 f 0.18 220.38 f 0.38
310.43 292.47 271.48 -
306.90 290.42 274.15 258.32 242.86 227.62
K x 107 (exp) 1.263 f 1.267 i 1.292 f 1.297 f 1.325 f 1.387 f
LbUsing matrix elements obtained from optical spectroscopy b Using ab initio matrix elements.
0.006 0.012 0.008 0.008 0.010 0.022
Al (MHZ) fexp) 4.91 4.53 4.19 3.94 3.82 3.61
f f f f f i
0.12 0.24 0.18 0.16 0.22 0.36
dl (MHZ) (calf) 4.78 4.50 4.20 3.89 3.57 3.24
(7, S),
The spectra were obtained using Stark modulation at 33-j- kHz. The microwave frequencies were measured by a Hewlett-Packard .534OA electronic frequency counter with a precision of 1 part in 10S. The same counter was alternately used to measure the oscillator frequency of the NMR probe. Signals were displayed on an X-Y chart recorder. Under optimum conditions, a signal-to-noise ratio of 5: 1 to 10: 1 could be achieved for excited vibrational lines; ground state lines were about 20 times stronger,
For each of the vibrational states there are 18 transitions, 9 in the low-field region and 9 in the high-field region. These transitions were observed at a fixed microwave frequency and the line positions were, respectivefy, given by (I)
for the low-field lines, and
for the high-field lines. Here Yis the microwave frequency, PAis the A-doubling frequency, gJ- and gJ+ are the molecular g factors of the A-doublets, kT2 is the coefficient of the second order Zeeman effect, and A1 is the hyperfine interaction constant. Three different spectra were recorded at three distinct microwave frequencies (9.0, 9.4, and 9.8 GHz) and all three were used to determine the desired molecular constants for each of the vibrationaf states up to 3 = 5 by the method of least squares fitting. The experimental values of these constants are shown in Tables I and II. The experimental errors quoted have been safely chosen as double the standard deviations obtained from the fitting. The calculated values of VA,g,$, and 111shown in Tables ‘I and XI were found from the expressions of vLtas given by Dousmanis et GE. (6) and from the expressions of g.i* and A1 as given by Radford (1, Z). The molecular constants involved in these expressions are the spin-orbit coupling constant d, the rot.ational constants H, and B, of the II and 2 states, respectively. The values of these molecular constants shown in Table III were obtained from C’oson (Table VII of Ref. (7)). Al so in the expressions of v.t and
i’ 0 1 2 3 4 5
0.88917 * 0.00001 0.88931 0.88698 f 0.~2 0.88733 0.88500 f 0.~2 0.88536 0.88307 i 0.00002 -0.88112 f 0.00002 .O.87913f 0.00003 _ - .- ._~...I__~_ ______~.__
u Using matrix elements BI’sing ai) inilio matrix
obtained elements.
0.88930 0.88968zk 0.00001 0.88733 0.88754f 0.00002 0.88535 0.88548 i 0.~2 0.88334 0.88353 rt 0.00002 0.88131 0.88154 f 0.00002 0.879'5 0.X7943 A 0.00005 ____~ _ _ ._._
from optical
s1jectroscnpy
0.88983 0.88785 0.88S8.k
.-.-
0.88980 0.88781 0.88.5X2 O.XW!, O.XXli.5 O.X7YOi
(7, S1.
matrix elements between the .l?II state and the tirst RJ . > the following perturbation erciled electronic state A%+ (neglecting interactions of other X states) :cppew:
TIULIS
111
Values of si~i~~-~r~~~t Coupling Conslant (. 1j, Rotational C’onstants B, and B, of the I J nnrl B States, and Effective Inverse Energy Separations (I!/
i’
.A (cm-l)
8,
(cm+)
R, (cm-l)
lo”;‘/:”
KASHID,
LEE, AND
SASTKY
Values ul Overlap Integrals (v 1D’), Matrix Elcrnc~~IS (u 1U
1II'),
R Centroids P,,’ (A), and reff 4) V
v’ = 0
bw)
WW P Yeff
v’ = 1
Mv’)
Wlv’) P reii v’ = 2
0’ = 3
blv’)
WW 7 Teff
v’ = 4
blv’)
Wlv’) i; reff
gr = 5
MJ’)
WV’) P roff
v’ = 6
(+I’) Wlv’) i: rerr
v’ = 7
64fJ’) MW) P
Teeff
2)’ = 8
04~‘) Wlv’) P Yeff
0’ = 9
+Jlv’) WW i; 7eff
0
1
2
3
4
5
0.9345 8.8636 1.0027 0.9950
0.3458 2.1042 1.1848 1.2716
0.0830 0.4315 1.3374 1.3414
0.0139 0.0479 1.5088 1.7439
0.0016 0.0064 1.7110 1.3849
0.0001 0.0003 1.9084 1.8476
0.3389 4.1829 0.8494 0.8804
0.7946 7.3563 1.0285 1.0026
0.4790 2.8518 1.2054 1.2828
0.1525 0.7702 1.3555 1.3624
0.0315 0.1100 1.5226 1.7148
0.0043 0.0160 1.7197 1.4823
0.1039 1.6988 0.6905 0.7767
0.4578 5.3661 0.8841 0.8996
0.6381 5.8067 1.0549 1.0055
0.5639 3.2774 1.2275 1.2956
0.2264 1.1112 1.3747 1.3831
0.0562 0.1968 I .5380 1.6974
0.0303 0.6731 0.5155 0.6828
0.1853 2.8031 0.7376 0.8022
0.5210 5.8115 0.9191 0.9184
0.4686 4.2571 1.0819 0.9982
0.6113 3.4615 1.2510 1.3101
0.3031 1.4458 1.3953 1.4036
0.0087 0.2723 0.3107 0.5989
0.0668 1.3307 0.5811 0.7130
0.2637 3.7037 0.7837 0.8279
0.5397 5.7458 0.9544 0.9358
0.2917 2.7582 1.1087 0.9649
0.6228 3.4287 1.2763 1.3263
0.0025 0.1149 0.0580 0.5258
0.0231 0.6200 0.4052 0.6325
0.1138 2.0456 0.6429 0.7436
0.3336 4.3623 0.8290 0.8534
0.5165 5.2745 0.9902 0.9505
0.1149 1.3682 1.1292 0.8340
0.0079 0.2935 0.1987 0.5612
0.0461 1.0779 0.4904 0.6669
0.1692 2.7566 0.7018 0.7746
0.3875 4.7326 0.8738 0.8783
0.4533 4.4797 1.0264 0.9600
0.0027 0.1438 0.0519 0.4999
0.0182 0.5657 0.3191 0.5982
0.0789 1.6234 0.5684 0.7020
0.2284 3.3903 0.7585 0.8056
0.4169 4.7781 0.9185 0.9019
0.0072 0.3025 0.1210 0.5380
0.0357 0.9367 0.4244 0.6365
0.1216 2.2149 0.6409 0.7377
0.2845 3.8668 0.8135 0.8363
0.0029 0.1668 0.1114 0.4865
0.0160 0.5435 0.2652 0.5783
0.062 1 1.3969 0.5185 0.6758
0.1717 2.7902 0.7093 0.7737
.?O.Z
5
n.ooi2 0.0955 0.3817 0.4437
0.3219 0.0867 0.5276
0.0313 0.8759 0.3885 0.6204
0.0981 1.9158 0.6@41 0.71hO
0.0034 0.1961 0.1134 O.4844
0.0159 0.5552 0.2942 O.SilS
0.0551 1.2940 0.4966 0.6640
0.0016 0.1236 0.3341 0.4484
cm082 0.3592 0.0994 0x92
0.0.711) 0.8758 0.3850 o.st7x
O,OO44 0.2386 0.0601 0.4932
0.017i 0.600.5 0.2720 0.5773
0.0023 0.1630 0.2266 0.3630
0.0104 0.419; 0.1.5.57 0.5425
0.0073
0.0063 0.3000 0.0390 11.5131
The matrix elements p. and q,, for D = 0, 1, and 2 were obtained by Coson (7, 8) from analysis of the A2Z+-X2B system of OD. A11 of the above matrix elements are also calculated by ah initio methods initiated by Coson (8). The matrix elements can by rewritten as (notations below are standard)
304
RASHID,
LEE, AND
SASTRY
The Ah Initio Matrix Elementsa 0
0 1 2 3 4 5
Pv
4v
-..
-0.1233 -0.1205 -0.1176 -0.1146 -0.1117 -0.1086
h
0.01086 0.01059 0.01031 0.01003 0.00974 0.00944
su
Y”
--
---__
-0.001560 -0.001567 -0.001573 -0.001580 -0.001586 -0.001592
0.1769 0.1775 0.1782 0.1788 0.1795 0.1801
0.0001357 O.OOQ1325 0.~1291 0.0001258 0.0001247 0.0001200
a The units (where relevant) are cm-l.
and
(~+)2,eff(~l~‘)~(~I~I’U’)
1 s, =
2
Ix,,?
(4e)
-
The electronic matrix elements {AL+) and (L+) are calculated by Coxon. The quantities (vlo’), (z@lv’), Pwt (r centroid), and (r)off are computed by Nicholls’ (9) method treating OD as a Morse molecule. Their values are given in Table IV. The molecular constants involved in this computation are obtained from Coxon (7). Values of the perturbation matrix elements are given in Table V. The explicit expressions of PA are given by Dousmanis et ul. (6). The expressions of the molecular g factors g.$ derived by Radford (1) can be written as gJ+ = gJ” + &J)S gJ-
=
where terms on the right-hand 9 -
(3x/2) x
gJ”
+
@g.f)s
+ (QJ)N + (&)t+,
tsa)
+
(Ib)
@gJ)N
+
side are (for an inverted
@g.r)t-,
*III, J = $ state)
1’
(64
x-j-2-x
X
(M + x - S)(Y,, + 6sJ + 6
~-
2
-
2
>I
su ,
(6d)
rntcrpolateti Values of the Parameters rt, h, nntl c (nil in hlHLi of f)I) _..~_“~__~~~~~~~. . . _. _-.. _~ -. _. .““_ -..
2’
a
b
c
0
13.20 12.75 12.24 11.80 11.30 10.78 _- ...”.._.. ..-.. ~~ --..-
-18.27 - 18.44 - 18.61 -1X.79 - IX.98 - IO.18
LO.45 20.00 19.52 1o.w 1x.5-’ 17.w
1 2 3 4 5 _. an
._ ._--.
..--. _
I- .-.-
-
“.. .“__
(1
(ag,ljr.-
=I
!~!+!I p3 [
(2 -
x
[
A)
!b (,-;)-(o”+u)]+J-~
-(x+x+l)(r,-2&)+6
X42--x ---7..+2
(
>I
SL. . 16e)
Here x = _4,‘Np, .Y = +[16 + X(X - 4)]?, the electronic spin g factor gs has a value 2.W2.32(1) and end-over-end rotational g factor gN (OD) = -2.72 X 10w4. The h~perfine structure constant Ar is expressed (I, -I) (for an inverted ?II;, J = !j state) as AI = 1~~15_Y[2U(2.~+ 2 - X) + b(X + 16 - 2X) + C(.Y - -l - 2X)],
(II
where molecular parameters a, b, and c are explicitly deiined by Radford (1, 2,). The -42 term of Radford has been omitted from the energy expressions (1) and (2) since it is negligible compared to our experimental uncertainties. The parameters (2, b, and c were obtained by interpolating Kayama’s (IO) theoretical calculations of the OH ground state and using the relation (1) ~(01)) = [gr(D)/gI(H)]a(OH) and corresponding relations for b(OD) and c(OD). The values have been scaled so as to bring the theoretical calculations for 21= 0 into coincidence with the txperimental results trf Radford. These values are shown in Table 1’1.
The experimental values of v.\ for the vibrational levels are self-consistent; the\, decrease in a regular fashion, as espected, with the higher vibrations. The anharmonic stretching of the molecule due to higher vibrations slotw down the molecular rotations and thereby makes the L uncoupling less prominent. This brings the members of the A doublet closer with vibrational escitations. Our experimental values of v.i agree reasonably well, though far beyond our experimental uncertainties, with the calculated values. The discrepancies are higher for the higher vibrational levels. The decreasing trend of the vaIues of molecular g factors reflects the fact that tht: s uncoupling due to molecular rotations becomes less with higher vibrations. However, the discrepancy between the observed and calculated values is notable. Experimental values of g factors are always lower than the calculated values by an amount mwll
306
K.dSHID, LEE, AND SASTRY
higher 1han t lw (~~I~~ri~~l~~nlal~il~cer~ain~i~s. (‘ocfficients or the st~tnd or&r &elnari ct‘fect increased with the vibrational excitations. Similar efrects were observed hy ~3ougl1 e/ aE. (.?) in their experiments with OH. ‘The observed values of the hyperfine structure constant A1 are in reasonable agreement with the calculated values. Kayama’s theoretical calculations were performed for only two different internuclear separations and so interpolated values might not be up to expectation. Also, due to too much superimposition of the spectral lines the observed values of A1 were much higher than the actual values especially for the two highest observed vibrational levels. Our experimental values of all the constants for the ground vibrational level agree well within the experimental errors with t.hose of Radford. ACKNOWLEDGiMENTS We are grateful to the National Research Council of Canada for financial support. We also wish to thank Dr. R. Kaiser for the use of his magnet and Mr. D. Hornibrook for fabricating (.hc Microwave Cavities.
RECEIVED : May 6, 1977 REFERENCES 1. H. E. RADFORD,Phys. Rev. 122, 114 (1961). 2. H. E. RADFORD,Phys. Rev. 126, 1035 (1962). 3. P. N. CLOUGH, A. H. CURRAN, AND B. A. THRUSH, Chew. Pkgs. Lett. 1, 86 (1970) ; Pm. Roy. SOG. Ser. A 323, 541 (1971). 8. K. P. LEE, W. G. TAPS,R. L,IROUCHE,Ais= G. A. WOONTOX, &?a&. J. Pfiys. 49, 2207 (1971). 5. IS. P. LEE ANDW. G. TAM, Cheat.Plzys. 4, 434 (1974). 6. G. C. DOUSMANIS, T. M. SANDERS, AND C. H. TOWNJB, Phys. Rev. 100, 1735 (1955). 7. J. A. COXON,J. Mol. Spectrosc. 58, 1 (1975). 8. J. A. COXONAND R. E. HAMXXRSLEY, J. Moi. Spectrosc. 58, 29 (1975). 9. R. W. NICHOLLS,J. Res. #at. 3~. S&d. Ser. it 65, 451 (1961). 10. X. KAYAKA, J. Clew. P&s. 39, 1507 (1963).
‘I’hc paramagnetic resonance absorption spectrum of the OD radical in the exited villrational levels up to z = 5 of the ground *II<, J = 4 state has been observed at X-band frcquencies. The theory of the Zeeman effect of a paramagnetic W state of a light diatomic molecule has been aTplied to analyze the spectrum. The &doubling frequencies, the molecular r factors. coeliicients of the second order Zeeman effect, and the hyperline interaction constant?; wcrc determined for each of the vibrational levels. The experimental results agree reasonaM well with the values calculated from (a) optical data and (b) ab initio data. The experimental determinations are still much hetter than theoretical calculations.
ISTRODUCTION Electron paramagnetic resonance measurements provide a convenient tool for studies of gaseous molecules or free radicals having unpaired electrons. The free hydroryl radicals OH and OD have a 211 ground state which is paramagnetic. Radford (I) lirst used this technique to observe transitions betJveen Zeeman components of a few rotational levels of the hydrosyl radicals produced by an electric discharge in low-pressure. \vater vapor. Later Clough et al. (3) and Lee et al. (4, 5) could populate the excited vibrational levels of OH by reacting H with ozone and independently observed paramagnetic resonance in vibrationally exited OH. We have now extended the study to 01) radicals in several low vibrational states of the !%;, J = 3 electronic state.
The 01) radical was prepared by the reaction of ozone \vith atomic deuterium produced by a microwave discharge of Dr. The two gases were conveyed in separate quartz tubes through a g-in. port to the EPR cavity and were mixed inside the cavity. Tht product and the residual gases were pumped out through a similar third port via liquid nitrogen cold traps by an Alcatel vacuum pump (pumping speed -1000 litersi’min). The total gas pressure (not true pressure) measured at the outlet of the cavity by ~1 Pirani gauge was maintained between 0.035 and 0.050 Torr. The magnetic field was provided by a 9-in. electromagnet. The field strength leas measured by a proton NMR probe placed by the side of the cavity. The field values were corrected for the difference in field strengths at the center of the cavity and at the site of the NMR probe. This method might have introduced a relatively large systematic error (-0.5 G), but relative line positions could be estimated with an accuracy of 0.2 G. 199
A-Lkrultlit~g lCrequcncics, Cocllicicr~ts of the Secontl Order %ccmatr Elfecl, anrl
Hyperiine Structure Constants for ?I$, J = 3 State of OD 21
0
1 2 3 4 5
VA(MHz)
VA(MHz)
(exd
(Cal+
VA(MHz) (talc) b
310.15 ziz0.10 292.28 f 0.22 274.30 i 0.14 256.64 i 0.12 238.80 f 0.18 220.38 f 0.38
310.43 292.47 271.48 -
306.90 290.42 274.15 258.32 242.86 227.62
K x 107 (exp) 1.263 f 1.267 i 1.292 f 1.297 f 1.325 f 1.387 f
LbUsing matrix elements obtained from optical spectroscopy b Using ab initio matrix elements.
0.006 0.012 0.008 0.008 0.010 0.022
Al (MHZ) fexp) 4.91 4.53 4.19 3.94 3.82 3.61
f f f f f i
0.12 0.24 0.18 0.16 0.22 0.36
dl (MHZ) (calf) 4.78 4.50 4.20 3.89 3.57 3.24
(7, S),
The spectra were obtained using Stark modulation at 33-j- kHz. The microwave frequencies were measured by a Hewlett-Packard .534OA electronic frequency counter with a precision of 1 part in 10S. The same counter was alternately used to measure the oscillator frequency of the NMR probe. Signals were displayed on an X-Y chart recorder. Under optimum conditions, a signal-to-noise ratio of 5: 1 to 10: 1 could be achieved for excited vibrational lines; ground state lines were about 20 times stronger,
For each of the vibrational states there are 18 transitions, 9 in the low-field region and 9 in the high-field region. These transitions were observed at a fixed microwave frequency and the line positions were, respectivefy, given by (I)
for the low-field lines, and
for the high-field lines. Here Yis the microwave frequency, PAis the A-doubling frequency, gJ- and gJ+ are the molecular g factors of the A-doublets, kT2 is the coefficient of the second order Zeeman effect, and A1 is the hyperfine interaction constant. Three different spectra were recorded at three distinct microwave frequencies (9.0, 9.4, and 9.8 GHz) and all three were used to determine the desired molecular constants for each of the vibrationaf states up to 3 = 5 by the method of least squares fitting. The experimental values of these constants are shown in Tables I and II. The experimental errors quoted have been safely chosen as double the standard deviations obtained from the fitting. The calculated values of VA,g,$, and 111shown in Tables ‘I and XI were found from the expressions of vLtas given by Dousmanis et GE. (6) and from the expressions of g.i* and A1 as given by Radford (1, Z). The molecular constants involved in these expressions are the spin-orbit coupling constant d, the rot.ational constants H, and B, of the II and 2 states, respectively. The values of these molecular constants shown in Table III were obtained from C’oson (Table VII of Ref. (7)). Al so in the expressions of v.t and
i’ 0 1 2 3 4 5
0.88917 * 0.00001 0.88931 0.88698 f 0.~2 0.88733 0.88500 f 0.~2 0.88536 0.88307 i 0.00002 -0.88112 f 0.00002 .O.87913f 0.00003 _ - .- ._~...I__~_ ______~.__
u Using matrix elements BI’sing ai) inilio matrix
obtained elements.
0.88930 0.88968zk 0.00001 0.88733 0.88754f 0.00002 0.88535 0.88548 i 0.~2 0.88334 0.88353 rt 0.00002 0.88131 0.88154 f 0.00002 0.879'5 0.X7943 A 0.00005 ____~ _ _ ._._
from optical
s1jectroscnpy
0.88983 0.88785 0.88S8.k
.-.-
0.88980 0.88781 0.88.5X2 O.XW!, O.XXli.5 O.X7YOi
(7, S1.
matrix elements between the .l?II state and the tirst RJ . > the following perturbation erciled electronic state A%+ (neglecting interactions of other X states) :cppew:
TIULIS
111
Values of si~i~~-~r~~~t Coupling Conslant (. 1j, Rotational C’onstants B, and B, of the I J nnrl B States, and Effective Inverse Energy Separations (I!/
i’
.A (cm-l)
8,
(cm+)
R, (cm-l)
lo”;‘/:”
KASHID,
LEE, AND
SASTKY
Values ul Overlap Integrals (v 1D’), Matrix Elcrnc~~IS (u 1U
1II'),
R Centroids P,,’ (A), and reff 4) V
v’ = 0
bw)
WW P Yeff
v’ = 1
Mv’)
Wlv’) P reii v’ = 2
0’ = 3
blv’)
WW 7 Teff
v’ = 4
blv’)
Wlv’) i; reff
gr = 5
MJ’)
WV’) P roff
v’ = 6
(+I’) Wlv’) i: rerr
v’ = 7
64fJ’) MW) P
Teeff
2)’ = 8
04~‘) Wlv’) P Yeff
0’ = 9
+Jlv’) WW i; 7eff
0
1
2
3
4
5
0.9345 8.8636 1.0027 0.9950
0.3458 2.1042 1.1848 1.2716
0.0830 0.4315 1.3374 1.3414
0.0139 0.0479 1.5088 1.7439
0.0016 0.0064 1.7110 1.3849
0.0001 0.0003 1.9084 1.8476
0.3389 4.1829 0.8494 0.8804
0.7946 7.3563 1.0285 1.0026
0.4790 2.8518 1.2054 1.2828
0.1525 0.7702 1.3555 1.3624
0.0315 0.1100 1.5226 1.7148
0.0043 0.0160 1.7197 1.4823
0.1039 1.6988 0.6905 0.7767
0.4578 5.3661 0.8841 0.8996
0.6381 5.8067 1.0549 1.0055
0.5639 3.2774 1.2275 1.2956
0.2264 1.1112 1.3747 1.3831
0.0562 0.1968 I .5380 1.6974
0.0303 0.6731 0.5155 0.6828
0.1853 2.8031 0.7376 0.8022
0.5210 5.8115 0.9191 0.9184
0.4686 4.2571 1.0819 0.9982
0.6113 3.4615 1.2510 1.3101
0.3031 1.4458 1.3953 1.4036
0.0087 0.2723 0.3107 0.5989
0.0668 1.3307 0.5811 0.7130
0.2637 3.7037 0.7837 0.8279
0.5397 5.7458 0.9544 0.9358
0.2917 2.7582 1.1087 0.9649
0.6228 3.4287 1.2763 1.3263
0.0025 0.1149 0.0580 0.5258
0.0231 0.6200 0.4052 0.6325
0.1138 2.0456 0.6429 0.7436
0.3336 4.3623 0.8290 0.8534
0.5165 5.2745 0.9902 0.9505
0.1149 1.3682 1.1292 0.8340
0.0079 0.2935 0.1987 0.5612
0.0461 1.0779 0.4904 0.6669
0.1692 2.7566 0.7018 0.7746
0.3875 4.7326 0.8738 0.8783
0.4533 4.4797 1.0264 0.9600
0.0027 0.1438 0.0519 0.4999
0.0182 0.5657 0.3191 0.5982
0.0789 1.6234 0.5684 0.7020
0.2284 3.3903 0.7585 0.8056
0.4169 4.7781 0.9185 0.9019
0.0072 0.3025 0.1210 0.5380
0.0357 0.9367 0.4244 0.6365
0.1216 2.2149 0.6409 0.7377
0.2845 3.8668 0.8135 0.8363
0.0029 0.1668 0.1114 0.4865
0.0160 0.5435 0.2652 0.5783
0.062 1 1.3969 0.5185 0.6758
0.1717 2.7902 0.7093 0.7737
.?O.Z
5
n.ooi2 0.0955 0.3817 0.4437
0.3219 0.0867 0.5276
0.0313 0.8759 0.3885 0.6204
0.0981 1.9158 0.6@41 0.71hO
0.0034 0.1961 0.1134 O.4844
0.0159 0.5552 0.2942 O.SilS
0.0551 1.2940 0.4966 0.6640
0.0016 0.1236 0.3341 0.4484
cm082 0.3592 0.0994 0x92
0.0.711) 0.8758 0.3850 o.st7x
O,OO44 0.2386 0.0601 0.4932
0.017i 0.600.5 0.2720 0.5773
0.0023 0.1630 0.2266 0.3630
0.0104 0.419; 0.1.5.57 0.5425
0.0073
0.0063 0.3000 0.0390 11.5131
The matrix elements p. and q,, for D = 0, 1, and 2 were obtained by Coson (7, 8) from analysis of the A2Z+-X2B system of OD. A11 of the above matrix elements are also calculated by ah initio methods initiated by Coson (8). The matrix elements can by rewritten as (notations below are standard)
304
RASHID,
LEE, AND
SASTRY
The Ah Initio Matrix Elementsa 0
0 1 2 3 4 5
Pv
4v
-..
-0.1233 -0.1205 -0.1176 -0.1146 -0.1117 -0.1086
h
0.01086 0.01059 0.01031 0.01003 0.00974 0.00944
su
Y”
--
---__
-0.001560 -0.001567 -0.001573 -0.001580 -0.001586 -0.001592
0.1769 0.1775 0.1782 0.1788 0.1795 0.1801
0.0001357 O.OOQ1325 0.~1291 0.0001258 0.0001247 0.0001200
a The units (where relevant) are cm-l.
and
(~+)2,eff(~l~‘)~(~I~I’U’)
1 s, =
2
Ix,,?
(4e)
-
The electronic matrix elements {AL+) and (L+) are calculated by Coxon. The quantities (vlo’), (z@lv’), Pwt (r centroid), and (r)off are computed by Nicholls’ (9) method treating OD as a Morse molecule. Their values are given in Table IV. The molecular constants involved in this computation are obtained from Coxon (7). Values of the perturbation matrix elements are given in Table V. The explicit expressions of PA are given by Dousmanis et ul. (6). The expressions of the molecular g factors g.$ derived by Radford (1) can be written as gJ+ = gJ” + &J)S gJ-
=
where terms on the right-hand 9 -
(3x/2) x
gJ”
+
@g.f)s
+ (QJ)N + (&)t+,
tsa)
+
(Ib)
@gJ)N
+
side are (for an inverted
@g.r)t-,
*III, J = $ state)
1’
(64
x-j-2-x
X
(M + x - S)(Y,, + 6sJ + 6
~-
2
-
2
>I
su ,
(6d)
rntcrpolateti Values of the Parameters rt, h, nntl c (nil in hlHLi of f)I) _..~_“~__~~~~~~~. . . _. _-.. _~ -. _. .““_ -..
2’
a
b
c
0
13.20 12.75 12.24 11.80 11.30 10.78 _- ...”.._.. ..-.. ~~ --..-
-18.27 - 18.44 - 18.61 -1X.79 - IX.98 - IO.18
LO.45 20.00 19.52 1o.w 1x.5-’ 17.w
1 2 3 4 5 _. an
._ ._--.
..--. _
I- .-.-
-
“.. .“__
(1
(ag,ljr.-
=I
!~!+!I p3 [
(2 -
x
[
A)
!b (,-;)-(o”+u)]+J-~
-(x+x+l)(r,-2&)+6
X42--x ---7..+2
(
>I
SL. . 16e)
Here x = _4,‘Np, .Y = +[16 + X(X - 4)]?, the electronic spin g factor gs has a value 2.W2.32(1) and end-over-end rotational g factor gN (OD) = -2.72 X 10w4. The h~perfine structure constant Ar is expressed (I, -I) (for an inverted ?II;, J = !j state) as AI = 1~~15_Y[2U(2.~+ 2 - X) + b(X + 16 - 2X) + C(.Y - -l - 2X)],
(II
where molecular parameters a, b, and c are explicitly deiined by Radford (1, 2,). The -42 term of Radford has been omitted from the energy expressions (1) and (2) since it is negligible compared to our experimental uncertainties. The parameters (2, b, and c were obtained by interpolating Kayama’s (IO) theoretical calculations of the OH ground state and using the relation (1) ~(01)) = [gr(D)/gI(H)]a(OH) and corresponding relations for b(OD) and c(OD). The values have been scaled so as to bring the theoretical calculations for 21= 0 into coincidence with the txperimental results trf Radford. These values are shown in Table 1’1.
The experimental values of v.\ for the vibrational levels are self-consistent; the\, decrease in a regular fashion, as espected, with the higher vibrations. The anharmonic stretching of the molecule due to higher vibrations slotw down the molecular rotations and thereby makes the L uncoupling less prominent. This brings the members of the A doublet closer with vibrational escitations. Our experimental values of v.i agree reasonably well, though far beyond our experimental uncertainties, with the calculated values. The discrepancies are higher for the higher vibrational levels. The decreasing trend of the vaIues of molecular g factors reflects the fact that tht: s uncoupling due to molecular rotations becomes less with higher vibrations. However, the discrepancy between the observed and calculated values is notable. Experimental values of g factors are always lower than the calculated values by an amount mwll
306
K.dSHID, LEE, AND SASTRY
higher 1han t lw (~~I~~ri~~l~~nlal~il~cer~ain~i~s. (‘ocfficients or the st~tnd or&r &elnari ct‘fect increased with the vibrational excitations. Similar efrects were observed hy ~3ougl1 e/ aE. (.?) in their experiments with OH. ‘The observed values of the hyperfine structure constant A1 are in reasonable agreement with the calculated values. Kayama’s theoretical calculations were performed for only two different internuclear separations and so interpolated values might not be up to expectation. Also, due to too much superimposition of the spectral lines the observed values of A1 were much higher than the actual values especially for the two highest observed vibrational levels. Our experimental values of all the constants for the ground vibrational level agree well within the experimental errors with t.hose of Radford. ACKNOWLEDGiMENTS We are grateful to the National Research Council of Canada for financial support. We also wish to thank Dr. R. Kaiser for the use of his magnet and Mr. D. Hornibrook for fabricating (.hc Microwave Cavities.
RECEIVED : May 6, 1977 REFERENCES 1. H. E. RADFORD,Phys. Rev. 122, 114 (1961). 2. H. E. RADFORD,Phys. Rev. 126, 1035 (1962). 3. P. N. CLOUGH, A. H. CURRAN, AND B. A. THRUSH, Chew. Pkgs. Lett. 1, 86 (1970) ; Pm. Roy. SOG. Ser. A 323, 541 (1971). 8. K. P. LEE, W. G. TAPS,R. L,IROUCHE,Ais= G. A. WOONTOX, &?a&. J. Pfiys. 49, 2207 (1971). 5. IS. P. LEE ANDW. G. TAM, Cheat.Plzys. 4, 434 (1974). 6. G. C. DOUSMANIS, T. M. SANDERS, AND C. H. TOWNJB, Phys. Rev. 100, 1735 (1955). 7. J. A. COXON,J. Mol. Spectrosc. 58, 1 (1975). 8. J. A. COXONAND R. E. HAMXXRSLEY, J. Moi. Spectrosc. 58, 29 (1975). 9. R. W. NICHOLLS,J. Res. #at. 3~. S&d. Ser. it 65, 451 (1961). 10. X. KAYAKA, J. Clew. P&s. 39, 1507 (1963).