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Rotational analysis of the Hopfield emission system of O2+
JOURNAL
OF MOLECULAR
SPECTROSCOPY
55, 56-65 (1975)
Rotational Analysis of the Hopfield Emission System of O,+ l H. S. OGAWA AND~M. OGAWA De#artment
of Physics, University of Soulhem Califorka, Los Angeles, Calqornia 90007
The spectrum of the Hopfield emission bands of OX+, c ?Z,--b B,; has been reinvestigated with improved resolution. Spin splitting of the rotational lines has been observed for the first time, and the difference between the upper- and lower-state splittings due to spin-spin interaction was observed to be 3e’ - 3~” = 0.87 cm-‘. A rotational analysis has been made for seven bands, four of which (CM, O-1, &2, and (r3) are new. The rotational constants for the upper state G 2,are Bo = 1.5615 cm-l and DO = 6.7 X 10e6 cm-‘. For the lower state b 8,-, the rotational constants B, and D, are obtained for ZJ= O-6 and the vibrational constants are ws = 1197.8 cm-* and wLxs = 17.3 cm-l. I. INTRODUCTION
A progression of bands in the far ultraviolet region produced in a condensed discharge with a mixture of oxygen and helium was first reported by Hopfield (I) and later extended by Tanaka, Jursa, and LeBlanc (2). The progression was originally thought to be due to emission in the neutral oxygen molecule; however, the transition could not be satisfactorily explained from the known states of Oz. Later, from a rotational analysis of three bands (&4, O-5, O-6), LeBlanc (3) identified the lower state to be the b 4Zo- of OS+which is the upper state of the first negative system of O,+, b 42oM-a 411,. Assuming an allowed transition, Le Blanc identified the Hopfield emission bands as due to the transition G4ZU- + b 42ge of OS+.Later, the upper state, c 4.ZU-, had been observed by Codling and Madden (4) as a convergence limit of two Rydberg absorption series of O2 in the wavelength region, 500-600 A. Le Blanc reported that the observed bands were slightly diffuse and appeared to be composed of a single P and a single R branch with no Q branch. The resolution was not sufficient to separate the spin components. Presented in this paper are the results extending Le Blanc’s observation by increasing the resolution to separate the spin components. II. EXPERIMENT A McPhearson 3-m vacuum spectrograph with a grating of 1920 lines/mm, and reciprocal dispersion of 1.7 A/ mm was used to record the spectra in the first order. A mixture of oxygen (1.2 Torr) and helium (15 Torr) was fed into a a-shaped, water cooled discharge tube. The discharge tube had an inside diameter of -1 cm and was -18 cm in 1This research Office-Durham
was supported in part by Grant No. DA-ARO-D-31-124-73-G41 of the Army Research and Contract No. N00014-67-A-0269-0014 of the Office of Naval Research. 56
Copyright
@
1975 by Academic
All rights of reproduction
Press, Inc.
in any form reserved.
ROTATIONAL
r
FIG.
lapping
ANALYSIS
OF 02’
BANDS
57
1.
Enlargement of two bands of the Hopfield Emission system of OP+. The (O-l) band has overP and R branches, and the (O-3) band has P and R branches completely separated.
length, and utilized aluminum electrodes. The mixture was excited by an a.c. condensed spark discharge to produce the Hopfield emission bands. The spectra were calibrated by a mercury and carbon comparison spectrum. Another r-shaped discharge tube with quartz windows was positioned behind the main discharge tube. This tube had an inside diameter of -6 mm and was - 11 cm in length and utilized copper electrodes. Helium was added with a drop of mercury and excited by a condensed spark discharge to produce the comparison spectrum. The spectra were photographed on Kodak SWR plates. III.
RESULTS
AND
DISCUSSION
1. Spectra The Hopfield system of O,+ is a v’ = 0 progression in the region between 1900-2400 A. All bands shade toward the shorter wavelength. The measured bands were CO, O-l, O-2, O-3, O-4, O-5, and (t6, with bands heads at 1940.4, 1985.3, 2030.8, 2076.9, 2123.6, 2171.2 and 2218.5 A respectively (vacuum wavelengths). The intensity of the (O-3) band is maximum, and the intensity diminishes on either side of the progression. The (OM) band had such a low intensity that mesaurements for this band are not accurate. The spectrum was relatively free of impurity bands except for the (O-6) band. An enlargement of two bands (O-1 and O-3) is shown in Fig. 1. At first sight, there appears to be a single P and a single R branch with no Q branch. The lines are diffuse and for some bands (especially O-1) the P and R branches overlap. On closer examination, however, each line of each branch is composed of two separate components, the components, on the shorter wavelength side having the larger intensity. The separation of the components appears to be nearly constant for all lines except near the band head where they become slightly larger. The average separation between the components (excluding the first three lines N = 1, 2, and 5) was found to be 0.87 cm-‘. Although there is a clear separation of each line, the components are still rather diffuse. This may be due to the blending of two lines for each component observed. All bands measured exhibit this splitting except the O-O band. For this band, the intensity is extremely weak and the lines are too diffuse to show a separation. As a final remark, it is unfortunate that the intensities of the satellite branches are too low to be observed, for they are essential in obtaining accurate values for the fine structure constants (spin splitting constants).
OGAWA
58
AND OGAWA
2. Theory Since the nuclear spin of 1602 is zero (I = 0), all antisymmetric leaving only the transitions between symmetric levels. The allowed fore between levels of even N in the upper state (c “&,-) and levels state (b “I?,). From the selection rules eighteen branches are allowed; however, compose ten among them. The eight remaining main branches are
K(N) =
vo +
levels are missing, transitions are thereof odd N in the lower the satellite branches given by
Fi’(N + 1) - Fi”(N) i = 1, 2, 3, 4.
Pi(N)
= vo + Fi’(N -
1) - F;‘(N)
I
0)
The subscript (i) is representative of the four values of J for a given N (for i = 14, J = N + s, N + 3, N - 3, and N - $, respectively). The band origin vo, is constant for a given vibrational level and the rotational term values Fi (N) are given by Fi(N)
= B,N(N+
1) - D,W(N+
The term fi(N) takes four values corresponding are given as follows by Budo (5) :
l)“+
f<(N).
to the four J values for a given N and
_fl = - 441 - l3/(2N
+ 3)1} + 3rN,
f:! = + &{I + [3/(2N
+ 3)]} + r(N
f3 = + %(I
- [3/(2N
-
l)]}
- r(N + 4),
&{l + [3/(2N
-
l)])
- 3r(N + 1).
f4 = -
(2)
- 3),
(3)
Each value of fi is composed of two terms, the first arising from the mutual interaction of the electron spins, and the second from the interaction of N and S. The fi versus N curves for the lower state (b “I?Z,-) are shown in Fig. 2 with e = 0.1487 cm-l and Y = - 0.00033 cm-r which were obtained by Nevin (6). Several facts should be noted from the curves which are characteristic of the b 4ZUstate. First, for N > 3 the energy level order in increasing wavenumber is f4, f~, f3, and f2. Second, the curves converge rapidly with increasing N into two groups which are separated by approximately 3~ and are nearly independent of N. The levels fi and fz form the upper group and the levels jr and ja form the lower group. These two groups
FIG. 2. Spin splitting of rotational levels of the b 2,given by Budo and constants given by Nevin.
state, calculated according to the equations
ROTATIONAT,
ANALYSIS
59
OF Oz+ BANDS
appear to be nearly symmetrical about the horizontal axis. The value of Y is three orders due to the spin-rotation of magnitude smaller than E and, as such, the contribution interaction is negligible even for large !li. 3. Koluliurd
.~mlysi.s
From the above discussion, the four observed branches are most likely the blended ones of the expected eight main branches. Thus the P, and Pa branches were assumed to form one blended branch (P2, P,), and the K, and Ka branches form another branch. Similarly- the Pi and 1’4 branches form one blended branch, and RI and Rd form the other one. On the basis of line strengths given in Kovacs (7), it was determined that the branches of highest intensity were (P2, 1’3) and (R2, R3). -4s mentioned in Section 1, the short wavelength components of both I’ and K branches are stronger than the others. Therefore, they are considered as (P2 + P3) and (R, + Rx), respectively. Wavenumbers (expressed in vat. cm-‘) of all measured lines and their identifications are listed in Table I. No splitting of the components was observed for the (OH)) band and the wavenumbers listed for this band are an average over the four components. Since the vibrational level, z’ = 0, of the upper state r4EU- is common to all bands, the combination differences A!$’ (.V) were obtained for all bands and compared. They agree within the experimental errors and their average values (escluding the O-0 band) were calculated and are listed in Table II. According to equations (l), (2), and (3) the second combination differences are A$:
= Rl(;Y) - PI(N)
= (4Bn - 60,) (iv + 3) - SD,(,V + +)” - [18~/(2.\-
A.$‘,’
= R,(il’)
-
I’,(;\:)
=
(4H, - 60,)(V
+ 1)(2N + 5)1+
6r,
+ 3)
- 8D,, (IV + f)” - [l&,/(2.\’
+ 1) (21’ + 3)] + 2Y, (4)
A&,’ = &(;V) - Pz(fV) = (4& - 60,) (-V + ;) - 8D,(N + 3)” + [18t,“(LV + 1)(2N - 3)] - 2Y, AZF,’ = R,(iT’) - Pd(YV) = (4h’v - 60,) (1Vf
3)
-_8D,(,V + $)3 + [(1&,‘(2V
+ 1)(2.V - 3)] - 6~.
The experimental errors in the observed A2F’ values are the same order or larger than the magnitude of the terms which include the fine structure constants 6 and y. Consequently the fine structure constants cannot be obtained without knowledge of the satellite branches or without higher-precision measurements. Nevertheless, the rotational constants R, and D, for both the upper and lower states and the values for the band origins may still be computed with very good accuracy. The essential feature in these calculations is the approximation that the separation between group (Fz, FJ and group (Fl, F4) is constant and independent of LVfor both the upper and lower states. For the upper state this separation is 3~’ and for the lower state it is 3~“. Under this approsimation
OGAWA
60
AND
OGAWA
The approximation is valid and is within experimental N = 0 because only one level, PI(O), exists.
Table I.
Wavenumbers
of the rotational
errors for N > 1, but is not for
lines of (O-O), (O-i), (O-Z),
(O-3), (O-4), (O-5), and (O-6) bands
-
T
N -
(o-o)**
(0-l)
P, ,P2,P3’P4
R, >R2,R3,R4
I
Rl'R4
Pl'P4
R2'R3
Pz,P3
50383.2
50375.2
50384.0
*
1
51548.6
3
58.0
36.7
93.1
71.1
93.8
50372.0
5
69.4
35.4
50405.0
71.1
50405.9
71.6
7
83.3
36.6
19.0
72.0
20.2
73.1
51539.6
99.4
39.6
35.6
76.5
36.5
77.3
11
51617.5
45.6
54.8
83.2
55.9
84.0
13
38.0
53.7
76.6
92.5
77.5
93.1
15
60.9
63.8
50500.7
50404.5
50501.5
50405.0
17
85.9
76.0
26.9
18.2
28.0
19.0
19
51713.0
90.8
34.9
56.9
35.6
88.8
54.8
9
21 23
,-
51608.7
(O-2)
N
Rl'R4
Pl'P4
1
49255.0
49245.4
49256.2
3
64.6
42.0
65.4
5
76.6
42.0
R2'R3
'2"3
49243.0
77.4
43.0
Rl'R4
Pl'P4
48161.0
48152.1
48162.1
70.8
48.9
71.7
48150.0
83.4
48.9
84.2
50.0
7
91.6
44.7
92.3
45.4
98.8
51.7
99.7
52.9
9
49308.8
49.5
49309.6
50.2
48216.9
57.7
48217.7
58.6
11
29.0
57.1
29.7
57.9
38.0
66.3
38.8
67.2 78.4
13
51.6
67.4
52.4
68.2
61.9
78.0
62.6
15
77.1
80.2
77.9
81.0
88.3
91.8
89.2
92.7
17
49405.2
95.9
49405.8
96.6
48318.0
48208.9
48318.8
48209.6
49314.1
35.9
49314.9
50.3
29.0
51.0
29.7
69.4
35.7
19 21
59.1
23
-
* **
1
No line exists for R4 (l), P2 (1). P3 (1), p4 (1) No component
splitting
observed
(average of four components
were measured)
86.0
52.7
48424.2
78.2
ROTATIONAL ANALYSIS OF Oz+ 13ANDS Table I (Continued) (O-5)
1
3 5
pl'p4
47094.5
47104.1
46078.4
46068.4
46079.j
90.7
13.3
47092.0
89.0
66.7
89.9
: 46068.4
I
24.4
90.7
26.1
92.0
46101.2
66.7
46102.4
68.4
~
94.5
42.2
72.4
~
:
7
41.4
18.1
71.2
19.1
rl
60.4
47101.6
61.3
47102.2
37.5
78.4
39.0
11
82.3
10.8
83.4
11.6
60.8
89.0
61.R
13
47207.1
23.5
47202.3
24.4
87.1
46102.4
15
35.7
39.0
36.1
39.n
46216.2
19.1
17 19
1'2.1';
R2.1~3
11.6
47103. I
3
Rl'R4
66.3 473OO.LI
95.5
57.6
67.1
78.8
47301.1
79.9
3?..3
47204.4
77.5
31.9
21
-)
23
53.3
I
~
-
79.3
~
89.9
/
87.8
46103.4
(
~ 46217.3
20.4
1
49.8
40.4
:
85.7
64.1
~
; 46324.3
90.5
;
46219.9
:
~
39.0 j
i
66.6
(O-6) N
Rl'R4
Pl'P4
R23R3
1
45086.4
45077.4
45087.5
3
98.0
75.1
98.8
45076.8
5
45110.9
76.8
45111.8
77.5 82.3
7
28.4
81.3
29.2
9
48.8
89.8
49.5
90.5
11
72.7
45100.5
73.6
45101.7
13
45200.2
15.6
45200.9
16.7
15
30.6
34.1
31.4
'35.0
17
64.5
55.9
65.3
56.7
19
45302.4
21
43.1
23
SO.8 45209.3
I
45303.3 43.9
41.3
81.4 45210.0 42.0
.?a. Rotational constants for the upper state. If the approximation combination differences A,F’(N) are simplified to AzF((N)
= Ri(l\‘) - I’i(L$r) = 4B,‘(N
above is made, the
+ 3) - 8D,‘(N f
$)”
or A~F((N)/(M
+ 3) = 4&’ - SD,‘(!V + 3)‘.
(6)
If no perturbations are present in the upper state, the AzF’(N) values for both groups are equal for a given N. No discrepancies were found between the two groups, as shown
OGAWA
62 Table
II.
AND OGAWA
A2F values of the V=CIlevel of the c 4Z; state (cm-').
_____ TN
A2Fl'A2F4
'ZF2'*ZF3
1
9.1
3
22.1
21.7
5
34.2
34.2
7
47.0
46.9
9
59.1
59.3
11
71.8
71.8
13
84.0
84.2
15
96.7
96.6
17
108.9
109.0
19
121.3
121.4
21
133.8
23
146.1
in Table II. The A,F’(N) values averaged over all bands (excluding the O-O band) were utilized according to equation (6) by graphical techniques described in Herzberg (8) to obtain the rotational constants Bo and Do. This calculation was done for each group (A2F2, A2F3) and (A2F1, A,F,) independently and the results are listed in Table IIIa. The values for the upper-state rotational constants were taken as the average of each group and are listed in the third column of Table IIIa. The value obtained in Le Blanc’s measurement is included for a comparison. 3b. Rotational constadsfor the lower state afad bad origins. The rotational constants B,” and D,” may be obtained by treating A,F”(N) in a similar manner as for the upper state; however, a more accurate method which also yields the band origins was used. From Eqs. (1) and (S), R&V)
-
F’(N + 1)
Pi(N)
-
F’(N -
VO- S(t’ -
E”) - [B,“N(N
+ 1) - D,“N2(N
+ 1)“]
1) (for i = 1 and
4),
(7a)
and R;(N)
-
F’(N + 1)
Pi(N)
-
F’(N - 1) I
= Y,,+ $(E’ - e”) - [B,“N(N
+ 1) - D,“N2(N
+ l)“]
(for i = 2 and
3),
(7b)
where F’(N)
= Bo’N(N + 1) - Do’N2(N + 1)“.
The F’(N) values were computed for each group using the Bo’ and Do’ values listed in Table IIIa. From the measured values of R;(N) and Pi(N), the left-hand sides of equa-
ROTATIONAL
Table
Table
IIIa.
IIIb.
Rotational
Rotatlnnal
ANALYSIS
constants
constants
OF Ot+ BANDS
for the c 4.; State
far
the b 4: 9 state
63
(cm-')
(CK')
B i
0”
1.27(#(5)
1.27626
(Nevin)
1.2539
1.2528
,.25iI4)
1.?54211
(P;evin)
1.2315
l.i306
1.23111)
1.23213
(Nevin)
l.LlOO
1.x90
l.'OG(5)
1.1863
l.lR60
l.l8E(Z)
1.1651
1.1647
l.I64iR)
1.15c
(Le clam!
1.1403
1.1405
1.14'(4)
1.135
(Le Blanc)
x
1.1111 (LE Blanc)
3"
d(F,,F3)
(x 16-61
5.91
(Nevin)
6 0
/.A
il 5
6.07
(Nevin)
5.7
5.3
5.3
6.28
(N&n)
c
u.0
I.4
c5.n
6.0
6.0
9.!)
9.9
9.5
7.1
4.0
6
..l
2
49248.7
49247.9
~ 49248.3
:
48155.0
48154.1
I :
4
47096.4
I
47095.6
48154.6 47096.0
47097.1
(Le Blanc)
46071.5
(Le Elanc)
45080.3
(Le Blanc)
64
OGAWA
Table
IV.
Be, CI~, we,
AND OGAWA
and WAX,
of the
b "Eg
state
(cm-')
_-. -.___---..~
0.0225
I I
+ 0.0005
tion (7a) and (7b) were calculated. These values were used graphically to determine B,“, D,“, and vo f $(E’ - E”). No apparent discrepancies were obtained in using the R and P branches so the average value of [Ri(N) - F’(N + 1) and Pi(N) - F’(N - l)] were used in the calculation. The rotational constants are listed in Table TIIb. The first two columns give the rotational constants obtained for each group, the third column the averages, and the last column measurements from other investigators. The values for vo + $(c’ - E”) for the Fz and FS group, and v. - $(E’ - d’) for the F1 and Fd group are listed in the first two columns of Table 111~. The average of these two values will give the band origins ~0 which are listed in column three, and the difference of these two values will give the difference in the spin-spin interaction separations between the upper and lower states, 3~’ - 3~“. The average value and the standard deviation were calculated to be 3~’ - 3~” = 0.88 * 0.13 cm-‘. This is to be compared with the average measured R,(N)
- RI(N) = P,(N)
separation
of the line splitting
- PI(N) = 0.87 cm-’
which was previously discussed. If Nevin’s value of t” is combined, then the upper-state separation 3~’ (= 1.32 cm-r) is nearly three times as large as the lower-state separation. In determining the constants B, and LY,for the b 4.2gMstate, previous investigators (Nevin and Le Blanc) had measured only three bands involving this state. In the present work, seven bands were utilized, and the values obtained are shown in Table IV along with comparisons from the other investigators. The vibrational constants W, and w,X, were obtained by using the wavenumbers of the band origins (excluding the measurement of WI band) and the values are listed in Table IV. Values obtained by Tanaka et al. were obtained using the band heads for nine bands of the progression. The present values for we and w,X, were used to calculate G”(v) and were added to the appropriate vo values to obtain V, + G’(0). These values were constant to within f 0.5 cm-l, and from these calculations the band origin voo was calculated to be voo
This is to be compared
=
51540.7 f. 0.5 cm-‘.
with the measured
value
~00 =
51542.3 cm-l. The discrepancy
ROTATIONAL
ANALYSIS
of this measured value may be attributed (O-O) band as previously described.
OF Oz+ BANDS
to the low intensity
65 and diffuseness
of the
RECEIVED: July- 8, 1974 REFERENCES I. J. J. HWFIELD, Plrys. Rw. 36, 789 (1930). 2. I-. TANAKA, A. S. JURSA, ANDF. J. LE BLANC,J. Chem. Phys. 24, 915 (1956). 3. F. J. LE BLANC, J. Chem. Phys. 38, 487 (1963). J. 5. 6. 7.
K. CODLINGANDR. P. MADDEN,J. Chem. Phys. 42, 3935 (1965). A. BUDO, 2. Phys. 105, 73 (1937). T. E. NEVIN, Phil. Trans. Roy. Sot. London Ser. A 237, 471 (1938). I. KWACS, “Rotational Structure in the Spectra of Diatomic Molecules,” p. 145, Elsevier, New York, 1969. ,S’. G. HERZBERG,“Spectra of Diatomic Molecules,” Van Nostrand, New York, 19.50.
OF MOLECULAR
SPECTROSCOPY
55, 56-65 (1975)
Rotational Analysis of the Hopfield Emission System of O,+ l H. S. OGAWA AND~M. OGAWA De#artment
of Physics, University of Soulhem Califorka, Los Angeles, Calqornia 90007
The spectrum of the Hopfield emission bands of OX+, c ?Z,--b B,; has been reinvestigated with improved resolution. Spin splitting of the rotational lines has been observed for the first time, and the difference between the upper- and lower-state splittings due to spin-spin interaction was observed to be 3e’ - 3~” = 0.87 cm-‘. A rotational analysis has been made for seven bands, four of which (CM, O-1, &2, and (r3) are new. The rotational constants for the upper state G 2,are Bo = 1.5615 cm-l and DO = 6.7 X 10e6 cm-‘. For the lower state b 8,-, the rotational constants B, and D, are obtained for ZJ= O-6 and the vibrational constants are ws = 1197.8 cm-* and wLxs = 17.3 cm-l. I. INTRODUCTION
A progression of bands in the far ultraviolet region produced in a condensed discharge with a mixture of oxygen and helium was first reported by Hopfield (I) and later extended by Tanaka, Jursa, and LeBlanc (2). The progression was originally thought to be due to emission in the neutral oxygen molecule; however, the transition could not be satisfactorily explained from the known states of Oz. Later, from a rotational analysis of three bands (&4, O-5, O-6), LeBlanc (3) identified the lower state to be the b 4Zo- of OS+which is the upper state of the first negative system of O,+, b 42oM-a 411,. Assuming an allowed transition, Le Blanc identified the Hopfield emission bands as due to the transition G4ZU- + b 42ge of OS+.Later, the upper state, c 4.ZU-, had been observed by Codling and Madden (4) as a convergence limit of two Rydberg absorption series of O2 in the wavelength region, 500-600 A. Le Blanc reported that the observed bands were slightly diffuse and appeared to be composed of a single P and a single R branch with no Q branch. The resolution was not sufficient to separate the spin components. Presented in this paper are the results extending Le Blanc’s observation by increasing the resolution to separate the spin components. II. EXPERIMENT A McPhearson 3-m vacuum spectrograph with a grating of 1920 lines/mm, and reciprocal dispersion of 1.7 A/ mm was used to record the spectra in the first order. A mixture of oxygen (1.2 Torr) and helium (15 Torr) was fed into a a-shaped, water cooled discharge tube. The discharge tube had an inside diameter of -1 cm and was -18 cm in 1This research Office-Durham
was supported in part by Grant No. DA-ARO-D-31-124-73-G41 of the Army Research and Contract No. N00014-67-A-0269-0014 of the Office of Naval Research. 56
Copyright
@
1975 by Academic
All rights of reproduction
Press, Inc.
in any form reserved.
ROTATIONAL
r
FIG.
lapping
ANALYSIS
OF 02’
BANDS
57
1.
Enlargement of two bands of the Hopfield Emission system of OP+. The (O-l) band has overP and R branches, and the (O-3) band has P and R branches completely separated.
length, and utilized aluminum electrodes. The mixture was excited by an a.c. condensed spark discharge to produce the Hopfield emission bands. The spectra were calibrated by a mercury and carbon comparison spectrum. Another r-shaped discharge tube with quartz windows was positioned behind the main discharge tube. This tube had an inside diameter of -6 mm and was - 11 cm in length and utilized copper electrodes. Helium was added with a drop of mercury and excited by a condensed spark discharge to produce the comparison spectrum. The spectra were photographed on Kodak SWR plates. III.
RESULTS
AND
DISCUSSION
1. Spectra The Hopfield system of O,+ is a v’ = 0 progression in the region between 1900-2400 A. All bands shade toward the shorter wavelength. The measured bands were CO, O-l, O-2, O-3, O-4, O-5, and (t6, with bands heads at 1940.4, 1985.3, 2030.8, 2076.9, 2123.6, 2171.2 and 2218.5 A respectively (vacuum wavelengths). The intensity of the (O-3) band is maximum, and the intensity diminishes on either side of the progression. The (OM) band had such a low intensity that mesaurements for this band are not accurate. The spectrum was relatively free of impurity bands except for the (O-6) band. An enlargement of two bands (O-1 and O-3) is shown in Fig. 1. At first sight, there appears to be a single P and a single R branch with no Q branch. The lines are diffuse and for some bands (especially O-1) the P and R branches overlap. On closer examination, however, each line of each branch is composed of two separate components, the components, on the shorter wavelength side having the larger intensity. The separation of the components appears to be nearly constant for all lines except near the band head where they become slightly larger. The average separation between the components (excluding the first three lines N = 1, 2, and 5) was found to be 0.87 cm-‘. Although there is a clear separation of each line, the components are still rather diffuse. This may be due to the blending of two lines for each component observed. All bands measured exhibit this splitting except the O-O band. For this band, the intensity is extremely weak and the lines are too diffuse to show a separation. As a final remark, it is unfortunate that the intensities of the satellite branches are too low to be observed, for they are essential in obtaining accurate values for the fine structure constants (spin splitting constants).
OGAWA
58
AND OGAWA
2. Theory Since the nuclear spin of 1602 is zero (I = 0), all antisymmetric leaving only the transitions between symmetric levels. The allowed fore between levels of even N in the upper state (c “&,-) and levels state (b “I?,). From the selection rules eighteen branches are allowed; however, compose ten among them. The eight remaining main branches are
K(N) =
vo +
levels are missing, transitions are thereof odd N in the lower the satellite branches given by
Fi’(N + 1) - Fi”(N) i = 1, 2, 3, 4.
Pi(N)
= vo + Fi’(N -
1) - F;‘(N)
I
0)
The subscript (i) is representative of the four values of J for a given N (for i = 14, J = N + s, N + 3, N - 3, and N - $, respectively). The band origin vo, is constant for a given vibrational level and the rotational term values Fi (N) are given by Fi(N)
= B,N(N+
1) - D,W(N+
The term fi(N) takes four values corresponding are given as follows by Budo (5) :
l)“+
f<(N).
to the four J values for a given N and
_fl = - 441 - l3/(2N
+ 3)1} + 3rN,
f:! = + &{I + [3/(2N
+ 3)]} + r(N
f3 = + %(I
- [3/(2N
-
l)]}
- r(N + 4),
&{l + [3/(2N
-
l)])
- 3r(N + 1).
f4 = -
(2)
- 3),
(3)
Each value of fi is composed of two terms, the first arising from the mutual interaction of the electron spins, and the second from the interaction of N and S. The fi versus N curves for the lower state (b “I?Z,-) are shown in Fig. 2 with e = 0.1487 cm-l and Y = - 0.00033 cm-r which were obtained by Nevin (6). Several facts should be noted from the curves which are characteristic of the b 4ZUstate. First, for N > 3 the energy level order in increasing wavenumber is f4, f~, f3, and f2. Second, the curves converge rapidly with increasing N into two groups which are separated by approximately 3~ and are nearly independent of N. The levels fi and fz form the upper group and the levels jr and ja form the lower group. These two groups
FIG. 2. Spin splitting of rotational levels of the b 2,given by Budo and constants given by Nevin.
state, calculated according to the equations
ROTATIONAT,
ANALYSIS
59
OF Oz+ BANDS
appear to be nearly symmetrical about the horizontal axis. The value of Y is three orders due to the spin-rotation of magnitude smaller than E and, as such, the contribution interaction is negligible even for large !li. 3. Koluliurd
.~mlysi.s
From the above discussion, the four observed branches are most likely the blended ones of the expected eight main branches. Thus the P, and Pa branches were assumed to form one blended branch (P2, P,), and the K, and Ka branches form another branch. Similarly- the Pi and 1’4 branches form one blended branch, and RI and Rd form the other one. On the basis of line strengths given in Kovacs (7), it was determined that the branches of highest intensity were (P2, 1’3) and (R2, R3). -4s mentioned in Section 1, the short wavelength components of both I’ and K branches are stronger than the others. Therefore, they are considered as (P2 + P3) and (R, + Rx), respectively. Wavenumbers (expressed in vat. cm-‘) of all measured lines and their identifications are listed in Table I. No splitting of the components was observed for the (OH)) band and the wavenumbers listed for this band are an average over the four components. Since the vibrational level, z’ = 0, of the upper state r4EU- is common to all bands, the combination differences A!$’ (.V) were obtained for all bands and compared. They agree within the experimental errors and their average values (escluding the O-0 band) were calculated and are listed in Table II. According to equations (l), (2), and (3) the second combination differences are A$:
= Rl(;Y) - PI(N)
= (4Bn - 60,) (iv + 3) - SD,(,V + +)” - [18~/(2.\-
A.$‘,’
= R,(il’)
-
I’,(;\:)
=
(4H, - 60,)(V
+ 1)(2N + 5)1+
6r,
+ 3)
- 8D,, (IV + f)” - [l&,/(2.\’
+ 1) (21’ + 3)] + 2Y, (4)
A&,’ = &(;V) - Pz(fV) = (4& - 60,) (-V + ;) - 8D,(N + 3)” + [18t,“(LV + 1)(2N - 3)] - 2Y, AZF,’ = R,(iT’) - Pd(YV) = (4h’v - 60,) (1Vf
3)
-_8D,(,V + $)3 + [(1&,‘(2V
+ 1)(2.V - 3)] - 6~.
The experimental errors in the observed A2F’ values are the same order or larger than the magnitude of the terms which include the fine structure constants 6 and y. Consequently the fine structure constants cannot be obtained without knowledge of the satellite branches or without higher-precision measurements. Nevertheless, the rotational constants R, and D, for both the upper and lower states and the values for the band origins may still be computed with very good accuracy. The essential feature in these calculations is the approximation that the separation between group (Fz, FJ and group (Fl, F4) is constant and independent of LVfor both the upper and lower states. For the upper state this separation is 3~’ and for the lower state it is 3~“. Under this approsimation
OGAWA
60
AND
OGAWA
The approximation is valid and is within experimental N = 0 because only one level, PI(O), exists.
Table I.
Wavenumbers
of the rotational
errors for N > 1, but is not for
lines of (O-O), (O-i), (O-Z),
(O-3), (O-4), (O-5), and (O-6) bands
-
T
N -
(o-o)**
(0-l)
P, ,P2,P3’P4
R, >R2,R3,R4
I
Rl'R4
Pl'P4
R2'R3
Pz,P3
50383.2
50375.2
50384.0
*
1
51548.6
3
58.0
36.7
93.1
71.1
93.8
50372.0
5
69.4
35.4
50405.0
71.1
50405.9
71.6
7
83.3
36.6
19.0
72.0
20.2
73.1
51539.6
99.4
39.6
35.6
76.5
36.5
77.3
11
51617.5
45.6
54.8
83.2
55.9
84.0
13
38.0
53.7
76.6
92.5
77.5
93.1
15
60.9
63.8
50500.7
50404.5
50501.5
50405.0
17
85.9
76.0
26.9
18.2
28.0
19.0
19
51713.0
90.8
34.9
56.9
35.6
88.8
54.8
9
21 23
,-
51608.7
(O-2)
N
Rl'R4
Pl'P4
1
49255.0
49245.4
49256.2
3
64.6
42.0
65.4
5
76.6
42.0
R2'R3
'2"3
49243.0
77.4
43.0
Rl'R4
Pl'P4
48161.0
48152.1
48162.1
70.8
48.9
71.7
48150.0
83.4
48.9
84.2
50.0
7
91.6
44.7
92.3
45.4
98.8
51.7
99.7
52.9
9
49308.8
49.5
49309.6
50.2
48216.9
57.7
48217.7
58.6
11
29.0
57.1
29.7
57.9
38.0
66.3
38.8
67.2 78.4
13
51.6
67.4
52.4
68.2
61.9
78.0
62.6
15
77.1
80.2
77.9
81.0
88.3
91.8
89.2
92.7
17
49405.2
95.9
49405.8
96.6
48318.0
48208.9
48318.8
48209.6
49314.1
35.9
49314.9
50.3
29.0
51.0
29.7
69.4
35.7
19 21
59.1
23
-
* **
1
No line exists for R4 (l), P2 (1). P3 (1), p4 (1) No component
splitting
observed
(average of four components
were measured)
86.0
52.7
48424.2
78.2
ROTATIONAL ANALYSIS OF Oz+ 13ANDS Table I (Continued) (O-5)
1
3 5
pl'p4
47094.5
47104.1
46078.4
46068.4
46079.j
90.7
13.3
47092.0
89.0
66.7
89.9
: 46068.4
I
24.4
90.7
26.1
92.0
46101.2
66.7
46102.4
68.4
~
94.5
42.2
72.4
~
:
7
41.4
18.1
71.2
19.1
rl
60.4
47101.6
61.3
47102.2
37.5
78.4
39.0
11
82.3
10.8
83.4
11.6
60.8
89.0
61.R
13
47207.1
23.5
47202.3
24.4
87.1
46102.4
15
35.7
39.0
36.1
39.n
46216.2
19.1
17 19
1'2.1';
R2.1~3
11.6
47103. I
3
Rl'R4
66.3 473OO.LI
95.5
57.6
67.1
78.8
47301.1
79.9
3?..3
47204.4
77.5
31.9
21
-)
23
53.3
I
~
-
79.3
~
89.9
/
87.8
46103.4
(
~ 46217.3
20.4
1
49.8
40.4
:
85.7
64.1
~
; 46324.3
90.5
;
46219.9
:
~
39.0 j
i
66.6
(O-6) N
Rl'R4
Pl'P4
R23R3
1
45086.4
45077.4
45087.5
3
98.0
75.1
98.8
45076.8
5
45110.9
76.8
45111.8
77.5 82.3
7
28.4
81.3
29.2
9
48.8
89.8
49.5
90.5
11
72.7
45100.5
73.6
45101.7
13
45200.2
15.6
45200.9
16.7
15
30.6
34.1
31.4
'35.0
17
64.5
55.9
65.3
56.7
19
45302.4
21
43.1
23
SO.8 45209.3
I
45303.3 43.9
41.3
81.4 45210.0 42.0
.?a. Rotational constants for the upper state. If the approximation combination differences A,F’(N) are simplified to AzF((N)
= Ri(l\‘) - I’i(L$r) = 4B,‘(N
above is made, the
+ 3) - 8D,‘(N f
$)”
or A~F((N)/(M
+ 3) = 4&’ - SD,‘(!V + 3)‘.
(6)
If no perturbations are present in the upper state, the AzF’(N) values for both groups are equal for a given N. No discrepancies were found between the two groups, as shown
OGAWA
62 Table
II.
AND OGAWA
A2F values of the V=CIlevel of the c 4Z; state (cm-').
_____ TN
A2Fl'A2F4
'ZF2'*ZF3
1
9.1
3
22.1
21.7
5
34.2
34.2
7
47.0
46.9
9
59.1
59.3
11
71.8
71.8
13
84.0
84.2
15
96.7
96.6
17
108.9
109.0
19
121.3
121.4
21
133.8
23
146.1
in Table II. The A,F’(N) values averaged over all bands (excluding the O-O band) were utilized according to equation (6) by graphical techniques described in Herzberg (8) to obtain the rotational constants Bo and Do. This calculation was done for each group (A2F2, A2F3) and (A2F1, A,F,) independently and the results are listed in Table IIIa. The values for the upper-state rotational constants were taken as the average of each group and are listed in the third column of Table IIIa. The value obtained in Le Blanc’s measurement is included for a comparison. 3b. Rotational constadsfor the lower state afad bad origins. The rotational constants B,” and D,” may be obtained by treating A,F”(N) in a similar manner as for the upper state; however, a more accurate method which also yields the band origins was used. From Eqs. (1) and (S), R&V)
-
F’(N + 1)
Pi(N)
-
F’(N -
VO- S(t’ -
E”) - [B,“N(N
+ 1) - D,“N2(N
+ 1)“]
1) (for i = 1 and
4),
(7a)
and R;(N)
-
F’(N + 1)
Pi(N)
-
F’(N - 1) I
= Y,,+ $(E’ - e”) - [B,“N(N
+ 1) - D,“N2(N
+ l)“]
(for i = 2 and
3),
(7b)
where F’(N)
= Bo’N(N + 1) - Do’N2(N + 1)“.
The F’(N) values were computed for each group using the Bo’ and Do’ values listed in Table IIIa. From the measured values of R;(N) and Pi(N), the left-hand sides of equa-
ROTATIONAL
Table
Table
IIIa.
IIIb.
Rotational
Rotatlnnal
ANALYSIS
constants
constants
OF Ot+ BANDS
for the c 4.; State
far
the b 4: 9 state
63
(cm-')
(CK')
B i
0”
1.27(#(5)
1.27626
(Nevin)
1.2539
1.2528
,.25iI4)
1.?54211
(P;evin)
1.2315
l.i306
1.23111)
1.23213
(Nevin)
l.LlOO
1.x90
l.'OG(5)
1.1863
l.lR60
l.l8E(Z)
1.1651
1.1647
l.I64iR)
1.15c
(Le clam!
1.1403
1.1405
1.14'(4)
1.135
(Le Blanc)
x
1.1111 (LE Blanc)
3"
d(F,,F3)
(x 16-61
5.91
(Nevin)
6 0
/.A
il 5
6.07
(Nevin)
5.7
5.3
5.3
6.28
(N&n)
c
u.0
I.4
c5.n
6.0
6.0
9.!)
9.9
9.5
7.1
4.0
6
..l
2
49248.7
49247.9
~ 49248.3
:
48155.0
48154.1
I :
4
47096.4
I
47095.6
48154.6 47096.0
47097.1
(Le Blanc)
46071.5
(Le Elanc)
45080.3
(Le Blanc)
64
OGAWA
Table
IV.
Be, CI~, we,
AND OGAWA
and WAX,
of the
b "Eg
state
(cm-')
_-. -.___---..~
0.0225
I I
+ 0.0005
tion (7a) and (7b) were calculated. These values were used graphically to determine B,“, D,“, and vo f $(E’ - E”). No apparent discrepancies were obtained in using the R and P branches so the average value of [Ri(N) - F’(N + 1) and Pi(N) - F’(N - l)] were used in the calculation. The rotational constants are listed in Table TIIb. The first two columns give the rotational constants obtained for each group, the third column the averages, and the last column measurements from other investigators. The values for vo + $(c’ - E”) for the Fz and FS group, and v. - $(E’ - d’) for the F1 and Fd group are listed in the first two columns of Table 111~. The average of these two values will give the band origins ~0 which are listed in column three, and the difference of these two values will give the difference in the spin-spin interaction separations between the upper and lower states, 3~’ - 3~“. The average value and the standard deviation were calculated to be 3~’ - 3~” = 0.88 * 0.13 cm-‘. This is to be compared with the average measured R,(N)
- RI(N) = P,(N)
separation
of the line splitting
- PI(N) = 0.87 cm-’
which was previously discussed. If Nevin’s value of t” is combined, then the upper-state separation 3~’ (= 1.32 cm-r) is nearly three times as large as the lower-state separation. In determining the constants B, and LY,for the b 4.2gMstate, previous investigators (Nevin and Le Blanc) had measured only three bands involving this state. In the present work, seven bands were utilized, and the values obtained are shown in Table IV along with comparisons from the other investigators. The vibrational constants W, and w,X, were obtained by using the wavenumbers of the band origins (excluding the measurement of WI band) and the values are listed in Table IV. Values obtained by Tanaka et al. were obtained using the band heads for nine bands of the progression. The present values for we and w,X, were used to calculate G”(v) and were added to the appropriate vo values to obtain V, + G’(0). These values were constant to within f 0.5 cm-l, and from these calculations the band origin voo was calculated to be voo
This is to be compared
=
51540.7 f. 0.5 cm-‘.
with the measured
value
~00 =
51542.3 cm-l. The discrepancy
ROTATIONAL
ANALYSIS
of this measured value may be attributed (O-O) band as previously described.
OF Oz+ BANDS
to the low intensity
65 and diffuseness
of the
RECEIVED: July- 8, 1974 REFERENCES I. J. J. HWFIELD, Plrys. Rw. 36, 789 (1930). 2. I-. TANAKA, A. S. JURSA, ANDF. J. LE BLANC,J. Chem. Phys. 24, 915 (1956). 3. F. J. LE BLANC, J. Chem. Phys. 38, 487 (1963). J. 5. 6. 7.
K. CODLINGANDR. P. MADDEN,J. Chem. Phys. 42, 3935 (1965). A. BUDO, 2. Phys. 105, 73 (1937). T. E. NEVIN, Phil. Trans. Roy. Sot. London Ser. A 237, 471 (1938). I. KWACS, “Rotational Structure in the Spectra of Diatomic Molecules,” p. 145, Elsevier, New York, 1969. ,S’. G. HERZBERG,“Spectra of Diatomic Molecules,” Van Nostrand, New York, 19.50.