JOURNAL
The
OF MOLECULAR
SPECTROSCOPY
Absorption
Poti VI. Rotational
Spectra
(1965)
l&265-307
of the Molecules
Hz,
HD,
and D2
Analysis of the B’, B”, D, D’, and D” States
A. MONFILS
Institut
d’Astrophysique,
Cointe-Sclessin,
Belgium
The rotational levels belonging to the B’, B”, D D’ D” states have been
computed from the absorption spectra of Hz , HD’, aid Dz. The rotational
analysis has been worked out for these states as well as for the higher vibrational levels of the B and C states. B, , D, , and H, constants have been computed by least square analysis. From these data, we have determined
the
equilibrium constants B, and D, aa well as the coupling constants (Y, , 0.) ye,
& and e, . The interatomic distances at equilibrium rb have been computed and
an average value for the three molecules has been given for each substate. The
evolution of ?, with the principal quantum number n is shown.
I. INTRODUCTION
The increasing importance
of a precise knowledge of the spectra of the hydrogen molecule results from two different developments.
The possibility,
brought
about by space research techniques, of recording far ultraviolet
spectra of celestial
objects has made possible the detection of the molecular hydrogen by means of
its absorption
spectrum;
this problem has been taken up by several authors
(1, 2). From a completely
different point of view, the progress made by theoreticians in obtaining
truly synthetic molecular constants with the help of electronic computing machines has allowed them, in the case of molecular hydrogen,
to obtain results that are more precise than many available experimental
data
(3). This has created a need for new spectra recorded at higher dispersion and
measured with high precision.
This paper is the sixth of a series (4), the first five of which have been devoted
to the perturbation
between the B and C states (I), the vibrational
analysis of
new states (II, IlI), the study of the isotopic effect in the B-C perturbations
(IV), and in the A-type doubling of the C states (V).
Experimental
details about the spectra have been published
in a paper by
Herzberg and Monfils (5). We will only mention here that the spectra have been
recorded in the sixth order of a 3-m focal distance concave grating vacuum
spectrograph.
The continuum
used was generated
by a helium source, and the
useful spectral region was isolated by means of a fore-grating
(6). The mono265
266
MONFILS
deuterated hydrogen (HD) was prepared in a high state of purity by a chemical
method using lithium aluminium hydride (LiilH,) (7’). No absorption lines of
Hz or Dz have been detected in the spectra of HD.
II. ROTATIONAL
LEVELS
The levels of the BlZ,,+ and PII, states have been published in papers I and IV.
We have collected in Table II the rotational levels observed for the (3p)B’,
(4p)B”, (3p)D, (4p)D’, and (5p)D” states of the hydrogen molecule. Tables III
and IV give similar results for the HD and Dz molecules. The rotational
constants of the ground states have been taken from Stoicheff’s results (8) ; the
corresponding F” values are given in Table I.
It is well known that the B and C states are severely perturbed. In the case
of the other states no such large mutual perturbations have been observed.
However, the study of the rotational structures of the bands belonging to the
B’, B”, D’, and D” states indicates the presence of other perturbations. Unfortunately, the interactions have not been resolved, except in the following
Molecule Hz : B’ state; v = 4 vibrational level with B” state; v = 0 vibrational
level. The perturbation constant has been found to be LY= 5.3
cm-‘.
Molecule HD : D state; v = 5 vibrational level with D’ state; v = 2 level.
a! = 2.1 cm-l.
Molecule Dz : D state; v = 5 level with D” state; v = 0 level. (Y- 1 cm-l.
Whenever a perturbation has been analyzed, a deperturbation of the displaced
levels has been made before proceeding to the computation of the rotational
constants.
TABLE I
F”
VALUE3
(cm-l)
J
HZ
HD
DZ
1
2
3
4
5
6
7
8
9
118.50
354.39
705.54
1168.80
1740.19
2414.97
3187.90
4053.42
89.23
267.08
532.32
883.16
1317.30
1831.95
2423.98
3089.92
3826.19
59.78
179.06
357.30
593.70
887.21
1236.50
1640.06
2096.11
2602.72
267
SBSORF’TION SPECTRA OF HP, HD, AND Dz
Table
Rotational
(3~)
110
1(-)
529.74
2(t)
629.96
112
111
b(t)
7(-)
115
074.48
117.4q
645.75
203.
727. 59
632. 92
332. 3b
97
l(-)
117
848.37
116
016.15
501. 28
712. O6
202. o4
521. 9.
313. 26
963.56
432.
853. 53
624.
2E~0.6~
685. 98
v-4
116
604.42
9
495. 44
l2
115
973.26
J
2(t)
114
357.95
043.24
113
228.67
8(t)
0(t)
v=3
v=2
1
816. 2.
980. l4
4(t)
(cn?)
403.7
781.56
3(-)
5(-J
state
y=
477. B7
II
of the H2 molecule
B&:
v=o
J
0(+)
levels
v=
907.03
117
v=6
5
861.47
943. o5
883.27
000.
lg
931. b3
57
3(-J
096.
a+)
225.51
5( -)
382.5
b(t)
9
571.51
7(-)
780.1,
118
002.
b7
089. 86
199.24
328.9,
118
336.22
350.
99
92
MONFILS
268
Table
(4P)
0(+t
1(-l
2(t)
116
885.33
118
038.5
3(-)
5
190. b8
4(+)
392.52
(cm-l)
1
v-
944.03
119
093.32
v=3
v=2
120
993. 85
931.55
117
state
&:
v=o
J
II-Continued
121
122
868.38
655. 9.
917. 43
703. a5
014.44
798.29
241. 45
156. 45
438. 75
349. 31
938. 45
123
125.58
5(-)
645. l9
682. 47
587. O8
360. 77
6(+)
943. 6.
972. 22
865.75
625. l5
190.40
931. 3.
7(-)
118
55
120
124
307.06
312.16
122
v=6
v=5
v=4
J
0(t)
278.
125
828. lo
127
201.80
I(-)
353. 65
867. O8
246. Oq
2(+)
452. 84
971. o.
320.
I1
581. 48
437.
72
4(t)
745. 3.
582. 3.
5(-)
949. 77
752.82
3( -)
ABSORPTION
SPECTRA OF Hz, HD, AND
269
D2
Table II-Continued
(3~)
v=o
J
I(-)
(+I
2(t)
C-1
112
935.07
DITu
1
v:
115
state (cm-‘)
153. l4
v=2
117
250.77
v=3
119
217.94
215.0
930. 87
151.86
246.87
058.83
269. 86
363. 62
9
322. 2l
048. 54
265. 47
353. 21
313.9
243. 22
437. 88
526. l7
9
471. 64
224. Ol
431. 58
510.62
462. 8l
4(t)
484. 66
656. 8.
735. 56
(-)
455. 34
650. 73
718. O7
5(-)
783. 32
922. 47
989.6,
741. 71
921.37
976.26
113
3(-)
(+)
(+)
6(+)
114
130.10
(-)
080. O1
7(-)
525. 43
(+)
469. 33
8(+)
972. 56
v=4
J
121
062.13
222.12
118
893. l6
289.93
276. 97
243. 5.
120
176.61
629. 61
621.4)
609.77
117
(-)
I(-)
116
658. 63
028.12
v=6
v=5
122
787.82
124
392. 53
v=7
125
883.99
(+)
064. b8
784. 6.
390. 51
875. 76
2(+)
161. 65
880. O7
474. 46
945. I2
(-)
156. 47
873. 48
473, 7.
954. 95
3(-)
308. 64
010.29
594.9*
123
(+)
294. 54
005. 35
597. 26
4(+)
496. 42
183. 44
746.45
(-)
478. O8
178. 7.
760. l4
6(+)
(-)
06a.80
221.52
943. o2
5(-)
(+)
126
402. 7a
957. lo
708. 99
125
156.57
188. 62
616. 84
457. 24
860.64
7(-)
(+)
a(+)
(-)
756. 92
127
141.07
2i0
MONFILS
Table
(3~)
J
l(-)
I
v=a
1
127 248.00
II-Continued
DIVu
state (cm-‘)
v= 9
I
128
495.07
495. a7
320. l1
v= 10
I
620.7,
]
d
v=
130
11
618.27
627.37
618. 79
559. 51
681. 46
668. 27
318.05
560.6*
680. 99
672. 36
3(-J
420. 5.
648. a6
765. 26
738. 3.
(+I
424. 92
747. a7
(+I
2(t)
(-)
248. fj9
1.29
4(t)
566. O4
t-1
657. 28
773. o4
75%. I*
872. 44
776. O4
878. 68
852. 63
894. 54
5(-l
731. 47
(+I
J
1(-J
(+I
2(t)
C-1
3(-)
(+)
4(+)
v=
131
12
982. 4.
v=
483.73
132
13
211.70
v=
132
14
792.47
481.26
210. 96
791. 73
529. E5
255. 66
820. l5
528. 96
252. 34
824.4,
592. l3
313.ag
600. 35
317.27
871.27
406. 54
933. o*
673.
lo
(-)
696. O8
5( -)
769. a0
(+)
800. 27
504. 48
ABSORPTION
271
SPECTRA OF Hi, HD, AND Dz
Table II-Continued
(4~)
v=o
J
1(-J
(t)
2(t)
C-J
117
118
3(-)
(+)
4(f)
(-)
897.60
119
(-)
7(-)
203.31
272. a2
217. 37
207. 73
381. 62
425. 7.
326.73
5
009. 77
94
182. 93
368. 27
429. 24
365. 21
454.9a
604. 3.
623. 97
495. 65
413. 64
589. 7q
634, l3
560. 2.
878. 26
871.91
125.42
195.56
179.57
543. 34
552. 41
9(-)
555.48
v=4
I(-)
125
942. 5a
126
037. 92
2(+)
3(-)
179. 77
4(t)
365. 63
5(-)
599. 36
6(+)
868. o2
7(-)
176.44
704.11
797. a5
857. 44
121
032. 24
867.61
127
111.86
117. l4
120
(+)
124
198. l9
(-)
(-)
167.62
271.81
022.78
(+)
122
211.
119
(-)
094.6~
022.5
120
(+)
v:3
v=2
1
167. 62
8(t)
J
(cm-‘)
092. 92
423. 9,
(+)
(-)
120
state
892.8a
694. 69
(+)
(+)
v=
761. 25
5(-)
6(+)
D”TT,
123
946. 49
158.39
125
081.07
477. 46
407.21
777. I2
-4
MONFILS
272
Table II-Continued
(5~)
J
I(-)
(+I
2(+)
D”
v=o
120
240.6,
1
v-
122
jl-
u
state
1
426.
-I
)
v=2
433.37
230. 4.
(cm
124
51
494.31
500.0,
611.2
359.72
553.3
C-J
3(-1
346.51
536.43
538. 62
736. 68
(+I
4(+)
519. 92
699.
777.20
964. l9
125
912. 54
124
970.E~~
246.E5
125
309.
(-)
SC-)
(+)
6(t)
7 54.45
121
068.81
123
9
606.
9
5q
I8
019.44
l4
223, 82
571. 96
644. a7
ABSORPTION
SPECTRA OF Hz, HI), AND L)z
Table
Rotational
(3~)
v=o
J
0(+)
110
630.70
levels
III
of the HD molecule
B”Z:
v=
112
273
state
(crr~-~)
v=3
v=2
1
281.03
113
807.16
115
203.48
1(-)
670. 37
315.88
841.9,
236. O4
2(t)
741. 89
386. 87
908. 92
302. 37
010.3
401. 86
114
3( -)
849. lo
495. 78
4(+)
993.71
637.02
9
144. 54
813. O6
311. ?3
683. 78
024. l2
508. 53
872.
265. 63
739. 45
5( -)
111
175.88
6(+)
394. 84
7(-)
655. 57
113
8(+)
538. 65
9(-)
844. 56
v=4
J
0(+)
116
445.97
Y=
117
5
491.
lo
l(-)
472. 26
2(+)
527. Z9
563. 33
3(-)
609. 49
634. 96
4(t)
717. 93
732. 77
5( -)
854. O3
850. 66
6(t)
117
515. 94
015.95
7(-)
199. bq
8(+)
405. 64
989. O9
118
151.28
115
001.6~
291. l4
524. 78
116
l5
093.33
MONFILS
274
Table III-Continued
(4~)
v=o
J
0(t)
117
118
v=3
v-2
1
v:
028.28
state (cm-‘)
B”‘r:
830.99
120
532.76
122
136.S6
168. 35
570.04
1(-J
066. 36
868. l2
2(t)
145. 64
945. 72
644.55
242.
059.So
755. 71
351. o4
903.94
497.
089.92
681. 48
119
3(-)
264. S8
4(+)
417. O6
210. 33
5(-)
606.89
397.28
6(+)
834. 7.
7(-)
118
0(+)
123
305.82
551. o7
099.22
v=
v-4
s
629.25
125
5
050.42
077.37
l(-)
666.27
2(+)
732. 72
136.70
830.
228.
3(-)
4(+)
5(-)
124
121
l6
l7
954.51
343. 78
105.S1
487.15
6(+)
283. S8
7(-)
486. 9q
59
92
899. 36
123
147.S7
275
ABSORPTION SPECTRA OF Hz, HI), AND 112
Table III-Continued
(3~)
J
I(-)
D’rr,,
v=l
v=O
113
066.76
(+)
2(t)
(-1
state
115
004.53
(cm-l)
v=3
v=2
116
846.92
118
598.14
063. 24
000.54
846. 59
595.57
155. o5
094.08
934. 53
678.07
151. 69
089.17
928.38
672. 3.
294. l9
224. 35
060. l3
791.65
283. 7.
214. 44
049. la
787. 27
4(f)
474. 23
401. 62
222. 92
950. lo
(-)
459. 94
382. O2
208. 36
940. 69
3(-I
(+I
5(
-)
(+)
6(t)
(-)
7(-I
114
(+)
612. a3
422. 49
591. 26
406. 54
128. 95
962. l4
864. I4
660.98
363. 43
936. l3
832. 75
644.6,
348.07
931. .s7
621.77
909. 7.
602.95
212.25
890.31
l5
231.76
116
1l1.23
119
138.25
625. 2.
(-1
564.2
913.11
429. 66
9
v=5
v-4
J
1(-I
696. 26
678.31
271.
a(+)
117
120
(+I
2(t)
(-)
3(-I
(+I
254. 55
121
292.a4
v-7
124
677A.
817. 54
290. 4.
677.68
330. 54
888. o5
360. O6
741.0,
325. 9.
887. O7
357. o9
738. 72
443.48
995. 79
460. 9.
838. 5.
455.
831.5
127. 69
585. 59
954. a4
l4
591. o.
(-)
v=6
123
254.71
433.
4(t)
818.7o
118
568.61
122
990.78
123.57
76
606. o9
9
962. l6
766. 63
304. 26
761. 9.
(+)
749. bq
297.41
745.71
106.81
6(+)
977. 65
946. 35
288. a5
(-)
959. 56
498. a4
930.38
280. 97
5(-j
7(-I
121
(+I
199. o3
a(+-)
510. 36
(-1
124
224.13
727. O5
125
112. l3
167.59
146. 66
479. 65
386.34
698. 29
MONFILS
276
Table III-Continued
(3~)
v=8
J
I(-)
125
973.60
(+I
2(t)
126
034. 5.
972. 89
031. 22
t-1
124.6
3(-)
9
119.06
(+)
4(+)
239. 48
(-)
235. 96
372.9
5(-)
9
379. 93
(+)
536.05
6(t)
(-)
547. 87
7(-)
722. 63
736. 9q
(+)
935.
8(+)
(-)
9(-)
l1
954. O6
127
171.28
D1ru
state
(cm-‘)
ABSORPTION
277
SPECTRA OF Hz, HD, AND Dz
Table III-Continued
(4p)
J
1(-l
y=
v-o
118
119
032.60
(t)
027. 62
2(t)
121. a3
C-1
3(-)
(+)
4(t)
(-)
5(-)
(+)
D’lTIU
120
state
(cIr/)
v=3
v=2
1
952. 53
121
774.45
950. 33
511.42
038.73
861.
588.03
l6
116. 33
034. fa
858. a9
586. 42
167.61
986. a5
699. 57
246. a6
160. 3.
976. 72
695.90
149.a2
846.01
l3
122
431. 2.
335.
420.95
324. 71
135. 26
652. 7.
543.31
348. o.
635. 9a
531. a2
329. 99
558. 42
773. 76
(-)
121
030. 92
019. 73
229.
64
096.07
472. 72
(+)
125
2(t)
3(-)
(+)
126
146.65
128
705.03
166.17
151. a6
702.77
163. 21
225. O.
782.0,
229. 36
764. 4a
220. ba
329.71
881. 35
320. 92
319. 3a
858. 6.
308. o9
444. 64
1
223.2
(-)
Y=
Y’5
v=4
(+)
467.97
127
010.42
(-)
452. 3.
126
980.1
5(-)
638. 3a
127
174.Z6
592. I2
367. 33
766. 33
4(t)
1
616.57
(+)
837. 73
6(+)
803.
(-)
7(-)
840. 92
124
251. 62
798. 81
7(-)
I(-)
504.75
777. 65
254. O4
6(+)
J
123
126
5.
074.30
590. 63
MONFILS
278
Table
(5~)
I(-)
D” h,,
v=o
J
120
III-Continued
state
(cm-‘)
v=2
V=l
122
377.aa
2a9.49
124
104.17
363. O4
282. 2a
102. 26
2(t)
l-1
467. 4.
379.19
187. o4
451.42
365.
3(-j
601.19
514. 62
583. 2.
49s.
777.9l
684. 44
(+I
t+)
4(f)
5(-I
(+I
(-1
7(-j
(+I
303.61
302. 76
6a
755.2l
(-1
6(t)
184. o6
5.
121
469.
6.
464.
53
995. 25
905.45
672.67
977. 65
a91.20
669. a7
164.53
920. a6
123
256.a9
233. 45
559. a5
543.3
9
477.
ll
125
209.4a
279
ABSORPTION SPECTRA OF Hz, HD, AND Dz
Table
Rotational
(3~)
J
0(+)
v=o
110
IV
of the D2 molecule
state
B’lZ’,
112
(cm-‘)
v=3
v=2
1
v-
815.00
113
180.10
466.12
114
668.03
I(-)
840.06
204. 48
490. 33
690.
2(+)
894.26
254. 49
537. 57
732. 55
3(-)
4(+)
111
972. 59
329.2
076.3
427.2
5(-)
9
204. 42
6(+)
7(-)
J
0(+)
lo
816.27
696. 58
954.21
538. 5.
865. 72
272.
054.4
441.73
o1
779. 93
113
116
991.71
115
9
v=
v=5
783. O8
117
802. 42
799.29
l(-)
798.
884.34
358. 77
v=4
115
608. 37
700. 88
9
0
J2
550.21
‘740.
8(+)
661.06
7
98
v=7
6
674. 86
119.0
118
355.7
9
369.01
2(t)
839.83
840. 78
707. 58
396. 77
3(-1
901. 7.
898. 78
754. 89
437. 37
4(+)
983.52
975.
821.14
489.44
901.5)
557.13
995. 78
634. 74
5(-)
--
levels
116
083.72
116
l2
070.04
6(+)
205.85
183. 53
7(-)
345.85
314. b8
8(t)
499.71
118
107.85
MONFILS
280
Table
B+:
(4~)
Bh;
state
(cI-I?)
v=8
J
118
0(t)
820.46
I(-)
831.17
2(t)
850.08
3(-)
872. 34
902. 3l
4(f)
940. 7.
)
5(-
(3~)
IV-Continued
980. o.
6(t)
119
7(-)
J
0(t)
1(-J
2(t)
024.22
118
196.4,
120
686.a5
487. 38
538. 45
845.21
266. 9.
616. 63
949. o.
369.3
3(-)
356. 92
4(+)
465. 45
5( -)
598. lo
6(+)
759. a4
5
9
080.30
9
498. a3
235.6,
652. LT2
833.27
7(-)
0(+)
1(-J
2(t)
122
755.
v=5
l2
123
978. 56
124
031.2,
778. 23
822. 4l
990. 21
3( -)
894. o2
084. 79
4(+)
983. l4
150.47
5(-)
123
090.05
464.47
188. l5
276. a1
v=4
121
764.78
712.
J
110.28
v=3
137. 5.
222.46
119
(cm-l)
v=2
v=l
v=o
117
state
ABSORPTION
281
SPECTRA OF H2, HD, AND Dz
Table IV-Continued
(3~)
J
I(-)
(+I
2(t)
t-1
v:o
113
state (cm-‘)
D1ru
v=
114
223.67
v=3
v=2
1
823. l2
116
117
357.33
828.54
822. 3.
356.31
829. 37
282. B4
883. 26
415. 6.
886. 3.
280. 81
879. a3
412. 92
882. 34
371. E.
972. 75
498. 36
966. B.
371. o9
965. 55
495. o5
091.26
609. 94
489. 3.
078. 7,3
604. 45
066. 55
639. 67
233. O.
746.71
208.91
632. 53
220.08
738. 63
196. 24
6(t)
813. 23
397.88
910. 57
364.
(-)
807. 9*
387. 92
902. 69
347. I*
014.71
599. o2
096.34
(+)
012. 49
582. 4.
089.4l
543.8
9
525. 63
a(+)
240. 77
815. a6
305. a7
747.76
(-)
237. B7
801. 52
299. 99
729.
541. 39
977. 32
221. 53
3(-)
(+)
492.
4(+)
(-)
5(-)
(+)
7(-)
114
18
116
(+)
1(-)
117
495. o.
9(-)
J
115
v-4
119
236.99
239.
(+)
18
l9
l7
v=7
v=6
583.80
075.57
533. l7
044.25
v=5
120
958. 58
118
121
123
872.04
095.35
587. l7
870.
l3
091. 93
141. 29
2(+)
289. 7.
634. 27
918. 2.
(-)
289. 23
631. l1
914. 97
3(-)
368. 8q
709. 97
989.1
363. 22
704. 66
985. 57
207. 77
084.79
304. 23
(+)
4(+)
(-)
5(-)
122
473. 24
811.34
465.28
802. 56
080. a2
295. 95
600. 73
933. 75
197. l7
416. 63
923. 1,
195. a0
407.04
332.
537. 26
(+)
592. 19
6(+)
749. 77
(-)
741. o2
066. B.
920.01
248. a6
7(-)
(-)
121
081.67
l3
687.98
910. 52
(+)
a(+)
139. 89
210.81
1
120
119.33
105. 92
420.
854. 46
I8
9(-)
(+)
627. 92
124
040.2q
Table IV-Continued
(3~)
1(-l
(+)
v=9
v=8
J
124
2(t)
state
Dh,
125
261.46
(cmol)
v:
366.94
v=
10
126 414. 94
258.90
366.
58
413.
305. 38
410. 35
455.17
127
11
402.
O8
402. O8
63
438.
88
303.55
407. 91
453.
3(-J
370. 4.
472. 44
515.8
(+)
368. 53
466.
510.7,
458.
554. lo
594. 71
571.
549. 51
587. 5
565. O4
9
551. 86
651. 2.
685.9,
656. 59
682.53
764. 93
796.97
754.37
t-1
4(+)
93
453. 48
(-)
82
(+)
495. 86
9
491. 48
9
692. 72
565. 1
5(-J
36
57
6(+)
t-1
7(-1
(+)
820.
56
980.
53
921. 74
8(+)
(-)
127
069.
l6
227.
l3
9(-)
(+I
v=
J
1( -1
128
12
330.51
329.2
(+I
9
366. 38
2(+)
(-)
3(-I
(+)
v129
v=
13
130
196.28
v-
14
O03.18
130
15
744.24
196. 76
003. 22
746. 5.
231. 24
033. O8
771. 23
366. Oq
231. 65
034. 25
173.
420. 3.
280. 38
078. 3.
817.45
416.11
277.
081.26
816.
55
lo
92
347. 86
140. 78
875.61
(-1
481. 31
341.
98
140. 8.
873. 79
5(-I
581. 94
432.
I8
213. 66
937. o5
1
301. 38
492.
4(+)
64
946. 84
561. B7
(+)
6(+)
684, 75
527.1
(-)
657. 3.
506. O1
7(-)
(+I
799. 25
635. 27
770.
611.
9.
I8
8(+)
(-)
894. 2.
728. 87
031.16
857.8,
9(-1
(+)
129
282
406.
95
ABSORPTION
SPECTRA OF Hz, HD, AND Dz
Table IV-Continued
(4p)
118
(+)
state
“=
V=O
J
I(-)
D’fru
189.87
119
(cm-l)
v=2
1
775.83
121
294.71
190. l4
774. 22
2(+)
249.84
831.76
346.48
(-)
246.55
831.31
350.
3(-)
340.58
916. 58
424.44
335. 39
915. 73
432.08
030.04
528. 72
452.86
028. o9
540. 69
609. 99
169. 47
654.
(+)
4(t)
463.
(-)
5(-)
(+)
11
120
295.18
53
I9
597. 2.
168. 32
675. 24
6(+)
785. 77
334.18
805. 26
(-)
771. a6
333. 43
835.18
990.51
525. 96
976. 9.
7(-)
(+)
526. 67
122
012.30
a(+)
(-)
9(-)
747. s3
119
486.g9
(5p)
J
1(-)
(+)
v=
120
D”l$
0
state
v=
528.78
122
524.2
1
(cm-‘)
v=2
1o8.72
123
624.24
107. 7.
622. 76
167. 92
682. 56
2(+)
9
591. 96
(-)
585. 26
163. 32
677.98
3( -)
684. 23
258. O5
764.
672.1
247.
759. 5.
(+)
4(+)
(-)
5(-)
(+)
6(+)
9
51
811.33
378. 7.
788.
360.
l6
966. a2
9q
523. a0
7.
868. 2.
124
017.06
500. 74
697.56
(-)
7( -)
879.
53
901. 45
117. 97
283
MONFILS
284
Table
Rotational
constants
(Xp) B1zt
V
of the H2 molecule
state
(cm-l)
u
B
v
D
tv
Iv x lo5
lv
Hv x lo5
0
19.452
0.016
1.4
18
9.942
0.006
- 3.2
1
18.473
0.013
O.“<
19
9.595
0.000
-
1.2
o. 006
-
1.2
‘2
17.659
0.012
1.9
20
9.311
3
16.928
0.012
1.0
21
8.896
-0.002
- 7.6
4
16.261
0.010
1.2
22
8.558
-0.005
-19.8
5
15.648
0.009
1.0
23
8.170
-0.008
6
15.314
24
8.041
0.004
- 3.3
- 0.9
-18.5
7
14.702
25
7.781
0.003
8
14.118
0.000
26
7.556
0.014
0.3
0.038
27
7.151
0.008
- 0.7
9
14.210
10
13.372
0.013
28
6.998
0.022
8.6
11
11.858
-0.028
29
6.622
0.029
21.5
12
13.184
-0.020
30
6.326
0.019
3.6
13
11.946
0.014
31
14
11.077
-0.014
32
5.301
0.020
15
10.986
0.006
33
4.192
0.004
16
10.516
-0.001
-8.5
34
3.605
0.007
17
10.378
0.005
-5.7
35
2.725
-0.041
(3~)
v
i-
”
B+:
Bv
state
D
v
0
25.375
0.011
1
22.903
-0.002
21.574
0.010
20.623
0.019
15.917
-0.007
12.038
0.030
7.445
(cm-‘)
0.041
(4~)
Hv x 10’
B”‘z:
B
v
state
D
v
- 3.6
26.085
0.034
-13.7
24.896
0.010
- 0.2
24.258
0.011
- 7.1
23.798
0.018
-22.0
23.451
0.030
22.128
0.034
19.886
0.048
2.1
t
1.8
(cm”)
Table V-Continued
(2~)
Clm:
sub-state
(2~)
(cm-l)
C’lT;
sub-state
t
v
v
B
D
v
(cm-‘)
v
Hv x
lo5
0
31.135
0
30.543
0.020
18.3
1
29.548
1
28.954
0.019
10.0
2
28.181
2
27.436
0.020
3
25. 909
0.021
4
24. 576
0.025
0.030
0.023
-1.5
3
14.6
4
24.637
0.001
5
23.739
0.034
25.0
5
23.279
6
21.987
0.025
17.6
6
21.347
0.015
19.896
0.020
7.5
-
5.0
7
20.287
0.015
5.4
7
8
18.920
0.020
6.8
8
18.445
0.030
19.7
9
17.061
0.020
9.6
9
16.346
o. 016
11.0
10
14.894
0.004
10
14.657
0.015
10.1
11
12.560
0.007
11
12.708
0.028
16.3
26.0
21.1
-20.4
3. 1
12
9.858
0.008
12
9.244
0.041
13
7.700
0.007
13
6.775
0.042
(3~)
v
1 +
D r,
sub-state
B”
(cm
-1
)
(3~)
y--p2
0
31.184
0.027
1
29.502
0.012
2
28.199
0.058
v
-
D’r;
B
sub-state
(~III-~)
Hv x lo5
v
5.9
0
29.604
0.022
33.8
1
28.215
0.026
2
26.584
0.015
4.2
6.9
-
6.8
3
26.284
3
25.288
0.034
10.4
4
25.671
4
23.070
0.009
24. 5
5
23.440
5
22.467
6
20.766
7
18.628
8
18.200
9
15. 695
10
15.295
11
12.880
12
11.217
13
10.825
0.048
0.050
29.2
-
0.034
6
21.161
0.033
15.8
7
20.004
0.044
25.5
8
17.822
0.010
9
16.762
10
15.183
11
12.854
0.001
12
12.324
0.021
13
10.578
-0.010
14
7.074
14
6.890
15
2.716
15
4.280
285
5.8
MONFILS
286
Table V-Continued
(4~)
D’lJT:
sub-state
(cm-‘)
sub-state
(crr~-~)
(4~)
DIlT;
sub-state
(cI-II-~)
““‘TT;
sub-state
(cm
31.095
29.165
26.089
21.667
(5~)
D’llT:
L
v
(5~)
v
B
v
D
”
-1
)
Hv x IO5
0
30.178
0
30.226
-
-
1
31.370
1
28.186
-
2. 0
2
31.265
2
27.322
-
28. 1
ABSORPTION SPECTRA OF Hz, HD, AND D8
Table
Rotational
constants
(2~)
B
v
18
Y
Dv
13vx
B1z:
10
0.028
-
3.6
0.020
18. 1
23. 9
5.972
0.014
- 1.5
5.556
0.002
25.3
0.013
21
7.492
0.005
- 0.7
22
7,121
-0.022
-37.9
23
7. 160
0.007
-7.207
25
6.681
0.014
12.0
26
6.390
-0.001
- 4.7
B”z:
B
v
18.368
5.876
0.034
5. 530
0.033
35.6
4.940
0.005
-13.6
4.213
-0.010
8.3
4. 1
24
0.015
state (cm-‘)
(4~)
B”‘,E;
state (cm-l)
HIV x IO5
D”
0.017
28.2
16.8
17.818
0.000
- 6.7
-10.5
16.924
0.003
8.8
28.7
1
2
3
16.738
0.027
4
13.594
0.000
-10.6
5
12.014
.o. 001
-10.7
(2~)
v
6.210
7.969
l-
B
6.321
7.840
F
5
5.0
19
0
state (cm-l)
0.010
20
”
of the HD molecule
8.408
0.005
(3~)
VI
C’lr:
sub-state
D
”
4
v
-0.007
(cm-‘)
(2~)
Hv x lo5
C1r;
sub-state
Dv
(cm”)
Hv x lo5
-34.2
5
18.284
0.013
6
17.345
0.011
0.017
7. 1
7
16.413
0.011
6.9
0.010
4. 1
8
15.626
0.025
22.8
0.007
1.3
9
14.217
0.001
-10.1
0.019
18. 1
10
13.171
0.002
- 8.9
0.013
3.2
11
11.665
-0.010
-28. 5
0.014
0.9
8.4
0.016
14.6
288
MONFILS
Table
(3~)
D’r:
sub-state
B
v
(4~)
v
”
0.021
22.607
0.033
21.952
0.057
19; 621
0.011
19.728
0.048
(3~)
Hvx
10
5
D1r,
sub-state
Hv x 10’
v
14.5
-
45.4
20.310
0.3
19.570
-
0.007
17. 610
17.459
0.010
16.857
0.022
15.696
0.011
15.664
0.046
14.951
0.013
D
-1
(cm
)
(4~)
B
v
0.014
33.1
45. 6
sub-state
D”r;
v
22.184
D
Y
0.022
21.901
0.037
21.105
0.012
20.786
0.020
20.076
0.010
20.166
0.053
18.742
0.022
18.415
0.028
16.743
0.001
17.997
0.046
15. 892
15. 567
0.002
DTnliT:
B
sub-state
Y
Dv
(cm-‘)
(5~)
10
5
v
““‘IT;
B
v
0
22.865
0.021
-
0
22.144
1
22.618
0.022
-
1
22.310
2
19.645
-0.027
2
20.398
-24.2
6. 6
-
9.2
4.4
5.1
-
6.0
1. 5
(cm
-1
F-Iv x
)
IO5
24. 2
1. 8
-14.2
10.7
-25.
1
14.816
-27.3
Hvx
5.0
0.019
0.032
16.5
-
.o. 003
16. 558
sub-state
2.3
12.8
0.040
.I’,:
(cm-‘)
7
17.977
22.289
v
(cm-‘)
23.106
BY
(5~)
D
VI-Continued
sub-state
D
v
0.013
(cm-‘)
Hv x lo5
15.2
0.027
-
ABSORPTION
SPECTRA
Table
Rotational
B
v
21
v
5.975
D
v
BIZ;
Hv x lo5
0.020
22
5.745
0.015
23
24. 9
289
VII
constants
(2~)
OF Hz, HD, AND Dz
of the D2 molecule
state
(cm-l)
Hv x lo5
B
v
”
33
4.293
o. 006
8.2
34
4.088
0.001
0.4
5.354
0.001
35
4.151
0.010
24
5.493
0.016
40. 5
36
3.949
0.007
10.0
25
5.246
0.008
12.2
37
3.803
0.005
8.2
26
5.075
0.005
7.3
38
3.704
0.005
1.7
- 2.7
39
3.252
-0.005
- 2.3
-11.2
40
3.272
.O. 008
-15.2
- 0.8
41
3.298
0.011
27
4.907
0.001
28
4.688
-0.005
29
4.639
0. coo
30
4. 528
0.000
31
4.476
0,003
32
4.323
0.001
(3~)
B’lE:
- 0.6
- 2.6
42
3.196
2.3
43
2.671
1.7
44
-
state
(cm-‘)
D
I”
v
13.350
0.014
12.530
0.009
12.043
0.020
(4~)
x
lo5
11.4
Y
B”lZ:
B
9. 9
17.0
-
o. 006
-13.6
-0.013
state
(cm-l)
4”
v
5.0
x
lo5
0
13.399
-0.004
-
12.4
1
13.033
-0.009
-19.4
25. 6
2
13.033
0.007
10.692
-0.003
1.3
3
12.478
0.005
10.191
-0.006
7. 8
4
11.341
-0.007
9.675
0.004
0.9
5
7.706
-0.015
6.939
0.014
4.287
0.012
-25.6
18. 5
- 0.6
__A
9. 128
0.013
8.4
10.2
-
0.5
290
MONFILS
Table VII-Continued
(2P)
sub-state
cy
D
B
v
”
5
13.570
6
12.563
7
8
-1
(cm
)
H,x
v
10
(2P)
5
sub-state
A;
v
B
5
12.375
.o. 009
6
11.968
0.001
x lo5
I”
”
)
0.016
15.2
11.962
0.016
18.9
7
11.741
0.007
11.251
0.005
0.7
8
11.184
0.007
8.4
9
10.374
-0.001
1.2
10
9.980
0.005
1.9
3.8
11
9.473
0.004
0.5
9
10.796
0.009
10
10.016
0.003
11
9.681
0.009
12
9.134
13
8.108
14
7.725
15
7.089
16
5.878
-
-
0.006
0.002
1.8
4. 5
19.6
14
7.484
0.001
3.5
15
6.739
0.009
16
6.058
0.005
0.000
17
4. 956
-0.006
5.318
__-
0.040
18
3.346
-0.013
-1
(cm
4.5
0.007
5.195
sub-state
1.8
-
8.229
18
D’T:
3.0
8.755
-20.2
-0.007
1.6
12
-10.5
0.012
-
13
12.2
0.014
-0.006
17
(3~)
-1
(cm
)
(3~)
Dir,
sub-state
-
1.5
3. 8
-
1.0
-14.2
(cm
-1
)
v
B
HY x 10E
v
0
14.950
0.002
1
15.437
0.031
2
14.034
0.004
3
14.019
0.017
4
13.414
0.009
5
12.595
-0.001
6
12.238
7
11.671
-
-
,
-
D
v
v
4.7
0
14.974
0.008
2.8
21.0
1
14.373
0.005
0.4
5.7
2
13.849
0.005
5.9
3
13.137
0.004
-
0.6
4
12.538
-0.003
-
7.7
5
11.827
-0.010
-12.3
6
11.399
-0.021
-41.0
7
11.597
0.012
4.8
-11.5
0.018
0.002
8
10.921
-0.002
8
11. 158
9
10. 532
0.0
9
9.907
-0.014
10.267
0.013
10
9.686
-0.003
10
11
9.658
-
12
8.905
-0.009
13
8.301
14
7.690
15
8.2
,
-0.008
o. 006
0.021
1
Hv x 10’
11
9.063
-23.3
12
8.811
-21.5
13
8.086
14
7.784
15
6.986
4. 1
0.010
0.020
-0.006
0.1
4.6
-
1.0
-
-12.9
14. 6
-
ABSORPTION
SPECTRA
Table
(4~)
D’ ‘Tr;
sub-state
(cm
-1
OF HI, HD,
AND
291
DP
VII-Continued
)
(4~)
D’l”;
sub-state
(cm
-1
)
B
v
II
D
v
v
Hv x 10
5
B”
v
0
14.481
1
14.303
2
13.607
(5P)
i
DSN1iT: sub-state
(cm-l)
1
(5~)
D”‘“;
D
Hv x lo5
H
v
-0.008
-17.2
0.010
-0.004
sub-state
6. 1
-18.1
(cm
-1
)
0
2
III. ROTATIONAL
CONSTANTS
If we consider that the hydrogen molecule is a nonrigid rotator, and if we include a third-order term in J(J + l), the rotational energy may be expressed
(9) by the equation
Fi(J)
=
Ki
+
BviJ(J + 1) - DviJ2(J + 1)” + HviJ3(J + 1)3 ..a ,
(1)
where the B, i, D, i, and H, i are the so-called “effective” values of the rotational
constants. These are related to the “true” corresponding constants through the
relations
Bvi = B, + 6i,
Dvi = D, + pi
where the corrections 6i and ~a, usually very small, are due to the interaction
of the neighboring states. In the case of the II states, this leads to the wellknown A-doubling. However, it is to be stressed that, even in the case of the z
levels, constants K; , pi , and 6i may have to be taken into account. Unfortunately, in the first case, only differences of the constants due to the two levels are
observable, and in the second (Z states) these constants have to be evaluated
with the help of theoretical considerations which are outside the scope of this
paper. As a consequence, we will consider here only the B,” values as such, and
for the sake of simplicity, we will drop the subscript ‘5.” From Eq. (l), it is easy
to deduce the second differences,
AzF(J)
= F(J + 1) - F(J - 1) = R(J) - P(J),
292
MONFILS
B,(cm-‘1
A
Herrbeg
and
Present
work.
Howe.
A
0
+
01
,
0
,
,
,
I
IO
20
”
.
FIG. 1. (2p)BQ,+
I
30
“.
1
40
”
”
V
state
to obtain the well-known expression
AzF(J)/4(J
+ %) = B,’ - 20,’
[(J + %)” + %I
+ 3H,’ [(J + SW2
+
J + 37/12) + 9/16].
(2)
Equation (2) is in a very suitable form for the computation of the rotational
constants B,‘, D,‘, and H,’ by a least squares method.
A second procedure would consist of using Eq. (1) directly, starting from the
rotational levels and allowing for a combined electronic and vibrational term
vO. However, it is desirable to adopt a method starting directly from the observed data. The equation generally used for the determination of vg has a very
appropriate shape for the computation of B’, D’, and H’:
s[R(J
- 1) + P(J)] = vo + (B,’ - B:‘,Jz - (Dy’ - D:‘)J2(J2 + 1)
+ (H,’ - H:)J3(J3 + 3J).
(3)
Strictly speaking, the B,‘, D,‘, H,’ values so obtained depend on the corresponding values of the ground state, but the relation here is straightforward. The
equation giving the frequencies of the Q branches is utilizable as such:
Q(J) = vo + (B,’ - B:)J(J
+ 1) - (D,’ - D:)J2(J + 1)”
+ (H,’ -
H:)J3(J
+ 1)“.
(4)
ABSORPTION SPECTRA OF Hz, HD, AND Dz
B,
293
km-‘)
6
io
f
FIG. 2. (3p)B’%+
v
state
This second method may seem preferable because of the advantage of determining v. simultaneously. In the present work, we have used both for two reasons:
first, the As’(J)/4 (J + j+$) h ave to be computed during the assignment procedure; therefore they were directly available. Furthermore, it was thought that
the computational errors might not be the same in both methods, thus providing
a control of the results. This is what was observed: the results obtained both
ways have roughly the same dispersion but the averages show a reduced one.
The H, constant1 has been taken into account in Eqs. (1) and (2) for technical
reasons only: the precision of our measurements combined with the low number
of rotational levels observable makes it impossible to obtain significant values
for H, . However, the simultaneous determination of a third-order parameter is
an easy way to detect incorrect values for B, and D, . When a faulty experimental point was capable of distorting the results of the mean square computa
tion, it was found that H, was the most sensitive in that its order of magnitude
1Where we deal only with the excited states, we shall simplify the symbols B’, D',H' to
B, D, H.
MONFILS
294
B,(cfri’)
0
5
10
v
FIG. 3. (4p)B”%+ state
could be changed easily before D, and B, were seriously affected. When necessary,
because of the small number of data or their poor quality, H, was assumed to
be zero. In rare cases, the same process had to be applied to D, . It should be
mentioned here that averages have been computed only between equivalent
solutions, i.e., solutions with the same number of rotational constants. When
one of the methods had to be simplified by assuming H, or H, and D, to be zero,
the most complete set of solutions has been accepted. Tables V to VII present
the results obtained for the three molecules and Figs. 1 to 11 show how the experimental B, values behave when plotted against v. In each figure, the points
relative to the three molecules are collected.
Although the abscissa do not correspond physically, the very important isotopic effect is easy to observe. In Fig. 1, we have plotted the data of Herzberg
and Howe (10) along with ours for HZ ; the large amount of experimental points
is due to the very small value of B, .
In the case of the B”Z,+ state, it is seen that the experimental results are very
difficult to interpret as belonging to a single curve for any of the three molecules.
This appears to be partly the consequence of vibrational perturbations (11)
although there seems to remain a significant change in the slope of the curves
around v = 3 for Hz to v = 5 for Dt . For the B’l Z,+ state, no clear separation
may be seen between the small-slope part and the larger slope part: there is a
smooth transition, and as a result, the experimental points are fitted quite ac-
ABSORPTION SPECTRA OF H,, HD, AND Dz
295
Bv(cm-’ 1
A
Disks.
.
30.
Prtsont
0
work.
10
01
I
5
0
.
.
I
I
I
20 v
K
10
FIG. 4. (2p)C%1~+ state
curately by one curve. It is remarkable in any case that the characters of the
curves are the same, state by state, for the three molecules examined.
As a result of the A-doubling, each of the II states gives rise to two curves,
corresponding to the II+ and II- substates. Generally, the second set is more
regular, apparently because of the absence of states of the same symmetry which
could perturb them. As was to be expected, the length of the experimental sets
of data decreases steadily for the D' and especially D" states. This is due to the
decrease of the intensities of the lines and to an increase of the complexity of the
spectrum toward high frequencies.
IV. EQUILIBRIUM VALUES
The variation of B, and D, with the vibrational
expressed in a polynomial form:
B, = B, -
(Y.(u + %> + re(v + %I” -
quantum number v may be
E,(V + %>” +
D, = D, - ,&(v
+ $4)+ 6,(v
+ 35)'- I...
... ,
(5)
(6)
MONFILS
296
B, (cm-’
I
)
-1
I
0
I
,(I
I
5
A
Dicko.
.
0
Presont
,,(,,,,,,I
work.
I
lo
FIG. 5. (2p)011~-
t5
r,
20 v
state
The signification of the constants has been determined by various authors one
of whom is Dunham (la), who has developed detailed formulas by taking into
account the finer interaction between rotation and vibration. This may prove
very important, especially for light molecules. However, the experimental uncertainties that affect our constants allow the use of well-known simplified formulas such as
(7)
and
De = 4B,3/w,2.
@I
Expressions for the coupling constants are derived in Dunham’s paper, but the
corresponding experimental values will not be discussed here. In order to compute the equilibrium constants, the B, and D, values shown in Tables V to VII
have been introduced in a least squares program. It is well known that in the
ABSORPTION
SPECTRA
OF Hz, HD, AND
DP
297
B, (cm-‘)
0
0
I
5
x
’
-
*
FIG. 6. (3p)D’&+
I
10
*
’
r
.
1’
15
v
state
case of B, , a difficulty has been expressed by Herzberg and Howe (IO): these
authors have not been able to determine B, with the expected accuracy by least
squares methods as a result of the peculiar shape of the beginning
of the B,
versus u curve. There is no clear convergence for the calculated coefficients when
the number of experimental
points introduced
in the equations is increased. We
have not been limited by such an effect, except in the B’ state when a single
curve is to be computed. The reason for this situation probably can be found in
the experimental
errors that are more important
here, this in turn being connected to the very short wavelength
region where the spectra have been recorded. A difficulty arises however with the very long series of data, where a
considerable
decrease of the B, values takes place for the very last value of a:
it has not been proved that the procedure consisting of increasing the number of
constants
has a physical signification.
The potential
curve may indeed be distorted by mutual influence as for the B’ state, in which case a single set of constants computed to account for the whole set of data probably has no meaning.
MONFILS
298
B,(cm-‘)
O_
,,
h
O_
‘L
O_
O__
0
;
’
.
’
.
IO
$
”
FIG. 7. (3p)D%,,- state
However, the necessity of the extrapolation of the curves towards the dissociation limits makes it necessary to approximate the experimental data as much as
possible. This is why constants have been computed whose physical significance
has not been discussed. They will be used in a future paper for the computation
of experimental potential curves. In Table VIII, we have collected the B, values
obtained for the three molecules.
The values given for the B state in the case of H, have been quoted from
Herzberg and Howe (10). They compare favorably with those computed from
Dieke’s results (13) :
B, = 19.995 cm-l;
r, = 1.2934 Ai.
Although the second decimal for B, is very sensitive to the type of extrapolation
made, it seems that Herzberg and Howe’s values are more reliable, as they proceed from experimental data which are somewhat more complete. For the B’
state, the second row is definitely to be preferred to the first, because of the
ABSORPTION
01
,
.
SPECTRA
.
OF Ht, HD, AND De
.
lb
0
FIG. 8. (kp)D”&+
299
v
state
already mentioned peculiarities of the curves taken as a whole. Since we have
not observed the first bands of the B and C states, and since in the case of HD
and Dz we do not have recent data about the first levels, we have not computed
the B, values in these cases. The third, fifth, and seventh columns of Table
VIII show the variation of the equilibrium distances, computed from expression
(4). It can be seen that although the values obtained for the three molecules are
subject to some dispersion, no systematic trend does appear in terms of the
reduced mass: the isotopic relations hold as exactly as can be verified here. This
means that the correction terms computed by Dunham are of no use in the
present case. The local disagreements between results related to different molecules seem to be linked to perturbations. The eighth column gives the average
values: these values should be relatively free from perturbation errors and give
rise to much smoother curves when plotted against the principal quantum
number 72 of the united atom. These curves are shown in Fig. 12. The interatomic distances for the I&+ states decrease steadily from n = 2 to n = 4.
MONFILS
300
B,(d)
FIG. 9. (4p)D’Uu-
state
B&cm-‘1
FIG. 10. (5p)D’%+
state
ABSORPTION
SPECTRA OF Hz, HD, AND 1)s
301
6, (cm-‘)
30
o HD
1:
0
20
D2
0
0
IO
t
of , . . ,
0
5
FIG. 11. (5p)D’W,-
I
10
*
v
state
Simultaneously, the r, values corresponding to the II states increase, although
at a slower rate. The values obtained for the (5p)‘II, state seem to indicate a
decrease but the effect is smaller than the uncertainty of the result. As a whole,
there is a rough convergence. The 21+and II+ states are known to perturb each
other whereas the Z- states seem to be free from important interactions. Indeed,
if the curve for the II- states is extrapolated toward very high values of rz, it
converges very near to the value quoted by Herzberg (9) for Hz+. This is not
the case if we extrapolate the curves corresponding to the Z+ and rI+ states: the
first would give too high an V, value and the second one a value which is too low
by approximately the same amount. The explanation of the deviations in both
groups is not in the scope of this paper, but it seems acceptable that the deviations must be in opposite directions and of a not too different order of magnitude.
In fact, if we take an average for each n of the values obtained for the Z+ and
the IIf states, we obtain the dotted curve shown in Fig. 12. This curve does
converge very clearly toward the JF curve, and to a value which is very near
the 1.06 x for Hz+. Actuahy, it may be noted that our most probable extrapolated value seems to be a trifle higher than 1.06, being situated at 1.063 f 0.003
B.
The coupling constants LY,y and Echaracterizing the interactions between the
rotational and vibrational movements of the molecule are listed in Table IX.
In this table, the constant (Ymay be considered as well determined (except in
MONFILS
TABLE
VIII
B, AND rc CONSTANTS
states
B ‘Z”f
B’ ‘Z +
L‘
B” ‘Z u+
c 1rL+
c
1n,,-
D ‘FL,+
D ‘II,D' ‘II +
D' ‘Il,”
D”
I=
D”
In
+
11
u
-
HZ
B,(cm-I)
20.035
25.8,
26.7s
27.1~
32.04
31.5”
32.5,
30.8,
31.51
29.89
30.12
30.76
D2
HD
r,(A)
1.29253
1.13s
1.118
1.11,
1.022
1.03,
1.014
1.04,
1.030
1.058
1.05,
1.04,
B,(cm-'1 r.(A)
B&n-')
r,(A)
f,(A)
18.36
18.87
20.8,
1.169
1.153
1.096
13.98
13.86
13.6~
1.094
1.09s
1.10s
23.74
22.9,
22.73
22.3s
24.1~
22.93
1.029
1.04,
1.05,
1.060
1.020
1.046
15.54
15.1,
15.80
14.79
16.8~
15.31
1.038
1.052
1.029
1.06,
0.998
1.04s
(a) Computed from Hereberg and Howe’s results (10).
(b) Computed from all the data.
cc) Extrapolation
of the beginning of the curve.
(d) If the extrapolation
bears only upon the five first points,
and r. = 1.034.
1.293
1.13,
1.123
1.10,
1.022
1.03,
1.027
1.04,
1.031
1.06,
1.023
1.04,
it is found
Rem.
0.038
0.022
0.006
(c)
(4
0.009
0.005
0.012
0.002
0.023
0.002
that B, = 31.3,
the D” state). The constant /3 has a real significance only for the low lying states
whereas E, which has been introduced in the equations only to account for the
drop in the B, occurring for high v’s, is only to be considered as a parameter whose
physical significance is not necessarily clear. Many irregularities in Table IX
are due to perturbations that have not been analyzed and y and E are particularly sensitive to any kind of displaced experimental points. The B state has very
small a, y, and t coupling constants, and this is true for the three molecules.
However, since in the case of HD and Dz we have no reliable values for the first
vibrational levels, B, has been computed by means of the isotopic rule and introduced in the equations giving the coupling constants. The same procedure has
been applied to the C states for the same molecules. As expected by the theory,
all values decrease when the reduced mass increases but remain positive. The
B’ and B” states may be considered together: we have already mentioned the
curious behavior of the B’ state, in that it seems that two sets of constants are
necessary to account for the data. These two sets are designated by (b) and (c)
in the table. From one to the other the increase of ry is quite considerable in Hz
and still more in HD. No determination of Ewas possible because of the reduced
amount of data in each half-curve. But if we want to consider all the data, not
only does the constant 6 become necessary but it is found to be abnormally large.
The same situation is found for the B” state: very large positive E values are
necessary to accourit for the whole curve, and if we split the data, the first part
ABSORPTION
303
SPECTRA OF Hz, HD, AND Dz
lT-
1
i
i
1--
5
n
FIG. 12. Interatomic distances in the HZ molecule
gives small values for cyand the last part large values. In Figs. 2 and 3, the curves
illustrate the proposed solution, as far as a choice may be made. The results
concerning the C and D states are very similar to each other. Furthermore, the
two substates II+ and II- give, at least for HZ , values which are very close together. For HD and Dz , the E values seem to be difficult to determine, the obtained data being somewhat irregular. Furthermore, when c is set to zero, the
y values are much more significant, as is shown by comparing the two successive
rows corresponding to each substate PII,+ and Cl&-. Exactly the same behavior
is observed in the case of the D substates, where t seems to be significant only
for Hz . It is seen how the suppression of t affects only y, the constant (Ykeeping
relatively constant.
Only a small number of vibrational levels have been observed for the D’ states.
This is the reason why the y values are not to be taken here as anything more
304
MONFILS
TABLE
IX
VIBRATION-ROTATION COUPLING CONSTANTS LY, 7, AND c(cm-1)
-
-
-
I
HD
-
States
a
y
x
CX
10
103
y
a
x
10
6)
(cl
I?” IX,+
(a)
(b)
(cl
c
‘II”+
c
‘II,_
0.52
1.49
5.08
4.62
2.56
1.30
1.78
1.76
-
0.30
0.43
5.80
0.28
6.66
1.33
0.49
3‘9.1
‘2 , I)
-
0.60
0.055
0.94
2.56
2.26
1.04
1.94
1.31
1.00
0.69
-
5.4
1.88
-
0.9s
6.9
0.75
0.94
D ‘IT,+
2.00
-
0.71
-
4.0
11 ‘II,‘_
1.96
-
1.02
-
5.3
0.95
0.91
0.97
1.17
0.84
1.25
1.61
0.87
D’ IIl u+
D’ ‘II,-
0.64
1.11
-0.64
1.45
-6.23
-0.65
-
-
-
L
(n) Computed from all the experimental
(‘) First part of the data.
(‘) Second part of the data.
x
101
y
01
x
10
CX
103
__
-I-
B ‘2u +
R’ lZ,+ (a)
e
D2
-
0.17
-1i.l
0.91
0.24
13.5
8.66
1.36
121
-
-
0.77
-0.04
-0.58
-0.06
0.09
-0.06
-0.28
-0.26
1.07
-0.06
-
4.9
-3.1
1.0
-4.0
-.
-
0.039
1.7
0.26
-
0.26
1.20
0.92
1.69
0.78
0.13
0.27
1.87
0.44
0.46
0.038
18.7
-
S.61
-0.37
-
67.6
0.12
-0.09
-0.13
-
0.77
0.49
0.47
0.49
0.72
0.54
1.07
0.42
-0.07
-0.07
0.04
0.29
-0.02
-
1.9
-
0.44
1.17
0.60
-
-
-0.16
1 1.1
-
data.
than tentative data. Since a number of results given in Table IX have only such
an indicative value, we have printed in italics those that we think to be physically significant.
In Table X we have collected the data concerning the centrifugal constants
D, and their coupling constants ,6 and 6. The last one has been determined only
in the case of the B and C states. For the B state, we have made in the case of
Hz two parallel computations: first with Dieke’s results to be able to compare the
constant obtained with Herzberg and Howe’s and finally by taking all of the
results of these last authorsand ours. For HD and Dz , we have introduced in
the equation a D, value computed from Herzberg and Howe’s with the help of
the isotopic relations. This procedure has allowed us to determine 0 and 6 with
accuracy. In the case of the B’ and B” states, we give in Table X several sets of
constants corresponding to progressively simplified solutions: the sensitivity of
the remaining constants to the suppression of others gives an idea of the uncertainty involved.
ABSORPTIOK
SPECTRA
TABLE
CENTRIFUGAL STRETCHING CONSTANT D,
OF HI, HL), AND
Dz
305
S
AND VIBRATIONAL COUPLINGS B AND
b(cm-I)
IB lx<<+ (b)
1.625
(di
(c)
H’ ‘Z,‘+ (c)
1.64
c In,,+
1.63(a)
0.58
0.53
0.97
1.28
9.42
8.01
c ‘II,,_
2.16
I:;
R” 1.Z,,+ (c)
(c)
8.16,
1.9 “1 1.0
1.9
6.0
-0.83
6
-1.25
0.01
-0.01
3.3
2.83
1.91
2.15
-1.0
1 .lS
-1.2
D' III )I
-
2.78
8.35
17
4.;
3.1
0.92(a)
-
;
0.58 ~ 2.2 ~
~ 1 .!I ~ --
1.33
0.77
2.oti
1.23
1,13(a)
1.13(a)
-3.Q
D 'n,+
D TI,D"II u+
/
-‘-/
0.2
0.2
0.69
--0.37
1.13
-0.02
-0.96
-
1.22(a)
2.87
1.24
: 1.99
1 2.33
-
1.89
1.20
4.1
2.0
20
_
-
~ o.g2 ~ 2.3
1.58
0.54
-0.i
2.7
-
0.3
0.41(a)
-
1.9
j-2.8
-
0.08
-5.4
-
0.50(a)
0.50(a)
O..%(a)
0.54(a)
1 .lS
0.20
1.23
0.03
-0.37
-0.07
3.6
3.0
-0.27
0.43
0.34
0.62
0.24
0.71
-
8.5
-2
0
-
1
(‘*I Imposed value.
(b) Herzberg and Howe (10).
(‘) Computed from all the experimental
(d) Computed from the first five values
data.
of D,
(13).
Here again, what we consider as physically significant has been printed in
italics. The very small value of D, of the B’ state is remarkable. The constant
6 has been computed for the C state iu H, : the very mm11 values obtained for
the two substates are to be noted, as well as the corresponding p values. The
change in the sign of p from the II+ to the II- substate is probably not real: both
values may be considered as zero withiu the over-all uncertainty.
1.. CONCLUSIONS
If we consider ouly the data printed in italics, it appears that they show a
very good coherence. The values are not very different for corresponding substates, and they decrease when the reduced mass increases.
Many of the results that have been considered unreliable are probably the
result of perturbations and not necessarily lack of precision; so they may retaiu
some signifieanee.
This is the reasou why apparently unreliable data have beer1
MONFILS
306
included in Tables IX and X. Future comparison with other studies may help
to make the best choice. The same remark applies to Table VIII : we have given
in the last column the average departure of the three re from the mean value, in
order to allow a quick judgment of the values tinally adopted but this does not
mean that the T,‘Sare affected by experimental errors: it is probable that if the
perturbation could be removed, a much better agreement would be obtained.
This, however, will not be practicable with our spectra: an increased resolving
gower will be necessary. With the present work, the spectral region down to 800
A may be considered as almost completely assigned. Between 800 and 750 d,
however, our spectra show a majority of unassigned lines, which probably belong
to the higher terms of the two Rydberg series considered here (@II, and npQ,f)
together with other series (nyZ,+, nj% , . . e). Unfortunately, the increase of
the number of blends has prevented us from extending our results in that direction. The B, C,and B' states of Hz may be considered well known, apart from
absolute intensity considerations. Many publications have been devoted to the
first two of these states since the first works of Lyman and Werner (14, 15).
Completing our results for the very last vibrational levels of the B and C states,
Namioka (16) has confirmed that it is the B' state that is responsible for the
photodissociation of the molecule at 845 A. The B" state, somewhat predissociated, presents intense bands. Unfortunately, these are merging progressively in
the bands of the D state and could not be studied very far up. A higher resolving
power will probably be necessary in order to solve the remaining problems.
Although known for almost thirty-five years (17), the D state stil1 cannot be
considered well known. Our results extend almost to the dissociation limit, but
the bands keep a number of features which cannot be explained by the close
vicinity of the bands of the BN and D states. The D' and D" states are of very
low intensity: they behave as not predissociated and, in our spectra, the higher
order terms are soon blended in the complex structure of the very low wavelength part of the spectrum.
The present work has been made possible by the financial help of the Air
Research and Development Command.
RECEIVED:
March 2, 1964
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