JOURNAL
OF MOLECULAR
SPECTROSCOPY
7,
Band Spectrum W~RSH~LL
64-80
of the GaH
L. GINTERt
Department of Chemistry,
(1961)
.~ND K.
Vanderbilt
Molecule*
KEITH
INKES
University, Nashville,
Tennessee
An extensive emission system of GaH, in the region 5200-6400 A, has been obtained from a King furnace containing gallium metal and hydrogen at 1500°C. Fourteen bands have been measured and analyzed on the assumption, previously made by Neuhaus, that they arise from a Q,,o-X’Z+ transition. The following constants have been determined (cm-l) : T, Ql
+
3II,+ X?Z+
17622.01 17337.08 0
16&i 1640.54 1604.52
D,XlW
2%
Y%
&
58.22 62.72 28.77
-7.47 -6.195
6.692 6.394
O.f;26 0.276
+0.360
6.137
0.181
-0:;315 -0.0400 -0.0005
4.89 2.62 3.37
A relatively weak fifteenth band has been analyzed as the O-O band of the transition 3nz-%+. Its band center and rotational constants are just those one would expect if each of the above constants, an, obeys the equation al - a, = al - ao . Finally, diffuse features corresponding to transitions from an unstable state to the lowest three vibrational levels of the ground state have been observed between 4220 A and 4850 A. INTRODUCTION The m$jor difference between the spectra of GaH and those of the boron and aluminum hydrides should be t,he occurrence of intercombination systems for the heavier molecule. In fact, Neuhaus (1) recent’ly discovered the GaH molecule by observing a 3&‘2 transition at 5700 A. He discussed the reasons for the assignment and recognized t,hat the multiplet splitting (280 cm-‘) was sufficiently large that bands arising from the components with Q = 0, 1, 2 (t,he latt’er not observed\ could be analyzed formally as ‘2-‘3, ‘lS’2, and ‘A-‘2 systems, respectively. Rotational analyses were given for the O-O bands of the 311-12 and 3~0-1~ systems. In addition, Neuhaus (1) observed a diffuse band at 4200 A, which was assigned to a ‘E’z transition and led to an estimate of the dissociation energy as 23,600 cm-‘. Throughout this previous work, the correlation of atomic and molecular states was t,hat of Kleman (9). In a study of gallium carbides, we have obtained a number of very weak cmis-
* Some of the result,s presented here were reported at the June, 1960 Symposium of Molecular Structure and Spectroscopy in Columbus, Ohio. More complete details of the researh may be found in the Ph.D. thesis of M. I,. Ginter, filed in the library of Vanderbilt University, 1961. t Texaco Fellow, 1959-1960.
SPECTRIJM OF THE GaH M(~)I~IXUI,I<
li;l
sion hands of the “&‘z syst,em of GaH at resolutjion suficient,ly high for rotational analysis. l\Iost of t,he above conclusions have been confirmed. In additjion. I here have been obt,ained the constant8s of vibration and of vibration-rot’at’ion intjrruction, analysis of the O-O band involving &’ = 2, resolutions of Ga6’H lines from Ga’lH lines in some bands, a lower limit, for the dissociation ewrgp, antI more informat.ion about, the diffuse syst,em.
Gallium and hydrogen were placed in a King furnure ( 3) and heated to about lCiOO”C,at’ atmospheric pressure. More than fifteen bands of the 3&‘Z system of (;aH and three stronger diffuse bands in the region 4200 A. wuld t’hen bc photographed on 10:3a-I; film in a few minutes wit,h a Bausch and I,omh Model 11 1.5-m&r spectrograph. IJigure 1 reproduws an exposure made in this way. Spwt,rograms used for rotational analysis were made in the first. and second orders of ;L X&meter Jarrell-Ash spectrograph equipped with a l.jO,OOO-lint Bausch and Lomb plane grating (3). Exposure times were one to six hours and the rff&ivc resolving power was about 100,000. The spect’ra were mraslnwl against8 iron lines, using a David W. 1lann hlodrl 1300 wmparatjor. I>ESCRIPTI( 1X OF THE SPIXTRUlI
The opelj structure of t.he general view given in 12ig. 1 and t.he enlargement of a band which exhibits almost no degrading (Fig. 2) show that t,hc cmitt,er of the bands is a diatomic hydride with an inertial constant, of about, 6 canl-~‘. Since the bands are obtained only if gallium is in the furnaw the emitter mlwt t w GaH It is evident, from Fig. 1 t,hat, band-head measurements cannot lead to nwural~~ vibrational differenres, that is that, rotational analysis must precede vibrational :lnnlysis. There are red-degraded hands and blur-degraded bands as well :IS bands like t.hat of Fig. 2. In nddit,ion t,o the bands of Fig. 1 thcrr were photographed five or six diffuw heads which, by rough measurement, were found to lie at (23,754, 2:2,714( ?i 1, (22,206, 22,lUX 1, and (20,713, 20,672 J cm--‘. The first band ( or pair) is strongest :u~l is an order of magnitude stronger than the most intense emission of Fig. 1. ROTATIONAL
ANALYSIS
The long wavelength system will be discwsscd first. The wavp numbers of the lilies are given in Table I. After a number of branches had been picked out, it was found t,hat at least t,wo types of bands were involved: Swen bands showed I’ and R branches only, no lines missing, with the P branch slightly weaker, while eight bands showed P, Q, and R branches, Q( 0) and I’( 1) missing, with the R brunch. the weakest,. Exwpt~ for the italicized point the bands are like those of S-S and n-s transitions, respectively. But the weak K-branches (.4 ) as well :w comparison with InH (5) incline r)l~e to the view that the upper states :w
do)
(0
I -‘I
FIG. 1
‘l-L2 -‘c
‘n,
$0)
(3,3)
I
SPECTRUM OF THE GaH MOLkXULE:
a_
In
0
a
(ii
.J
75.93
18013.24
31.93
(63.76)
59.19
(56.67)
(55.31)
(55.31)
(56.67)
58.42
5
6
7
a
9
10
11
12
56.96 52.51 (49.03) 46.46 44.80 (44.03) (44.03) 44.96
83.96 109.80 36.90 64.93 93.81 223.56 53.92 85.08
63.17 76.22 90.45 18005.86 22.37 (39.89) 58.32 77.63
63.04
68.09
74.28
81.52
13
14
15
35.73
22.69
710.44
99.01
88.26
78.30
69.18
60.88
53.43
51.41
62.23
41.18
36.45
32.65
29.78
17627.87
Q(J)
= 17628.83
(59.11)
0
O-O Band
46.87
V
68.65
35.55
84.28
92.14
24.31
(17870.97)
4
41.01
593.43
2
17603.63
NJ)
71.92
R(J)
17949.40
(17911.21)
Q(J)
17909.43
17.09
NJ)
0
=
O-O Band
- ?E+
3
1
0
V
%2
Table I WAVE NUMBERS OF THE GaH BANDS* -1 (vvat' cm )
35.72
(911.09)
87.24
63.80
40.84
818.70
97.20
76.42
56.39
37.18
18.78
701.24
84.55
68.78
17653.83
NJ)
3 m
2
5
2
a
51.38
34
*
Where two lines
listed,
73.02
76.37
33
are
67.39
32
of
24.81
(59.90)
31
lines,
(411.14)
50.61
30
( ) Blended
77.90 95.42
(39.89)
29
the
first
isotopic
43.23
35.69
58.91
components. is
assigned
to
94.73
66.86
29.03
28
38.81
17.07
27
607.46
76.03
44.23
511.98
79.45
46.66
413.91
81.26
48.83
(37.67)
96.07
R(J) 316.75
317.77
92.14
18004.72
26
73.83
206.22
25
66.64
54.17
22
79.36
28.77
41.99
21
24
83.81
30.26
20
23
61.60
19.01
19
39.80
118.44
98.57
908.31
18
exclusive
Q(J) 97.68
17
P(J)
89.46
J
16
69 Ga H, the
P(J)
second
17.09
12.27
06.81
600.93
94.72
.88.49
82.08
75.94
70.79
65.37
60.45
56.09
52.25
(49.03)
47.00
to
Ga71H.
Q(J)
74.88
65.76
54.99
42.82
29.59
15.50
900.73
85.45
69.99
54.28
38.56
22.94
807.43
92.17
(77.28)
62.83
48.89
R(J)
(38.70)
215.36
91.11
66.28
41.19
115.17
88.95
63.34
37.39
18011.55
85.96
60.63
J
R(J)
89.91 98.65
80.76
79.89
78.76
77.14
72.55
69.21
02.39
290.70
78.77
66.77
54.35
41.58
28.34
7
8
9
10
11
12
13
18.75
68.04
50.61
17
18
689.76
21.11
24.67 81.29
087.30
21
22 23
56.78 40.91
06.90 894.48
71.63
86.27
798.94
11.02
21.48
30.66
38.57
44.50
51.51
56.52
(64.64) (60.88)
67.75
70.31
31.48
57.83
71.63
786.27
00.30
72.44
74.01
(18875.11)
Q(J)
18876.17
2-l
10.66
306.19
92.83
82.20
70.00
57.56
44.81
31.95
19.04
205.92
14.00
27.27
18852.39
=
19
30.17
41.28
(28.33)
(27.57)
(26.67)
(25.53)
(24.34)
(23.18)
(22.04)
(21.01)
93.03
0
P(J)
V
20
54.46
184.10
16
52.01
62.65
65.05
(59.88)
14.55
00.08
72.41
83.54
(18994.03)
04.55
15.05
25.77
36.61
47.60
15
21.48
(507.35)
70.40
60.04
14
75.52
(80.34)
17381.40
13.94
6
(20.11)
49.41
58.71
25.34
5
80.05
(19119.17)
70.11
38.04
36.86
4
67.38
19142.07
NJ)
54.62
Q(J)
81.65
(48.43)
3
0
1-o = 19117.28
27.66
16.32
P(J)
Y
19093.36
405.05
17393.69
(17359.88)
Q(J)
2
P(J)
1
0
" = 17382.20 0
2-2
3nl - 1x+
Table I (Continued)
m m
2 !a
2
SPECTRUM OF THE GaH MOLECULE;
71
components of a 3~ state. This view already had been adopted by Neuhaus i I ) and is confirmed by t,he discussion given below. A& indicated above and in the t,ables, lines were observed usually down t,o t,hc lowest J-values so that numbering was unambiguous in most cases. The rot,ational conskmts of both states were obtained, for each band, from the combinat ion relation ( 6 ) A$’ = (-CIA -
tiD,> + “7/‘4 H,. ) (J + “5 ) -
(SO,, -
%SH,,) (J + ,; i I:< +lZH,,(
&F" = Xi./-
where
A2Ff =
and
1) -
P(./
+
./ +
1.”j5
11
R(./,- l'(J).
lpor the hands w&h Q branches the magnkude of A-doubling was determined by forming the quantities [R(J)- Q(.I)- Q(J + 1 ) + P( J + 1 )]:‘a. Rmd origins were obtained from the equation f-2(.I Results :ud II.
I) + P(J)
of the rotational
= 2V” + ‘1(R,.’ - B,” ).I” analyses
of the sharp
2(D,
bands
- D,.” )J”( ./ + 1 I”.
are collected
in Tables
I
With band centers at hand (Table I ) most of the bands are identified easily as memhcrs of two sequences for each of the ( “~I-‘S and h-‘~ I syst,cms. namely, AP = 0 and Ao = + 1. The highest vibrational number involved for each state is ii. 111 addition to bands of the above sequences, the O-l band of thcb the ?I~ -‘s system was studied. The following equation s were found to represent origins: :‘11,-‘5
v = 1iti28.8:3 + 1X7.34
I” -
tiY.44 17’” - 1576.02
7.47 1””
1”’ + 2823
T”‘” -
OX0
lY”:
(My OIIC of the fifteen bands of the rotational analysis does not, fit into the above pattern. The band has the characteristics of the “III--IS bands except that I more lines of low ./ seem to be missing. Its band center is 281 m1 to the high energy sitlc of the O-O band of the “rIP’Z system and 2 X 282 cm-’ to the highetlcrgy side of the O-O band of the “rIo-lpy syskm. It is much weaker than cithel O-O band and it shows the same lower-state constants as were found for 11” = 0 of s’s’. There can br little doubt, that this weak hut well-developtad hand i+ hy the selection rule the O-O hand of the system 3112-‘X, which is forbidden Ai! = 0, + 1. ;-\s mentioned, the vihr:~tional constants for the “& stattb seem to
J
0
NJ)
98.89 (106.44) (06.72) 15.69
33.70
28.18
28.50
(24.57)
(21.15)
22.14
38.99
38.65
26.33
26.05
98.60
33.36
(24.86)
91.92 92.22
39.78
87.02
47.81
40.11
38.65 38.99
86.77
47.45
65.69
41.67
218.68
97.16
96.79
76.26
56.89
22.06
83.07
21.75
82.77
(06.72)
81.00
57.27
(106.44)
92.22
16091.92
16080.69
Q(J)
16056.82
P(J)
78.68
878.24
01.93
01.47
22.11
21.64
39.74
39.25
16989.27
P(J)
997.73
05.02
04.74
10.75
15.57
19.44
17019.09
Q(J)
3-3 Y = 17018.72 0
Y = 16078.84 0
Table I (Continued) o-1
R(J)
59.12
(64.37)
65.96
(64.37)
59.67
51.23
(44.09)
(34.35)
17023.51
l-1
(93.40)
(88.49)
(84.27)
80.69
77.42
74.78
72.48
70.79
17569.80
Q(J)
" = 17569.18 0
20 35.67
313.27
77.46
77.10
19
70.76
50.59
31.39
213.16
95.86
91.62
57.27
56.82
48.69
46.36
41.09
40.85
34.64
34.43
29.62
29.33
25.72
25.31
18
17
16
15
14
13
12
73.91
58.50
57.90
773.36
(01.99)
(26.78)
(49.70)
72.02
71.55
92.23
891.80
10.94
28.89
28.53
Q(J)
25.90
(698.79)
44.00
43.46
84.80
784.31
21.10
20.48
52.07
51.14
P(J)
525.28
94.39
93.79
62.37
31.62
401.72
72.61
44.35
317.13
64.50
(22.55)
11
79.61
Y0.96
50.55
(21.15)
10
22.97
R(J)
Q(J)
P(J)
J
R(J)
49.03
44.76
42.47
37.54
30.71
24.37
19.43
13.77
08.23
(605.04)
(97.67)
C(J)
0
63.96
16.25
42.49
20
95.53
96.04
39.88
70.96
82.01
24.42
16.43
2-2
on p. 76)
194.81
00.08
03.85
06.94
(09.60)
(12.50)
(12.50)
11.76
(09.60)
06.48
202.39
97.44
(91.74)
85.30
(78.18)
70.46
62.16
53.28
43.87
34.41
17123.62
R(J)
= 17112.53
(Table Z continued
(51.65)
788.08
(03.28)
(27.38)
(49.22)
98.65
092.97
507.92
88.75
03.72
70.29
78.44
890.34
09.45
27.59
45.19
(79.38)
993.75
08.88
23.51
37.57
51.23
(64.37)
77.16
089.40
17101.29
0
14.42
67.76
56.77
45.53
34.10
22.66
411.23
99.17
87.32
(75.52)
63.70
51.84
31.33
(60.78)
19
90.75 (94.03)
16.32 28.09
P(J)
Y
25.08
35.70
46.35
57.06
(68.04)
78.74
189.78
00.84
(12.50)
23.47
34.72
46.20
57.76
69.85
17304.54
NJ)
(37.39)
78.53
18
0
l-1
= 17292.60
22
595.93
17
86.94
82.46
(77.14)
71.31
64.85
57.81
50.31
25.04
15.79
905.73
v
I (Continued)
17281.06
P(J)
Table
21
12.65
76.65
12
29.15
691.57
11
16
06.50
15
21.11
9
10
60.98
35.54
a
(45.20)
49.74
7
14
43.36
63.65
13
33.89
77.19
5
6
96.15
85.77
03.28
790.51
3
4
(75.09)
18828.82
1
2
NJ) 18852.39
F'(J)
= 18840.75
0
J
Y
1-o
show a linear variat,ion
with t’hose of t.he t’wo other multiplet
componcnt,s.
lcinnl
vonfirmat,ion comes from a comparison of t’he rot,atjional constants detcrmincd from the three O-O bands. Table II shows t#hesc to be 0.811, 6.521, and 6.246 for t hc Iinn , :‘I11 , and “& states, r~sprc,tively~-allother variation which is t1c~:ul~ Iitlcar with 13. ;2ftrr t hc ground-state vibrat)ional differences had beell drtrrmincd it WI.‘: cavitlcllt, that its intervals ~1” = 0 t,o I and 1 to 2 ww just those observed for thv t hrw diffuse features. Brcordingly, the lat’ter art’ assigned to trdusitions from ;111~mstablc st*ate to the lowest thrct vibrational lwcls of the ground etato, itt :qqwmc~~lt with Yvcvthaus ( 1 ) . l)I8cT18sIc)s ‘l’hc natural gallium used here was presumably 60 5% (.;a@ and -lO %. ( ;:I”. ‘I’has (L”“H and Ga7’H should gi\Tc almost eclually strong lines whclr t hb isotopic doubling is resolved, yet thcw should he wough diffwenw that cwh spwtral liw can be identified with its parent isotope. Moreover, the obwr\-cd dw~bliug shollld provide a most sensitive chwk of the rotational and \-ihrutiolul :~~~lysw. This has hew found to bc the case for thr only three bands for which tloubling \v:ts rwolwd, namely the O-l band of the “III-‘S system and tht two :<-:‘,bands. OIIP of thelattrr is shown ill I’ig. 3 whcrc the doublets cshibit a spavillg \\-hic*h is almost, though not quite, illdepcndrlrt of .J. That is, the rot)atioll;ll isotope effwt is small. For this hand w would wlrulat,c~ from thr aho\-r (*ollst,:ult s Y(C+aRy)~V((;a”) = -0.38 cm-’ for J = 12 and -0.12 UK’ for .I = 16. The olwrvc4 diticnwws nrr -0.38 and -0.53 cniC’. wspwtiwly. The otlly srlcctiou rules to which wcvptiolrs hnvfx not lwwl fo~uld for this :‘II__‘x tralwit,ion are AJ = 0, fl (for R = 0, A./ = f I only) and + u -. Hut the \4olatious of the rules AS = 0 and A11 = 0, f I UT “wcdc”. Thr spiltr111cviolation is not strong enough to indiwtc Hund’s cwupling wse ((4I for t hc, t riplct statv. III faczt all cviderw indicates ww (a I ( 7). \Tick note part~icxlarl~ the> appawltt cwnstant~ multiplet spacing mcntionrtl above alld thr c+lost~obctlicliffrrwcw ill B,,‘s for !! = wI(‘(’ to tlw critrrion AB = 2B,“; :I for the swwssivv 0, 1, 2. I-Ic~rc~ .-I is the splitting collstaut, 284.!):3 cm- ‘. Nwhaus ( 1 ) has discussed the disswiation of (;;tH from the molw~~lnr st,atcls t r(xatrd hcrc into ground-state atoms ‘P + “45’.It is vspwted (8) that gallimn ‘I’,,z will give the molecular states ‘S ‘, ?I,,- , and “II1 (no others ). That, is \vh? it has IWW assumed in tht foregoing discttssioll that the Ion-rr statv was t h gl.cJlllld St:lt(', Is+. Gallium “I’:, ‘:! will givch the states ‘?I,,~, ‘%I~, ‘IT, :ud “Ed, XC: \\v~ll as OIW other with !1 = 1. ,111 of the predic*tc~d molccrdar state.s but the last, t\vo alIt :?I,,ha\-c IXWI drscarihed in the prtxsc>11twork, z’f thr diffuscl, dollt,l+ hctdrd hands arc assigned to a ‘~--Y’S’ t ransitioll. Norcover, tht> sign of t hv .I-doubling defcc+ found in Section 11 for the “II,-S’S and “II~-_J~~s bands sho\vs that. t ht> “II’ Icvc~ls are the lower components of the S-doublets. Thv s:irn(L point (~1111)~ ma&~ about InH by stlldying the datn of Svuhat1s (;ii. Itr this VOIIIIW-
60.84
52.28
44.29
36.84
29.90
23.47
a
9
10
11
12
13
54.78
37.39
20.46
503.83
87.57
71.68
79.20 79.58 66.83 67.24
47.67 la.74 19.26
89.28
47.10
88.93
73.91
96.73
73.36
796.38
98.65
(01.99)
(05.30)
(06.94)
(06.94)
(05.30)
(801.99)
598.17
21.60
21.13
43.13
42.70
63.16
62.77
al.78
41.10
79.38
56.18
al.39
26.33
(89.41)
69.85
14.79 698.79
411.97
299.85
389.00
11.14
32.24
52.42
71.59
489.92
07.43
(23.82)
39.78
54.74
68.95
(72.98)
(75.48)
(76.65)
(76.65)
(75.48)
(72.98)
(69.21)
64.63
59.08
52.52
45.20
36.71
29.67
97.98
10.72
97.64
27.49
82.27
18595.93
91.78
21.97
(16743.71)
84.56
84.42
R(J)
71.16
P(J)
0
2-l = 18606.38.
17332.74
NJ)
Y
10617.55
P(J)
0
3-3 = 16766.24
16777.18
NJ)
Y
17358.18
P(J)
7
J
o-o
v0 = 17345.78
Table I (Continued)
90.31
608.66
(12.39)
07.89
03.85
(00.08)
(197.44)
94.81
92.82
(91.74)
(89.78)
15
16
17
18
19
20
21
22
23
76.42 (95.28) 812.54 28.83 44.23
25
26
27
28
29
59.23
24
40.60
21.78
702.78
83.81
664.83
45.96
27.21
72.48
17.77
R(J)
P(J)
J
14
17.96
(60.63)
12
28.85
34.38
07.48
9
38.70
(992.14)
47.41
8
(41.11)
11
71.77
7
(41.11)
40.30
(38.10)
10
(15.17) 094.50
6
52.87 35.14
5
68.84
3 4
(83.81)
2
32.31
25080
(18197.79)
R(J)
1
= 18207.95
18217.96
WOJ)
Y
54.59
0
J
3-2
53.95
39.79
85.67
82.10
40.45
685.04
381.56
11.26 11.79
20.02
33.83
20.61
33.24
55.92
52.11
55.41
88.74
R(J) 51.65
P(J) 488.27
-
R(J)
583.81
68.84
60.78
03.76
20.74
34.91
46.62
56.07
63.52
(69.21)
196.92
24.03
57.33
288.86
16.75
41.47
65.92
PC.0
6.137
0.181
-0.0005
1.663
3.37
Be
a,
re
r,(A)
De x lo4
4 x 10 -0.01
4.89 1.24
-0.75
1.5g2
-0.0315
0.326
6.692
20.1t.10
7.01_+.08
4.91+.08
2.62
1.62g
'-0.040
0.276
6.394
7.252.10
5.40&05
4.072.05
(4.6)
7.352.20
5.642.08
5.602.06
(4.83)
5.682_+.008
6.150_+.008
6.5282.004
3111- *
6.262.04
6.811+.003
3 iII)+
6.14k.07
6.811+.006
3n9 - *
However, the values of H, determined from the equation of Section D are not of an accuracy which -8 -1 warrants listing here. All are of the order + 10 cm . * Determined from plots of Q(J) vs. .J(J+l)and the known lower-state constants.
m.145 0.835 t The effects of terms in .J3(J+1)3in the rotational energies are apparent in all bands.
3.572.08
D3 x lo4
re
3.462.04
D2 x lo4
-0.06
3.442.04
Dl x lo4
5.170+.008
4.934+.008
5.508+.008 4.482.03
5.680+.004
5.4545.004
5.681_+.004
3.032.03
6.1322.004
5.890+.003
5.8642.004
3.422.03
6.521+.002 -
6.246_+.002
6.046+.002
Do x lo4
B3
B2
B1
BO
X1X+
Table II Rotational Constants (cm-l)
SPECTRUM
OF THE (1
:CULE
79
CD-
ID-
*-
a i
m-
”
dN
--
O-
--
CK
(urr)*-
21 I
5
d
80
GINTER
AND INNES
tion it should be emphasized that most of the constants determined here been for lower components. The shortest wavelength band of the diffuse ‘II-X’Z+ system puts the ciation energy of GaH at less than 23,700 cm-‘. The highest vibrational showing sharp fine structure ( ?I1 , 21= 3) indicates a lower limit, at 22,500 Thus the dissociation energy is probably between 2.79 and 2.9-1 ev.
have dissolevel cm-‘.
ACKNOWLEDGMENTS We are greatly indebted to Dr. Bengt Kleman for helpful discussion of the Group III hydrides. Support by the Naval Ordnance Laboratory of White Oak, Maryland under Contract X60921-5700 is gratefully acknowledged. Finally we wish to thank Mrs. Dorothy Ginter, Mr. Travis Stone, and Mr. Robert Horton for assistance with the measurements, calculations, and figures. RECEIVED:
December
12, 1960 REFERENCES
1. H. NEUHAUS, Arkiv. Pysik 14, 551 (1959). 2. B. KLEMAN, thesis, Stockholm, 1953. 3. C. N. MCKINNEY AND K. K. INNES, J. ililol. Spectroscopy
3, 235 (1959).
4. A. BvD~, 2. Physik 106, 579 (1937). 5. H. 6. F. 7. R. 8. R.
NEUHAUS, 2. Physik 162, 402 (1958). H. CRAWFORD AND T. J$RGENSEN, Phys. Rev. 47, 358 (1935). S. MULLIKEN, Revs. Modern Phys. 3, 117 (1931). S. MULLIKEN, Revs. Modern Phys. 4, 71 (1932).