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The IR spectrum of T218O
JOURNAL OF MOLECULAR SPECTROSCOPY 104, ‘to5-4
13 ( 1984)
The IR Spectrum of T2”0 IR (1, 2) and microwave (3, 4) spectra of tritiated water (160) have been studied extensively. Recently we observed the ir spectrum of T*‘*O, whose fundamentals and band constants of Y*will be reported in the present study. T2’s0 was obtained from the reaction of 4 Ci of T2 with excess ‘*Or (99.9%) on platinum black at the Tritium Research Center, Toyama University. The ir spectrum in Fig. 1 was recorded by use of the JASCOIRA-3 spectrometer at a temperature of about 80°C. The observed wavenumbers were calibrated with reference to the spectra of ammonia and carbon dioxide (5), and were believed to be accurate to kO.2 cm-’ for vs and +0.5 cm-’ for Y, and q. They are given for or in Table I. The bands in the region 2300-2350 cm-’ are strong in intensity and may correspond to Q branches of Y,. The strong band at 2344 cm-i, which is arrowed by a in Fig 1A, may correspond to a Q branch of T2i60 at 2364 cm-’ (2). Then us is estimated to be at 2350 + 5 cm-’ with reference to Y, of T2i60 at 2370 + 5 cm-’ (2). Fundamentals of T2’*0 may be estimated from normal frequencies and anharmonic constants. Normal frequencies of T2’*0 were estimated from force constants of T2160 (6, 7) and anharmonic constants, x,, from the relation (8): (x~)TI~Y) = (w~j~~ldX~~lso/(~~j~*,~, where wk denotes a normal frequency. The
2450
2400
2350
2300 I
2250 I
2200 I
(Cf.&2150
I
B
1100
1060
1020
980
940
(cm-‘)
goo
FIG. 1. (A) The IR spectrum of the Y, and v3 regions. (B) The observed (a) and calculated (b) spectra of the v2 region.
405
0022-2852184 $3.00 Copyright Q 1984 by Acxkmic
F’ress,Inc.
All rights of reproduction in my form reserved.
NOTES
406
TABLE I The Observed and Calculated Frequencies (cm-‘) and Their Assignments of v2 Lines of Tz”O Assi.p.
Calc.
Ohs.
J' T 1093.52’
1093.v
50
1092.69*
61
Sl
1092.34
12_7
11-7
53
41
52
42
1092.s* 1085.20* 1084.99
1084.9'
62
J",
i 1084.91 1083.62
10-S
g-5
75
73
1083.37
IS-15
14-13
{ 1083.25
13-11
12-g
1083.2
1077.00
44
32
{ 1076.97*
43
33
1071.73
13-12
12-12
1071.72
13-13
12-11
11-8
'O-8
1075.a*
1072.3
i 1071.41 1070.21* 1070.3* { 1069.98 1068.7
1066.1
6-l
s-1
11-9
IO-7
1068.78
51
4-l
1065.81
12-11
11-11
1065.79
12
11-10
1 1065.60
-12
IO-7
g-7
1062.89
63
( 1062.87
108
'6
1062.09
73
71
1062.3
%
1061.7 ( 1061.98
81
8-l
1060.16
9-6
1059.83
11-10
IO-10
i 1059.78
II-11
10-g
1060.3
1057.94*
1058.0*
41
31
1055.2?
8-5
7-5
1055.21
9-7
8-5
1053.79
10-g
g-9
1055.3 (
8-6
1054.2 I 1053.69
10-10
g-0
1050.75
7-4
6-4
1050.69"
33
21
1051.0"
*They are weighted in the least-squares fit.
407
NOTES TABLE I-Continued Assign.
Calc.
Obs.
J' T
1047.2
J'lT
1047.80
10-3
10-5
1047.71
'-8
8-8
1047.50
9-9
8-7
1046.79
8-6
7-4
1046.45*
6-3
s-3
1043.83
43
4l
1043.74
7O
7-2
1043.56*
I
1046.6* I
1043.3*
%
6-l
1041.96
5-2
4-2
1041.70
9-7
g-9
1041.63
8-7
7-7
1041.57
62
60
1039.36
71
7-l
1037.46
7-5
6-3
I 1037.42
g-5
8-7
1037.04
31
2-l
1036.93*
4-l
3-1
1034.6
1034.66
7-7
6-5
1032.8
1032.87
9-l
9-3
1029.70*
6-5
5-5
1
1041.9
1 1039.4 1037.4
1036.8* i
1029.7* ( 1029.61 1028.07 1027.87*
6-l
6-3
11-3
11-5
6-6
5-4
1027.8" 1027.79
50
5-2
1 1027.74
11-5
11-7
1027.29
6-4
5-2
1026.92
9-5
9-7
1026.68*
41
4-l
1026.41
22
10
1025.96*
1026.8*
1
6-3
6-S
i 1025.86
7-S
7-7
1024.91
7-3
6-I
1024.90
33
31
1024.61"
21
11
1026.1"
1024.4*
NOTES
408 TABLE
Obs.
1024.1*
I-Continued Assign.
Calc.
J'T
J" T
1024.03"
5-4
4-4
1021.14*
51
5-1
5-2
5-4
s-5
4-3
8-4
8-6
60
6-2
1021.2* I 1021.11 1020.8"
1018.8*
1020.64*
1018.74 i 1019.02 1018.57*
4-3
3-3
g-3
9-5
6-4
6-6
4-1
4-3
7-l
7-3
5-3
4-l
8-2
8-4
1018.0 1017.79 i 1017.92
1016.9 1016.56 1016.93 1016.46 i 1017.02
1013.0 1012.86 1012.68 i 1013.12
3-2
2-2
4-4
3-2
7-3
7-5
1010.3*
1010.26"
5-3
5-5
1007.2*
1007.29*
2-1
l-1
1005.88"
5-1
5-3
1006.0* 1005.72
31
3-l
1005.2"
1005.16*
40
4-2
1004.7"
1004.51'
3-3
2-l
1003.6'
1003.90'
4-2
4-4
QQQ.l*
999.13"
3-l
3-3
995.98*
20
2-2
2-2
10
994.0*
994.17*
11
l-1
978.2*
978.21*
l-1
11
976.47
10
2-2
976.37*
2-2
20
973.4*
973.19*
3-3
3-l
969.5*
969.66*
4-2
40
995.8' i 995.82
976.3R
409 TABLE I-continued Obs.
Calc.
Assign. J'T
969.18 968.7*
3-l
J",
31
968.91"
5-3
5-1
968.40
4-4
4-2
968.01
2O
22
967.6*
1 967.65*
2-l
3-3
966.5*
966.57*
6-4
6-2
965.3*
964.95"
1-l
2-l
963.2”
963.48"
2-l
21
962.40
7-5
7-3
962.11
7-3
7-l
962.02"
5-5
5-3
959.11
3-2
4-4
958.95*
2-2
3-2
958.40
4-l
5-3
961.8*
i 959.0*
t 958.7*
I 958.39* 957.69
5-l "-6
51 10-4
957.3”
r 957.36" 955.23
4-3
4-l
10-4
IO-2
955.1*
t 955.10*
31
33
953.28"
3-3
4-3
953.18
4-l
41
952.96
5-4
5-2
951.0*
951.06"
4-3
5-5
950.11
950.36*
953.3*
i
11
21
947.75"
6-5
6-3
947.70
5-2
6-4
947.56
4-4
5-4
I 947.26
7-l
71
943.92
4l
43
943.73
941.1"
943.7*
20
30
i 943.69*
6-l
61
943.46*
5-4
6-6
943.23
8-5
8-3
5-5
6-5
943.2" 941.7*
941.53*
NOTES
410
TABLE I-continued Obs.
Calc.
Assign. J'T
938.37
10-5
LO-3
937.92
3-l
4-l
937.69
2-l
31
937.61
6-3
7-5
936.15
6-S
7-7
935.39
8-7
8-5
935.28
7l
73
935.16
6-6
7-6
935.06
8-l
81
934.88
61
63
929.69
22
32
929.45
8-3
g-5
929.41"
21
33
928.50
7-7
8-7
928.37
7-4
'-6
1 928.31
938.1
936.4
935.3
929.4”
J'lT
I i
928.4
921.9*
5-3
6-3
921.97'
31
41
921.89
8-7
g-9
( 921.66
'-8
'-8
920.74
12-g
12_7
920.8
i 920.56
30
42
919.96
8-5
9-7
i 919.63
7-5
8-5
915.08
40
50
914.78
9-a
lo-la
914.75
'-6
'-6
914.67
g-9
10-g
910.91
4-1
51
910.88*
33
43
32
44
919.7
914.8
I
910.9"
i 910.85
909.5
909.72
4-3
s-1
909.29
9-7
10-7
909.26
s-1
6-l
411
NOTES TABLE I-Continued Obs.
J’r
J” T
10-g
ll-11
lo-10
11-10
10-S
11-7
902.63
42
s2
902.43*
41
s3
907.63
907.6
907.58 907.28
902.5*
900.68 900.42
900.4
900.40 894.63 894.4
i
894.59
893.48 893.0
886.2
869.2
862.2
8-3 12-12
ll-11
12-11
Sl
61
9-S
10-S
44
54
43
55
i
=-11
13-13
893.15
885.82
885.10 884.87
877.4
7-3 11-10
i
885.12 885.3
Assign.
Calc.
877.40
868.99
862.61
i 12-12
13-12
i 13-12
14-14
l3-13
14-13
53
63
s2
64
6-1
71
SS
65
s4
66
64
74
63
75
66
76
65
77
locations of the fundamentals thus obtained are Y, = 2220, Y*= 988, and Y) = 2346 cm-‘. Since Y, is a B-type band, it is estimated to be at 2228 cm-‘, which is arrowed by b in Fig. lA, with reference to the calculated one. The rotation-vibration spectrum of usin Fig. IB was analyzed on the basis of a rigid rotor approximation. The band constants estimated initially from the ir study (I) of Ts’60 are given in the tirst column of Table II and those of T2i60 are also given in the last column. The results are given in Tables I and II and Fig. IBb. In Table II the inertia defect (A) and the atomic distance (r) and
412
NOTES TABLE II The Band Constants (cm-‘) of v2 of T2180 T2 v
”
0
0
T2
initial
final(o)
988.0
985.87(S)
Ibob)
995.37
A"
10.956
10.952(8)
11.301
B"
4.837
4.863(7)
4.837
C"
3.314
3.315(S)
3.344
*,,a)
0.105
0.132
0.105
r"(A)
0.9583
0.9567
0.9583
a"(") 1
180
104.97
104.81
104.97
A'
11.618
11.600(7)
11.982
B'
4.868
4.877(7)
4.868
C'
3.288
3.280(S)
3.316
,*a)
0.355
0.381
0.355
r'(A)
0.9461
0.9459
0.9461
106.41
a '(")
a)10-40g.cmZ.
106.32
106.41
b)F,om Ref. 1.
from the microwave study (3) of T2160 (r” = 0.957OA, a” = IO4.85”, and A” = 0.130 X IO-” g cm*). This indicates that the band constants obtained are reliable. A Coriohs coupling constant may be calculated from the relation (9. 10) (!%)f = {Ai - F,,/(G-‘)i,M&
-
X2),
(1)
where the superscript c indicates the component parallel to the C axis, Xi = 4tr2c2uf, Fii is the F matrix element, and (G-‘), , isthe matrix element of the G-’ matrix. Then we can calculate inertia defects, A, (9, I I), by the use of the fundamentals. The results obtained are summarized in Table III. It is found from Tables II and III that the vibrational analysis is consistent with the rotation-vibration analysis of v2. TABLE III The Force Constants and the Related Constants K(O-T)
8.086
H(T-O-T)
0.883
F(T..-T)
-0.316
F11
7.690
c2 (513)c
0.0474
A"
c
0.125
A'c
0.388
K, F and Fll/mdyne*A -l. H/mdyne-A.
NOTES
413
ACKNOWLEDGMENTS We are deeply indebted to Professor K. Watanabe and Mr. M. Matsuyama of the Tritium Research Center, Toyama University, for their advice in the handling of tritium. REFERENCES 1. R. A. CARPENTER, N. M. GAILAR, H. W. MORGAN, AND P. A. STAATS,J. Mol. Spectrosc. 44, 197205 ( 1972). 2. P. A. STAA~S,H. W. MORGAN, AND J. H. GOLDSTEIN,J. Chem. Phys. 24,9 16-917 (1956). 3. F. C. DE LUCIA, P. HELMINGER,W. GORDY, H. W. MORGAN, AND P. A. STAATS,Phys. Rev. 8,27852791 (1973). 4. P. HELMINGER,F. C. DE LUCIA, W. GORDY, P. A. STAATS,AND H. W. MORGAN, Phys. Rev. 10, 1072-1081 (1974). 5. A. R. D~WNIE, M. C. MAGOON, T. PURCELL,AND B. CRAWFORD,JR., J. Opt. Sot. Amer. 43,941951 (1953). 6. W. F. LIBBY,J. Chem. Phys. 11, 101-109 (1943). 7. P. THIRUGNANASAMBANDAUAND S. MOHAN, J. Chem. Phys. 61.470-477 (1974). 8. G. HERZBERG,“Infrared and Raman Spectra of Polyatomic Molecules,” Van Nostrand, Princeton, 1945. 9. Y. MORINO, Y. KIKUCHI, S. SAITO,AND E. HIROTA,J. Mol. Spectrosc. 13, 95-l 18 (1964). 10. J. H. MEAL AND S. R. POLO, J. Chem. Phys. 24, 1119-l 125 (1956); 24, 1126-I 133 (1956). Il. J. BELLET,W. J. LA~RTY, AND G. STEENBECKELIERS, J. Mol. Spectrosc. 47, 388-402 (1973). I. KAN~~AKA M. TSUCHIDA K. KAWAI T. TAKEUCHI
Factdty of Science Toyama University Gofuku. Toyama 930, Japan Received September 30, 1983
13 ( 1984)
The IR Spectrum of T2”0 IR (1, 2) and microwave (3, 4) spectra of tritiated water (160) have been studied extensively. Recently we observed the ir spectrum of T*‘*O, whose fundamentals and band constants of Y*will be reported in the present study. T2’s0 was obtained from the reaction of 4 Ci of T2 with excess ‘*Or (99.9%) on platinum black at the Tritium Research Center, Toyama University. The ir spectrum in Fig. 1 was recorded by use of the JASCOIRA-3 spectrometer at a temperature of about 80°C. The observed wavenumbers were calibrated with reference to the spectra of ammonia and carbon dioxide (5), and were believed to be accurate to kO.2 cm-’ for vs and +0.5 cm-’ for Y, and q. They are given for or in Table I. The bands in the region 2300-2350 cm-’ are strong in intensity and may correspond to Q branches of Y,. The strong band at 2344 cm-i, which is arrowed by a in Fig 1A, may correspond to a Q branch of T2i60 at 2364 cm-’ (2). Then us is estimated to be at 2350 + 5 cm-’ with reference to Y, of T2i60 at 2370 + 5 cm-’ (2). Fundamentals of T2’*0 may be estimated from normal frequencies and anharmonic constants. Normal frequencies of T2’*0 were estimated from force constants of T2160 (6, 7) and anharmonic constants, x,, from the relation (8): (x~)TI~Y) = (w~j~~ldX~~lso/(~~j~*,~, where wk denotes a normal frequency. The
2450
2400
2350
2300 I
2250 I
2200 I
(Cf.&2150
I
B
1100
1060
1020
980
940
(cm-‘)
goo
FIG. 1. (A) The IR spectrum of the Y, and v3 regions. (B) The observed (a) and calculated (b) spectra of the v2 region.
405
0022-2852184 $3.00 Copyright Q 1984 by Acxkmic
F’ress,Inc.
All rights of reproduction in my form reserved.
NOTES
406
TABLE I The Observed and Calculated Frequencies (cm-‘) and Their Assignments of v2 Lines of Tz”O Assi.p.
Calc.
Ohs.
J' T 1093.52’
1093.v
50
1092.69*
61
Sl
1092.34
12_7
11-7
53
41
52
42
1092.s* 1085.20* 1084.99
1084.9'
62
J",
i 1084.91 1083.62
10-S
g-5
75
73
1083.37
IS-15
14-13
{ 1083.25
13-11
12-g
1083.2
1077.00
44
32
{ 1076.97*
43
33
1071.73
13-12
12-12
1071.72
13-13
12-11
11-8
'O-8
1075.a*
1072.3
i 1071.41 1070.21* 1070.3* { 1069.98 1068.7
1066.1
6-l
s-1
11-9
IO-7
1068.78
51
4-l
1065.81
12-11
11-11
1065.79
12
11-10
1 1065.60
-12
IO-7
g-7
1062.89
63
( 1062.87
108
'6
1062.09
73
71
1062.3
%
1061.7 ( 1061.98
81
8-l
1060.16
9-6
1059.83
11-10
IO-10
i 1059.78
II-11
10-g
1060.3
1057.94*
1058.0*
41
31
1055.2?
8-5
7-5
1055.21
9-7
8-5
1053.79
10-g
g-9
1055.3 (
8-6
1054.2 I 1053.69
10-10
g-0
1050.75
7-4
6-4
1050.69"
33
21
1051.0"
*They are weighted in the least-squares fit.
407
NOTES TABLE I-Continued Assign.
Calc.
Obs.
J' T
1047.2
J'lT
1047.80
10-3
10-5
1047.71
'-8
8-8
1047.50
9-9
8-7
1046.79
8-6
7-4
1046.45*
6-3
s-3
1043.83
43
4l
1043.74
7O
7-2
1043.56*
I
1046.6* I
1043.3*
%
6-l
1041.96
5-2
4-2
1041.70
9-7
g-9
1041.63
8-7
7-7
1041.57
62
60
1039.36
71
7-l
1037.46
7-5
6-3
I 1037.42
g-5
8-7
1037.04
31
2-l
1036.93*
4-l
3-1
1034.6
1034.66
7-7
6-5
1032.8
1032.87
9-l
9-3
1029.70*
6-5
5-5
1
1041.9
1 1039.4 1037.4
1036.8* i
1029.7* ( 1029.61 1028.07 1027.87*
6-l
6-3
11-3
11-5
6-6
5-4
1027.8" 1027.79
50
5-2
1 1027.74
11-5
11-7
1027.29
6-4
5-2
1026.92
9-5
9-7
1026.68*
41
4-l
1026.41
22
10
1025.96*
1026.8*
1
6-3
6-S
i 1025.86
7-S
7-7
1024.91
7-3
6-I
1024.90
33
31
1024.61"
21
11
1026.1"
1024.4*
NOTES
408 TABLE
Obs.
1024.1*
I-Continued Assign.
Calc.
J'T
J" T
1024.03"
5-4
4-4
1021.14*
51
5-1
5-2
5-4
s-5
4-3
8-4
8-6
60
6-2
1021.2* I 1021.11 1020.8"
1018.8*
1020.64*
1018.74 i 1019.02 1018.57*
4-3
3-3
g-3
9-5
6-4
6-6
4-1
4-3
7-l
7-3
5-3
4-l
8-2
8-4
1018.0 1017.79 i 1017.92
1016.9 1016.56 1016.93 1016.46 i 1017.02
1013.0 1012.86 1012.68 i 1013.12
3-2
2-2
4-4
3-2
7-3
7-5
1010.3*
1010.26"
5-3
5-5
1007.2*
1007.29*
2-1
l-1
1005.88"
5-1
5-3
1006.0* 1005.72
31
3-l
1005.2"
1005.16*
40
4-2
1004.7"
1004.51'
3-3
2-l
1003.6'
1003.90'
4-2
4-4
QQQ.l*
999.13"
3-l
3-3
995.98*
20
2-2
2-2
10
994.0*
994.17*
11
l-1
978.2*
978.21*
l-1
11
976.47
10
2-2
976.37*
2-2
20
973.4*
973.19*
3-3
3-l
969.5*
969.66*
4-2
40
995.8' i 995.82
976.3R
409 TABLE I-continued Obs.
Calc.
Assign. J'T
969.18 968.7*
3-l
J",
31
968.91"
5-3
5-1
968.40
4-4
4-2
968.01
2O
22
967.6*
1 967.65*
2-l
3-3
966.5*
966.57*
6-4
6-2
965.3*
964.95"
1-l
2-l
963.2”
963.48"
2-l
21
962.40
7-5
7-3
962.11
7-3
7-l
962.02"
5-5
5-3
959.11
3-2
4-4
958.95*
2-2
3-2
958.40
4-l
5-3
961.8*
i 959.0*
t 958.7*
I 958.39* 957.69
5-l "-6
51 10-4
957.3”
r 957.36" 955.23
4-3
4-l
10-4
IO-2
955.1*
t 955.10*
31
33
953.28"
3-3
4-3
953.18
4-l
41
952.96
5-4
5-2
951.0*
951.06"
4-3
5-5
950.11
950.36*
953.3*
i
11
21
947.75"
6-5
6-3
947.70
5-2
6-4
947.56
4-4
5-4
I 947.26
7-l
71
943.92
4l
43
943.73
941.1"
943.7*
20
30
i 943.69*
6-l
61
943.46*
5-4
6-6
943.23
8-5
8-3
5-5
6-5
943.2" 941.7*
941.53*
NOTES
410
TABLE I-continued Obs.
Calc.
Assign. J'T
938.37
10-5
LO-3
937.92
3-l
4-l
937.69
2-l
31
937.61
6-3
7-5
936.15
6-S
7-7
935.39
8-7
8-5
935.28
7l
73
935.16
6-6
7-6
935.06
8-l
81
934.88
61
63
929.69
22
32
929.45
8-3
g-5
929.41"
21
33
928.50
7-7
8-7
928.37
7-4
'-6
1 928.31
938.1
936.4
935.3
929.4”
J'lT
I i
928.4
921.9*
5-3
6-3
921.97'
31
41
921.89
8-7
g-9
( 921.66
'-8
'-8
920.74
12-g
12_7
920.8
i 920.56
30
42
919.96
8-5
9-7
i 919.63
7-5
8-5
915.08
40
50
914.78
9-a
lo-la
914.75
'-6
'-6
914.67
g-9
10-g
910.91
4-1
51
910.88*
33
43
32
44
919.7
914.8
I
910.9"
i 910.85
909.5
909.72
4-3
s-1
909.29
9-7
10-7
909.26
s-1
6-l
411
NOTES TABLE I-Continued Obs.
J’r
J” T
10-g
ll-11
lo-10
11-10
10-S
11-7
902.63
42
s2
902.43*
41
s3
907.63
907.6
907.58 907.28
902.5*
900.68 900.42
900.4
900.40 894.63 894.4
i
894.59
893.48 893.0
886.2
869.2
862.2
8-3 12-12
ll-11
12-11
Sl
61
9-S
10-S
44
54
43
55
i
=-11
13-13
893.15
885.82
885.10 884.87
877.4
7-3 11-10
i
885.12 885.3
Assign.
Calc.
877.40
868.99
862.61
i 12-12
13-12
i 13-12
14-14
l3-13
14-13
53
63
s2
64
6-1
71
SS
65
s4
66
64
74
63
75
66
76
65
77
locations of the fundamentals thus obtained are Y, = 2220, Y*= 988, and Y) = 2346 cm-‘. Since Y, is a B-type band, it is estimated to be at 2228 cm-‘, which is arrowed by b in Fig. lA, with reference to the calculated one. The rotation-vibration spectrum of usin Fig. IB was analyzed on the basis of a rigid rotor approximation. The band constants estimated initially from the ir study (I) of Ts’60 are given in the tirst column of Table II and those of T2i60 are also given in the last column. The results are given in Tables I and II and Fig. IBb. In Table II the inertia defect (A) and the atomic distance (r) and
412
NOTES TABLE II The Band Constants (cm-‘) of v2 of T2180 T2 v
”
0
0
T2
initial
final(o)
988.0
985.87(S)
Ibob)
995.37
A"
10.956
10.952(8)
11.301
B"
4.837
4.863(7)
4.837
C"
3.314
3.315(S)
3.344
*,,a)
0.105
0.132
0.105
r"(A)
0.9583
0.9567
0.9583
a"(") 1
180
104.97
104.81
104.97
A'
11.618
11.600(7)
11.982
B'
4.868
4.877(7)
4.868
C'
3.288
3.280(S)
3.316
,*a)
0.355
0.381
0.355
r'(A)
0.9461
0.9459
0.9461
106.41
a '(")
a)10-40g.cmZ.
106.32
106.41
b)F,om Ref. 1.
from the microwave study (3) of T2160 (r” = 0.957OA, a” = IO4.85”, and A” = 0.130 X IO-” g cm*). This indicates that the band constants obtained are reliable. A Coriohs coupling constant may be calculated from the relation (9. 10) (!%)f = {Ai - F,,/(G-‘)i,M&
-
X2),
(1)
where the superscript c indicates the component parallel to the C axis, Xi = 4tr2c2uf, Fii is the F matrix element, and (G-‘), , isthe matrix element of the G-’ matrix. Then we can calculate inertia defects, A, (9, I I), by the use of the fundamentals. The results obtained are summarized in Table III. It is found from Tables II and III that the vibrational analysis is consistent with the rotation-vibration analysis of v2. TABLE III The Force Constants and the Related Constants K(O-T)
8.086
H(T-O-T)
0.883
F(T..-T)
-0.316
F11
7.690
c2 (513)c
0.0474
A"
c
0.125
A'c
0.388
K, F and Fll/mdyne*A -l. H/mdyne-A.
NOTES
413
ACKNOWLEDGMENTS We are deeply indebted to Professor K. Watanabe and Mr. M. Matsuyama of the Tritium Research Center, Toyama University, for their advice in the handling of tritium. REFERENCES 1. R. A. CARPENTER, N. M. GAILAR, H. W. MORGAN, AND P. A. STAATS,J. Mol. Spectrosc. 44, 197205 ( 1972). 2. P. A. STAA~S,H. W. MORGAN, AND J. H. GOLDSTEIN,J. Chem. Phys. 24,9 16-917 (1956). 3. F. C. DE LUCIA, P. HELMINGER,W. GORDY, H. W. MORGAN, AND P. A. STAATS,Phys. Rev. 8,27852791 (1973). 4. P. HELMINGER,F. C. DE LUCIA, W. GORDY, P. A. STAATS,AND H. W. MORGAN, Phys. Rev. 10, 1072-1081 (1974). 5. A. R. D~WNIE, M. C. MAGOON, T. PURCELL,AND B. CRAWFORD,JR., J. Opt. Sot. Amer. 43,941951 (1953). 6. W. F. LIBBY,J. Chem. Phys. 11, 101-109 (1943). 7. P. THIRUGNANASAMBANDAUAND S. MOHAN, J. Chem. Phys. 61.470-477 (1974). 8. G. HERZBERG,“Infrared and Raman Spectra of Polyatomic Molecules,” Van Nostrand, Princeton, 1945. 9. Y. MORINO, Y. KIKUCHI, S. SAITO,AND E. HIROTA,J. Mol. Spectrosc. 13, 95-l 18 (1964). 10. J. H. MEAL AND S. R. POLO, J. Chem. Phys. 24, 1119-l 125 (1956); 24, 1126-I 133 (1956). Il. J. BELLET,W. J. LA~RTY, AND G. STEENBECKELIERS, J. Mol. Spectrosc. 47, 388-402 (1973). I. KAN~~AKA M. TSUCHIDA K. KAWAI T. TAKEUCHI
Factdty of Science Toyama University Gofuku. Toyama 930, Japan Received September 30, 1983