James O. Hornkohl,1
Christian G. Parigger,1
and László Nemes2
1J. O. Hornkohl (jhornkoh@utsi.edu) and C. G. Parigger (cparigge@utsi.edu) are with The University of Tennessee Space Institute, 411 B. H. Goethert Parkway, Tullahoma, Tennessee 37388
2L. Nemes (nemesl@cric.chemres.hu) is with the Laboratory for Laser Spectroscopy, Chemical Research Center, Hungarian Academy of Sciences, Pusztaszeri ut 59-67, H-1025 Budapest, Hungary
A new method is presented for computation of diatomic rotational line strengths, or Hönl–London factors. The traditional approach includes separately calculating line positions and Hönl–London factors and assigning parity labels. The present approach shows that one merely computes the line strength for all possible term differences and discards those differences for which the strength vanishes. Numerical diagonalization of the upper and lower Hamiltonians is used, which directly obtains the line positions, Hönl–London factors, total parities, and e/f parities for both heteronuclear and homonuclear diatomic molecules. The fortran computer program discussed is also applicable for calculating n-photon diatomic spectra.
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Even for a single electronic state, the case a matrix elements do not compose a diagonal Hamiltonian matrix, indicating that Hund’s case a is not desirable in a physical description. However, highly accurate diatomic solutions can be found by writing the eigenfunction as a sum of case a basis functions. This sum must always include at least two electronic states (e.g., |2Σ〉 + |2Π〉) to ensure that the eigenfunction is indeed an angular momentum eigenfunction.
Table 2
Hund’s Case a Hamiltonian Matrix Elements that Mix Electronic Statesa
By mixing case a basis functions for different electronic states one relinquishes the quantum numbers Ω, Λ, and Σ, meaning that components of angular momentum Jz′, Nz′, and Sz′ are no longer constants of the motion. Strictly speaking, J and Jz are the only angular momentum constants of the motion, and the more closely one approximates this mathematical requirement of angular momentum the more closely one’s solutions will agree with experimental results.
Table 3
HLFs for the Terrestrially Abundant Isotope of C2, C2(d3IIu ↔ a3IIg) (0,0) Banda
J′
J″
Branch
p′
p″
N′
N″
FJ′
FJ″
SJ′J″
0.0
1.0
P12
+e
−e
1
1
20928.963
1555.352
19373.611
0.96178
0.0
1.0
P11
+e
−e
1
0
20928.963
1538.446
19390.517
0.03841
1.0
2.0
P11
+f
−f
0
1
20916.943
1522.542
19394.401
0.06318
1.0
2.0
P12
+f
−f
0
2
20916.943
1544.529
19372.414
1.45812
1.0
2.0
P13
+f
−f
0
3
20916.943
1561.861
19355.082
0.00723
1.0
2.0
P22
−f
−f
1
2
20932.092
1544.529
19387.564
0.03864
1.0
2.0
P23
+f
−f
1
3
20932.092
1561.861
19370.232
1.93368
1.0
1.0
Q12
+f
−e
0
1
20916.943
1555.352
19361.591
0.05431
1.0
1.0
Q11
+f
−e
0
0
20916.943
1538.446
19378.497
1.36140
1.0
1.0
Q22
+f
−f
1
1
20932.092
1555.352
19376.740
0.00325
1.0
1.0
Q21
+f
−e
1
0
20932.092
1538.446
19393.647
0.08105
1.0
0.0
R11
+f
−f
0
1
20916.943
1550.108
19366.834
0.05633
1.0
0.0
R21
+f
−f
1
1
20932.092
1550.108
19381.984
0.94367
2.0
3.0
P33
+e
−e
3
4
20941.675
1574.474
19367.201
2.93372
2.0
3.0
P32
+e
−e
3
3
20941.675
1554.105
19387.570
0.02356
2.0
3.0
P23
+e
−e
2
4
20923.686
1574.474
19349.212
0.00524
2.0
3.0
P22
+e
−e
2
3
20923.686
1554.105
19369.581
2.60804
2.0
3.0
P21
+e
−e
2
2
20923.686
1530.930
19392.756
0.04316
2.0
3.0
P11
+e
−e
1
2
20902.697
1530.930
19371.767
1.71980
2.0
2.0
Q32
+e
−f
3
2
20941.675
1544.529
19397.146
0.09560
2.0
2.0
Q33
+e
−f
3
3
20941.675
1561.861
19379.814
0.01227
2.0
2.0
Q21
+e
−f
2
1
20923.686
1522.542
19401.144
0.05588
2.0
2.0
Q22
+e
−f
2
2
20923.686
1544.529
19379.157
0.71694
2.0
2.0
Q23
+e
−f
2
3
20923.686
1561.861
19361.825
0.08784
2.0
2.0
Q11
+e
−f
1
1
20902.697
1522.542
19380.156
3.17202
2.0
2.0
Q12
+e
−f
1
2
20902.697
1544.529
19358.169
0.02739
2.0
1.0
R32
+e
−e
3
1
20941.675
1555.352
19386.323
1.90991
2.0
1.0
R31
+e
−e
3
0
20941.675
1538.446
19403.229
0.02524
2.0
1.0
R22
+e
−e
2
1
20923.686
1555.352
19368.334
0.07075
2.0
1.0
R21
+e
−e
2
0
20923.686
1538.446
19385.240
1.41308
2.0
1.0
R11
+e
−e
1
0
20902.697
1538.446
19364.252
0.08082
Although one would expect to see Λ doublets in this type of band system for both heteronuclear and homonuclear molecules, half of each Λ doublet is missing here because the nuclei have zero spin-exchange symmetry prohibits one line of each Λ doublet. J′, Upper total angular momentum quantum number; J″, Lower total angular momentum quantum number; N′, Upper total orbital angular momentum quantum number; N″, Lower total orbital angular momentum quantum number; branch, The line designation based on J′ and J″;p′, The upper total parity, + or −, followed by the upper e/f parity; p″, The lower total parity, + or −, followed by the lower e/f parity; FJ′, Term computed by diagonalization of the upper Hamiltonian, cm −1; FJ′, Term computed from lower Hamiltonian, cm−1;
, Vacuum wavenumber computed from Hamiltonian eigenvalues,
, cm−1; Sj′j″, HLF, unitless.
Table 4
Diatomic HNLs for 12C 13C, 12C 13C Swan (d3IIu ↔ a3IIg) (0,0) Band
J′
J″
Branch
p′
p″
N′
N″
Fj′
Fj″
SJ′J″
0.0
1.0
P12
−f
+f
1
1
20928.877
1555.122
19373.755
0.96431
0.0
1.0
P11
−f
+f
1
0
20928.877
1538.288
19390.589
0.03569
0.0
1.0
P11
+e
−e
1
0
20927.642
1538.236
19389.406
0.04197
0.0
1.0
P12
+e
−e
1
1
20927.642
1553.830
19373.812
0.95803
1.0
2.0
P11
−e
+e
0
1
20916.771
1522.426
19394.345
0.05996
1.0
2.0
P12
−e
+e
0
2
20916.771
1544.154
19372.616
1.45905
1.0
2.0
P13
−e
+e
0
3
20916.771
1561.294
19355.477
0.00678
1.0
2.0
P23
+f
−f
1
3
20932.965
1562.502
19370.463
1.94471
1.0
2.0
P22
+f
−f
1
2
20932.965
1544.289
19388.676
0.03225
1.0
2.0
P13
+f
−f
0
3
20916.831
1562.502
19354.329
0.00620
1.0
2.0
P12
+f
−f
0
2
20916.831
1544.289
19372.542
1.45653
1.0
2.0
P11
+f
−f
0
1
20916.831
1522.427
19394.404
0.05987
1.0
2.0
P22
−e
+e
1
2
20931.791
1544.154
19387.637
0.03653
1.0
2.0
P23
−e
+e
1
3
20931.791
1561.294
19370.497
1.93627
1.0
1.0
Q12
−e
+f
0
1
20916.771
1555.122
19361.648
0.05079
1.0
1.0
Q11
−e
+f
0
0
20916.771
1538.288
19378.483
1.37072
1.0
1.0
Q21
+f
−e
1
0
20932.965
1538.236
19394.729
0.06513
1.0
1.0
Q11
+f
−e
0
0
20916.831
1538.236
19378.595
1.37216
1.0
1.0
Q12
+f
−e
0
1
20916.831
1553.830
19363.001
0.05984
1.0
1.0
Q21
−e
+f
1
0
20931.791
1538.288
19393.503
0.07649
1.0
0.0
R11
−e
+e
0
1
20916.771
1550.055
19366.716
0.05269
1.0
0.0
R21
+f
−f
1
1
20932.965
1551.399
19381.567
0.95488
1.0
0.0
R11
+f
−f
0
1
20916.831
1551.399
19365.433
0.04540
1.0
0.0
R21
−e
+e
1
1
20931.791
1550.055
19381.736
0.94760
2.0
3.0
P11
+e
−e
1
2
20902.580
1530.514
19372.066
1.71644
2.0
3.0
P21
+e
−e
2
2
20923.118
1530.514
19392.605
0.04137
2.0
3.0
P22
+e
−e
2
3
20923.118
1553.146
19369.972
2.61317
2.0
3.0
P23
+e
−e
2
4
20923.118
1572.320
19350.798
0.00524
2.0
3.0
P33
−f
+f
3
4
20941.038
1573.435
19367.603
2.93627
2.0
3.0
P32
−f
+f
3
3
20941.038
1553.371
19387.668
0.02232
2.0
3.0
P32
+e
−e
3
3
20939.957
1553.146
19386.811
0.02430
2.0
3.0
P33
+e
−e
3
4
20939.957
1572.320
19367.637
2.92741
2.0
3.0
P23
−f
+f
2
4
20923.270
1573.435
19349.834
0.00512
2.0
3.0
P22
−f
+f
2
3
20923.270
1553.371
19369.899
2.60900
2.0
3.0
P21
−f
+f
2
2
20923.270
1530.518
19392.751
0.04125
2.0
3.0
P11
−f
+f
1
2
20902.581
1530.518
19372.063
1.71646
2.0
2.0
Q12
+e
−f
1
2
20902.580
1544.289
19358.291
0.02530
2.0
2.0
Q11
+e
−f
1
1
20902.580
1522.427
19380.153
3.18002
2.0
2.0
Q23
+e
−f
2
3
20923.118
1562.502
19360.616
0.07105
2.0
2.0
Q22
+e
−f
2
2
20923.118
1544.289
19378.829
0.72286
2.0
2.0
Q21
+e
−f
2
1
20923.118
1522.427
19400.692
0.05404
2.0
2.0
Q32
−f
+e
3
2
20941.038
1544.154
19396.884
0.09035
2.0
2.0
Q33
−f
+e
3
3
20941.038
1561.294
19379.744
0.01082
2.0
2.0
Q33
+e
−f
3
3
20939.957
1562.502
19377.455
0.01079
2.0
2.0
Q32
+e
−f
3
2
20939.957
1544.289
19395.668
0.10462
2.0
2.0
Q21
−f
+e
2
1
20923.270
1522.426
19400.844
0.05366
2.0
2.0
Q22
−f
+e
2
2
20923.270
1544.154
19379.115
0.72408
2.0
2.0
Q23
−f
+e
2
3
20923.270
1561.294
19361.976
0.08266
2.0
2.0
Q11
−f
+e
1
1
20902.581
1522.426
19380.156
3.18000
2.0
2.0
Q12
−f
+e
1
2
20902.581
1544.154
19358.427
0.02581
2.0
1.0
R11
+e
−e
1
0
20902.580
1538.236
19364.344
0.07737
2.0
1.0
R21
+e
−e
2
0
20923.118
1538.236
19384.882
1.41799
2.0
1.0
R22
+e
−e
2
1
20923.118
1553.830
19369.288
0.07427
2.0
1.0
R32
−f
+f
3
1
20941.038
1555.122
19385.916
1.91552
2.0
1.0
R31
−f
+f
3
0
20941.038
1538.288
19402.750
0.02418
2.0
1.0
R31
+e
−e
3
0
20939.957
1538.236
19401.721
0.02623
2.0
1.0
R32
+e
−e
3
1
20939.957
1553.830
19386.127
1.90584
2.0
1.0
R22
−f
+f
2
1
20923.270
1555.122
19368.147
0.06738
2.0
1.0
R21
−f
+f
2
0
20923.270
1538.288
19384.982
1.41685
2.0
1.0
R11
−f
+f
1
0
20902.581
1538.288
19364.293
0.07692
Table 5
Diatomic HNLs for 13C2, 13C2 Swan (d3IIu ↔ a3IIg) (0,0) Band
J′
J″
Branch
p′
p″
N′
N″
FJ′
FJ″
SJ′J″
0.0
1.0
P12
−f
+f
1
1
20896.632
1525.302
19371.330
0.72524
0.0
1.0
P11
−f
+f
1
0
20896.632
1508.563
19388.070
0.02489
0.0
1.0
P11
+e
−e
1
0
20895.409
1508.514
19386.894
0.00973
0.0
1.0
P12
+e
−e
1
1
20895.409
1524.002
19371.407
0.24031
1.0
2.0
P11
−e
+e
0
1
20884.434
1492.711
19391.723
0.04245
1.0
2.0
P12
−e
+e
0
2
20884.434
1514.208
19370.225
1.09618
1.0
2.0
P13
−e
+e
0
3
20884.434
1531.123
19353.311
0.00501
1.0
2.0
P23
+f
−f
1
3
20900.527
1532.345
19368.182
0.48716
1.0
2.0
P22
+f
−f
1
2
20900.527
1514.335
19386.191
0.00765
1.0
2.0
P12
+f
−f
0
2
20884.489
1514.335
19370.154
0.36469
1.0
2.0
P11
+f
−f
0
1
20884.489
1492.712
19391.778
0.01410
1.0
2.0
P22
−e
+e
1
2
20899.359
1514.208
19385.150
0.02597
1.0
2.0
P23
−e
+e
1
3
20899.359
1531.123
19368.236
1.45599
1.0
1.0
Q12
−e
+f
0
1
20884.434
1525.302
19359.131
0.03546
1.0
1.0
Q11
−e
+f
0
0
20884.434
1508.563
19375.871
1.03450
1.0
1.0
Q21
+f
−e
1
0
20900.527
1508.514
19392.013
0.01519
1.0
1.0
Q11
+f
−e
0
0
20884.489
1508.514
19375.975
0.34531
1.0
1.0
Q12
+f
−e
0
1
20884.489
1524.002
19360.487
0.01401
1.0
1.0
Q21
−e
+f
1
0
20899.359
1508.563
19390.796
0.05321
1.0
0.0
R11
−e
+e
0
1
20884.434
1520.403
19364.030
0.03678
1.0
0.0
R21
+f
−f
1
1
20900.527
1521.752
19378.775
0.23947
1.0
0.0
R11
+f
−f
0
1
20884.489
1521.752
19362.737
0.01053
1.0
0.0
R21
−e
+e
1
1
20899.359
1520.403
19378.956
0.71322
2.0
3.0
P11
+e
−e
1
2
20870.198
1500.512
19369.685
0.42868
2.0
3.0
P21
+e
−e
2
2
20890.541
1500.512
19390.029
0.00992
2.0
3.0
P22
+e
−e
2
3
20890.541
1522.849
19367.692
0.65427
2.0
3.0
P33
−f
+f
3
4
20908.228
1542.791
19365.437
2.20554
2.0
3.0
P32
−f
+f
3
3
20908.228
1523.063
19385.165
0.01630
2.0
3.0
P32
+e
−e
3
3
20907.146
1522.849
19384.297
0.00590
2.0
3.0
P33
+e
−e
3
4
20907.146
1541.657
19365.489
0.73356
2.0
3.0
P22
−f
+f
2
3
20890.682
1523.063
19367.619
1.95922
2.0
3.0
P21
−f
+f
2
2
20890.682
1500.517
19390.165
0.02947
2.0
3.0
P11
−f
+f
1
2
20870.199
1500.517
19369.682
1.28580
2.0
2.0
Q12
+e
−f
1
2
20870.198
1514.335
19355.862
0.00600
2.0
2.0
Q11
+e
−f
1
1
20870.198
1492.712
19377.486
0.79708
2.0
2.0
Q23
+e
−f
2
3
20890.541
1532.345
19358.196
0.01672
2.0
2.0
Q22
+e
−f
2
2
20890.541
1514.335
19376.206
0.18230
2.0
2.0
Q21
+e
−f
2
1
20890.541
1492.712
19397.829
0.01272
2.0
2.0
Q32
−f
+e
3
2
20908.228
1514.208
19394.019
0.06407
2.0
2.0
Q33
−f
+e
3
3
20908.228
1531.123
19377.105
0.00717
2.0
2.0
Q32
+e
−f
3
2
20907.146
1514.335
19392.811
0.02456
2.0
2.0
Q21
−f
+e
2
1
20890.682
1492.711
19397.971
0.03774
2.0
2.0
Q22
−f
+e
2
2
20890.682
1514.208
19376.473
0.54827
2.0
2.0
Q23
−f
+e
2
3
20890.682
1531.123
19359.559
0.05889
2.0
2.0
Q11
−f
+e
1
1
20870.199
1492.711
19377.488
2.39150
2.0
2.0
Q12
−f
+e
1
2
20870.199
1514.208
19355.991
0.01825
2.0
1.0
R11
+e
−e
1
0
20870.198
1508.514
19361.683
0.01823
2.0
1.0
R21
+e
−e
2
0
20890.541
1508.514
19382.027
0.35533
2.0
1.0
R22
+e
−e
2
1
20890.541
1524.002
19366.539
0.01760
2.0
1.0
R32
−f
+f
3
1
20908.228
1525.302
19382.926
1.43987
2.0
1.0
R31
−f
+f
3
0
20908.228
1508.563
19399.665
0.01730
2.0
1.0
R31
+e
−e
3
0
20907.146
1508.514
19398.632
0.00622
2.0
1.0
R32
+e
−e
3
1
20907.146
1524.002
19383.145
0.47745
2.0
1.0
R22
−f
+f
2
1
20890.682
1525.302
19365.380
0.04759
2.0
1.0
R21
−f
+f
2
0
20890.682
1508.563
19382.119
1.06565
2.0
1.0
R11
−f
+f
1
0
20870.199
1508.563
19361.636
0.05446
Tables (5)
Table 1
Hund’s Case a Hamiltonian Matrix Elements that Do Not Mix Electronic Statesa
Even for a single electronic state, the case a matrix elements do not compose a diagonal Hamiltonian matrix, indicating that Hund’s case a is not desirable in a physical description. However, highly accurate diatomic solutions can be found by writing the eigenfunction as a sum of case a basis functions. This sum must always include at least two electronic states (e.g., |2Σ〉 + |2Π〉) to ensure that the eigenfunction is indeed an angular momentum eigenfunction.
Table 2
Hund’s Case a Hamiltonian Matrix Elements that Mix Electronic Statesa
By mixing case a basis functions for different electronic states one relinquishes the quantum numbers Ω, Λ, and Σ, meaning that components of angular momentum Jz′, Nz′, and Sz′ are no longer constants of the motion. Strictly speaking, J and Jz are the only angular momentum constants of the motion, and the more closely one approximates this mathematical requirement of angular momentum the more closely one’s solutions will agree with experimental results.
Table 3
HLFs for the Terrestrially Abundant Isotope of C2, C2(d3IIu ↔ a3IIg) (0,0) Banda
J′
J″
Branch
p′
p″
N′
N″
FJ′
FJ″
SJ′J″
0.0
1.0
P12
+e
−e
1
1
20928.963
1555.352
19373.611
0.96178
0.0
1.0
P11
+e
−e
1
0
20928.963
1538.446
19390.517
0.03841
1.0
2.0
P11
+f
−f
0
1
20916.943
1522.542
19394.401
0.06318
1.0
2.0
P12
+f
−f
0
2
20916.943
1544.529
19372.414
1.45812
1.0
2.0
P13
+f
−f
0
3
20916.943
1561.861
19355.082
0.00723
1.0
2.0
P22
−f
−f
1
2
20932.092
1544.529
19387.564
0.03864
1.0
2.0
P23
+f
−f
1
3
20932.092
1561.861
19370.232
1.93368
1.0
1.0
Q12
+f
−e
0
1
20916.943
1555.352
19361.591
0.05431
1.0
1.0
Q11
+f
−e
0
0
20916.943
1538.446
19378.497
1.36140
1.0
1.0
Q22
+f
−f
1
1
20932.092
1555.352
19376.740
0.00325
1.0
1.0
Q21
+f
−e
1
0
20932.092
1538.446
19393.647
0.08105
1.0
0.0
R11
+f
−f
0
1
20916.943
1550.108
19366.834
0.05633
1.0
0.0
R21
+f
−f
1
1
20932.092
1550.108
19381.984
0.94367
2.0
3.0
P33
+e
−e
3
4
20941.675
1574.474
19367.201
2.93372
2.0
3.0
P32
+e
−e
3
3
20941.675
1554.105
19387.570
0.02356
2.0
3.0
P23
+e
−e
2
4
20923.686
1574.474
19349.212
0.00524
2.0
3.0
P22
+e
−e
2
3
20923.686
1554.105
19369.581
2.60804
2.0
3.0
P21
+e
−e
2
2
20923.686
1530.930
19392.756
0.04316
2.0
3.0
P11
+e
−e
1
2
20902.697
1530.930
19371.767
1.71980
2.0
2.0
Q32
+e
−f
3
2
20941.675
1544.529
19397.146
0.09560
2.0
2.0
Q33
+e
−f
3
3
20941.675
1561.861
19379.814
0.01227
2.0
2.0
Q21
+e
−f
2
1
20923.686
1522.542
19401.144
0.05588
2.0
2.0
Q22
+e
−f
2
2
20923.686
1544.529
19379.157
0.71694
2.0
2.0
Q23
+e
−f
2
3
20923.686
1561.861
19361.825
0.08784
2.0
2.0
Q11
+e
−f
1
1
20902.697
1522.542
19380.156
3.17202
2.0
2.0
Q12
+e
−f
1
2
20902.697
1544.529
19358.169
0.02739
2.0
1.0
R32
+e
−e
3
1
20941.675
1555.352
19386.323
1.90991
2.0
1.0
R31
+e
−e
3
0
20941.675
1538.446
19403.229
0.02524
2.0
1.0
R22
+e
−e
2
1
20923.686
1555.352
19368.334
0.07075
2.0
1.0
R21
+e
−e
2
0
20923.686
1538.446
19385.240
1.41308
2.0
1.0
R11
+e
−e
1
0
20902.697
1538.446
19364.252
0.08082
Although one would expect to see Λ doublets in this type of band system for both heteronuclear and homonuclear molecules, half of each Λ doublet is missing here because the nuclei have zero spin-exchange symmetry prohibits one line of each Λ doublet. J′, Upper total angular momentum quantum number; J″, Lower total angular momentum quantum number; N′, Upper total orbital angular momentum quantum number; N″, Lower total orbital angular momentum quantum number; branch, The line designation based on J′ and J″;p′, The upper total parity, + or −, followed by the upper e/f parity; p″, The lower total parity, + or −, followed by the lower e/f parity; FJ′, Term computed by diagonalization of the upper Hamiltonian, cm −1; FJ′, Term computed from lower Hamiltonian, cm−1;
, Vacuum wavenumber computed from Hamiltonian eigenvalues,
, cm−1; Sj′j″, HLF, unitless.
Table 4
Diatomic HNLs for 12C 13C, 12C 13C Swan (d3IIu ↔ a3IIg) (0,0) Band
J′
J″
Branch
p′
p″
N′
N″
Fj′
Fj″
SJ′J″
0.0
1.0
P12
−f
+f
1
1
20928.877
1555.122
19373.755
0.96431
0.0
1.0
P11
−f
+f
1
0
20928.877
1538.288
19390.589
0.03569
0.0
1.0
P11
+e
−e
1
0
20927.642
1538.236
19389.406
0.04197
0.0
1.0
P12
+e
−e
1
1
20927.642
1553.830
19373.812
0.95803
1.0
2.0
P11
−e
+e
0
1
20916.771
1522.426
19394.345
0.05996
1.0
2.0
P12
−e
+e
0
2
20916.771
1544.154
19372.616
1.45905
1.0
2.0
P13
−e
+e
0
3
20916.771
1561.294
19355.477
0.00678
1.0
2.0
P23
+f
−f
1
3
20932.965
1562.502
19370.463
1.94471
1.0
2.0
P22
+f
−f
1
2
20932.965
1544.289
19388.676
0.03225
1.0
2.0
P13
+f
−f
0
3
20916.831
1562.502
19354.329
0.00620
1.0
2.0
P12
+f
−f
0
2
20916.831
1544.289
19372.542
1.45653
1.0
2.0
P11
+f
−f
0
1
20916.831
1522.427
19394.404
0.05987
1.0
2.0
P22
−e
+e
1
2
20931.791
1544.154
19387.637
0.03653
1.0
2.0
P23
−e
+e
1
3
20931.791
1561.294
19370.497
1.93627
1.0
1.0
Q12
−e
+f
0
1
20916.771
1555.122
19361.648
0.05079
1.0
1.0
Q11
−e
+f
0
0
20916.771
1538.288
19378.483
1.37072
1.0
1.0
Q21
+f
−e
1
0
20932.965
1538.236
19394.729
0.06513
1.0
1.0
Q11
+f
−e
0
0
20916.831
1538.236
19378.595
1.37216
1.0
1.0
Q12
+f
−e
0
1
20916.831
1553.830
19363.001
0.05984
1.0
1.0
Q21
−e
+f
1
0
20931.791
1538.288
19393.503
0.07649
1.0
0.0
R11
−e
+e
0
1
20916.771
1550.055
19366.716
0.05269
1.0
0.0
R21
+f
−f
1
1
20932.965
1551.399
19381.567
0.95488
1.0
0.0
R11
+f
−f
0
1
20916.831
1551.399
19365.433
0.04540
1.0
0.0
R21
−e
+e
1
1
20931.791
1550.055
19381.736
0.94760
2.0
3.0
P11
+e
−e
1
2
20902.580
1530.514
19372.066
1.71644
2.0
3.0
P21
+e
−e
2
2
20923.118
1530.514
19392.605
0.04137
2.0
3.0
P22
+e
−e
2
3
20923.118
1553.146
19369.972
2.61317
2.0
3.0
P23
+e
−e
2
4
20923.118
1572.320
19350.798
0.00524
2.0
3.0
P33
−f
+f
3
4
20941.038
1573.435
19367.603
2.93627
2.0
3.0
P32
−f
+f
3
3
20941.038
1553.371
19387.668
0.02232
2.0
3.0
P32
+e
−e
3
3
20939.957
1553.146
19386.811
0.02430
2.0
3.0
P33
+e
−e
3
4
20939.957
1572.320
19367.637
2.92741
2.0
3.0
P23
−f
+f
2
4
20923.270
1573.435
19349.834
0.00512
2.0
3.0
P22
−f
+f
2
3
20923.270
1553.371
19369.899
2.60900
2.0
3.0
P21
−f
+f
2
2
20923.270
1530.518
19392.751
0.04125
2.0
3.0
P11
−f
+f
1
2
20902.581
1530.518
19372.063
1.71646
2.0
2.0
Q12
+e
−f
1
2
20902.580
1544.289
19358.291
0.02530
2.0
2.0
Q11
+e
−f
1
1
20902.580
1522.427
19380.153
3.18002
2.0
2.0
Q23
+e
−f
2
3
20923.118
1562.502
19360.616
0.07105
2.0
2.0
Q22
+e
−f
2
2
20923.118
1544.289
19378.829
0.72286
2.0
2.0
Q21
+e
−f
2
1
20923.118
1522.427
19400.692
0.05404
2.0
2.0
Q32
−f
+e
3
2
20941.038
1544.154
19396.884
0.09035
2.0
2.0
Q33
−f
+e
3
3
20941.038
1561.294
19379.744
0.01082
2.0
2.0
Q33
+e
−f
3
3
20939.957
1562.502
19377.455
0.01079
2.0
2.0
Q32
+e
−f
3
2
20939.957
1544.289
19395.668
0.10462
2.0
2.0
Q21
−f
+e
2
1
20923.270
1522.426
19400.844
0.05366
2.0
2.0
Q22
−f
+e
2
2
20923.270
1544.154
19379.115
0.72408
2.0
2.0
Q23
−f
+e
2
3
20923.270
1561.294
19361.976
0.08266
2.0
2.0
Q11
−f
+e
1
1
20902.581
1522.426
19380.156
3.18000
2.0
2.0
Q12
−f
+e
1
2
20902.581
1544.154
19358.427
0.02581
2.0
1.0
R11
+e
−e
1
0
20902.580
1538.236
19364.344
0.07737
2.0
1.0
R21
+e
−e
2
0
20923.118
1538.236
19384.882
1.41799
2.0
1.0
R22
+e
−e
2
1
20923.118
1553.830
19369.288
0.07427
2.0
1.0
R32
−f
+f
3
1
20941.038
1555.122
19385.916
1.91552
2.0
1.0
R31
−f
+f
3
0
20941.038
1538.288
19402.750
0.02418
2.0
1.0
R31
+e
−e
3
0
20939.957
1538.236
19401.721
0.02623
2.0
1.0
R32
+e
−e
3
1
20939.957
1553.830
19386.127
1.90584
2.0
1.0
R22
−f
+f
2
1
20923.270
1555.122
19368.147
0.06738
2.0
1.0
R21
−f
+f
2
0
20923.270
1538.288
19384.982
1.41685
2.0
1.0
R11
−f
+f
1
0
20902.581
1538.288
19364.293
0.07692
Table 5
Diatomic HNLs for 13C2, 13C2 Swan (d3IIu ↔ a3IIg) (0,0) Band