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Table 1 Overview of the spectroscopic and graph-theoretical characteristics of the four molecules selected for this study, H\(_2^{~16}\)O [23], \(^{32}\)S\(^{16}\)O\(_2\) [24], H\(_2^{~12}\)C\(^{16}\)O [25], and \(^{14}\)NH\(_{3}\) [26]; unc. = uncertainty, \(|H_i|\) is the number of vertices in the \(H_i\) subgraph, \(u_i\) is \(|H_i|/l_i\), where \(l_i\) is the shortest path length from \(h_0\) to \(h_i\), and \(h_i\) is the contraction of \(H_i\) to a single vertex

From: Selecting lines for spectroscopic (re)measurements to improve the accuracy of absolute energies of rovibronic quantum states

Molecule

Unc. threshold

\(|H_0|\)

Top suggestions

 

(cm\(^{-1}\))

 

\(u_i\)

\(|H_i|\)

\(l_i\)

Transition pool, if \(l_i=1\)

H\(_2^{~16}\)O

\(1\times 10^{-6}\)

165

No suggestions

 

\(5 \times 10^{-6}\)

207

43

43

1

405

   

39

39

1

330

 

\(1\times 10^{-5}\)

212

45

45

1

424

   

43

43

1

360

   

29

29

1

267

 

\(5 \times 10^{-5}\)

910

No suggestions

 

\(1\times 10^{-4}\)

1038

No suggestions

 

\(5 \times 10^{-4}\)

4274

86

86

1

26

 

\(1\times 10^{-3}\)

4831

88

88

1

27

 

\(5 \times 10^{-3}\)

15 278

14

14

1

2

\(^{32}\)S\(^{16}\)O\(_2\)

\(1 \times 10^{-6}\)

3

32

32

1

1

   

8

16

2

 

\(5 \times 10^{-6}\)

139

59

118

2

   

27

27

1

6

 

\(1 \times 10^{-5}\)

157

71

142

2

   

29

29

1

11

   

28

28

1

36

 

\(5 \times 10^{-5}\)

405

91.5

183

2

   

56

56

1

89

 

\(1 \times 10^{-4}\)

407

91.5

183

2

   

91

91

1

168

 

\(5 \times 10^{-4}\)

14216

No suggestions

 

\(1 \times 10^{-3}\)

14928

No suggestions

 

\(5 \times 10^{-3}\)

15129

No suggestions

H\(_2^{~12}\)C\(^{16}\)O

\(1 \times 10^{-6}\)

8

12

12

1

1

   

8

8

1

3

 

\(5 \times 10^{-6}\)

37

35.5

71

2

   

14.5

29

2

   

14

14

1

43

   

14

14

1

35

   

13

13

1

30

 

\(1 \times 10^{-5}\)

37

36

72

2

   

14.5

29

2

   

14

14

1

43

   

14

14

1

35

   

13

13

1

30

 

\(5 \times 10^{-5}\)

41

36

72

2

   

14.5

29

2

   

14

14

1

43

   

14

14

1

35

   

13

13

1

30

 

\(1 \times 10^{-4}\)

41

36

72

2

   

14.5

29

2

   

14

14

1

43

   

14

14

1

35

   

13

13

1

30

 

\(5 \times 10^{-4}\)

3699

12

12

1

3

 

\(1 \times 10^{-3}\)

4221

18

18

1

3

 

\(5 \times 10^{-3}\)

4981

No suggestions

\(^{14}\)NH\(_{3}\)

\(5 \times 10^{-6}\)

151

14

14

1

6

 

\(1 \times 10^{-5}\)

153

38

38

1

293

   

30

30

1

299

 

\(5 \times 10^{-5}\)

192

38

38

1

349

   

30

30

1

366

   

28

28

1

41

 

\(1 \times 10^{-4}\)

512

86

86

1

76

 

\(5 \times 10^{-4}\)

2497

20

20

1

4

 

\(1 \times 10^{-3}\)

3663

32

32

1

1

 

\(5 \times 10^{-3}\)

4649

53

53

1

3