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Table 5 Behaviour of the likelihood estimator: ten first knapsack fragments for CFC-11 and \(\text {CCl}_{{4}}\), set out in order according to their likelihood value calculated at the first iteration of Step 5. Some fragments may be deleted at subsequent iterations

From: Automated fragment formula annotation for electron ionisation, high resolution mass spectrometry: application to atmospheric measurements of halocarbons

Fragment

Exact mass

% Assigned signal of the fragment

% Assigned signal of all (sub)fragments

Likelihood

Ranking

Maximal fragment?

CFC-11 (\(\text {CFCl}_{{3}}\))

 \(\text {CFCl}_{{3}}^{+}\)

135.90496

0.0

98.4

88.6

1

True

 \(\text {CFCl}_{{2}}^{+}\)

100.93611

81.9

96.3

84.3

2

False

 CFCl\(^{+}\)

65.96726

5.6

11.9

11.9

3

False

 *CHFCl\(^{+}\)

66.97508

0.0

12.0

9.3

4

True

  \(\text {CCl}_{{3}}^{+}\)

116.90656

2.1

10.0

8.0

5

False

* \(\text {CHCl}_{{3}}^{+}\)

117.91438

0.0

10.2

7.9

6

True

  \(\text {CCl}_{{2}}^{+}\)

81.93771

2.6

8.0

6.0

7

False

*  \(\text {CHCl}_{{2}}^{+}\)

82.94553

0.0

8.1

5.8

8

False

 CCl\(^{+}\)

46.96885

3.1

5.4

5.4

9

False

 \(\text {C}_{{3}}\text {Cl}_{{2}}^{+}\)

105.93771

0.0

8.0

3.2

10

False

\(\text {CCl}_{{4}}\)

 \(\text {CCl}_{{3}}^{+}\)

116.90656

71.2

92.4

73.9

1

False

* \(\text {CHCl}_{{3}}^{+}\)

117.91438

0.4

93.9

73.0

2

True

* \(\text {CHCl}_{{2}}^{+}\)

82.94553

0.5

22.3

16.0

3

False

 \(\text {CCl}_{{2}}^{+}\)

81.93771

11.6

21.2

15.9

4

False

 *\(\text {COCl}_{{2}}^{+}\)

97.93262

0.3

21.8

12.1

5

True

 CCl\(^{+}\)

46.96885

5.5

9.5

9.5

6

False

* HCl\(^{+}\)

35.97668

0.7

4.7

4.7

7

False

 Cl\(^{+}\)

34.96885

4.0

4.0

4.0

8

False

* \(\text {CF}_{{2}}\)Cl\(^{+}\)

84.96566

0.2

9.7

3.6

9

True

* \(\text {OCl}_{{2}}^{+}\)

85.93262

0.3

4.3

2.2

10

False

  1. \(1^{\mathrm{st}}\) column: chemical formula of the fragment, containing only abundant isotopes. * indicates that the fragment is not part of the molecular ion. \(2^{\mathrm{nd}}\) col.: calculated exact mass of ionised fragment. \(3^{\mathrm{rd}}\) col.: percent signal of the fragment and its isotopocules relative to the total measured signal. \(4^{\mathrm{th}}\) col.: percent signal of the fragment, all its sub-fragments and all associated isotopocules relative to the total measured signal, computed from Eq. (5). \(5^{\mathrm{th}}\) col.: likelihood value computed from Eq. (6). \(6^{\mathrm{th}}\) col.: ranking according to decreasing likelihood value. For CFC-11, \(\text {CFCl}_{{3}}\) ranked first is the molecular ion