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Table 4 (A) Two-tuple total spatial-(dis)similarity matrix for k = 1, \({\mathbb{G}}^{1}\), computed from 3D coordinates of the molecule Chloro(methoxy)methane (see Table 1A), (B) examples of two-tuple local-fragment spatial-(dis)similarity matrices, \({\mathbb{G}}_{\varvec{F}}^{1}\), obtained with different chemical fragments

From: Examining the predictive accuracy of the novel 3D N-linear algebraic molecular codifications on benchmark datasets

 

C1

C2

O3

Cl4

(A) Two-tuple total spatial-(dis)similarity matrices, \({\mathbb{G}}^{1}\)

 C1

0.000

2.408

1.439

3.939

 C2

2.408

0.000

1.438

1.757

 O3

1.439

1.438

0.000

2.598

 Cl4

3.939

1.757

2.598

0.000

(B) two-tuple local-fragment spatial-(dis)similarity matrices, \({\mathbb{G}}_{F}^{1}\)

 \({\mathbb{G}}_{F}^{1}\) based on halogens fragment

  C1

0.000

0.000

0.000

1.969

  C2

0.000

0.000

0.000

0.878

  O3

0.000

0.000

0.000

1.299

  Cl4

1.969

0.878

1.299

0.000

 \({\mathbb{G}}_{F}^{1}\) based on methyl groups fragment

  C1

0.000

1.204

0.719

1.969

  C2

1.204

0.000

0.000

0.000

  O3

0.719

0.000

0.000

0.000

  Cl4

1.969

0.000

0.000

0.000

 \({\mathbb{G}}_{F}^{1}\) based on heteroatoms fragment

  C1

0.000

0.000

0.719

1.969

  C2

0.000

0.000

0.719

0.878

  O3

0.719

0.719

0.000

2.598

  Cl4

1.969

0.878

2.598

0.000