The molecular descriptors computed with MOLGEN

General references:

·    TodCon : Todeschini, R.; Consonni, V. Handbook of Molecular Descriptors, Wiley-VCH, Weinheim and New York, 2000

·    Trin: Trinajstić, N. Chemical Graph Theory, 2^nd edition, CRC Press, Boca Raton, FL, 1992

0 number of atoms

A, A (incl. H) and N_H are descriptors of the category 'arithmetic'.

Notation in text: ,  and

 is the number of atoms excluding H atoms.  is the number of atoms including H atoms.  is the number of H atoms.

1 number of atoms incl. H atoms

A (incl. H) see 0.

2 number of H atoms

N_H see 0.

3 relative number of H atoms

rel. N_H, rel. N_C, rel. N_O, rel. N_N, rel. N_S,  rel. N_F, rel. N_Cl, rel. N_Br, rel. N_I and rel. N_P are descriptors of the category 'arithmetic'.

Notation in text: , , , , , , , ,  and

Relative means divided by the number of atoms (inclusive H atoms):

Correspondingly , , , , , , , ,  and .

For  see 2, for  see 1.

4 number of C atoms

N_C, N_O, N_N, N_S, N_F, N_Cl, N_Br, N_I and N_P  are descriptors of the category 'arithmetic'.

Notation in text: , , , , , , ,  and

 is the number of C atoms in a molecule.

Correspondingly , , , , , ,  and .

5 relative number of C atoms

rel. N_C see 3.

6 number of O atoms

N_O see 4.

7 relative number of O atoms

rel. N_O see 3.

8 number of N atoms

N_N see 4.

9 relative number of N atoms

rel. N_N see 3.

10 number of S atoms

N_S see 4.

11 relative number of S atoms

rel. N_S see 3.

12 number of F atoms

N_F see 4.

13 relative number of F atoms

rel. N_F see 3.

14 number of Cl atoms

N_Cl see 4.

15 relative number of Cl atoms

rel. N_Cl see 3.

16 number of Br atoms

N_Br see 4.

17 relative number of Br atoms

rel. N_Br see 3.

18 number of I atoms

N_I see 4.

19 relative number of I atoms

rel. N_I see 3.

20 number of P atoms

N_P see 4.

21 relative number of P atoms

rel. N_P see 3.

22 number of bonds

B and B (incl. H)  are descriptors of the category 'arithmetic'.

Notation in text: ,

 is the number of bonds in the H-suppressed molecule.  is the number of  bonds in a molecule containing H atoms.

23 number of bonds (incl. H atoms)

B (incl. H) see 22.

24 number of localized bonding electron pairs

loc. B and loc. B (incl. H) are descriptors of the category 'arithmetic'.

Notation in text:  and

 is the number of localized bonding electron pairs in an H-suppressed molecule. Aromatic π-electrons are delocalized and therefore not counted here.

 is analogous to  but includes bonds to H atoms.

25 number of localized bonding electron pairs (incl. H)

loc. B (incl. H) see 24.

26 number of single bonds

n- and n- (incl. H) are descriptors of the category 'arithmetic'.

Notation in text:  and

 is the number of single bonds in an H-suppressed molecule.  is analogous to  but includes bonds to H atoms.

27 rel. number of single bonds

rel. n- and rel n- (incl. H) are descriptors of the category 'arithmetic'.

Notation in text:  and

rel. n- is relative to the number of bonds of an H-suppressed molecule:

Analogous is:

For  see 26, for  see 22, for  see 28 and for  see 23.

28 number of single bonds (incl. H atoms)

n- (incl. H) see 26.

29 rel. number of single bonds (incl. H atoms)

rel. n- (incl. H) see 27.

30 number of double bonds

n=, n# and n aromatic are descriptors of the category 'arithmetic'.

Notation in text: ,  and

 is the number of double bonds,  the number of triple bonds and  is the number of aromatic bonds.

31 relative number of double bonds

rel. n=, rel. n= (incl. H) , rel. n#, rel. n# (incl. H), rel. n aromatic and rel. n aromatic (incl. H)  are descriptors of the category 'arithmetic'.

Notation in text: , , , ,  and

 is relative to the number of bonds in an H-suppressed molecule.  is relative to the number of bonds in a molecule with H atoms.

Correspondingly , ,  and .

32 relative number of double bonds (incl. H atoms)

rel. n= (incl. H) see 31.

33 number of triple bonds

n# see 30.

34 relative number of triple bonds

rel. n# see 31.

35 relative number of triple bonds (incl. H atoms)

rel. n# (incl. H) see 31.

36 number of aromatic bonds

n aromatic see 30.

37 relative number of aromatic bonds

rel. n aromatic see 31.

38 relative number of aromatic bonds (incl. H atoms)

rel. n aromatic (incl. H) see 31.

39 cyclomatic number

C is a descriptor of the category 'arithmetic'.

Notation in text:

For molecules (connected graphs)  is defined as:

For  see 0, for  see 22.

40 molecular weight

MW and MW (incl. H) are descriptors of the category 'arithmetic'.

Notation in text:  and

 is the sum of the atomic weights in an H-suppressed molecule. The atomic weight is that of the natural abundance isotope mixture.  takes account of the H atoms.

Source:

·    TodCon, page 332

41 mean atomic weight (or average atomic weight)

mean AW and mean AW (incl. H) are descriptors of the category 'arithmetic'.

Notation in text:  and

mean  AW is defined as:

Analogous :

For  and  see 40 and 42. For  and  see 0 and 1.

42 molecular weight (incl. H atoms)

MW (incl. H) see 40.

43 mean atomic weight (incl. H atoms)

mean AW (incl. H) see 41.

44 Wiener index

W is a descriptor of the category 'topological'.

Notation in text:

W is the half-sum of the entries of the distance-matrix of the H-suppressed molecule:

where  is the number of non-H atoms and  is the entry in the i^th row and the j^th column of the distance matrix.

For  see 0 and for  see distance matrix.

Source:

·    Wiener, H. Structural Determination of Paraffin Boiling Points. J. Am. Chem. Soc. 1947, 69, 17-20

·    TodCon, page 497

45 1st Zagreb index

M_1  is a descriptor of the category 'topological'.

Notation in text:

 is the sum over the squares of the vertex degree of each atom in an H-suppressed molecule:

where  is the number of non-H atoms and  is the number of neighbours of atom i in an H-suppressed molecule.

For  see 0. For  see vertex degree.

Source:

·    Gutman, I.; Ruščić, B.; Trinajstić, N.; Wilcox, C. F. Graph Theory and Molecular Orbitals. XII. Acyclic Polyenes. J. Chem. Phys. 1975, 62, 3399-3405

·    TodCon, page 509

·    Trin, page 226

46 2nd Zagreb index

M_2 is a descriptor of the category 'topological'.

Notation in text:

 is the following sum over all edges:

where  is the number of neighbours of atom i in an H-suppressed molecule.

For  see vertex degree.

Source:

·    Gutman, I.; Ruščić, B.; Trinajstić, N.; Wilcox, C. F. Graph Theory and Molecular Orbitals. XII. Acyclic Polyenes. J. Chem. Phys. 1975, 62, 3399-3405

·    TodCon, page 509

·    Trin, page 226

47 1st modified Zagreb index

m^M_1 and m^M_2 are descriptors of the category 'topological'.

Notation in text:  and

 is the sum over the squares of the reciprocal vertex degree of each atom in an H-suppressed molecule:

 is defined as the following sum over all edges:

 

where  is the number of non-H atoms and  is the number of neighbours of atom i in an H-suppressed molecule.  stands for modified.

For  see 0. For  see vertex degree.

Source:

·    Nikolić, S.; Kovačević, G.; Miličević, A.; Trinajstić, N. The Zagreb Indices 30 Years After. Croat. Chem. Acta, 2003, 76, 113-124

48 2nd modified Zagreb index

m^M_2 see 47.

49 Randic index of order 0 (or connectivity index of order 0)

0^Chi is a descriptor of the category 'topological'.

Notation in text:

This is the zeroth descriptor in the series m^Chi with m = 1, 2, 3, …

Notation in text:

The definition of :

 

where  is the number of non H-atoms and  is the number of neighbours of atom i in an H-suppressed molecule.

For  see 0. For  see vertex degree.

The definition of :

with . The sum runs over all paths of length  (this is the number of edges of the path).  is the number of the atoms in a path . The product runs over all atoms of path .  is the vertex degree of the i^th atom in path .

For  see vertex degree.

Source:

·    Randić, M. On Characterization of Molecular Branching. J. Am. Chem. Soc. 1975, 97, 6609-6615

·    Kier, L. B.; Murray, W. J.; Randić, M.; Hall, L. H. Molecular Connectivity V: Connectivity Series Applied to Density. J. Pharm. Sci., 1976, 65, 1226-1230

·    Kier, L. B.; Hall L. H. The Nature of Structure-Activity Relationships and their Relation to Molecular Connectivity. Eur. J. Med. Chem., 1977, 12, 307-312

·    Kier, L. B.; Hall L. H. Molecular Connectivity in Structure-Activity Analysis. Research-Studies Press - Wiley, Chichester (UK), 1986

·    TodCon, pages 84-85

·    Trin, page 226

50 Randic Index of order 1

1^Chi see 49.

51 Randic Index of order 2

2^Chi see 49.

52 solvation connectivity index of order 0

0^Chi^s is a descriptor of the category 'topological'.

Notation in text:

is the zeroth member in the series m^Chi^s with m = 1, 2, 3, …

Notation in text:

The definition of :

where  is the number of non-H atoms and  is the number of neighbours of atom i in an H-suppressed molecule.  is the principal quantum number of atom i (for C, N, O, F: =2; for Si, P, S, Cl: =3).

For  see 0. For  see vertex degree.

The definition of :

with . The sum runs over all paths of length  (this is the number of edges in the path).  is the number of the atoms in a path . The product runs over all atoms in path .  is the vertex degree of the i^th atom in path .  is the principal quantum number of atom i in path .

For  see vertex degree.

Source:

·    Zefirov, N. S.; Palyulin, V. A. QSAR for Boiling Points of “Small” Sulfides. Are the “High-Quality Structure-Property-Activity Regressions” the Real High Quality QSAR Models? J. Chem. Inf. Comput. Sci. 2001, 41, 1022-1027

·    TodCon, pages 88-89

53 solvation connectivity index of order 1

1^Chi^s see 52.

54 solvation connectivity index of order 2

2^Chi^s see 52.

55 solvation connectivity index of order 3

3^Chi^s see 52.

56 solvation connectivity index for clusters

3^Chi^s (cluster) is a descriptor of the category 'topological'.

Notation in text:

The definition of  is:

The sum runs over all clusters of size 3:

The product runs over all four atoms of cluster .  is the vertex degree of the i^th atom in cluster .  is the principal quantum number of atom i in cluster .

For  see vertex degree.

Source:

·    TodCon, pages 88-89

57 Kier and Hall index of order 0

0^Chi^v is a descriptor of the category 'topological'.

Notation in text:

 is the zeroth member of the series m^Chi with m = 1, 2, 3, …

Notation in text:

The definition of :

 

where  is the number of non-H atoms and  is the valence vertex degree of atom i in an H-suppressed molecule.

For  see 0. For  see valence vertex degree.

The definition of :

 

with . The sum runs over all paths of length  (this is the number of edges of the path).  is the number of atoms in a path . The product runs over all atoms of path .

For  see valence vertex degree.

Source:

·    Kier, L. B.; Murray, W. J.; Randić, M.; Hall, L. H. Molecular Connectivity V: Connectivity Series Applied to Density. J. Pharm. Sci., 1976, 65, 1226-1230

·    Kier, L. B.; Hall L. H. The Nature of Structure-Activity Relationships and Their Relation to Molecular Connectivity. Eur. J. Med. Chem. 1977, 12, 307-312

·    TodCon, pages 85-86

·    Trin, page 229

58 Kier and Hall index of order 1

1^Chi^v see 57.

Source:

·    Kier, L. B.; Hall L. H. Derivation and Significance of Valence Molecular Connectivity. J. Pharm. Sci. 1981, 70, 583-589

·    TodCon, pages 85-86

·    Trin, page 229

59 Kier and Hall index of order 2

2^Chi^v see 57.

60 Kier and Hall index of order 3

3^Chi^v see 57.

61 Kier shape index 1

1^kappa is a descriptor of the category 'topological'.

Notation in text:

where  is the number of atoms and  is the number of bonds in an H-suppressed molecular graph.

For  see 0. For  see 22.

Source:

·    Kier, L. B. Shape Indexes of Orders One and Three from Molecular Graphs. Quant. Struct.-Act. Relat. 1986, 5, 1-7

·    Kier, L. B. Indexes of Molecular Shape from Chemical Graphs. Acta Pharm. Jugosl. 1986, 36, 171-188

·    TodCon, pages 248-249

62 Kier shape index 2

2^kappa is a descriptor of the category 'topological'.

Notation in text:

where  is the number of atoms and  is the number of paths of length 2 in an H-suppressed molecular graph.

For  see 0.

Source:

·    Kier, L. B. A Shape Index from Molecular Graphs. Quant. Struct.-Act. Relat. 1985, 4, 109-116

·    Kier, L. B. Indexes of Molecular Shape from Chemical Graphs. Acta Pharm. Jugosl. 1986, 36, 171-188

·    TodCon, pages 248-249

63 Kier shape index 3

3^kappa is a descriptor of the category 'topological'.

Notation in text:

where  is the number of atoms and  is the number of paths of length 3 in an H-suppressed molecular graph.

For  see 0.

Source:

·    Kier, L. B. Shape Indexes of Orders One and Three from Molecular Graphs. Quant. Struct.-Act. Relat. 1986, 5, 1-7

·    Kier, L. B. Indexes of Molecular Shape from Chemical Graphs. Acta Pharm. Jugosl. 1986, 36, 171-188

·    TodCon, pages 248-249

64 Kier molecular flexibility index non-alpha-modified

Phi_non-alpha is a descriptor of the category 'topological'.

Notation in text:

where  is the number of atoms. ,  are the Kier shape indices 1 and 2.

For  and  see 61 and 62. For  see 0.

Source:

·    No source! Definition is analogous to 68 without modifying alpha.

65 Kier alpha-modified shape index 1

1^kappa_alpha is a descriptor of the category 'topological'.

Notation in text:

where  is the number of atoms and  is the number of bonds in an H-suppressed molecular graph.  is derived from the covalent radius of each atom.

For  see alpha. For  see 0. For  see 22.

Source:

·    Kier, L. B. Distinguishing Atom Differences in a Molecular Graph Shape Index. Quant. Struct.-Act. Relat. 1986, 5, 7-12

·    Kier, L. B. Shape Indexes of Orders One and Three from Molecular Graphs. Quant. Struct.-Act. Relat. 1986, 5, 1-7

·    Kier, L. B. Indexes of Molecular Shape from Chemical Graphs. Acta Pharm. Jugosl. 1986, 36, 171-188

·    TodCon, pages 249-250

66 Kier alpha-modified shape index 2

2^kappa_alpha is a descriptor of the category 'topological'.

Notation in text:

where  is the number of atoms and  is the number of paths of length 2 in an H-suppressed molecular graph.  is derived from the covalent radius of each atom.

For  see alpha. For  see 0.

Source:

·    Kier, L. B. Distinguishing Atom Differences in a Molecular Graph Shape Index. Quant. Struct.-Act. Relat. 1986, 5, 7-12

·    Kier, L. B. Indexes of Molecular Shape from Chemical Graphs. Acta Pharm. Jugosl. 1986, 36, 171-188

·    TodCon, pages 249-250

67 Kier alpha-modified shape index 3

3^kappa_alpha is a descriptor of the category 'topological'.

Notation in text:

where  is the number of atoms and  is the number of paths of length 3 in an H-suppressed molecular graph.  is derived from the covalent radius of each atom.

For  see alpha. For  see 0.

Source:

·    Kier, L. B. Shape Indexes of Orders One and Three from Molecular Graphs. Quant. Struct.-Act. Relat. 1986, 5, 1-7

·    Kier, L. B. Indexes of Molecular Shape from Chemical Graphs. Acta Pharm. Jugosl. 1986, 36, 171-188

·    TodCon, pages 249-250

68 Kier molecular flexibility index

Phi is a descriptor of the category 'topological'.

Notation in text:

where  is the number of atoms. ,  are the Kier alpha-modified shape indices 1 and 2.  is derived from the covalent radius of each atom.

For  and  see 65 and 66. For  see 0.

Source:

·    Kier, L. B. An Index of Molecular Flexibility from Kappa Shape Attributes. Quant. Struct.-Act. Relat. 1989, 8, 221-224

·    TodCon, page 178

69 Platt number

F is a descriptor of the category 'topological'.

Notation in text:

where  is the number of neighbours of atom i. The sum runs over all edges in an H-suppressed molecular graph.

Source:

·    Platt, J. R. Influence of Neighbor Bonds on Additive Bond Properties in Paraffins. J. Chem. Phys. 1947, 15, 419-420

·    Platt, J. R. Prediction of Isomeric Differences in Paraffin Properties. J. Phys. Chem. 1952, 56, 328-336

·    TodCon, page 125

·    Trin, page 245

70 Gordon-Scantlebury index

N_GS is a descriptor of the category 'topological'.

Notation in text:

 is the number of path subgraphs of length 2 in an H-suppressed molecular graph.

Source:

·    TodCon, page 125

·    Trin, 245

71 Balaban index

J is a descriptor of the category 'topological'.

Notation in text:

where  is the number of bonds and  is the cyclomatic number.  is the i^th vertex distance degree. The sum runs over all edges of an H-suppressed molecular graph.

For   see 22. For  see 39. For  see vertex distance degree.

Source:

·    Balaban, A. T. Highly Discriminating Distance-Based Topological Index. Chem. Phys. Lett. 1982, 89, 399-404

·    Balaban, A. T. Topological Indices Based on Topological Distances in Molecular Graphs. Pure Appl. Chem. 1983, 55, 199-206

·    TodCon, page 21

·    Trin, page 246

72 unsaturated Balaban index

J_unsat is a descriptor of the category 'topological'.

Notation in text:

where  is the number of bonds and  is the cyclomatic number.  is the i^th vertex unsaturated distance degree, i.e. the row sum in the unsaturated distance matrix.

For   see 22. For  see 39. For  see vertex unsaturated  distance degree.

Source:

·    Balaban, A. T. Highly Discriminating Distance-Based Topological Index. Chem. Phys. Lett. 1982, 89, 399-404

·    Balaban, A. T.; Filip, P. Computer Program For Topological Index J. MATCH – Commun. Math. Comp. Chem. 1984, 16, 163

73 Schultz molecular topological index

MTI is descriptor of the category 'topological'.

Notation in text:

 is defined for an H-suppressed molecular graph:

where  is the adjacence matrix (here not the descriptor : number of atoms),  is the distance matrix,  the number of atoms,  the second  descriptor ,  is the vertex degree of the i^th atom and  is the first Zagreb index. The letter  specifies the transposition of a vector or a matrix:  in a symmetric matrix.

For  see adjacence matrix, for  see distance matrix, for  see 74, for  see vertex degree, for  see 45.

Source:

·    Schultz, H. P. Topological Organic Chemistry. 1. Graph Theory and Topological Indices of Alkanes. J. Chem. Inf. Comput. Sci. 1989, 29, 227-228

·    Schultz, H. P.; Schultz, T. P. Topological Organic Chemistry. 6. Graph Theory and Molecular Topological Indices of Cycloalkanes. J. Chem. Inf. Comput. Sci. 1993, 33, 240-244

·    TodCon, page 381 (The formula given there is incorrect.)

·    Trin, page 257

74 MTI'-index

MTI' is a descriptor of the category 'topological'.

Notation in text:

 is defined for an H-suppressed molecular graph:

where  is the adjacence matrix (here not the descriptor : number of atoms),  is the distance matrix,  the number of atoms,  is the vertex degree of the i^th atom,  is the vertex distance degree of the i^th atom. The letter  specifies the transposition of a vector or a matrix:  in a symmetric matrix.

For  see adjacency matrix, for  see distance matrix, for  see vertex degree and for  see vertex distance degree.

Source:

·    Müller, W. R.; Szymanski, K.; Knop, J. v.; Trinajstić, N. Molecular Topological Indices. J. Chem. Inf. Comput. Sci. 1990, 30, 160-163

·    Mihalić, Z.; Nikolić, S; Trinajstić, N. Comparative Study of Molecular Descriptors Derived from the Distance Matrix. J. Chem. Inf. Comput. Sci. 1992, 32, 28-37

·    TodCon, page 381

75 Harary number

H is a descriptor of the category 'topological'.

Notation in text:

The sums run over all pairs of atoms in an H-suppressed molecular graph:

where  is the number of non-H atoms and  is the entry in the i^th row and the j^th column of the distance matrix.

For  see 0 and for  see distance matrix.

Source:

·    Ivanciuc, O.; Balaban, T.-S.; Balaban, A. T. Design of Topological Indices. Part 4. Reciprocal Distance Matrix, Related Local Vertex Invariants and Topological Indices. J. Math. Chem. 1993, 12, 309-318

·    Plavsić, D.; Nikolić, S; Trinajstić, N.; Mihalić, Z. On the Harary Index for the Characterization of Chemical Graphs. J. Math. Chem. 1993, 12, 235-250

·    Lucić, B.; Milicević, A.; Nikolić, S; Trinajstić, N. Harary Index – Twelve Years Later. Croat. Chem. Acta 2002, 75, 847-867

·    TodCon, pages 209-210

76 total walk count

twc is a descriptor of the category 'topological'.

Notation in text:

The sum runs over all lengths (from length  to length ) of walks in an H-suppressed molecular graph:

where  is the number of atoms and  is the molecular walk count of length k.

For  see 77-83.

Source:

·    Rücker, G.; Rücker, C. Counts of All Walks as Atomic and Molecular Descriptors. J. Chem. Inf. Comput. Sci. 1993, 33, 683-695

·    Rücker, G.; Rücker, C. Walk Counts, Labyrinthicity, and Complexity of Acyclic and Cyclic Graphs and Molecules. J. Chem. Inf. Comput. Sci. 2000, 40, 99-106

·    Gutman, I.; Rücker, C.; Rücker, G. On Walks in Molecular Graphs J. Chem. Inf. Comput. Sci. 2001, 41, 739-745

·    Nikolić, S; Trinajstić, N.; Tolić, I. M.; Rücker, G.; Rücker, C. On Molecular Complexity Indices. Chapter 2, pages 29-89 in Complexity in Chemistry (Bonchev, D.; Rouvray, D. H., Eds.), Taylor and Francis, London, 2003

·    TodCon, pages 480-482

77-83 molecular walk count of length k

mwc2, mwc3, mwc4, mwc5, mwc6, mwc7 and mwc8 are descriptors of the category 'topological'.

Notation in text: ; e.g.:

The sums run over all atoms in an H-suppressed molecular graph:

where  is the k^th power of the adjacency matrix  (here not the descriptor : number of atoms) and  the number of atoms.

Remark:  is equal to the number of atoms,  is equal to .

For  see adjacency matrix, for  see 22.

Source:

·    Rücker, G.; Rücker, C. Counts of All Walks as Atomic and Molecular Descriptors. J. Chem. Inf. Comput. Sci. 1993, 33, 683-695

·    Rücker, G.; Rücker, C. Walk Counts, Labyrinthicity, and Complexity of Acyclic and Cyclic Graphs and Molecules. J. Chem. Inf. Comput. Sci. 2000, 40, 99-106

·    Gutman, I.; Rücker, C.; Rücker, G. On Walks in Molecular Graphs J. Chem. Inf. Comput. Sci. 2001, 41, 739-745

·    Nikolić, S; Trinajstić, N.; Tolić, I. M.; Rücker, G.; Rücker, C. On Molecular Complexity Indices. Chapter 2, pages 29-89 in Complexity in Chemistry (Bonchev, D.; Rouvray, D. H., Eds.), Taylor and Francis, London, 2003

·    TodCon, pages 480-482

84 unsaturated total walk count

twc_unsat is a descriptor of the category 'topological'.

Notation in text:

The sum runs over all lengths (from length  to length ) of walks in an H-suppressed molecular graph:

where  is the number of atoms and  is the molecular walk count of length  derived from the “unsaturated” adjacency matrix, i. e. a matrix with entries  for multiple bonds.

For  see 85-91. See also unsaturated adjacency matrix.

Source:

·    No source. Definition is analogous to 76.

85-91 unsaturated molecular walk count of length k

mwc2_unsat, mwc3_unsat, mwc4_unsat, mwc5_unsat, mwc6_unsat, mwc7_unsat and mwc8_unsat are descriptors of the category 'topological'.

Notation in text: ; e.g.:

The sums run over all atoms in an H-suppressed molecular graph:

where  is the k^th power of the unsaturated adjacency matrix  with entries  for multiple bonds, and  is the number of atoms.

For  see unsaturated adjacency matrix, for  see 22.

Source:

·    No source. Definition is analogous to 77-83.

92 gravitational index (pairs, topo. dist.)

G_1 (topo. dist.) is a descriptor of the category 'topological'.

Notation in text:

The sum runs over all pairs of atoms in an H-suppressed molecular graph.

where  is the average weight of atom i (expressed in amu, i.e. 12.0110 for carbon) and  is the entry in the i^th row and the j^th column of the distance matrix.  is the number of atoms.

For  see distance matrix. For  see 0.

Source:

·    No source. Definition is analogous to 96 with topological distances.

93 gravitational index (pairs, topo. dist., incl. H atoms)

G_1 (topo. dist.,incl. H) is a descriptor of the category 'topological'.

Notation in text:

The sum runs over all pairs of atoms in a molecular graph containing H atoms.

where  is the average weight of atom i and  is the entry in the i^th row and the j^th column of the distance matrix.  is the number of atoms.

For  see distance matrix. For  see 0.

Source:

·    No source. Definition is analogous to 97 with topological distances.

94 gravitational index (bonds, topo. dist.)

G_2 (topo. dist.) is a descriptor of the category 'topological'.

Notation in text:

The sum runs over all edges of an H-suppressed molecular graph.

where  is the average weight of atom .

Source:

·    No source. Definition is analogous to 98 with topological distances.

95 gravitational index (bonds, topo. dist., incl. H atoms)

G_2 (topo. dist.,incl. H) is a descriptor of the category 'topological'.

Notation in text:

The sum runs over all edges of a molecular graph containing H atoms.

where  is the average weight of atom .

Source:

·    No source. Definition is analogous to 99 with topological distances.

96 gravitational index (pairs, 3D-dist.)

G_1 is a descriptor of the category 'geometrical'.

Notation in text:

The sum runs over all pairs of an H-suppressed molecular graph.

where  is the average weight of atom  and  is the interatomic distance (expressed in Ångström Å) of atom i and atom j.  is the number of atoms.

For  see 0.

Source:

·    Katritzky, A. R.; Mu L.; Lobanov, V. S.; Karelson, M. Correlation of Boiling Points with Molecular Structure. 1. A Training Set of 298 Diverse Organics and a Test Set of 9 Simple Inorganics. J. Phys. Chem. 1996, 100, 10400-10407

·    TodCon, page 412

97 gravitational index (pairs, 3D-dist., incl. H atoms)

G_1 (incl. H) is a descriptor of the category 'geometrical'.

Notation in text:

The sum runs over all pairs of atoms in a molecular graph containing H atoms.

where  is the average weight of atom  and  is the interatomic distance (expressed in Ångström Å) of atom i and atom j.  is the number of atoms.

For  see 0.

Source:

·    Katritzky, A. R.; Mu L.; Lobanov, V. S.; Karelson, M. Correlation of Boiling Points with Molecular Structure. 1. A Training Set of 298 Diverse Organics and a Test Set of 9 Simple Inorganics. J. Phys. Chem. 1996, 100, 10400-10407

·    TodCon, page 412

98 gravitational index (bonds, 3D-dist.)

G_2 is a descriptor of the category 'geometrical'.

Notation in text:

The sum runs over all edges of an H-suppressed molecular graph.

where  is the average weight of atom  and  is the interatomic distance (expressed in Ångström Å) of atom i and atom j.

Source:

·    Katritzky, A. R.; Mu L.; Lobanov, V. S.; Karelson, M. Correlation of Boiling Points with Molecular Structure. 1. A Training Set of 298 Diverse Organics and a Test Set of 9 Simple Inorganics. J. Phys. Chem. 1996, 100, 10400-10407

·    TodCon, page 412

99 gravitational index (bonds, 3D-dist., incl. H atoms)

G_2 (incl. H) is a descriptor of the category 'geometrical'.

Notation in text:

The sum runs over all edges of a molecular graph containing H atoms.

where  is the average weight of atom  and  is the interatomic distance (expressed in Ångström Å) of atom i and atom j.

Source:

·    Katritzky, A. R.; Mu L.; Lobanov, V. S.; Karelson, M. Correlation of Boiling Points with Molecular Structure. 1. A Training Set of 298 Diverse Organics and a Test Set of 9 Simple Inorganics. J. Phys. Chem. 1996, 100, 10400-10407

·    TodCon, page 412

100 Hosoya Z-index

Z is a descriptor of the category 'topological'.

Notation in text:

where  is the number of atoms in the H-suppressed molecular graph and  is the number of sets of  mutually non-adjacent edges. , .

For  see 0, for  see 22.

Source:

·    Hosoya, H. Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons. Bull. Chem. Soc. Jpn. 1971, 44, 2332-2339

·    TodCon, page 215

·    Trin, page 132

101 Basak information content of order 0

IC_0, IC_1, IC_2, TIC_0, TIC_1, TIC_2, CIC_0, CIC_1, CIC_2, N*CIC_0, N*CIC_1, N*CIC_2, SIC_0, SIC_1, SIC_2, N*SIC_0, N*SIC_1, N*SIC_2, BIC_0, BIC_1, BIC_2, N*BIC_0, N*BIC_1 and N*BIC_2 are descriptors of the category 'topological'.

Notation in text: , , , , , , , , , , , , , , , , , , , , , , ,

For calculating these descriptors a molecular graph inclusive H atoms is considered.

Explanation:

Every atom is characterized by itself and its neighbours. Here the characterization of the i^th atom itself depends on the atom number  and on the number of bonding electron pairs  (without H atoms). The characterization of the neighbourhood depends on the depth  of the neighbourhood (e.g.  for the next neighbours) and the characterization of the connected atoms and their bond multiplicities:

To calculate  only the characterization of the atoms is needed: C₁, C₂, C₃, C₄, C₅ are C-atoms and have all

 

with  is the number of atoms and  is the number of bonds.

For  see 1, for  see 23.

Source:

·    Basak, S. C. Information Theoretic Indices of Neighborhood Complexity and Their Applications, chapter 12 in Topological Indices and Related Descripors in QSAR and QSPR (Devillers, J.; Balaban, A. T., Eds.) Gordon and Breach, Amsterdam, 1999

·    Basak, S. C. Use of Molecular Complexity Indices in Predictive Pharmacology and Toxicology: A QSAR Approach. Med. Sci. Res. 1987, 15, 605-609

·    Basak, S. C.; Gute, B. D. Characterization of Molecular Structures Using Topological Indices. SAR QSAR Environ. Res. 1997, 7, 1-21

102 Basak total information content of order 0

TIC_0 see 101.

103 Basak complementary information content of order 0

CIC_0 see 101.

104 total complementary information content of order 0

N*CIC_0 see 101.

105 Basak structural information content of order 0

SIC_0 see 101.

106 total structural information content of order 0

N*SIC_0 see 101.

107 bonding information content of order 0

BIC_0 see 101.

108 total bonding information content of order 0

N*BIC_0 see 101.

109 Basak information content of order 1

IC_1 see 101.

110 Basak total information content of order 1

TIC_1 see 101.

111 Basak complementary information content of order 1

CIC_1 see 101.

112 total complementary information content of order 1

N*CIC_1 see 101.

113 Basak structural information content of order 1

SIC_1 see 101.

114 total structural information content of order 1

N*SIC_1 see 101.

115 bonding information content of order 1

BIC_1 see 101.

116 total bonding information content of order 1

N*BIC_1 see 101.

117 Basak information content of order 2

IC_2 see 101.

118 Basak total information content of order 2

TIC_2 see 101.

119 Basak complementary information content of order 2

CIC_2 see 101.

120 total complementary information content of order 2

N*CIC_2 see 101.

121 Basak structural information content of order 2

SIC_2 see 101.

122 total structural information content of order 2

N*SIC_2 see 101.

123 bonding information content of order 2

BIC_2 see 101.

124 total bonding information content of order 2

N*BIC_2 see 101.

125 mean square distance index

MSD is a descriptor of the category 'topological'.

Notation in text:

The sums run over all atoms of an H-suppressed molecular graph:

where  is the number of non-H atoms and  is the entry in the i^th row and the j^th column of the distance matrix.

For  see 0 and for  see distance matrix.

Source:

·    Balaban, A. T. Topological Indices Based on Topological Distances in Molecular Graphs. Pure Appl. Chem. 1983, 55, 199-206

·    TodCon, page 113 (The formula given there is incorrect.)

126 detour index

w is a descriptor of the category 'topological'.

Notation in text:

The sums run over all atoms of an H-suppressed molecular graph:

where  is the number of non-H atoms and  is the entry in the i^th row and the j^th column of the detour matrix.

For  see 0 and for  see detour matrix.

Source:

·    Ivanciuc, O.; Balaban, A. T. Design of Topological Indices. Part 8. Path Matrices and Derived Molecular Graph Invariants. MATCH – Commun. Math. Comp. Chem. 1994, 30, 141-152

·    Amić, D.; Trinajstić, N. On the Detour Matrix. Croat. Chem. Acta. 1995, 68, 53-62

·    Lukovits, I. The Detour Index. Croat. Chem. Acta 1996, 69, 873-882

·    Lukovits, I.; Razinger, M. On Calculation of the Detour Index. J. Chem. Inf. Comput. Sci. 1997, 37, 283-286

·    TodCon, page 103

127 detour index (incl. half main diagonal)

w (incl. half diag.) is a descriptor of the category 'topological'.

Notation in text:

The sums run over all atoms of an H-suppressed molecular graph:

where  is the number of non-H atoms and  is the entry in the i^th row and the j^th column of the detour matrix containing diagonal elements .

For  see 0 and for  see detour matrix.

Source:

Rücker, G.; Rücker, C. Symmetry-Aided Computation of the Detour Matrix and the Detour Index. J. Chem. Inf. Comput. Sci. 1998, 38, 710-714

128-135 total acyclic path count and molecular acyclic path counts of length k

P_acyc, 2^P_acyc, 3^P_acyc, 4^P_acyc, 5^P_acyc, 6^P_acyc, 7^P_acyc, 8^P_acyc, 9^P_acyc and higher are descriptors of the category 'topological'.

Notation in text: , , , , , , , ,

where  is the number of paths of length  in the H-suppressed molecular graph without counting any closed paths (rings).  is the maximum length of all unclosed paths.

Source:

·    Randić, M.; Brissey, G. M.; Spencer, R. B.; Wilkins, C. L. Search for All Self-Avoiding Paths for Molecular Graphs. Comput. & Chem. 1979, 3, 5-13

·    Randić, M. Characterization of Atoms, Molecules, and Classes of Molecules Based on Paths Enumeration. MATCH – Commun. Math. Comp. Chem. 1979, 7, 5-64

·    TodCon, page 344

136 molecular acyclic path count of length 9 and higher

9^P_acyc and higher see 128-135.

137-144 total path count and molecular path counts of length k

P, 2^P, 3^P, 4^P, 5^P, 6^P, 7^P, 8^P, 9^P and higher are descriptors of the category 'topological'.

Notation in text: , , , , , , , ,

where  is the number of paths of length  in the H-suppressed molecular graph including closed paths (rings).  is the maximum length of all paths.

Source:

·    Randić, M.; Brissey, G. M.; Spencer, R. B.; Wilkins, C. L. Search for All Self-Avoiding Paths for Molecular Graphs. Comput. & Chem. 1979, 3, 5-13

·    Randić, M. Characterization of Atoms, Molecules, and Classes of Molecules Based on Paths Enumeration. MATCH – Commun. Math. Comp. Chem. 1979, 7, 5-64

·    TodCon, page 344

145 molecular path count of length 9 and higher

9^P and higher see 137-144.

146-152 total ring count and molecular ring count of length k

rings, 3^rings, 4^rings, 5^rings, 6^rings, 7^rings, 8^rings, 9^rings and higher are descriptors of the category 'topological'.

Notation in text: , , , , , , ,

where  is the number of rings of length (size)  in the H-suppressed molecular graph.  is the maximum size of all rings.

Source:

·    TodCon, page 94

153 molecular ring count of length 9 and higher

9^rings and higher see 146-152.

154 moment of inertia A

I_A, I_B, I_C are descriptors of the category 'geometrical'.

Notation in text: , ,

,  and  are the three principal moments of inertia of the molecule with .

Source:

·    TodCon, page 352

155 moment of inertia B

I_B see 154.

156 moment of inertia C

I_C see 154.

157-164 topological charge index of order k

ch. G_1, ch. G_2, ch. G_3, ch. G_4, ch. G_5, ch. G_6, ch. G_7, ch. G_8 are descriptors of the category 'topological’.

Notation in text: , , , , , , ,

The sums run over all atoms in an H-suppressed molecular graph.

where  is the charge term matrix,  is the number of atoms,  is the distance from atom  to atom , , and is the Kronecker delta:

For  see 0, for  see distanc matrix, for  see charge term matrix.

Source:

·    Gálvez, J.; Garcìa, R.; Salabert, M. T.; Soler, R. Charge Indexes. New Topologcal Descriptors. J. Chem. Inf. Comput. Sci. 1994, 34, 520-525

·    Gálvez , J.; Garcìa-Domenech, R.; De Julián-Ortiz, V.; Soler, R. Topological Approach to Drug Design. J. Chem. Inf. Comput. Sci. 1995, 35, 272-284

·    TodCon, pages 445-446

165-172 mean topological charge index of order k

ch. J_1, ch. J_2, ch. J_3, ch. J_4, ch. J_5, ch. J_6, ch. J_7, ch. J_8 and ch. J [5] are descriptors of the category 'topological'.

Notation in text: , , , , , , , ,

, mean topological charge index

, global topological charge index

where  is the number of atoms, , and  is the topological charge index of order .

For  see 157, for  see 0.

Source:

·    Gálvez, J.; Garcìa, R.; Salabert, M. T.; Soler, R. Charge Indexes. New Topologcal Descriptors. J. Chem. Inf. Comput. Sci. 1994, 34, 520-525

·    Gálvez , J.; Garcìa-Domenech, R.; De Julián-Ortiz, V.; Soler, R. Topological Approach to Drug Design. J. Chem. Inf. Comput. Sci. 1995, 35, 272-284

·    TodCon, pages 445-446

173 global topological charge index

ch. J [5] see 165-172.

174 Crippen slog P

slog P is a descriptor of the category 'miscellaneous'.

Notation in text:

where  is the number of atoms of Crippen type ,  is an increment for the  hydrophobicity of atom type . Structure-based types are attributed to atoms using a special table.

Source:

·    Wildman, S. A.; Crippen, G. M. Prediction of Physicochemical Parameters by Atomic Contributions J. Chem. Inf. Comput. Sci. 1999, 39, 868-873

175 Crippen sMR

sMR is a desriptor of the category 'miscellaneous'.

Notation in text:

where  is the number of atoms of Crippen type ,  is an increment for the molar refractivity of atom type . Structure-based types are attributed to atoms using a special table.

Source:

·    Wildman, S. A.; Crippen, G. M. Prediction of Physicochemical Parameters by Atomic Contributions J. Chem. Inf. Comput. Sci. 1999, 39, 868-873

176 steric energy

st. energy is a descriptor of the category 'geometrical'.

Notation in text:

This is the steric energy, as calculated by molecular mechanics in MOLGEN.

177 diameter

D is a descriptor of the category 'topological'.

Notation in text:  

is the short name of the topological diameter:

where  is the number of atoms in the H-suppressed molecular graph and  is an entry in the distance matrix.

For  see 0 and for  see distance matrix.

Source:

·    TodCon, page 112

178-245 Crippen atom type Xxnn

at C01- at C27, at H01- at H04, at O01- at O12, at N01- at N14, at Hal, at Cl, at Br, at I, at F, at P, at S01- at S03, at Me01, at Me02 are descriptors of the category 'miscellaneous'.

Notation in text: , , …, , …,

Source:

·    Wildman, S. ; Crippen, G. M. A. Prediction of Physicochemical Parameters by Atomic Contributions J. Chem. Inf. Comput. Sci. 1999, 39, 868-873

246 sum of subgraphs of order 0 to 8

0-8^K is a descriptor of the category 'overall'.

Notation in text:

where  is the number of subgraphs of  edges.

For  see 247-255.

Source:

·    Bonchev, D. Novel Indices for the Topological Complexity of Molecules. SAR QSAR Environ. Res. 1997, 7, 23-43

·    Rücker, G.; Rücker, C. Automatic Enumeration of All Connected Subgraphs. MATCH – Commun. Math. Comp. Chem. 2000, 41, 145-149

247-255 subgraphs of order k

0^K, 1^K, 2^K, 3^K, 4^K, 5^K, 6^K, 7^K and 8^K are descriptors of the category 'overall'.

Notation in text: , , …,

where  is the H-suppressed molecular graph.

Source:

·    Bonchev, D. Novel Indices for the Topological Complexity of Molecules. SAR QSAR Environ. Res. 1997, 7, 23-43

·    Rücker, G.; Rücker, C. Automatic Enumeration of All Connected Subgraphs. MATCH – Commun. Math. Comp. Chem. 2000, 41, 145-149

256 eccentric connectivity index

Xi^c is a descriptor of the category 'topological'.

Notation in text:

where  is the maximum entry in the i^th line of the distance matrix.  is the vertex degree of atom .

For  see vertex degree, for  see eccentricity.

Source:

·    Sharma, V.; Goswami, R.; Madan, A. K. Eccentric Conectivity Index: A Novel Highly Discriminating Topological Descriptor for Structure-Property and Structure-Activity Studies J. Chem. Inf. Comput. Sci. 1997, 37, 273-282

·    TodCon, page 124

257 principal eigenvalue of A

lambda_1^A is a descriptor of the category 'topological'.

Notation in text:

 is the principal eigenvalue of the adjacency matrix .

For  see adjacency matrix.

Source:

·    TodCon, page 131

258 sum of coefficents of princ. eigenvec. of A

SCA1, SCA2 and SCA3 are descriptors of the category 'topological'.

Notation in text: , ,

The sum runs over all atoms of an H-suppressed molecule:

where  is the number of atoms,  is the i^th coefficient of the eigenvector of the principal eigenvalue of . All coefficients in a principle eigenvector have the same sign, here always the positive sign is assumed.

The descriptors SCR2 and SCR3 are calculated analogously to VEA in TodCon, page 132.

For  see adjacency matrix.

Source:

·    Rücker, G.; Rücker, C.; Gutman, I. On Kites, Comets, and Stars. Sums of Eigenvector Coefficients in (Molecular) Graphs. Z. Naturforsch. A 2002, 57a, 143-153

259 mean coefficent of princ. eigenvec. of A

SCA2 see SCA1.

260 log of sum of coeff. of princ. eigenvec. of A

SCA3 see SCA1.

261 principal eigenvalue of D

lambda_1^D is descriptor of the category 'topological'.

Notation in text:

 is the principal eigenvalue of the distance matrix .

For  see distance matrix.

Source:

·    Schultz, H. P.; Schultz, E. B.; Schultz, T. P. Topological Organic Chemistry. 2. Graph Theory, Matrix Determinants and Eigenvalues, and Topological Indices of Alkanes. J. Chem. Inf. Comput. Sci. 1990, 30, 27-29

·    TodCon, page 134

262 total charge

cha is a descriptor of the category 'arithmetic'.

Notation in text:

 is the charge of the molecule.

263 number of radicals

n_rad is a descriptor of the category 'arithmetic'.

Notation in text:

 is the number of radical sites in a molecule.

264 total Chi index

Chi_T is a descriptor of the category 'topological'.

Notation in text:

The product runs over all atoms of an H-suppressed molecular graph.

where  is the vertex degree of atom .  is the number of atoms.

For  see vertex degree, for  see 0.

Source:

·    Needham, D. E.;Wei, I. C.; Seybold, P. G. Molecular Modeling of the Physical Properties of the Alkanes. J. Am. Chem. Soc. 1988, 110, 4186-4194

·    TodCon, page 86

265 number of methyl groups

T_m is a descriptor of the category 'topological'.

Notation in text:

 is the number of methyl groups in a molecular graph with H atoms.

Source:

·    Needham, D. E.;Wei, I. C.; Seybold, P. G. Molecular Modeling of the Physical Properties of the Alkanes. J. Am. Chem. Soc. 1988, 110, 4186-4194

266 number of pairs of methyl groups at distance 3

T_3 is a descriptor of the category 'topological'.

Notation in text:

 is the number of pairs of methyl groups at distance 3.

For  see 0 and for  see distance matrix.

Source:

·    Needham, D. E.;Wei, I. C.; Seybold, P. G. Molecular Modeling of the Physical Properties of the Alkanes. J. Am. Chem. Soc. 1988, 110, 4186-4194

267 number of hydrogen bond donors

HBD is a descriptor of the category 'arithmetic'.

Notation in text:

 is the number of H atoms attached to O and N atoms, in accord with the ACD definition.

Source:

·    STNotes 2002, 28, 3

·    TodCon, page 221-222

268 number of hydrogen bond acceptors

HBA is a descriptor of the category 'arithmetic'.

Notation in text:

 is the number of N and O atoms, in accord with the ACD definition.

Source:

·    STNotes 2002, 28, 3

·    TodCon, page 221-222

269 freely rotatable bonds

FRB is a descriptor of the category 'topological'.

Notation in text:

Source:

·    Veber, D. F.; Johnson, S. R.; Cheng, H.-Y.; Smith, B. R.; Ward, K. W.; Kopple, K. D. Molecular Properties that Influence the Oral Bioavailability of Drug Candidates. J. Med. Chem. 2002, 45, 2615-2623

·    TodCon, page 178

270 XY shadow

SHDW1, SHDW2 , SHDW3, SHDW4, SHDW5, SHDW6, SHDW1/ SHDW2, SHDW1/ SHDW3, SHDW2/ SHDW3, ssSHDW1, ssSHDW2 , ssSHDW3, ssSHDW4, ssSHDW5, ssSHDW6, ssSHDW1/ SHDW2, ssSHDW1/ SHDW3, ssSHDW2/ SHDW3 are descriptors of the category 'geometrical'.

Notation in text: , , , …, , …, ,

where ,  and  are the principle axes of inertia of the molecule (incl. H atoms). Each atom is projected using its vdw radius.

where ,  and  are the maximum dimension of the molecular surface in ,  and  direction using vdw radii.

Source:

·    Jurs, P. C.; Hasan, M. N.; Hansen, P. J.; Rohrbaugh, R. H. Prediction of Physicochemical Properties of Organic Compounds from Molecular Structure, pages 209-233 in Physical Property Prediction (Jochum, C., Ed.) Springer, Berlin 1988

·    Rohrbaugh, R. H.; Jurs, P. C. Description of Molecular Shape Applied in Studies of Structure/Activity and Structure/Property Relationships Anal. Chim. Acta 1987, 199, 99-109

·    Rohrbaugh, R. H.; Jurs, P. C. Molecular Shape and the Prediction of HPLC Retention Indexes of Polycyclic Aromatic Hydrocarbons Anal. Chem. 1987, 59, 1048-1054

·    TodCon, page 389

where  is the largest value,  is the second largest value, and   is the smallest value of  .   stands for size-sorted.

,  and  span the respective plane of projection.

Source:

·    TodCon, page 389

 

271 XZ shadow

SHDW2 see 270.

272 YZ shadow

SHDW3 see 270.

273 standardized XY shadow

SHDW4 see 270.

274 standardized XZ shadow

SHDW5 see 270.

275 standardized YZ shadow

SHDW6 see 270.

276 XY/XZ shadow

SHDW1/SHDW2 see 270.

277 XY/YZ shadow

SHDW1/SHDW3 see 270.

278 XZ/YZ shadow

SHDW2/SHDW3 see 270.

279 size sorted shadow 1

ssSHDW1 see 270.

280 size sorted shadow 2

ssSHDW2 see 270.

281 size sorted shadow 3

ssSHDW3 see 270.

282  size sorted standardized shadow 1

ssSHDW4 see 270.

283 size sorted standardized shadow 2

ssSHDW5 see 270.

284 size sorted standardized shadow 3

ssSHDW6 see 270.

285 size sorted shadow 1/2

ssSHDW1/SHDW2 see 270.

286 size sorted shadow 1/3

ssSHDW1/SHDW3 see 270.

287 size sorted shadow 2/3

ssSHDW2/SHDW3 see 270.

288 Van der Waals volume

V_vdw, density_vdw, V_vdw^s, V_cub are descriptors of the category 'geometrical'.

Notation in text: , , ,

, ,  and  are calculated for molecules including H atoms.

where ,  and  are the maximum dimensions of the molecular surface in ,  and  direction by using , where ,  and  are the principle axes of inertia of the molecule (incl. H atoms).

Source:

·    TodCon, page 326

289 density by Van der Waals volume

rho_vdw see 288.

290 standardized Van der Waals volume

V_vdw^s see 288.

291 enclosing cuboid

V_cub see 288.

292-371 Sum of E-state of atomic subgraphs

S(atomic subgraph) are descriptors of the category 'electrotopol./AI’;

e.g. S(sCH3) for subgraph: -CH3.

Notation in text: , …

 is the sum of electrotopological state values of all  subgraphs.

 

The S(sCH3) is descriptor 292. Here is the list of all E-state descriptors from 292 to 371:

 

 

where s means a single bond, ss two single bonds, d a double bonds, t a triple bond, a an aromatic bond, etc. connected to the specified atom, not counting the single bonds to the attached H atoms. H2 means two attached H atoms.

Source:

·    Kier, L. B.; Hall, L. H. Molecular Structure Description. The Electrotopological State. Academic Press, San Diego (California) and London, 1999

 

372 Szeged index

SZD, SZDp are indices of the category 'topological'.

Notation in text: ,

The sums run over an H-suppressed molecular graph:

where  is the number of atoms in the H-suppressed molecular graph and  is the Szeged matrix.

For  see 0 and for  see Szeged matrix.

Source:

·    Khadikar, P. V.; Deshpande, N.V.; Kale, P. P.; Dobrynin, A.; Gutman, I.; Dömötör, G. The Szeged Index and an Analogy with the Wiener Index. J. Chem. Inf. Comput. Sci., 1995, 35, 547-550

·    Gutman, I; Klavzar, S. An Algorithm for the Calculation of the Szeged Index of Benzenoid Hydrocarbons. J. Chem. Inf. Comput. Sci. 1995, 35, 1011-1014

·    Zerovnik, J. Computing the Szeged Index. Croat. Chem. Acta. 1996, 69, 837-843

·    Zerovnik, J. Szeged Index of Symmetric Graphs. J. Chem. Inf. Comput. Sci. 1999, 39, 77-80

·    TodCon, page 438

373 hyper-Szeged index

SZDp see 372.

374 Van der Waals surface

S_vdw is a descriptor of the category 'geometrical'.

Notation in text:

 is the surface of the molecule by using vdw radii for each atom.

375 solvent-accessible surface (H2O)

SASA H2O is a descriptor of the category 'geometrical'.

Notation in text:

 is the solvent accessible surface of the molecule by using vdw radii and an H₂O molecule (r = 1.5Å) as a probe.

376 solvent-accessible surface (H)

SASA H is a descriptor of the category 'geometrical'.

Notation in text:

 is the solvent accessible surface of the molecule by using vdw radii and an H atom (r = 1.2Å) as a probe.

377-456 AI of atomic subgraph

AI(atomic subgraph) are descriptors of the category 'electrotopol./AI’;

eg. AI(sCH3) for subgraph: -CH3.

Notation in text: , …

The sums run over an H-suppressed molecular graph:

where  is the number of  subgraphs,  (or ) is the modified vertex degree of atom  and   is the vertex distance degree of atom .

For the subgraphs considered see 292-371, for  see modified vertex degree and for  see vertex distance degree.

 

The AI(sCH3) is descriptor 377. Here is the list of all AI descriptors from 377 to 456:

 

 

where s means a single bond, ss two single bonds, d a double bonds, t a triple bond, a an aromatic bond, etc. connected to the specified atom not counting the single bonds to the attached H atoms. H2 means two attached H atoms.

Source:

·  Ren, B. Novel Atomic-Level-Based AI Topological Descriptors: Application to QSPR/QSAR Modeling. J. Chem. Inf. Comput. Sci. 2002, 42, 858-868

·  Ren, B. Novel Atomic-Level-Based AI Topological Descriptors for Structure-Property Correlations. J. Chem. Inf. Comput. Sci. 2003, 43, 161-169

·  Ren, B. Novel Atom-Type AI Indices for QSPR Studies of Alcohols. Comput. & Chem. 2002, 26, 223-235

·  Ren, B. Application of Novel Atom-Type AI Topological Indices to QSPR Studies of Alkanes. Comput. & Chem. 2002, 26, 357-369

457 Xu index

Xu, Xu^m are descriptors of the category 'electrotopol./AI'.

Notation in text: ,

The sum runs over all atoms of an H-suppressed molecule:

where  is the number of atoms in an H-suppressed molecule,  is the vertex degree of the i^th atom,  is the vertex distance degree of the i^th atom.  (or ) is the modified vertex degree of atom .

For  see 0, for  see vertex degree, for  see vertex distance degree and for  see modified vertex degree.

Source:

·    Ren, B. A New Topological Index for QSPR of Alkanes. J. Chem. Inf. Comput. Sci. 1999, 39, 139-143

·    TodCon, page 507

458 modified Xu index

Xu^m see 457.

459-488 connectivity indices for substructures

m^Chi_q and m^Chi^v_q are descriptors of the category 'topological'. Substructures are paths, clusters, path-clusters and chains.

 

Available are:

 

Notation in text: ,

where  is the vertex degree and  is the valence vertex degree of atom  of the subgraph of type  in the H-suppressed molecular graph.  is the order (this is also called the “size” or “the number of edges”) of the subgraphs considered.  means paths, clusters, path-clusters or chains.  is the number of subgraphs of type  and size .  is the number of atoms of the subgraph considered.

 

Type of subgraphs:

·    If a subgraph contains a cycle it is of type chain () for ,

·    otherwise if every vertex has one or more than two non-H neighbours it is of type cluster () for ,

·    otherwise if every vertex has one or two non-H neighbours it is of type path () for ,

·    otherwise it is of type path-cluster () for . So a path-cluster has no cycles but vertices with one, two and more than two non-H neighbours.

 

For example paths are:

 

For example chains are:

 

For example clusters are:

 

For example path-clusters are:

 

For  see vertex degree, for  see valence vertex degree.

Source:

·    Kier, L. B.; Hall L. H. The Nature of Structure-Acticity Relationships and their Relation to Molecular Connectivity. Eur. J. Med. Chem., 1977, 12, 307-312

·    Kier, L. B.; Hall L. H. Molecular Connectivity in Structure-Activity Analysis. Research Studies Press - Wiley, Chichester (UK), 1986.

·    TodCon, pages 84-86 and page 314

489-699 overall indices

m^TO, m^TO*, m^TO_q, m^TO*_q, TO, TO*, TO_q, TO*_q are descriptors of the category 'overall'.

 

Available are:

Notation in text: , , , , , , ,

 is the overall-index sign. For the molecule each connected subgraph up to size  is constructed.  is one of these: M_1 for first Zagreb index , M_2 for second Zagreb index , W for Wiener index . C represents the sum over vertex degree  of each atom . C^v represents the sum over valence vertex degree  of each atom