sarchitect
Theory – Descriptors
Molecular descriptors are numerical values obtained by the quantification of various structural and physicochemical characteristics of the molecule. It is envisaged that molecular descriptors quantify these attributes so as to determine the behavior of the molecule and the way the molecule interacts with a physiological system. Since the exact mechanism of drug activity is unknown in many cases, it is desirable to start with descriptors spanning as many attributes of the molecules as possible and then assess their ability to predict the desired activity/property. Sarchitect computes over a thousand descriptors covering constitutional, topological and conformational spaces of compounds.
Terminology
Conventional
bond order 
of
a bond b
is 1, 2, 3 and 1.5 for single, double, triple and aromatic bonds
respectively.
Molecular Graph. A molecule may be considered as a graph with the atoms as the vertices and bonds as the edges. When a molecular graph is defined without hydrogens, it is called a H-depleted molecular graph.
Terminal Vertices. A vertex in a graph is called terminal if it has only one neighbor in the graph.
Topological distance. This is the shortest distance between a pair of atoms in a graph, defined as the number of edges in the shortest path between the atom pair in the molecular graph. For instance, the topological distance between the two carbons in ethane is 1 and that between the farthest carbons in benzene is 3.
Adjacency
Matrix. The
adjacency matrix for a molecule with n atoms is a n
n matrix in
which the ijth entry is 1
if the atoms i and j are
connected by a bond and 0 otherwise.
Geometric Matrix G is defined as a square matrix whose ijth entry is the Euclidean distance between the ith and jth atoms.
Multigraph distance matrix D* is a weighted distance matrix given by
where the sum runs through the sequence of bonds (edges) along the shortest path between atoms i and j.
Multigraph
distance degree 
of
the ith
atom is defined as sum of the corresponding row in the multigraph
distance
matrix :
Topological
Distance/Level
Matrix. The Distance/Level Matrix is a nn matrix in which
the ijth entry is the
topological distance between the atoms i
and j.
Vertex degree δi of an atom i is defined as the number of atoms adjacent to it in the H-depleted molecular graph.
Constitutional descriptors
Counts
Atom Counts
|
numAtoms |
Number of atoms |
|
nSK |
Number of non-H atoms |
|
NH |
Number of Hydrogen atoms |
|
NC |
Number of Carbon atoms |
|
NN |
Number of Nitrogen atoms |
|
NO |
Number of Oxygen atoms |
|
NP |
Number of Phosphorous atoms |
|
NS |
Number of Sulfur atoms |
|
NF |
number of Fluorine atoms |
|
nCl |
number of chlorine atoms |
|
nBr |
number of bromine atoms |
|
nI |
number of Iodine atoms |
|
NB |
number of Boron atoms |
|
nHM |
number of heavy atoms |
|
NX |
number of halogen atoms |
Bond Counts
|
numBonds |
Number of bonds |
|
nBO |
Number of non-H bonds |
|
nCIC |
Number of rings |
|
nCIR |
Number of circuits |
|
nBM |
Number of multiple bonds |
|
SCBO |
sum of conventional bond orders |
|
RBN |
Number of rotatable bonds |
|
RBF |
rotatable bond fraction |
|
nSB |
Number of single bonds |
|
nDB |
Number of double bonds |
|
nTB |
Number of triple bonds |
|
nAB |
Number of aromatic bonds |
Ring Counts
|
NR03 |
Number of 3-membered rings |
|
NR04 |
Number of 4-membered rings |
|
NR05 |
Number of 5-membered rings |
|
NR06 |
Number of 6-membered rings |
|
NR07 |
Number of 7-membered rings |
|
NR08 |
Number of 8-membered rings |
|
NR09 |
Number of 9-membered rings |
|
NR10 |
Number of 10-membered rings |
|
NR11 |
number of 11-membered rings |
|
NR12 |
number of 12-membered rings |
|
NBNZ |
number of benzene like rings |
Atom centered fragments
(1) The following atom centered fragment descriptors (Viswanadhan, 1989; Viswanadhan, 1993) are defined by looking at the first neighbors of carbon atoms. The neighbors of a carbon atom can be Hydrogens (represented as H), Carbons (represented as R) and heteroatoms (represented as X) in various combinations. = and # indicate double and triple bonds respectively.
|
CH3R |
|
CH2R2 |
|
CHR3 |
|
CH3X |
|
CH2RX |
|
CH2X2 |
|
CHR2X |
|
CHRX2 |
|
CHX3 |
|
CR4 |
|
CR3X |
|
CR2X2 |
|
CRX3 |
|
CX4 |
|
=CH2 |
|
=CHR |
|
=CR2 |
|
=CHX |
|
=CRX |
|
=CX2 |
|
#CH |
|
#CR |
|
#CX |
(2) The following atom centered fragment descriptors are defined for each ring atom that has three neighbors. The typical formats are A - - BC - - D, A – B (=C) – D and A – BC where the atom C on a ring is viewed as the center with A and D being its ring neighbors and B (that is not on the same ring as A, C and D) is connected to B. The atoms A, C and D can be Hydrogens (represented as H), Carbons (represented as R) and heteroatoms (represented as X). '-', -', '=' and '#' stand for a single, aromatic, double and triple bonds respectively. For example, R - - CH - - R can be defined as a central Carbon atom (C) on an aromatic ring that has two carbon neighbors (R) on the same aromatic ring and the third neighbor outside this ring is a Hydrogen (H).
|
R-CH-R |
|
R-CR-R |
|
R-CX-R |
|
R-CH-X |
|
R-CR-X |
|
R-CX-X |
|
X-CH-X |
|
X-CR-X |
|
X-CX-X |
|
R-C(=X)-X |
|
X-C(=X)-X |
Functional group Counts
|
nCp number of total primary Carbons (sp3) |
|
nCs number of total secondary Carbons (sp3) |
|
nCt number of total tertiary Carbons (sp3) |
|
nCq number of total quaternary Carbons (sp3) |
Property based descriptors
Physical
|
[ MW ] molecular weight |
|
[ AMW ] average molecular weight |
|
[ Sv ] sum of atomic van der Waals volumes (scaled on Carbon atom) |
|
[ Mv ] mean atomic van der Waals volume (scaled on Carbon atom) |
|
[ Hy ] hydrophilic factor 1 (empirical descriptors) |
Hydrophilicity index (HyOld)
It is an empirical index related to Hydrophilicity of
compounds (Todeschini,
2000).
It is defined as:
where, NHy is the number of hydrophilic groups (-OH, -SH, -NH), NC is the number of carbon atoms, and A the number of atoms (hydrogen excluded)
HyOld has values between -1 and 3.64.
Electronic
|
[ Se ] sum of atomic Sanderson electronegativities (scaled on Carbon atom) |
|
[ Sp ] sum of atomic polarizabilities (scaled on Carbon atom) |
|
[ Me ] mean atomic Sanderson electronegativity (scaled on Carbon atom) |
|
[ Mp ] mean atomic polarizability (scaled on Carbon atom) |
mlogP
mLOGP is the Moriguchi octanol-water partition coefficient (logP) calculated using the model developed by Moriguchi et al. (Moriguchi, 1992; Moriguchi, 1994).
mlogP is defined as:
Further, the 13 structural
parameters
comprising the above mentioned regression equation have also been
listed as
independent descriptors by themselves, namely:
|
[ MLOGP ] Moriguchi octanol-water partition coefficient (logP) |
|
[ mlogpCX ] Moriguchi based lipophilicity descriptor (carbon and halogen atoms) |
|
[ mlogpON ] Moriguchi based lipophilicity descriptor (nitrogen and oxygen atoms) |
|
[ mlogpPRX ] Moriguchi based lipophilicity descriptor (proximity efffect) |
|
[ mlogpUB ] Moriguchi based lipophilicity descriptor (unsaturated bonds) |
|
[ mlogpHB ] Moriguchi based lipophilicity descriptor (intramolecular H bonds) |
|
[ mlogpPOL ] Moriguchi based lipophilicity descriptor (Polar substituents) |
|
[ mlogpAMP ] Moriguchi based lipophilicity descriptor (amphotericity) |
|
[ mlogpALK ] Moriguchi based lipophilicity descriptor (alkanes and alkenes) |
|
[ mlogpRNG ] Moriguchi based lipophilicity descriptor (ring structures) |
|
[ mlogpQN ] Moriguchi based lipophilicity descriptor (quarternary nitrogen) |
|
[ mlogpNO2 ] Moriguchi based lipophilicity descriptor (Nitro groups) |
|
[ mlogpNCS ] Moriguchi based lipophilicity descriptor (NCS ) |
|
[ mlogpBLM ] Moriguchi based lipophilicity descriptor (beta lactam) |
Pharmacophoric Features
|
[ nHDon ] number of hydrogen-bond donors |
|
[ nHAcc ] number of hydrogen-bond acceptors |
|
[ a_hyd ] number of hydrophobic atoms |
Topological (2D) descriptors
BCUT indices
The BCUT (Burden - CAS - University of Texas eigen values) descriptors are the eigen values of a modified connectivity matrix known as the Burden matrix [Burden, 1989].
The Burden matrices M are defined such that :
The diagonal elements Mww are the weights wi for atom Ai where the weights may be some property associated with the atoms such as m (relative atomic mass), p (polarizability), e (Sanderson electronegativity) and v (Van der Waals volume).
The non-diagonal elements Mwk are 1 if k = dij and 0 otherwise, where k is the lag defined as the topological distance d between the atom pair i-j and may have a value between 0-8. Thus for a given k, the non-diagonal element Mij will be unity if the atoms i and j are apart by a topological distance k and zero otherwise.
For a given w and k, there are two BCUT descriptors BEHwk and BELwk – BEHwk is the highest positive eigen value of the matrix Mwk and will be zero if there are no positive eigen values. BELwk is the lowest negative eigen value of the matrix Mwk and zero if there are no negative eigen values [Burden 1997; Pearlman & Smith 1998, 1999; Benigni 1999].
There are 64 BCUT descriptors in sarchitect:
Mass weighted
BEHm1, BEHm2, BEHm3, BEHm4, BEHm5, BEHm6, BEHm7, BEHm8
BELm1, BELm2, BELm3, BELm4, BELm5, BELm6, BELm7, BELm8
van der Waals volume
BEHv1, BEHv2, BEHv3, BEHv4, BEHv5, BEHv6, BEHv7, BEHv8
BELv1, BELv2, BELv3, BELv4, BELv5, BELv6, BELv7, BELv8
Electronegativity
BEHe1, BEHe2, BEHe3, BEHe4, BEHe5, BEHe6, BEHe7, BEHe8
BELe1, BELe2, BELe3, BELe4, BELe5, BELe6, BELe7, BELe8
Polarizability
BEHp1, BEHp2, BEHp3, BEHp4, BEHp5, BEHp6, BEHp7, BEHp8
BELp1, BELp2, BELp3, BELp4, BELp5, BELp6, BELp7, BELp8
Relative mass is defined as the ratio of atomic mass of an atom to that of carbon. Similarly, the other three weights p, e and v are scaled by the corresponding values for Carbon.
where 
and the lag 
as in Autocorrelation
descriptors.
Autocorrelation descriptors.
2D Auto Correlation Indices
The following Autocorrelation descriptors are available in sarchitect. Broto-Moreau Autocorrelation Descriptors (labeled as ATS) Moran Autocorrelation Descriptors (labeled as MATS) Geary Autocorrelation Descriptors (labeled as GATS)
The symbol for each of the autocorrelation descriptors is followed by two indices d and w where d stands for the lag and w stands for the weight. Thus, for example, ATS4m means the Broto-Moreau Autocorrelation Descriptor of lag 4 that is weighted by mass.
The lag is defined as the topological distance d between pairs of atoms. The topological distance between a pair of atoms (i, j) is given in the ijth entry in the Topological Level Matrix. The lag can have any value from the set {0, 1, 2, 3, 4, 5, 6, 7, 8}.
The weight can be m (relative atomic mass), p (polarizability), e (Sanderson electronegativity) and v (Van der Waals volume). Relative mass is defined as the ratio of atomic mass of an atom to that of carbon. Similarly, the other three weights p, e and v are scaled by the corresponding values for Carbon.
Let n be the number of atoms in the molecule. For any chosen value for lag d and any chosen weight w, we compute the Autocorrelation Descriptors using the following formulae.
Broto-Moreau Autocorrelation Descriptors
where,
wi and wj
are the weights of the atoms i and j,
, and δij
is Kronecker delta, that is, δij
=1 if the ijth
entry in the Topological Level Matrix is = d, and
δij
= 0 otherwise.
(Moreau & Broto, 1980a; Moreau & Broto, 1980b; Broto, 1984a; Broto, 1984b; Broto & Devillers, 1990)
|
[ ATS1m ] Broto-Moreau autocorrelation of a topological structure - lag 1 / weighted by atomic masses |
|
[ ATS2m ] Broto-Moreau autocorrelation of a topological structure - lag 2 / weighted by atomic masses |
|
[ ATS3m ] Broto-Moreau autocorrelation of a topological structure - lag 3 / weighted by atomic masses |
|
[ ATS4m ] Broto-Moreau autocorrelation of a topological structure - lag 4 / weighted by atomic masses |
|
[ ATS5m ] Broto-Moreau autocorrelation of a topological structure - lag 5 / weighted by atomic masses |
|
[ ATS6m ] Broto-Moreau autocorrelation of a topological structure - lag 6 / weighted by atomic masses |
|
[ ATS7m ] Broto-Moreau autocorrelation of a topological structure - lag 7 / weighted by atomic masses |
|
[ ATS8m ] Broto-Moreau autocorrelation of a topological structure - lag 8 / weighted by atomic masses |
|
[ ATS1v ] Broto-Moreau autocorrelation of a topological structure - lag 1 / weighted by atomic van der Waals volumes |
|
[ ATS2v ] Broto-Moreau autocorrelation of a topological structure - lag 2 / weighted by atomic van der Waals volumes |
|
[ ATS3v ] Broto-Moreau autocorrelation of a topological structure - lag 3 / weighted by atomic van der Waals volumes |
|
[ ATS4v ] Broto-Moreau autocorrelation of a topological structure - lag 4 / weighted by atomic van der Waals volumes |
|
[ ATS5v ] Broto-Moreau autocorrelation of a topological structure - lag 5 / weighted by atomic van der Waals volumes |
|
[ ATS6v ] Broto-Moreau autocorrelation of a topological structure - lag 6 / weighted by atomic van der Waals volumes |
|
[ ATS7v ] Broto-Moreau autocorrelation of a topological structure - lag 7 / weighted by atomic van der Waals volumes |
|
[ ATS8v ] Broto-Moreau autocorrelation of a topological structure - lag 8 / weighted by atomic van der Waals volumes |
|
[ ATS1e ] Broto-Moreau autocorrelation of a topological structure - lag 1 / weighted by atomic Sanderson electronegativities |
|
[ ATS2e ] Broto-Moreau autocorrelation of a topological structure - lag 2 / weighted by atomic Sanderson electronegativities |
|
[ ATS3e ] Broto-Moreau autocorrelation of a topological structure - lag 3 / weighted by atomic Sanderson electronegativities |
|
[ ATS4e ] Broto-Moreau autocorrelation of a topological structure - lag 4 / weighted by atomic Sanderson electronegativities |
|
[ ATS5e ] Broto-Moreau autocorrelation of a topological structure - lag 5 / weighted by atomic Sanderson electronegativities |
|
[ ATS6e ] Broto-Moreau autocorrelation of a topological structure - lag 6 / weighted by atomic Sanderson electronegativities |
|
[ ATS7e ] Broto-Moreau autocorrelation of a topological structure - lag 7 / weighted by atomic Sanderson electronegativities |
|
[ ATS8e ] Broto-Moreau autocorrelation of a topological structure - lag 8 / weighted by atomic Sanderson electronegativities |
|
[ ATS1p ] Broto-Moreau autocorrelation of a topological structure - lag 1 / weighted by atomic polarizabilities |
|
[ ATS2p ] Broto-Moreau autocorrelation of a topological structure - lag 2 / weighted by atomic polarizabilities |
|
[ ATS3p ] Broto-Moreau autocorrelation of a topological structure - lag 3 / weighted by atomic polarizabilities |
|
[ ATS4p ] Broto-Moreau autocorrelation of a topological structure - lag 4 / weighted by atomic polarizabilities |
|
[ ATS5p ] Broto-Moreau autocorrelation of a topological structure - lag 5 / weighted by atomic polarizabilities |
|
[ ATS6p ] Broto-Moreau autocorrelation of a topological structure - lag 6 / weighted by atomic polarizabilities |
|
[ ATS7p ] Broto-Moreau autocorrelation of a topological structure - lag 7 / weighted by atomic polarizabilities |
|
[ ATS8p ] Broto-Moreau autocorrelation of a topological structure - lag 8 / weighted by atomic polarizabilities |
Moran Autocorrelation Descriptors:
where,
and
where,
wi
and wj
are the weights of the atoms i and j,
is the mean of wi
over the entire molecule, and δij
is Kronecker delta,
that is, δij
= 1 if the ijth
entry in the Topological Level Matrix is = d, and
δij
= 0 otherwise (Moran, 1950).
|
[ MATS1m ] Moran autocorrelation - lag 1 / weighted by atomic masses |
|
[ MATS2m ] Moran autocorrelation - lag 2 / weighted by atomic masses |
|
[ MATS3m ] Moran autocorrelation - lag 3 / weighted by atomic masses |
|
[ MATS4m ] Moran autocorrelation - lag 4 / weighted by atomic masses |
|
[ MATS5m ] Moran autocorrelation - lag 5 / weighted by atomic masses |
|
[ MATS6m ] Moran autocorrelation - lag 6 / weighted by atomic masses |
|
[ MATS7m ] Moran autocorrelation - lag 7 / weighted by atomic masses |
|
[ MATS8m ] Moran autocorrelation - lag 8 / weighted by atomic masses |
|
[ MATS1v ] Moran autocorrelation - lag 1 / weighted by atomic van der Waals volumes |
|
[ MATS2v ] Moran autocorrelation - lag 2 / weighted by atomic van der Waals volumes |
|
[ MATS3v ] Moran autocorrelation - lag 3 / weighted by atomic van der Waals volumes |
|
[ MATS4v ] Moran autocorrelation - lag 4 / weighted by atomic van der Waals volumes |
|
[ MATS5v ] Moran autocorrelation - lag 5 / weighted by atomic van der Waals volumes |
|
[ MATS6v ] Moran autocorrelation - lag 6 / weighted by atomic van der Waals volumes |
|
[ MATS7v ] Moran autocorrelation - lag 7 / weighted by atomic van der Waals volumes |
|
[ MATS8v ] Moran autocorrelation - lag 8 / weighted by atomic van der Waals volumes |
|
[ MATS1e ] Moran autocorrelation - lag 1 / weighted by atomic Sanderson electronegativities |
|
[ MATS2e ] Moran autocorrelation - lag 2 / weighted by atomic Sanderson electronegativities |
|
[ MATS3e ] Moran autocorrelation - lag 3 / weighted by atomic Sanderson electronegativities |
|
[ MATS4e ] Moran autocorrelation - lag 4 / weighted by atomic Sanderson electronegativities |
|
[ MATS5e ] Moran autocorrelation - lag 5 / weighted by atomic Sanderson electronegativities |
|
[ MATS6e ] Moran autocorrelation - lag 6 / weighted by atomic Sanderson electronegativities |
|
[ MATS7e ] Moran autocorrelation - lag 7 / weighted by atomic Sanderson electronegativities |
|
[ MATS8e ] Moran autocorrelation - lag 8 / weighted by atomic Sanderson electronegativities |
|
[ MATS1p ] Moran autocorrelation - lag 1 / weighted by atomic polarizabilities |
|
[ MATS2p ] Moran autocorrelation - lag 2 / weighted by atomic polarizabilities |
|
[ MATS3p ] Moran autocorrelation - lag 3 / weighted by atomic polarizabilities |
|
[ MATS4p ] Moran autocorrelation - lag 4 / weighted by atomic polarizabilities |
|
[ MATS5p ] Moran autocorrelation - lag 5 / weighted by atomic polarizabilities |
|
[ MATS6p ] Moran autocorrelation - lag 6 / weighted by atomic polarizabilities |
|
[ MATS7p ] Moran autocorrelation - lag 7 / weighted by atomic polarizabilities |
|
[ MATS8p ] Moran autocorrelation - lag 8 / weighted by atomic polarizabilities |
Geary Autocorrelation Descriptors
where,
and
where,
wi and wj
are the weights of the atoms i and j,
, is the mean of wi
over the entire molecule, and δij
is Kronecker delta,
that is, δij
=1 if the ijth
entry in the Topological Level Matrix is = d, and
δij
=0 otherwise (Geary, 1954).
Given below is the list of Autocorrelation descriptors implemented in sarchitect:
|
[ GATS1m ] Geary autocorrelation - lag 1 / weighted by atomic masses |
|
[ GATS2m ] Geary autocorrelation - lag 2 / weighted by atomic masses |
|
[ GATS3m ] Geary autocorrelation - lag 3 / weighted by atomic masses |
|
[ GATS4m ] Geary autocorrelation - lag 4 / weighted by atomic masses |
|
[ GATS5m ] Geary autocorrelation - lag 5 / weighted by atomic masses |
|
[ GATS6m ] Geary autocorrelation - lag 6 / weighted by atomic masses |
|
[ GATS7m ] Geary autocorrelation - lag 7 / weighted by atomic masses |
|
[ GATS8m ] Geary autocorrelation - lag 8 / weighted by atomic masses |
|
[ GATS1v ] Geary autocorrelation - lag 1 / weighted by atomic van der Waals volumes |
|
[ GATS2v ] Geary autocorrelation - lag 2 / weighted by atomic van der Waals volumes |
|
[ GATS3v ] Geary autocorrelation - lag 3 / weighted by atomic van der Waals volumes |
|
[ GATS4v ] Geary autocorrelation - lag 4 / weighted by atomic van der Waals volumes |
|
[ GATS5v ] Geary autocorrelation - lag 5 / weighted by atomic van der Waals volumes |
|
[ GATS6v ] Geary autocorrelation - lag 6 / weighted by atomic van der Waals volumes |
|
[ GATS7v ] Geary autocorrelation - lag 7 / weighted by atomic van der Waals volumes |
|
[ GATS8v ] Geary autocorrelation - lag 8 / weighted by atomic van der Waals volumes |
|
[ GATS1e ] Geary autocorrelation - lag 1 / weighted by atomic Sanderson electronegativities |
|
[ GATS2e ] Geary autocorrelation - lag 2 / weighted by atomic Sanderson electronegativities |
|
[ GATS3e ] Geary autocorrelation - lag 3 / weighted by atomic Sanderson electronegativities |
|
[ GATS4e ] Geary autocorrelation - lag 4 / weighted by atomic Sanderson electronegativities |
|
[ GATS5e ] Geary autocorrelation - lag 5 / weighted by atomic Sanderson electronegativities |
|
[ GATS6e ] Geary autocorrelation - lag 6 / weighted by atomic Sanderson electronegativities |
|
[ GATS7e ] Geary autocorrelation - lag 7 / weighted by atomic Sanderson electronegativities |
|
[ GATS8e ] Geary autocorrelation - lag 8 / weighted by atomic Sanderson electronegativities |
|
[ GATS1p ] Geary autocorrelation - lag 1 / weighted by atomic polarizabilities |
|
[ GATS2p ] Geary autocorrelation - lag 2 / weighted by atomic polarizabilities |
|
[ GATS3p ] Geary autocorrelation - lag 3 / weighted by atomic polarizabilities |
|
[ GATS4p ] Geary autocorrelation - lag 4 / weighted by atomic polarizabilities |
|
[ GATS5p ] Geary autocorrelation - lag 5 / weighted by atomic polarizabilities |
|
[ GATS6p ] Geary autocorrelation - lag 6 / weighted by atomic polarizabilities |
|
[ GATS7p ] Geary autocorrelation - lag 7 / weighted by atomic polarizabilities |
|
[ GATS8p ] Geary autocorrelation - lag 8 / weighted by atomic polarizabilities |
Topological Indices
Topological Distances
Let {x1…xk} be the atoms of a particular chemical element x in the molecule. Similarly, {y1 … ym} are the atoms of a particular chemical element y in the molecule. We permit the case of x = y as well. Then the Atom Pair Topological Distance between the chemical elements x and y is given by:
where,
dij is the topological
distance (see Appendix A) between xi
and yi
(Bonchev, 1991; Trinajstic, 1992). Following
are the pairs of chemical elements for which the Atom Pair Topological
Distances are computed:
|
[ T(N..N) ] sum of topological distances between N..N |
|
[ T(N..O) ] sum of topological distances between N..O |
|
[ T(N..S) ] sum of topological distances between N..S |
|
[ T(N..P) ] sum of topological distances between N..P |
|
[ T(N..F) ] sum of topological distances between N..F |
|
[ T(N..Cl) ] sum of topological distances between N..Cl |
|
[ T(N..Br) ] sum of topological distances between N..Br |
|
[ T(N..I) ] sum of topological distances between N..I |
|
[ T(O..O) ] sum of topological distances between O..O |
|
[ T(O..S) ] sum of topological distances between O..S |
|
[ T(O..P) ] sum of topological distances between O..P |
|
[ T(O..F) ] sum of topological distances between O..F |
|
[ T(O..Cl) ] sum of topological distances between O..Cl |
|
[ T(O..Br) ] sum of topological distances between O..Br |
|
[ T(O..I) ] sum of topological distances between O..I |
|
[ T(S..S) ] sum of topological distances between S..S |
|
[ T(S..P) ] sum of topological distances between S..P |
|
[ T(S..F) ] sum of topological distances between S..F |
|
[ T(S..Cl) ] sum of topological distances between S..Cl |
|
[ T(S..Br) ] sum of topological distances between S..Br |
|
[ T(S..I) ] sum of topological distances between S..I |
|
[ T(P..P) ] sum of topological distances between P..P |
|
[ T(P..F) ] sum of topological distances between P..F |
|
[ T(P..Cl) ] sum of topological distances between P..Cl |
|
[ T(P..Br) ] sum of topological distances between P..Br |
|
[ T(P..I) ] sum of topological distances between P..I |
|
[ T(F..F) ] sum of topological distances between F..F |
|
[ T(F..Cl) ] sum of topological distances between F..Cl |
|
[ T(F..Br) ] sum of topological distances between F..Br |
|
[ T(F..I) ] sum of topological distances between F..I |
|
[ T(Cl..Cl) ] sum of topological distances between Cl..Cl |
|
[ T(Cl..Br) ] sum of topological distances between Cl..Br |
|
[ T(Cl..I) ] sum of topological distances between Cl..I |
|
[ T(Br..Br) ] sum of topological distances between Br..Br |
|
[ T(Br..I) ] sum of topological distances between Br..I |
|
[ T(I..I) ] sum of topological distances between I..I |
Connectivity indices
Kier-Hall Connectivity Indices
The following Kier-Hall Connectivity Indices are calculated from the Hydrogen-depleted molecular graph (Kier & Hall, 1986).
- Connectivity index Chi-0 through Chi-5
- Average Connectivity index Chi-0 through Chi-5
- Valence Connectivity index Chi-0 through Chi-5
- Average Valence Connectivity index Chi-0 through Chi-5
Connectivity indices Chi-0 through Chi-5 are defined as follows.
:
Connectivity index Chi-0 is defined as:
where,
n is the number of nodes in the Hydrogen-depleted graph,
δi is the vertex degree of the ith atom defined as the number of non-Hydrogen neighbours in the molecular graph.
The Average Connectivity index Chi-0 is:
:
Connectivity index Chi-1 is defined as:
where,
b is the number of bonds, the sum runs through all bond in the Hydrogen-depleted molecule, and for each bond δi δj is the product of the vertex degrees of the end atoms i and j.
The Average Connectivity index Chi-1 is
Higher 
Indices:
Connectivity indices Chi-m
for 2 ≤ m ≤ 5 is defined as:
where,
(II δi)k is the product of the vertex degrees of the atoms that form a connected subgraph with m edges, and
K is the total number of such distinct connected sub graphs (the H-depleted molecular graph) each having m edges.
For
any m, 0 ≤ m
≤ 5, if we replace the vertex degree δi
by the valence
vertex degree 
for each atom i in the Connectivity index Chi-m, then we get Valence Connectivity Indices Chi-m (Kier & Hall, 1981; Kier & Hall, 1983). That is,
where,
is the product of the valence vertex
degrees of the atoms that form a connected subgraph with m
edges, and
K is the total number of such distinct connected subgraphs (the H-depleted molecular graph) each having m edges.
The Valence Connectivity Indices account for the presence of heteroatoms and double and triple bonds.
The Average Valence Connectivity index Chi-1 is defined similarly:
|
[ X0 ] connectivity index chi-0 |
|
[ X1 ] connectivity index chi-1 (Randic connectivity index) |
|
[ X2 ] connectivity index chi-2 |
|
[ X3 ] connectivity index chi-3 |
|
[ X4 ] connectivity index chi-4 |
|
[ X5 ] connectivity index chi-5 |
|
[ X0A ] average connectivity index chi-0 |
|
[ X1A ] average connectivity index chi-1 |
|
[ X2A ] average connectivity index chi-2 |
|
[ X3A ] average connectivity index chi-3 |
|
[ X4A ] average connectivity index chi-4 |
|
[ X5A ] average connectivity index chi-5 |
|
[ X0v ] valence connectivity index chi-0 |
|
[ X1v ] valence connectivity index chi-1 |
|
[ X2v ] valence connectivity index chi-2 |
|
[ X3v ] valence connectivity index chi-3 |
|
[ X4v ] valence connectivity index chi-4 |
|
[ X5v ] valence connectivity index chi-5 |
|
[ X0Av ] average valence connectivity index chi-0 |
|
[ X1Av ] average valence connectivity index chi-1 |
|
[ X2Av ] average valence connectivity index chi-2 |
|
[ X3Av ] average valence connectivity index chi-3 |
|
[ X4Av ] average valence connectivity index chi-4 |
|
[ X5Av ] average valence connectivity index chi-5 |
Balaban indices
Balaban Distance Connectivity Index, J
J is defined as (Balaban, 1982):
where,
σi and σj are vertex distance degrees of two adjacent atoms i and j that are connected by the bond b, and
the sum runs over all the bonds b in the molecule,
B is the total number of bonds in the molecule, and
C is the cyclomatic number.
The vertex distance degree is the row sum σi of the Topological Level Matrix (see Appendix A), that is
where,
dij is the ith entry in the Topological Level Matrix.
The cyclomatic number is the number of independent cycles C in a molecule or equivalently, the number of non-overlapping cycles. It is equal to the minimum number of edges that must be removed from the molecular graph to make it acyclic (that is, equal to the number of back edges in DFS tree). The cyclomatic number is given by:
C = B – n + 1,
where,
n is the number of atoms and B is the number of bonds in the molecule.
Balaban Modified Distance Connectivity Indices
Multi-graph
distance matrix D* is
defined as a weighted distance matrix where the distance from an atom i
to an atom j is obtained by counting the edges in
the shortest path
between them, where each edge b counts as the
inverse of the
conventional bond order , that is,
where,
b
represents the bond whose bond order is and the sum runs through the sequence
of bonds along the shortest path between the atoms i and
j.
Conventional
bond order of a bond b
is equal to 1, 2, 3 and 1.5 for single, double, triple and aromatic
bonds
respectively. Thus we can count each edge as 1, 0.5, 0.333 and 0.667
when it is
single, double, triple and aromatic bonds respectively.
Multigraph
distance degree of the ith
atom is defined as the row sum in the Multigraph distance matrix, that
is,
The Balaban Modified Distance Connectivity Indices JU, JX, JY and JZ are defined as follows (Balaban, 1986; Balaban, 1990).
where,
Xi, Yi and Vi are electronegativity, covalent radius and van der Waal volume of the ith atom,
and 
are the
multigraph distance degrees of two adjacent atoms i
and j
connected by the bond b, and
the sum runs over all the bonds b in the molecule,
B,is the total number of bonds in the molecule, and
C is the cyclomatic number.
Note that JU is the unweighted Balaban Modified Distance Connectivity Index.
Balaban-type Indices
The multigraph factor for the ith atom is defined as:
where,
Vi is the set of neighbors of the ith atom, and
is the
conventional bond order of the bond between the atoms i and
a.
A Balaban-type Index, DJ is defined as follows (Balaban, 1993):
where,
; σi
is vertex distance degree and fi
is the multigraph factor for
the ith atom (defined
above),
Vi is the set of neighbors of the ith atom, that is the inner sum runs over all neighbors of the ith atom, and
w is one of m, e, p, v, Z which are relative mass, relative electronegativity, relative polarizability, relative van der waal volume and relative atomic number respectively, of the ith atom with respect to carbon.
The Balaban indices in sarchitect are:
|
[ J ] Balaban J index |
|
[ Uindex ] Balaban U index |
|
[ Vindex ] Balaban V index |
|
[ Xindex ] Balaban X index |
|
[ Yindex ] Balaban Y index |
|
[ Jhetm ] Balaban-type index from mass weighted distance matrix |
|
[ Jhetv ] Balaban-type index from van der Waals weighted distance matrix |
|
[ Jhete ] Balaban-type index from electronegativity weighted distance matrix |
|
[ Jhetp ] Balaban-type index from polarizability weighted distance matrix |
|
[ JhetZ ] Balaban-type index from Z weighted distance matrix (Barysz matrix) ) |
Charge indices
The Topological Charge Indices were proposed to evaluate the charge transfer between pairs of atoms and therefore, the global charge transfer in the molecule (Galvez, 1994; Galvez, 1995). The Topological Charge Indices are computed using the Topological Level Matrix, Reciprocal Square Distance Matrix and the Adjacency Matrix defined as follows.
The Topological Level Matrix contains the topological distance between a pair of atoms i and j at its ijth entry.
The Reciprocal Square Distance Matrix D-2
is
defined as the square matrix in which the ith
entry is: 
if i ≠
j and = 0 , otherwise,
where,
dij is the ijth entry in the topological level matrix.
The Adjacency Matrix
is defined as the square matrix
in which the ijth entry is:
=1 if i and j are connected
by a bond = 0, otherwise.
The Galvez Matrix M is defined as:
M = A.D-2.
here A and D-2 are as defined above.
The vertex degree δi of an atom i is defined as the number of atoms adjacent to it in the H-depleted molecular graph.
The Charge Term Matrix CT is defined as follows:
CTij = δi if i = j
where,
δi
is the
vertex degree of the ith
atom. That is, the diagonal entries
in the matrix are the vertex degrees of the corresponding atom, and 
if i ≠
j
where,
mij and mji are the elements of the Galvez Matrix M. That is, the non-diagonal entries are the differences mij – mji.
The Topological Charge Index GGk is defined as:
where,
n is the total number of non-Hydrogen atoms in the molecule,
δ(k; dij) indicates Kronecker delta, namely:
δ(k; dij) = 1, if dij = k and
δ(k; dij) = 0, otherwise.
The Mean Topological Charge Index JGk is defined as:
The Global Topological Charge Index (JGT) is given by:
|
[ GGI1 ] topological charge index of order 1 |
|
[ GGI2 ] topological charge index of order 2 |
|
[ GGI3 ] topological charge index of order 3 |
|
[ GGI4 ] topological charge index of order 4 |
|
[ GGI5 ] topological charge index of order 5 |
|
[ GGI6 ] topological charge index of order 6 |
|
[ GGI7 ] topological charge index of order 7 |
|
[ GGI8 ] topological charge index of order 8 |
|
[ GGI9 ] topological charge index of order 9 |
|
[ GGI10 ] topological charge index of order 10 |
|
[ JGI1 ] mean topological charge index of order1 |
|
[ JGI2 ] mean topological charge index of order2 |
|
[ JGI3 ] mean topological charge index of order3 |
|
[ JGI4 ] mean topological charge index of order4 |
|
[ JGI5 ] mean topological charge index of order5 |
|
[ JGI6 ] mean topological charge index of order6 |
|
[ JGI7 ] mean topological charge index of order7 |
|
[ JGI8 ] mean topological charge index of order8 |
|
[ JGI9 ] mean topological charge index of order9 |
|
[ JGI10 ] mean topological charge index of order10 |
|
[ JGT ] global topological charge index |
Shape indices
Path/Walk Shape Indices
Atomic path/Walk
Index for the ith
atom is the ratio between Atomic Path Count 
and Atomic walk Count 
of same
length m, m = 2, 3, 4,5
(Randic, 1999), i.e.
Molecular Path/Walk Index is defined as the average sum of atomic path/walk indices of equal length:
The shape descriptor, Petitjean Shape index I2 (labelled as PJI2) is a topological anisometry descriptor (Petitjean, 1992). It is defined as:
I2
= (D - R) /R
|
[ PW2 ] path/walk 2 - Randic shape index |
|
[ PW3 ] path/walk 3 - Randic shape index |
|
[ PW4 ] path/walk 4 - Randic shape index |
|
[ PW5 ] path/walk 5 - Randic shape index |
|
[ PJI2 ] Petiti Jean shape index |
Eccentricity Indices
Let n be the total number of atoms (including Hydrogens) in a molecule. Consider the Topological Level Matrix (see Appendix A). For each atom i, the maximum value entry in the ith row is called the atom eccentricity vi of the atom i. Based on this, the molecular graph can be characterized by two molecular descriptors, the topological radius R = mini (vi) of the molecule and the topological diameter D = maxi (vi) of the molecule. Sarchitect has the following descriptors based on vi, R and D (Konstantinova, 1996)
Eccentricity v (labelled as ECC):
Average Atom Eccentricity 
(labelled as AECC):
= v/n
Eccentric 
(labelled as DECC):
|
[ ECC ] eccentricity |
|
[ AECC ] average eccentricity |
|
[ DECC ] eccentric |
Eigenvalue-based Indices
Eigenvalue Sum Descriptors
The Eigenvalue Sum Descriptors are computed from Weighted Distance Matrices of a Hydrogen-depleted Molecular Graph. The following weighted distance matrices are required for computation of the descriptors.
Barysz Distance Matrix Dz: This is a weighted distance matrix accounting for the presence of heteroatoms and multiple bonds. The ijth entry in the matrix Dz is defined as follows (Barysz, 1983):
if i
= j
if i
≠ j
where,
ZC is the atomic number of carbon atom,
Zi is the atomic number of the ijth atom, and
the sum runs over all the bonds b in the shortest path from the atom i to the atom j, dij is the topological distance (i.e. the number of bonds from the atom i to the atom j in the molecule)
is the
conventional bond order of the bond b, that is
1,2,3 and 1.5 for single,
double, triple and aromatic bonds respectively,
Zb(1) and Zb(1) are the atomic numbers of the atoms on the bond b
Electronegativity-weighted Distance Matrix DX:
The Electronegativity-weighted Distance Matrix DX is similar to the Barysz Distance Matrix. It can be obtained from the Barysz Distance Matrix by replacing atomic number by relative atom electronegativity (Ivanciuc, 1998). That is,
, if i ≠ j
, if i ≠ j
where,
Xi is the relative atomic electronegativity of ijth atom with respect to the carbon atom,
the sum runs over all the bonds b in the shortest path from the atom i to the atom j, dij is the topological distance.
is the
conventional bond order of the bond b, that is 1,
2, 3 and 1.5 for
single, double, triple and aromatic bonds respectively,
Xb(1) and Xb(2) are the relative atomic electronegativity of the atoms forming the bond b
Covalent radius-weighted Distance Matrix DY:
The Covalent radius-weighted Distance Matrix DY is defined (Ivanciuc, 1998) as:
, if
i = j
, if
i ≠ j
where,
Yi is the relative atomic covalent radius of ith atom to the carbon atom.
Polarizability weighted distance matrix:
It is defined as:
, if
i = j
, if
i ≠ j
where,
Pi is the relative atomic polarizability of ith atom to the carbon atom.
Mass weighted distance matrix:
It is defined as:
, if
i = j
, if
i ≠ j
where,
Mi is the relative atomic mass of ith atom to the carbon atom
For each of the above defined matrices, the sum of their eigenvalues is computed to get the corresponding Eigenvalue Sum Descriptor.
VEA Indices
VEA indices (Balaban, 1991) are defined by the coefficients liA of the eigenvector associated with the largest negative eigenvalue (that is the last in the decreasing order of magnitude) of the Adjacency Matrix (see Appendix A).
We have the following three VEA Indices:
where A is the number of atoms in the molecule.
VEA2 = (VEA1)/A
VEA3 = (A/10) (log (VEA1))
|
[ SEigm ] Eigenvalue sum from mass weighted distance matrix |
|
[ SEigv ] Eigenvalue sum from van der Waals weighted distance matrix |
|
[ SEige ] Eigenvalue sum from electronegativity weighted distance matrix |
|
[ SEigp ] Eigenvalue sum from polarizability weighted distance matrix |
|
[ SEigZ ] Eigenvalue sum from Z weighted distance matrix (Barysz matrix) |
|
[ VEA1 ] eigenvector coefficient sum from adjacency matrix |
|
[ VEA2 ] average eigenvector coefficient sum from adjacency matrix |
|
[ VEA3 ] log of eigenvector coefficient sum from adjacency matrix |
E-state
The E-state Topological Parameter - TIE
The E-state Topological Parameter is a Balaban-type index derived from E-state indices and is similar to the Balaban Modified Distance Connectivity Indices (Voelkel, 1994). It is given as:
where,
si and sj are the Electro-Topological State Indices for the two adjacent non-Hydrogen atoms i and j that are on the bond b, and
the sum runs over all the bonds b in the Hydrogen-depleted molecular graph,
B is the total number of bonds in the Hydrogen-depleted molecular graph, and
C is the cyclomatic number.
Aromaticity Indices
|
[ BLI ] Kier benzene-likeliness index |
Super-Pendentic Index - SPI
Super-Pendentic Index is a topological descriptor computed from the H-depleted molecular graph (Gupta, 1999). By definition, it is calculated from the pendent matrix which is a sub-matrix of the topological distance matrix (see Appendix A) with one row for each atom and m, the number of columns corresponding to the number of terminal vertices (in the H-depleted molecular graph). The super-pendentic index is defined as:
where,
n is the number of non-Hydrogen atoms, and
IIdij is the product of the topological distances from the ith atom to all the terminal vertices j.
Topological Paths/Walks
Molecular path and walk counts
Walk and Path counts are atomic and molecular descriptors obtained from a H-depleted molecular graph based on the graph theory (Rucker & Rucker, 1993; Rucker & Rucker, 1994; Diudea, 1994; Randic, 1980; Razinger, 1986; Rucker & Rucker, 2000).
The adjacency matrix A of a molecular graph is an n by n matrix (where n is the number of atoms in the molecule) that has a value =1 at (i, j) if the atoms i and j are connected by a bond, and zero otherwise.
Let Ak
be the kth
power matrix of the adjacency matrix A, that is the
product that we get
when A is multiplied by itself k
times. Its elements are denoted
as 
.
Each entry (i, j)
in the kth
power matrix Ak denotes the
number of walks of length k
from the ith atom to jth
atom. The atomic
walk count of order k for
the ith atom
denoted by 
is
given by the sum of the ith
row elements in the kth
power matrix Ak, given as:
That
is, is the number of
walks of
length k originating from
the ith atom.
Note that a walk can revisit a vertex any number of times.
Self-returning walk counts
A walk starting and ending on the same vertex, i.e. closed in itself is called a self-returning walk.
In particular, the diagonal elements (i, j) in the kth power matrix Ak denote the number of self-returning walks from the ith atom to itself
|
[ MWC02 ] molecular walk count of order 2 |
|
[ MWC03 ] molecular walk count of order 3 |
|
[ MWC04 ] molecular walk count of order 4 |
|
[ MWC05 ] molecular walk count of order 5 |
|
[ MWC06 ] molecular walk count of order 6 |
|
[ MWC07 ] molecular walk count of order 7 |
|
[ MWC08 ] molecular walk count of order 8 |
|
[ MWC09 ] molecular walk count of order 9 |
|
[ MWC10 ] molecular walk count of order 10 |
|
[ TWC ] total walk count |
|
[ SRW01 ] self-returning walk count of order 1 |
|
[ SRW02 ] self-returning walk count of order 2 |
|
[ SRW03 ] self-returning walk count of order 3 |
|
[ SRW04 ] self-returning walk count of order 4 |
|
[ SRW05 ] self-returning walk count of order 5 |
|
[ SRW06 ] self-returning walk count of order 6 |
|
[ SRW07 ] self-returning walk count of order 7 |
|
[ SRW08 ] self-returning walk count of order 8 |
|
[ SRW09 ] self-returning walk count of order 9 |
|
[ SRW10 ] self-returning walk count of order 10 |
Molecular path count
A Path
(or self-avoiding walk) is a walk
with no vertex repeated. Atomic path count is the number of paths of
length m
starting from the ith atom
to any other atom in the molecule.
Molecular path count Pm is the count of all paths in the molecule of length m, that is,
Molecular Multiple Path Count of Order m, piPCm is defined as follows. We define wi, the weight of a path pi as the sum of the bond orders of the bonds in the path pi (the bond orders are respectively 1, 2, 3 and 1.5 for single, double, triple and aromatic bonds). piPCm is defined as the sum of the weights of the paths of length m in the molecule.
Meaning of Atomic Walk counts as a descriptor
Atomic Walk counts have the following significance: Atomic Walk count is a measure of something like "involvedness" or centrality of the atom in the molecular graph. It is a measure of the complexity of the vertex environment. Atomic Walk count coincides with the extended connectivity defined by Morgan (Morgan, 1965; Razinger, 1982; Rucker and Rucker, 1993; Figueras, 1993)
|
[ MPC01 ] molecular path count of order 1 |
|
[ MPC02 ] molecular path count of order 2 |
|
[ MPC03 ] molecular path count of order 3 |
|
[ MPC04 ] molecular path count of order 4 |
|
[ MPC05 ] molecular path count of order 5 |
|
[ MPC06 ] molecular path count of order 6 |
|
[ MPC07 ] molecular path count of order 7 |
|
[ MPC08 ] molecular path count of order 8 |
|
[ MPC09 ] molecular path count of order 9 |
|
[ MPC10 ] molecular path count of order 10 |
|
[ piPC01 ] molecular multiple path count of order 1 |
|
[ piPC02 ] molecular multiple path count of order 2 |
|
[ piPC03 ] molecular multiple path count of order 3 |
|
[ piPC04 ] molecular multiple path count of order 4 |
|
[ piPC05 ] molecular multiple path count of order 5 |
|
[ piPC06 ] molecular multiple path count of order 6 |
|
[ piPC07 ] molecular multiple path count of order 7 |
|
[ piPC08 ] molecular multiple path count of order 8 |
|
[ piPC09 ] molecular multiple path count of order 9 |
|
[ piPC10 ] molecular multiple path count of order 10 |
Information Content Descriptors
Information Content Indices
The Information Content indices (Magnuson, 1983) are calculated based on the pairwise equivalence atoms in a Hydrogen-filled molecule. A pair of atoms are said to be equivalent at a particular level-r, if they are of the same element and their neighborhood is equivalent up to level-r. The equivalence of the neighborhoods of a pair of atoms a and b upto level-r is defined as follows: Let set (a) be the set of paths of length upto r originating from the atom a. Similarly, the set (b) corresponding to atom b is defined. Then the atoms a and b are said to be equivalent up to level-r, if there exists a one-to-one onto mapping between the sets set (a) and set (b). We say that a mapping exists between a pair of paths if the corresponding atoms and bonds are the same in both the paths. For example, if the path C-C=N-O exists in each of the sets set (a) and set (b), then these two paths can be mapped to each other.
The Information Content indices are calculated from level-0 to level-5 in Sarchitect, level zero.
In sarchitect the indices have been calculated from level-0 to level-5 and are given as:
|
Information Content Indices |
|
|
|
[ IC0 ] information content index (neighborhood symmetry of 0-order) |
|
|
[ IC1 ] information content index (neighborhood symmetry of 1-order) |
|
|
[ IC2 ] information content index (neighborhood symmetry of 2-order) |
|
|
[ IC3 ] information content index (neighborhood symmetry of 3-order) |
|
|
[ IC4 ] information content index (neighborhood symmetry of 4-order) |
|
|
[ IC5 ] information content index (neighborhood symmetry of 5-order) |
|
Bonding Information Content |
|
|
|
[ BIC0 ] bond information content (neighborhood symmetry of 0-order) |
|
|
[ BIC1 ] bond information content (neighborhood symmetry of 1-order) |
|
|
[ BIC2 ] bond information content (neighborhood symmetry of 2-order) |
|
|
[ BIC3 ] bond information content (neighborhood symmetry of 3-order) |
|
|
[ BIC4 ] bond information content (neighborhood symmetry of 4-order) |
|
|
[ BIC5 ] bond information content (neighborhood symmetry of 5-order) |
|
Structural Information Content |
|
|
|
[ SIC0 ] structural information content (neighborhood symmetry of 0-order) |
|
|
[ SIC1 ] structural information content (neighborhood symmetry of 1-order) |
|
|
[ SIC2 ] structural information content (neighborhood symmetry of 2-order) |
|
|
[ SIC3 ] structural information content (neighborhood symmetry of 3-order) |
|
|
[ SIC4 ] structural information content (neighborhood symmetry of 4-order) |
|
|
[ SIC5 ] structural information content (neighborhood symmetry of 5-order) |
|
Complementary Information Content |
|
|
|
[ CIC0 ] complementary information content (neighborhood symmetry of 0-order) |
|
|
[ CIC1 ] complementary information content (neighborhood symmetry of 1-order) |
|
|
[ CIC2 ] complementary information content (neighborhood symmetry of 2-order) |
|
|
[ CIC3 ] complementary information content (neighborhood symmetry of 3-order) |
|
|
[ CIC4 ] complementary information content (neighborhood symmetry of 4-order) |
|
|
[ CIC5 ] complementary information content (neighborhood symmetry of 5-order) |
|
Total Information Content |
|
|
|
[ TIC0 ] total information content index (neighborhood symmetry of 0-order) |
|
|
[ TIC1 ] total information content index (neighborhood symmetry of 1-order) |
|
|
[ TIC2 ] total information content index (neighborhood symmetry of 2-order) |
|
|
[ TIC3 ] total information content index (neighborhood symmetry of 3-order) |
|
|
[ TIC4 ] total information content index (neighborhood symmetry of 4-order) |
|
|
[ TIC5 ] total information content index (neighborhood symmetry of 5-order) |
Centric Indices
Lopping centric index (Balaban, 1979) is defined as the mean information content derived from the pruning partition of acyclic graphs. The pruning portions of an acyclic graph are obtained as follows. Vertices of degree one are removed from the graph recursively. Let Ai denote the number of vertices removed in the ith iteration and the graph will be empty after k iterations. Therefore the set of vertices in the graph is partitioned into A1, A2,…, Ak, that is k partitions. Then the lopping centric index is defined as:
This definition is suitably modified in Sarchitect in order to include cyclic graphs.
Conformational (3D) Descriptors
Conformational descriptors are sensitive to the spatial positions of the atoms and their values vary for the same molecule depending upon the conformer chosen.
Randic profiles
Molecular profile
The Randic molecular profile DPk (Randic 1995a, 1995b; Randic & Razinger 1995) is derived from the distance distribution moments of the geometric matrix G as the average row sum of its entries raised to the kth power and normalized by the factor k!.
where
is the kth
power of
the ijth entry of the
geometric matrix, and
n is the number of atoms.
As k increases, the contributions from the most distant pairs of atoms dominate. Sarchitect computes Randic molecular profiles for k=1,20:
DP01, DP02, DP03, DP04, DP05, DP06, DP07, DP08, DP09, DP11, DP12, DP13, DP14, DP15, DP16, DP17, DP18, DP19, DP20
Radial Distribution Function
The radial distribution
function (RDF)
descriptors are based on the distance distribution in the molecule. The
radial
distribution function of an ensemble of n atoms can
be interpreted as
the probability distribution of finding an atom in a spherical volume
of radius
R. A typical RDF descriptor is denoted by RDFsw
where s and
w take the values 10 ≤ s
≤ 155 in units of 5
and 
,
and it is defined as follows:
where,
f is a scaling factor,
rij is the Euclidean distance between the atoms i and j,
wi and wj are the weights of the atoms i and j respectively,
n is the total number of atoms,
β is the smoothing parameter which defines the probability distribution of the individual inter-atomic distance. β can be interpreted as the temperature factor that defines the movement of the atoms. We have chosen the value of 0.5 for R in our program.
The RDF descriptors given are:
|
Unweighted |
|
|
|
[ RDF010u ] Radial Distribution Function - 1 / unweighted |
|
|
[ RDF015u ] Radial Distribution Function - 1.5 / unweighted |
|
|
[ RDF020u ] Radial Distribution Function - 2 / unweighted |
|
|
[ RDF025u ] Radial Distribution Function - 2.5 / unweighted |
|
|
[ RDF030u ] Radial Distribution Function - 3 / unweighted |
|
|
[ RDF035u ] Radial Distribution Function - 3.5 / unweighted |
|
|
[ RDF040u ] Radial Distribution Function - 4 / unweighted |
|
|
[ RDF045u ] Radial Distribution Function - 4.5 / unweighted |
|
|
[ RDF050u ] Radial Distribution Function - 5 / unweighted |
|
|
[ RDF055u ] Radial Distribution Function - 5.5 / unweighted |
|
|
[ RDF060u ] Radial Distribution Function - 6 / unweighted |
|
|
[ RDF065u ] Radial Distribution Function - 6.5 / unweighted |
|
|
[ RDF070u ] Radial Distribution Function - 7 / unweighted |
|
|
[ RDF075u ] Radial Distribution Function - 7.5 / unweighted |
|
|
[ RDF080u ] Radial Distribution Function - 8 / unweighted |
|
|
[ RDF085u ] Radial Distribution Function - 8.5 / unweighted |
|
|
[ RDF090u ] Radial Distribution Function - 9 / unweighted |
|
|
[ RDF095u ] Radial Distribution Function - 9.5 / unweighted |
|
|
[ RDF100u ] Radial Distribution Function - 10 / unweighted |
|
|
[ RDF105u ] Radial Distribution Function - 10.5 / unweighted |
|
|
[ RDF110u ] Radial Distribution Function - 11 / unweighted |
|
|
[ RDF115u ] Radial Distribution Function - 11.5 / unweighted |
|
|
[ RDF120u ] Radial Distribution Function - 12 / unweighted |
|
|
[ RDF125u ] Radial Distribution Function - 12.5 / unweighted |
|
|
[ RDF130u ] Radial Distribution Function - 13 / unweighted |
|
|
[ RDF135u ] Radial Distribution Function - 13.5 / unweighted |
|
|
[ RDF140u ] Radial Distribution Function - 14 / unweighted |
|
|
[ RDF145u ] Radial Distribution Function - 14.5 / unweighted |
|
|
[ RDF150u ] Radial Distribution Function - 15 / unweighted |
|
|
[ RDF155u ] Radial Distribution Function - 15.5 / unweighted |
|
mass weighted |
|
|
|
[ RDF010m ] Radial Distribution Function - 1 / weighted by atomic masses |
|
|
[ RDF015m ] Radial Distribution Function - 1.5 / weighted by atomic masses |
|
|
[ RDF020m ] Radial Distribution Function - 2 / weighted by atomic masses |
|
|
[ RDF025m ] Radial Distribution Function - 2.5 / weighted by atomic masses |
|
|
[ RDF030m ] Radial Distribution Function - 3 / weighted by atomic masses |
|
|
[ RDF035m ] Radial Distribution Function - 3.5 / weighted by atomic masses |
|
|
[ RDF040m ] Radial Distribution Function - 4 / weighted by atomic masses |
|
|
[ RDF045m ] Radial Distribution Function - 4.5 / weighted by atomic masses |
|
|
[ RDF050m ] Radial Distribution Function - 5 / weighted by atomic masses |
|
|
[ RDF055m ] Radial Distribution Function - 5.5 / weighted by atomic masses |
|
|
[ RDF060m ] Radial Distribution Function - 6 / weighted by atomic masses |
|
|
[ RDF065m ] Radial Distribution Function - 6.5 / weighted by atomic masses |
|
|
[ RDF070m ] Radial Distribution Function - 7 / weighted by atomic masses |
|
|
[ RDF075m ] Radial Distribution Function - 7.5 / weighted by atomic masses |
|
|
[ RDF080m ] Radial Distribution Function - 8 / weighted by atomic masses |
|
|
[ RDF085m ] Radial Distribution Function - 8.5 / weighted by atomic masses |
|
|
[ RDF090m ] Radial Distribution Function - 9 / weighted by atomic masses |
|
|
[ RDF095m ] Radial Distribution Function - 9.5 / weighted by atomic masses |
|
|
[ RDF100m ] Radial Distribution Function - 10 / weighted by atomic masses |
|
|
[ RDF105m ] Radial Distribution Function - 10.5 / weighted by atomic masses |
|
|
[ RDF110m ] Radial Distribution Function - 11 / weighted by atomic masses |
|
|
[ RDF115m ] Radial Distribution Function - 11.5 / weighted by atomic masses |
|
|
[ RDF120m ] Radial Distribution Function - 12 / weighted by atomic masses |
|
|
[ RDF125m ] Radial Distribution Function - 12.5 / weighted by atomic masses |
|
|
[ RDF130m ] Radial Distribution Function - 13 / weighted by atomic masses |
|
|
[ RDF135m ] Radial Distribution Function - 13.5 / weighted by atomic masses |
|
|
[ RDF140m ] Radial Distribution Function - 14 / weighted by atomic masses |
|
|
[ RDF145m ] Radial Distribution Function - 14.5 / weighted by atomic masses |
|
|
[ RDF150m ] Radial Distribution Function - 15 / weighted by atomic masses |
|
|
[ RDF155m ] Radial Distribution Function - 15.5 / weighted by atomic masses |
|
volume weighted |
|
|
|
[ RDF010v ] Radial Distribution Function - 1 / weighted by atomic van der Waals volumes |
|
|
[ RDF015v ] Radial Distribution Function - 1.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF020v ] Radial Distribution Function - 2 / weighted by atomic van der Waals volumes |
|
|
[ RDF025v ] Radial Distribution Function - 2.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF030v ] Radial Distribution Function - 3 / weighted by atomic van der Waals volumes |
|
|
[ RDF035v ] Radial Distribution Function - 3.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF040v ] Radial Distribution Function - 4 / weighted by atomic van der Waals volumes |
|
|
[ RDF045v ] Radial Distribution Function - 4.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF050v ] Radial Distribution Function - 5 / weighted by atomic van der Waals volumes |
|
|
[ RDF055v ] Radial Distribution Function - 5.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF060v ] Radial Distribution Function - 6 / weighted by atomic van der Waals volumes |
|
|
[ RDF065v ] Radial Distribution Function - 6.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF070v ] Radial Distribution Function - 7 / weighted by atomic van der Waals volumes |
|
|
[ RDF075v ] Radial Distribution Function - 7.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF080v ] Radial Distribution Function - 8 / weighted by atomic van der Waals volumes |
|
|
[ RDF085v ] Radial Distribution Function - 8.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF090v ] Radial Distribution Function - 9 / weighted by atomic van der Waals volumes |
|
|
[ RDF095v ] Radial Distribution Function - 9.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF100v ] Radial Distribution Function - 10 / weighted by atomic van der Waals volumes |
|
|
[ RDF105v ] Radial Distribution Function - 10.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF110v ] Radial Distribution Function - 11 / weighted by atomic van der Waals volumes |
|
|
[ RDF115v ] Radial Distribution Function - 11.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF120v ] Radial Distribution Function - 12 / weighted by atomic van der Waals volumes |
|
|
[ RDF125v ] Radial Distribution Function - 12.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF130v ] Radial Distribution Function - 13 / weighted by atomic van der Waals volumes |
|
|
[ RDF135v ] Radial Distribution Function - 13.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF140v ] Radial Distribution Function - 14 / weighted by atomic van der Waals volumes |
|
|
[ RDF145v ] Radial Distribution Function - 14.5 / weighted by atomic van der Waals volumes |
|
|
[ RDF150v ] Radial Distribution Function - 15 / weighted by atomic van der Waals volumes |
|
|
[ RDF155v ] Radial Distribution Function - 15.5 / weighted by atomic van der Waals volumes |
|
electronegativity weighted |
|
|
|
[ RDF010e ] Radial Distribution Function - 1 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF015e ] Radial Distribution Function - 1.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF020e ] Radial Distribution Function - 2 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF025e ] Radial Distribution Function - 2.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF030e ] Radial Distribution Function - 3 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF035e ] Radial Distribution Function - 3.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF040e ] Radial Distribution Function - 4 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF045e ] Radial Distribution Function - 4.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF050e ] Radial Distribution Function - 5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF055e ] Radial Distribution Function - 5.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF060e ] Radial Distribution Function - 6 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF065e ] Radial Distribution Function - 6.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF070e ] Radial Distribution Function - 7 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF075e ] Radial Distribution Function - 7.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF080e ] Radial Distribution Function - 8 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF085e ] Radial Distribution Function - 8.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF090e ] Radial Distribution Function - 9 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF095e ] Radial Distribution Function - 9.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF100e ] Radial Distribution Function - 10 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF105e ] Radial Distribution Function - 10.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF110e ] Radial Distribution Function - 11 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF115e ] Radial Distribution Function - 11.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF120e ] Radial Distribution Function - 12 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF125e ] Radial Distribution Function - 12.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF130e ] Radial Distribution Function - 13 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF135e ] Radial Distribution Function - 13.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF140e ] Radial Distribution Function - 14 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF145e ] Radial Distribution Function - 14.5 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF150e ] Radial Distribution Function - 15 / weighted by atomic Sanderson electronegativities |
|
|
[ RDF155e ] Radial Distribution Function - 15.5 / weighted by atomic Sanderson electronegativities |
|
polarizability weighted |
|
|
|
[ RDF010p ] Radial Distribution Function - 1 / weighted by atomic polarizabilities |
|
|
[ RDF015p ] Radial Distribution Function - 1.5 / weighted by atomic polarizabilities |
|
|
[ RDF020p ] Radial Distribution Function - 2 / weighted by atomic polarizabilities |
|
|
[ RDF025p ] Radial Distribution Function - 2.5 / weighted by atomic polarizabilities |
|
|
[ RDF030p ] Radial Distribution Function - 3 / weighted by atomic polarizabilities |
|
|
[ RDF035p ] Radial Distribution Function - 3.5 / weighted by atomic polarizabilities |
|
|
[ RDF040p ] Radial Distribution Function - 4 / weighted by atomic polarizabilities |
|
|
[ RDF045p ] Radial Distribution Function - 4.5 / weighted by atomic polarizabilities |
|
|
[ RDF050p ] Radial Distribution Function - 5 / weighted by atomic polarizabilities |
|
|
[ RDF055p ] Radial Distribution Function - 5.5 / weighted by atomic polarizabilities |
|
|
[ RDF060p ] Radial Distribution Function - 6 / weighted by atomic polarizabilities |
|
|
[ RDF065p ] Radial Distribution Function - 6.5 / weighted by atomic polarizabilities |
|
|
[ RDF070p ] Radial Distribution Function - 7 / weighted by atomic polarizabilities |
|
|
[ RDF075p ] Radial Distribution Function - 7.5 / weighted by atomic polarizabilities |
|
|
[ RDF080p ] Radial Distribution Function - 8 / weighted by atomic polarizabilities |
|
|
[ RDF085p ] Radial Distribution Function - 8.5 / weighted by atomic polarizabilities |
|
|
[ RDF090p ] Radial Distribution Function - 9 / weighted by atomic polarizabilities |
|
|
[ RDF095p ] Radial Distribution Function - 9.5 / weighted by atomic polarizabilities |
|
|
[ RDF100p ] Radial Distribution Function - 10 / weighted by atomic polarizabilities |
|
|
[ RDF105p ] Radial Distribution Function - 10.5 / weighted by atomic polarizabilities |
|
|
[ RDF110p ] Radial Distribution Function - 11 / weighted by atomic polarizabilities |
|
|
[ RDF115p ] Radial Distribution Function - 11.5 / weighted by atomic polarizabilities |
|
|
[ RDF120p ] Radial Distribution Function - 12 / weighted by atomic polarizabilities |
|
|
[ RDF125p ] Radial Distribution Function - 12.5 / weighted by atomic polarizabilities |
|
|
[ RDF130p ] Radial Distribution Function - 13 / weighted by atomic polarizabilities |
|
|
[ RDF135p ] Radial Distribution Function - 13.5 / weighted by atomic polarizabilities |
|
|
[ RDF140p ] Radial Distribution Function - 14 / weighted by atomic polarizabilities |
|
|
[ RDF145p ] Radial Distribution Function - 14.5 / weighted by atomic polarizabilities |
|
|
[ RDF150p ] Radial Distribution Function - 15 / weighted by atomic polarizabilities |
|
|
[ RDF155p ] Radial Distribution Function - 15.5 / weighted by atomic polarizabilities |
MoRSE descriptors
3D MoRSE descriptors (3D Molecule Representation of Structures based on Electron diffraction) are derived from Infrared spectra simulation using a generalized scattering function (Soltzberg and Wilkins, 1977). A typical MoRSE descriptor is denoted by
M orsw
where s and w take
the values 1≤ s ≤ 32
and , where,
● u is unweighted
● m is weighted by mass
● v is weighted by van der Waals volume
● e is weighted by electronegativity
● p is weighted by polarizability
The MoRSE descriptor is defined as follows:
where,
rij is the Euclidean distance between the atoms i and j , and
wi and wj are the weights of the atoms i and j respectively.
(Schuur & Gasteiger, 1996; Schuur, 1996; Gasteiger, 1996; Schuur and Gasteiger, 1997)
The MoRSE descriptors given in sarchitect are:
|
|
|
|
|
[ Mor01u ] - signal 1 / unweighted |
|
|
[ Mor02u ] - signal 2 / unweighted |
|
|
[ Mor03u ] - signal 3 / unweighted |
|
|
[ Mor04u ] - signal 4 / unweighted |
|
|
[ Mor05u ] - signal 5 / unweighted |
|
|
[ Mor06u ] - signal 6 / unweighted |
|
|
[ Mor07u ] - signal 7 / unweighted |
|
|
[ Mor08u ] - signal 8 / unweighted |
|
|
[ Mor09u ] - signal 9 / unweighted |
|
|
[ Mor10u ] - signal 10 / unweighted |
|
|
[ Mor11u ] - signal 11 / unweighted |
|
|
[ Mor12u ] - signal 12 / unweighted |
|
|
[ Mor13u ] - signal 13 / unweighted |
|
|
[ Mor14u ] - signal 14 / unweighted |
|
|
[ Mor15u ] - signal 15 / unweighted |
|
|
[ Mor16u ] - signal 16 / unweighted |
|
|
[ Mor17u ] - signal 17 / unweighted |
|
|
[ Mor18u ] - signal 18 / unweighted |
|
|
[ Mor19u ] - signal 19 / unweighted |
|
|
[ Mor20u ] - signal 20 / unweighted |
|
|
[ Mor21u ] - signal 21 / unweighted |
|
|
[ Mor22u ] - signal 22 / unweighted |
|
|
[ Mor23u ] - signal 23 / unweighted |
|
|
[ Mor24u ] - signal 24 / unweighted |
|
|
[ Mor25u ] - signal 25 / unweighted |
|
|
[ Mor26u ] - signal 26 / unweighted |
|
|
[ Mor27u ] - signal 27 / unweighted |
|
|
[ Mor28u ] - signal 28 / unweighted |
|
|
[ Mor29u ] - signal 29 / unweighted |
|
|
[ Mor30u ] - signal 30 / unweighted |
|
|
[ Mor31u ] - signal 31 / unweighted |
|
|
[ Mor32u ] - signal 32 / unweighted |
|
atomic mass weighted |
|
|
|
[ Mor01m ] - signal 1 / weighted by atomic masses |
|
|
[ Mor02m ] - signal 2 / weighted by atomic masses |
|
|
[ Mor03m ] - signal 3 / weighted by atomic masses |
|
|
[ Mor04m ] - signal 4 / weighted by atomic masses |
|
|
[ Mor05m ] - signal 5 / weighted by atomic masses |
|
|
[ Mor06m ] - signal 6 / weighted by atomic masses |
|
|
[ Mor07m ] - signal 7 / weighted by atomic masses |
|
|
[ Mor08m ] - signal 8 / weighted by atomic masses |
|
|
[ Mor09m ] - signal 9 / weighted by atomic masses |
|
|
[ Mor10m ] - signal 10 / weighted by atomic masses |
|
|
[ Mor11m ] - signal 11 / weighted by atomic masses |
|
|
[ Mor12m ] - signal 12 / weighted by atomic masses |
|
|
[ Mor13m ] - signal 13 / weighted by atomic masses |
|
|
[ Mor14m ] - signal 14 / weighted by atomic masses |
|
|
[ Mor15m ] - signal 15 / weighted by atomic masses |
|
|
[ Mor16m ] - signal 16 / weighted by atomic masses |
|
|
[ Mor17m ] - signal 17 / weighted by atomic masses |
|
|
[ Mor18m ] - signal 18 / weighted by atomic masses |
|
|
[ Mor19m ] - signal 19 / weighted by atomic masses |
|
|
[ Mor20m ] - signal 20 / weighted by atomic masses |
|
|
[ Mor21m ] - signal 21 / weighted by atomic masses |
|
|
[ Mor22m ] - signal 22 / weighted by atomic masses |
|
|
[ Mor23m ] - signal 23 / weighted by atomic masses |
|
|
[ Mor24m ] - signal 24 / weighted by atomic masses |
|
|
[ Mor25m ] - signal 25 / weighted by atomic masses |
|
|
[ Mor26m ] - signal 26 / weighted by atomic masses |
|
|
[ Mor27m ] - signal 27 / weighted by atomic masses |
|
|
[ Mor28m ] - signal 28 / weighted by atomic masses |
|
|
[ Mor29m ] - signal 29 / weighted by atomic masses |
|
|
[ Mor30m ] - signal 30 / weighted by atomic masses |
|
|
[ Mor31m ] - signal 31 / weighted by atomic masses |
|
|
[ Mor32m ] - signal 32 / weighted by atomic masses |
|
vdw volume weighted |
|
|
|
[ Mor01v ] - signal 1 / weighted by atomic van der Waals volumes |
|
|
[ Mor02v ] - signal 2 / weighted by atomic van der Waals volumes |
|
|
[ Mor03v ] - signal 3 / weighted by atomic van der Waals volumes |
|
|
[ Mor04v ] - signal 4 / weighted by atomic van der Waals volumes |
|
|
[ Mor05v ] - signal 5 / weighted by atomic van der Waals volumes |
|
|
[ Mor06v ] - signal 6 / weighted by atomic van der Waals volumes |
|
|
[ Mor07v ] - signal 7 / weighted by atomic van der Waals volumes |
|
|
[ Mor08v ] - signal 8 / weighted by atomic van der Waals volumes |
|
|
[ Mor09v ] - signal 9 / weighted by atomic van der Waals volumes |
|
|
[ Mor10v ] - signal 10 / weighted by atomic van der Waals volumes |
|
|
[ Mor11v ] - signal 11 / weighted by atomic van der Waals volumes |
|
|
[ Mor12v ] - signal 12 / weighted by atomic van der Waals volumes |
|
|
[ Mor13v ] - signal 13 / weighted by atomic van der Waals volumes |
|
|
[ Mor14v ] - signal 14 / weighted by atomic van der Waals volumes |
|
|
[ Mor15v ] - signal 15 / weighted by atomic van der Waals volumes |
|
|
[ Mor16v ] - signal 16 / weighted by atomic van der Waals volumes |
|
|
[ Mor17v ] - signal 17 / weighted by atomic van der Waals volumes |
|
|
[ Mor18v ] - signal 18 / weighted by atomic van der Waals volumes |
|
|
[ Mor19v ] - signal 19 / weighted by atomic van der Waals volumes |
|
|
[ Mor20v ] - signal 20 / weighted by atomic van der Waals volumes |
|
|
[ Mor21v ] - signal 21 / weighted by atomic van der Waals volumes |
|
|
[ Mor22v ] - signal 22 / weighted by atomic van der Waals volumes |
|
|
[ Mor23v ] - signal 23 / weighted by atomic van der Waals volumes |
|
|
[ Mor24v ] - signal 24 / weighted by atomic van der Waals volumes |
|
|
[ Mor25v ] - signal 25 / weighted by atomic van der Waals volumes |
|
|
[ Mor26v ] - signal 26 / weighted by atomic van der Waals volumes |
|
|
[ Mor27v ] - signal 27 / weighted by atomic van der Waals volumes |
|
|
[ Mor28v ] - signal 28 / weighted by atomic van der Waals volumes |
|
|
[ Mor29v ] - signal 29 / weighted by atomic van der Waals volumes |
|
|
[ Mor30v ] - signal 30 / weighted by atomic van der Waals volumes |
|
|
[ Mor31v ] - signal 31 / weighted by atomic van der Waals volumes |
|
|
[ Mor32v ] - signal 32 / weighted by atomic van der Waals volumes |
|
electronegativity weighted |
|
|
|
[ Mor01e ] - signal 1 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor02e ] - signal 2 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor03e ] - signal 3 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor04e ] - signal 4 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor05e ] - signal 5 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor06e ] - signal 6 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor07e ] - signal 7 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor08e ] - signal 8 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor09e ] - signal 9 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor10e ] - signal 10 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor11e ] - signal 11 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor12e ] - signal 12 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor13e ] - signal 13 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor14e ] - signal 14 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor15e ] - signal 15 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor16e ] - signal 16 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor17e ] - signal 17 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor18e ] - signal 18 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor19e ] - signal 19 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor20e ] - signal 20 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor21e ] - signal 21 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor22e ] - signal 22 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor23e ] - signal 23 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor24e ] - signal 24 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor25e ] - signal 25 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor26e ] - signal 26 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor27e ] - signal 27 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor28e ] - signal 28 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor29e ] - signal 29 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor30e ] - signal 30 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor31e ] - signal 31 / weighted by atomic Sanderson electronegativities |
|
|
[ Mor32e ] - signal 32 / weighted by atomic Sanderson electronegativities |
|
polarizability weighted |
|
|
|
[ Mor01p ] - signal 1 / weighted by atomic polarizabilities |
|
|
[ Mor02p ] - signal 2 / weighted by atomic polarizabilities |
|
|
[ Mor03p ] - signal 3 / weighted by atomic polarizabilities |
|
|
[ Mor04p ] - signal 4 / weighted by atomic polarizabilities |
|
|
[ Mor05p ] - signal 5 / weighted by atomic polarizabilities |
|
|
[ Mor06p ] - signal 6 / weighted by atomic polarizabilities |
|
|
[ Mor07p ] - signal 7 / weighted by atomic polarizabilities |
|
|
[ Mor08p ] - signal 8 / weighted by atomic polarizabilities |
|
|
[ Mor09p ] - signal 9 / weighted by atomic polarizabilities |
|
|
[ Mor10p ] - signal 10 / weighted by atomic polarizabilities |
|
|
[ Mor11p ] - signal 11 / weighted by atomic polarizabilities |
|
|
[ Mor12p ] - signal 12 / weighted by atomic polarizabilities |
|
|
[ Mor13p ] - signal 13 / weighted by atomic polarizabilities |
|
|
[ Mor14p ] - signal 14 / weighted by atomic polarizabilities |
|
|
[ Mor15p ] - signal 15 / weighted by atomic polarizabilities |
|
|
[ Mor16p ] - signal 16 / weighted by atomic polarizabilities |
|
|
[ Mor17p ] - signal 17 / weighted by atomic polarizabilities |
|
|
[ Mor18p ] - signal 18 / weighted by atomic polarizabilities |
|
|
[ Mor19p ] - signal 19 / weighted by atomic polarizabilities |
|
|
[ Mor20p ] - signal 20 / weighted by atomic polarizabilities |
|
|
[ Mor21p ] - signal 21 / weighted by atomic polarizabilities |
|
|
[ Mor22p ] - signal 22 / weighted by atomic polarizabilities |
|
|
[ Mor23p ] - signal 23 / weighted by atomic polarizabilities |
|
|