Quantum Chemical Descriptors in Computational Medicinal Chemistry for Chemoinformatics

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Quantum Chemical Descriptors in Computational
Medicinal Chemistry for Chemoinformatics
Feb 17- 2005, Pondicherry Central University

• V. Subramanian
• Chemical Laboratory
• Central Leather Research Institute
• Chennai 600 020

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Schematics

• Introduction to Informatics
• Molecular Models
• QSAR
• Descriptors for QSAR
• Conceptual DFT
• DFT based Reactivity Descriptors
• Applications
• Summary

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Information technology designed to generate and
access genetic data and derive information from it
Bioinformatics
Informatics
Chemoinformatics
Information technology used to design molecular
libraries to interact with identified targets
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Chemoinformatics

• IT for managing chemical information and
  solving chemical problems
• Chemistry information science
• computer science
• Driven by drug discovery research

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Chemoinformatics

• Chemoinformatics is the amalgamation of those
  chemical information resources to transform data
  into vital information and chemical information
  into knowledge for the intended purpose of making
  better decisions faster in the area of drug lead
  identification and organization

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Chemoinformatics tasks

• Manage information about
• Chemical properties
• Chemical synthesis
• Biological effects

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Combinatorial chemistry

• Synthesizing large numbers of related chemical
  compounds
• Can help design drug leads
• Information rich
• Physiology of the biological effect
• Starting material properties
• Synthesis protocols

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Central Paradigm of Bioinformatics
Genetic Information
Molecular Structure
Biochemical Function
Symptoms (Phenotype)
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Drug discovery
Chemical biological system ? desired
response?
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Related Aspects

• Bioinformatics and chemoinformatics are
  generic terms that encompass the design,
  creation, organization, management, retrieval,
  analysis, dissemination, visualization and use of
  chemical and biological information

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Chemometrics strategies
problem
goal
hypothesis
experiment planning
experiments
data
Data exploration
Cluster analysis
classification
regression
optimization
Qualitative model
Quantitative model
Empirical model
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Molecular Models
Semi Empirical
Ab initio/DFT
Empirical/ Molecular Modeling
Full Accounting of Electrons
Neglect Electrons
Neglect Core Electrons Approximate/ parameterize
HF Integrals
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Quantum Methods
Wavefunction
Density Function
Hartree-Fock
DFT
MP2, CI
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Brief summary of methods
HF Most simple MO method CI Very
accurate, very expensive method MP2 More
accurate and marginally more expensive than
HF DFT Significantly more accurate while
marginally more expensive than HF
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Locality of the model
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QSAR

• The quantitative structure- activity
  relationship (QSAR) and the quantitative
  structure- property relationship (QSPR) are the
  important tools of the bio-chemo-informatics
  which can be built essentially based on the data
  generated from the molecular modeling and
  computational chemistry

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QSAR

• Quantitative Structure Activity Relationship is a
  set of methods that tries to find a mathematical
  relationship between a set of descriptors of
  molecules and their activity.
• The descriptors can be experimentally or
  computationally derived. Using regression
  analysis, one can extract a mathematical
  relationship between chemical descriptors and
  activity.

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QSAR Postulates

• the molecular structure is responsible for all
  the activities
• Similar compounds have similar biological and
  chemico-physical properties (Meyer 1899)
• Hansch postulate (1963)
• biological system compound
• 
  f1(Lipolificity) f2(Electronics)
  f3(Steric) f4(Molecular-prop)
• Congenericity postulate
• QSAR is applicable only to similar
  compounds

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Descriptors in QSAR study

• Constitutional Descriptors
• Topological Descriptors
• Geometrical Descriptors
• Electrostatic Descriptors
• Quantum Chemical Descriptors
• MO Related Descriptors
• Thermodynamic Descriptors
• DFT based Reactivity Descriptors

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Constitutional Descriptors

• Total number of atoms in the molecule
• Absolute and relative numbers of atoms of certain
  chemical identity (C, H, O, N, F, etc.) in the
  molecule
• Absolute and relative numbers of certain chemical
  groups and functionalities in the molecule
• Total number of bonds in the molecule
• Absolute and relative numbers of single, double,
  triple, aromatic or other bonds in the molecule
• Total number of rings, number of rings divided by
  the total number of atoms
• Total and relative number of 6 membered aromatic
  rings
• Molecular weight and average atomic weight

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Topological Descriptors

• Wiener index
• Randi's molecular connectivity index
• Randi indices of different orders
• Balaban's J index
• Kier and Hall valence connectivity indices
• Kier shape indices
• Kier flexibility index
• Mean information content index
• Structural information content index
• Complementary information content index
• Bonding information content index
• Topological electronic indices

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Geometrical Descriptors

• Molecular surface area
• Solvent-accessible molecular surface area
• Molecular volume
• Solvent-excluded molecular volume
• Gravitational indexes
• Principal moments of inertia of a molecule
• Shadow areas of a molecule
• Relative shadow areas of a molecule

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Electrostatic Descriptors

• Gasteiger-Marsili empirical atomic partial
  charges
• Zefirov's empirical atomic partial charges
• Mulliken atomic partial charges
• Minimum (most negative) and maximum (most
  positive) atomic partial charges
• Polarity parameters
• Dipole moment
• Molecular polarizability
• Molecular hyperpolarizability
• Average ionization energy
• Minimum electrostatic potential at the molecular
  surface
• Maximum electrostatic potential at the molecular
  surface
• Local polarity of molecule
• Total variance of the surface electrostatic
  potential
• Electrostatic balance parameter

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Quantum Chemical Descriptors

• Total energy of the molecule
• Total electronic energy of the molecule
• Standard heat of formation
• Electron-electron repulsion energy for a given
  atomic species
• Nuclear-electron attraction energy for a given
  atomic species
• Electron-electron repulsion between two given
  atoms
• Nuclear-electron attraction energy between two
  given atoms
• Nuclear repulsion energy between two given atoms
• Electronic exchange energy between two given
  atoms
• Resonance energy between given two atomic species
  
• Total electrostatic interaction energy between
  two given atomic species
• Total interaction energy between two given two
  atomic species
• Total molecular one-center electron-electron
  repulsion energy
• Total molecular one-center electron-nuclear
  attraction energy
• Total intramolecular electrostatic interaction
  energy
• Electron kinetic energy density
• Energy of protonation 21

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Quantum Chemical Descriptors
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MO Related Descriptors

• Highest Occupied Molecular Orbital (HOMO) energy
• Lowest Unoccupied Molecular Orbital (LUMO) energy
• Absolute hardness
• Activation hardness
• Fukui atomic nucleophilic reactivity index
• Fukui atomic electrophilic reactivity index
• Fukui atomic one-electron reactivity index
• Mulliken bond orders
• Free valence

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Thermodynamic Descriptors

• Vibrational enthalpy of the molecule
• Translational enthalpy of the molecule
• Vibrational entropy of the molecule
• Rotational entropy of the molecule
• Translational entropy of the molecule
• Vibrational heat capacity of the molecule
• Normal coordinate eigen values (EVA)

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Density Functional Theory (DFT)

• Instead of calculating a wavefunction, tries to
  calculate the exact density of the molecule
• Based on the Hohenberg-Kohn proof, which
  stipulates that a given density corresponds to a
  particular wavefunction and potential
• Calculate the exact density ? obtain the exact
  wavefunction from the exact density ? Do
  everything youd normally do with a MO
  wavefunction

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DFT Evolution

• Thomas-Fermi Theory (1926-28)- established the
  direct mapping between electron density and
  potential.
• Landau Theory of Fermi liquids(1956-58) -
  introduced the energy of the system as a
  functional of charge distribution.
• Hohenberg-Kohn-Shem Theory (1964-65) - proved
  one-to-one mapping of the density and potential.
  Derived the equations for single electron wave
  functions, which can be solved in a mode of
  self-consistent-field.
• Talman-Shadwick Theory (1976) and Its
  Krieger-Li-Iafrate approximation (1992) - exact
  expression for exchange potential.

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DFT based Reactivity Descriptors

• Global Descriptors
• Chemical Potential
• Chemical Hardness
• Softness
• Electrophilicity Index
• Local Descriptors
• Condensed Fukui Function
• Philicity
• Group Philicity

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Chemical Potential
The Chemical Potential of DFT measures the
escaping tendency of an electronic cloud. It is a
constant, through all space, for the ground state
of an atom, molecule or solid, and equals the
slope of the Energy versus N curve at constant
Potential v ( r ),
It is the negative of Electronegativity,
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Finite difference approximation to Chemical
Potential gives,
where HOMO Highest Occupied Molecular
Orbital LUMO Lowest Unoccupied Molecular
Orbital I and A are the Ionization Potential and
Electron Affinity of the molecules respectively
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Related Concept (Sandersons Electronegativity
Equalization Principle) When atoms of
different chemical potential unite to form a
molecule with its own characteristic chemical
potential, to the extent that the atoms retain
their identity their chemical potential must
equalize
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Chemical Hardness The theoretical definition
of chemical hardness has been provided by the
density functional theory as the second
derivative of electronic energy with respect to
the number of electrons N, for a constant
external potential V(r)
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Finite difference approximation to Chemical
Hardness gives,
For Insulator and Semiconductor, hardness is half
of the band gap
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Softness
Related concept (Hard Soft Acid Base (HSAB)
Principle) Hard Acids prefer Hard Bases, and
Soft Acids prefer Soft Bases
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Electrophilicity Index
Electrophilicity index is a measure of energy
lowering due to maximal electron flow between
donor and acceptor. Electrophilicity index (?) is
defined as,
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Fukui Function
Fukui function measures how sensitive a systems
chemical potential is to an external perturbation
at particular point. It is defined as, where
is the electron density
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Condensed Fukui Function
In order to describe the reactivity of an atom in
a molecule, it is necessary to condense the
values of f(r) around each atomic site into a
single value (fk) that characterizes the atomic
contribution in a molecule. For an atom k in a
molecule, the fk values are defined as
Nucleophilic attack Electrophilic attack Radical
attack
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Related concept (Frontier-electron theory) Of
two different sites with generally similar
dispositions for reacting with a given reagent,
the reagent prefers the one, which on the
reagents approach is associated with the maximum
response of the systems chemical potential
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Philicity
Chattaraj et al. has provided a unified treatment
of chemical reactivity and selectivity through a
generalized philicity concept by using a
resolution of identity. This local philicity
index is given as
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or its condensed- to- atom variants for the
atomic site k in a molecule is defined as
(? , -, 0) represents nucleophilic,
electrophilic and radical attack respectively.
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Group Philicity
The condensed philicity summed over a group of
relevant atoms is defined as the group
philicity. It can be expressed as where n
number of atoms coordinated to the reactive
atom, local electrophilicity of the atom
k , ?g? group philicity obtained by adding the
local philicity of the nearby
bonded atoms, (? , -, 0) represents
nucleophilic, electrophilic and radical attack
respectively
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Polarizability
The electric dipole polarizability is a measure
of the linear response of the electron density in
the presence of an infinitesimal electric field F
and it represents a second order variation in
energy
The polarizability is calculated as the mean
value as given in the following equation,
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Charge Transfer
The amount of charge transfer between any two
systems (say, A and B) can be obtained by
applying the formula,
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Applications Bio-chemo-informatics related
studies have been carried out by our group using
Conceptual Density Functional Theory derived
global and local quantum chemical descriptors on
the following selected systems

• Polychlorinated biphenyls
• Benzidine
• Testosterone and Estrogen derivatives
• Alkanes (C2-C8)

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Polychlorinated biphenyls
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Optimized Structures of PCBs
33445- PCBP
22'55'- TCBP
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Analysis of PCBs

• The geometry of 22'55'- TCBP and 33445- PCBP
  were optimized by using Beckes three parameter
  hybrid density functional, B3LYP/6-31G, which
  includes both Hartree-Fock exchange and DFT
  exchange correlation functionals.
• Above calculations are carried out using the
  GAUSSIAN 98 package.
• The optimized geometries were characterized by
  harmonic vibrational frequencies which confirmed
  that the structure of 22'55'- TCBP is a minimum
  on the potential energy surface.

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Table 1 Calculated Relative Energy, Chemical
Hardness, Chemical Potential, Polarizability, and
Electrophilicity Index of 2,2,5,5-TCBP
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Figure 1 The variation of relative energy
(kJ/mol), chemical hardness (eV) and scaled
hardness (eV) with the torsional angle (degrees)
for 33'44'5 - PCBP.
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Analysis of PCBs

• To select proper electronic descriptor based on
  DFT, for the possible toxicity of the 22'55'-
  TCBP, the various reactivity and selectivity
  descriptors such as chemical hardness, chemical
  potential, polarizability, electrophilicity index
  and the local electrophilic power are calculated
  for all the rotated conformations (Table 1).
• It has been found that 2255- TCBP has very
  large rotational energy barrier at ?0? and
  ?180? with relative energy of 53.17 kJ/mol. Due
  to large rotational barrier, this molecule cannot
  adapt planar conformation and hence it is less
  toxic.

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Analysis of PCBs

• In the case of 33445- PCBP with very small
  rotational energy barrier of 7.36 kJ/mol at the
  planar orientation (Figure 1), is shown to have
  flexible planarity so that it changes its
  conformation while moving in biological systems,
  thereby interacting readily, exhibiting its toxic
  properties.

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The electron accepting nature of PCB is evident
from the charge transfer calculation.
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LRD Profiles of PCBs
22'55' - TCBP
33445 - PCBP
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Optimized geometry of Benzidine
N
N
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Benzidine
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Interaction of benzidine with B-DNA through (a)
minor groove, (b) major groove and (c)
intercalation
a
c
b
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Benzidine
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Table 2Calculated Global Parameters for Benzidine
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Analysis of Benzidine

• The relative energy of benzidine is calculated as
  a function of torsional angle , (rotation through
  the C (atom No.7)-C (atom No. 3) bond).
• To calculate the relative energy, the geometry at
  various values were optimized at B3LYP/6-31G
  level.

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Analysis of Benzidine

• It is possible to note from the rotational energy
  barrier (Table 2), which has a small variation (0
  to 11.19 kJ/mol) that this molecule is highly
  flexible and it can adopt variety of
  conformations.
• This rotational freedom allows benzidine to
  freely interact with the cellular components in
  the realistic environment and hence their toxic
  nature.

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The molecular electrostatic potential surfaces
for various conformation of Benzidine.
 
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Charge Transfer(?N) between Benzidine and
constituents of Biomolecules
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MESP for Benzidine

• The MESP surface of benzidine reveals the site of
  attack and also provides clues for the role of
  electrostatic interactions involved in the
  reactivity.
• Further the charge transfer between benzidine and
  nucleic acid bases/base pairs, AHH receptors has
  clearly revealed the electron donating nature of
  benzidine.

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GRD Profiles
Benzidine
22'55' - TCBP
33445 - PCBP
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LRD Profiles of Benzidine
?k
?k-
?k0
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Testosterone and Estrogen Derivatives
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Structure of Testosterone and Estrogen
OH
D
C
OH
B
A
D
C
O
Testosterone
B
A
HO
Estrogen
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Table 3 Electrophilicity index of testosterone
derivatives with their observed and calculated
biological activity in terms of relative binding
affinity (RBA)
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Table 4 Electrophilicity index of
16?-substituted estradiol derivatives with their
observed and calculated biological activity
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Relationship between various biological activity
of Testosterone derivatives and Electrophilicity
index
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Relationship between RBA valuesof Estrogen
derivatives and Electrophilicity index
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QSAR analysis of testosterone and estrogen
derivatives

• The biological activity of testosterone and
  estrogen derivatives has been analyzed by our
  group using electrophilicity index as a
  descriptor.
• In this context, the SAR based on
  electrophilicity has been shown to be promising.

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QSAR analysis of testosterone and estrogen
derivatives

• Since the electrophilicity index is a chemical
  reactivity descriptor and its definition has
  strong foundation from the density functional
  theory, it is appropriate to make use of this
  descriptor in the QSAR parlance and the
  usefulness of such application was evident from
  our investigation.
• Results emanated from that study (above Tables
  and Figures) showed that the electrophilicity can
  be used as a descriptor of biological activity
  and it is quite interesting that a single
  descriptor can provide such a beautiful
  correlation.

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Group Philicity
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Group Philicity
The condensed philicity summed over a group of
relevant atoms is defined as the group
philicity
where n is the number of atoms coordinated to the
reactive atom
is the local electrophilicity of the
atom k, and is the group philicity
obtained by adding the local philicity of the
nearby bonded atoms, (? , -, 0) represents
nucleophilic, electrophilic and radical attack
respectively
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Calculated local molecular reactivity descriptors
of the carbonyl carbon atoms of selected molecules
fk sk Group Softness sk/ sk- ?k ?g Mullik
en Population Analysis HCHO 0.303 0.019
0.063 0.577 0.298 0.983 CH3CHO 0.287 0.018
0.040 0.590 0.222 0.493 CH3COCH3 0.246 0.016
0.021 0.557 0.165 0.221 C2H5COC2H5 0.251 0.
016 0.019 0.563 0.157 0.186 C6H5CHO 0.156
0.013 0.040 0.366 0.168 0.501 p-MeOC6H4CHO
0.141 0.012 0.039 0.345 0.115 0.366 CH2C
HCHO 0.152 0.012 0.038 0.358 0.186 0.615 CH
3CHCHCHO 0.155 0.012 0.038 0.367 0.161 0.50
8 C6H5CHCHCHO 0.096 0.009
0.021 0.248 0.107 0.243 CH3COCl 0.033 0.002
0.046 0.164 0.037 0.823 CH3COOCH3 0.303 0.01
7 0.028 0.546 0.194 0.316 Hirshfeld
Population Analysis HCHO 0.397 0.102
0.258 0.170 1.856 4.673 CH3CHO 0.300 0.072
0.185 0.129 1.027 2.654 CH3COCH3 0.211 0.049
0.137 0.109 0.590 1.630 C2H5COC2H5 0.135 0.
031 0.089 0.090 0.355 1.010 C6H5CHO 0.142
0.043 0.127 0.080 0.783 2.303 p-MeOC6H4CHO
0.142 0.042 0.119 0.070 0.642 1.847 CH2C
HCHO 0.206 0.067 0.158 0.154 1.300 3.075 CH
3CHCHCHO 0.174 0.055 0.170 0.111 0.933 2.90
2 C6H5CHCHCHO 0.108 0.039
0.132 0.083 0.733 2.490 CH3COCl 0.233 0.047
0.159 0.076 0.952 3.246 CH3COOCH3 0.129 0.02
3 0.072 0.079 0.258 0.818
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Reactivity trends using Philicity

• Group philicity values derived from both MPA and
  HPA schemes have provided the expected reactivity
  trends in all sets of molecules considered for
  evaluation.
• Hence philicity and group philicity can be used
  as better chemical reactivity descriptors when
  compared to all other local reactivity
  descriptors.

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QSAR studies on Alkanes (C2-C8)
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Table 6 Abbreviations of the selected alkanes
and their isomers (C2-C8)
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Table 7 Regression equations and statistical
parameters of the six quantum chemical
descriptors for the five macroscopic properties
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Table 8 Experimental and calculated values of
five selected macroscopic properties of C2-C8
alkanes and their isomers using ionisation
potential as a descriptor
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QSAR/QSPR analysis on Alkanes (C2-C8)

• The present study reveals that ionisation
  potential can be used as a descriptor to
  understand structure activity and structure
  property relationship.
• Within the framework of Hartree-Fock theory, the
  computed IP has excellent correlation with the
  macroscopic properties such as boiling point,
  heat of formation or enthalpy, entropy, heat
  capacity and heat of vaporisation.
• The correlation coefficient has been found to be
  high for the relationship between I and BP.

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QSAR/QSPR analysis on Alkanes (C2-C8)

• Hardness and softness indices exhibit similar
  correlation coefficient in the range of 0.80-0.95
  for all the macroscopic properties, which
  confirms the fact that both the microscopic
  properties are interrelated.
• Maximum correlation coefficient for both the
  indices has been found to be 0.945 for heat of
  formation. This observation reinforces the
  existing fact that, hardness (?) holds direct
  relationship with the stability of a molecule.

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Summary

• The success of DFT based global and local quantum
  chemical descriptors in predicting the Chemo and
  Bio-activities of several systems selected by our
  group are highlighted in this work.
• The simple calculation procedure and the
  usefulness of all DFT based descriptors in the
  QSAR and QSPR parlance have also been probed in
  detail.
• In this study, the applications of global and
  local descriptors in the development of QSAR and
  QSPR have been presented for prediction of
  physical properties of series of alkanes,
  biological activity of testosterone and estrogen
  derivatives and toxicity of polychlorinated
  biphenyls, and benzidines.

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Summary

• It has been shown that the global descriptors
  such as electrophilicity and ionization potential
  are capable of predicting the biological activity
  of the selected molecules
• Local descriptors such as philicity and group
  philicity are capable of identifying the activity
  of a particular site in the molecule and also in
  analyzing its toxicity as well as its behavior
  during an intermolecular reaction.

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Acknowledgements

• T. Ramasami
• P. K. Chattaraj
• R. Parthasarathi
• J. Padmanabhan
• M. Elango
• DST and CSIR for funding

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Thank you