Rajah Serfoji Govt. College (Autonomous),
Thanjavur – 613 005
M.Sc., Chemistry SEMESTER – I Organic Chemistry – I
Code: R1PCH1
UNIT - IV
Correlation analysis
'Linear Free-Energy Relationships



Chemical and physical properties
o
A typical LFER
relation for predicting the equilibrium concentration of a compound or solute
in the vapor phase to a condensed (or solvent) phase can be defined as follows:
Ø
log SP = c + eE +
sS +aA + bB + lL
o
where SP is some free energy related property, such as an adsorption or absorption constant, log K,
anesthetic potency, etc. The lower case letters (e, s, a, b, l) are system
constants describing the contribution of the aerosol phase to the sorption process. The capital
letters are solute descriptors representing the
complementary properties of the compounds. Specifically, L is the gas-liquid
partition constant on hexadecane at 298 K; E the excess molar refraction; S the ability of a solute to
stabilize a neighboring dipole by virtue of its capacity for
orientation and induction interactions; A the solute’s effective hydrogen bond acidity;
and B the solute’s effective hydrogen-bond basicity.
The complementary system constants are identified as the contribution from
cavity formation and dispersion interactions, l, the contribution from
interactions with solute n- or Pi electrons,
e, the contribution from dipole-type interactions, s, the contribution from
hydrogen-bond basicity (because a basic sorbent will interact with an acidic solute),
a, and b the contribution from hydrogen-bond acidity to the transfer of the
solute from air to the aerosol phase.
·
SImilarly, the
correlation of water to solvent partition coefficients as log Ps, is given by
Ø
Log Ps = c + eE +
sS + aA + bB + vV
o
where V is
McGowan’s characteristic molecular volume in cubic centimeters per mole divided
by 100.
Hammett
equation


Ø
The basic
equation is:




Hammett Sigma
Constants
v
Core-electron
binding energy (CEBE) shifts correlate linearly with the Hammett substituent
constants (σ) in substituted benzene derivatives.
Ø
ΔCEBE ≈ κσp (1)
v
Consider
para-disubstituted benzene p-F-C6H4-Z, where Z is a substituent such as NH2, NO2,
etc. The fluorine atom is para with respect to the substituent Z in the benzene
ring. The image on the right shows four distinguished ring carbon atoms, C1(ipso), C2(ortho), C3(meta), C4(para) in p-F-C6H4-Z
molecule. The carbon with Z is defined as C1(ipso) and fluorinated carbon as
C4(para). This definition is followed even for Z = H. The left-hand side of [1]
is called CEBE shift or ΔCEBE, and is defined as the difference between the
CEBE of the fluorinated carbon atom in p-F-C6H4-Z and
that of the fluorinated carbon in the reference molecule FC6H5.
Ø
ΔCEBE ≡ CEBE(C4
in p-F-C6H4-Z) – CEBE(C4 in p-F-C6H5)
(2)
v
The right-hand
side of Eq. 1 is a product of a parameter κ and a Hammett substituent constant
at the para position, σp. The parameter κ is defined by eq. 3:
Ø
κ = 2.3kT(ρ - ρ*)
(3)
v
where ρ and ρ*
are the Hammett reaction constants for the reaction of the neutral molecule and
core ionized molecule, respectively. ΔCEBEs of ring carbons in p-F-C6H4-Z were
calculated with density functional theory to see how they correlate with Hammett
σ-constants. Linear plots were obtained when the calculated CEBE shifts at the
ortho, meta and para Carbon were plotted against Hammett σo, σm and σp constants respectively.
v
κ value
calculated ≈ 1. Hence the approximate agreement in numerical value and in sign
between the CEBE shifts and their corresponding Hammett σ constant.
Rho
value
o
With knowledge of substituent constants it is now possible to
obtain reaction constants for a wide range of organic reactions.
The archetypal reaction is the alkaline hydrolysis ofethyl benzoate (R=R'=H) in a water/ethanol mixture at
30 °C. Measurement of the reaction rate k0 combined with that of many substituted
ethyl benzoates ultimately result in a reaction constant of +2.498.
Reaction constants are known
for many other reactions and equilibria. Here is a selection of those provided
by Hammett himself (with their values in parenthesis):
Ø the hydrolysis of
substituted cinnamic acid ester in ethanol/water
(+1.267)
Ø the ionization of
substituted phenols in
water (+2.008)
Ø the acid catalyzed esterification of
substituted benzoic esters in ethanol (-0.085)
Ø the acid catalyzed bromination
of substituted acetophenones (Ketone halogenation) in an acetic acid/water/hydrochloric
acid (+0.417)
Ø the hydrolysis of
substituted benzyl chlorides in acetone-water
at 69.8 °C (-1.875).
o The reaction constant, or
sensitivity constant, ρ, describes the susceptibility of the
reaction to substituents, compared to the ionization of benzoic acid. It is
equivalent to the slope of the Hammett plot. Information on the reaction and
the associated mechanism can be obtained based on the value obtained for ρ.
If the value of:
1. ρ>1, the reaction is more
sensitive to substituents than benzoic acid and negative charge is built during
the reaction (or positive charge is lost).
2. 0<ρ<1, the reaction is less
sensitive to substituents than benzoic acid and negative charge is built (or
positive charge is lost).
3. ρ=0, no sensitivity to
substituents, and no charge is built or lost.
4. ρ<0, the reaction builds positive
charge (or loses negative charge).
v These relations can be
exploited to elucidate the mechanism of a reaction. As the value of ρ is
related to the charge during the rate determining step, mechanisms can be
devised based on this information. If the mechanism for the reaction of an
aromatic compound is thought to occur through one of two mechanisms, the compound
can be modified with substituents with different σ values and
kinetic measurements taken. Once these measurements have been made, a Hammett
plot can be constructed to determine the value of ρ. If one of
these mechanisms involves the formation of charge, this can be verified based
on the ρ value. Conversely, if the Hammett plot shows that no charge is
developed, i.e. a zero slope, the mechanism involving the building of charge
can be discarded.
Ø Hammett plots may not always
be perfectly linear. For instance, a curve may show a sudden change in slope,
or ρ value. In such a case, it is likely that the mechanism of
the reaction changes upon adding a different substituent. Other deviations from
linearity may be due to a change in the position of the transition state. In
such a situation, certain substituents may cause the transition state to appear
earlier (or later) in the reaction mechanism.
Ø The
Hammett equation applies to meta- and para- substituents (provided that
resonance interaction from the substituents does not occur) but not to
ortho-substituents.
Taft equation
o The Taft
equation is a linear free energy relationship (LFER)
used in physical organic chemistry in the
study of reaction mechanisms and in the development
of quantitative structure activity
relationships for organic
compounds. It was developed by Robert W. Taft in
1952[2][3][4] as a
modification to the Hammett equation.[5] While
the Hammett equation accounts for how field, inductive,
and resonance effects influence reaction
rates, the Taft equation also describes the steric
effects of a substituent.
The Taft equation is written as:
o where log(ks/kCH3) is the
ratio of the rate of the substituted reaction compared
to the reference reaction, σ* is the polar substituent constant that describes
the field and inductive effects of the substituent, Es is the
steric substituent constant, ρ* is the sensitivity factor for the reaction
to polar effects,
and δ is the sensitivity factor for the reaction to steric effects.
Polar Substituent Constants, σ*
Polar
substituent constants describe the way a substituent will influence a reaction
through polar (inductive, field, and resonance) effects. To determine σ* Taft studied thehydrolysis of methyl esters (RCOOMe).
The use of ester hydrolysis rates to study polar effects was first suggested by
Ingold in 1930. The hydrolysis of
esters can occur through either acid and base catalyzed mechanisms, both of which proceed through a tetrahedral intermediate. In the base catalyzed mechanism the reactant goes
from a neutral species to negatively charged intermediate in the rate determining
(slow) step, while in the acid
catalyzed mechanism a positively charged reactant goes to a positively charged
intermediate.
Swain-Scott equation
§
The first such attempt is found in the Swain–Scott
equation derived in 1953:
§
This free-energy relationship relates
the pseudo first order reaction rate constant (in water at
25 °C), k, of a reaction, normalized to the reaction rate, k0, of a
standard reaction with water as the nucleophile, to a nucleophilic
constant n for a given nucleophile and a substrate
constant s that depends on the sensitivity of a substrate to
nucleophilic attack (defined as 1 for methyl bromide).
This treatment results in the following values for
typical nucleophilic anions: acetate 2.7, chloride 3.0, azide 4.0, hydroxide 4.2, aniline 4.5, iodide 5.0,
and thiosulfate 6.4.
Typical substrate constants are 0.66 for ethyl
tosylate, 0.77 for β-propiolactone §
1.00 for 2,3-epoxypropanol,
0.87 for benzyl chloride, and 1.43 for benzoyl
chloride.
§
The equation predicts that, in a nucleophilic displacement on benzyl
chloride, the azide anion reacts 3000 times faster than water.
Grunwald–Winstein equation
o In physical organic chemistry,
the Grunwald–Winstein equation is a linear free energy relationship between
relative rate constants and the ionizing power
of various solventsystems,
describing the effect of solvent as nucleophile on
different substrates. The equation, which was developed by Ernest
Grunwald and Saul Winstein in
1948, could be written[1][2]
o where the kx, sol and kx,
80% EtOH are the solvolysis rate constants for a certain
compound in different solvent systems and in the reference solvent, 80%
aqueous ethanol,
respectively. The m is a parameter of the compound measuring sensitivity of
solvolysis rate to Y, the measure of ionizing power of the solvent.
o Hammett
equation (Equation 1) provides the relationship between
the substituent on the benzene ring and the ionizing rate constant of the
reaction. Hammett use the ionization of benzoic acid as
the standard reaction to define a set of substituent parameters σX,
and then generate the ρ values, which represent ionizing abilities of different
substrate, through Hammett Plot.
(1)
o However, if the solvent of the
reaction is changed, but not the structure of the substrate, the rate constant
may change too. Following this idea, a plot of relative rate constant vs. the
change of solvent system can be generate through an equation, which is the
Grunwald-Winstein Equation. Since it has the same pattern with Hammett equation
but dealing with the change of solvent system, we can also consider it as a
supplement of Hammett Equation.
applications
Reference compound
The Substitution reaction of tert-Butyl chloride was chosen as
reference reaction. The first step, ionizing step, is the rate determining step, SO stands for the
nucleophilic solvent.
§ The reference solvent is 80%
Ethanol and 20% water by volume. Both of them can carry out the nucleophilic attack on the carbocation.
§ The SN1
reaction is performed through a stable carbocation intermediate,
the more nucleophilic solvent can stabilize the carbocation better,
thus the rate constant of the reaction could be larger. Since there’s no sharp
line between SN1 and SN2
reaction, a reaction goes through SN1 mechanism more is
preferred to achieve a better linear relationship, hence t-BuCl was
chosen.
Y values
(2)
§
In equation 2, kt-BuCl, 80%
EtOH stands for the rate constant of t-BuCl
reaction in 80% aqueous Ethanol, it is a constant. kt-BuCl, sol. stands for
the k of the same reaction in different solvent system, such as ethanol-water,
methanol-water, and acetic acid-formic acid.
Thus Y reflects the ionizing power of different nucleophile solvents.
m values
§
The equation
parameter, sensitivity factor of solvolysis, m describes the compound’s ability
to form the carbocation intermediate in certain solvent system. It is the slope
of the plot of log(ksol/k80%EtOH) vs Y values. Since the
reference reaction has little solvent nucleophilic assistance, the reactions
with m equal to 1 or lager than 1 have almost full ionized intermediate. If the
compounds are not so sensitive to the ionizing ability of solvent, then the m
values are smaller than 1. That is:
§
m ≥ 1, the
reactions go through SN1 mechanism.
§
m < 1, the
reactions go through the mechanism between SN1 and SN2.
Disadvantage
v
This equation could not fit into all different kind
of solvent mixtures. The combinations are restrained in only certain systems
and only the nucleophilic solvents.
v
Relationships between many reactions and
nucleophilic solvent systems are not linear. This derives from the growing SN2 reaction character within the mechanism.
SOLVENT
§ A solvent is a
substance that dissolves a solute (a chemically different liquid, solid or
gas), resulting in a solution. A solvent is usually a liquid but can also be a
solid or a gas. The maximum quantity of solute that can dissolve in a specific
volume of solvent varies with temperature.
Common uses for organicsolvents are in dry cleaning (e.g., tetrachloroethylene), as paint
thinners (e.g., toluene, turpentine),
as nail polish removers and glue solvents (acetone, methyl
acetate, ethyl acetate), in spot removers (e.g., hexane, petrol
ether), in detergents (citrus terpenes) and in perfumes (ethanol).
Solvents find various applications in chemical, pharmaceutical, oil and gas
industries, including in chemical syntheses and purification processes.
§ The global solvent market is
expected to earn revenues of about US$33 billion in 2019. The dynamic economic
development in emerging markets like China, India, Brazil, orRussia will
especially continue to boost demand for solvents. Specialists expect the
worldwide solvent consumption to increase at an average annual rate of 2.5%
over the subsequent years. Accordingly, the growth rate seen during the past
eight years will be surpassed.
Solvent classifications
§
Solvents can be broadly classified into two categories: polar and non-polar. Generally, the dielectric constant of
the solvent provides a rough measure of a solvent's polarity. The strong
polarity of water is indicated, at 0 °C, by a dielectric constant of 88. Solvents
with a dielectric constant of less than 15 are generally considered to be
non polar.Technically, the dielectric constant measures the
solvent's ability to reduce the field strength of the electric field
surrounding a charged particle immersed in it. This reduction is then compared to the field strength of
the charged particle in a vacuum. In
layperson's terms, dielectric constant of a solvent can be thought of as its
ability to reduce the solute's effective internal charge. Generally, the dielectric constant of a solvent
is an acceptable approximation of the solvent's ability to dissolve common ionic compounds, such as salts.
Methods of determing
reaction mechanism
energy profie
diagrams
v
For a chemical reaction or process an energy profile (or reaction coordinate diagram)
is a theoretical representation of a single energetic pathway, along the
reaction coordinate, as the reactants are transformed into products. Reaction
coordinate diagrams are derived from the corresponding potential energy surface (PES),
which are used in computational
chemistry to model chemical
reactions by relating the energy of a molecule(s) to its structure (within the Born–Oppenheimer approximation). The reaction coordinate is a parametric curve that
follows the pathway of a reaction and indicates the progress of a reaction.
v
Qualitatively the reaction coordinate diagrams
(one-dimensional energy surfaces) have numerous applications. Chemists use
reaction coordinate diagrams as both an analytical and pedagogical aid for
rationalizing and illustrating kinetic and thermodynamic events.
The purpose of energy profiles and surfaces is to provide a qualitative
representation of how potential energy varies with molecular motion for a given
reaction or process.
Potential energy
surfaces

o E= f(q1, q2,…, qn)
o For the quantum mechanical
interpretation a PES is typically defined within the Born–Oppenheimer
approximation (in order to distinguish between nuclear and electronic motion
and energy) which states that the nuclei are stationary relative to the
electrons. In other words, the approximation allows the kinetic energy of the
nuclei (or movement of the nuclei) to be neglected and therefore the nuclei
repulsion is a constant value (as static point charges) and is only considered
when calculating the total energy of the system. The electronic energy is then
taken to depend parametrically on the nuclear coordinates meaning a new
electronic energy (Ee) need to be calculated for each corresponding atomic configuration.
PES is an important concept in computational chemistry and greatly aids in
geometry and transition state optimization.
Degrees of
freedom
o An N-atom system is defined by
3N co-ordinates- x, y, z for each atom. These 3N degrees of freedom can be
further broken down into 3 translational and 3 (or 2) rotational degree of
freedom for a non-linear system (or a linear system). However, for constructing
a PES we are not concerned with overall translational or rotational degrees of
behavior as these do not affect the potential energy of the system. Thus, the
potential energy only depends on the internal co-ordinates and an N-atom system
will be defined by a 3N-6 (linear) or 3N-5 (non-linear) co-ordinates. These
internal coordinates may be represented by simple stretch, bend, torsion
coordinates, or symmetry-adapted linear combinations, or redundant coordinates,
or normal modes coordinates, etc. For a system described by N-internal
co-ordinates a separate potential energy function can be written with respect
to each of these co-ordinates by holding the other (N-1) parameters at a
constant value allowing the potential energy contribution from a particular
molecular motion (or interaction) to be monitored while the other (N-1)
parameters are defined.

Transition state vs. intermediate
Ø
An intermediate is a short-lived unstable
molecule in a reaction. It shows a slight reduction in energy on the reaction
coordinate.
Ø
A transition state is the transition to a new
molecule. It has everything it needs to be the new molecule, and is the highest
point on the reaction coordinate.
Ø An
intermediate would be something like a carbocation, and a transition state
would be the 5-membered carbon complex that forms in an Sn2 reaction.
Ø Intermediates
can actually be isolated during the course of a reaction, whereas transition
states are purely just a state of high energy that cannot be isolated.
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