SEMESTER – I Organic Chemistry – I

  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

       In physical organic chemistry, a free-energy relationship or linear Gibbs energy relation relates the logarithm of a reaction rate constant or equilibrium constant for one series of reactions with the logarithm of the rate or equilibrium constant for a related series of reactions. Establishing free-energy relationships helps in the understanding of the reaction mechanism for a chemical reaction and allows the prediction of reaction rates and equilibrium constants.

       The Brønsted catalysis equation describes the relationship between the ionization constant of a series of catalysts and the reaction rate constant for a reaction on which thecatalyst operates. The Hammett equation predicts the equilibrium constant or reaction rate of a reaction from a substituent constant and a reaction type constant. The Edwards equation relates the nucleophilic power to polarisability and basicity.

       It has been suggested that this name should be replaced by linear Gibbs energy relation, but at present there is little sign of acceptance of this change. The area of physical organic chemistry which deals with such relations is commonly referred to as '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

      The Hammett equation in organic chemistry describes a linear free-energy relationship relating reaction rates and equilibrium constants for many reactions involving benzoic acid derivatives with meta- and para-substituents to each other with just two parameters: a substituent constant and a reaction constant. This equation was developed and published by Louis Plack Hammett in 1937 as a follow-up to qualitative observations in a 1935 publication.

      The basic idea is that for any two reactions with two aromatic reactants only differing in the type of substituent, the change infree energy of activation is proportional to the change in Gibbs free energy. This notion does not follow from elementalthermochemistry or chemical kinetics and was introduced by Hammett intuitively.

Ø  The basic equation is:

      relating the equilibrium constant, K, for a given equilibrium reaction with substituent R and the reference K₀ constant when R is a hydrogen atom to the substituent constant σ which depends only on the specific substituent R and the reaction constant ρwhich depends only on the type of reaction but not on the substituent used.

      The equation also holds for reaction rates k of a series of reactions with substituted benzene derivatives:

      In this equation k₀ is the reference reaction rate of the unsubstituted reactant, and k that of a substituted reactant.

      A plot of log(K/K₀) for a given equilibrium versus log(k/k₀) for a given reaction rate with many differently substituted reactants will give a straight line.

Hammett Sigma Constants

v  Core-electron binding energy (CEBE) shifts correlate linearly with the Hammett substituent constants (σ) in substituted benzene derivatives.

Ø  ΔCEBE ≈ κσ_p (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 σ_o, σ_m and σ_p 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(k_s/k_CH3) 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, E_s 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 k_{x, sol} and k_{x, 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 σ_X, 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 S_N1 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 S_N1 and S_N2 reaction, a reaction goes through S_N1 mechanism more is preferred to achieve a better linear relationship, hence t-BuCl was chosen.

Y values

(2)

§  In equation 2, k_{t-BuCl, 80% EtOH} stands for the rate constant of t-BuCl reaction in 80% aqueous Ethanol, it is a constant. k_{t-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(k_sol/k_80%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 S_N1 mechanism.

§  m < 1, the reactions go through the mechanism between S_N1 and S_N2.

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 S_N2 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

      In simplest terms, a potential energy surface or PES is a mathematical or graphical representation of the relation between energy of a molecule and its geometry. The methods for describing the potential energy are broken down into a classical mechanics interpretation (molecular mechanics) and a quantum mechanical interpretation. In the quantum mechanical interpretation an exact expression for energy can be obtained for any molecule derived from quantum principles (although an infinite basis set may be required) but ab initio calculations/methods will often use approximations to reduce computational cost.  Molecular mechanics is empirically based and potential energy is described as a function of component terms that correspond to individual potential functions such as torsion, stretches, bends, Van der Waals energies,electrostatics and cross terms.  Each component potential function is fit to experimental data. Molecular mechanics is useful in predicting equilibrium geometries and transition states as well as relative conformational stability. As a reaction occurs the atoms of the molecules involved will generally undergo some change in spatial orientation through internal motion as well as its electronic environment.[1]Distortions in the geometric parameters result in a deviation from the equilibrium geometry (local energy minima). These changes in geometry of a molecule or interactions between molecules are dynamic processes which call for understanding all the forces operating within the system. Since these forces can be mathematically derived as first derivative of potential energy with respect to a displacement, it makes sense to map the potential energy E of the system as a function of geometric parameters q1, q2, q3 and so on. The potential energy at given values of the geometric parameters (q1, q2,…, qn) is represented as a hyper-surface (when n >2 or a surface when n ≤ 2). Mathematically, it can be written as-

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.

      Consider a diatomic molecule AB which can macroscopically visualized as two balls (which depict the two atoms A and B) connected through a spring which depicts the bond. As this spring (or bond) is stretched or compressed, the potential energy of the ball-spring system (AB molecule) changes and this can be mapped on a 2-dimensional plot as a function of distance between A and B, i.e. bond length.

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.