These reactions provide interesting examples of how stereochemistry and reactivity are determined by the structure of the transition state. Patterns of stability and reactivity are illustrated by discussing some of the absolute rate data that are available for free radical reactions.
Lewis Structures of Simple Molecules Single Bonds
- Hybridization
- The Origin of Electron-Electron Repulsion
- Electronegativity and Polarity
- Electronegativity Equalization
- Differential Electronegativity of Carbon Atoms
Pauling defined the concept of unequal sharing in terms of electronegativity5 and defined the term as 'the power of an atom in a molecule to attract electrons to itself'. Electronegativity depends on the number of protons in the nucleus and is therefore closely related to its position in the periodic table. As each successive shell is filled, the electrons in the valence shell "sense" the effective nuclear charge as screened by the filled inner shells.
Polarizability, Hardness, and Softness
The principle can be applied to chemical equilibria in the form of the principle of maximum hardness,25 which states that "molecules are arranged in such a way that This result is consistent with both the properties and reactivities of methyl halides.
Molecular Polarizability a
- Resonance and Conjugation
- Hyperconjugation
- Covalent and van der Waals Radii of Atoms
- Molecular Orbital Theory and Methods
- The Hückel MO Method
- Semiempirical MO Methods
- Ab Initio Methods
- Pictorial Representation of MOs for Molecules
Contour maps of electron density for 1,3,5-hexatriene and benzene in the planes of the molecules. Note in particular the increase in energy of the orbital as the number of nodes goes from 0 to 5.
Characteristics of ab Initio MO Methods
Qualitative Application of MO Theory to Reactivity: Perturbational MO Theory and Frontier OrbitalsMO Theory and Frontier Orbitals
Thus, analysis of the predicted reaction pathway focuses attention on the relative energy and symmetry of the frontier orbitals. The HOMO in ethenamine is similar to the 2 allylic anion and is higher in energy than the HOMO of ethene.
CHCH = O
Numerical Application of MO Theory
The energy minimization process can provide detailed information about the most stable structure of the molecule. The effect of solvent can be investigated by examining the effect of the dielectric constant on the structure and energy of molecules. The calculations require information about the shape of the molecule and its charge distribution, which are available from the MO calculation.
We might ask: "How much stabilization?" One way to answer this question is to compare the total energy of the two compounds, but since they are not isomers, simple numerical comparison is not feasible.
Comparison of Computed and Experimental Bond Lengths a
Electron Density Functionals
Combining such "pure DFT" functionalities with the Hartree-Fock form of the exchange is the basis for the hybrid methods. Due to the systematic variation, it is possible to apply a scaling factor that predicts C-H bond lengths with high accuracy. There is some evidence that B3LYP calculations underestimate the stability of hydrocarbons as the size of the molecule increases.
The trend for the MP2/6-311+ +Gd p was in the same direction, but significantly closer to the experimental value.73 The difficulty is attributed to an underestimation of the C-C binding strength.
Representation of Electron Density Distribution
- Mulliken Population Analysis
- Natural Bond Orbitals and Natural Population Analysis
- Atoms in Molecules
- Comparison and Interpretation of Atomic Charge Calculations
- Electrostatic Potential Surfaces
- Relationships between Electron Density and Bond Order
Panel (b) shows the accumulation of electron density in the C–H bond regions and that corresponding to unshared oxygen electrons. MO calculations give the total electron density distribution as the sum of the electrons in all filled molecular orbitals. We would expect the electron density to correspond to the electronegativity of the atoms forming the bond.
We would expect there to be a relationship between the electron density between the nuclei and the bond length.
The Origin of the Rotational (Torsional) Barrier in Ethane and Other Small Moleculesand Other Small Molecules
The origin of the rotational (torsional) barrier in ethane and other small molecules and other small molecules. The repulsive electronic interactions were highlighted in early efforts to understand the origin of the rotational barrier.104 In particular, the character of z, y,z and andy (see Figure 1.34) was highlighted.105 The repulsive interactions between these orbitals are maximized. in the eclipsed conformation. The methanol rotation barrier was further investigated using the approach described above for ethane.109 The effect of changes in molecular structure accompanying rotation was included.
The approach chosen was to systematically compare the effect on the rotational barrier of each specific interaction, e.g., hyperconjugation and exchange repulsion, and to determine the effect on molecular geometry, i.e., bond lengths and angles.
Heteroatom Hyperconjugation (Anomeric Effect) in Acyclic MoleculesMolecules
At the HF/6-31G∗∗ level, it is 4.8 kcal/mol more stable than the anti conformation and 2.4 kcal/mol more stable than the darkened conformation.113 Only the gauche conformation aligns the lone pair with the C–F bond. NPA analysis was used to isolate the then→∗ component and the hyperconjugation of the heteroatom was assigned a value of 18 kcal/mol. MP2/6-31G*∗ calculations show that the anti-arrangement of the nitrogen lone pair and the C–F bond is the most stable conformation by 7.5 kcal/mol.114 Some structural effects expected for hyperconjugation, such as lengthening of the C–F bond are visible but not dramatic.115.
Overall, there is a rather small preference for the gauche, gauche conformation, but NPA analysis suggests that there is a →∗component of 5–6 kcal/mol that is accounted for by other factors.117.
Bonding in Cyclopropane and Other Small Ring CompoundsCompounds
The carbon-carbon bonds in the plane of the ring are then considered to be derived from six unhybridized carbon 2-porbitals. According to this picture, the orbital derived from lobes pointing towards the center of the ring should be particularly stable, since it provides for the delocalization of the electrons in this orbital. Using estimates of other components of the strain, such as eclipse, they arrived at a value of 11.3 kcal/mol as stabilization due to delocalization.
The molecules show enhanced reactivity that can be attributed to the characteristics of the unhybridized orbitals.
AIM Charge Distribution and Strain Energy (kcal/mol) for Cyclic Hydro- carbons
All four bonds to the bridgehead carbon atoms point to the same side of the nucleus.130 There have been many computational studies of the [1.1.1]propellane molecule. One of the main objectives was to understand the nature of the bridgehead-bridgehead bond and the extension of the orbital outside the molecule. In the case of propellanes, homolytic breakage of the central bond is expected to be the first step in the dissolution.
This implies that there is a lower barrier to the observed reaction than to homolytic cleavage of the central bond.
Representation of Electron Density by the Laplacian FunctionFunction
This shows increased electron density around oxygen, which is consistent with the expectation that carbon will have a partial positive change.
Application of Density Functional Theory to Chemical Properties and ReactivityProperties and Reactivity
DFT Formulation of Chemical Potential, Electronegativity, Hardness and Softness, and Covalent and van der Waal Radiiand Softness, and Covalent and van der Waal Radii
E/*Nv (1.31) which is the slope of a curve for the energy of the system as a function of the change in the number or electrons. Since % is the slope of the electron energy as a function of the change in electron number, the Mulliken equation gives the energy for the +1 (IP) and −1 (EA) ionization states. The covalent radius in the AIM context is determined by the location of the critical point of attachment.
This is the point at which the electrostatic potential goes from negative to positive and where the sum of the kinetic energy and exchange and correlation functionalities is zero.
DFT Formulation of Reactivity—The Fukui Function
The response of the electron density to interaction with another field is non-uniform across the molecule. The electron density distribution should have regions of different susceptibility to the approach of nucleophiles and electrophiles. This response to changes in the electron distribution is expressed in terms of the Fukui function, which describes the ease of shift of electron density in response to a shift in the external field.
It is necessary to distinguish that in the MO formulation the result is formed on the basis of a certain orbital combination – HOMO and LUMO.
DFT Concepts of Substituent Groups Effects
We know that the acidity of the hydrides of the elements in the second row increases sharply to the right of the periodic table. The electronegativity order F>Cl>Br is reflected in the size of the bond dipole. XXX resulted in the following values for the gas-phase energy (in hartrees) of the acids and anions and the resulting G for gas-phase ionization.
Cyclic amines such as piperidine and its derivatives show substantial changes in the properties of the C(2) and C(6) axial bonds.
Configuration
- Configuration at Double Bonds
- Configuration of Cyclic Compounds
- Configuration at Tetrahedral Atoms
- Molecules with Multiple Stereogenic Centers
- Other Types of Stereogenic Centers
- The Relationship between Chirality and Symmetry
In the cis isomer, both branches of the fused ring are on the same side. For example, the odor of carvone R- (mint oil) and S- (caraway oil) enantiomers is quite different. Enantiomerically pure materials are called ashomochiralorenantiopures. A 1:1 mixture of enantiomers has zero net rotation (because the rotations caused by the two enantiomers exactly cancel) and is called an aramid mixture or racemate.
Note that in several of the connections there is both a center and a plane of symmetry.
Chiral and Achiral Disubstituted Cycloalkanes
Configuration at Prochiral Centers
Various di- and polysubstituted cyclic compounds provide other examples of molecules with symmetry elements. Since chirality depends on configuration, not conformation, cyclic molecules can be represented as planar structures to facilitate identification of symmetry elements. The diastereotopic centers are topologically nonequivalent. This means that their environments in the molecule are different and they respond differently to achiral as well as to chiral probes and reagents.
An example of this effect can be seen in the proton NMR spectra of 1-phenyl-2-butanol, as shown in
Resolution—The Separation of Enantiomers
Conceptual Representation of Resolution through Separation of Diastere-
Resolution of 3-Methyl-2-Phenylbutanoic Acid a
Conceptual Basis of Kinetic Resolution R,S-racemic mixture
Of course, the high conversion required for high enantiomeric purity when the relative reactivity is low has a serious drawback. Relative differences in reactivity <10 can achieve high enantiomeric purity only at the expense of low yield.
Examples of Kinetic Resolution
Conformation
- Conformation of Acyclic Compounds
- Conformations of Cyclohexane Derivatives
- Conformations of Carbocyclic Rings of Other Sizes
Substitution of a methyl group for hydrogen on one of the carbon atoms gives an increase of 0.4-0.6 kcal/mol in the height of the rotational energy barrier. The relative area of the two peaks is 3.4:1 in favor of the conformer with the axial hydrogen. The G difference favoring the diequatorial isomer is approximately the same for each case (about 1.9 kcal/mol) and is very close to the -Gc value of the methyl group (1.8 kcal/mol).
Rabideau, ed., The Conformational Analysis of Cyclohexenes, Cyclohexadiene and Related Hydroaromatic Compounds, VCH Publishers, Weinheim, 1989.
Molecular Mechanics
At distances smaller than the sum of the van der Waals radii, the much stronger electron-electron repulsion forces are dominant. Minimization of the total stress energy of a molecule, expressed by a parameterized equation for each of the force fields, can be achieved by iterative computation. This can be achieved by using a number of different initial geometries and comparing the structures and energies of the localized minima.
One approach is to apply MO or DFT calculations to the reactive part of the molecule to obtain structural information.
Stereoselective and Stereospecific Reactions
- Examples of Stereoselective Reactions
For example, high-level MO or DFT calculations can be applied to the reaction core, intermediate-level calculations to the part of the system immediately adjacent to the reaction core, and MM calculations for the rest of the molecule.97 Two examples of this approximations are given in section 2.5.4, where large catalytic molecules have been investigated using combined approaches. Usually such reactions favor addition of hydrogen from the least hindered face of the double bond; that is, both hydrogen atoms are added to the same face of the bond. These features are believed to be related to the interaction of the alkene with the catalytic surface during hydrogenation and are further discussed in Section 2.4.1.1.
One of the issues to consider in this case is the conformation of the reactant.
Examples of Stereoselective Reactions
The bond involves the interaction of the alkene and * orbitals with the acceptor and donor orbitals of the metal. In most cases, both hydrogen atoms are added to the same side of the reactant (syn addition). Adsorption to the catalyst surface normally involves the less sterically congested face of the double bond, and as a result hydrogen is added from the less constrained face of the molecule.
As in heterogeneous hydrogenation, substituents can affect the stereoselectivity of the reduction by forming an additional bond at the metal center.
OCH 3
The stereoselectivity for allylic and homoallylic alcohols is attributed to a chelate complex with the distribution of hydrogensinine with respect to the hydroxy group.107. These compounds reveal a change in the preferred direction of attack upon the introduction of 7,7-dimethyl substituents. As a result of the adjacent substituent, two diastereomers can be formed, depending on the direction of approach of the nucleophiles.
The stereoselectivity of the addition can be predicted based on a conformational model of the TS.
