Bonding Environments and Conformational Analysis of Drug Structures

Carbon Bonding and Molecular Geometry

• Hybridization and Geometric States of Carbon:

  • Tetrahedral Geometry ($sp^3$ Hybridization):

  • Characterized by $4$ single bonds attached to the central carbon atom.

  • Example molecule: Methane ($\text{CH}_4$).

  • Theoretical and observed bond angle: $109.5^\circ$.

  • Planar Geometry ($sp^2$ Hybridization):

  • Characterized by $1$ double bond and $2$ single bonds attached to the carbon atom.

  • Example molecule: Ethene ($\text{H}_2\text{C}=\text{CH}_2$).

  • Theoretical and observed bond angle: $120^\circ$.

  • Linear Geometry ($sp$ Hybridization):

  • Characterized by $1$ triple bond and $1$ single bond attached to the carbon atom.

  • Example molecule: Ethyne ($\text{H}-\text{C}\equiv\text{C}-\text{H}$, also known as acetylene).

  • Theoretical and observed bond angle: $180^\circ$.

• Resonance and Aromaticity in Benzene:

  • Ring structure: Six-membered carbocyclic ring with $sp^2$-hybridized carbon atoms.

  • Geometry: Completely planar ring system.

  • Electron delocalization: Exactly $6$ $\pi$ electrons are delocalized across the cyclic conjugated system rather than localized into distinct single and double bonds.

  • Bond lengths comparison:

  • Standard aliphatic $\text{C}-\text{C}$ single bond: $1.54\,\text{\AA}$.

  • Standard aliphatic $\text{C}=\text{C}$ double bond: $1.33\,\text{\AA}$.

  • Benzene $\text{C}-\text{C}$ bonds: All six bonds are of equal, intermediate length at $1.39\,\text{\AA}$.

  • Representation: Kekul\u00e9 structures represent benzene as two interconverting resonance contributors with alternating double bonds, equivalent to a circle inscribed within a hexagon depicting uniform electron density.

• Two-Dimensional Allotropes: Graphene:

  • Consists of a single layer of carbon atoms arranged in a two-dimensional hexagonal honeycomb lattice ($sp^2$ planar network).

  • Historical achievement: Awarded the 2010 Nobel Prize in Physics to Professor Andre Geim and Professor Konstantin Novoselov at the University of Manchester.

• Carbon Geometry in Pharmaceutical Compounds:

  • Paracetamol (Acetaminophen):

  • Marked position X (aromatic ring carbon): Planar geometry ($sp^2$ hybridization, $120^\circ$ bond angles).

  • Marked position Y (methyl group carbon, $-\text{CH}_3$): Tetrahedral geometry ($sp^3$ hybridization, $109.5^\circ$ bond angles).

• Efavirenz (Non-Nucleoside Reverse Transcriptase Inhibitor for HIV):

  • Alkyne carbon center (X): Linear geometry ($sp$ hybridization, $180^\circ$ bond angle).

  • Aliphatic saturated carbon center (Y): Tetrahedral geometry ($sp^3$ hybridization, $109.5^\circ$ bond angles).

Nitrogen and Oxygen Bonding Environments

• Nitrogen Geometries and Influences on Molecular Shape:

  • Amines:

  • Bonding environment: $3$ single bonds on nitrogen plus $1$ non-bonding lone pair.

  • Steric arrangement: Tetrahedral electron-pair arrangement resulting in a trigonal pyramidal atomic shape.

  • Characteristic bond angle: $107^\circ$ (compressed from the ideal $109.5^\circ$ due to lone pair-bonding pair repulsion).

  • Amides:

  • Geometry: Strictly planar nitrogen center with a $120^\circ$ bond angle.

  • Driving force: Resonance delocalization of the nitrogen lone pair into the adjacent carbonyl $\pi^*$ system creates partial double-bond character along the $\text{C}-\text{N}$ bond:       $\text{R}-\text{C}(=\text{O})-\ddot{\text{N}}\text{H}_2 \longleftrightarrow \text{R}-\text{C}(\text{O}^-)=\stackrel{+}{\text{N}}\text{H}_2$

  • The resulting restriction prevents free rotation about the amide bond and locks the planar configuration.

  • Nitriles:

  • Bonding environment: $1$ triple bond to carbon and $1$ non-bonding lone pair on nitrogen ($\text{R}-\text{C}\equiv\text{N}:$).

  • Geometry: Linear configuration with a bond angle of $180^\circ$.

• Oxygen Geometries and Influences on Molecular Shape:

  • Single-Bonded Oxygen Species (Water, Alcohols, Ethers):

  • Water ($\text{H}_2\text{O}$), Alcohols ($\text{ROH}$), and Ethers ($\text{ROR}$).

  • Bonding environment: $2$ single covalent bonds to oxygen plus $2$ non-bonding lone pairs.

  • Steric arrangement: Tetrahedral electron domain geometry producing a bent (angular) molecular shape.

  • Characteristic bond angle: $104.5^\circ$ (compressed from $109.5^\circ$ by repulsion between the two lone pairs).

  • Carbonyl Species ($\text{C}=\text{O}$):

  • Functional group classes:

    • Carboxylic acids ($X = \text{OH}$

    • Esters ($X = \text{OR}$

    • Amides ($X = \text{NH}_2$

    • Ketones ($X = \text{Alkyl}$

    • Aldehydes ($X = \text{H}$

    • Acid chlorides ($X = \text{Cl}$

    • Anhydrides ($X = \text{O(O)CR}$

  • Geometry: Planar arrangement around both the carbonyl carbon and oxygen atom with typical bond angles of $120^\circ$.

  • The carbonyl oxygen possesses $2$ localized lone pairs in $\text{sp}^2$-hybridized orbitals lying in the molecular plane.

Conformational Analysis of Ethane

• Fundamental Principles of Conformation:

  • Conformations: The different spatial arrangements of atoms that are freely inter-convertible through rotation around single covalent bonds without breaking bonds.

  • In ethane ($\text{C}_2\text{H}_6$), an infinite number of spatial arrangements exist as one methyl group rotates relative to the other around the central $\text{C}-\text{C}$ bond.

  • Two limiting conformational extremes define the rotational cycle:

  • Staggered conformation: The carbon-hydrogen bonds on adjacent carbons are spaced as far apart as possible.

  • Eclipsed conformation: The carbon-hydrogen bonds on adjacent carbons align directly in front of one another.

• Structural Depictions:

  • Wedge-Dash Projections: Depict the three-dimensional tetrahedral orientation of bonds in perspective, where solid wedges project forward and hashed wedges project backward.

  • Newman Projections: Depict the molecule viewed directly down the $\text{C}-\text{C}$ bond axis. The front carbon is represented by three radiating spokes intersecting at a center point, while the rear carbon is represented by a large circle with bonds extending from its perimeter.

• Energetics and Torsional Strain of Ethane:

  • Dihedral (Torsion) Angle ($\theta$): The angle between bonds on adjacent atoms viewed along the bond axis, varying continuously from $0^\circ$ to $360^\circ$.

• Stability profile: The staggered conformation represents the lowest energy state (energy minima), whereas the eclipsed conformation represents the highest energy state (energy maxima).

• Destabilization mechanism: Eclipsed forms suffer from torsional strain caused by electron-electron repulsions between aligned C-H bonding pairs.

• Rotational energy barrier: Approximately $3\,\text{kcal}\,\text{mol}^{-1}$ ($\approx 12.6\,\text{kJ}\,\text{mol}^{-1}$, plotted as $3\,\text{kJ}\,\text{mol}^{-1}$ relative difference on normalized comparative curves).

• Rotation kinetics: Thermal energy at ambient temperature permits extremely rapid rotation around the single $\text{C}-\text{C}$ bond.

• Equilibrium population distribution: Due to the energy difference, for every $160$ molecules of ethane, $159$ exist in the staggered conformation and only $1$ occupies the eclipsed conformation ($99.4\%$ staggered).

• Cycle extrema across $360^\circ$:

  • Staggered energy minima occur at: $\theta = 60^\circ$, $180^\circ$, and $300^\circ$.

  • Eclipsed energy maxima occur at: $\theta = 0^\circ$, $120^\circ$, $240^\circ$, and $360^\circ$.

Conformational Analysis of Butane and Acyclic Drug Chains

• Conformations of Butane Across the C2-C3 Bond:

  • Rotation about the central $\text{C}2-\text{C}3$ single bond produces four distinct conformational landmarks:

  • Syn (Fully Eclipsed):

    • Dihedral angle: $\theta = 0^\circ$ (and $360^\circ$).

    • Structure: Both terminal methyl groups ($-\text{CH}_3$) eclipse each other directly.

    • Energetic state: Least stable conformation due to combined steric hindrance (van der Waals strain) between bulky methyl groups and torsional strain.

• Gauche (Staggered):

  • Dihedral angles: $\theta = 60^\circ$ and $\theta = 300^\circ$.

  • Structure: Methyl groups are staggered with respect to adjacent bonds but sit adjacent at a $60^\circ$ dihedral angle.

  • Energetic state: Local energy minima; more stable than eclipsed forms, but less stable than the anti conformation due to steric crowding between the adjacent methyl groups (gauche interaction).

• Eclipsed (Partially Eclipsed):

  • Dihedral angles: $\theta = 120^\circ$ and $\theta = 240^\circ$.

  • Structure: Methyl groups eclipse hydrogen atoms ($\text{CH}_3 \leftrightarrow \text{H}$), and hydrogen atoms eclipse each other ($\text{H} \leftrightarrow \text{H}$).

  • Energetic state: Energy barrier maxima; less stable than gauche and anti conformers, but lower in energy than the syn-periplanar fully eclipsed state.

• Anti (Staggered):

  • Dihedral angle: $\theta = 180^\circ$.

  • Structure: Methyl groups reside in opposite directions, separated by a dihedral angle of $180^\circ$.

  • Energetic state: Most stable conformation (global energy minimum) because bulky groups are positioned as far apart as possible, eliminating steric clash while maintaining fully staggered bond geometry.

• Conformational Preferences in Small Molecule Drugs (GABA):

  • Compound: $\gamma$-Aminobutyric acid (GABA, 4-aminobutanoic acid, $\text{H}_2\text{N}-\text{CH}_2-\text{CH}_2-\text{CH}_2-\text{COOH}$), an inhibitory neurotransmitter.

• Conformational stability analysis across aliphatic single bonds:

  • Bonds 3\u20134 ($\text{C}3-\text{C}4$): Most stable conformation is Staggered.

  • Bonds 2\u20133 ($\text{C}2-\text{C}3$): Most stable conformation is Staggered.

• The preferred lowest-energy resting conformation of flexible linear carbon chains in biological systems corresponds to fully staggered (anti-extended) states along each successive bond.

Conformations of Cyclohexane

• Ring Strain and Planarity Considerations:

  • Cyclohexane rings are ubiquitous structural motifs in natural and pharmaceutical compounds, including steroid cores (e.g., cholesterol, testosterone).

  • If cyclohexane were planar:

  • The internal $\text{C}-\text{C}-\text{C}$ angles of a regular planar hexagon are $120^\circ$, introducing severe angle strain relative to the preferred tetrahedral angle of $109.5^\circ$.

  • All adjacent $\text{C}-\text{H}$ bonds would be forced into fully eclipsed alignments, producing massive torsional strain across all 12 hydrogens.

  • Consequently, cyclohexane puckers into non-planar three-dimensional conformations to minimize both angle and torsional strain.

• The Chair Conformation:

  • The chair conformation is the thermodynamically most stable conformation of cyclohexane.

  • Geometry:

  • $\text{C}-\text{C}-\text{C}$ bond angle: $111^\circ$, nearly identical to the ideal tetrahedral angle ($109.5^\circ$), eliminating angle strain.

  • All adjacent carbon-hydrogen bonds adopt perfectly staggered orientations, eliminating torsional strain.

• Axial and Equatorial Substituents:

  • The 12 hydrogen atoms in a chair conformation are divided into two distinct stereochemical positions:

  • Axial (A) Hydrogens ($6$ total): Oriented perpendicular to the mean plane of the ring. Three project vertically straight up on alternating carbons, and three project vertically straight down on alternating carbons.

  • Equatorial (E) Hydrogens ($6$ total): Oriented radially outward around the perimeter (equator) of the ring, roughly in the average ring plane.

• The Boat Conformation and Instability Factors:

  • The boat form is significantly less stable than the chair form.

  • Primary destabilizing features:

  • Flagpole Hydrogens: The two inward-pointing hydrogen atoms at carbons 1 and 4 are forced into close spatial proximity ($\text{C}1\leftrightarrow\text{C}4$), generating severe steric repulsion (van der Waals strain).

  • Torsional Strain: The carbon-hydrogen bonds along the two parallel base carbons of the boat are completely eclipsed.

• Energetics of Chair-Chair Interconversion (Ring Inversion):

  • Cyclohexane undergoes rapid interconversion between two degenerate chair conformations via a ring flip.

  • Thermodynamic values and transition states along the coordinate:

  • Chair Conformation: Baseline potential energy $0\,\text{kJ}\,\text{mol}^{-1}$ ($0\,\text{kcal}\,\text{mol}^{-1}$; global energy minimum).

  • Half-Chair: Highest-energy transition state with an energy barrier of $50.6\,\text{kJ}\,\text{mol}^{-1}$ ($12.1\,\text{kcal}\,\text{mol}^{-1}$).

  • Twist-Boat: Local energy minimum (metastable intermediate) at $22\,\text{kJ}\,\text{mol}^{-1}$ ($5.3\,\text{kcal}\,\text{mol}^{-1}$); relieves some flagpole and torsional strain of the true boat.

  • Boat: Transition state connecting two twist-boat conformations at an energy of $28\,\text{kJ}\,\text{mol}^{-1}$ ($6.8\,\text{kcal}\,\text{mol}^{-1}$).

• Conformational Flip Dynamics:

  • Pathway: $\text{Chair} \longleftrightarrow \text{Half-chair} \longleftrightarrow \text{Twist-boat} \longleftrightarrow \text{Boat} \longleftrightarrow \text{Twist-boat} \longleftrightarrow \text{Half-chair} \longleftrightarrow \text{Chair}$.

  • Consequence of ring flip: Every substituent that is axial in the initial chair becomes equatorial in the flipped chair, and every equatorial substituent becomes axial. The stereochemical "up" or "down" orientation of each substituent is preserved.

Substituted Cyclohexanes and Drug Ring Systems

• Methylcyclohexane Conformational Equilibrium:

  • Methylcyclohexane exists as an equilibrium between two chair conformations connected via the higher-energy boat pathway:

  • Conformer with the methyl group in the equatorial position.

  • Conformer with the methyl group in the axial position.

• Energetics and 1,3-Diaxial Interactions:

  • Energetic stability difference: The equatorial chair conformer is $7\,\text{kJ}\,\text{mol}^{-1}$ more stable than the axial chair conformer.

  • Population ratio: At equilibrium, out of every $19$ molecules of methylcyclohexane, approximately $18$ molecules possess an equatorial methyl group, while only $1$ molecule possesses an axial methyl group ($18:1$ ratio; $\approx 95\%$ equatorial).

  • Cause of axial destabilization: 1,3-diaxial interactions.

  • In the axial conformation, the methyl group points in the same direction as the axial hydrogens at positions 3 and 5 relative to carbon 1.

  • The steric clash between the van der Waals radii of the axial methyl group and the two syn-axial hydrogen atoms at C3 and C5 causes significant steric strain.

  • In the equatorial position, the methyl group projects outward into empty space, completely avoiding 1,3-diaxial interactions.

• Application to Drug Molecules: Methylphenidate (Ritalin):

  • Therapeutic context: Methylphenidate is a central nervous system stimulant used in the treatment of Attention Deficit Hyperactivity Disorder (ADHD).

  • Evaluation of the two rings within methylphenidate:

  • Piperidine ring: Saturated six-membered heterocyclic ring containing one nitrogen atom. Adopts a non-planar, flexible chair conformation to minimize angle and torsional strain.

  • Phenyl ring: Fully conjugated, six-membered aromatic ring with delocalized $\pi$ electrons. Retains a rigid, planar geometry with uniform $sp^2$ hybridization.

Recommended Literature and Reference Texts

• Primary Textbook Readings:

  • Pharmaceutical Chemistry, edited by Barber & Rostron, Oxford University Press (OUP), 2013:

  • Chapter 2: Electronic structure and bonding environments, pages 26\u201337, Sections 2.2, 2.3, and 2.4.

  • Chapter 3: Molecular conformations, Section 3.3, pages 51\u201356.

  • Organic Chemistry, Paula Yurkanis Bruice, Pearson, 2017 (Conformational analysis and cyclohexane dynamics).