Question

Draw an atomic-orbital picture of 1,4 -dichlorobutatriene, \(\mathrm{ClCH}=\mathrm{C}=\mathrm{C}=\mathrm{CHCl}\) Examine your diagram carefully and predict the number and kind of stereoisomers possible for this structure.

Short answer

Two stereoisomers are possible: cis and trans forms.

Step-by-step solution

Identify the Atoms and Bonds

1,4-Dichlorobutatriene consists of a chain of four carbon atoms with alternating double bonds and chlorine atoms attached to the terminal carbons. The structure is written as \( \text{Cl-CH}=\text{C}=\text{C}=\text{CH-Cl} \).

Draw the Atomic Orbitals

In a linear structure like butatriene, all the carbon atoms are sp2 hybridized, forming a linear arrangement. Each carbon atom forms \( p \text{-orbitals} \) on either side of the \( \text{sp}^2 \text{-orbitals} \) for \( \pi \text{-bonding} \). Draw each carbon with its three hybridized \( \text{sp}^2 \text{-orbitals} \) along with one unhybridized \( p \text{-orbital} \) perpendicular to the molecule’s plane.

Connect the Molecular Orbitals

Align the \( \pi \text{-orbitals} \) of each carbon atom to form \( \pi \text{-bonds} \). Since the structure is linear, each carbon shares \( \pi \text{-electrons} \) with its adjacent neighbor, resulting in a delocalized system.

Visualize the Potential Stereoisomers

Stereoisomers arise from the different possible configurations around double-bonded carbons. A compound like 1,4-dichlorobutatriene can exist in cis and trans forms at each of the double bonds, maximizing possible stereoisomers.

Determine the Types of Stereoisomers

Due to the presence of two non-terminal double bonds, each can theoretically have \( \text{cis-trans isomerism} \). Therefore, the possible stereoisomers are: \(1. \text{cis-1,4} \text{-dichlorobutatriene},2. \text{trans-1,4} \text{-dichlorobutatriene} \).

Key concepts

Atomic Orbitals

Atomic orbitals are regions around an atom's nucleus where electrons are likely to be found. These can be thought of as the shapes or spaces in which electrons move. Meeting between art and science, atomic orbitals are drawn using electron density plots or through mathematical equations. For a basic understanding, it is useful to visualize s, p, d, and f orbitals, which vary widely in shape. - **s-orbitals:** These are spherical shapes around the nucleus. - **p-orbitals:** These have a dumbbell shape and are aligned along x, y, or z axes. When we talk about the 1,4-dichlorobutatriene, each carbon atom uses sp² hybrid orbitals to form sigma (σ) bonds. This means that apart from the singular p-orbital left out for pi (π) bonding, the rest are involved in creating stable connections with adjacent atoms.

Hybridization

Hybridization is a concept that explains the mixing of atomic orbitals to form new, different sets of orbitals. This process is crucial in determining the geometry and bonding properties of organic molecules, like 1,4-dichlorobutatriene. In hybridization: - Atomic orbitals blend to create equivalent orbitals called hybrids. - For example, each carbon in butatriene goes through sp² hybridization. This sp² hybridization occurs when one s-orbital and two p-orbitals combine, forming three sp² orbitals that are in a plane 120° apart. The leftover unhybridized p-orbitals in these carbon atoms remain perpendicular to this plane, enabling the formation of pi-bonds necessary for the multiple double bonds present in the compound.

Pi-bonding

Pi-bonding (\( \pi \)-bonding) is an essential feature in molecules with double or triple bonds. They arise due to the lateral overlap of unhybridized p-orbitals between two atoms. Some notable characteristics of pi bonds are:- They add rigidity and strength, preventing rotation around the bond.- They accompany sigma bonds, as found in double bonds, which are composed of one sigma bond and one pi bond.In 1,4-dichlorobutatriene, pi-bonds are formed by the side-to-side overlap of p-orbitals from each carbon along the linear chain. This creates a delocalized electron cloud along the molecule, providing a unique electron pathway that further stabilizes the linear structure.

Cis-trans Isomerism

Cis-trans isomerism is a form of stereoisomerism evident in molecules with double bonds. It arises because of the restricted rotation around the double bond, which creates distinct spatial arrangements of atoms or groups. - **Cis configuration:** Atoms or groups are on the same side of the double bond. - **Trans configuration:** Atoms or groups are on opposite sides. In the context of 1,4-dichlorobutatriene, each central double-bonded carbon can permit cis-trans isomerism. Even though the molecule has alternating double bonds, it can still exhibit distinct configurations at each center. The possibilities can theoretically include combinations such as cis-cis, trans-trans, or even cis-trans configurations along its length, depending on how the chlorine atoms align relative to each other at separate double bonds. This gives rise to various stereosiomers.