In a simple cumulene such as allene, which statement best describes the types of orbital overlap that form the carbon carbon double bonds?

Introduction / Context:
Cumulenes are organic molecules that contain consecutive carbon carbon double bonds, such as in allene, which has the structure H2C=C=CH2. Understanding the bonding in cumulenes helps students apply valence bond theory and orbital overlap ideas beyond simple single bonds. Each carbon carbon double bond can be described in terms of sigma and pi overlaps. This question asks which statement best describes the types of orbital overlap involved in forming these double bonds in a simple cumulene.

Given Data / Assumptions:
- A cumulene contains adjacent carbon carbon double bonds, for example C=C=C in allene.
- Valence bond theory describes a double bond as consisting of one sigma bond and one pi bond between two carbon atoms.
- Sigma bonds arise from end to end overlap of hybrid orbitals, while pi bonds arise from sidewise overlap of p orbitals.
- The question focuses on describing these general types of overlap rather than on detailed hybridisation labels for each carbon in the chain.

Concept / Approach:
In valence bond theory, any carbon carbon double bond is composed of a sigma bond plus a pi bond. The sigma component is formed by end to end overlap of orbitals along the axis between the two carbon nuclei, which may involve sp2 or sp hybrid orbitals depending on the molecule. The pi component is formed by sidewise or lateral overlap of unhybridised p orbitals on each carbon, above and below the plane of the sigma bond. In cumulenes, each double bond follows this pattern, even though the orientation of the p orbitals can lead to interesting geometries. Therefore, the best description is that each double bond involves one sigma and one pi overlap, rather than only sigma or only pi bonding.

Step-by-Step Solution:
Step 1: Recall that a single covalent bond between two carbon atoms is a sigma bond formed by end to end overlap of appropriate orbitals. Step 2: Recognise that a double bond consists of one sigma bond plus one pi bond, where the pi bond is formed by sidewise overlap of p orbitals. Step 3: Understand that cumulenes have sequences of carbon atoms joined by double bonds, and each individual C=C bond follows the usual sigma plus pi pattern. Step 4: Note that there is always a sigma framework that holds the chain together, and additional pi bonds contribute extra bonding and influence geometry. Step 5: Conclude that the correct description is that each C=C bond in a cumulene involves one sigma overlap and one pi overlap, as stated in option B.

Verification / Alternative check:
Structural representations of allene and other cumulenes show central carbon atoms with linear or near linear arrangements and multiple pi systems oriented in different planes. However, these models always retain the concept that each double bond has a sigma component plus a pi component. Molecular orbital treatments of cumulenes also show sigma bonding orbitals along the chain and separate pi systems. No accepted model of carbon carbon double bonding uses only sigma or only pi interactions. Thus, the explanation that double bonds arise from both sigma and pi overlaps remains valid in cumulenes and supports the choice of option B.

Why Other Options Are Wrong:
Option A is incorrect because a structure with only sigma overlaps of sp3 orbitals would represent single bonds without any double bond character. Option C suggests that there are only pi overlaps without a sigma framework, which cannot produce stable covalent bonds between nuclei in the usual valence bond picture. Option D describes metallic type delocalisation, which is not appropriate for discrete organic molecules like cumulenes. Option E claims that no overlap is required and that bonding is purely ionic, which is not consistent with the covalent nature of carbon carbon bonds in organic chemistry. None of these alternatives fits the known bonding description for cumulenes.

Common Pitfalls:
Students can be confused by the geometry of cumulenes and may overemphasise the role of pi bonding, forgetting that sigma bonds are always present as the primary framework. Another pitfall is to assume that more complex molecules must require completely new bonding concepts, when in fact basic sigma and pi overlap ideas still apply. Keeping the standard description of double bonds in mind, namely one sigma and one pi bond, provides a solid foundation for understanding cumulenes without overcomplicating the picture.

Final Answer:
In a simple cumulene, each carbon carbon double bond is formed by One sigma overlap and one pi overlap, with sigma bonds formed by end to end overlap and pi bonds formed by sidewise overlap of p orbitals.