Question

Discuss the various bonding and antibonding orbital of butadiene. Place them in order of increasing energy. What is the electronic configuration of butadiene in both the ground and the excited state.

Short answer

In butadiene, there are four molecular orbitals (MOs) formed by the interactions of the p orbitals from each carbon atom in the conjugated π system. The energy order of these MOs is π1 < π2 < π3* < π4*. For the ground state electronic configuration, four π-electrons are distributed as π1^2π2^2π3*^0π4*^0. In the excited state, one electron is promoted from the HOMO to the LUMO, resulting in the electronic configuration π1^2π2^1π3*^1π4*^0.

Step-by-step solution

Draw the structure of butadiene and identify the conjugated π system

First, we need to draw the structure of butadiene. The molecular formula of butadiene is C4H6, and its structural formula is CH2=CH-CH=CH2. The double bonds between carbon atoms create a conjugated π system, which is essential for understanding its molecular orbitals and electronic configurations.

Construct the molecular orbitals based on symmetry

In butadiene, we will focus on the π-system. We have four available p orbitals (one p orbital from each carbon atom) to create the molecular orbitals. The number of molecular orbitals generated will be equal to the number of atomic orbitals combined (in this case, 4). Since butadiene is a linear molecule, we focus on the symmetry of the p orbitals. We can construct four molecular orbitals (MOs) based on their symmetries: 1. The lowest energy (bonding) MO, called π1, results from the constructive interaction of all four p orbitals. 2. The second-lowest energy MO, called π2, results from the constructive interaction of two adjacent p orbitals and destructive interaction of the other two. 3. The next MO, called π3*, is an antibonding MO resulting from the constructive interaction between two carbon atoms and destructive interaction with the other two. 4. The highest energy (antibonding) MO, called π4*, results from the destructive interaction of all four p orbitals. Therefore, the energy order of molecular orbitals from lowest to highest is: π1 < π2 < π3* < π4*.

Determine the number of π-electrons and the ground state electronic configuration

Now that we have the molecular orbitals, we should distribute the π-electrons among these orbitals. Butadiene has four π-electrons, one from each double bond between carbon atoms. According to the Aufbau principle, electrons occupy the lower energy orbitals first. Two electrons will occupy π1 and the other two electrons will occupy π2. So, the ground state electronic configuration of butadiene is: π1^2π2^2π3*^0π4*^0

Determine the excited state electronic configuration

For the excited state electronic configuration, we assume that one electron is promoted from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). In this case, one electron from π2 will move to π3*. Thus, the electronic configuration of butadiene in the excited state will be: π1^2π2^1π3*^1π4*^0 In conclusion, we have analyzed the bonding and antibonding molecular orbitals of butadiene, determined their energy order, and found the electronic configurations for both the ground and excited states.

Key concepts

Conjugated π System

In organic chemistry, a conjugated π system refers to a sequence of alternating single and multiple bonds, typically double bonds, in a molecule. This arrangement allows the p orbitals of adjacent atoms to overlap, facilitating the delocalization of π electrons across the system. Butadiene is a classic example with its alternating double bonds structure, denoted as CH extsubscript{2}=CH-CH=CH extsubscript{2}. The conjugation in butadiene allows the π electrons to spread out over the four carbon atoms involved. This delocalization stabilizes the molecule and lowers its energy, making it more reactive in certain chemical reactions. Key Characteristics of Conjugated Systems:

• Enhanced stability due to electron delocalization.
• Ability to absorb specific wavelengths of light, resulting in interesting optical properties.
• Important role in the electronic properties of molecules.

Understanding conjugated systems is crucial because they form the basis for many modern materials, including conductive polymers and organic semiconductors.

Butadiene Structure

Butadiene, with the chemical formula C extsubscript{4}H extsubscript{6}, is a simple conjugated diene. It is best visualized as two ethene units (CH extsubscript{2}=CH extsubscript{2}) connected with a single bond. The structure is often written as CH extsubscript{2}=CH-CH=CH extsubscript{2}. This linear arrangement of carbon atoms facilitates the conjugation of the π electrons. Each double bond contributes two π electrons to the system, resulting in a total of four π electrons in butadiene. There are four sp extsuperscript{2} hybridized carbon atoms, which allow the p orbitals to align parallel to each other, enabling the π electron cloud to form. Important Points about Butadiene:

• Highly reactive due to the presence of multiple double bonds.
• The double bonds' positioning allows for the delocalization of electrons.
• Formed by the combination of two ethylene units.

Its structure and properties make it a key building block in the manufacture of synthetic rubber and other industrial chemicals.

Ground State Electronic Configuration

The ground state of a molecule refers to its lowest energy configuration. For butadiene, the focus is on the distribution of its four π electrons across the molecular orbitals (MOs) that arise from the combination of individual p orbitals.Steps for Ground State Configuration:

• Identify the number of π electrons, which in the case of butadiene, is four.
• Distribute these electrons in the MOs, following the energy order: π extsubscript{1}, π extsubscript{2}, π extsuperscript{3*}, and π extsuperscript{4*}.
• Electrons fill the lowest energy orbitals first, analogous to the Aufbau principle.

For butadiene, this means two electrons fill the lowest energy orbital π extsubscript{1}, and the remaining two fill the next one, π extsubscript{2}. Thus, the ground state configuration is described as: \[\pi_1^2\pi_2^2\pi_3^{*0}\pi_4^{*0}\]In this stable state, all electrons are paired, contributing to the overall stability of the butadiene molecule.

Excited State Electronic Configuration

An excited state occurs when one or more electrons absorb energy and jump to a higher energy orbital. In butadiene, the transition from the ground state involves moving one electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO).Process for Excited State Configuration:

• Identify HOMO, which is π extsubscript{2}, and promote one electron to the LUMO, which is π extsuperscript{3*}.
• Resulting electron configuration becomes: \(\pi_1^2\pi_2^1\pi_3^{*1}\pi_4^{*0}\)
  
• This change leads to an excited state with unpaired electrons.

In the excited state, the molecule may exhibit different reactivity and optical properties due to the presence of unpaired electrons. Understanding these transitions is crucial for applications in photochemistry and spectroscopy.