Question

Describe the bonding in the first excited state of \(\mathrm{N}_{2}\) (the one closest in energy to the ground state) using the molecular orbital model. What differences do you expect in the properties of the molecule in the ground state as compared to the first excited state? (An excited state of a molecule corresponds to an electron arrangement other than that giving the lowest possible energy.)

Short answer

In the first excited state of N2, one electron is promoted from a \(\pi_{2p}\) bonding orbital to the antibonding \(\sigma^*_{2p}\) orbital, resulting in a lower bond strength and longer bond length compared to the ground state, where all bonding orbitals are fully occupied, and the antibonding orbitals are empty. Additionally, the first excited state may exhibit different chemical reactivity due to the presence of an unpaired electron in the antibonding \(\sigma^*_{2p}\) orbital.

Step-by-step solution

Understanding Molecular Orbital Theory

Molecular Orbital (MO) Theory is a method for determining the electronic structure of molecules by combining atomic orbitals to form molecular orbitals. These molecular orbitals are then occupied by electrons following the Aufbau principle, the Pauli Exclusion principle, and Hund's rule. The outcome of this process provides information about the structure, stability, and properties of molecules.

Electronic Configuration of Nitrogen Atoms

First, we need to determine the electronic configuration of nitrogen atoms. Nitrogen has 7 electrons in its atomic structure, and its electron configuration is \(1s^2 2s^2 2p^3\). There are 3 unpaired electrons in its 2p orbitals.

Constructing Molecular Orbitals for Nitrogen

Now, we'll create the molecular orbitals combining the atomic orbitals of each nitrogen atom, the \(2s\) and \(2p\) orbitals are particularly important here. Since there are two nitrogen atoms, we will have two molecular orbitals for each type of atomic orbital. Combining \(2s\) orbitals gives \( \sigma_{2s}\ (bonding)\) and \(\sigma^*_{2s} \ (antibonding)\) molecular orbitals. When we combine the \(2p\) orbitals, we get \( \sigma_{2p}\), \(\sigma_{2p}^*\), three \(\pi_{2p}\) (two bonding, one antibonding), and two \(\pi_{2p}^*\) orbitals.

Filling Molecular Orbitals with Electrons

We will now fill the molecular orbitals with electrons following the Aufbau principle, Pauli Exclusion principle, and Hund's rule. Nitrogen has 14 electrons in total (7 from each nitrogen atom). Ground state: - \( \sigma_{1s}\) - 2 electrons - \( \sigma^*_{1s}\) - 0 electrons - \( \sigma_{2s}\) - 2 electrons - \( \sigma^*_{2s}\) - 0 electrons - \( \sigma_{2p}\) - 2 electrons - Three \(\pi_{2p}\) - 6 electrons (2 for each bonding orbital) - \(\sigma^*_{2p}\) - 0 electrons - \(\pi^*_{2p}\) - 0 electrons First excited state: To obtain the first excited state, we must promote one electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). In this case, we move one electron from one of the \(\pi_{2p}\) bonding orbitals to the \(\sigma^*_{2p}\) antibonding orbital. Now, the molecular orbitals are filled as follows: - \( \sigma_{1s}\) - 2 electrons - \( \sigma^*_{1s}\) - 0 electrons - \( \sigma_{2s}\) - 2 electrons - \( \sigma^*_{2s}\) - 0 electrons - \( \sigma_{2p}\) - 2 electrons - Three \(\pi_{2p}\) - 5 electrons (2, 2, and 1 for each bonding orbital) - \(\sigma^*_{2p}\) - 1 electron - \(\pi^*_{2p}\) - 0 electrons

Comparison of Properties between Ground State and First Excited State

In the ground state, all bonding orbitals are fully occupied, while the antibonding orbitals are empty. This results in a strong bond between the two nitrogen atoms. In the first excited state, however, the \(\sigma^*_{2p}\) antibonding orbital is occupied by one electron, which weakens the bonding strength between the nitrogen atoms. As a result, we expect the nitrogen molecule in the first excited state to have a longer bond length and a lower bond strength compared to the ground state. In addition, the first excited state may exhibit different chemical reactivity due to the presence of an unpaired electron in the antibonding \(\sigma^*_{2p}\) orbital.

Key concepts

Excited State

The excited state of a molecule occurs when one or more electrons move from a lower energy level to a higher one. This happens when energy is absorbed, often from light. In this higher energy state, the molecule has a different electronic arrangement compared to its ground state.
The nitrogen molecule ( 2) has its first excited state when an electron from a bonding orbital is promoted to an antibonding orbital. This transition changes the molecule's properties significantly.
Understanding the excited state of a molecule is crucial because it can alter the molecule's reactivity, bond length, and strength. It also helps explain phenomena like fluorescence and phosphorescence.

Electronic Configuration

Electronic configuration describes how electrons are distributed among the various orbitals around the nucleus of an atom or a molecule. For nitrogen, the atomic electronic configuration is: \(1s^2 2s^2 2p^3\). This shows two electrons in the 1s orbital, two in the 2s orbital, and three in 2p orbitals.
In a nitrogen molecule, the electronic configuration combines the atomic configurations into molecular orbitals. Electrons fill these molecular orbitals following rules such as the Aufbau principle, Pauli Exclusion principle, and Hund's rule. These rules determine the order in which these orbitals are filled and ensure a stable configuration.
Understanding electronic configurations is essential as they dictate the molecule's bonding characteristics and reactivity.

Nitrogen Molecule Bonding

Nitrogen molecules (2) form a strong triple bond, which is one of the strongest found in nature. This is due to the sharing of three pairs of electrons between the two nitrogen atoms.
In the ground state, the nitrogen molecule has all its bonding orbitals filled, creating a stable configuration. The structure consists of \(\sigma\) and \(\pi\) bonding orbitals filled with electrons, forming a strong bond.
In the first excited state, an electron shifts from a bonding \(\pi_{2p}\) orbital to an antibonding \(\sigma^*_{2p}\) orbital. As a result, the bond is weakened due to the presence of electrons in the antibonding orbital, leading to a longer bond length and reduced strength. Understanding this helps us see how molecular bonding influences a molecule's stability and interaction with other substances.

Molecular Orbitals

Molecular orbitals are formed by the combination of atomic orbitals when atoms bond together. These orbitals can be either bonding or antibonding. Bonding orbitals help stabilize the molecule, while antibonding orbitals can destabilize it.
For nitrogen, molecular orbitals include \(\sigma\) and \(\pi\) bonding and \(\sigma^*\) antibonding orbitals. Electrons fill these orbitals in a way that minimizes energy, usually resulting in all bonding orbitals filled and antibonding empty in the ground state.

• Bonding molecular orbitals: \(\sigma_{1s}\), \(\sigma_{2s}\), \(\sigma_{2p}\), \(\pi_{2p}\)
• Antibonding molecular orbitals: \(\sigma^*_{2s}\), \(\sigma^*_{2p}\), \(\pi^*_{2p}\)

Understanding how these orbitals interact gives insights into molecular stability, chemical reactivity, and physical properties. In the excited state, the presence of electrons in antibonding orbitals explains the changes in molecular behavior.