The energy level of molecular orbitals is a fundamental concept in quantum chemistry that describes the distribution of electrons within a molecule. To understand the energy levels of molecular orbitals, we must first delve into the principles of quantum mechanics and the formation of molecular orbitals. In quantum mechanics, the behavior of electrons is described by wave functions, which are mathematical functions that provide information about the electron’s position, momentum, and energy. The Schrödinger equation, a fundamental equation in quantum mechanics, governs the wave function of an electron in an atom or molecule.
What is Molecular orbital theory?
When two or more atoms come together to form a molecule, their atomic orbitals, which describe the probability distribution of finding electrons around individual atoms, combine to form molecular orbitals. This process is known as molecular orbital theory.
Bonding and Antibonding Orbitals
Molecular orbitals are obtained by solving the Schrödinger equation for the system of atoms, considering their interactions and the constraints of quantum mechanics. The solutions to the equation result in a set of molecular orbitals with different energies. The number of molecular orbitals obtained depends on the number of atomic orbitals involved in the bonding. For example, when two atomic orbitals combine, they form two molecular orbitals: a bonding orbital and an antibonding orbital. The bonding orbital has lower energy than the original atomic orbitals, while the antibonding orbital has higher energy. The energy level of molecular orbitals is typically represented on an energy level diagram. The diagram depicts the molecular orbitals as horizontal lines, with the energy increasing from bottom to top. The molecular orbitals are labeled according to their symmetry and energy. The lower-energy orbitals are labeled with Greek letters, such as σ (sigma) and π (pi), while the higher-energy orbitals are labeled with asterisks.
Diatomic Molecule
In a diatomic molecule, such as hydrogen (H2), the energy level diagram shows the combination of two atomic orbitals. The 1s atomic orbitals of each hydrogen atom combine to form a bonding σ orbital and an antibonding σ* orbital. The bonding orbital is lower in energy, stabilizing the molecule, while the antibonding orbital is higher in energy, making it less favorable for electron occupation. As more atoms are added to a molecule, the complexity of the energy level diagram increases.
Homonuclear Diatomic molecule
For example, in a homonuclear diatomic molecule like oxygen (O2), which consists of two oxygen atoms, the molecular orbitals formed from the 2p atomic orbitals are considered. The oxygen molecule has a total of 16 electrons to distribute among the molecular orbitals. The 2p orbitals of each oxygen atom combine to form a set of six molecular orbitals: two σ2p, two π2p, and two π2p orbitals. The σ2p orbitals are lower in energy, followed by the π2p orbitals, and finally, the π2p orbitals, which are higher in energy. The electrons occupy the molecular orbitals according to the Aufbau principle, which states that electrons first fill the lowest energy orbitals. The energy level diagram for oxygen also reveals the presence of bonding and antibonding orbitals. The σ2p molecular orbitals are bonding orbitals, while the π2p orbitals are a combination of bonding and antibonding character. The π*2p orbitals are purely antibonding.
The energy levels of molecular orbitals are determined by the interplay of various factors. These include the nuclear charges of the atoms involved, the distance between the atoms, and the overlapping of atomic orbitals. As these factors change, the energy levels of the molecular orbitals can be modified, resulting in different electronic and chemical properties of molecules. In more complex molecules, the energy level diagram becomes even more intricate. The number of atomic orbitals and their interactions increase, leading to a larger number of molecular orbitals with varying energies.
Benzene
For example, in a molecule like benzene (C6H6), which consists of six carbon atoms and six hydrogen atoms, the energy level diagram involves the combination of carbon atomic orbitals. The carbon atoms contribute their 2s and 2p atomic orbitals to form a set of molecular orbitals. In benzene, the molecular orbitals are grouped into two sets: the bonding π orbitals and the antibonding π* orbitals. The bonding π orbitals are further divided into a lower-energy set, labeled π2p, and a higher-energy set, labeled π*2p. The π2p orbitals are responsible for benzene’s delocalized π electron system, giving it its aromatic properties. The energy level diagram for benzene also includes the σ orbitals, which result from the overlap of carbon 2s orbitals with hydrogen 1s orbitals. These σ orbitals, labeled σ2s and σ*2s, contribute to the bonding between the carbon and hydrogen atoms in the molecule. The distribution of electrons in molecular orbitals follows the Pauli exclusion principle and Hund’s rule. The Pauli exclusion principle states that each molecular orbital can accommodate a maximum of two electrons with opposite spins. Hund’s rule dictates that when filling degenerate orbitals (orbitals with the same energy), electrons occupy different orbitals with parallel spins before pairing up. The occupation of molecular orbitals by electrons influences the stability and reactivity of molecules.
Lower-energy molecular orbitals are generally more stable and filled with electrons, while higher-energy orbitals are less stable and may remain unoccupied or partially filled. The electronic configuration of a molecule determines its chemical properties and behavior, including its bonding, reactivity, and spectroscopic characteristics. The energy level diagram of molecular orbitals provides insights into the electronic structure of molecules and aids in understanding their properties. By examining the relative energies of different molecular orbitals, scientists can make predictions about the stability and behavior of molecules and their interactions with other molecules or external stimuli. It is important to note that the energy level diagram presented here provides a simplified representation of molecular orbitals. In reality, the energy levels of molecular orbitals can be affected by additional factors, such as electron-electron repulsion, molecular symmetry, and external electric or magnetic fields.
Furthermore, the complexity of molecular systems and the number of atoms involved can lead to even more intricate energy-level diagrams.
Conclusion
In conclusion, the energy level of molecular orbitals is a crucial aspect of quantum chemistry, describing the distribution of electrons within a molecule. Molecular orbitals are formed by the combination of atomic orbitals and are characterized by their relative energies, symmetries, and electron occupancies. The energy level diagram provides a visual representation of the molecular orbitals, allowing scientists to understand and predict molecules’ electronic structure and properties.
