Chemical Bonding Molecular Orbitals of H₂
The procedure can be explained using the H₂ molecule as an example. The valence-shell orbitals of each hydrogen atom, which are the atoms' 1s orbitals, are used to build its molecular orbitals. These two orbitals can be superimposed in two ways: one by adding them together, and the other by subtracting them.
In the former, the amplitudes of the two atomic orbitals constructively interact with one another, resulting in an increased amplitude between the two nuclei. As a result, any electron occupying this molecular orbital is more likely to be found between the two nuclei, and its energy is lower than when it is restricted to either atomic orbital alone. A bonding orbital is thus described as a combination of atomic orbitals. It is also designated as an orbital and numbered 1 since it has cylindrical symmetry around the internuclear axis.
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Chemical Bonding Molecular Orbitals of H₂ and He₂
Since the MO created by subtracting the two 1s orbitals has cylindrical symmetry, it is also an orbital. Taking the difference between the two atomic orbitals, on the other hand, causes destructive interference in the internuclear field, where one orbital's amplitude is subtracted from the other. Since the destructive interference is complete on a plane halfway between the nuclei, there is a nodal plane—that is, a plane with zero amplitude—between them. Any electron occupying this orbital is not allowed to enter the internuclear field, and its energy is higher than if it occupied either atomic orbital. The orbital that forms in this way is known as an antibonding orbital, and it is sometimes abbreviated as * (or “sigma star”) or 2 since it is the second of the two orbitals.
The molecular orbital energy-level diagram for the H2 molecule displays the relative energies of molecular orbitals. The energies of the 1s orbitals of atoms A and B are shown on either side of the central ladder, and the energies of bonding and antibonding combinations are shown on the central two-rung ladder. The electrons are only added at this stage after the energy-level diagram has been set up. According to the Pauli exclusion theorem, each orbital may only have two electrons. Two electrons are present in H₂, and they join and fill the lower-energy bonding combination using the building-up theory. As a result, the molecule's electron configuration is 12 and the molecule's stability is determined by the occupation of the bonding combination. Its low energy is because of the accumulation of electron density in the internuclear region due to positive interference between the contributing atomic orbitals (at least according to the traditional interpretation).
Molecular Orbitals Energy
Many aspects of bonding can be explained by the Valence Bond Principle, but not all. We use another theory called the molecular orbital (MO) theory to supplement this one. The molecular orbital theory is a more advanced paradigm for comprehending chemical bonding.
New molecular orbitals are produced using a mathematical process called a linear combination of atomic orbitals in MO theory, which takes the concept of atomic orbitals overlapping to a new stage (LCAO).
Molecular orbitals are similar to atomic orbitals in many ways: – They are filled from lowest to highest energy (Aufbau principle).]
Atomic orbitals depict electron density in space associated with a specific atom, while molecular orbitals represent electron density in space associated with a specific molecule. The electron density is delocalized (spread out) over more than one atom as molecular orbitals are associated with the whole molecule.
Noble Gas Configuration
The noble gases are mentioned in the Periodic Table of Elements' rightmost column: helium, neon, argon, krypton, xenon, and radon. At room temperature, both of these elements are gaseous, colourless, odourless, and non-reactive with other elements. The outer, or valence, atomic orbitals are fully filled in the noble gases' electron configuration.
Electronic Configurations
Each element is identified by the number of positively charged protons in the nucleus and the number of electrons orbiting around it. Quantum mechanics identify the most likely orbital positions. Shells, subshells, and atomic orbitals are formed by these sites. Two electrons can be kept in the smallest atomic orbital, s. The next orbital, p, has a maximum capacity of six electrons. The lightest noble gas, helium, has just two electrons in its s orbital. Many of the remaining noble gases have absolute ‘s’ and ‘p’ orbitals in their outer shells. The "octet law" for noble gases states that each gas's valance (or outermost) shell has two s electrons and six p electrons. When a valance shell is fully filled, it cannot exchange electrons with other elements, resulting in gases that are too "noble" to mix with other atoms.
Pauli’s Exclusion Principle
In chemistry, the Pauli exclusion principle, along with Aufbau's Principle and Hund's Rule, is one of the most essential concepts. It is critical for students to understand, especially when studying electrons. It primarily aids in the comprehension of electron structures in atoms and molecules, as well as the classification of elements in the periodic table.
FAQs on Molecular Orbitals of H₂ and He₂
1. How does Molecular Orbital Theory (MOT) explain the formation of the hydrogen (H₂) molecule?
According to Molecular Orbital Theory (MOT), the H₂ molecule is formed when the 1s atomic orbitals of two individual hydrogen atoms combine. This process, known as the Linear Combination of Atomic Orbitals (LCAO), results in the formation of two new molecular orbitals: a lower-energy bonding molecular orbital (σ1s) and a higher-energy antibonding molecular orbital (σ*1s). The two electrons from the hydrogen atoms then fill the lower-energy σ1s orbital, creating a stable covalent bond.
2. What is the difference between a bonding and an antibonding molecular orbital?
A bonding molecular orbital is formed by the constructive (additive) overlap of atomic orbitals. It has lower energy than the parent atomic orbitals and increases electron density between the nuclei, which helps hold the atoms together. In contrast, an antibonding molecular orbital is formed by the destructive (subtractive) overlap of atomic orbitals. It has higher energy and features a nodal plane where electron density is zero, which destabilises the bond between the atoms.
3. What is the molecular orbital configuration and bond order of the H₂ molecule?
The molecular orbital configuration for the H₂ molecule, which has 2 electrons, is (σ1s)². To calculate the bond order, we use the formula: Bond Order = ½ (Number of electrons in bonding orbitals - Number of electrons in antibonding orbitals). For H₂, this is ½ (2 - 0) = 1. A bond order of 1 indicates a stable, single covalent bond exists between the two hydrogen atoms.
4. Why does the helium molecule (He₂) not exist under normal conditions?
The helium molecule (He₂) has a total of 4 electrons (2 from each He atom). According to MOT, its electronic configuration is (σ1s)²(σ*1s)². The bond order is calculated as ½ (2 - 2) = 0. A bond order of zero implies that the stabilising effect of the electrons in the bonding orbital is completely cancelled out by the destabilising effect of the electrons in the antibonding orbital. Therefore, no stable bond is formed, and the He₂ molecule does not exist.
5. How do you determine the molecular orbital configuration and stability of the helium ion, He₂⁺?
The He₂⁺ ion has a total of 3 electrons. Its molecular orbital configuration is (σ1s)²(σ*1s)¹. The bond order is calculated as ½ (2 - 1) = 0.5. Since the bond order is positive (greater than zero), the He₂⁺ ion is predicted to be stable and can exist, although it is less stable than H₂. The presence of one electron in the antibonding orbital weakens the bond.
6. What is the fundamental difference between an atomic orbital and a molecular orbital?
The main difference lies in the number of nuclei they are associated with.
- An atomic orbital is monocentric, meaning it is associated with a single atomic nucleus and describes the probable location of an electron within that atom.
- A molecular orbital is polycentric, meaning it is associated with two or more nuclei in a molecule and describes the probable location of an electron across the entire molecule.
7. Can you draw the molecular orbital diagram for the H₂⁻ ion and determine its bond order?
Yes. The H₂⁻ ion has a total of 3 electrons (1 from each H, plus one extra). The molecular orbital diagram shows the two 1s atomic orbitals combining to form the σ1s and σ*1s molecular orbitals. The 3 electrons fill these orbitals according to the Aufbau principle, resulting in the configuration (σ1s)²(σ*1s)¹. The bond order is calculated as ½ (2 - 1) = 0.5. This indicates that the H₂⁻ ion can exist but is less stable than the H₂ molecule.
8. Why is an antibonding molecular orbital higher in energy than the atomic orbitals from which it is formed?
An antibonding molecular orbital is higher in energy due to destructive interference between the atomic orbital wave functions. This interference creates a nodal plane between the two nuclei—a region with zero electron probability. Electrons in this orbital are forced away from the internuclear region, leading to increased repulsion between the positively charged nuclei. This repulsion raises the overall energy of the system, making the orbital less stable and higher in energy than the original atomic orbitals.
