HOMO, LUMO, HOMO-LUMO Gap, Fermi Level

About

In molecular orbital theory, concepts like HOMO, LUMO, the HOMO-LUMO gap, and the Fermi level help describe the electronic properties of molecules, including how they interact with light, electricity, and each other. These terms are crucial in understanding reactivity, stability, and conductivity in molecular systems.

HOMO (Highest Occupied Molecular Orbital):

• The HOMO is the molecular orbital that contains the highest-energy electrons in a molecule. It is the highest energy orbital that is fully occupied by electrons under normal conditions.

• Significance: The electrons in the HOMO are the most likely to participate in chemical reactions, especially when the molecule donates electrons (acts as a nucleophile or Lewis base). The HOMO is also important in determining a molecule's reactivity and its ability to absorb light.

LUMO (Lowest Unoccupied Molecular Orbital):

• The LUMO is the molecular orbital that is the lowest in energy among the unoccupied orbitals. It is the orbital that will accept electrons when the molecule gains energy or participates in chemical reactions.

• Significance: The LUMO is the first orbital that can accept electrons during reactions, making it crucial when the molecule acts as an electron acceptor (acts as an electrophile or Lewis acid). It also plays a role in determining how a molecule absorbs energy (e.g., in spectroscopy or photochemistry).

HOMO-LUMO Gap:

• The HOMO-LUMO gap (sometimes called the "band gap" in materials science) is the energy difference between the HOMO and LUMO. It represents the minimum energy required to excite an electron from the HOMO to the LUMO, which often correlates with the molecule’s ability to absorb photons (light) and participate in electronic transitions.

• Significance:

  • Reactivity: Molecules with a small HOMO-LUMO gap are generally more reactive because it is easier to excite electrons. Molecules with a large gap are more stable and less reactive.

  • Optical Properties: The size of the HOMO-LUMO gap determines the color of light a molecule can absorb. For example, molecules with smaller gaps absorb lower-energy (longer-wavelength) light, such as red or infrared.

  • Conductivity: In semiconductors and conductive materials, the HOMO-LUMO gap affects the material's ability to conduct electricity. A smaller gap often means better conductivity.

Example:

• Ethylene (C₂H₄): Ethylene has a moderate HOMO-LUMO gap, making it reactive in certain chemical processes like polymerization.

• Conjugated molecules: Molecules with extended conjugation (like in dyes or pigments) typically have smaller HOMO-LUMO gaps, allowing them to absorb visible light and appear colored.

Fermi Level:

• The Fermi level is a concept borrowed from solid-state physics but is sometimes used for molecules, particularly in relation to extended systems like large conjugated molecules or molecular solids. In molecules, it is a theoretical energy level that represents the energy at which the probability of an electron occupying an energy state is 50% at absolute zero temperature.

• Significance:

  • Fermi level can be thought of as the "average" energy level of electrons in a system, sitting between the HOMO and LUMO in a molecule or between the valence and conduction bands in a material.

  • It provides insight into how a molecule or material will interact with external electrons or holes (charge carriers).

  • In molecules, the Fermi level can indicate where electrons are likely to be found in relation to the HOMO and LUMO, and it is useful in molecular electronics, photovoltaics, and quantum chemistry.

Relationships Between HOMO, LUMO, HOMO-LUMO Gap, and Fermi Level:

• HOMO and Fermi level: In a neutral molecule, the Fermi level often lies close to the HOMO, as the highest occupied state plays a large role in the molecule’s electronic behavior.

• LUMO and Fermi level: If the molecule accepts electrons (becoming reduced), those electrons will first occupy the LUMO, and the Fermi level will move closer to the LUMO in this case.

• HOMO-LUMO gap: The gap between the HOMO and LUMO defines the energy required for electronic excitations, such as those that occur in photochemical reactions or when a molecule absorbs light.

Applications:

• Organic Electronics: In organic photovoltaic cells, the HOMO of the donor material and the LUMO of the acceptor material must align appropriately to facilitate charge transfer and efficient energy conversion.

• Chemical Reactivity: The HOMO and LUMO are often referred to as "frontier orbitals" in the context of chemical reactivity. The interaction between the HOMO of one molecule and the LUMO of another can help predict how two molecules will react.

• Spectroscopy: The energy of light absorbed by a molecule corresponds to the energy difference between the HOMO and LUMO, making this gap critical for interpreting UV-Vis absorption spectra.

Example:

• In ethylene (C₂H₄), the HOMO is the π-bonding orbital, and the LUMO is the π* (anti-bonding) orbital. The energy gap between these orbitals is what determines how ethylene absorbs light or undergoes certain chemical reactions, such as electrophilic addition.

• In conjugated systems, like in polyacetylene or conductive polymers, the HOMO-LUMO gap is much smaller, allowing these materials to absorb visible light and conduct electricity. In such materials, the Fermi level often lies close to the midpoint between the HOMO and LUMO.

Summary:

• HOMO: The highest energy occupied molecular orbital, from which electrons can be donated.

• LUMO: The lowest energy unoccupied molecular orbital, into which electrons can be accepted.

• HOMO-LUMO Gap: The energy difference between the HOMO and LUMO, determining a molecule's reactivity, optical properties, and conductivity.

• Fermi Level: The theoretical energy level at which the probability of finding an electron is 50%, important in extended systems and molecular electronics.

These concepts are central to understanding molecular electronic structure, reactivity, and behavior in various fields, including organic electronics, photochemistry, and catalysis.

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The HOMO, LUMO, HOMO-LUMO Gap, and Fermi Level are found in the Globalproperty table: