Understanding HOMO and LUMO

HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) are fundamental concepts in molecular orbital theory. HOMO and LUMO are known as the "frontier molecular orbitals" because they are the highest occupied and lowest unoccupied molecular orbitals, respectively. These orbitals play a crucial role in determining the optical and electronic properties of molecules, such as their ability to absorb light, undergo chemical reactions, and conduct electricity. This information is essential for materials like the non-fullerene acceptor ITIC when determining their suitability for use in solar cells for harnessing the sun's energy.

Molecular Orbital Theory

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Orbitals are the space where the electrons are most likely to be found. Electrons in atoms inhabit atomic orbitals. The number of electrons in each atom determines the number of electrons within the whole molecule. Within a molecule the atomic orbitals combine to make up molecule orbitals. Molecular orbital diagrams show how each atom donates electrons from its atomic orbitals to form molecular orbitals.

This process of forming molecular orbitals occurs through the addition of atomic wavefunctions. Wavefunction is a quantum mechanical term that describes the probability of finding an electron. Wavefunctions can form bonding or antibonding orbitals respectively. When electrons inhabit the bonding orbital (HOMO), the energy of the molecule decreases, as the bonding orbital is lower in energy than the individual atomic orbitals, and is therefore favourable.

In molecular orbital theory, these electrons are not restricted to lone pairs or the specific bonds between the atoms. The electrons are delocalized throughout the whole molecule. The molecular orbitals encompass the entire molecule rather than the individual bonds. This provides a more accurate representation of the electronic structure of the molecule. As a result we can get a better understanding of their electronic and chemical properties.

Movement of Electrons in HOMO and LUMO Energy Levels

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An electron from the HOMO of a molecule can be promoted to the LUMO when exposed to light or heat. This forms a new HOMO and LUMO. The movement of electrons within molecules alters its chemical properties. The promotion of an electron results in the molecule being in its excited state. In the excited state, the molecule can undergo reactions that it otherwise would not be able to.

HOMO

• The HOMO is the highest energy orbital that is fully occupied by electrons in a molecule.
• It represents the highest energy molecular orbital from which an electron can be excited to a higher energy level, such as the LUMO.
• The energy of the HOMO is critical in determining the molecule's ability to donate electrons (i.e., its oxidation potential).

LUMO

• The LUMO is the lowest energy orbital that is not occupied by electrons.
• It represents the frontier molecular orbital that can accept an electron from the HOMO or another electron donor.
• The energy of the LUMO is important in determining the molecule's ability to accept electrons (i.e., its reduction potential).

Determining HOMO and LUMO Energy Levels

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Experimental Methods

Photoelectron Spectroscopy (PES)

The energies of ionized states can be directly determined using photoelectron spectroscopy techniques. UV photoelectron spectroscopy (UPS) is used to examine occupied levels, including the HOMO, while inverse photoelectron spectroscopy (IPES) is employed to study unoccupied levels, such as the LUMO.

UV-Vis Spectroscopy

The energy difference between the HOMO and LUMO can be estimated from the absorption spectrum of a molecule.

Electrochemical Methods

Cyclic voltammetry is generally preferred to be used to determine the oxidation and reduction potentials, which relate to the HOMO and LUMO energies. For example, spiro-OMeTAD which is a hole transport layer in perovskite solar cells show HOMO at -5.0 eV (calculated by cyclic voltammetry), LUMO = -2.05 eV (HOMO - E_g).

Computational Methods

Density Functional Theory (DFT)

DFT is a quantum mechanical method that is commonly used to calculate the electronic structure of molecules. It provides an approximation of HOMO and LUMO energies.

Molecular Orbital Calculations

These are performed using software packages like Gaussian, which solve the Schrödinger equation for molecules to give orbital energies.

Comparison to the Valence Band (VB) and Conduction Band (CB) in Semiconductors

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While HOMO and LUMO are concepts used in molecular systems, they have analogous counterparts in the context of solid-state semiconductors. Valence band consist of electrons bound tightly enough to atoms that they don’t move (much) from atom to atom. Conduction band consist of electrons that are not bound as strongly and can move about, thus allow electricity to be conducted. They are similar in function to the HOMO and LUMO in organic semiconductors.

HOMO vs. Valence Band

• The VB edge (VB maximum) is analogous to the HOMO. VB maximum is the highest energy level within the valence band that is occupied by electrons at absolute zero temperature. VB represents the highest energy band that is fully occupied by electrons in a semiconductor.
• Electrons in the VB can be excited to the conduction band, similar to electrons in the HOMO being excited to the LUMO.

LUMO vs. Conduction Band

• The CB edge (CB minimum) is analogous to the LUMO. CB minimum refers to the lowest energy level within the conduction band of a material. And CB is the lowest energy band that is typically unoccupied in a semiconductor at absolute zero temperature.
• Electrons can be promoted from the VB to the CB, allowing for electrical conduction.

HOMO-LUMO Energy Level Gap vs. Bandgap

• The band gap in semiconductors is the energy difference between the VB maximum and CB minimum, determining the electronic and optical properties of the material.
• The energy difference between the HOMO and LUMO is called the HOMO-LUMO gap and is generally the lowest energy electronic excitation that is possible in a molecule. The energy of the HOMO-LUMO gap can tell us about what wavelengths the compound can absorb. Or alternatively, measuring the wavelengths a compound absorbs via  experiments like UV-Vis spectroscopy can be used as a measure of the HOMO-LUMO gap.
• The HOMO-LUMO gap in molecules plays a similar role but is specific to the discrete energy levels of molecular orbitals rather than continuous energy bands.

Relevance in Organic Electronic Materials and Devices

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In the field of organic electronics, HOMO and LUMO energies are critical for understanding and designing materials for devices like organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic field-effect transistors (OFETs), perovskite photovoltaics, and perovskite LEDs. Their relevance includes:

Charge Transport

• The energy levels of the HOMO and LUMO dictate the ease with which charge carriers (electrons and holes) can be injected into the material and transported across it.
• An optimal HOMO-LUMO gap along with appropriate energy level alignment typically allows for better charge transport properties, which is crucial for efficient device performance.

Light Absorption and Emission

• In OPVs, the energy gap between the HOMO and LUMO determines the range of wavelengths the material can absorb, which affects the efficiency of light harvesting.
• In OLEDs, the recombination of electrons and holes within the material results in light emission, and the energy gap influences the color of the emitted light.
• It is possible to tune the bandgaps in organic materials by compositional engineering such that they have the optimum energy level gap and absorb incoming light efficiently.
• Proper alignment minimizes energy barriers, enhances charge extraction and injection, and ultimately improves the overall efficiency and performance of the devices.
• Appropriate energy level alignment can be achieved by various methods like compositional tuning, doping, tuning the work-function of the electrodes (in the case of active layer-electrode or charge transport layer-electrode junction), interface engineering by adding an interlayer which improves charge transport, and surface treatments by self assembled monolayers.

Outlook

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HOMO and LUMO are fundamental concepts for understanding the optoelectronic properties of organic molecules, especially in the context of organic electronic materials and devices. Their energies can be determined through various experimental and computational methods and are crucial in designing efficient materials for applications such as solar cells, LEDs, and transistors. Understanding the relationship between HOMO-LUMO and CB-VB helps bridge molecular and solid-state physics, providing a comprehensive framework for material design.

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