# Frontier orbital

In this energy level scheme , each circle represents an electron that occupies an orbital. When light of a suitable wavelength hits the molecule, it is absorbed and an electron is transferred from the HOMO to the LUMO with spin inversion.
3D model of the highest occupied molecular orbital of  CO 2
3D model of the lowest unoccupied molecular orbital of CO 2

In the context of molecular orbital theory, the highest occupied and the lowest unoccupied molecular orbital together are referred to as frontier orbitals . By means of the frontier orbital theory, various concepts of chemistry, e.g. B. understand the reactivity of molecules qualitatively. The Nobel laureate in chemistry, Kenichi Fukui, is considered to be the founder of the frontier orbital theory .

## HOMO

H ighest O ccupied M olecular O rbital (HOMO, engl.) Denotes the highest occupied molecular orbital of a molecule.

Different molecular orbitals are available in a molecule and are occupied by the electrons present . These orbitals have different orbital energies. They are filled as the energy level increases . The HOMO is the most energetic occupied orbital.

Of importance, the energy difference between the HOMO and the LUMO is ( L owest U noccupied M olecular O rbital ). The amount of this energy difference determines approximately how easily the electrons reach the excited state .

In organic solar cells , by combining different materials with different energy differences between HOMO and LUMO ( heterojunction ), the states excited by the incident light ( excitons ) can be better split. Such a split is necessary in order to be able to obtain free charge carriers and thus electricity from the solar cells.

## LUMO

L owest U noccupied M olecular O rbital (LUMO) referred to in English, the lowest unoccupied molecular orbital of a molecule.

The energetic level of the LUMO is also used as a measure of electrophilicity .

4. The difference between the frontier orbital energies represents a rough approximation for the excitation energy . If, for example, the excitation energy is approached in the formalism of Configuration Interaction (e.g. CIS), one can see that the orbital energy differences play an important role. However, this approximation neglects the changed electron-electron interactions (due to the excitation):${\ displaystyle \ omega _ {CIS} = \ sum _ {ia} (c_ {i} ^ {a}) (\ epsilon _ {a} - \ epsilon _ {i}) + \ sum _ {ia, jb} c_ {i} ^ {a} c_ {j} ^ {b} (ia || jb)}$