Electronic states in molecules involving charge separation, relevant for energy storage and optical properties.Charge transfer states are electronic configurations in molecules or materials where an electron has moved from one part of the system to another, creating a spatial separation of positive and negative charge. These states are crucial intermediates in many photophysical and photochemical processes, including photosynthesis, organic solar cells, and certain battery chemistries. They often have characteristic optical signatures, such as absorption or emission bands that differ from the ground state, and can be either 'bright' (optically active) or 'dark' (inaccessible by direct light absorption).
The concept of charge transfer states emerged in the mid-20th century with studies of organic donor-acceptor complexes. Robert Mulliken's work in the 1950s on charge-transfer complexes laid the theoretical foundation, and the concept was later extended to polymers and biological systems.
When a molecule absorbs light, an electron can be promoted to a higher energy level. If the molecule has donor and acceptor moieties, the excited electron may transfer from the donor to the acceptor, forming a charge-separated state. This state has a dipole moment and can be stabilized by the surrounding environment. In materials, charge transfer states can be delocalized or localized, and their dynamics—formation, migration, and recombination—determine the efficiency of processes like charge separation in solar cells or energy storage in batteries.
Central to the operation of organic photovoltaics and light-emitting diodes, where charge transfer states mediate the conversion between light and electrical energy. Also relevant in designing new battery materials with high energy density.
In some molecules, charge transfer states can be 'dark'—they do not absorb light directly—but they can still be populated via intersystem crossing from bright states, making them important but tricky to study.
| J | variable | joint density of states — density of states per joule per cubic metre |
| E | variable | photon energy — energy joule |
| E_c | variable | conduction band energy — energy joule |
| E_v | variable | valence band energy — energy joule |
| \mathbf{k} | variable | crystal momentum — wave vector per metre |
| \int_{\text{BZ}} d^3 | operator | integration over the first Brillouin zone — integral over brillouin zone |
| \delta | operator | selects states satisfying energy conservation — dirac delta function |
| L_stop | variable | stopping distance — length metre |
| m | variable | mass of particle — mass kilogram |
| v | variable | speed of particle — velocity metre per second |
| ρ | variable | density of medium — mass density kilogram per cubic metre |
| \Delta Q | variable | Accumulated charge change in the superconductor — electric charge coulomb |
| \Delta \Phi | variable | Change in magnetic flux through the superconducting loop — magnetic flux weber |
| \nu | variable | Filling factor (integer or fractional) of the quantum Hall state — dimensionless |
| e | constant | Magnitude of the electric charge of a single electron or proton — elementary charge = 1.602176634e-19 coulomb |
| \Phi_0 | constant | Superconducting flux quantum, h/(2e), the fundamental unit of magnetic flux in a superconductor — magnetic flux quantum = 2.067833848e-15 weber |
| J | variable | photolysis rate constant — rate constant per second |
| \sigma(\lambda) | variable | absorption cross-section as function of wavelength — cross section square metre |
| \phi(\lambda) | variable | quantum yield as function of wavelength — quantum yield |
| F(\lambda) | variable | actinic flux as function of wavelength — photon flux per square metre per second per metre |
| \lambda | variable | wavelength — wavelength metre |
| \int | operator | integration over wavelength — integral |
| E | variable | Kinetic energy of the charged particle — energy joule |
| x | variable | Path length in the material — length metre |
| \rho | variable | Density of the absorbing material — density kilogram per cubic metre |
| z | variable | Charge number of the incident particle — charge number |
| A | variable | Atomic mass number of the absorber — atomic mass number |
| \beta | variable | Speed of the particle relative to the speed of light — velocity ratio |
| \gamma | variable | Lorentz factor of the particle — lorentz factor |
| v | variable | Speed of the particle — velocity metre per second |
| W_{\text{max}} | variable | Maximum energy transfer in a single collision — energy joule |
| I | variable | Mean excitation potential of the absorber — energy joule |
| \delta | variable | Density correction factor — density correction |
| C | variable | Shell correction factor — shell correction |
| Z | variable | Atomic number of the absorber — atomic number |
| N_A | constant | Number of constituent particles per mole — avogadro constant = 6.02214076e23 per mole |
| r_e | constant | Radius of a classical electron — classical electron radius = 2.8179403262e-15 metre |
| m_e | constant | Rest mass of the electron — electron mass = 9.1093837015e-31 kilogram |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| -\frac{d}{dx} | operator | Negative derivative with respect to path length — negative derivative |
| \ln | operator | Natural logarithm — natural logarithm |















