phenomenon

charge transfer states

Electronic states in molecules involving charge separation, relevant for energy storage and optical properties.
27 related articles · 5 formulas

Description

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).

History

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.

How it works

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.

In practice

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.

Fun fact

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.

Concept graph →

Formulas

$$J(E) = \frac{2}{(2\pi)^3} \int_{\text{BZ}} d^3k \, \delta(E_c(\mathbf{k}) - E_v(\mathbf{k}) - E)$$
Number of electronic transitions per energy interval.
What is in the formula
Jvariablejoint density of states — density of states per joule per cubic metre
Evariablephoton energy — energy joule
E_cvariableconduction band energy — energy joule
E_vvariablevalence band energy — energy joule
\mathbf{k}variablecrystal momentum — wave vector per metre
\int_{\text{BZ}} d^3operatorintegration over the first Brillouin zone — integral over brillouin zone
\deltaoperatorselects states satisfying energy conservation — dirac delta function
g_{cv}(e)=\frac{ω}{(2π)^3}\sum_{cv}\int_{{bz}}d^3kδ(\varepsilon_{c{k}}-\varepsilon_{v{k}}-e) · 2607.08941
$$L_{\mathrm{stop}} \propto \frac{m v^2}{\rho}$$
Distance a charged particle travels before stopping due to energy loss.
What is in the formula
L_stopvariablestopping distance — length metre
mvariablemass of particle — mass kilogram
vvariablespeed of particle — velocity metre per second
ρvariabledensity of medium — mass density kilogram per cubic metre
l_{{stop}}\approx0{,}1{мм}(\frac{v_i}{10^{-3}})(\frac{m_x}{1{тэв}})(\frac{ρ_{{matter}}}{2{,}5{г/см}^3})^{-1} · 2607.09845
$$\Delta Q = \nu \frac{e \Delta \Phi}{\Phi_0}$$
Charge quantization in superconductors relates flux change to accumulated charge.
What is in the formula
\Delta QvariableAccumulated charge change in the superconductor — electric charge coulomb
\Delta \PhivariableChange in magnetic flux through the superconducting loop — magnetic flux weber
\nuvariableFilling factor (integer or fractional) of the quantum Hall state — dimensionless
econstantMagnitude of the electric charge of a single electron or proton — elementary charge = 1.602176634e-19 coulomb
\Phi_0constantSuperconducting flux quantum, h/(2e), the fundamental unit of magnetic flux in a superconductor — magnetic flux quantum = 2.067833848e-15 weber
δq_{\rma}/e=ν(δ\phi/\phi_0) · 2603.05341
$$J = \int \sigma(\lambda) \phi(\lambda) F(\lambda) d\lambda$$
Rate constant integrates cross-section, quantum yield, and flux.
What is in the formula
Jvariablephotolysis rate constant — rate constant per second
\sigma(\lambda)variableabsorption cross-section as function of wavelength — cross section square metre
\phi(\lambda)variablequantum yield as function of wavelength — quantum yield
F(\lambda)variableactinic flux as function of wavelength — photon flux per square metre per second per metre
\lambdavariablewavelength — wavelength metre
\intoperatorintegration over wavelength — integral
j=\intσ(λ)φ(λ)f(λ)dλ · 2607.15204
$$-\frac{dE}{dx} = \frac{4\pi N_A r_e^2 m_e c^2 \rho z^2}{A \beta^2} \left[ \ln\left(\frac{2m_e \gamma^2 v^2 W_{\text{max}}}{I^2}\right) - 2\beta^2 - \delta - 2\frac{C}{Z} \right]$$
Energy loss of charged particles due to ionization in matter.
What is in the formula
EvariableKinetic energy of the charged particle — energy joule
xvariablePath length in the material — length metre
\rhovariableDensity of the absorbing material — density kilogram per cubic metre
zvariableCharge number of the incident particle — charge number
AvariableAtomic mass number of the absorber — atomic mass number
\betavariableSpeed of the particle relative to the speed of light — velocity ratio
\gammavariableLorentz factor of the particle — lorentz factor
vvariableSpeed of the particle — velocity metre per second
W_{\text{max}}variableMaximum energy transfer in a single collision — energy joule
IvariableMean excitation potential of the absorber — energy joule
\deltavariableDensity correction factor — density correction
CvariableShell correction factor — shell correction
ZvariableAtomic number of the absorber — atomic number
N_AconstantNumber of constituent particles per mole — avogadro constant = 6.02214076e23 per mole
r_econstantRadius of a classical electron — classical electron radius = 2.8179403262e-15 metre
m_econstantRest mass of the electron — electron mass = 9.1093837015e-31 kilogram
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
-\frac{d}{dx}operatorNegative derivative with respect to path length — negative derivative
\lnoperatorNatural logarithm — natural logarithm
-\langle\frac{de}{dx}\rangle=2πn_ar_e^2c^2ρ\frac{z}{a}\frac{z^2}{β^2}[\ln(\frac{2m_eγ^2v^2w_{\max}}{i^2})-2β^2-δ-2\frac{c}{z}] · 2607.27531v1

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