Computational Chemistry Utility

Marcus and MLJ Rate Calculator

Calculate classical Marcus electron-transfer rates and one-effective-mode Marcus–Levich–Jortner rates using energies in electronvolts, vibrational frequencies in cm−1, and temperature in kelvin.

Calculation Inputs

The common inputs are sufficient for the classical Marcus rate. Add the effective vibrational-mode parameters to calculate the MLJ rate using the same electronic and thermodynamic inputs.

Common inputs

Required for both classical Marcus and MLJ calculations.

eV
May be positive or negative.
eV
Must be greater than zero.
eV
Enter the coupling magnitude in eV.
K
Must be greater than zero.

One-effective-mode MLJ inputs Optional

Supply these parameters to calculate the MLJ rate and vibrational-channel contributions.

—
Dimensionless and greater than or equal to zero.
cm⁻¹
Used to calculate ℏω and λin.
states
An integer between 0 and 500.

Calculation Results

Rates are reported in s−1. Logarithmic values are also shown because electron-transfer rates may be extremely small.

Classical Marcus rate

—

—

One-effective-mode MLJ rate

Not calculated

Supply the optional MLJ inputs.

MLJ relative to Marcus

—

MLJ inputs have not yet been supplied.

Marcus exponential term

—

Value of −(ΔG + λ)2 / (4λkBT).

Equations and constants used

Classical Marcus rate

k = (2π/ℏ)|Hab|² [1/√(4πλkBT)] exp[−(ΔG + λ)²/(4λkBT)]

One-effective-mode Marcus–Levich–Jortner rate

k = (2π/ℏ)|Hab|² [1/√(4πλskBT)] Σv [e−SSv/v!] exp[−(ΔG + λs + vℏω)² / (4λskBT)]
λin = Seffℏωeff     λs = λtotal − λin

kB = 8.617333262145 × 10−5 eV K−1

ℏ = 6.582119569 × 10−16 eV s

1 cm−1 = 1/8065.54429 eV

Disclaimer: This calculator is provided for general academic, educational, and research purposes only. The calculations are provided without warranty of any kind. Users are responsible for verifying the input parameters, assumptions, equations, units, and resulting values before using them in research, publications, decision-making, or other applications.

The author accepts no responsibility for errors, omissions, decisions, financial loss, legal consequences, research outcomes, or other losses or damages arising from the use or interpretation of results generated by this calculator.

Academic use: If this calculator or the associated methodology contributes to published work, please cite the following work:

ChemRxiv preprint — DOI: 10.26434/chemrxiv.15004265/v2