# Jablonski Diagram & FRET

Interactive Jablonski diagram and Förster resonance energy transfer (FRET) — watch how a molecule absorbs, fluoresces, phosphoresces, and transfers energy to a nearby acceptor, and how FRET efficiency falls off as the sixth power of distance.

> Canonical page: https://elysiatools.com/en/visualizations/jablonski-fret

- **Category:** Chemistry

## Overview

Interactive Jablonski diagram and Förster resonance energy transfer (FRET) — distinct from the existing spectrophotometry (an instrument-principle / Beer-Lambert case, not molecular photophysics) and all 41 chemistry cases, none of which cover photochemistry or photophysical kinetics. This is the only case covering the molecular fate of an absorbed photon and the dipole-dipole energy-transfer mechanism used as a molecular ruler. The model implements the complete Jablonski kinetics: first-order rate constants for fluorescence k_F (~1e8 s⁻¹), internal conversion k_IC, intersystem crossing k_ISC (S₁→T₁ spin flip), and phosphorescence k_P (~1-100 s⁻¹), from which the donor lifetime τ_D = 1/(k_F+k_IC+k_ISC) and the fluorescence quantum yield Φ_F = k_F/(k_F+k_IC+k_ISC) follow exactly. The FRET transfer rate k_T = (1/τ_D)(R₀/r)⁶ gives the efficiency E = 1/(1+(r/R₀)⁶), with the Förster radius R₀ = 0.02108·(κ²·n⁻⁴·Q_D·J)^(1/6) nm bundling the dipole-orientation factor κ² (0–4, 2/3 for dynamic averaging), the refractive index n, the donor quantum yield Q_D, and the spectral-overlap integral J = ∫F_D(λ)·ε_A(λ)·λ⁴dλ (computed by trapezoidal integration over a 1-nm grid of Gaussian donor-emission and acceptor-absorption peaks). The donor emission and acceptor absorption are modeled as normalized/peaked Gaussians with adjustable peak wavelengths, FWHM, and ε_max, so J, R₀, and E all respond live to spectral mismatch. Four visualization panels: (1) A wide Jablonski diagram with the donor (left) and acceptor (right) drawn side by side, each showing the S₀/S₁/S₂/T₁ energy levels as horizontal lines with animated arrows — absorption (blue, flowing dash), vibrational relaxation/internal conversion (gray wavy), fluorescence (green, weight ∝ donor QY quenched by FRET), intersystem crossing (gray dashed), phosphorescence (orange, slow pulse), and a horizontal magenta FRET arrow between D-S₁ and A-S₁ whose thickness/glow/flow-speed scale with E; the two molecules' horizontal separation widens with r and are draggable to change r. (2) Spectral-overlap plot of donor emission (green) and acceptor absorption (orange) with the overlap region shaded magenta and the live J value. (3) FRET-efficiency-vs-distance curve E = 1/(1+(r/R₀)⁶) over r/R₀ = 0.2–4 with the R₀ (E=0.5) reference and a pulsing current-point marker with drop-lines. (4) Emission-vs-distance plot showing the quenched donor fluorescence (green, falling) and the sensitized acceptor emission (orange, rising) crossing over at r = R₀ — the readout of a FRET distance sensor. Adjustable parameters: D–A distance r (0.5–15 nm, draggable in the diagram), donor emission peak (420–650 nm), acceptor absorption peak (420–720 nm), acceptor ε_max (1000–300000 M⁻¹cm⁻¹), orientation factor κ² (0–4), refractive index n (1.2–1.7), and ISC rate k_ISC on a log₁₀ slider (controlling the phosphorescence branch). Five real FRET-pair presets: CFP–YFP (R₀≈4.6 nm), FITC–Rhodamine (R₀≈5.5 nm), Alexa 488/555 (R₀≈7 nm), Cy3–Cy5 (R₀≈5.4 nm), and Trp–Dansyl (R₀≈2.1 nm). Real-time diagnostics: Förster radius R₀, FRET efficiency E, r/R₀ ratio, overlap integral J, transfer rate k_T, donor lifetime τ_D, donor quantum yield Φ_D, and the quenching fraction. Educational content covers the Jablonski diagram and Kasha's rule, rate constants and quantum yields, the Förster 1/r⁶ transfer and its derivation, the R₀ formula and its four ingredients, the spectral-overlap integral and the λ⁴ weighting, and applications to the molecular ruler (1–10 nm distance sensing), live-cell FRET microscopy (protein-protein interactions), PCR/sequencing probes (TaqMan, molecular beacons), and OLEDs/solar cells (exciton energy transfer). Multi-language support (zh, en, es, fr, de, ru, pt).

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