| Ligand type | Denticity | Rings | logβ | % Metal bound* |
|---|---|---|---|---|
| Monodentate analog | 1 | 0 | 5.0 | ~50–80 |
| Bidentate chelator | 2 | 1 | 7.5 | ~85–98 |
| Polydentate chelator | 4 | 2 | 12.0 | ~>99 |
Why chelation changes apparent stability
Chelation commonly increases complex stability because multiple donor atoms bind one metal ion in a single ligand framework. In screening workflows, a practical summary metric is Δlogβ_total, where positive values indicate a stronger complex than a chosen reference logβ. Typical literature formation constants for many 1:1 chelates fall between logβ ≈ 4 and logβ ≈ 20, depending on metal, ligand class, and medium overall.
How denticity and rings influence the estimator
The calculator models chelate advantage using two adjustable structure terms: (denticity−1)·entropy_bonus and rings·ring_bonus. With defaults (0.30 per extra donor, 0.10 per ring), a tetradentate ligand with two rings adds (4−1)·0.30 + 2·0.10 = 1.10 to the uplift term before comparing to the reference logβ. Use these parameters to align the estimator with your domain benchmarks.
Thermodynamics outputs you can compare
Stability constants map to free energy via ΔG° = −RT ln β. At 25 °C (298.15 K), each 1.0 increase in logβ changes ΔG° by about −5.71 kJ/mol (because ln(10)·RT/1000 ≈ 5.71). This makes ΔΔG° a convenient scale for ranking candidate ligands under the same temperature. If you shift temperature, ΔG° scales with T, so keep comparisons consistent. For quick checks, a 2‑logβ increase corresponds to roughly −11.4 kJ/mol at 25 °C.
Concentration-dependent binding fractions
Even large β values may not yield full binding if the ligand is limiting. The tool solves 1:1 mass balance to estimate [ML], percent metal bound, and remaining free concentrations. For example, at equal totals (1 mM metal and 1 mM ligand), increasing β_cond by 100× often pushes binding toward saturation. Adjust totals to match your assay or process conditions.
Ionic strength and charge corrections
When ionic strength is non‑negligible, activity coefficients can shift conditional stability. Using the Davies approximation (often applied up to about 0.5 M), the calculator estimates γ values from charges and ionic strength, then applies β_cond = β·(γ_ML/(γ_M·γ_L)). This helps you compare scenarios consistently such as dilute water (I ≈ 0.01) versus buffered media (I ≈ 0.10).
1) What does “Δlogβ_total” represent?
It combines a structural uplift term (denticity and rings) with the difference between your logβ and the chosen reference logβ. Positive values typically suggest stronger chelation versus the baseline.
2) Should I use overall logβ or stepwise logK values?
Use overall logβ when you have a reported stability constant. Use stepwise logK values when you have sequential association constants; the tool sums them to estimate overall logβ.
3) What is β_cond and why is it different from β?
β_cond is the activity-adjusted formation constant. It accounts for ionic strength and charge effects via activity coefficients, which can shift apparent binding in real solutions.
4) Why does percent bound change with concentrations?
Binding is limited by available ligand and metal totals. Even with strong β, if ligand is far below metal, the maximum complex concentration is capped by the limiting reagent.
5) Does this handle protonation or competing ligands?
No. The estimator uses a simplified 1:1 model without acid–base equilibria or competitors. For detailed speciation, use full equilibrium modeling with pKa values and competing ions.
6) How should I choose entropy_bonus and ring_bonus?
Start with defaults and calibrate using a small set of known complexes in your system. Adjust until predicted rankings align with measured logβ or binding outcomes.
- Overall logβ = Σ logKᵢ when stepwise values are provided.
- β = 10^(logβ) converts base‑10 stability to a formation constant.
- ΔG° = −RT ln β, with T in Kelvin and R = 8.314 J·mol⁻¹·K⁻¹.
- Activity correction (optional): Davies equation estimates γ, then β_cond = β · (γ_ML / (γ_M·γ_L)).
- 1:1 binding fraction solves analytically for [ML] using mass balance: x = ((Mt + Lt + 1/β_cond) − √((Mt+Lt+1/β_cond)² − 4MtLt))/2.
- Chelation advantage model: Δlogβ_total ≈ (denticity−1)·entropy_bonus + rings·ring_bonus + (logβ − logβ_ref).
- Enter an overall logβ, or choose stepwise logK values.
- Set denticity and ring count to reflect ligand structure.
- Provide total metal and ligand concentrations for binding fractions.
- Enable activity correction when ionic strength is significant.
- Press Submit to view results above the form instantly.