Calculator
Example Data Table
| Guest Total (M) | Host Total (M) | Observed Shift (ppm) |
|---|---|---|
| 0.0000 | 0.0010 | 7.120 |
| 0.0002 | 0.0010 | 7.248 |
| 0.0004 | 0.0010 | 7.365 |
| 0.0008 | 0.0010 | 7.552 |
| 0.0012 | 0.0010 | 7.675 |
| 0.0018 | 0.0010 | 7.793 |
| 0.0025 | 0.0010 | 7.870 |
Formula Used
This calculator fits a one-site 1:1 host–guest binding model. For each titration point, it solves the complex concentration using the quadratic mass-balance relation:
[HG] = (([H]t + [G]t + 1/Ka) - sqrt(([H]t + [G]t + 1/Ka)^2 - 4[H]t[G]t)) / 2
The predicted NMR shift is computed from the bound fraction of host:
δpred = δfree + (δbound - δfree) × ([HG]/[H]t)
The fit quality is evaluated by minimizing the sum of squared residuals (SSE) across all points. RMSE and R² are also reported.
How to Use This Calculator
- Enter the free-state and bound-state chemical shifts in ppm.
- Define the Ka search range and grid steps for fitting precision.
- Paste titration rows as: guest_total, host_total, observed_shift.
- Click Submit and Fit Data to calculate the best-fit Ka.
- Review the summary, residuals, and predicted values above the form.
- Use the export buttons to download CSV or a PDF report.
Baseline Data Quality and Signal Selection
Reliable NMR titration fitting begins with disciplined experimental setup. Track a resonance that stays separated from solvent and impurity signals during every addition. Keep temperature, solvent composition, and acquisition settings constant to prevent drift. Prepare stock solutions carefully and document concentration uncertainty. Include a host-only point and a near-saturation point to anchor the curve. Repeating selected additions improves confidence and helps detect pipetting or mixing mistakes early.
Model Inputs and Practical Parameter Ranges
This calculator fits a one-to-one host-guest model using total host concentration, total guest concentration, and observed chemical shift. Users enter free and bound limiting shifts, then define a Ka search window. A logarithmic range is best because binding strengths often span orders of magnitude. Start broad for unknown systems, then narrow after an initial run. Always keep concentration units consistent so Ka and Kd remain meaningful and comparable across experiments.
Fit Metrics and Interpretation of Output
The fitted output combines chemical interpretation with numerical diagnostics. Ka reports association strength, while Kd provides the inverse concentration-based perspective. SSE summarizes total squared residual error, and RMSE expresses average error in ppm for practical judgment. R squared offers a quick quality check, but it should not stand alone. Strong conclusions require realistic Ka values, low RMSE, adequate transition-region coverage, and residuals that remain small throughout the full titration.
Residual Analysis for Method Validation
Residual analysis is the most useful validation step after fitting. Residuals should scatter around zero without visible curvature or directional trend. Systematic patterns can indicate incorrect limiting shifts, concentration errors, peak overlap, or chemistry that departs from one-site behavior. Large isolated residuals commonly arise from pipetting mistakes, incomplete mixing, or peak misassignment. Review raw spectra when residuals look structured, then repeat questionable points and compare whether parameters stabilize.
Laboratory Reporting and Workflow Integration
In routine laboratory work, this calculator supports a repeatable reporting workflow. Analysts can paste titration rows, fit the model, inspect diagnostics, and export CSV or PDF outputs for notebooks and project meetings. The exported table preserves observed shifts, predicted shifts, residuals, and bound fractions for traceable review. For professional records, document sample identity, solvent, temperature, instrument frequency, and observed nucleus. Standardized formatting makes cross-compound comparison faster and clearer.
FAQs
1) What binding model does this calculator use?
It uses a one-site 1:1 host-guest binding model with quadratic mass balance. This suits fast-exchange systems where one host binds one guest molecule.
2) What concentration units should I enter?
Use any concentration unit if all host and guest values use the same unit. Molar concentrations are preferred for standard Ka reporting.
3) Why are my residuals not centered around zero?
That usually means input shifts are off, concentrations contain error, peak overlap is present, or the chemistry does not follow a one-site model.
4) How many titration points should I collect?
Collect at least six to eight points, including several near the curve transition. More points improve stability and make residual checks more trustworthy.
5) Can this calculator fit multi-site binding?
No. This version is built for one-site fitting only. Multi-site, cooperative, or competing equilibria require expanded equations and different fitting logic.
6) What Ka search range should I choose first?
Start broad, such as 10 to 106 M-1, then narrow the range after the first fit to refine precision and speed.