Integrate a PMF or compare endpoint states
Use a bulk-referenced profile. The integration mode includes coordinate geometry and a standard-state volume.
PMF integration with geometry and standard state
For a PMF referenced to a bulk level, this calculator estimates an effective solvation-region volume and compares it with the selected standard-state volume.
The endpoint method instead uses ΔG = Wsolv − Wbulk + ΔGcorrection. It is suitable only when your stated correction already matches the restraint, geometry, and standard-state convention.
Prepare the PMF before calculating
- Choose integrated PMF for a finite solvation region.
- Set temperature and the same energy unit used by your PMF.
- Paste ordered coordinate and PMF values into the data field.
- Set a bulk PMF reference, often zero after profile shifting.
- Define the solvation bounds and select matching coordinate geometry.
- Enter the area or cylinder length when that geometry requires it.
- Use 1 mol/L unless your protocol defines another standard state.
- Review the result, export CSV, or print the result as PDF.
Planar PMF example
A one square nanometer slab uses the default PMF. The region runs from 0.00 to 0.60 nm. The bulk PMF reference is zero.
| Coordinate (nm) | PMF (kJ/mol) | Interpretation |
|---|---|---|
| 0.00 | 0.00 | Bulk reference |
| 0.20 | -1.10 | Favorable approach |
| 0.30 | -1.65 | Local solvation minimum |
| 0.60 | 0.00 | Returned bulk reference |
From coordinate profiles to standard free energy
A potential of mean force describes relative free energy along a selected coordinate. It is not automatically an absolute solvation free energy. The coordinate may represent distance from an interface, radial separation, pore position, or another collective variable. A useful calculation begins by defining the physical solvation region. The region should include configurations considered solvated. It should exclude bulk configurations used as the reference state.
The integrated method converts the PMF into a Boltzmann-weighted effective volume. Low PMF values receive larger statistical weight. High PMF values contribute less. The calculator then compares that volume with a standard-state volume. This produces a standard free-energy estimate. A negative value indicates that the selected region is favored against the chosen bulk reference. A positive value indicates that the standard bulk reference is favored.
Geometry controls the measure used during integration. A planar coordinate needs a cross-sectional area. A cylindrical radial coordinate needs a cylinder length. A spherical radial coordinate uses the familiar four-pi-r-squared Jacobian. These factors are essential. Ignoring them changes the configuration volume and can change the free energy substantially. Use the coordinate definition from your simulation method. Do not apply a radial Jacobian to a PMF that already includes that transformation.
PMF values must share one energy unit. This page accepts kilojoules per mole or kilocalories per mole. Temperature sets RT and therefore changes Boltzmann weighting. The profile should be well converged. Adjacent umbrella windows should overlap. The unbiased PMF should become stable when sampling is extended. Inspect uncertainty estimates from WHAM, MBAR, or your chosen analysis workflow. This calculator reports a deterministic value from supplied inputs. It does not replace uncertainty propagation.
Set the bulk reference carefully. Many profiles are shifted so the distant bulk region equals zero. Enter that level in the bulk reference field. Then select integration bounds around the solvation basin. Test reasonable alternative bounds. A stable result strengthens confidence. Large changes can reveal inadequate sampling, ambiguous states, or an unsuitable coordinate. Record geometry, bounds, reference level, temperature, and standard concentration beside every reported free energy.
The endpoint option is simpler. It subtracts the bulk PMF from a selected solvation-state PMF. It can be appropriate for a clearly defined transfer coordinate. However, it does not automatically include configurational width, geometry, or restraint corrections. Add a correction only when it was derived for the same protocol. Integrated PMF calculations are generally more informative when a finite region defines the solvated state. Use both views as consistency checks, not interchangeable answers.
Use the result as a model-based thermodynamic quantity. It summarizes the sampled coordinate, not every microscopic solvent rearrangement. Compare values only when temperature, force field, solvent composition, coordinate definition, reference convention, and standard state are compatible. For interfaces or membranes, specify the direction of transfer and the bulk phase. Small numerical precision does not guarantee physical accuracy. Sampling quality and model limitations remain decisive during practical applications.
PMF solvation free energy FAQ
1. What does a negative solvation free energy mean?
It means the selected solvation region is thermodynamically favored against the stated bulk reference and standard-state convention. The conclusion depends on correct PMF zeroing, geometry, bounds, and corrections.
2. Which PMF reference should I enter?
Enter the PMF value representing the bulk reference state. This is often zero after shifting a flat, distant bulk segment. Use an averaged bulk level when that region has residual noise.
3. Why does this calculator need geometry?
A one-dimensional PMF hides coordinate-space volume. Planar, cylindrical, and spherical coordinates have different Jacobians. Geometry restores the appropriate volume element during Boltzmann-weighted integration.
4. Can I use a PMF from umbrella sampling?
Yes. First remove the bias with an accepted analysis method, such as WHAM or MBAR. Supply the unbiased, converged PMF and use coordinates consistent with its reported definition.
5. What are sensible integration limits?
Use bounds that isolate the physical solvation basin. Place them near clear state boundaries or barriers. Repeat the calculation with nearby defensible bounds to assess sensitivity.
6. What standard concentration should I use?
Use 1 mol/L for the conventional biochemical and chemical standard state unless your method specifies another convention. Record any nonstandard choice with the final result.
7. Does endpoint subtraction include entropy?
A PMF difference contains entropy projected onto its coordinate. Yet a single endpoint difference may omit configurational width, geometry, and restraint-volume effects needed for a standard-state quantity.
8. Can I mix nanometers and angstroms?
Yes, but select the matching coordinate unit. The calculator converts angstroms to nanometers before integration. Area and cylinder length inputs remain in nanometer-based units.
9. Why can a deeper PMF minimum give an unexpected result?
Free energy depends on both depth and accessible width. A narrow deep basin may contribute less than a wider shallow basin. Geometry can also change the effective volume strongly.
10. Does this calculate simulation uncertainty?
No. It evaluates the supplied profile deterministically. Obtain confidence intervals through replicate simulations, bootstrap PMF analysis, Bayesian methods, or uncertainty estimates provided by your PMF workflow.
11. Is this a replacement for alchemical solvation calculations?
No. It analyzes PMFs along defined coordinates. Alchemical approaches estimate related free energies through different thermodynamic paths. Choose the method matching your scientific question and sampling design.