Inputs
Choose a unit system. Enter either direct volumes, or estimate from geometry. For diameters/lengths, use Å.
Example data table
Sample scenarios using the default packing target (0.55) and a typical good-fit window (0.45–0.65).
| Scenario | Host volume | Guest volume | Flex factor | PC | Interpretation |
|---|---|---|---|---|---|
| Loose inclusion | 800 | 280 | 1.00 | 0.350 | Too small; weak dispersion contact. |
| Near optimal | 800 | 410 | 1.00 | 0.513 | Good fit; close to target packing. |
| Good with flexibility | 800 | 380 | 1.10 | 0.523 | Good fit; effective volume increases. |
| Tight binding | 800 | 560 | 1.00 | 0.700 | Tight; may strain host or guest. |
| Excluded | 800 | 720 | 1.00 | 0.900 | Too large; inclusion unlikely. |
Values shown are illustrative. Use experimental or computed cavity volumes where possible.
Formula used
- Packing coefficient (PC) = (Guest Volume × Flexibility Factor) ÷ Host Cavity Volume.
- Target packing defaults to 0.55, a common supramolecular guideline.
- Sphere volume: V = (π/6) d³. Cylinder volume: V = π (d/2)² L.
- Equivalent spherical diameter: d = (6V/π)^(1/3), used for intuitive sizing.
The calculator reports “good fit” when PC lies within your chosen window.
How to use this calculator
- Select a unit system, then keep inputs consistent.
- Enter host cavity size as volume or geometry.
- Enter guest size as volume or geometry.
- Adjust flexibility if the guest is compressible.
- Click Calculate to view fit, range, and score.
- Export results using the CSV or PDF buttons.
Article
Packing coefficient as a sizing metric
The packing coefficient (PC) compares the guest’s effective molecular volume to the host cavity volume. In supramolecular chemistry, PCs near 0.55 often correlate with strong dispersion contact without excessive steric strain. Values below about 0.45 can indicate poor surface contact and weak binding, while values above about 0.65 may signal crowding, distortion, or exclusion. Because PC is dimensionless, it lets you compare different host families on a common scale, including cyclodextrins, cucurbiturils, calixarenes, and metal-organic cages, provided the same volume definition is used across solvents and temperature ranges.
Building cavity volume estimates
Reliable cavity volume is the foundation of any fit calculation. When crystallographic or computational volumes are unavailable, geometry offers a fast approximation. A spherical cavity uses V = (π/6)d³, and a cylindrical pocket uses V = π(d/2)²L. The calculator also supports direct volume input so you can use tabulated host cavities, solvent-corrected values, or simulation outputs.
Accounting for flexibility and solvation
Guests rarely behave as perfectly rigid solids. Conformational motion, solvation shells, and substituent rotation can increase the effective occupied volume inside a cavity. The flexibility factor scales the guest volume to reflect these effects, allowing quick sensitivity checks. Use 1.00 for rigid guests, slightly below 1.00 for compressible species, and above 1.00 when bulky substituents persistently occupy space.
Interpreting score and fit window
The fit score quantifies how close PC is to your chosen target. A score near 100 indicates the guest’s effective size aligns closely with the target packing, while lower scores reflect underfilling or crowding. The good-fit window defines an acceptable PC range for your host family. Adjust it when comparing different hosts, solvents, or binding modes, and use the classification labels as a rapid triage cue.
Using outputs for screening and design
Use the recommended guest volume range to screen candidate ligands before synthesis or docking. The spherical diameter equivalents provide an intuitive “size” for communication across teams, even when true shapes are anisotropic. Combine these outputs with experimental trends such as association constants, enthalpy, and selectivity to refine thresholds. For lead optimization, small substituent changes that shift PC toward the target often improve occupancy and binding reliability.
FAQs
What does a packing coefficient of 0.55 mean?
It means the guest’s effective volume occupies about 55% of the cavity. This level often balances close contact and manageable strain, supporting stronger inclusion when other interactions, like hydrogen bonding or ion pairing, are also favorable.
Can I use computed molecular volumes from software?
Yes. Enter the cavity and guest volumes directly, but keep the same volume convention for both. If your software reports solvent-excluded volumes, use that consistently, and treat the flexibility factor as a calibration knob.
Why does the calculator offer sphere and cylinder options?
Many cavities approximate a rounded pocket or a tunnel-like channel. Sphere and cylinder formulas provide quick estimates from measurable dimensions, useful for early screening before you have crystallography or detailed simulations.
How should I choose the flexibility factor?
Start at 1.00. Reduce slightly for compact, rigid guests, and increase for guests with mobile substituents, rotatable bonds, or persistent solvation. If you have binding data, adjust the factor until known good guests fall in your preferred window.
What if my guest is not spherical?
Use volume-based input whenever possible, because PC depends on volume, not shape alone. Then use the diameter equivalents only as a communication aid. For highly anisotropic guests, also review steric clashes and entry pathways.
Does a good fit guarantee strong binding?
No. Size matching is necessary but not sufficient. Electrostatics, desolvation penalties, entropy, and specific interactions can dominate. Use the fit results to prioritize candidates, then confirm with experiments or higher-level modeling.