01
Preferred distance
RDF shows how likely one particle is to occur at distance r from another particle.
Computational Analyses · Basic to Advanced | AMRA-LAB
Radial Distribution Function Explained Clearly
What RDF measures, why peaks matter, how molecular shells are identified, how coordination numbers are obtained, and how to interpret solvent, ion, ligand, membrane, and biomolecular organization after molecular dynamics simulations.
02
Solvation shells
Peaks and minima reveal first, second, and later coordination shells.
03
Local structure
RDF describes molecular organization, not simply whether two atoms touched once.
1. What is RDF?
RDF stands for Radial Distribution Function. It measures how particle density changes with distance from a selected reference particle or group.
Simple definition
RDF answers: “At what distances is particle B most likely to be found around particle A?” The result is plotted as g(r) against distance r.
- g(r) = 0: particles are absent at that distance.
- g(r) ≈ 1: local density is similar to bulk density.
- g(r) > 1: particles are enriched at that distance.
- A sharp peak: strong preferred separation or structured shell.
বাংলায় সহজ করে: RDF দেখায় একটি atom বা molecule-এর চারপাশে অন্য atom বা molecule কোন দূরত্বে সবচেয়ে বেশি পাওয়া যায়।
2. Why is RDF important?
Solvation structure
Identifies water or solvent shells around proteins, ions, ligands, membranes, or functional groups.
বাংলা: Solvent shell বোঝায়।
Preferred interactions
Shows whether atoms or groups prefer particular separation distances.
বাংলা: কোন distance-এ interaction বেশি হয় তা দেখায়।
Coordination environment
Helps estimate how many neighbors surround a reference particle within a defined shell.
বাংলা: চারপাশে কতটি neighbor আছে তা বোঝায়।
3. How is RDF calculated?
Select reference and target groups
Choose atom/group A as reference and atom/group B as target.
Measure pair distances
For each frame, calculate distances from every reference particle to target particles under periodic boundary conditions.
Bin distances into spherical shells
Distances are placed into small radial bins of thickness Δr.
Normalize by shell volume and bulk density
The observed counts are divided by the expected number in an ideal uniform distribution.
Average over trajectory frames
The final g(r) curve is the time-averaged radial distribution.
Important: RDF depends strongly on atom selection, bin width, trajectory length, box size, and whether the system is homogeneous.
4. Animated RDF intuition
Pair-distance shell model
Change preferred distance and shell sharpness.
0.30 nmFirst peak position
2.4Peak height g(r)
4.8Coordination number
বাংলা: Peak position দেখায় preferred distance, peak height দেখায় local enrichment, আর first minimum পর্যন্ত integration করলে coordination number পাওয়া যায়।
Live publication-style g(r) plot
Interpretation: First peak = first shell; first minimum = shell boundary; second peak = second shell. At long distance, g(r) often approaches 1 in homogeneous bulk systems.
5. How should RDF peaks be interpreted?
Peak position
The x-axis position of a peak gives the preferred separation distance between the selected groups.
বাংলা: Peak কোথায় আছে সেটি preferred distance।
Peak height
A taller peak indicates stronger local enrichment or more ordered packing, but not necessarily stronger binding energy.
বাংলা: বড় peak মানে ওই distance-এ particle বেশি পাওয়া যায়।
Peak width
A narrow peak suggests a well-defined distance; a broad peak indicates a wider distribution and greater structural variability.
First minimum
The first minimum after the first peak is commonly used as the outer boundary of the first coordination shell.
Long-range behavior
For a homogeneous bulk liquid, g(r) tends toward 1 at large r. In confined or heterogeneous systems this may not occur cleanly.
6. Coordination number from RDF
Core equation
N(r) = 4πρ ∫₀ʳ g(r′)r′²dr′
The coordination number counts the average number of target particles around a reference particle up to distance r. Usually, r is chosen at the first minimum after the first RDF peak.
বাংলায় সহজ করে: First shell-এর ভিতরে গড়ে কতটি atom বা molecule আছে সেটাই coordination number।
Do not integrate blindly: The cutoff should be justified from the first minimum or another physically meaningful shell boundary.
7. Where is RDF useful?
Common applications
- Water oxygen around ions or charged residues.
- Solvent around ligand functional groups.
- Ion pairing and salt organization.
- Lipid headgroup and membrane-water organization.
- Protein–ligand atom-pair preferences.
- Polymer, solvent, and nanoparticle structure.
When RDF is not enough
- It does not directly provide binding free energy.
- It averages over orientation and time.
- It may hide multiple states with similar distances.
- It does not show angular geometry.
- It may be difficult to interpret in strongly heterogeneous systems.
8. Common mistakes
Calling the highest peak the strongest interaction
Peak height indicates local probability enrichment, not directly interaction energy.
Comparing different atom selections
RDFs from different atom groups answer different structural questions and should not be compared casually.
Ignoring PBC and box size
Maximum reliable r is limited by the simulation box. Poor PBC handling can distort pair distances.
Using too coarse or too fine bins
Very coarse bins hide structure; very fine bins create noisy curves.
Assuming g(r) must approach 1
That expectation is valid mainly for homogeneous bulk systems. Membranes, interfaces, pores, and finite clusters can behave differently.
9. RDF analysis in GROMACS
Example commands
gmx rdf -s md.tpr -f md.xtc -n index.ndx -o rdf.xvg -cn coordination.xvg
Choose the reference group and target group carefully. Custom groups can be prepared using gmx make_ndx or gmx select.
gmx rdf -s md.tpr -f md.xtc -ref 'group REF' -sel 'group TARGET' -bin 0.002 -rmax 1.5 -o rdf_ref_target.xvg -cn cn_ref_target.xvg
বাংলা: Reference আর target group ঠিকভাবে নির্বাচন করা RDF analysis-এর সবচেয়ে গুরুত্বপূর্ণ ধাপ।
10. What should be reported?
Reference and target atom/group definitions.
Trajectory time range and frame interval.
Bin width and maximum distance.
Temperature and simulation environment.
Whether coordination number was calculated.
Cutoff used for the first shell.
PBC treatment and box-size limitation.
Replicate handling and uncertainty.
Final interpretation rule
RDF describes how particle density changes with radial distance around a reference. Peaks reveal preferred separations and shells, while integration provides coordination numbers. RDF should be combined with structural visualization, contact analysis, hydrogen bonds, orientation metrics, and energetic analyses.
বাংলায় মূল কথা: RDF distance-based local organization বোঝায়; এটি interaction energy বা binding affinity-এর সরাসরি measure নয়।