Calculator Input
Example Data Table
| Point | rho au | ∇²rho | λ1 | λ2 | λ3 | Likely reading |
|---|---|---|---|---|---|---|
| O-H bond point | 0.245 | -0.820 | -1.120 | -1.050 | 1.350 | Shared interaction |
| H···O contact | 0.028 | 0.105 | -0.050 | -0.030 | 0.185 | Closed-shell contact |
| Ring region | 0.006 | 0.018 | -0.015 | 0.012 | 0.021 | Ring critical point |
Formula Used
Density conversion: rho(e/ų) = rho(e/bohr³) × 6.748334.
Laplacian: ∇²rho = λ1 + λ2 + λ3.
Ellipticity: ε = λ1 / λ2 - 1, using the two negative curvatures.
Total energy density: H(r) = G(r) + V(r).
Energy ratio: ratio = |V(r)| / G(r).
Volume electron estimate: N ≈ rho(e/ų) × volume(ų).
How to Use This Calculator
Enter the electron density from your AIMS output. Choose the matching density unit. Add the gradient norm if available. A small gradient means the point is near a critical point. Add the Laplacian directly, or enter three Hessian eigenvalues. The tool can then calculate the Laplacian.
Enter kinetic and potential energy density when your analysis provides them. These values help separate shared and closed-shell interactions. Add a volume only when you want a rough electron count estimate. Press the submit button. The interpretation appears above the form and below the header.
Understanding Electron Density Numbers from AIMS Calculations
Purpose
Electron density is one of the most direct outputs from an electronic structure calculation. It tells where charge is concentrated in real space. AIMS results often give density values at grid points, nuclei, or selected critical points. Those numbers become useful when they are read with gradients, Hessian curvatures, and energy density terms.
Density Meaning
A high rho value means electrons are locally concentrated. In a bond region, that often points to stronger sharing between atoms. A low rho value can still be meaningful. Weak contacts, hydrogen bonds, dispersion regions, and ionic contacts may all show small but organized density.
Critical Point Checks
The gradient norm checks whether the selected position is stationary. A near zero gradient supports a true critical point. A larger gradient means the point may be shifted from the topological feature. The Hessian eigenvalues classify the local shape. Two negative values and one positive value identify a bond critical point. One negative value and two positive values identify a ring critical point. Three positive values identify a cage critical point.
Laplacian Reading
The Laplacian is the sum of the three Hessian eigenvalues. A negative Laplacian indicates charge concentration. This is common in shared covalent regions. A positive Laplacian indicates local charge depletion. This is common in closed-shell interactions, ionic contacts, and many hydrogen bonds.
Energy Terms
Kinetic energy density G and potential energy density V add another layer. Their sum is H. Negative H often supports shared character. Positive H often supports closed-shell character. The ratio |V| divided by G is also useful. Large ratios suggest stronger sharing. Smaller ratios suggest weaker closed-shell behavior.
Best Practice
Do not interpret one number alone. Compare related points from the same calculation settings. Use the same functional, basis, grid, and geometry criteria. Check bond path length and chemical context. Report units clearly. Treat the result as a structured guide, not as a replacement for full topological analysis.
FAQs
What is rho in an AIMS density result?
Rho is the electron density at a point. It shows how much electronic charge is concentrated in a small region of space.
Why is the gradient norm important?
A small gradient norm means the point is close to stationary. That supports a valid critical point interpretation.
What does a positive Laplacian mean?
A positive Laplacian suggests local charge depletion. It is often seen in closed-shell, ionic, hydrogen bond, or van der Waals contacts.
What does a negative Laplacian mean?
A negative Laplacian suggests local charge concentration. It often supports a shared interaction, especially near covalent bond regions.
How are critical points classified?
The calculator checks the signs of the three Hessian eigenvalues. Their signature identifies nuclear, bond, ring, or cage critical behavior.
What does ellipticity show?
Ellipticity measures uneven curvature around a bond path. Larger values may suggest directional pi character or bond instability.
Why use G and V energy densities?
G and V help separate interaction types. Their sum H and the ratio |V|/G support shared or closed-shell interpretation.
Can this replace full AIM analysis?
No. It is a guide for interpretation. Confirm conclusions with full topology, geometry, convergence checks, and chemical context.