Real-Space Wavefunction Analysis

Multiwfn

Analyze electron density and its derivatives with NCI, IGM, IGMH, and IRI to visualize spatial patterns associated with molecular interactions.

Role: Wavefunction and real-space analysis
Typical input: fchk, wfn/wfx, molden, cube, XYZ
Typical output: Grid data, cube, critical points

1. Scope

Multiwfn analyzes orbitals, density, electrostatic potential, topology, populations, and many real-space functions. This chapter focuses on interaction-region visualization.

Visualization is not an energy decomposition

The presence, area, or color of an isosurface does not directly provide an interaction energy.

2. Input files and the three-dimensional grid

Input	Information available
fchk, wfn/wfx, Molden	Wavefunction-derived density, orbitals, and derivatives
Cube	A precomputed scalar field on a fixed grid
XYZ	Geometry and promolecular approximations only

Choose a grid that contains the interaction region with adequate margin and spacing. Record density source, grid, fragments, cutoff, and Multiwfn version.

3. NCI and reduced density gradient

NCI analysis identifies low-density, low-gradient regions using the reduced density gradient.

s (r) = \frac{1}{2 {(3 π^{2})}^{1 / 3}} \frac{| \nabla ρ |}{ρ^{4 / 3}}

Surfaces are commonly colored by sign(lambda2)rho to distinguish attractive-like and repulsive-like regions qualitatively.

The sign of the second Hessian eigenvalue multiplied by density is used as a qualitative coloring variable. Negative, near-zero, and positive regions are often described as attractive-like, weak/dispersion-like, and repulsive-like, but these are not unique energy assignments.

4. IGM

The independent gradient model compares an upper-bound gradient constructed from independent atomic contributions with the actual molecular-density gradient. The difference highlights regions where gradients cancel.

Traditional IGM commonly uses promolecular atomic densities. The gradient difference reflects cancellation between independent and actual gradients; it is an indicator, not an interaction energy.

5. IGMH

IGMH uses the actual molecular density in an IGM-like framework and can separate interfragment and intrafragment contributions. Fragment definitions are therefore part of the analysis.

IGMH uses Hirshfeld-partitioned molecular density and can separate interfragment and intrafragment terms. Save the atom-to-fragment assignment because changing it changes the field.

6. IRI

The interaction region indicator is designed to reveal covalent and noncovalent interaction regions in a unified representation. Isovalue and color scale must be stated when comparing systems.

IRI can display covalent bonds and noncovalent regions in one framework. This broader visibility does not remove dependence on isovalue, density source, grid, or color range.

7. Choosing NCI, IGM, IGMH, or IRI

Use NCI for the established RDG and signed-density picture, IGM for fast promolecular screening, IGMH when molecular density and fragment-resolved analysis are important, and IRI when covalent and noncovalent regions should be viewed together. Method choice should follow the chemical question rather than the appearance of the surface.

8. Practical workflow

Load a wavefunction file and verify geometry.
Choose the real-space function and fragment definition.
Set grid range, spacing, and cutoff.
Export shape and coloring cubes.
Visualize with fixed settings across the series.
Relate patterns to independent energetic or experimental evidence.

Multiwfn molecule.fchk

Use fixed visualization settings

For comparative figures, keep geometry alignment, grid spacing, isovalue, color range, opacity, and camera orientation constant. Menu numbers can change between releases, so record the Multiwfn version and selected menu path.

9. Work with the published example data

Use the acetone and water-dimer files generated for this site to examine what Multiwfn can do with each input type. The properties that can be recalculated depend on whether wavefunction information remains in the file.

WavefunctionWFN

Re-evaluate density and derivatives from orbital and basis information, then run NCI or IGMH.

Scalar fieldCube

Inspect, process, and compare an already evaluated three-dimensional field as grid data.

Presentation3D viewer

Manipulate isosurfaces and colors. The viewer does not perform wavefunction analysis.

Published file	Task in Multiwfn	Interpretive limit
Acetone density cube	`Multiwfn acetone-density.cube` Inspect the grid and process the imported scalar field.	A cube does not retain the original basis and orbital coefficients, so it cannot support a new orbital analysis.
HOMO cube / LUMO cube	Compare signs, nodes, grid extent, and isosurfaces.	Orbital energies and occupations cannot be recovered from a cube alone.
Water-dimer WFN	`Multiwfn water-dimer.wfn` Select NCI or IGMH from visual analysis of weak interactions.	Record the density model, fragments, grid, and isovalue.
RDG cube / signed-density cube	Load the NCIplot outputs as grid data, confirm matching grids, and compare their visualization.	These are NCIplot results. Use the WFN file to rerun the analysis from wavefunction data.

Menu numbers depend on the version

In recent Multiwfn releases, main function 20 leads to wavefunction-based NCI and IGMH, while main function 13 processes imported grid data. Follow the displayed menu names and record the version and menu path used.

Cube format and numerical validation Calculated NCIplot example Visualization with py3Dmol

Calculation settings are stored in each directory's metadata.json. Before comparing a newly exported cube, check origin, axis vectors, shape, and units.

10. References

Last reviewed: August 4, 2026. Check the linked official documentation for syntax specific to the installed software version.