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Wavefunction Analysis & Visualization

Learn how to analyze and visualize molecular electronic structure using wavefunction data from SCF calculations.

Overview​

After running an SCF calculation, you have a wavefunction file (.owf.json) - containing the complete electronic structure using the specified method and atomic orbital basis. There's pretty much no end to the information we can extract from a wavefunction file, but some popular options are:

  • Computing the electron density (or visualising MOs) i.e. cube files or isosurfaces
  • Computing the electrostatic potential at some set of points
  • Poppulation analysis (e.g. Hirshfeld, or Distributed Multipole Analysis)

Input Molecule​

Let's continue with the molecule(s) from the previous tutorial. Make sure you have the input file:

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Generate the Wavefunction​

First, run the SCF calculation if you don't already have one in local storage for the page:

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Electron Density Visualization​

Cube files store 3D volumetric data (electron density, electrostatic potential, etc.) on a regular grid (as always, Paul Bourke has a nice page on the format if you're curious). Let's start by computing and visualising the electron density (density keyword):

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Parameters:

  • density - Property to calculate (electron density ρ(r))
  • -n 50 - Grid resolution: 50×50×50 points (good default)
  • -o density.cube - Output filename

The cube file should automatically appear as a blue isosurface overlaid on the molecule in the viewer above. Use the slider to adjust the isovalue and explore different density contours!

tip

Cube files are quite space inefficient (using ASCII/plain text to store floating point numbers always is) but they're widely supported, so they've got that going for them!

Available Properties​

You can calculate various 3D properties. Click the command above to edit and try: Common properties:

  • density - Total electron density ρ(r)
  • esp - Electrostatic potential V(r)
  • grad_rho - Gradient of density ∇ρ(r)
  • laplacian_rho - Laplacian ∇²ρ(r)

Grid resolution tips:

  • -n 30-40 - Quick preview (~100 KB)
  • -n 50-60 - Good default (~450 KB)
  • -n 80-100 - High quality (~1.8 MB)

Distributed Multipole Analysis (DMA)​

DMA decomposes the electron density into multipole moments (charge, dipole, quadrupole, etc.) centered at atoms. This provides more accurate electrostatics than simple point charges.

Running DMA​

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Parameters:

  • --max-rank 2 - Include up to quadrupole moments (rank 0=charge, 1=dipole, 2=quadrupole)
  • -p dma.punch - Output file in GDMA punch format

Understanding the Output​

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Higher ranks for accuracy:

  • Rank 2: Good for most organic molecules
  • Rank 4: Better for highly polar/charged systems
  • Rank 5+: Diminishing returns, rarely needed

Higher order multipoles can be essential to reproduce some electrostatic interactions between molecules, but and beyond short range can be almost identical to the full QM electrostatic interactions - though they miss the short range charge density overlap contributions (so-called 'penetration' error).

tip

You don't have to worry about it for point charges, but for higher order multipoles generally depend on their axis frame and origin. This makes computing them/using them pretty fiddly - which is no doubt part of the reason they're not so widely used as point charges (also more terms, so slower to compute).

Experimenting with Different Options​

Click the commands above to edit them and try:

Cube file properties:

occ cube input.owf.json esp -n 50 -o density.cube        # Electrostatic potential
occ cube input.owf.json density --orbital=homo -n 50 -o density.cube  # highest occupied molecular orbital (

Grid resolution:

-n 30    # Fast, small file (~100 KB)
-n 50    # Good default (~450 KB)
-n 80    # High quality (~1.8 MB), might take an eternity for things like exact ESP

DMA rank:

--max-rank 0    # Charges only
--max-rank 2    # Up to quadrupole (good default)
--max-rank 4    # Higher accuracy for crystals

Next Steps​

Now you can visualize and analyze molecular electronic structure! Continue to: