Orbitals Calculation

Python API · stjames models · API example

How it works

Calculate molecular orbitals, electron density, electrostatic potential, atomic charges, bond orders, and multipole moments to explore bonding and reactivity. This is a single-point calculation at the supplied geometry; it does not optimize the structure. Results depend on the geometry, molecular charge, spin multiplicity, and chosen method.

Settings

Level of theory: The default is B97-3c; r²SCAN-3c and ωB97X-3c presets and “More methods” are available.
Orbitals: “N occupied orbitals” and “N virtual orbitals” select orbitals near the occupied–unoccupied boundary. Each defaults to 1 and accepts 0–10 in the web form. For a closed-shell molecule, the defaults save the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). Set both to 0 to skip orbital surfaces.
Density and potential: “Electron density?” and “Electrostatic potential?” are both on by default. Dipole, quadrupole, Mulliken/Löwdin charges, and Wiberg/Mayer bond orders are calculated regardless of these surface selections.
Excited states: Choose “TDDFT / UV-Vis spectroscopy” under “Level of theory mode” to add excitation energies, oscillator strengths, dominant orbital transitions, and natural transition orbitals (NTOs). “Num excitations” defaults to 5; “Use TDA?” enables the Tamm–Dancoff approximation by default. The charge and multipole results still describe the ground state.

Notes

Multipoles

The electric dipole describes charge separation and is reported in Debye. Its vector points from negative toward positive charge, opposite the conventional chemistry dipole arrow. The quadrupole is a 3 × 3 tensor describing the second moment of the charge distribution. Components depend on the coordinate frame; for ions, the dipole also depends on the origin.

Atomic charges

Mulliken and Löwdin charges partition the electron distribution differently. They are method- and basis-dependent estimates, rather than unique observable atomic charges. Compare trends using the same partitioning scheme and calculation settings.

Bond orders

Wiberg–Löwdin and Mayer indices summarize bonding between atom pairs. They can be fractional and depend on the electronic structure and definition; neither scheme is universally preferable or identical to formal bond order.

Isosurfaces

An isosurface joins points with the same value. Adjusting its cutoff changes the displayed shape and extent. Use the same cutoff when comparing surfaces across molecules.

Electron density

Total electron density shows the electron cloud. Open-shell results also provide alpha and beta densities and their difference, the spin density. Color the total-density surface by electrostatic potential to inspect electrostatic interactions: negative potential attracts positive charge, while positive potential attracts negative charge. This is a qualitative guide, not a reaction prediction.

Molecular orbitals

Orbital surfaces show positive and negative amplitudes, usually in different colors. These signs describe phase, not positive and negative charge; reversing an orbital’s overall sign changes no physical prediction. An orbital’s squared amplitude relates to probability density. The HOMO–LUMO energy gap is not itself an optical excitation energy.