Visualization of spinors

Visualization of spinors is more difficult than visualization of orbitals. A spinor Ψ is a two-component complex wave function, which can be described with four real functions φ: real part α φ_α^R, imaginary part α φ_α^I, real part β φ_β^R, imaginary part β φ_β^I:

The density ρ is:

ρ = Ψ^† Ψ

The spin magnetization density m is:

m = Ψ^† σ Ψ

where σ is the vector of the Pauli spin matrices. A spinor is fully determined by the spin magnetization density and a phase factor e^iθ, which both are functions of spatial coordinates. In ADF one can visualize the (square root of the) density and spin magnetization density, however, the phase factor e^iθ is summarized only with a plus or minus sign. For this small molecule a fine grid is chosen for better visualization.

Select the ADFinput window with the name 'TlH_SO.adf.
Select SCM → View
Rotate the molecule, such that one can see both atoms.
Select Fields → Grid → Fine
Select Add → Spinor: spin magnetization density
In the new control line, press on the pull-down menu and
Select Orbitals (occupied) → 3 → SCF_J1/2:1  22:  1.0  ....

The arrows in this picture are in the direction of the spin magnetization density m. All arrows are approximately in the same direction, which means that this spinor is an eigenfunction of spin in this direction of the arrows. In fact this 22 j1/2 spinor is almost a pure α orbital. The arrows are drawn staring from points in space where the square root of square root of the density is 0.03. The color of the arrows are default red or blue, indicating minus or plus for the phase factor e^iθ.

The (square root of the) density and the approximate phase vector e^iθ can also be viewed separately:

Select Add → 'Isosurface: Double (+/-)
In the new control line, press on the pull-down menu and
Select Orbitals (occupied) → 'SCF_J1/2:1  18:  1.0  ..
Deselect View → Molecule Ball & Sticks → Sticks
In the control line with 'Spinor' uncheck the check box at the left end of this line

This spinor 18j1/2 is almost a pure 5p1/2 Tl spinor. A p1/2 atomic orbital has a spherical atomic density, but a spin magnetization density which is not the same in each point in space.

In the control line with 'Spinor', press on the pull-down menu and
 Select Orbitals (occupied) → 3 → SCF_J1/2:1  18:  1.0  ...
Show the 'Spinor' (check the left checkbox for the spinor line)
Hide the 'Double Isosurface' (uncheck the left check box for the double iso line)