Spinor: spin magnetization density

Show the COSMO surface as used in a Cosmo calculation. Only accessible for .t21 files that contain COSMO results.

Only accessible in case of a spin-orbit coupled calculation with a TAPE21 (.t21) file to visualize a spinor.

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 σ_x, σ_y, and σ_z. A spinor is fully determined by the spin magnetization density and a phase factor e^iθ, which both are functions of spatial coordinates.

The (square root of the) density and spin magnetization density are visualized as a double isosurface and a vector field respectively. The phase factor e^iθ, reduced to a plus or minus sign, is visualized with the double isosurface and with the color of the vector field.

The main control bar is identical to the control bar of a normal isosurface. If you show the details, you will find that in addition to the controls available for a normal isosurface, you can also specify coloring information. In this case, the two numbers for the HSV colors define the colors of the minus and plus sign.