Molecular orbitals
This program can be used to display the wave function of the electrons in different orbitals of the hydrogen atom and the hydrogen molecule. The results are qualitatively transferable to other homonuclear molecules such as O2, N2, F2. The molecular orbitals are calculated as a simplified superposition of the two atomic orbitals. Despite this relatively rough approximation, the charge density distribution still has the same symmetry as the correct wave function. The distance between the atoms can be varied using a slider so that the development of the different molecular orbitals from the atomic orbitals can be observed. Either the wave function Psi or the charge density |Psi|2 can be displayed. The signs of the wave function are also marked in color for the charge density (red positive, blue negative) to make the symmetry of the orbitals easier to understand.
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Operation
The atomic orbitals of the two atoms can be set at the top left. For this purpose, the principal quantum number n (Principle quantum number), the angular quantum number l (Angular quantum number) and the magnetic quantum number m ( Magnetic quantum number) are selected. Please note that l<n</em> and |m|<=l must be fulfilled - if this is not the case, no orbital is displayed. When forming molecular orbitals, the atomic orbitals can be superimposed with the same (even) or opposite sign (odd). This difference leads to binding or antibonding orbitals in the molecule. The designation of the atomic orbitals and the molecular orbital is displayed for the selected combination of quantum numbers. The color intensity and zoom can be adjusted via sliders. At the bottom is the selection for wave function (Psi) or charge density |Psi|2. The nuclear locations are shown as black dots. The distance between the two atoms is set using the slider on the right-hand side of the screen. The distance between the atoms at the start of the program is 60 atomic units, the minimum adjustable distance is one atomic unit (1 a.u. = 0.5292 Angstrom). In the menu under File, the image can be saved as a graphic (bmp or jpg format) or printed out directly. By selecting the appropriate window size on the screen, the image section can be adjusted for saving and printing.
Numerical realization
The atomic wave function is calculated analytically. The wave functions of both atoms are added for each pixel.