513.001 Molecular and Solid State Physics

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Wolfram Alpha

Physical
Constants

Periodic System
of Elements

      

Methane molecular orbitals

In quantum mechanics, all of the electrons in a molecule should be described by a single multi-electron wave-function. For instance, methane (CH4) has 10 electrons. These electrons would be described by a many-electron wave-function that depends on the positions of the 10 electrons. The exact many-electron wave function is difficult to construct so usually an approximate form based on products of molecular orbitals is used.

(a) How are the molecular orbitals calculated?

(b) If the molecular orbitals are known, what is the many-electron wavefunction?

(c) What does it mean that the many-electron wave-function is antisymmetric?