CHEM 214 Lecture Notes - Lecture 24: Aufbau Principle, Molecular Vibration, Electron Configuration
26 Jun 2016
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Document Summary
If we can solve the swe for a particular hamiltonian, than exact energy levels and wavefunctions can be determined. Not that many problems you can solve with. Schrodinger equation: 1d box, ho, rigid rotor, hydrogen atom. When solving schrodinger equation, the lowest energy state is the ground state, with energy eo (obtain same value experimentally). The wavefunction of the ground state is the lowest energy configuration possible for the system we can rearrange the swe for this case: Variational theorem (cannot solve schrodinger equation): no matter what approximate wavefunction (phi) is used (instead of exact wavefunction), the calculated energy will be greater than or at best equal to the true energy => guessing schrodinger equation. The approximate wavefunction (phi) is called the trial wavefunction. Phi can have adjustable parameters (e. g. effective charge of atoms, or in molecules the sizes of orbital) Minimizing the calculated energy will bring the energy closer to the true ground state energy of the exact wavefunction.
