The Quantistic Approach Molecular Orbital MO Theory

The fundamental equation of quantum mechanics is the time-dependent Schro-dinger equation  

After normalization of the wavefunction, multiplying on the left by i j (a), and integrating over all space, one gets the expectation value of the electronic energy  

A hydrogen atom consists of a nucleus of unit positive charge and one electron. The quantum mechanical equation for a hydrogen atom is [1]  

For a polyatomic molecule, nuclei are considered motionless, because the motion of electrons is on a much faster timescale than the motion of nuclei (the Born-Oppenheimer approximation). The corresponding Hamiltonian is  

Solution of the Schrodinger equation provides two main pieces of information the total electronic energy of the system (the repulsion energy between motionless nuclei can be simply calculated by a Coulomb sum), and the wavefunction F(x, y, z, t), which in turn gives the electron density g(x,y,z) and a formal answer to the question where are the electrons , because the quantity  

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