Separation of the Nuclear Hamiltonian

Separation of the Nuclear Hamiltonian - Separation of the...

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Separation of the Nuclear Hamiltonian The nuclear Schrödinger equation can be approximately factored into translational, rotational, and vibrational parts. McQuarrie [ 1 ] explains how to do this for a diatomic in section 10-13. The rotational part can be cast into the form of the rigid rotor model, and the vibrational part can be written as a system of harmonic oscillators. Time does not allow further comment on the nuclear Schrödinger equation, although it is central to molecular spectroscopy. Solving the Electronic Eigenvalue Problem Once we have invoked the Born-Oppenheimer approximation, we attempt to solve the electronic Schrödinger equation ( 171 ), i.e. (183 ) But, as mentioned previously, this equation is quite difficult to solve! The Nature of Many-Electron Wavefunctions Let us consider the nature of the electronic wavefunctions . Since the electronic wavefunction depends only parametrically on , we will suppress in our notation from now on. What do we require of ? Recall that represents the set of all electronic coordinates, i.e., . So far we have left out one important item--we need to include the
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This note was uploaded on 11/22/2011 for the course CHEMISTRY CHM1025 taught by Professor Laurachoudry during the Fall '10 term at Broward College.

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Separation of the Nuclear Hamiltonian - Separation of the...

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