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There are a number of interrelated concepts associated with the term "Electronic Hamiltonian". These include the following:

# Full electronic Hamiltonian
# Electronic Hamiltonian
# Nuclear Hamiltonian
# Clampled Hamiltonian

Depending on the context, "full electronic Hamiltonian" may be used interchangably with "electronic Hamiltonian". Furthermore, the "Clamped Hamiltonian" or may be used interchangably with "Electronic Hamiltonian". The latter is usually used only when discussing various methods associated with the Born-Oppenheimer Approximation .


FULL ELECTRONIC HAMILTONIAN

Let R denote the vector of nuclear coordinates, and '''r''' the vector of electronic coordinates.

The full electronic Hamiltonian consists of 5 terms. They are

# The Kinetic Energy Operator s for each nuclei in the system;
# The kinetic energy operators for each electron in the system;
# The potential energy between the electrons and nuclei - the total electron-nucleus Coulombic attraction in the system;
# The potential energy arising from Coulombic electron-electron repulsions
# The potential energy arising from Coulombic nuclei-nuclei repulsions - also known as the nuclear repulsion energy. See Electric Potential for more details.

#\hat{T}^n = - \sum_i rac{\hbar^2}{2 M_i} rac{\partial^2}{\partial R_i^2}
#\hat{T}^e = - \sum_i rac{\hbar^2}{2 m_e} rac{\partial^2}{\partial r_i^2}