The electronic Hamiltonian for a multi-electron molecule in atomic units is: The Hamiltonian, denoted H, has two distinct but closely related meanings. ... In science, a molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. ... Atomic units(au) are a convenient system of units of measurement used in atomic physics, particularly for describing the properties of electrons. ...
The first term in the Hamiltonian is the sum of the kinetic energy operators for each electron in the system. The second term is the sum of the electron-nucleus Coulombic attractions. The third term is the sum of the electron-electron Coulombic repulsions. The final term is the sum of the nucleus-nucleus Coulombic repulsions, also known as the nuclear repulsion energy. This article may be too technical for most readers to understand. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... This article may be too technical for most readers to understand. ... In mathematical formulations of quantum mechanics, an operator is a linear transformation from a Hilbert space to itself. ...
to separate the variables corresponding to the nuclear and electronic coordinates in the Schrödinger equation associated to the molecularHamiltonian).
Considering that the eigenfunction of the electronicmolecularHamiltonian are slowly depending on the geometry is called the Born-Oppenheimer approximation.
The Born-Oppenheimer approximation consists in replacing the electronicmolecularHamiltonian in the molecularHamiltonian by its eigenvalues (which are adiabatically dependent on the molecular geometry) called in this context potential energy surfaces.
In molecular physics, the molecular term symbol is a shorthand expression of the group representation and angular momenta that characterize the state of a molecule, i.e.
its electronic quantum state which is an eigenstate of the electronicmolecularHamiltonian.
In the case of less symmetric molecule the molecular term symbol contains the symbol of the group representation to which the molecularelectronic state belongs.
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