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Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry . [ 1 ] The term ab initio was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene. [ 2 ] [ 3 ] The background is described by Parr. [ 4 ] In its modern meaning ('from first principles of quantum mechanics') the term was used by Chen [ 5 ] (when quoting an unpublished 1955 MIT report by Allen and Nesbet), by Roothaan [ 6 ] and, in the title of an article, by Allen and Karo, [ 7 ] who also clearly define it. Almost always the basis set (which is usually built from the LCAO ansatz ) used to solve the Schrödinger equation is not complete, and does not span the Hilbert space associated with ionization and scattering processes (see continuous spectrum for more details).
Density functional theory (DFT) is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure (principally the ground state ) of many-body systems , in particular atoms, molecules, and the condensed phases . With this theory, the properties of a many-electron system can be determined by using functionals , i.e. functions of another function , which in this case is the spatially dependent electron density . Hence the name density functional theory comes from the use of functionals of the electron density.
In quantum mechanics and particle physics , spin is an intrinsic form of angular momentum carried by elementary particles , composite particles ( hadrons ), and atomic nuclei . [ 1 ] [ 2 ] Spin is a solely quantum-mechanical phenomenon; it does not have a counterpart in classical mechanics (despite the term spin being reminiscent of classical phenomena such as a planet spinning on its axis). [ 2 ]
Fermi heap and Fermi hole refer to two closely related quantum phenomena that occur in many-electron atoms.
You may have learned the "rule" that no more than two electrons can be in the same orbital. If you have, you may also have puzzled about why such a rule is so.
A vibrating string can be modeled as a point in a Hilbert space. The decomposition of a vibrating string into its vibrations in distinct overtones is given by the projection of the point onto the coordinate axes in the space.