Computational chemical methods in solid state physics
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Computational chemical methods in solid-state physics
follow the same approach as they do for molecules, but with two differences. First, the translational symmetry of the solid has to be utilised, and second, it is possible to use completely delocalised basis functions such as plane waves as an alternative to the molecular atom-centered basis functions
. The electronic structure of a crystal is in general described by a band structure, which defines the energies of electron orbitals for each point in the Brillouin zone
. Ab initio and semi-empirical calculations yield orbital energies, therefore they can be applied to band structure calculations. Since it is time-consuming to calculate the energy for a molecule, it is even more time-consuming to calculate them for the entire list of points in the Brillouin zone.
Calculations can use the Hartree–Fock method, some post-Hartree–Fock methods, particularly Møller–Plesset perturbation theory to second order (MP2) and density functional theory
(DFT).
Solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from...
follow the same approach as they do for molecules, but with two differences. First, the translational symmetry of the solid has to be utilised, and second, it is possible to use completely delocalised basis functions such as plane waves as an alternative to the molecular atom-centered basis functions
Basis set (chemistry)
A basis set in chemistry is a set of functions used to create the molecular orbitals, which are expanded as a linear combination of such functions with the weights or coefficients to be determined. Usually these functions are atomic orbitals, in that they are centered on atoms. Otherwise, the...
. The electronic structure of a crystal is in general described by a band structure, which defines the energies of electron orbitals for each point in the Brillouin zone
Brillouin zone
In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. The boundaries of this cell are given by planes related to points on the reciprocal lattice. It is found by the same method as for the Wigner–Seitz cell in the Bravais lattice...
. Ab initio and semi-empirical calculations yield orbital energies, therefore they can be applied to band structure calculations. Since it is time-consuming to calculate the energy for a molecule, it is even more time-consuming to calculate them for the entire list of points in the Brillouin zone.
Calculations can use the Hartree–Fock method, some post-Hartree–Fock methods, particularly Møller–Plesset perturbation theory to second order (MP2) and density functional theory
Density functional theory
Density functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure 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...
(DFT).