Computational chemical methods in

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 l ...

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 In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position \vec x in space and any time t, th ...

as an alternative to the molecular atom-centered

basis functions In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be repres ...

. The electronic structure of a crystal is in general described by a

band structure In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or '' ...

, which defines the energies of electron orbitals for each point in the

Brillouin zone In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice i ...

. 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 In computational chemistry, post-Hartree–Fock methods are the set of methods developed to improve on the Hartree–Fock (HF), or self-consistent field (SCF) method. They add electron correlation which is a more accurate way of including the rep ...

methods, particularly Møller–Plesset perturbation theory to second order (MP2) and

density functional theory Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body ...

(DFT).

References

*''Computational Chemistry'', David Young, Wiley-Interscience, 2001. Chapter 41, pg 318. The extensive references in that chapter provide further reading on this topic. * ''Computational Chemistry and molecular modeling Principles and applications'',K.I.Ramachandran, G.Deepa and Krishnan namboori P.K.

Springer-Verlag GmbH Computational chemistry Theoretical chemistry Computational science Condensed matter physics Computational physics fr:Chimie numérique#Méthodes de chimie numérique dans les systèmes solides {{compu-physics-stub

See also

References