Abstract
The formulation of the augmented-plane-wave (APW) method of solving the energy-band problem is reexamined from a fully variational point of view, and various ways of increasing the power and efficiency of the method are suggested. Classes of variational expressions for the energy are derived which are suitable for trial wave functions discontinuous on a separation surface in the crystal unit cell. New trial functions are constructed which permit better matching across the (spherical) separation surface; one of these permits both the function and its derivative to be continuous and is still simple. The matrix elements of a secular equation for the energy are obtained for two classes of variational expressions and three kinds of trial function. Comparison with standard APW matrix elements shows certain differences arising from the fully variational approach; these are discussed along with relative merits of the different secular equations, and the best choice of numerous parameters appearing in the formulation, but no numerical results are given.
Keywords
ComputationMatrix (chemical analysis)Simple (philosophy)Variational methodFunction (biology)Plane (geometry)MathematicsWave functionMatching (statistics)Mathematical analysisApplied mathematicsSecond derivativeEnergy (signal processing)PhysicsAlgorithmGeometryQuantum mechanicsChemistry
Related Publications
Linear methods in band theory
Two approximate methods for solving the band-structure problem in an efficient and physically transparent way are presented and discussed in detail. The variational principle fo...
Electronic States as Linear Combinations of Muffin-Tin Orbitals
A general method for the calculation of electronic states in solids and molecules is proposed. As in the augmented-plane-wave scheme, we use the variational principle for the Ha...
An Augmented Plane-Wave Method for the Periodic Potential Problem. II
It is shown that the augmented plane-wave method recently proposed can be given an alternative interpretation which leads to a much simpler analytical formulation. We join a pla...
Use of energy derivative of the radial solution in an augmented plane wave method: application to copper
By a suitable combination inside the muffin-tin sphere of a radial solution to the Schrodinger equation and its energy derivative, the dependence of the APW matrix elements on t...
Molecular properties from perturbation theory: A Unified treatment of energy derivatives
Abstract The definition of a molecular property as a derivative of the electronic energy with respect to one or more applied perturbations is reviewed. The explicit enumeration ...
Publication Info
- Year
- 2009
- Type
- article
- Volume
- 1
- Issue
- S1
- Pages
- 567-588
- Citations
- 38
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
38
OpenAlex
Cite This
Paul Marcus
(2009).
Variational methods in the computation of energy bands.
International Journal of Quantum Chemistry
, 1
(S1)
, 567-588.
https://doi.org/10.1002/qua.560010659
Identifiers
- DOI
- 10.1002/qua.560010659