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Electrons
International Tables for Crystallography (2013). Vol. D, ch. 2.2, pp. 314-333 [ doi:10.1107/97809553602060000912 ]
... a notation so that we can write . Note that k is quantized due to the periodic boundary conditions according to ... factor . At the moment (2.2.4.13) suggests the use of k as label for the wavefunction . Generalization to three dimensions ... wavevector or propagation vector. Figure 2.2.5.1 | | Plane waves. The wavevector k and the unit vector e are normal to the ...
Core electron spectra
International Tables for Crystallography (2013). Vol. D, Section 2.2.16.3, p. 332 [ doi:10.1107/97809553602060000912 ]
... between theory and experiment for the compounds NbC and NbN (Schwarz, 1977). Note again that the present description is based ... spectra in simple metals. Solid State Commun. 32, 645-649. Schwarz, K. (1977). The electronic structure of NbC and NbN. ...
[more results from section 2.2.16 in volume D]
Theoretical approach
International Tables for Crystallography (2013). Vol. D, Section 2.2.15.3, pp. 328-330 [ doi:10.1107/97809553602060000912 ]
... of the potential can be used and this procedure yields (Schwarz et al., 1990) for : with , and the spherical Bessel function ... asymmetry count, illustrated below for the oxygen sites in YBa2Cu3O7 (Schwarz et al., 1990), the unit cell of which is shown ... three oxygen sites). Excellent agreement with experiment is found (Schwarz et al., 1990). In a more complicated situation, ...
[more results from section 2.2.15 in volume D]
The density of states (DOS)
International Tables for Crystallography (2013). Vol. D, Section 2.2.14.6, pp. 326-327 [ doi:10.1107/97809553602060000912 ]
The density of states (DOS) 2.2.14.6. The density of states (DOS) The density of states (DOS) is the number of one-electron states (in the HF method or DFT) per unit energy interval and per unit cell volume. It is better to start with the integral quantity , the number of states ...
[more results from section 2.2.14 in volume D]
Interpretation for bonding
International Tables for Crystallography (2013). Vol. D, Section 2.2.13.2, p. 325 [ doi:10.1107/97809553602060000912 ]
Interpretation for bonding 2.2.13.2. Interpretation for bonding Chemical bonding is often described by considering orbitals (e.g. a or a atomic orbital) which are defined in polar coordinates, where the z axis is special, in contrast to Cartesian coordinates, where x, y and z are equivalent. Consider for example an atom coordinated ...
[more results from section 2.2.13 in volume D]
The linearized augmented plane wave method
International Tables for Crystallography (2013). Vol. D, Section 2.2.12, pp. 323-324 [ doi:10.1107/97809553602060000912 ]
... description of the computer code WIEN (Blaha et al., 1990; Schwarz & Blaha, 1996). An excellent book by Singh (1994) is ... full-potential calculations this problem practically disappears. References Andersen, O. K. (1975). Linear methods in band theory. Phys. Rev. B, 12, 3060-3083. Blaha, P., Schwarz, K., Sorantin, P. I. & Trickey, S. B. (1990). ...
Order N schemes
International Tables for Crystallography (2013). Vol. D, Section 2.2.11.8, pp. 322-323 [ doi:10.1107/97809553602060000912 ]
... to N which requires diagonalization of matrices, where the prefactor k depends on the basis set and the method used. In ...
[more results from section 2.2.11 in volume D]
Density functional theory
International Tables for Crystallography (2013). Vol. D, Section 2.2.10, pp. 320-321 [ doi:10.1107/97809553602060000912 ]
... Rev. Lett. 45, 566-572. Dreizler, R. M. & Gross, E. K. U. (1990). Density functional theory. Berlin, Heidelberg, New York ... J. Quantum Chem. 19, 497-523. Perdew, J. P., Burke, K. & Ernzerhof, M. (1996) Generalized gradient approximation made simple. Phys. Rev. ...
Relativistic effects
International Tables for Crystallography (2013). Vol. D, Section 2.2.9.4, p. 320 [ doi:10.1107/97809553602060000912 ]
Relativistic effects 2.2.9.4. Relativistic effects If a solid contains only light elements, non-relativistic calculations are well justified, but as soon as heavier elements are present in the system of interest relativistic effects can no longer be neglected. In the medium range of atomic numbers (up to about 54), so-called ...
[more results from section 2.2.9 in volume D]
Bloch functions
International Tables for Crystallography (2013). Vol. D, Section 2.2.8, p. 319 [ doi:10.1107/97809553602060000912 ]
Bloch functions 2.2.8. Bloch functions We can provide a physical interpretation for a Bloch function by the following considerations. By combining the group-theoretical concepts based on the translational symmetry with the free-electron model, we can rewrite a Bloch function [see (2.2.4.18)] in the form where denotes the plane wave ...
International Tables for Crystallography (2013). Vol. D, ch. 2.2, pp. 314-333 [ doi:10.1107/97809553602060000912 ]
... a notation so that we can write . Note that k is quantized due to the periodic boundary conditions according to ... factor . At the moment (2.2.4.13) suggests the use of k as label for the wavefunction . Generalization to three dimensions ... wavevector or propagation vector. Figure 2.2.5.1 | | Plane waves. The wavevector k and the unit vector e are normal to the ...
Core electron spectra
International Tables for Crystallography (2013). Vol. D, Section 2.2.16.3, p. 332 [ doi:10.1107/97809553602060000912 ]
... between theory and experiment for the compounds NbC and NbN (Schwarz, 1977). Note again that the present description is based ... spectra in simple metals. Solid State Commun. 32, 645-649. Schwarz, K. (1977). The electronic structure of NbC and NbN. ...
[more results from section 2.2.16 in volume D]
Theoretical approach
International Tables for Crystallography (2013). Vol. D, Section 2.2.15.3, pp. 328-330 [ doi:10.1107/97809553602060000912 ]
... of the potential can be used and this procedure yields (Schwarz et al., 1990) for : with , and the spherical Bessel function ... asymmetry count, illustrated below for the oxygen sites in YBa2Cu3O7 (Schwarz et al., 1990), the unit cell of which is shown ... three oxygen sites). Excellent agreement with experiment is found (Schwarz et al., 1990). In a more complicated situation, ...
[more results from section 2.2.15 in volume D]
The density of states (DOS)
International Tables for Crystallography (2013). Vol. D, Section 2.2.14.6, pp. 326-327 [ doi:10.1107/97809553602060000912 ]
The density of states (DOS) 2.2.14.6. The density of states (DOS) The density of states (DOS) is the number of one-electron states (in the HF method or DFT) per unit energy interval and per unit cell volume. It is better to start with the integral quantity , the number of states ...
[more results from section 2.2.14 in volume D]
Interpretation for bonding
International Tables for Crystallography (2013). Vol. D, Section 2.2.13.2, p. 325 [ doi:10.1107/97809553602060000912 ]
Interpretation for bonding 2.2.13.2. Interpretation for bonding Chemical bonding is often described by considering orbitals (e.g. a or a atomic orbital) which are defined in polar coordinates, where the z axis is special, in contrast to Cartesian coordinates, where x, y and z are equivalent. Consider for example an atom coordinated ...
[more results from section 2.2.13 in volume D]
The linearized augmented plane wave method
International Tables for Crystallography (2013). Vol. D, Section 2.2.12, pp. 323-324 [ doi:10.1107/97809553602060000912 ]
... description of the computer code WIEN (Blaha et al., 1990; Schwarz & Blaha, 1996). An excellent book by Singh (1994) is ... full-potential calculations this problem practically disappears. References Andersen, O. K. (1975). Linear methods in band theory. Phys. Rev. B, 12, 3060-3083. Blaha, P., Schwarz, K., Sorantin, P. I. & Trickey, S. B. (1990). ...
Order N schemes
International Tables for Crystallography (2013). Vol. D, Section 2.2.11.8, pp. 322-323 [ doi:10.1107/97809553602060000912 ]
... to N which requires diagonalization of matrices, where the prefactor k depends on the basis set and the method used. In ...
[more results from section 2.2.11 in volume D]
Density functional theory
International Tables for Crystallography (2013). Vol. D, Section 2.2.10, pp. 320-321 [ doi:10.1107/97809553602060000912 ]
... Rev. Lett. 45, 566-572. Dreizler, R. M. & Gross, E. K. U. (1990). Density functional theory. Berlin, Heidelberg, New York ... J. Quantum Chem. 19, 497-523. Perdew, J. P., Burke, K. & Ernzerhof, M. (1996) Generalized gradient approximation made simple. Phys. Rev. ...
Relativistic effects
International Tables for Crystallography (2013). Vol. D, Section 2.2.9.4, p. 320 [ doi:10.1107/97809553602060000912 ]
Relativistic effects 2.2.9.4. Relativistic effects If a solid contains only light elements, non-relativistic calculations are well justified, but as soon as heavier elements are present in the system of interest relativistic effects can no longer be neglected. In the medium range of atomic numbers (up to about 54), so-called ...
[more results from section 2.2.9 in volume D]
Bloch functions
International Tables for Crystallography (2013). Vol. D, Section 2.2.8, p. 319 [ doi:10.1107/97809553602060000912 ]
Bloch functions 2.2.8. Bloch functions We can provide a physical interpretation for a Bloch function by the following considerations. By combining the group-theoretical concepts based on the translational symmetry with the free-electron model, we can rewrite a Bloch function [see (2.2.4.18)] in the form where denotes the plane wave ...
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