Computational Methods in Band Theory pp 447-457 | Cite as

# The Self-Consistent Field Method for Crystals

Chapter

## Abstract

In a self-consistent-field calculation, where Σ(i↑) indicates that we are summing only over the spin- orbitals with spin up, and similarly for Σ(i↓).

^{1}we start with assumed spin-orbitals u_{i}, which can correspond either to spin up or spin down. We let the occupation number of the ith spin-orbital be n_{i}, which would be unity for occupied spin-orbitals, zero for empty ones, in a Hartree-Fock scheme, but which in certain cases can be considered to be continuously variable between zero and unity. The charge density of spin up and spin down can be defined as$$\rho = \rho \uparrow + \rho \downarrow = \Sigma\left( {i \uparrow } \right){n_i}{u_i}*{u_i} + \Sigma \left( {i \downarrow } \right){n_i}{u_i}*{u_i}$$

(1)

## Keywords

Excitation Energy Occupation Number Optical Excitation Discrete Level Localize Excitation
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## References

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## Copyright information

© Plenum Press, New York 1971