The Self-Consistent Field Method for Crystals

  • J. C. Slater
Part of the The IBM Research Symposia Series book series (IRSS)


In a self-consistent-field calculation,1 we start with assumed spin-orbitals ui, which can correspond either to spin up or spin down. We let the occupation number of the ith spin-orbital be ni, 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
$$\rho = \rho \uparrow + \rho \downarrow = \Sigma\left( {i \uparrow } \right){n_i}{u_i}*{u_i} + \Sigma \left( {i \downarrow } \right){n_i}{u_i}*{u_i}$$
where Σ(i↑) indicates that we are summing only over the spin- orbitals with spin up, and similarly for Σ(i↓).


Excitation Energy Occupation Number Optical Excitation Discrete Level Localize Excitation 
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Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • J. C. Slater
    • 1
  1. 1.University of FloridaGainesvilleUSA

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