By J.R. Sabin (Eds.)

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Uniform accuracy control is also a problem. As a result, only diatomic quantum chemical calculations are sometimes performed with Slater bases. On the other hand, when solid-state calculations are performed in p space, all crystal integrals can be expressed as reciprocal lattice sums. This is described in a series of papers by Harris, Monkhorst and coworkers; a summary is provided in ‘Hartree–Fock density of states for extended systems’, by Monkhorst [5], and references therein. In this formulation, the reciprocal lattice sums are over terms involving Fourier transforms of basis functions only.

A formal solution for WðEÞ of equation (7) is ^ ^ vÞ ^ I^ K PðEÞ ^ K1 h v^ ^3K1 ðEÞ WðEÞ Z vð (9) ^ with the dielectric ‘matrix’ 3^ Z I^K P^ v. P^ is the central quantity in the GW method, and carries many-body effects ^ 0, the self-energy limits to beyond the HF approximation. In the limit P/ ^ SðEÞ/ S^ HF Z iG^ HF 5^v (10) S^ HF is energy independent, but non-local. ^ is a multiplicative operator in r Note that in equations (1) and (4), ðV^ C CÞ ^ representation, and a convolution operator in p representation.

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