Fermi operator expansions

A tight-binding (TB) MD study to examine the pressure effect on structural and dynamical properties of a-Ge has also been reported [274], The calculations were performed based on the order-iV nonorthogonal TB framework using the Fermi operator expansion method [275], The TB MD calculations were run with... 

In the following sections, we will provide an overview of density matrix-based SCF theory that allows one to exploit the naturally local behavior of the one-particle density matrix for molecular systems with a nonvanishing HOMO-LUMO gap. Besides the density matrix-based theories sketched below, " a range of other methods exists, including divide-and-conquer methods, Fermi operator expansions (FOE), °° Fermi operator projection (FOP), ° orbital minimization (OM), ° ° and optimal basis density-matrix minimization (OBDMM). ° ° Although different in detail, many share as a common feature the idea of (imposed or natural) localization regions in order to achieve an overall 0 M) complexity. This notion implies that the density matrix (or the molecule) may be divided into smaller... 

The basic formula to take Fermi motion into account can be derived along lines very similar to those followed in the appendix to Chapter 16 [see eqn (16.9.19)]. The difference, of course, is that now V represents the momentum distribution of a nucleon in the nucleus. The following convolution formula emerges either using the techniques of the operator product expansion, or more simply, by considering the kinematics of Fig. 17.11 which shows a nucleus of atomic number A in a reference frame in which it is moving very fast with momentum P along OZ. A nucleon i inside the nucleus has -component of momentum pz = zP/A and a parton. 

In single-reference CC the excitation operators contain only creation operators (particle or hole) with respect to the Fermi vacuum. In MRCC there is no unique choice of Fermi vacuum, but for any choice annihilation operators will appear in the excitation manifold so that the BCH-expansion of the similarity-transformed Hamiltonian will not truncate to quartic order. 

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