Direct-diagonalization , electronic structure

The ACSE has important connections to other approaches to electronic structure including (i) variational methods that calculate the 2-RDM directly [36-39] and (ii) wavefunction methods that employ a two-body unitary transformation including canonical diagonalization [22, 29, 30], the effective valence Hamiltonian method [31, 32], and unitary coupled cluster [33-35]. A 2-RDM that is representable by an ensemble of V-particle states is said to be ensemble V-representable, while a 2-RDM that is representable by a single V-particle state is said to be pure V-representable. The variational method, within the accuracy of the V-representabihty conditions, constrains the 2-RDM to be ensemble N-representable while the ACSE, within the accuracy of 3-RDM reconstruction, constrains the 2-RDM to be pure V-representable. The ACSE and variational methods, therefore, may be viewed as complementary methods that provide approximate solutions to, respectively, the pure and ensemble V-representabihty problems. 

Efros A. L. and Rosen M. (1998), Comment on Comparison of the k P and the direct diagonalization approaches for describing the electron structure of quantum dots , App/. Phys. Lett. 73, 1155-1156. 

The information on the bulk of the interparticle interactions is contained in I o, even though the decay properties are obtained only after input from Xas has been added, it follows that its accurate and systematic computation is of prime importance, instead of following procedures of brute-force diagonalization, the calculation of I o for electronic structures is done directly, via the solution of state-specific Hartree-Fock (HE) equations under special orbital constraints. The practicality of this approach even for open-(sub)shell multiply excited resonances was demonstrated in the 1972 paper, thereby opening the way for later computations that start with state-specific mul-ticonfigurational HF equations and tackle efficiently the MEP and electron correlation in the context of appropriate formalisms for resonance states. 

On the other hand, there is an obvious demand for electronic-structure methods from first principles which are able to treat huge chemical systems composed of, say, several thousands of atoms. Let us think of nano- and biomaterials, just to name two important research directions. Unfortunately, standard methods will not do here simply because their scaling behavior with respect to the number of atoms is insufficient. We recall that the time needed to diagonalize a DFT-based Hamiltonian goes with the third power of the size of the system. In the real world, mathematical tricks may fortunately be used to bring this cubic scaling down to something of the order of Nonethe-... 

In electronic structure calculations, the zero point for the energy function has all particles (electrons and nuclei) infinitely removed from each other, and this common reference state allows energies for systems with different numbers of particles to be directly compared. If the same reference is used in force field methods, the energy function becomes an absolute measure of molecular stability. The difference relative to the normal reference state for force field functions is the sum of all bond dissociation energies, at least for a simple diagonal force field. If correction terms are added to the... 

Monoxides of 3d transition metals, TiO to NiO, possess the rocksalt structure and exhibit properties shown in Table 6.3. While TiO and VO exhibit properties characteristic of itinerant (or nearly itinerant) d electrons, MnO, FeO, CoO and NiO show localized electron properties. The properties can be understood in terms of the possible cation-cation and cation-anion-cation interactions in the rocksalt structure (Fig. 6.12(a)). Direct cation-cation interaction can occur through the overlap of cationic t2g orbitals across the face diagonal of the cubic structure. When this interaction is strong R < and b > b, cationic t2g orbitals are transformed into a cation sublattice t%g band if this band is partly occupied, the material would be... 

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