LDA-Hartree

It is also shown in Table 10 that excitation energies are underestimated compared to CC3 and CCSD, by approximately 1 eV for B3LYP and around 2 eV for BLYP and LDA. Hartree-Fock on the the other hand overshoots around 1-2 eV. 

Fig. 1 Size dependence of optical gaps of silicon nanocrystals calculated using quantum Monte Carlo (QMC), time-dependent local-density approximation (TD-LDA), Hartree-Fock configuration interactions (HF-CI), and semiempirical tight binding (TB). The inset shows schematically the bandgap enlargement due to reducing die nanocrystal size...

This LDA "Hartree" calculation was provided by C. Kune independently very similar results were found by D. Glotzel. 

Fig. 6.6. LDA and GGA xc potentials for the argon atom. The dashed-dotted line corresponds to minus the Hartree potential evaluated with the GGA density. The LDA Hartree potential is however indistinguishable from this curve. Furthermore, the dashed line represents the argon nuclear potential, — 18/r, and the sohd line the total Kohn-Sham potential...

The exchange-correlation energy density can be split into two parts exchange component Ex n) and correlation component e Cn). The explicit expression for the exchange component is known from Hartree-Fock theory but the correlation component is known only numerically. Several parametrisations exist for the exchange-correlation energy and potential of a homogeneous gas system which can be used for the LDA calculations within DFT. 

Florian and Johnson50 calculated vibrational frequencies in isolated formamide using the DFT calculations at the LDA (SVWN) and post-LDA (B88/LYP) levels. The DFT frequencies were compared with the ones derived from the Hartree-Fock and MP2 calculations, and from experiment. The authors found that the DFT(B88/LYP) frequencies were more in line with experiment then the MP2 ones. The DFT(SVWN) calculations led to geometry, force constants, and infrared spectra fully comparable to the MP2 results. The equilibrium geometry and vibrational frequencies of formamide were also the subject of studies by Andzelm et al.51. It was found that the DFT(B88/P86) calculations led to frequencies in a better agreement with experiment than those obtained from the CISD calculations. 

Density-functional theory, developed 25 years ago (Hohenberg and Kohn, 1964 Kohn and Sham, 1965) has proven very successful for the study of a wide variety of problems in solid state physics (for a review, see Martin, 1985). Interactions (beyond the Hartree potential) between electrons are described with an exchange and correlation potential, which is expressed as a functional of the charge density. For practical purposes, this functional needs to be approximated. The local-density approximation (LDA), in which the exchange and correlation potential at a particular point is only a function of the charge density at that same point, has been extensively tested and found to provide a reliable description of a wide variety of solid-state properties. Choices of numerical cutoff parameters or integration schemes that have to be made at various points in the density-functional calculations are all amenable to explicit covergence tests. 

The inherent problems associated with the computation of the properties of solids have been reduced by a computational technique called Density Functional Theory. This approach to the calculation of the properties of solids again stems from solid-state physics. In Hartree-Fock equations the N electrons need to be specified by 3/V variables, indicating the position of each electron in space. The density functional theory replaces these with just the electron density at a point, specified by just three variables. In the commonest formalism of the theory, due to Kohn and Sham, called the local density approximation (LDA), noninteracting electrons move in an effective potential that is described in terms of a uniform electron gas. Density functional theory is now widely used for many chemical calculations, including the stabilities and bulk properties of solids, as well as defect formation energies and configurations in materials such as silicon, GaN, and Agl. At present, the excited states of solids are not well treated in this way. 

The intraatomic d-d electron-electron interaction includes Coulomb and exchange interactions, and it is responsible for orbital and spin polarization. To account for orbital polarization, the idea of the LDA + U method was followed.70 A generalized Hartree-Fock approximation including all possible pairings was then used to write... 

This survey of theoretical methods for a qualitative description of homogeneous catalysis would not be complete without a mention to the Hartree-Fock-Slater, or Xot, method [36]. This approach, which can be formulated as a variation of the LDA DFT, was well known before the formal development of density functional theory, and was used as the more accurate alternative to extended Hiickel in the early days of computational transition metal chemistry. 

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