Hartree-Fock calculations models

DFT methods are attractive because they include the effects of electron correlation—the fact that electrons in a molecular system react to one another s motion and attempt to keep out of one another s way—in their model. Hartree-Fock calculations consider this effect only in an average sense—each electron sees and... 

As a final note, be aware that Hartree-Fock calculations performed with small basis sets are many times more prone to finding unstable SCF solutions than are larger calculations. Sometimes this is a result of spin contamination in other cases, the neglect of electron correlation is at the root. The same molecular system may or may not lead to an instability when it is modeled with a larger basis set or a more accurate method such as Density Functional Theory. Nevertheless, wavefunctions should still be checked for stability with the SCF=Stable option. ... 

CBS models typically include a Hartree-Fock calculation with a very large basis set, an MP2 calculation with a medium-sized basis set (and this is also the level where the CBS extrapolation is performed), and one or more higher-level calculations with a medium-to-modest basis set. The following table outlines the components of the CBS-4 and CBS-Q model chemistries ... 

Pempointner, M., Seth, M. and Schwerdtfeger, P. (1998) A Point-Charge Model for the Nuclear Quadmpole Moment. Accurate Coupled-Cluster, Dirac-Fock, Douglas-KroD and Nomelativistic Hartree-Fock Calculations... 

Hamiltonian equations, 627-628 II electronic states, 632-633 triatomic molecules, 587-598 minimal models, 615-618 Hartree-Fock calculations ... 

This mechanistic question is one of the examples of the success of density functional theory methods in organometallic chemistry. Earlier work on the reaction mechanism could not discriminate between the two alternatives. Analysis of the different orbitals based on extended Hiickel calculations came to the result that the [3+2] pathway is more likely, but could not exclude the possibility of a [2+2] pathway [13]. Similar conclusions where obtained from the results of Hartree-Fock calculations in combination with QCISD(T) single point calculations [21], Attempts to use Ru04 as a model for osmium tetraoxide indicated that the formation of an oxetane is less favorable compared to the [3+2] pathway, but still possible [22, 23],... 

Duncanson and Coulson [242,243] carried out early work on atoms. Since then, the momentum densities of aU the atoms in the periodic table have been studied within the framework of the Hartree-Fock model, and for some smaller atoms with electron-correlated wavefunctions. There have been several tabulations of Jo q), and asymptotic expansion coefficients for atoms [187,244—251] with Hartree-Fock-Roothaan wavefunctions. These tables have been superseded by purely numerical Hartree-Fock calculations that do not depend on basis sets [232,235,252,253]. There have also been several reports of electron-correlated calculations of momentum densities, Compton profiles, and momentum moments for He [236,240,254-257], Li [197,237,240,258], Be [238,240,258, 259], B through F [240,258,260], Ne [239,240,258,261], and Na through Ar [258]. Schmider et al. [262] studied the spin momentum density in the lithium atom. A review of Mendelsohn and Smith [12] remains a good source of information on comparison of the Compton profiles of the rare-gas atoms with experiment, and on relativistic effects. 

Numerical Hartree-Fock calculations of [87], on the other hand, convincingly show that our results in real space are the same as those of the orbital space model [Eq. (4.32)] and that we are thus justified to write... 

On the basis of mean absolute errors, bond lengths from Hartree-Fock calculations, local density calculations and density functional calculations do not improve significantly in moving from the 6-3 IG to the 6-311+G basis set. However, results from the MP2/6-311+G model are significantly better than those from the MP2/6-3 IG model. 

BP, BLYP, EDFl and B3LYP density functional models all lead to significant improvements over both Hartree-Fock and local density models, at least in terms of mean absolute deviations. While most reactions are better described, there are exceptions. Most notable among these is the bond separation reaction for tetrachloromethane. All four models show a highly exothermic reaction in contrast with both G3 and experimental results which show a nearly thermoneutral reaction. Similar, but somewhat smaller, effects are seen for isobutane and trimethylamine. As was the case with Hartree-Fock calculations. 

All the above methods are somehow based on an orbital hypothesis. In fact, in the multipolar model, the core is typically frozen to the isolated atom orbital expansion, taken from Roothan Hartree Fock calculations (or similar [80]). Although the higher multipoles are not constrained to an orbital model, the radial functions are typically taken from best single C exponents used to describe the valence orbitals of a given atom [81]. Even tighter is the link to the orbital approach in XRCW, XAO, or VOM as described above. Obviously, an orbital assumption is not at all mandatory and other methods have been developed, for example those based on the Maximum Entropy Method (MEM) [82-86] where the constraints/ restraints come from statistical considerations. 

Historically, crystal field theory was the first theoretical model (11, 86, 101, 123) used to explain d-d transition energies in metal complexes. Its usefulness is restricted to those complexes whose bonding is largely ionic, and its mqjor deficiency arises from its inability to account for charge transfer transitions. The iterative extended Hiickel and the ab initio, limited basis set, Hartree-Fock calculations are capable of de-... 

Model Hartree-Fock calculations which include only the electrostatic interaction in terms of the Slater integrals F0, F2, F and F6, and the spin-orbit interaction , result in differences between calculated and experimentally observed levels596 which can be more than 500 cm-1 even for the f2 ion Pr3. However, inclusion of configuration interaction terms, either two-particle or three-particle, considerably improves the correlations.597,598 In this way, an ion such as Nd3+ can be described in terms of 18 parameters (including crystal field... 

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