Hartree-Fock calculations effects

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... 

The stability of gold(III) compared with silver(III) has been ascribed to relativistic effects causing destabilization of the 5d shell, where the electrons are less tightly held. Hartree-Fock calculations on AuX4 (X = F, Cl, Br) indicate that relativistic effects make a difference of 100-200 kJ mol-1 in favour of the stability of AuXJ (Table 4.12) [110]. 

How does a rigorously calculated electrostatic potential depend upon the computational level at which was obtained p(r) Most ab initio calculations of V(r) for reasonably sized molecules are based on self-consistent field (SCF) or near Hartree-Fock wavefunctions and therefore do not reflect electron correlation in the computation of p(r). It is true that the availability of supercomputers and high-powered work stations has made post-Hartree-Fock calculations of V(r) (which include electron correlation) a realistic possibility even for molecules with 5 to 10 first-row atoms however, there is reason to believe that such computational levels are usually not necessary and not warranted. The Mpller-Plesset theorem states that properties computed from Hartree-Fock wave functions using one-electron operators, as is T(r), are correct through first order (Mpller and Plesset 1934) any errors are no more than second-order effects. 

As it is now very well known, accurate studies of the water-water interaction by means of ab-initio techniques require the use of larger and flexible basis sets and methods which consider correlation effects [85,94-96], Since high level ab-initio post-Hartree-Fock calculations are unfeasible because of their high computational cost for systems with many degrees of freedom, Density Functional Theory, more economical from the computational point of view, is being more and more considered as a viable alternative. Recently, we have presented [97] results of structural parameters and vibrational frequencies for the water clusters (H20) , n=2 to 8, using the DFT method with gradient corrected density functionals. 

Marathe and Trautwein (1983) quote values of 5.09 and 5.73 au-3 from Hartree-Fock calculations on Fe2+ (3d6) and Fe3+ (3d5), respectively, showing that the radial contraction (i.e., the k parameter in the diffraction formalism) has a pronounced effect on the 3(J values. 

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. 

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. 

Tables 12-23 to 12-26 examine the effect of geometry on dipole moments in a small collection of hydrocarbons and amines. Singlepoint 6-31G, EDF1/6-31G, B3LYP/6-31G and MP2/6-31G dipole moment calculations have been carried out using MMFF, AMI and (except for the Hartree-Fock calculations) 6-3IG geometries, and compared with dipole moments obtained from exact structures. While subtle differences exist, for the most part they are very small. In fact, using mean absolute error as a criterion, there is little to differentiate dipole moments obtained from use of approximate geometries from those calculated using exact geometries.

Eieiat. describes relativistic effects (such as variations in spin couplings - see Chap. A) and 8Econ. other electron-electron (and also electron-vibrational) many-body correlation effects (which are not included in Hartree-Fock calculations). 

One-center expansion was first applied to whole molecules by Desclaux Pyykko in relativistic and nonrelativistic Hartree-Fock calculations for the series CH4 to PbH4 [81] and then in the Dirac-Fock calculations of CuH, AgH and AuH [82] and other molecules [83]. A large bond length contraction due to the relativistic effects was estimated. However, the accuracy of such calculations is limited in practice because the orbitals of the hydrogen atom are reexpanded on a heavy nucleus in the entire coordinate space. It is notable that the RFCP and one-center expansion approaches were considered earlier as alternatives to each other [84, 85]. 

In both the extended Hartree-Fock calculation and the valence bond calculation effects of spin correlation are included, but not in the simple Huckel scheme. The x-energy levels for the allyl radical arc shown schematically below. 

Two groups have studied the bonding in pentadienyl-metal-tricar-bonyl complexes (119, 238) and are agreed that effective overlap between the pentadienyl nonbonding orbital and an orbital of suitable symmetry on the metal (Fig. 17) makes a major contribution to the stability of these complexes. However, the two types of molecular orbital calculation [one an extended Hiickel (119) and the other a parameter-free approximate Hartree-Fock calculation (255)] disagree about the precise ordering of energy levels in this type of complex. 

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