Hartree-Fock theory predictions from

Hartree-Fock theory does quite a poor job of predicting the structures and frequencies for these compounds. It produces highly distorted structures in all three cases, and its computed frequencies bear little resemblance to the experimental observations. MP2 theory generally does better for the structures, although it fails to located a distorted structure for Na F3. The frequencies computed at the MP2 level also vary widely from experiment. 

The Fermi liquid as well as the Hartree-Fock theory, however, can hardly account for the observed temperature dependence of the spin susceptibility obtained at constant volume - namely, corrected for thermal dilatation of the sample - which shows a monotonic but sizable growth as the temperature increases (Fig. 8) [53, 54, 58]. This variation turns out to be much faster than the one expected from the H-F theory, which only predicts a F (T) with a very slow temperature dependence that is spread out over on a temperature scale [58, 59]. 

However, one must also be cautious when interpreting the results of approximate MO models. It is all too easy to endow the approximate method with the same virtues as the more rigorous ab initio scheme from which they are derived. Fenske has described [23] some of the possible pitfalls. For example, in Hartree-Fock theory there is a rigorous relationship between the stability of a molecule and its computed energy. Taking two isomeric species as an example, the one with the lowest computed energy is predicted to be the most stable. This relationship is often employed with approximate MO methods but it is no longer strictly valid. 

The Hartree-Fock values range from good to quite poor. For the first reaction, cancellation of errors allows Hartree-Fock theory to predict a good value for AH (it overestimates the energies for both ethane and acetone, and underestimates the one for acetaldehyde). 

Optimize the structure of acetyl radical using the 6-31G(d) basis set at the HF, MP2, B3LYP and QCISD levels of theory. We chose to perform an Opt Freq calculation at the Flartree-Fock level in order to produce initial force constants for the later optimizations (retrieved from the checkpoint file via OptsReadFC). Compare the predicted spin polarizations (listed as part of the population analysis output) for the carbon and oxygen atoms for the various methods to one another and to the experimental values of 0.7 for the C2 carbon atom and 0.2 for the oxygen atom. Note that for the MP2 and QCISD calculations you will need to include the keyword Density=Current in the job s route section, which specifies that the population analysis be performed using the electron density computed by the current theoretical method (the default is to use the Hartree-Fock density). 

Ab initio Hartree-Fock and density functional theory (DFT) calculations were performed to study transition geometries in the intramolecular hetero-Diels-Alder cycloaddition reactions of azoalkenes 20 (LJ = CH2, NFI, O) (Equation 1). The order of the reactivities was predicted from frontier orbital energies. DFT calculations of the activation energies at the B3LYP level were in full agreement with the experimental results described in the literature <2001JST(535)165>. 

In most cases, the orbital relaxation contribution is negligible and the Fukui function and the FMO reactivity indicators give the same results. For example, the Fukui functions and the FMO densities both predict that electrophilic attack on propylene occurs on the double bond (Figure 18.1) and that nucleophilic attack on BF3 occurs at the Boron center (Figure 18.2). The rare cases where orbital relaxation effects are nonnegligible are precisely the cases where the Fukui functions should be preferred over the FMO reactivity indicators [19-22], In short, while FMO theory is based on orbitals from an independent electron approximation like Hartree-Fock or Kohn-Sham, the Fukui function is based on the true many-electron density. 

Continuum model has been applied for the first time to predict the Fukui functions of formaldehyde, methanol, acetone, and formamide in water medium [54], The results reveal that the potential for electrophilic and nucleophilic attack increases when passing from the gas phase to an aqueous medium. The calculated Fukui functions for formaldehyde at Hartree-Fock (HF) level of theory are presented in Table 26.2. 

Figure 4 Overview of several theoretical predictions for the SE Brueckner-Hartree-Fock (continuous choice) with Reid93 potential (circles), self-consistent Green function theory with Reid93 potential (full line), variational calculation from [9] with Argonne Avl4 potential (dashed line), DBHF calculation from [16] (triangles), relativistic mean-field model from [22] (squares), effective field theory from [23] (dash-dotted fine).

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