HF level of theory

The tables below give some examples of atomic charges and bond orders calculated by various methods as a function of the basis set at the HF level of theory. It is evident that the Mulliken and Ldwdin methods do not converge as the basis set is increased, and the values in general behave unpredictably. Especially the presence of diffuse functions lead to absurd behaviours, as the aug-cc-pVXZ basis sets illustrate for CH4. Note also that... 

We need to look at the convergence as a function of basis set and amount of electron correlation (Figure 4.2). For the former we will use the correlation consistent basis sets of double, triple, quadruple, quintuple and, when possible, sextuple quality (Section 5.4.5), while the sensitivity to electron correlation will be sampled by the HF, MP2 and CCSD(T) methods (Sections 3.2, 4.8 and 4.9). Table 11.1 shows how the geometry changes as a function of basis set at the HF level of theory. 

Table 11.1. H2O geometry as a function of basis set at the HF level of theory ...

At the HF level of theory, the operator corresponds to addition of an extra term to the Fock matrix elements (Section 3.5). 

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. 

Structure and reactivity of (thionitroso)ethylene 9 have been examined by ab initio methods at the post-Hartree-Fock (HF) level of theory. This compound is expected to undergo electrocyclic ring closure to the more stable 4/7-1,2-thiazete 3. Geometrical bond length and dihedral angle parameters at the stationary points of the electrocyclic reactions of thionitrosoethylene were calculated at the RMP2/6-31G level of theory (Scheme 1) <1996LA1615>. 

The error associated with the HF level of theory with regard to the neglect of electron correlation (see Section 6.II) tends to lower the energy difference between X+ and X. This is because the correlation effects are larger for the neutral species that has one more electron than the cation (a more comprehensive quantum chemical treatment, including electron correlation would lower the energy of X more than the one of X+). 

In general, for each acid HA, the HA-(H20) -Wm model reaction system (MRS) comprises a HA (H20) core reaction system (CRS), described quantum chemically, embedded in a cluster of Wm classical, polarizable waters of fixed internal structure (effective fragment potentials, EFPs) [27]. The CRS is treated at the Hartree-Fock (HF) level of theory, with the SBK [28] effective core potential basis set complemented by appropriate polarization and diffused functions. The W-waters not only provide solvation at a low computational cost they also prevent the unwanted collapse of the CRS towards structures typical of small gas phase clusters by enforcing natural constraints representative of the H-bonded network of a surface environment. In particular, the structure of the Wm cluster equilibrates to the CRS structure along the whole reaction path, without any constraints on its shape other than those resulting from the fixed internal structure of the W-waters. 

Quantum chemical calculations of the Ne potential-energy hypersurface have shown that the qualitative shape shongly depends on the choice of the theoretical method and basis set. All the geometries represented in Scheme 6 have been shown to be minima on the potential smface, but most of them do not possess minima at all the levels of theories applied. Hexaazabenzene (13), for example, has a minimum for a stmctme at the HF level of theory. However, this geometry is a second-order saddle point with the density functional theory (DFT) and also at the MP2 level of theory. D2 hexaazabenzene has a minimum structure at DFT, but at the CCSD(T)/aug-cc-pVDZ level, the D2 geometry resembles a van der Waals complex of two N3 units, whereas it is a minimum structure at the CCSD(T)/cc-pVTZ level of theory. Similar behavior has been observed for most of the other isomers. 

Wang, Y.-G. andWerstiuk, N.H. (2003) A practical and efficient method to calculate AIM localization and delocalization indices at post-HF levels of theory. /. Comput. Chem., 24, 379—385. 

In section 5.2 the concepts of hermiticity and time-reversal where introduced in the discussion of the first order response of the wave function. In this section we shall see that these concepts allows us to determine whether the linear response function is real or imaginary. The linear response function is given by (51), but using the first-order response equation (49) it may be simplified to (54). This may reduce the precision in the numerical evaluation, but is of no consequence for the following arguments. In the notation of section 5.2 the linear response function at the closed-shell HF level of theory is accordingly written... 

The reason for this unusual geometry was the availability of only the stereochemically active electrons for bonding. Thus, a SO modification of the valence shell electron pair repulsion (VSERP) theory was suggested in [130]. Han et al. [129], however, claim that this modification should be applied with caution, since no non-linear II8F2 structure has been detected as a minimum at the HF level of theory. An important observation was made that the fluorides of element 118 will most probably be ionic rather than covalent, as in the case of Xe. This prediction might be useful for future gas-phase chromatography experiments. 

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