Hartree-Fock energy curve

A major weakness of the Hartree-Fock method is its failure to give accurate molecular dissociation energies. For example, an extended-basis-set calculation [P. E. Cade et al., /. Chem. Phys., 44,1973 (1966)] gives = 5.3 eV for N2, as compared with the true value 9.9 eV. (To calculate the Hartree-Fock D the molecular energy at the minimum in the U R) Hartree-Fock curve is subtracted from the sum of the Hartree-Fock energies of the separated atoms.) For F2 the true /) is 1.66 eV, while the Hartree-Fock is —1.4 eV. In other words, the Hartree-Fock calculation predicts the separated atoms to be more stable than the fluorine molecule. A related defect... 

Fig. 8.10. Ground-state potential-energy curves of BH in the cc-pCVTZ basis (in atomic units). On the left, we have plotted the Hartree-Fock energy (thick grey line), the FCI energy with a frozen core (thin full line) and the FQ energy without a frozen core (dotted line). On the right, we have plotted the corresponding valence correlation energy (full line) and core correlation eneigy (dotted line).

Fig. SJZl. The error in the N2 Hartree-Fock energy (in mEh) for the cc-pVXZ basis sets as a function of the cardinal number X. The upper curve represents the error in the molecular energy, whereas the lower curve represents the error in the energy of the atomic fragments.

The presence or absence of a homoaromatic interaction is often based solely on the distance between the non-bonded atoms. Distances greatly over 2.0 A are thought to lead to a p-p overlap that is too small to make any significant contribution. This simplistic approach is not necessarily reliable as shown by Cremer et al. (1991). Their calculations on the homotropylium cation [12] indicate a double-minimum potential energy surface with respect to variations of the C(l)-C(7) distance at the Hartree-Fock level of theory. At the MP4(SDQ) level of theory, only a single-minimum curve was found with the minimum at 2.03 A. The calculated potential energy curves are quite flat in this region. 

As an illustrative example, the energy curves showing the convergence of the overall process for both the regulated CSE process without purification and the regulated CSE process with 15 purification iterations of the calculations of the Li2 molecule are shown in Fig. 9. The two horizontal lines correspond to the Hartree-Fock and the full Cl energy values. As can be noticed, both the accuracy and the convergence rate are remarkably improved when purification is carried out. 

Figure 10. Stretching potential energy curve of Li2 calculated by the Hartree-Fock, regulated CSE-NS, and full Cl methods.

Figure 1 This figure shows the ground-state energies of the 6-electron iso-electronic series of atoms and ions, C, iV, 0 +, etc., as a function of the atomic number, Z. The energies in Hartrees, calculated in the crudest approximation, with only one 6-electron Sturmian basis function (as in Table 1), are represented by the smooth curve, while dementi s Hartree-Fock values [10] are indicated by dots. 

Figure 2. Total energy of the alternate chain versus A-subband filling. Upper curve Hartree-Fock result, Lower curve Gutzwiller result. The 2 minima are clearly different.

Fig. 3.6 Binding energy curves for the hydrogen molecule (lower panel). HF and HL are the Hartree-Fock and Heitler-London predictions, whereas LDA and LSDA are those for local density and local spin density approximations respectively. The upper panel gives the local magnetic moment within the LSDA self-consistent calculations. (After Gunnarsson and Lundquist (1976).)...

---