Hartree Fock stability

J. Paldus, Hartree-Fock Stability and Symmetry Breaking. In R. Garbo and M. Klobukowski (Eds.) Self-Consistent Field Theory and Applications (Elsevier, Amsterdam, 1990), pp. 1-45. 

Thouless, D. J., The Quantum Mechanics of Many-Body Systems, Academic Press, New York, 1961. The transition from a restricted to an unrestricted wave function is part of the Hartree-Fock stability problem and is closely related to the random phase approximation. The original source of information on this problem is this book. 

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. ... 

DFT and post-Hartree-Fock ab initio studies on the different tautomers and rotamers of 2-hydroxy- (94) and 2,3-dihydroxypyrazine (95) indicate that the former species is stabilized by about -3 kcal/mol with respect to its keto tautomer in the gas phase [99JST229]. In solution the opposite appears to be true. For 95, the hydroxyoxo 95b and diketo tautomers 95c are most stable in the gas phase (Scheme 61). 

Trioxane 210 has been used as a model system by Gu and coworkers to study the antimalarial drug artemisinin 211 (Scheme 137) [97CPL234, 99JST103]. It is the boat/twist form rather than the chair conformer of 210 that describes the subunit in 211. Moreover, geometric parameters and vibrational frequencies can only reliably be computed at the DFT level and by post-Hartree-Fock methods. B3-LYP/6-31G calculations on the conformers of 3,3,6,6-tetramethyl-1,2,4,5-tetroxane show that the chair conformer is stabilized with respect to the twisted conformer by about -2.8 kcal/mol [00JST85]. No corresponding boat conformer was found. 

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]. 

Fischer-type carbene complexes, generally characterized by the formula (CO)5M=C(X)R (M=Cr, Mo, W X=7r-donor substitutent, R=alkyl, aryl or unsaturated alkenyl and alkynyl), have been known now for about 40 years. They have been widely used in synthetic reactions [37,51-58] and show a very good reactivity especially in cycloaddition reactions [59-64]. As described above, Fischer-type carbene complexes are characterized by a formal metal-carbon double bond to a low-valent transition metal which is usually stabilized by 7r-acceptor substituents such as CO, PPh3 or Cp. The electronic structure of the metal-carbene bond is of great interest because it determines the reactivity of the complex [65-68]. Several theoretical studies have addressed this problem by means of semiempirical [69-73], Hartree-Fock (HF) [74-79] and post-HF [80-83] calculations and lately also by density functional theory (DFT) calculations [67, 84-94]. Often these studies also compared Fischer-type and... 

Ab initio Hartree-Fock calculations have been used to study the stability of the 4H- and 9a//-tautorners (17 and 18, respectively) of a series of derivatives of tetramethyl quinolizine-l,2,3,4-tetracarboxylate. These calculations (Table 1) have confirmed that the 411-tautomer is the thermodynamically more stable form <2003JST719>. 

The inherent problems associated with the computation of the properties of solids have been reduced by a computational technique called Density Functional Theory. This approach to the calculation of the properties of solids again stems from solid-state physics. In Hartree-Fock equations the N electrons need to be specified by 3/V variables, indicating the position of each electron in space. The density functional theory replaces these with just the electron density at a point, specified by just three variables. In the commonest formalism of the theory, due to Kohn and Sham, called the local density approximation (LDA), noninteracting electrons move in an effective potential that is described in terms of a uniform electron gas. Density functional theory is now widely used for many chemical calculations, including the stabilities and bulk properties of solids, as well as defect formation energies and configurations in materials such as silicon, GaN, and Agl. At present, the excited states of solids are not well treated in this way. 

As has been pointed out in the past (e.g. concerning the linear-cyclic equilibrium in Ceand Cio carbon clusters (40)), Hartree-Fock underestimates the resonance stabilization of aromatic relative to non-aromatic systems (in the case at hand, between the N- and / -protonated isomers) and MP2 overcorrects. The structures are found to be nearly isoenergetic at the CCSD level inclusion of connected triple excitations favors the N-protonated ion. The direction of the effect of connected quadruples is somewhat unclear, and a CCSD(TQ) or CCSDT(Q) calculation impossible on systems this size, but the contribution will anyhow be much smaller in absolute magnitude than that of connected triple excitations, particularly for systems like these which are dominated by a single reference determinant. We may therefore infer that at the full Cl limit, the N-protonated species will be slightly more stable than its / -protonated counterpart. 

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