Hartree-Fock convergence

Bacskay G B 1981 A quadratically convergent Hartree-Fock (QC-SCF) method. Applications to the closed-shell case Chem. Phys. 61 385... 

Schmidt M W and Ruedenberg K 1979 Effective convergence to compiete orbitai bases and to the atomic Hartree-Fock iimit through systematic sequences of Gaussian primitives J. Chem. Phys. 71 3951-62... 

Not all iterative semi-empirical or ab initio calculations converge for all cases. For SCF calculations of electronic structure, systems with a small energy gap between the highest occupied orbital and the lowest unoccupied orbital may not converge or may converge slowly. (They are generally poorly described by the Hartree-Fock method.)... 

Ab initio calculations are iterative procedures based on self-consistent field (SCF) methods. Normally, calculations are approached by the Hartree-Fock closed-shell approximation, which treats a single electron at a time interacting with an aggregate of all the other electrons. Self-consistency is achieved by a procedure in which a set of orbitals is assumed, and the electron-electron repulsion is calculated this energy is then used to calculate a new set of orbitals, which in turn are used to calculate a new repulsive energy. The process is continued until convergence occurs and self-consistency is achieved." ... 

The UHF curve is much higher than those for the correlation methods Hartree-Fock theory does a relatively poor job of describing this process. The MP2 curve is somewhat higher than those for the MP3 and MP4(SDTQ) levels, which appear to have converged. 

The MPn method treats the correlation part of the Hamiltonian as a perturbation on the Hartree-Fock part, and truncates the perturbation expansion at some order, typically n = 4. MP4 theory incorporates the effect of single, double, triple and quadruple substitutions. The method is size-consistent but not variational. It is commonly believed that the series MPl, MP2, MP3,. .. converges very slowly. 

Lowdin, P.-O., Phys. Rev. 97, 1474, 1490, 1509, Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin-orbitals and convergence problems in the method of configuration interaction. II. Study of the ordinary Hartree-Fock approximation. III. Extension of the Har-tree-Fock scheme to include degenerate systems and correlation effects. ... 

The difficulty of determining the Half-Projected Hartree-Fock function has somewhat hampered its utilization [3-10]. Some calculations, however, exist in literature. At present time, because of the increasing computing facilities, as well as the introduction of more powerful convergence techniques, the HPHF model is expected to play a more important role, especially in the field of medium size molecules, in which the use of more sophisticated procedure are not yet possible [9-10]. 

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