Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: Where it is shown how finite oligomer chains tend to the infinite periodic polymer The calculation of the static first and second susceptibilities of crystalline urea: A comparison of Hartree-Fock and density functional theory results obtained with the periodic coupled perturbed Hartree-Fock/Kohn-Sham scheme We compute molecular Hartree-Fock-Kohn-Sham correlation potentials from ab initio coupled-cluster densities via a modified Zhao, Morrison and Parr Phys. Rev. A, 50, 1994 2138 scheme involving exact exchange. We examine the potential for several small systems, and observe complex structure. By fitting a functional expansion to our potentials we obtain a closed-shell functional which is an improvement over other pure correlation functionals in Hartree-Fock-Kohn-Sham calculations. The leading term in our functional is dependent on the number of electrons. Our results lead us to question the utility of correlation defined within the Hartree-Fock-Kohn-Sham scheme, and to consider alternative partitionings of the exchange-correlation energy.
Local ͑multiplicative͒ effective exchange potentials obtained from the linear-combinationof-atomic-orbital ͑LCAO͒ optimized effective potential ͑OEP͒ method are frequently unrealistic in that they tend to exhibit wrong asymptotic behavior ͑although formally they should have the correct asymptotic behavior͒ and also assume unphysical rapid oscillations around the nuclei. We give an algebraic proof that, with an infinity of orbitals, the kernel of the OEP integral equation has one and only one singularity associated with a constant and hence the OEP method determines a local exchange potential uniquely, provided that we impose some appropriate boundary condition upon the exchange potential. When the number of orbitals is finite, however, the OEP integral equation is ill-posed in that it has an infinite number of solutions. We circumvent this problem by projecting the equation and the exchange potential upon the function space accessible by the kernel and thereby making the exchange potential unique. The observed numerical problems are, therefore, primarily due to the slow convergence of the projected exchange potential with respect to the size of the expansion basis set for orbitals. Nonetheless, by making a judicious choice of the basis sets, we obtain accurate exchange potentials for atoms and molecules from an LCAO OEP procedure, which are significant improvements over local or gradient-corrected exchange functionals or the Slater potential. The Krieger-Li-Iafrate scheme offers better approximations to the OEP method.
Using the optimized effective potential (OEP) method in conjunction with an orbital-dependent correlation functional developed on the basis of second-order many-body perturbation theory [MBPT(2)], we perform ab initio correlated density functional calculations. Unlike other density functional methods, this offers the first correlation approximation in a converging series of approximations analogous to that in wave function theory. The OEP-MBPT(2) correlation potentials of the helium isoelectronic series and the neon atom are in excellent agreement with prior quantum Monte Carlo (QMC) results, while the widely used conventional approximate density functional theory correlation potentials have qualitatively incorrect behavior. Furthermore, the correlation energies, total energies, and the highest occupied orbital energies calculated by the OEP-MBPT(2) method are also remarkably accurate. Unlike QMC, our procedure can be applied to general molecules.
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