On a Khovanskii transformation for continued fractions

AbstractSome aspects of a transformation for continued fractions due to Khovanskii are studied. It is shown that the transformation does not in general establish an identity, but has many interesting properties. It permits to transform some difficult continued fractions into suitable ones. Its even part is identical to the even part of Sn(−12) modification. It may also give acceleration for some slow continued fractions

Density-functional embedding using a plane-wave basis

The constrained electron density method of embedding a Kohn-Sham system in a substrate system (first described by P. Cortona, Phys. Rev. B {\bf 44}, 8454 (1991) and T.A. Wesolowski and A. Warshel, J. Phys. Chem {\bf 97}, 8050 (1993)) is applied with a plane-wave basis and both local and non-local pseudopotentials. This method divides the electron density of the system into substrate and embedded electron densities, the sum of which is the electron density of the system of interest. Coupling between the substrate and embedded systems is achieved via approximate kinetic energy functionals. Bulk aluminium is examined as a test case for which there is a strong interaction between the substrate and embedded systems. A number of approximations to the kinetic-energy functional, both semi-local and non-local, are investigated. It is found that Kohn-Sham results can be well reproduced using a non-local kinetic energy functional, with the total energy accurate to better than 0.1 eV per atom and good agreement between the electron densities.Comment: 11 pages, 4 figure

Obtaining a gradient-corrected kinetic-energy functional from the Perdew-Wang exchange functional

Lee, Lee, and Parr (LLP) have shown that the kinetic energy can be written in the same form as Becke's exchange energy. This conjecture of LLP has been generalized to another exchange functional, namely, the Perdew-Wang exchange functional. As demonstrated by Lee and Parr, the exchange energy can be written K=πFFsΓ(r,s)drds with Γ(r,s)=||γ(r,s)||2¯/n2(r), where ||γ(r,s)||2¯ is the spherical average of ||γ(r,s)||2. Using the generalization of LLP's conjecture, it is demonstrated that Γ(r,s)= e-s2/β(r)+a[s4/β02(r)]e-s2/β0(r), a=const, β0(r)=5[3π2n(r)]-2/3. At zeroth order, β(r)=β0(r), the function Γ(r,s), gives exactly the modified Gaussian approximation proposed by Lee and Parr

Gradient-corrected exchange potential with the correct asymptotic behavior and the corresponding exchange-energy functional obtained from the virial theorem

In density-functional theory (DFT), Perdew, Parr, Levy, and Balduz [Phys. Rev. Lett. 49, 1691 (1982)] have shown that for all the electronic systems, the energy of the highest occupied molecular orbital (HOMO) is equal to the negative of the ionization potential. This equality is not recovered within the different approximations of the exchange-correlation functional proposed in the literature. The main reason is that the exchange-correlation potentials of various functionals used in DFT calculations decay rapidly to zero whereas they should exhibit a Coulombic asymptotic -1/r behavior. In this work we propose a gradient-corrected (GC) exchange potential with a correct asymptotic -1/r form for large values of r. The energy of the HOMO calculated with this potential is improved compared to the local-density approximation (LDA) and to the GC functionals widely used in the DFT. Our HOMO eigenvalues are compared to the optimized-potential-model eigenvalues which are the exact values for the exchange-only potential. Using the fact that the LDA satisfies the virial theorem, the exchange energy corresponding to this GC exchange potential can be calculated under a simple assumption