Correlation Energy Estimators based on M{\o}ller-Plesset Perturbation Theory

Some methods for the convergence acceleration of the M{\o}ller-Plesset perturbation series for the correlation energy are discussed. The order-by-order summation is less effective than the Feenberg series. The latter is obtained by renormalizing the unperturbed Hamilton operator by a constant factor that is optimized for the third order energy. In the fifth order case, the Feenberg series can be improved by order-dependent optimization of the parameter. Alternatively, one may use Pad{\'e} approximants or a further method based on effective characteristic polynomials to accelerate the convergence of the perturbation series. Numerical evidence is presented that, besides the Feenberg-type approaches, suitable Pad{\'e} approximants, and also the effective second order characteristic polynomial, are excellent tools for correlation energy estimation.Comment: 21 pages, 87 references, LaTeX2e, elsart.cls, uuencoded compressed tar file created by csh script uufiles. J. Mol. Struct. (THEOCHEM), in press. Postscript and dvi also available via http://www.chemie.uni-regensburg.de/preprint.html and ftp://rchs1.uni-regensburg.de/pub/preprint/TC-QM-96-

Series Prediction based on Algebraic Approximants

It is described how the Hermite-Pad\'e polynomials corresponding to an algebraic approximant for a power series may be used to predict coefficients of the power series that have not been used to compute the Hermite-Pad\'e polynomials. A recursive algorithm is derived and some numerical examples are given.Comment: 9 pages, ISRN Applied Mathematics, in pres

On Convergence Acceleration of Multipolar and Orthogonal Expansions

Multipolar expansions arise in many branches of the computational sciences. They are an example of orthogonal expansions. We present methods for the convergence acceleration of such expansions. As an example, the computation of the electrostatic potential and its multipolar expansion is treated for the case of a two-center charge density of exponential-type orbitals. This potential may also be considered as a special molecular integral, namely as a three-center nuclear attraction integral. It is shown that in this example, the extrapolation to the limit of the corresponding expansions via suitable nonlinear sequence transformations leads to a pronounced convergence acceleration

Spin-Lattice Relaxation in Metal-Organic Platinum(II) Complexes

The dynamics of spin-lattice relaxation (slr) of metal-organic Pt(II) compounds is studied. Often, such systems are characterized by pronounced zero-field splittings (zfs) of the lowest-lying triplets. Previous expressions for the Orbach slr process do not allow to treat such splitting patterns properly. We discuss the behavior of a modified Orbach expression for a model system and present results of a fit of the temperature dependence of the spin-lattice relaxation rate of Pt(2-thpy)$_2$ based on the modified expression.Comment: 9 pages, 3 figures (made from 4 .eps files), elsart.cls. Using dvips (dvipsk 5.58f), it may be necessary to manually edit the generated file letter.ps to change in the first line from PS-Adobe-2.0 to PS-Adobe-3.0. Chemical Physics Letters, in pres