Convergent summation of Moller-Plesset perturbation theory

Rational and algebraic Pade approximants are applied to Moller-Plesset (MP) perturbation expansions of energies for a representative sample of atoms a nd small molecules. These approximants can converge to the full configurati on-interaction result even when partial summation diverges. At order MP2 (t he first order beyond the Hartree-Fock approximation), the best results are obtained from the rational [0/1] Pade approximant of the total energy. At MP3 rational and quadratic approximants are about equally good, and better than partial summation. At MP4, MP5, and MP6, quadratic approximants appear to be the most dependable method. The success of the quadratic approximant s is attributed to their ability to model the singularity structure in the complex plane of the perturbation parameter. Two classes of systems are dis tinguished according to whether the dominant singularity is in the positive half plane (class A) or the negative half plane (class B). A new kind of q uadratic approximant, with a constraint on one of its constituent polynomia ls, gives better results than conventional approximants for class B systems at MP4, MP5, and MP6. For CH3 with the C-H distance at twice the equilibri um value the quadratic approximants yield a complex value for the ground-st ate electronic energy. This is interpreted as a resonance eigenvalue embedd ed in the ionization continuum. (C) 2000 American Institute of Physics. [S0 021-9606(00)30208-2].