Convergent summation of Møller–Plesset perturbation theory

Abstract

Rational and algebraic Padé approximants are applied to Møller–Plesset (MP) perturbation expansions of energies for a representative sample of atoms and small molecules. These approximants can converge to the full configuration–interaction result even when partial summation diverges. At order MP2 (the first order beyond the Hartree–Fock approximation), the best results are obtained from the rational [0/1] Padé 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 approximants is attributed to their ability to model the singularity structure in the complex plane of the perturbation parameter. Two classes of systems are distinguished 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 quadratic approximant, with a constraint on one of its constituent polynomials, 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 equilibrium value the quadratic approximants yield a complex value for the ground-state electronic energy. This is interpreted as a resonance eigenvalue embedded in the ionization continuum.