Diagrammatic perturbation theory: Many-body effects in the X1Σ+ states of first-row and second-row diatomic hydrides

Diagrammatic many-body perturbation theory is employed in a study of the X1Σ+ states oif first- and second-row diatomic hydrides at their respective equilibrium nuclear separations. All two-, three-, and four-body terms are determined through third-order in the energy within the algebraic approximation (i.e., parameterization of state functions by expansion in a finite basis). Padé approximants to the energy are constructed. From the first-order wavefunction rigorous upper bounds to the expectation value of the electronic energy are obtained from the Rayleigh quotient. Two different zero-order Hamiltonians are used, and the convergence properties of the resulting perturbation expansions are compared. In both schemes three- and four-body terms are significant, having a magnitude that is as much as 24% of the sum of the second- and third-order terms.