The convergence of energy expansions for molecules in electrostatic fields: A linear‐response coupled‐cluster study

Abstract

The radii of convergence of power series expansions describing energy of a molecule in external electrostatic field are investigated usingD’Alembert ratio test, standard and generalized Cauchy–Hadamardcriteria, and Pade approximants. The corresponding coefficients at various field and field‐gradient components, representing multipole moments and (hyper)polarizabilities and including terms of tenth or even twentieth order, are determined using an ab initio linear responsecoupled‐cluster theory. Most calculations are performed for the HF molecule described by the basis set of double zeta quality, while the role of basis set is discussed by comparing the results with estimates of the radii of convergence obtained with the basis set of [5s3p2d/3s2p] quality. Emphasis is placed on the dependence of the interval of convergence of power series expansion describing energy of a molecule in applied electrostatic field on the nuclear geometry. The results might have important implications for various numerical methods used to calculate electrostatic molecular properties as functions of the internuclear geometry, including the finite‐field andfixed‐point‐charge approaches.