Stieltjes imaging of photoabsorption and dispersion profiles

Abstract

Variational and moment‐theory techniques for the construction of accurate approximations to photoabsorption and dispersion profiles in atoms and molecules are described and applied to simple atomic systems. It is shown that appropriately defined principal pseudostates, when employed in ab initio variational calculations, furnish the discrete transition frequencies and oscillator strengths that provide so‐called principal representations of spectral moments. The Tchebycheff‐Stieltjes‐Markoff moment theory ensures that the principal frequencies and strengths furnish the information necessary for constructing convergent images of both the discrete and continuum portions of photoabsorption profiles. Evaluation of the appropriate principal value integrals results in convergent Stieltjes images of the associated photodispersion profiles. Detailed applications in the cases of the negative hydrogen ion and atomic hydrogen show that the Stieltjes imaging procedure is rapidly convergent for both the discrete and continuum portions of absorption and dispersion profiles in simple systems. Additional illustrative applications in the cases of atomic helium and lithium show that photoabsorption profiles with simple structures can be accurately imaged even when the pseudostates employed are not necessarily principal ones. The present development extends previously described variational and moment‐theory techniques for approximating frequency‐dependent dipole polarizabilities in their analytic regions to the real frequency axis within photoabsorption intervals. Moreover, the Stieltjes theory shows that conventional configuration interaction methods with square‐integrable basis functions can be employed in the calculation of principal pseudostates and associated photoabsorption and dispersion profiles, thereby avoiding the explicit construction of accurate approximations to the complete set of discrete and continuum eigenstates required in more customary approaches.