Generalized x-ray scattering factors in diatomic molecules

Abstract

Generalized x‐ray scattering factors for atoms (pseudoatoms) in diatomic molecules are determined from a finite multipole expansion of the charge density about each nucleus. The Fourier–Bessel coefficients of the pseudoatom radial density functions are determined by a least squares fit to the molecular form factor. All molecular one‐center averages of the form 〈g (r_a) P_j(cosϑ_a) 〉 are correctly given by the pseudoatom superposition whenever j?J, where J is the highest order multipole included in the a pseudoatom, regardless of the highest multipole order K for the b pseudoatom. To illustrate this property, a number of relationships between moments of the molecular charge distribution and of the pseudoatom are given. In addition, a sum rule relating the molecular form factor to the expectation values 〈r_a^−(j+1)P_j(cosϑ_a) 〉 and 〈r_b^−(k+1)P_k(cosϑ_b) 〉 is derived. For H₂ the theoretical, coherent x‐ray scattering intensity is reproduced to about 1% for J=K=1 and to about 0.1% for J=K=2.