Ansatz for the evaluation of the relativistic contributions to core ionization energies in complex molecules involving heavy atoms

Abstract

ABSTRACT:On the basis of numerical, ab initio ⌬DF and ⌬HF computations of 1s-core, 2s-core, and 2p-core ionization energies of atoms, from Li through Xe, an allometric empirical formula that was proposed for evaluating relativistic corrections (including QED effects) to nonrelativistic values is assessed for homogeneous sets of elements in the periodic table. The two coefficients involved in this formula are precisely determined for 1s-core ionization in the sets of atoms Be-Ne, Mg-Ar, Zn-Kr, and Cd-Xe; 2s-core ionization in the sets of atoms Mg-Ar, Zn-Kr, and Cd-Xe; and 2p-core ionization in the set Mg-Ar. It is shown that the medium relative error on the results obtained using this formula, with respect to those directly computed, decreases from a few percent to a few hundredths of 1% when the depth of the ionized level increases. This formula could be used to include relativistic (and QED) corrections to results yielded by simpler, nonrelativistic calculations on complex molecules involving heavy atoms.

Electron cross relaxation as a function of single relaxation contributions in double‐core ionization energies and spin–orbit splitting of atoms from Ar to Ba. I. 1s−2p− double‐core holes

“…For elements from Ar to Ba (excluding transition elements), we have computed the nonrelaxed and relaxed core ionization energies for the single 1s, 2p 1/2 , and 2p 3/2 and double 1s‐2p 1/2 and 1s‐2p 3/2 ionizations, using procedures similar to those used in earlier papers 14–17.…”

“…In previous papers 14–17 we have investigated the relaxation and relativity effects in the 1s 14, 16, 2s 15, 16 and 2p 16, 17 core ionization energies of neutral atoms in the series LiXe, BXe, and ClBa. Owing to shell effects 18, 19, the variations of the energy contributions with atomic number Z are not monotonous but involve an irregular oscillating part.…”

“…Therefore, no monotonous expression can yield a perfect fit of these contributions through the periodic table. Different expressions were fitted separately for families of atoms whose external configuration expresses the filling of a given subshell 16, 17.…”

“…In earlier work 27 we have tried to relate two satellites observed in the XPS near‐edge spectrum of SF 6 to (1s, 2p) “singlet” and “triplet” double‐core excitations, using a procedure of progressive corrections to simpler computations that was to be developed in later papers 14–17. The contribution of “cross relaxation,” due to the simultaneous occurrence of two core holes, played an important role in the methodology that we used.…”

Accurate calculation of C1s core electron binding energies of some carbon hydrates and substituted benzenes

“…The relativistic correction to the 1s carbon CEBE of 0.05 eV is small, but it is not negligible. For heavier atoms, the relativistic correction and its inclusion is indispensable [11,12]. This is the rationale for considering a relativistic effect.…”