Static and Frequency‐Dependent Dipole–Dipole Polarizabilities of All Closed‐Shell Atoms up to Radium: A Four‐Component Relativistic DFT Study

Abstract

We test the performance of four-component relativistic density functional theory by calculating the static and frequency-dependent electric dipole-dipole polarizabilities of all (ground-state) closed-shell atoms up to Ra. We consider 12 nonrelativistic functionals, including three asymptotically shape-corrected functionals, by using two smooth interpolation schemes introduced by the Baerends group: the gradient-regulated asymptotic connection (GRAC) procedure and the statistical averaging of (model) orbital potentials (SAOP). Basis sets of doubly augmented triple-zeta quality are used. The results are compared to experimental data or to accurate ab initio results. The reference static electric dipole polarizability of palladium has been obtained by finite-field calculations using the coupled-cluster singles, doubles, and perturbative triples method within this work. The best overall performance is obtained using hybrid functionals and their GRAC shape-corrected versions. The performance of SAOP is among the best for nonhybrid functionals for Group 18 atoms but its precision degrades when considering the full set of atoms. In general, we find that conclusions based on results obtained for the rare-gas atoms are not necessarily representative of the complete set of atoms. GRAC cannot be used with effective core potentials since the asymptotic correction is switched on in the core region.

Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

“…[132][133][134][135][136] and references therein). Aiming at a comprehensive assessment, one could furthermore take into account complexes of Mössbauer active isotopes such as 127 I or 129,131 Xe for which it would be interesting to study the p 1/2 contributions to the relative shift. Concerning the performance of the coupled-cluster wave function methods, on the other hand, we observe a partially distinctive effect of the inclusion of perturbative triples on the relative shift of the electron density.…”

“…This is contrary to what one would expect from looking at the 6s 1/2 orbital energy in the neutral atom, which at the TZ?2s1p level is À0:328 E h ; À0:261 E h and -0.274 E h at the HF, LDA and B3LYP levels, respectively. DFT, however, yields a more compact 6s 1/2 orbital (the radial rms value is 4:33 a 0 ; 4:06 a 0 and 4:14 a 0 for HF, LDA and B3LYP, respectively) which in turn leads to a smaller polarizability [131] and larger contact density (cf. Table 10).…”

Relativistic Time-Dependent Density Functional Theory and Excited States Calculations for the Zinc Dimer

“…For excited states resulting from a single excitation that present a single jump from the ground state to an excited state, I used in this work the LRA as implemented in Dirac-Package [26][27][28] and well-known approximations of density functionals like LDA (SVWN5 correlation) [29,30], PBE [31], PB86 [32][33][34], BPW91 (Becke exchange [32] and Perdew-Wang correlation [35]), long-range corrected PBE0 [36] and its gradient corrected functional GRAC-PBE0 [37,38], BLYB and B3LYP [32,[39][40][41], or newly developed range-separated functionals such as CAMB3LYP [42]. Today's available DFT cannot describe the ground state of the group IIB dimers accurately due to a large contribution of dispersion in the bonding [12], despite this when calculating the covalently well-bound excited states the error is reduced considerably, quite possible accompanied with error cancellations.…”

“…Exciting electrons from σ 2 g or σ 2 u to the lowest set of molecular orbitals spanned by the atomic orbitals Atom(ns 2 ) + Atom(nsnp) or Atom(ns 2 ) + Atom(ns(n + 1)s), or Atom(ns 2 ) + Atom(ns(n + 1)p) gives rise to a manifold of states (see Table 2) among them states which strongly have covalent contributions as we will see in Section 4 Results and Discussion. This makes TDDFT using LRA and well-known functional approximations, adequate to describe these states [26].…”

“…In the relativistic Dirac theory in absence of electromagnetic field, the DCH has the same generic form as the NR Hamiltonian (for molecules) [26,48]:…”