Calculations of electric dipole moments and static dipole polarizabilities based on the two-component normalized elimination of the small component method

Abstract

The analytical energy gradient and Hessian of the two-component Normalized Elimination of the Small Component (2c-NESC) method with regard to the components of the electric field are derived and used to calculate spin-orbit coupling (SOC) corrected dipole moments and dipole polarizabilities of molecules, which contain elements with high atomic number. Calculated 2c-NESC dipole moments and isotropic polarizabilities agree well with the corresponding four-component-Dirac Hartree-Fock or density functional theory values. SOC corrections for the electrical properties are in general small, but become relevant for the accurate prediction of these properties when the molecules in question contain sixth and/or seventh period elements (e.g., the SO effect for At is about 10% of the 2c-NESC polarizability). The 2c-NESC changes in the electric molecular properties are rationalized in terms of spin-orbit splitting and SOC-induced mixing of frontier orbitals with the same j = l + s quantum numbers.

2018 Table of static dipole polarizabilities of the neutral elements in the periodic table

“…[154] S 0 , 4d 10 48. 1 S 0 , 4f 14 144.6 ± 5.6 R, Dirac, coupled cluster [180] 1 S 0 , 4f 14 140.7 ± 7.0 R, Dirac + Gaunt, CCSD(T) 14 141 ± 6 R, Dirac, CI + MBPT + experimental data, see also ref [182] for error estimates [183] 1 S 0 , 4f 14 142.6 ECP, CCSD(T) [174] S 0 , 4f 138.9 R, Dirac, CI + MBPT + CP(RPA); (α D = 312.2 for the 4f 14 6s 1 6p 1 configuration) [138] 1 S 0 , 4f 14 142 R, RPA, PolPot [184] 1 S , 4f 14 144 R, CCSD, PolPot [185] 1 S 0 , 4f 14 141 ± 2 R , C I + MBPT + RPA [186] 1 S 0 , 4f 14 141 ± 4 R , D H F + Breit + QED, PP [82,179] 1 S 0 , 4f 14 145.3 ± 4.4 R, Dirac, CCSD(T) [187] 1 S 0 , 4f 14 135.73 R, DFT, CAM-B3LYP, 2c-NESC [187] 1 S 0 , 4f 14 147.26 R, DFT, PBE0, 2c-NESC [180] 1 S 0 , 4f 14 140.44 R, Dirac, CCSD(T) [179] 1 S 0 , 4f 14 152.9 R, Dirac, CCSD(T) [188] 1 S 0 , 4f 14 143 R, DCHF, CCSD(T), ECP [144] 1 S 0 , 4f 14…”

Dieter Cremer's contribution to the field of theoretical chemistry

“…For example, for the series of HgX 2 molecules (X = F, Cl, Br, I), the interplay between SOC and ligand field effects leads to a change of the character of low‐lying valence spinors from predominantly σ ‐type to π ‐type . Recently, analytical first derivatives were developed for the two‐component NESC method as well as for the calculation of electric dipole moments and static dipole polarizabilities and atomic magnetic nuclear shielding constants …”

Quasi-Relativistic Calculation of EPR g-Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

“…This one-electron Hamiltonian is then commonly combined with the non-relativistic two-electron interaction. Herein, we account for the missing two-electron picture-change correction with the modied screened nuclear spinorbit (mSNSO) ansatz, 57,61,117,118…”