Fully relativistic coupled cluster and DFT study of electric field gradients at Hg in 199Hg compounds

Abstract

We investigate the magnitude and interplay of relativistic and electron correlation effects on the electric field gradient (EFG) at the position of Hg in linear and bent HgL(2) (L = CH(3), Cl, Br, I) and trigonal planar [HgCl(3)](-) compounds using four-component relativistic Dirac-Coulomb (DC) and non-relativistic (NR) calculations at the Hartree-Fock (HF), DFT, MP2 and coupled cluster (CC) levels. The relativistic and electron correlation contributions to EFG have opposite signs and are not additive, demonstrating the importance of taking into account relativistic and electron correlation contributions on an equal footing. DC-MP2 overestimates the electron correlation correction by 0.48-0.56 a.u. for Hg-halides and by 0.8 a.u. for Hg(CH(3))(2), respectively, while DC-CCSD underestimates the correlation correction by 0.57-0.66 a.u. compared to the reference DC-CCSD-T data. EFGs obtained at the DC-DFT level vary considerably with the functional; DC-CAMB3LYP and DC-BH&H reproduce DC-CCSD-T results within 0.08-0.24 a.u. (1%-3%) for Hg(CH(3))(2) and Hg-halides, respectively. An updated value of the nuclear quadrupole moment of the I = 5/2 excited state of (199)Hg, Q((199)Hg) = 0.675(12) b is derived from the literature. This value compares well with that derived from our calculated EFG at the DC-CCSD-T level and the experimental data for Hg(CH(3))(2); Q((199)Hg) = 0.650 b.

Calculation of response properties with the normalized elimination of the small component method

“…Using the NESC EFG formalism in connection with correlation corrected ab initio methods, FZC investigated a series of molecules and found that the EFG values obtained are in good agreement with measured values as well as the results as the four‐component relativistic calculations, especially. Table compares the EFG principal values obtained at the NESC/HF and the NESC/MP2 level of theory with four‐component Dirac–Coulomb HF and CCSD‐T results . The NESC/MP2 EFG values are in an excellent agreement with the state of the art 4c‐DC‐CCSD‐T calculations .…”

“…Table compares the EFG principal values obtained at the NESC/HF and the NESC/MP2 level of theory with four‐component Dirac–Coulomb HF and CCSD‐T results . The NESC/MP2 EFG values are in an excellent agreement with the state of the art 4c‐DC‐CCSD‐T calculations . Using the 199 Hg NQM value of 0.675 ± 0.012 barn, the NESC/MP2 calculation yields 2414 ± 43 MHz for the NQCC of Hg(CH 3 ) 2 , which is in good agreement with the NQCC of 2400 MHz obtained by PAC in frozen neat Hg(CH 3 ) 2 .…”

Relativistic corrections to the electric field gradient given by linear response elimination of the small component formalism

“…Mastalerz et al applied Douglas‐Kroll‐Hess (DKH), and Cheng and Gauss within SF exact two component one electron scheme (SFX2c‐1), and Filatov et al used SF NESC scheme . In second place we choose the heavy nuclei molecular set, Hg X 2 ( X = Cl, Br, and I), to study the dependence on DFT and RPA levels of approach within LRESC and 4c regimes, which will be compared with results provided by Mastalerz et al (DKH), Arcisauskaite et al (4c and DFT), and Filatov et al (NESC) …”

“…Regarding basis sets, dyall.cv3z and dyall.cv4z basis sets were used for all nuclei in relativistic calculations. The small component basis set was obtained from the large component basis set applying the unrestricted kinetic balance prescription, as it was shown to improve results with respect to using restricted kinetic balance instead …”

“…Calculation of electric properties including relativistic effects requires a consistent treatment of the involved operators coming from the full relativistic framework . In this line, relativistic corrections to EFG have been studied within different formalisms …”