The accuracy of current density functionals for the calculation of electric field gradients: A comparison with ab initio methods for HCl and CuCl

Abstract

The performance of current density functionals is analyzed in detail for the electric field gradients (EFG) of hydrogen chloride and copper chloride by comparison with ab initio methods and available experimental data. The range of density functionals applied shows good agreement with coupled cluster H and Cl field gradients for HCl, as has been demonstrated previously for other main-group element containing compounds. However, the performance of most density functionals is very poor for the Cu EFG in CuCl (EFG for Cu -0.44 a.u. at the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] level, compared to, e.g., +0.54 a.u. at the B-LYP level). Only the “half-and-half” hybrid functionals give field gradients with the correct sign. The reason for the poor performance of the density functional theory is analyzed in detail comparing density functional with ab initio total electronic densities ρ(r). Due to the conservation of the number of particles, a change in the valence part of the electron density can lead to changes in the core part of the density. Errors in valence electronic properties like the dipole moment and in core properties like the Cu and Cl EFGs may therefore be connected. In fact the errors in both properties show a distinct linear relationship, indicating that if the dipole moment is correctly described by density functionals, the Cu and Cl EFGs may be accurate as well. Furthermore, at the atomic level, electric field gradients are described with reasonable accuracy by current density functionals as calculations for the Cu 2P excited state and the Cu2+ 2D ground state show. A comparison between the different density functionals shows that the incorrect behavior of the electronic density appears to be mainly due to defects in the exchange part of the functional.

Density functional calculations of nuclear quadrupole coupling constants in the zero-order regular approximation for relativistic effects

“…On the other hand, the calculated EFGs at the halogen centers in the Cu and Ag halides are not in good agreement with experiment, which confirms the results previously found in Ref. 18 for CuCl. Since the discrepancy cannot be due to ''technical'' problems ͑ZORA, basis sets͒ it is to be attributed to deficiency of the used density functional: LDA plus gradient corrections due to Becke ͑Becke88͒ 19 and Perdew.…”

“…For these molecules the used density functional fails to describe the electric field gradient with sufficient accuracy. Schwerdtfeger et al 18 showed that many of the presently used functionals, with the exception of some hybrid functionals, give poor results for CuCl. They showed that the results are even worse for the calculation of the EFG at the copper nucleus.…”

Nuclear Quadrupole Moment ofF57efrom Microscopic Nuclear and Atomic Calculations

“…If we accept the coupled-cluster result as the most accurate value, the hybrid GGA functionals perform well for Fe(CO) 5 , while the non-hybrid GGA functionals are preferred for Fe(C 5 H 5 ) 2 . We note that for CuCl the BHH functionals gave the best description [19]. This is clearly not a satisfying situation.…”

“…The use of the density functional theory for the calculation of EFGs in transition metals is questionable. Recent calculations on CuF showed a variation of the Cu EFG ranging from +0.50 au for the local density approximation (LDA), and +0.44 au at the generalized gradient approximation (GGA) level (BPW91) to +0.07 au at the hybrid level (B3PW91) [19,20], as compared to the experimental value of −0.31(2) au [21]. In contrast, relativistic ab initio coupled-cluster calculations give −0.34 au [19], in perfect agreement with the experimental result.…”

“…We have adopted a wide range of exchange and correlation functionals for the electronic structure calculations of the free molecules Fe(CO) 5 and Fe(C 5 H 5 ) 2 (for the terminology see Refs. [19,22] 5 we investigated solid state effects to the iron electric field gradient by performing HF, B3LYP, and LDA calculations using the program CRYS-TAL98 [24] and the solid state structure given by Böse and Bläser [25]. Detailed structural data and basis sets used will be published elsewhere [26].…”