Extent of Spin Contamination Errors in DFT/Plane-wave Calculation of Surfaces: A Case of Au Atom Aggregation on a MgO Surface

Abstract

The aggregation of Au atoms onto a Au dimer (Au2) on a MgO (001) surface was calculated by restricted (spin-un-polarized) and unrestricted (spin-polarized) density functional theory calculations with a plane-wave basis and the approximate spin projection (AP) method. The unrestricted calculations included spin contamination errors of 0.0–0.1 eV, and the errors were removed using the AP method. The potential energy curves for the aggregation reaction estimated by the restricted and unrestricted calculations were different owing to the estimation of the open-shell structure by the unrestricted calculations. These results show the importance of the open-shell structure and correction of the spin contamination error for the calculation of small-cluster-aggregations and molecule dimerization on surfaces.

Diradical Characters of s-Indaceno[1,2,3-cd;5,6,7-c’d’]Diphenalene with and without Interaction with MgO(001)

“…The spin contamination error decreased as the d value decreased. It has already been reported in detail along with the mechanism that the spin contamination error is reduced by the interaction with the surface; this is because the energy difference between the singlet biradical and triplet states becomes small (the singlet biradical state becomes relatively unstable) [20,21,23]. These results also shows that the properties of singlet biradical molecules are affected by the surface interactions even without electron transfer and covalent bond formation with the surfaces.…”

“…It is known that spin contamination error affects the calculated results of diradical states by single-referenced method, such as Kohn-Sham DFT [7,8,36]. Then, the errors in biradical molecules were corrected via approximate spin projection scheme for DFT/plane-wave calculation (AP-DFT/plane-wave scheme) [20][21][22][23]36]. The corrected energy (E AP ) of singlet biradical state is,…”

“…In addition, the analysis technique for the diradical state using the results of density functional calculations with a plane-wave basis (DFT/planewave), which is a general calculation method for the electronic states of solid surfaces, is insufficient. Hence, detailed analyses of the diradical state with surface interactions are scarce [9,[19][20][21][22][23]. Although magnetic interactions between radical molecules adsorbed on Au(111) were analysed by molecular orbital calculation, discussions incorporating the effects of the Au band were difficult because the Au models used were the Au 10 clusters because of the high computational cost [16].…”

First-principles study of CO2 hydrogenation to formic acid on single-atom catalysts supported on SiO2

“…37 Moreover, spin contamination errors (SCE) were considered for the broken symmetric states (BS) and corrected using Yamaguchi's equation 38 with modification for DFT/plane-wave calculations. 39,40 where LS and HS denote low spin state and high spin state, respectively. The subscript exact indicates the exact value (the eigenvalue of Ŝ 2 ), and U means the value estimated by spin-polarized (unrestricted) calculations.…”

Mixed Two-Dimensional Organic-Inorganic Halide Perovskites for Highly Efficient and Stable Photovoltaic Application

“…We carried out an ab initio study on the physical properties of 2D-HOIPS, focusing on (RNH 3 ) 2 (MA) n−1 B n X 3n+1 (R: long-chain alkyl or aromatic group; n : the number of metal-halide sheets), and the effects of phase, thickness and surface molecule based on density-functional theory (DFT) [43,44,45,46] and Perdew-Burke-Eznerhof generalized gradient approximation (PBE-GGA) [47,48] to accurately calculate the total energy. The Vienna ab initio simulation package (VASP) with the projector augmented wave (PAW) scheme was used [46,49,50]. The Monkhorst-Pack method was used to generate k-point meshes in the first Brillouin zone [51,52].…”