Relativistic shape-consistent ECP calculations of eka-Hg compounds:

spin-orbit DFT modeling of Hg-Au_n and E112-Au_n systems

E.A.Rykova⁽¹⁾, A.Zaitsevskii⁽²⁾, N.S.Mosyagin⁽³⁾, T.I.Isaev⁽³⁾, A.V.Titov⁽³⁾

⁽¹⁾ Photochemistry Center, Russian Academy of Sciences, Moscow; rykova@photonics.ru
⁽²⁾ HEPTI, RRC "Kurchatov Institute" and Chemistry Dept., M.Lomonosov Moscow State University, Moscow; zaitsevskii@kintech.ru
⁽³⁾ Petersburg Nuclear Physics Institute, Gatchina; titov@pnpi.spb.ru

homepages

http://www.kintech.ru/rel/
http://qchem.pnpi.spb.ru/

abstract
motivation
method of calculations
exchange-correlation functional adjustment
main results
conclusions
acknowledgments

abstract

Interactions of eka-Hg (element 112, E112) and Hg atoms with small Au clusters were studied by the relativistic DFT method incorporating spin-dependent (magnetic) interactions. The effects of relativity were introduced through relativistic shape-consistent effective potentials of small atomic cores (RECPs) leaving 19 electrons of Au and 20 electrons of E112 or Hg for explicit correlation treatment. The RECPs were derived from valence-shell solutions of atomic Hartree-Fock-Dirac-Breit equations with the Fermi nuclear model. The correlations of valence (including outermost d, actively contributing to the bond formation) and outer-core shells must be included to achieve the necessary accuracy because of comparable average radii of the outermost d and outer-core s, p spinors. The choice of exchange-correlation functionals was based on a comparison of (1) scalar relativistic DFT results for E112Au and HgAu with those of extensive CCSD(T) calculations employing the UHF reference and (2) fully relativistic DFT results for Au₂ with the experimental data. It was found that most of the widely used generalized gradient-corrected density functionals cannot ensure the quantitative description of Hg-Au and 112-Au bonding; however, the popular Becke exchange functional (B86) combined with the Perdew-Wang (1991) GGA correlation functional provides reasonable estimates for both bond lengths and energies. A better accuracy is generally achieved with hybrid exchange-correlation functionals, in particular, with the Schmider-Becke (B98) one. The attachment energies for E112 are smaller than those for Hg by ca. 0.1-0.2 eV, and this difference does not depend on n strongly. The equilibrium distances between E112 and the nearest Au atom in Au_nE112 were found to be larger than the shortest Hg-Au distances in corresponding Au_nHg systems. The role of magnetic effects in E112-Au_n bonding, relaxation of Au_n due to the attachment of E112 or Hg, and implications for E112 adsorption properties on the Au surface are discussed.

motivation

theoretical studies of interactions of element 112 (E112, eka-Hg) with coinage metals are of primary importance for its chemical identification; successfull experimental identification of E112 through adsorption on Au surface had been performed in FNRL in May '06

accurate purely ab initio calculations incorporating magnetic relativistic effects (huge for E112!) are extremely difficult even for diatomics (E112Au)

utility of references to the Hg - E112 homology is questionable: the degree of similarity between Hg and E112 is not well studied

theoretical modeling of E112 / Au surface and Hg / Au surface interactions: relativistic all-electron DFT (C.Sarpe-Tudoran et al., Eur.J.Phys. D 24 (2003) 65-67) reproduced the experimental adsorption energy for Hg (~ 1 eV) and predicted that for E112 (~0.9 eV) by

simulating the unstable (100) Au surface
employing local density approximation which overshoots twice the Hg-Au interaction energy in diatomic
neglecting completely the relaxation of the surface on adsorption
etc.

more reliable calculations on E112 - gold interactions are needed

method of calculation

basic model:
shape-consistent ECP for small atomic cores

inner core replaced by semilocal (radially local) RECP
outer-core and valence electrons
(n-1)s (n-1)p (n-1)d ns (20 for Hg, E112, 19 for Au)
are treated explicitly

scalar & spin-dependent (SO) relativistic effects reside in effective 1-e potentials		kinetic energy & e-e interactions as in non-rel hamiltonian -> quasi-non-relativistic (+SO) methods usable
RECP extracted from atomic HDFB solutions		Breit and finite-nuclei effects incorporated
derived from valence spinors by effective 1-e equation inversion		“chemical accuracy” for ground and low-lying excited states is provided

correlation treatment:
relativistic (spin-orbit) DFT – magnetic terms included

so included from the beginning		ideal for huge spin-orbit amplitudes in SHE
fully unrestricted determination of 1-el two-component spinors		certain cases of “strong configuration mixing” can be recovered
various non-relativistic pure-density GGA and meta-GGA XC functionals hybrid XC functionals usable		flexible gaussian bases [8s6p5d2f] Au [7s6p5d3f] Hg [8s7p6d3f] E112

code used:
nwchem, version 4.7
E.Apra, T.L.Windus, T.P.Straatsma et al.
pacific northwest national laboratory, 2005

xc functional adjustment

we estimate the accuracy of DFT correlation treatment through the comparison DFT vs high-level ab initio (UCCSD(T)) data (A.Zaitsevskii et al., Cent.Eur.J.Phys, in press) for HgAu & E112Au at scalar relativistic level as given by spin-averaged RECP

(note that the reference molecular parameters are obtained from accurate solution for simpified (spin-orbit-free) Hamiltonian and, in the case of E112, are quite far from the true parameters)

	dissociation	energies, eV
	Hg	E112
reference (UCCSD(T))	0.49	0.22
XC functional:
pure-density GGA
x Becke 88 - c Perdew 86	0.58	0.28
x Becke 88 - c Perdew Wang 91 (b88p91)	0.51	0.21
x&c Perdew Wang 91	0.63	0.34
Perdew - Burke - Ernzerhof 96	0.61	0.31
hybrid
adiabatic connection method 93	0.46	0.18
pbe0	0.52	0.24
schmider-becke 98 (b98)	0.46	0.21
b3lyp	0.40	0.16

b88p91 xc functional was used in most cases

main results

fully optimized structures & binding energies (MAu - MAu₄), M=Hg, E112
energy of MAu₁₀ simulating the atom on the (111) surface at the "hollow" position (only M-surface distance optimized, Au₁₀ geometry taken from the bulk Au)

MAu_n	XC functional	M detachment	energy, eV	min(R	_M-Au),A
		Hg	E112	Hg	E112
	b88p91(GGA) b98(hybrid)	0.55 0.50	0.39 0.35	2.68 2.72	2.74 2.78
	b88p91(GGA) b98(hybrid)	0.61 0.57	0.46 0.41	2.67 2.70	2.72 2.76
	b88p91(GGA)	0.70	0.47	2.80	2.86
	b88p91(GGA)	0.62	0.44	2.68	2.74
non relaxed Au₁₀	b88p91(GGA)	0.32	0.24	3.02	3.11

cluster relaxation upon M attachment:
significant in "bridge" position (in MAu₃): 0.06 eV energy lowering for M=E112

conclusions

high degree of E112Au_n - HgAu_n similarity in spite of rather different nature of bonding (spin-orbit contributions ~ 1/2 binding energy in E112-Au)

only slight differences in equilibrium structures;

(min 112-Au bond lengths) = (min Hg-Au bond lengths) + 0.05-0.09 A

(112-Au_n bond energy) = (Hg-Au_n bond energy) – 0.1-0.2 eV;

(112-Au_n bond energy) = 68-75% (Hg-Au_n bond energy);
no simple dependence on cluster size

exptl 1.01 eV Hg / Au surface adsorption energy is not related to the stable (111) surface; both E112 and Hg seem to attach to irregularities

acknowledgements

the present work is partially supported by the Russian Foundation for Basic Research (grants Nos. 06-03-33060 and 06-03-32346)

computer facilities: Kinetic Technologies Ltd

Relativistic shape-consistent ECP calculations of eka-Hg compounds:

spin-orbit DFT modeling of Hg-Aun and E112-Aun systems

spin-orbit DFT modeling of Hg-Au_n and E112-Au_n systems