Relativistic DFT and ab initio
calculations on the seventh-row
superheavy elements: E113 ˗ E114
A.Zaitsevskii
C. van Wüllen
A.Rusakov

A.Titov

RNC “Kurchatov Institute”
Technische Universität Kaiserslautern
P.G.Demidov Yaroslavl State University
B.P.Konstantinov Petersburg Nuclear
Physics Institute: http://qchem.pnpi.spb.ru

Supported by RFBR grant 11-03-12155
Oriented targeted basic research on key interdisciplinary topics

Motivation• Analysis of atomic data and accurate calculations of diatomics with SHEs
Cn, E113 and E114 is not sufficient for reliable prediction of theiradsorption properties on gold surface.
• Disagreement of different RDFT studies with the exptl value of adsorptionof Hg on gold clusters is too high, whereas it is rather good for Pb on
gold. In turn, the exptl statistics with SHEs is yet rather poor.
• Discrepancies in RDFT studies of the binding energies of Hg & Cn on
gold surface are rather high (LDA vs. GGA & hybrid RDFT: factor of 2).
• Applicability of RDFT with primitive XC functionals to more or lesscomplex systems with Cn was never examined in details.
• To-date, the problem of adsorption of E112-E114 is most interesting us
from theoretical point of view in connections with SHEs. It cannot be
solved by "brute-force" improvement in computational (quantum chemical)
technique but require involving some new ideas to overcome it.

SHEs in the“island of stability”
subperiodic structure
closedshells6d5/26 7s2

closed(sub)shells
6d5/26 7s2 7p1/22

closedshells6d5/26 7s2
7p1/22 7p3/24

subperiod:

subperiod:

subperiod:

6d5/2 is being filled

7p1/2 is7p3/2 is being filled

being filled

Features of even elements of VIIth period

๏ contraction andstabilization of s- andp1/2- shells

๏ large spin-orbit
splitting p1/2 - p3/2

๏ rather diffuse andunstable sub-valenced-shell)Cn(E112) & E114: closed-shell like structurethFeatures of odd elements of VII period

E113 & E115: 1 electron over the closed shellIonization potentials, eV
periodperiod

Binding energy M-Au in diatomics MAu, eV
periodperiod

Binding energy M-M in dimer M2, eV
periodperiodInteraction energy of Cn-Aun & E113-Aun:
RDFT vs. ab initio
MBPT+SO (pilot):[A.Zaitsevskii et al., JCP 132, 081102 (2010)]
CCSD(T),CBS+SO (reliable): [A.Zaitsevskii et al., to be published (2011)]• Very time consuming calculations, thus:• The Au-Au distances are experimental (bulk);• Only the distance adatom-Au plane isoptimized:- to check influence of dispersion-like int-n;- to reduce computational efforts;- to forbid forming plane structures (Cn / Au)•The only goal is to assess theDFT applicability

We never declared and even thought smth like:“the opposite trend in Cn/An vs. Hg/Au binding energies in sometests means inapplicability of DFT to these `closed shell’ systems”

Model features:
Small-core relativistic pseudopotential (Gatchina)[Mosyagin et al., Progr.Theor.Chem.Phys. B15 ,229 (2006),
Zaitsevskii et al., Russ.Chem.Rev., 78, 1173, (2009),
Mosyagin et al., Int.Rev.At.Mol.Phys. 1, 63 (2010)]

inner core is simulated by relativistic pseudopotential;
outer core: 6s2 6p6 6d10 & valence: 7s 7p (E112 - E115),
5s2 5p6 5d10
6s 6p (Au, Hg - Bi)
are treated explicitly (small-core PP)• “non-relativistic-type” n-electron system in aspin-dependent pseudopotential(radially(semi)-local or generalized)• nonrelativistic symmetry for scalar studies• relativistic symmetry for spin-dependent ones

“chemical accuracy” (and better!) is attainable & sufficient(~ 1 kcal/mol ≈ 0.043 eV ≈ 350 cm-1) for potential curves etc.

Ab initio study of simple models ofadsorption complexes Cn-Aun и E113-Aun

full two-component ab initio calculation:
๏ low symmetry => huge number of calculations
๏ extremely slow convergence on the basis set extension, in
which the Hamiltonian is discretizedcalculations are very expensive even for diatomic molecules

scalar-relativistic:๏ СCSD(T) as a means of describing the electron correlations
๏ sequence of correlation-consistent Gaussian bases
 complete basis set (CBS) limit
effects of magnetic interactions:

1comp. vs. 2comp. RDFT

E113-Aun vs. Tl-Aun
CCSD(T): accurate scalarRDFT: quite reasonable
relativist. model; contribution of approximation, but calibration
magnetic effects within RDFT on diatomic data is not reliable

contribution of correlations involving 6d-shell of E113
to the binding energy ~0.3 eV/bond; is it transition element?

E113-Aun and Cn-Aun: RDFT vs. CCSD(T)The only adatom – Au surface
distance is varied; the Au-Au
distances are experimental.

Results:• E113-Aun: RDFT is in areasonable agreement withCCSD(T), CBS+SO• Cn-Aun: wrong trend ofRDFT results:
underestimate seriously thebinding energy

Correlation contributions to interaction energyof non-overlapping subsystems of electrons(London interaction)interaction of neutral non-polar separated many-electron
systems “instantaneous dipole ̶ instantaneous dipole”
effect of electron correlation of different subsystemsris not determined by the distribution of the charge density offree subsystems (as electrostatic, e.g., dipole-dipole int-n)
is not associated with a significant change in the charge
density of subsystems (as induction one)is not describedby simple DFT models

Correlation contributions to interaction energy
of non-overlapping subsystems of electrons(London interaction)Cn:

6d is well polarizable but more compact than 7sAu:
5d is more compact than 6s

when forming Au-Cn bond the filled dshells are almost not overlapping
interaction 5d10 Au - 6d10 Cn
is like London (dispersion) attractionof aurophilic typenot described by simple DFT models

Correlation contributions to interaction energy
of non-overlapping subsystems of electrons(London interaction)Cn:

6d is well polarizable but more compact than 7s
Au:
5d is more compact than 6s

when forming Au-Cn bond the filled dshells are almost not overlapping
interaction 5d10 Au - 6d10 Cn
is like London (dispersion) attractionof aurophilic typenot described by simple DFT models

Correlation contributions to interaction energy
of non-overlapping subsystems of electrons(London interaction)Cn:

6d is well polarizable but more compact than 7s
Au:
5d is more compact than 6s

when forming Au-Cn bond the filled dshells are almost not overlapping
interaction 5d10 Au - 6d10 Cn
is like London (dispersion) attractionof aurophilic typenot described by simple DFT models

Correlation contributions to interaction energy
of non-overlapping subsystems of electrons(London interaction)Cn:

6d is well polarizable but more compact than 7s
Au:
5d is more compact than 6s

when forming Au-Cn bond the filled dshells are almost not overlapping
interaction 5d10 Au - 6d10 Cn
is like London (dispersion) attractionof aurophilic typenot described by simple DFT models

Correlation contributions to interaction energy
of non-overlapping subsystems of electrons(London interaction)Cn:

6d is well polarizable but more compact than 7s
Au:
5d is more compact than 6s

when forming Au-Cn bond the filled dshells are almost not overlappinginteraction 5d10 Au - 6d10 Cn
is like London (dispersion) attractionof aurophilic typenot described by simple DFT models

Modeling of adsorption complexes E113 etc. / Aun• It is necessary to start from ab initio studies
of small but not diatomic systems and thenchoose appropriate exchange-correlation functional๏ solution of many-electron problem: two-component
unrestricted non-collinear relativistic DFT (RDFT)[van Wüllen, Z.Phys.Chem. 224, 413 (2010)]

๏ basis sets optimized for large differences of one-electronstates nll+1/2 & nll-1/2
in practice, close to the complete basis sets limit๏ Au clusters up to 37 atoms (~ limit on the cluster size)๏ If necessary, applying ab initio corrections (Cn/Au, Hg/Au)

Large cluster models: E113 etc. / Au: RDFT
adsorption energy on Au, eV• complex113-Au37 :position of E113 is over the Auatom in second and third layer ofsurface (111)• quite close binding energies forboth positions and functionals:
Becke – Perdew & PBE0
ca. 1.2 eV

2.1

cd0.5
0.6

1.2
1.3
0.44
correctionExperiment (Eichler)Some conclusions• Cn• E113is “more or less” homologue of Hg;
is doubtful homologue of Tl: notably less stablebonding with Au, completely due to magnetic interactions;significant contributions of filled 6d to bond;• E114• E115??? transition-like element ???
is only “formal” homologue of Pb;
is a good homologue of Bi;• E113 & E114 form an unique “ultra-short” subperiod.
Supported byRFBR grant N 09-03-00655-а

• http://rel.kintechlab.com/; http://www.qchem.pnpi.spb.ru/

Thank you for attention!

What is required for accurate relativistic calculation?

Choosing a suitable methods for calculating the electronic structure taking
account of the required accuracy of properties, complexity of the system(number of atoms and electrons, features of the valence structure, types ofatoms: s-, p-, d- or f-elements, etc.), acceptable computational cost :method of accounting for electron correlation(fixing the subset of correlated electrons);
optimal effective Hamiltonian (relativistic, scalar-relativistic=without SO) andrelated one-electron basis set (choosing / generation for each atom treated)

Correlation methods• Coupled-clusters (CC)Relativistic coupled-clusters with single and double excitations (RCCSD)[U.Kaldor, E.Eliav, A. Landau, Tel-Aviv Uni., Israel;
N.S. Mosyagin et al., JCP , 115, 2007 (2001)]
scalar-relativistic (without SO) CCSDT (srCCSDT) to use large basis sets:
within CFOUR package [www.cfour.de];multi-reference CC code by M.Kállay (MRCC)- the most advanced approach now; allows one to achieve the best
accuracy for relatively small systems with simple valence structure. There
are many different single- and multi-reference developments, combined
ones including CI & many-body perturbation theory.

Effective Hamiltonian:Relativistic pseudopotential (GRECP or Generalized PP):
A.V. Titov & N.S. Mosyagin, IJQC 71, 359 (1999);
Mosyagin et al., Int.Rev.At.Mol.Phys. 1, 63 (2010).

N.S.

Restoration of electronic structure in heavy-atom cores:
A.V. Titov et al., PTCP B15, 253 (2006).

Basis Sets: GC-basis: N.S. Mosyagin et al., JPB 33, 667 (2000).

Dirac-Coulomb (4-comp.) vs. pseudopotential (2-comp.)
Spectroscopic constants for low-lying excited state 2П3/2 of HgH.
Year: MethodRe(Å)

we(cm-1) Te(cm-1)

1993: Stuttgart PP / MR-CI

1.610

193028714

1996: shape-consistent PP / MRD-CI

1.615

2033

28490

2001: Generalized PP / RCC-SDT

1.579

2083

28275

2001: Dirac-Coulomb / RCC-SD(T)

1.594

2005

28122

1950-1988: Experiment1.580 2079
±0.001 ±12

28270
±14

PP :
relativistic pseudopotential;
MR-CI: multi-reference configuration interaction;
RCC-SD: relativistic coupled cluster with single and double excitations.

What makes the core pseudopotential (PP)?
Reduces the electronic structure calculation to an explicit treatment of
only valence electrons:
exclusion of chemically inactive (core) electrons from the calculation,
while
maintaining a sufficiently accurate description of the electronic
structure and interactions in the valence region;
providing Pauli orthogonality with respect to the occupied (explicitly excluded)core states, i.e., prevent the “collapse" of valence electrons into core;
efficient treatment of relativistic effects (scalar -relativistic , spin-orbit , Breit);smoothing the pseudospinors to minimize atomic basis set size andcomputational cost depending on the task .

Being universal in applications, the PP method is the most flexible
approach for calculating the electronic structures.

Concluding remarks
computational accuracy can be higher than experimental; the properties whichcannot be obtained experimentally to-date can be evaluated with good
accuracy, that is important for many (fundamental) experiments;

good prospects for further improvement of accuracy with accounting forcorrelation and relativistic effects, the application field can be extended on
more complicated systems, other properties and processes;
the pseudopotential method (+ electronic structure restoration in atomic coresfor studying core properties) is the most efficient, prospective and universal
approach for calculating not only polyatomic systems but even for diatomic
ones when relativistic effects are important;though there is no universal scheme to uniquely select a method forcorrelation treatment, reasonable recommendations can be formulated;
pseudopotentials and basis sets are accessible by internet.