Atomic properties of elements 114 and 118 and their adsorption on inert surfaces

We present fully relativistic coupled cluster calculations of ionization potentials, electron affinities, and polarizabilities of superheavy elements 114 and 118, along with their lighter homologues, lead and radon. The combination of the 4-component Dirac Hamiltonian with the state of the art coupled cluster approach allows us to achieve very good agreement with experimental values for the lighter elements; similar precision can be expected for our predictions for the superheavy atoms. The trends in the atomic properties are discussed, demonstrating the strong relativistic effects. Using the calculated atomic properties, adsorption enthalpies of the superheavy atoms on inert surfaces are estimated and shown to be rather low for both elements.


Introduction
Theoretical investigations of atomic properties of the superheavy elements allow us to gain a fundamental insight into the influence of relativity on electronic structure.As relativistic effects become more pronounced with increase in the atomic number, superheavy elements will experience the most dramatic influence of both scalar relativistic and spin orbit effects on their atomic and chemical properties.
Knowledge of atomic properties of the superheavy elements can also assist in experimental studies.One of the possible chemical experiments on these extremely short lived species is gas-phase chromatography, where the elements are deposited, according to their volatilities, on alpha-detectors located along a chromatography column with a temperature gradient [1,2].The deposition temperatures are then measured and related to the adsorption enthalpies, 4H ads .Using this method, the adsorption properties of the superheavy elements on various surfaces (usually on gold) can be compared to those of their lighter homologues in the groups.Recently, the adsorption enthalpies of Cn (Z=112) and element 114 on gold were estimated using this technique [3,4].Theoretical predictions of the adsorption enthalpies are important for such experiments, in order to assess the feasibility of separation of the homologues on a given surface.Knowledge of 4H ads on inert materials, such as Teflon and polyethylene is also valuable, as these materials are used as transport capillaries from the target chamber to the experimental setup.
Here we collect the previously published calculated ionization potentials (IPs) [5,6], electron affinities (EAs) [7,8], and polarizabilities (.) [9,6] of element 114 and element 118.Using these properties and a simple physisorption model, we also calculate the adsorption enthalpies of these atoms and of their lighter homologues on inert surfaces.These two elements, due to their different valence atomic orbitals (7p 1/2 for element 114 and 7p 3/2 for element 118) are good study cases for illustrating the influence of relativistic effects on atomic and chemical properties.

Methods and computational details
The quality of any calculation is determined by three parameters: treatment of relativity, treatment of correlation, and the choice of the basis set.Any calculation performed on heavy and superheavy elements must treat relativity on the highest possible level.As we go down in the periodic table, the relativistic effects become the dominant parameter determining the atomic properties.Therefore, in order to get meaningful results, relativity should be included from the start, via a 4component Dirac-Coulomb Hamiltonian [10], and not treated as a perturbation.
On the other hand, correlation is no less important for obtaining reliable results.Currently, the most powerful method for treatment of correlation is the coupled cluster approach.We employ two variants of this method: single reference coupled cluster with single, double, and perturbative triple excitations (SR CCSD(T)), which is EPI Web of Conferences (5) well suited for closed shell systems, and a multireference Fock space CC method (FSCC) [11], for open shell systems.
The basis sets employed in the calculations are specially developed for relativistic methods [12,13], and we extend them by adding diffuse and high angular momentum functions until convergence with respect to the calculated properties is reached.
Alongside the calculations for the superheavy elements, we perform similar calculations for their lighter homologues, lead and radon, for which experimental atomic properties are known.We can thus compare our results to experiment and assess the accuracy of our calculations and the reliability of our predictions for the superheavy elements.
Full details of the calculations can be found in References [5][6][7][8][9].Here we give a general outlook upon the computational methods that we employ.

Ionization potentials and electron affinities
The ionization potential and electron affinity calculations were performed within the framework of the projected Dirac-Coulomb-Breit Hamiltonian [10], (1) i<j Here, h D is the one electron Dirac Hamiltonian, w.here U and ~are the four dimensional Dirac matrices.
The two electron terms include the nonrelativistic electron repulsion and the Breit term, IJ and are correct to second order in the fine structure constant u.For the EA of element 118, the result was also corrected for higher order quantum electrodynamic (QED) effects [8].
Electron correlation is included by the Fock space coupled cluster method, augmented by the intermediate Hamiltonian approach, described in detail elsewhere [14].This approach allows us to employ extremely large model spaces while avoiding convergence difficulties, and to achieve benchmark, typically meV quality for the calculated IPs and EAs.

Polarizabilities
Static dipole polarizabilities were obtained using the finite field approach [15,16], with atomic energies calculated for free atoms and in the presence of uniform electric field acting in the z direction, F z .The atomic energy in the presence of an electric field is given by The first term in the above equation is the ground state energy of an atom in the absence of the electric field, the second term contains the dipole moment, which vanishes for atoms, and the static dipole polarizability appears in the third term, a = -2 a 2 E(Fz ) a 2 p z Relativistic SRCCSD(T) atomic energy calculations were performed for F z = 0.000, 0.0005, and 0.001 a.u. and the polarizabilities were obtained by numerical differentiation.

Adsorption enthalpies
It was shown [17] that the dispersion interaction energy of an atom with an inert solid surface can be rather accurately estimated using the following equation, derived from a model of an atom-slab interaction, Here, IP slab and IP a10m are the ionization potentials of the surface material and the adsorbed atom, respectively, U al is the polarizability of the adsorbed element, £ is the dielectric constant of the surface material, and x is the adatom-surface distance.It was also shown [18] that x can be well approximated by Van der Waals radius (R vdW ) of the adsorbed atom.We obtain the R vdW of the superheavy elements from a linear correlation between the radii of the maximal charge distribution of the valence orbital and the experimental R vdW of the lighter homologues in the groups.Table 1 contains the experimental IPs and the dielectric constants of the inert materials considered here.

Results and discussion
The trends in the atomic properties discussed here, and thus also the trends in the adsorption enthalpies will be set by the trends in the valence atomic orbitals.Element 114 has a quasiclosed 7pll2 valence shell, which experiences relativistic contraction and stabilization.Figure 1 presents the Dirac-Fock binding energies [19] of the npll2 orbital in group 14 against the atomic number Z. From carbon to tin a decrease in the binding energy is observed, as the atomic number increases.However, this trend is reversed at tin, and the binding energies increase from tin to lead to element 114, due to the strong relativistic stabilization of the npll2 valence orbital.Figure 2 shows the binding energies of the npll2 and the outer np3/2 atomic orbitals of group 18 elements.Here the most striking feature is the spin-orbit splitting between the sublevels, which increases with increase in Z.While the npll2 orbitals behave in a manner similar to that of the group 14 elements, a different trend is observed for the np3/2 electrons, which become less bound with increase in the atomic number.
In contrast to group 14, the ionization potentials of the rare gases do, indeed, decrease more or less monotonously (Fig. 4), as do the energies of their valence np3/2 orbitals.These orbitals are destabilized through an indirect relativistic influence; however, the effect is rather small, and in line with the general trend in the group of decrease in the IP with the increase in the atomic number.Our calculations predict no electron affinity for element 114, while lead, its lighter homologue, has an EA of about 0.4 eV.The probable reason for this is twofold.The 7P3/2 LUMO orbital, where the extra electron would attach, is destabilized by relativity.On the other hand, the relativistically contracted occupied 7P1l2 orbital should create a rather strong shielding of the nucleus, also lowering the binding energy of an additional electron.;;;r

Ionization potentials and electron affinities
The calculated ionization potentials and electron affinities of element 114 and element 118 can be found in Table 2.There we also present the calculated and the experimental IPs and EAs for their lighter homologues, Pb and Rn.Our results for the lighter atoms are in excellent agreement with experimental values; similar accuracy can be expected for our predictions for the superheavy elements.
Figure 3 presents the ionization potentials of group 14 elements.It is easy to see that the IP follow the trends set by the binding energies of the valence np1l2 orbitals.The ionization potential decreases from carbon to tin, and then increases again, so that the IP of element 114 is even higher than that of silicon.This increase is a purely relativistic effect; without relativity the IP of element 114 would be the lowest in the group.Fig. 2. DF binding energies (a.u.) of the np1l2 (squares, solid line) and the np3/2 (rhomboids, dashed line) electrons of group 18 elements.
The following subsections demonstrate how these trends will affect the chemical properties of elements 114 and 118.

05002-p.3 EPJ Web of Conferences
Noble gases are chemically inert, and do not have electron affinity.Element 118, however, is rather special: calculations have shown that it should have an electron affinity of 0.056 eV, which can be attributed to the relativistic stabilization of the next 8s shell.
In group 18, the polarizabilities increase monotonously, and element 118 will have the highest polarizability in the group.Here, we do not find a trend reversal like we do in group 14, as the valence np3/2 shell does not experience relativistic contraction.  of elements 114 and 118 and their lighter homologues on inert surfaces [69]   The adsorption enthalpies of the elements under study on quartz, ice, and Teflon, obtained in Ref. [9] and Ref. [6], are presented in Table 3.There we also show the Van der Waals radii of the atoms, derived through a liner correlation in the same publications.

31.5
The adsorption entha1pies of group 14 elements on all the surfaces studied here follow the trends set by the po1arizabi1ities (Figure 7), with a maximum at tin, and element 114 being similar to silicon.The low I1H ads of element 114 on Teflon should guarantee its transport through Teflon capillaries from the target chamber to the experimental set up.On quartz, its I1H ads is about 6 kJ/mol lower than that of lead, making possible their separation on this surface.The calculated polarizabilities of all the atoms under study are shown in Table 2. Polarizability of Rn is yet to be measured, and the experimental polarizability of Pb has a rather large uncertainty of about 15%.Thus, together with the superheavy elements, we also make benchmark predictions of the polarizability of their lighter homologues.The electric dipole polarizability is a measure of the distortion of the overall atomic or molecular charge distribution by an external electric field.It can thus be intuitively connected to the atomic volume.For group 14, the polarizability increases from carbon to tin, with the increase of the atomic size.However, from tin to lead, the valence np1l2 orbital experiences relativistic contraction, which reduces the polarizability.This contraction is even stronger for element 114, and it should have an even lower polarizability than Si.Adsorption enthalpies of group 18 elements on inert surfaces are shown in Figure 8.There is a steady increase in I1H ads on all the surfaces with an increase in atomic number, up to lead and element 118.The adsorption entha1pies of these two atoms are extremely close in values, which would preclude their separation using gas chromatography technique on all the surfaces studied here.This is caused by the compensation of the increase in po1arizabi1ity by an increase in R vdW from lead to the heavier homologue.As is the case with element 114, the low !:i.H ads of element 118 on Teflon will allow its transport to the chemistry set up.

Figures 5 and 6
Figures 5 and 6 show the polarizabilities of group 14 and group 18 elements, respectively.The values for Pb, Rn, element 114 and element 118 are from the SR CCSD(T) calculations, for the lighter homologues we use experimental values, where available, or best theoretical values from Ref. [23].The electric dipole polarizability is a measure of the distortion of the overall atomic or molecular charge distribution by an external electric field.It can thus be intuitively connected to the atomic volume.For group 14, the polarizability increases from carbon to tin, with the increase of the atomic size.However, from tin to lead, the valence np1l2 orbital experiences relativistic contraction, which reduces the polarizability.This contraction is even stronger for element 114, and it should have an even lower polarizability than Si. z

Table 1 .
Properties of the inert surfaces.

Table 2 .
Ionization potentials (eV), electron affinities (eV), and polarizabilities (a.u.) of elements 114 and 118 and their lighter homologues, Pb and Rn. 05002-p.2 Element 118 will have the lowest IP in the group.