ON THE ACCURACY OF THE UNIVERSAL ZIEGLER-BIERSACK-LITTMARK POTENTIAL IN DESCRIPTION OF KR – C INTERACTION
V. Kuzmin
It is well known that the universal ZieglerBiersack-Littmark (ZBL) potential1 is an average of potentials, obtained from non-selfconsistent calculations on overlapping Hartree-Fock-Slater atoms in the free-electrongas approximation, for randomly selected
atomic pairs. Considerable discrepancies between available experimental data2-4 and theoretical predictions of the standard ZBL theory1 on range parameters of heavy ions in light
targets can be considered as an evidence of
rather poor accuracy of the ZBL potential for
such systems. This work aimed at study of
reliability of a description of interatomic interaction between a heavy atom and a light
atom with the ZBL potential. As beams of Kr
ions are widely used in various researches on
surface modification of different polymers, it
is important to expose an accuracy of the ZBL
potential for an evaluation of interaction between Kr and C atoms. Moreover, Kr – C system can be of great interest as carbon-based
materials are very promise for future technologies including nanotechnologies.
Interatomic potentials for Kr – C have been
calculated with ab initio Hartree-Fock (HF)
and density functional theory (DFT) methods
by GAMESS program system5, taking into
account relativistic corrections by RESC
scheme6. For the present work large 20s13p
for C and 26s20p14d for Kr well-tempered
basis sets7,8 were completely decontracted and
augmented with polarization and diffuse orbitals. Completeness and flexibility of the resulting basis sets (uWTBS) were tested
against fully-numerical Hartree-Fock calculations (2D) with computer code by Kobus et
al.9. 3Σ state as giving a lowest energy of the
neutral Kr – C system was followed. As it is
seen from Fig. 1, normalized difference of the
potentials calculated with the two methods for
the Kr – C system do not exceed 2% for interatomic distances between 0.08 and 2 Å. This
interval is most important in a description of
(quasi)elastic scattering of Kr ions with energies
from
a
few
eV
to
Fig. 1. Normalized difference of interatomic potentials of Kr – C system calculated with finite
basis sets (VWTBS) and fully numerical (V2D)
methods at Hartree-Fock level of theory.
almost 200 keV by C. The accuracy within
2% seems quite enough for the purposes of
the present study. The potential calculated
with DFT method in the local-spin-density
approximation (LSDA) including relativistic
corrections by RESC is compared with the
ZBL potential in Fig. 2. One can observe very
good agreement (within 4%) in wide interval
of interatomic separations from origin up to
0.8 Å. However, the deviation rapidly increases at larger distances and surpass 35% at
Fig. 2. Normalized difference of the ZBL and
DFT interatomic potentials for Kr – C system.
Thus, the widely used ZBL potential adequately describes Kr – C interaction at small
distances giving correct value of the nuclear
stopping power for Kr ions in C at energies
above 1 keV. In sub-keV region a more accurate potential is necessary.
REFERENCES
Fig. 3. The nuclear stopping powers as calculated with DFT potential (filled circles), Molière-like fit to HF potential (dash-dotted line)
and that of SRIM2003 (ZBL, solid line). Inset
shows the same data at small energies.
1.2 Å. This distance corresponds to the closest approach between Kr and C at about 120
eV. Therefore, at energies below a few hundreds eV considerable differences between
scattering angles determined by these potentials are expected.
Relativistic corrections yield only marginal
changes of the calculated potential in the studied range of interatomic separations.
In Fig. 3 the nuclear stopping powers as
calculated with the DFT potential, Molièrelike fit to HF potential and the ZBL potentials
(SRIM 2003) are shown. One can see that
there are no notable differences in the nuclear
stopping power as calculated with the potentials in question over the range of the displayed energies. However, the inset of the
Fig. 3 demonstrate that at energy of 200 eV
the nuclear stopping power given by the ZBL
potential are about 20% too high in comparison with that of DFT, increasing to nearly
40% at 100eV.
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