AB INITIO CALCULATIONS ON He3

1
Semiempirical modelling of helium cluster cations
I. Paidarová a), R. Polák a), F. Karlický b), I.
Janecek b), D. Hrivnák b), R. Kalus b), and F. X.
Gadéa c)
a) J. Heyrovský Institute of Physical Chemistry,
Praha b) University of Ostrava, Ostrava c)
Université P. Sabatier, Toulouse
AIM The principal aim of the present work is to
provide sufficiently accurate and still
computationally cheap tools for theoretical
modelling of the intra-cluster interactions in
singly charged helium cluster cations, Hen. This
is achieved in two steps. Firstly, highly
accurate ab initio calculations are performed for
the electronic ground state and the first two
excited states of the helium trimer cation, He3,
and the three three-body potential energy
surfaces are represented analytically using
standard formulae with the adjustable parameters
estimated via a least-squares fitting
procedure. Secondly, the analytical potential
energy surfaces are used in semiempirical
modellings of the interactions in larger ionized
clusters of helium, Hen. It is well known that
the inclusion of the three-body interactions is
crucial for describing the intra-cluster
interactions in the Hen complexes correctly 1.
Accordingly, a semiempirical triatomics-in-molecul
es model, within which the three-body
contributions are taken into account explicitly,
is proposed for the helium cluster cations. The
model will be subsequently employed in
calculations of the the electronic and geometric
structure of these clusters and their absorption
spectra. 1 P.J. Knowles, J.N. Murrell, E.J.
Hodge, Mol. Phys. 85, 243 (1995)
LEAST-SQUARES FITS FOR He3 Coordinates
Analytical formula Configurations
TRIATIOMICS-IN-MOLECULES (TRIM) MODEL
FOR HeN TRIM expansion of the electronic
Hamiltonian Localized (diabatic) basis
set TRIM Hamiltonian matrices for
HeN Example TRIM Hamiltonian
matrices for He4 Independent inputs
for the TRIM method Eneut (ABC) ground-state
energies of neutral triatomic fragments
(calculated using semiempirical two- and
three-body potentials for helium) Ej(ABC)
energies of ionic triatomic fragments for their
electronic ground state (j 1) and the lowest
two excited states (j 2,3) (calculated using
the analytical formula given above and fitted
to the ab initio data presented in the left
panel) xkj expansion coefficients
of the eigenstates of ionic triatomic fragments
with respect to the localized basis set
(approximate estimates are obtained using the
diatomic-in- molecules method since the
triatomic contributions to the total interaction
energy of He3 represent only a small
perturbation to the triatomic electronic
Hamiltonian, this approximation should give
energies accurate up to the first order of the
perturbation theory)
? - anticipated three-body configurations in Hen
clusters (n 13) ? - configurations included in
fitting procedure Restrictions imposed on the
configurations (about 1000 points for each PES)
AB INITIO CALCULATIONS ON He3 Computational met
hod CASSCF(5,10) / icMRCI (5 active electrons in
10 active orbitals) 2 basis set d-aug-cc-pVTZ p
rogram package MOLPRO 2000.1 3 H.-J. Werner
and P. J. Knowles, J. Chem. Phys. 89, 5803
(1988) P. J. Knowles and H.-J. Werner, Chem.
Phys. Letters 145, 514 (1988) Results Potential
energy surface for C2v geometries
? our calculations M. F. Satterwhite and
G. I. Gellene, J. Phys. Chem. 99, 1339
(1995) subplots comparison with literatura
data A detailed plot of the C2v / C8v PESes
for the electronic ground state Equ
ilibrium structure of He3 (comparison with
literature) method Emin Re
De hartree bohr eV
QICSD(T), aug-cc-pVTZ 3 -7.896672 2.340
2.598 QICSD(T), aug-cc-pVQZ
3 -7.902103 2.336 2.640 MRD-CI,
cc-pVTZ 4 -7.8954 2.34 2.59 this
work -7.897021 2.339 2.639 3 M. F.
Satterwhite and G. I. Gellene, J. Phys. Chem. 99,
1339 (1995) 4 E. Buonomo et al., Chem.
Phys. Letters 259, 641 (1996)
Grant No. 203/04/2146 of the Grant Agency of the
Czech Republic
Fourth International Conference on Photodynamics,
Havana, 6 10 February, 2006