1. Semiempirical modelling of helium cluster cations
I. Paidarová a), R. Polák a), F. Karlický b), I. Janeček b), D. Hrivňák 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-molecules 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
method CASSCF(5,10) / icMRCI (5 active electrons in 10 active orbitals) [2]
basis set d-aug-cc-pVTZ
program package MOLPRO
[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 / C∞v PESes for the electronic ground state
Equilibrium structure of He3+ (comparison with literature)
method Emin Re De [hartree] [bohr] [eV]
QICSD(T), aug-cc-pVTZ [3] QICSD(T), aug-cc-pVQZ [3]
MRD-CI, cc-pVTZ [4]
this work [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)
C2v
C∞v
Fourth International Conference on Photodynamics, Havana, 6 – 10 February, 2006
Grant No. 203/04/2146 of the Grant Agency of the Czech Republic