Benchmark calculations Computational method CASSCF(5,10) / icMRCI (5 active electrons

1. Ab initio calculation on He3+ of interest for semiempirical modelling of Hen+ Ivana Paidarováa), Rudolf Poláka), František Karlický b), Daniel Hrivňákb), and René Kalus b) a) J. Heyrovský Institute of Physical Chemistry, Praha, b) University of Ostrava, Ostrava Aim The principal aim of the present calculations is to provide highly accurate potential energy surfaces (PES) for the electronic ground state and the first two excited states of the He3+ ion to be employed in subsequent semiempirical modellings of larger helium cluster cations, Hen+. It is well known that the diatomics-in-molecule (DIM) approach, which performs well for the heavier rare gases, fails remarkably even for the smallest Hen+. It is argued that this is mainly due to the neglect of three-body interactions [1] within the DIM framework and, consequently, the three-body contributions to the Hen+ interaction energy have to be extracted from ab initio calculations and included in semiemirical models for them to become acceptably accurate. This can be done, e. g., within the triatomics-in-molecules (TRIM) approach [2], which represents a natural generalization of the DIM method. [1] P.J. Knowles, J.N. Murrell, E.J. Hodge, Mol. Phys. 85, 243 (1995) [2] this poster session, D. Hrivňák et al., Semiempirical modelling of Hen+ clusters. Economy calculations Computational method Equation-Of-Motion Coupled Clusters [4] basis set d-aug-cc-pVTZ [5] program package ACES II [4] J.F. Stanton and R.J. Bartlett, J. Chem. Phys. 98, 7029 (1993) [5] Basis set converged results were obtained with daug-cc-pVTZ basis set, in the series of aug-cc-pVXZ calculations, X=D,T,Q. Results Comparison of potential energy curves for the first three electronic states and for selected C2v geometries with the benchmark results ● – economy calculations ○ – benchmark calculations subplots – a detailed view of local minimum Differences between the economy and benchmark calculations for two selected geometries (C2v and D∞h) A detailed plot of the C∞v PES for the electronic ground state The C∞v PES is extremely flat for the electronic ground state Potential energy surface Computational Coordinates where r1 ≤ r2≤r3 are inter-atomic distances. Analytical formula Computationally cheap Morse potential (Easymp→ 0) with (X = D, A, R) Configurations ○- anticipated three-body configurations in Hen+ clusters (n ≤ 13) ● - configurations included in fitting procedure Least-square fits rough optimization: genetic algorithm (with binary encoded strings) fine-tuning: Levenberg-Marquardt Newton-Raphson (program by V. Špirko) Results Examples of 1D fits for a representative set of geometries and for the electronic ground state ● - ab initio points from economy calculations —— - least-square fits subplots - deviations of the least-square fits from the ab initio data Distribution of the least-square fitsresidues for electronic ground state points Dependence of the Morse potential parameters on He3+ shape (electronic ground state) Benchmark calculations Computational method CASSCF(5,10) / icMRCI (5 active electrons in 10 active orbitals) [3] basis set d-aug-cc-pVTZ program 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 curves for the electronic ground state and the first two excited states calculated for C2v geometries ○ – our calculations + – M. F. Satterwhite and G. I. Gellene, J. Phys. Chem. 99, 1339 (1995) subplots – comparison with literatura data Potential energy surfaces for C2v geometries A detailed plot of the C2v PES for the electronic ground state Equilibrium structure of He3+(comparison with literature) method EminReDe [hartree] [bohr] [eV] QICSD(T), aug-cc-pVTZ [6] -7.896672 2.340 2.598 QICSD(T), aug-cc-pVQZ [6] -7.902103 2.336 2.640 MRD-CI, cc-pVTZ [7] -7.8954 2.34 2.59 this work, benchmark -7.897021 2.339 2.639 this work, economy -7.896084 2.341 2.639 (?) [6] M. F. Satterwhite and G. I. Gellene, J. Phys. Chem. 99, 1339 (1995) [7] E. Buonomo et al., Chem. Phys. Letters 259, 641 (1996) Grant No. 203/06/XXXX (submitted) of the Grant Agency of the Czech Republic Grant No. 203/04/2146 of the Grant Agency of the Czech Republic