OSTRAVA

1. OSTRAVA Q-th P-th P-th Q-th N multielectron wave functions of the form where Nis number of He atoms, n=2N-1 is number of electrons, ai is helium 1s-spinorbital with centre on i-th atom (dash over a label denotes opposite spin orientation), ||represents Slater determinant (antisymetrizator).K-th wavefunction of the base represents electronic state with the electron hole on K-th helium atom. Q-th P-th P-th P-th Q-th P-th THEORY II – TRIATOMICS-IN-MOLECULES METHOD (TRIM) General theory: R. Kalus, Universitas Ostraviensis, Acta Facultatis Rerum Naturalium, Physica-Chemia 8/199/2001. TRIM Hamiltonian Triatomic inputs Eneut(ABC) … energy of a neutral (ABC) fragment in the electronic ground-state, calculated usingsemiempirical two- and three-body potentials for helium,EJ(ABC) … energy of an ionic (ABC) fragment in the electronic ground (i = 1) and the first two excited (J = 2,3) states, taken from ab initio calculations on He3+ (see also this poster session: I. Paidarová et al., Ab initio calculations on He3+ of interest for semiempirical modelling.) Hamilton Matrix , where where is energy of the adiabatic (stationary) state Coefficients xKJ are calculated using the DIM method; in case the three-body correction to the He3+ interaction energy is a small perturbation, the resulting Hamiltonian matrix is expected to be correct up to 1st order of perturbation theory. Asymmetric (false) configuration results from standard DIM model and from DIM with overlap model with Zef >= 2. 1 Median of deviations: DIM – 137 meV Overlap (FIT) – 122 meV Overlap (Z = 1.9) – 65 meV Symmetric (true) configuration results from ab-initio model and DIM with overlap model with Zef <2. 1 1 Median of deviations: Median of deviations: DIM – 117 meV DIM – 168 meV Overlap (FIT) – 96 meV Overlap (FIT) – 143 meV Overlap (Z = 1.9) – 52 meV Overlap (Z = 1.9) – 67 meV Semiempirical Modelling of HeN+ ClustersDaniel Hrivňáka, František Karlickýa, Ivan Janečeka, Ivana Paidarováb, and René KalusaaDepartment of Physics, University of Ostrava, Ostrava, Czech RepublicbJ. Heyrovsky Institut of Physical Chemistry, Prague, Czech republicFinancial support: the Grant Agency of the Czech Republic (grants No. 203/02/1204 and 203/04/2146), Ministry ofEducation of the Czech Republic (grant No. 1N04125). THEORY I – DIATOMICS-IN-MOLECULES METHOD (DIM) General theory: F. O. Ellison, J. Am. Chem. Soc. 85 (1963), 3540. Application to HeN+: Knowles, P. J., Murrel, J. N., and Hodge, E. J., Mol. Phys. 85 (1995), 243. Ovchinnikov et al., J. Chem. Phys. 108/22 (1998), 9350. DIM Hamiltonian Diatomic inputs Thee potential energy curves for He2 and He2+: Eneut(r) – ground-state for He2 [R. A. Aziz, A. R. Janzen, and M. R. Moldover, Phys. Rev. Letters 74 (1995) 1586 ]. Eu+(r), Eg+(r) – ground state (2Su+) and first excited state (2Sg+) of He2+ [F.X. Gadéa, I. Paidarová, Chem. Phys. 209 (1996) 281. J. Xie, B. Poirier, and G. I. Gellene, J. Chem. Phys. 122 (2005) Art. No. 184310. ] DIM Basis Overlap matrix for He3+ where Hamilton Matrices b) Overlap included a) Overlap neglected and is overlap integral of atomic orbitals localized on the J-th and K-th atom respectively. For hydrogen-like orbitals it has the form as where and where CONCLUSIONS RESULTS – COMPARISON WITH AB INITIO DATA2 • Standard DIM method gives no satisfactory results for Hen+ clusters. Stable configuration of He3+trimer in DIM approach is a linear asymmetrical instead of the linear symmetrical, for example3. • Inclusion of the overlap to the DIM method gives relevant changes of results. Parameters of the overlap formula can be set properly to minimize deviation between ab initio data and resulted data from DIM model. The most important parameter is effective atomic number Zef. • Correct (i. e. symmetrical) stable configuration of He3+ results from model DIM + overlap with Zef < 2. The best agreement with ab initio data has been achieved for values of Zef between 1.6 and 1.9, but resulting typical deviation about 60 meV in potential energy is not quite satisfactory. • Next possibility to enhance accuracy of the DIM + overlap method is to fit some parameters in the overlap formula. How indicate our first results, this way is not very hopeful. • We want to attain really better results by using the so called triatomics-in-molecules method (TRIM). In opposite of the DIM method, the TRIM method organically involves three-body corrections to the diatomic energies. • As an input to the TRIM method serve three-atomic potential energy hypersurfaces for three lowest energy levels. Construction of these accurate hypersurfaces is our topical goal. • The semiempirical methods mentioned above are based on the semi-classical Born-Oppenheimer approach, whose application to the lightweight helium atoms is quite limited. The main advantage of these methods is their computational inexpensivity. • It will be necessary to use some fully quantum method for more exact results(Path Integral Monte Carlo, Diffusion Monte Carlo etc.). 3Very good known results, see Knowles, P. J., Murrell, J. N., Mol. Phys. 87 (1996), 827, for example. 1 Fitted generalized overlap formula: 2 See this poster session, Paidarová a kol., Ab initio calculations on He3+ of interest for semiempirical modelling of Hen+.