Search

We demonstrate that, if a truncated expansion of a wave function is Large, then the standard excited states computational method, of optimizing one root of a secular equation, according to the theorem of Hylleraas, Undheim and McDonald (HUM), tends to the correct excited wave function, comparable to that obtained via our proposed minimization principle for excited states [J. Comput. Meth. Sci. Eng. 8, 277 (2008)] (independent of orthogonality to lower lying approximants). However, if a truncated expansion of a wave function is Small - that would be desirable for large systems - then the HUM-based methods may lead to an incorrect wave function - despite the correct energy (: according to the HUM theorem) whereas our method leads to correct, reliable, albeit Small truncated wave functions. The demonstration is done in He excited states, using truncated series Small expansions both in Hylleraas coordinates, and via standard configuration-interaction truncated Small expansions, in comparison with corresponding Large expansions. Beyond that, we give some examples of linear combinations of Hamiltonian eigenfunctions that have the energy of the 1st excited state, albeit they are orthogonal to it, demonstrating that the correct energy is not a criterion of correctness of the wave function., 12 pages, 5 figures, 3 tables, ICCMSE2016 conference. arXiv admin note: text overlap with arXiv:1605.07967

There is an unresolved discrepancy between theory and experiment about the observed hindrance in dissociative adsorption of O2 on Al(111). In an attempt to understand the hindrance, we have investi...

Employing both multireference configuration interaction (MRCI) and density functional theory (DFT) methods, we have studied the interaction of O2 with a tetrahedral Al4 cluster in the total spin triplet state. For a parallel to the base approach of O2 facing an apex of the pyramid, the O2 adsorption is hindered by a barrier. Both the MRCI and the DFT calculations show that after a small barrier, there are two local energy minima: a shallow one just above the apex atom and another deeper one below the apex atom. The latter corresponds to dissociative O2 adsorption. We discuss the implications of these findings for the understanding of O2 adsorption on defect sites of Al surfaces.

We have studied the interaction of an oxygen molecule with Al clusters and Al(111) using both wave-function-based quantum chemistry methods and density functional theory (DFT). These calculations were motivated by the fact that molecular beam experiments indicate that the adsorption of O2 on Al(111) should be activated whereas periodic DFT calculations yield purely attractive adsorption paths for almost all impact configurations of O2 on Al(111). On small Al4 clusters, accurate wave-function-based quantum chemistry methods find a non-vanishing barrier in the O2 adsorption. The DFT calculations for slabs and larger Al clusters confirm the important role of spin effects for the O2 dissociation barrier on Al. The results indicate that exchange-correlation effects play a crucial role for the determination of the adsorption barrier in the O2/Al system but their determination is hampered by serious technical problems that are discussed in detail.

We demonstrate that, if a truncated expansion of a wave function is small, then the standard excited states computational method, of optimizing one root of a secular equation, may lead to an incorrect wave function - despite the correct energy according to the theorem of Hylleraas, Undheim and McDonald - whereas our proposed method [J. Comput. Meth. Sci. Eng. 8, 277 (2008)] (independent of orthogonality to lower lying approximants) leads to correct reliable small truncated wave functions. The demonstration is done in He excited states, using truncated series expansions in Hylleraas coordinates, as well as standard configuration-interaction truncated expansions., 4 pages, 1 figure, 2 tables, ICCMSE2016: International Conference of Computational Methods in Science and Engineering

It is shown that the standard methods of computing excited states in truncated spaces must yield wave functions that, beyond truncation, are in principle veered away from the exact, and a remedy is demonstrated via a presented functional, F$_n$, obeying a minimization principle for excited states. It is further demonstrated that near avoided crossings, between two MCSCF 'flipped roots' the wave function that leads to the excited state has the lowest F$_n$., 4 pages, 1 figure, International Conference of Computational Methods in Sciences and Engineering - 2015 / Computational Chemistry, 20-23 March 2015, Athens, GREECE

Concise analytic, nonorthogonal but selectively orthogonalizable, modified Laguerre type atomic orbitals are developed, providing conciseness, clear physical interpretation, and near-equivalent accuracy with numerical multi-configuration self-consistent field, to atomic configuration interaction calculations. By analyzing the general Eckart theorem, which introduces an energy augmentation to the variational criterion for excited states, securing against variational collapse, we use them to calculate several excited atomic states known to be in danger of suffering from variational collapse. We also use them to calculate highly excited states, applied to computation of recently measured VUV spectra of He states near the second ionization threshold. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

We construct transferable tight-binding (TB) parameters for ferromagnetic and paramagnetic iron by fitting the total energy and the electronic band structure to three prototype crystal structures of Fe (BCC, both ferromagnetic and paramagnetic; and FCC, paramagnetic only) calculated by the general-potential linearized augmented plane wave (LAPW) method. We use these TB parameters to calculate the total energy and other properties of Fe in various other crystal structures, which we compare with independent LAPW results. The agreement between LAPW and TB results is very good, suggesting a realistic parametric physical description in the tight-binding approximation for any structure of Fe.

We have performed Monte Carlo simulations of magnetic semiconductors above and below the nearest-neighbour percolation threshold (NNPT) using a classical Heisenberg Hamiltonian with up to third nearest-neighbour (nn) interactions. Large clusters were created allowing use of realistically low magnetic fields (10 G). Above NNPT our results, apart from confirming the existing picture of this class of materials, also show that the inclusion of the second and third (nn) interactions increases the frustration, thus making the transition temperature smaller and closer to experiment than calculated via the first nn interactions only. A physically plausible explanation is given. Below NNPT our results strongly support the validity of the hypothesis (D. Karaoulanis, J.P. Xanthakis, C. Papatriantafillou, J. Magn. Magn. Mater. 161 (1996) 231), that the experimentally observed susceptibility is the sum of two contributions: a paramagnetic one due to isolated magnetic clusters, and a spin-glass contribution due to an ‘infinite’ percolative cluster formed from exchange interactions of further than first nearest neighbours. Our calculated phase diagram is in very good agreement with the experiment.

Calculations of low-lying quartet states of He2 - are reported, in which a positively charged core He2 + holds two remote electrons in antibonding orbitals, i.e. spending most time either side of and away from the central nodal plane, of similarly large RMS extent. A previously reported 4 u state is reinterpreted and shown to be a Rydberg state. Further, a 4 u state and a 4 g , the lowest state of this category, are reported. The calculation, performed in prolate spheroidal coordinates, is variational, utilizing one-electron diatomic-molecule-type orbitals, in full configuration interaction.