FWO G022914N (DVN/PB/SDB) FWOOPR2014002001

The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes.

It was shown recently that Birkho's theorem for doubly stochastic matrices
can be extended to unitary matrices with equal line sums whenever the dimension
of the matrices is prime. We prove a generalization of the Birkho
theorem for unitary matrices with equal line sums for arbitrary dimension.

Atomistic calculations are performed to investigate plastic slip in the {321} system in body-centred cubic iron. Several modern interatomic potentials, developed over the last decade, are applied to compute the stacking fault -line energy in the {321} plane and the results are compared with the ab initio prediction. The applied potentials have shown strong deviations, but several potentials acquired good qualitative agreement with the ab initio data. Depending on the applied potential, the lowest value of the Peierls stress for the edge dislocation (ED) is 50MPa (Ackland and Bacon from 1997) and the highest is 550MPa (Dudarev and Derlet from 2005), while for the screw dislocation it is much higher, in the range 1-2GPa. At finite temperature, however, the flow stress of the ED is found to decrease exponentially reaching a negligible value at about 200K, irrespective of the applied potential. On the basis of the data obtained using Ackland-Mendelev potential from 2004, we conclude that the slip resistance of the {321} system is in between the resistance of the {110} and {112} slip systems.

Starting from integrable su(2) (quasi-)spin Richardson–Gaudin (RG) XXZ models we derive several properties of integrable spin models coupled to a bosonic mode. We focus on the Dicke–Jaynes–Cummings–Gaudin models and the two-channel (p + ip)-wave pairing Hamiltonian. The pseudo-deformation of the underlying su(2) algebra is here introduced as a way to obtain these models in the contraction limit of different RG models. This allows for the construction of the full set of conserved charges, the Bethe ansatz state, and the resulting RG equations. For these models an alternative and simpler set of quadratic equations can be found in terms of the eigenvalues of the conserved charges. Furthermore, the recently proposed eigenvalue-based determinant expressions for the overlaps and form factors of local operators are extended to these models, linking the results previously presented for the Dicke–Jaynes–Cummings–Gaudin models with the general results for RG XXZ models.

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