Search results for "Degenerate energy levels"
showing 10 items of 221 documents
Tensorial development of the rovibronic Hamiltonian and transition moment operators for octahedral molecules
2001
Abstract We present a development of the Hamiltonian, dipole moment and polarizability operators of octahedral XY 6 molecules in a degenerate electronic state. These rovibronic operators are written with the aid of a tensorial formalism derived from the one already used in Dijon in the case of molecules in a non-degenerate electronic state. Electronic operators are defined from the group theory properties. Transition moment operators are introduced in order to consider rovibronic transitions. Spectrum simulations are made thanks to a new version of the HTDS sofware [J. Quant. Spectrosc. Radiat. Transfer 66 (2000) 16] used for the calculation of rovibrational spectra.
Interpretation of the electronic absorption spectrum of free base porphin by using multiconfigurational second-order perturbation theory
1998
Abstract Multiconfigurational second-order perturbation (CASPT2) calculations have been performed on the low-lying optically allowed valence excited states of the free base porphin molecule in order to assign the four lowest bands of the spectrum. The low-lying triplet states have also been characterized. A basis set of the atomic natural orbital type of split-valence plus polarization quality for first-row atoms has been employed. Polarization functions are important for an accurate description of the transitions. These CASPT2 results provide a consistent picture of the experimental spectrum. Each band of the spectrum up to 4.5 eV is composed of a pair of states, which become degenerate in…
Dimethoxy Aromatic Compounds. VIII. Degenerate Dealkylation-Realkylation Reaction of 1-Bis(2,4-dimethoxyphenyl)-2-methylpropane.
1994
The condensation reaction under acid condition of the benzylic alcohols 1, 2 and 3 with the hexadeutero dimethoxybenzenes 4, 5 and 6 leads to the expected hexadeutero bis(dimethoxyphenyl)-2-methylpropanes 7, 8 and 9, respectively. However, the presence of both dodecadeutero and unlabelled 1-bis(2, 4-dimethoxyphenyl)-2-methylpropanes 10 and 11 indicates that 9 undergoes a rapid degenerate dealkylation-alkylation reaction.
Mechanics of invagination and folding: Hybridized instabilities when one soft tissue grows on another
2015
We address the folding induced by differential growth in soft layered solids via an elementary model that consists of a soft growing neo-Hookean elastic layer adhered to a deep elastic substrate. As the layer/substrate modulus ratio is varied from above unity towards zero we find a first transition from supercritical smooth folding followed by cusping of the valleys to direct subcritical cusped folding, then another to supercritical cusped folding. Beyond threshold the high amplitude fold spacing converges to about four layer thicknesses for many modulus ratios. In three dimensions the instability gives rise to a wide variety of morphologies, including almost degenerate zigzag and triple-ju…
easyPAC: A Tool for Fast Prediction, Testing and Reference Mapping of Degenerate PCR Primers from Alignments or Consensus Sequences
2012
Video abstract A video abstract by the authors of this paper is available. video-abstract8870.mov
On some partial data Calderón type problems with mixed boundary conditions
2021
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. T…
Variational parabolic capacity
2015
We establish a variational parabolic capacity in a context of degenerate parabolic equations of $p$-Laplace type, and show that this capacity is equivalent to the nonlinear parabolic capacity. As an application, we estimate the capacities of several explicit sets.
A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics
2011
International audience; We present a complete, exact and efficient implementation to compute the edge-adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the edge-adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always comp…
On the Porosity of Free Boundaries in Degenerate Variational Inequalities
2000
Abstract In this note we consider a certain degenerate variational problem with constraint identically zero. The exact growth of the solution near the free boundary is established. A consequence of this is that the free boundary is porous and therefore its Hausdorff dimension is less than N and hence it is of Lebesgue measure zero.
Beyond the spin model: exchange coupling in molecular magnets with unquenched orbital angular momenta.
2011
In this critical review we review the problem of exchange interactions in polynuclear metal complexes involving orbitally degenerate metal ions. The key feature of these systems is that, in general, they carry an unquenched orbital angular momentum that manifests itself in all their magnetic properties. Thus, interest in degenerate systems involves fundamental problems related to basic models in magnetism. In particular, the conventional Heisenberg-Dirac-Van Vleck model becomes inapplicable even as an approximation. In the first part we attempt to answer two key questions, namely which theoretical tools are to be used in the case of degeneracy, and how these tools can be employed. We demons…