Theoretical investigation of the cyclic conformer of ozone

Ab initio SCF and CI calculations are reported which find the cyclic conformer of ozone to lie 16 kcal/mole above the preferred (open-chain) form of this substance. Polarization functions in the AO basis set are found to be quite important in this determination, strongly favoring the cyclic species. The possible experimental significance of such a relatively stable ring conformer of ozone is assessed.     

Aluminium

Ohne Zusammenfassung     

Calculation of wavefunctions and frequencies for noninfinitesimal vibrations: Comparison of various methods using ab initio CI potential curves

Three computational methods employing different means of representing molecular potentials are used to obtain wavefunctions and energy levels for noninfinitesimal vibrations. An interpolation scheme based on a cubic spline fitting procedure is introduced to supplement the CI energy results obtained explicitly in actual calculations. As long as a representative set of potential points is available it is found that the results of all three methods (two of variational and one of numerical integration type) are quite consistent, for both bending and stretching vibrations of ground and electronically excited states (examples for HCN and O₂ are considered). In addition a comparison of one- and two-dimensional bending vibrational treatments is made.     

Certification with optimal control strategies

The optimal control methodology called concentration-of-measure optimal control (COMOC), seeks to minimise a concen- tration-of-measure upper bound on the probability of failure of an uncertain system. This bound is computed for a system characterised by a single performance measure depending on random inputs. This work considers controlled multibody dynamics taking place in an uncertain environment. The goal is to quantify uncertainty in a controlled robot manoeuvre and to minimise the probability of failure with regard to a performance measure. First, a deterministic optimal control problem is solved, yielding state and control trajectories that minimise an objective function. Boundary conditions for the optimal control problem are chosen such that the system performs ideally in the sense of the performance measure. Secondly, the obtained manoeuvre is reconsidered in the presence of uncertainty. Using a concentration-of-measure inequality, a rigorous upper bound for the probability of failure is derived. Finally, an optimisation is performed that searches for a control sequence (in the neighbourhood of the given one), that minimises the probability of failure. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-empirical CI potential curves for the ground and excited states of PH and its positive ion

A series of calculated potential curves is reported for the low lying valence and (selected) Rydberg states of the PH molecule by employing the multi-reference (single- and) double-excitation CI method. A large AO basis including f functions on phosphorous is chosen for this study and up to twenty main configurations are used to generate a given MRD-CI space in the accompanying theoretical treatment. Very good agreement is obtained between calculation and experiment for a variety of spectroscopic constants and a number of predictions for electronically excited states of PH are made for cases in which no comparable empirical data are yet available. The repulsive ⁵∑^- state is shown to be responsible for the predissociation of several states of the neutral system and is also thought to explain the failure to detect a number of low lying Rydberg states experimentally. Analogous calculations for the PH⁺ molecular ion have also been carried out and spectroscopic constants for this system are reported. In this case the ⁴Π state plays much the same role as the neutral ⁵∑^- species in bringing about predissociation in its electronic spectrum. Finally a comparison is made throughout between the results for PH and PH⁺ and a number of isovalent systems, especially NH and NH⁺ and also SiH.     

On frequency estimations in phase fitted variational integrators for the general N-body problem

In the present work, the advantages of high order variational integrator methods are combined with phase lag properties for the numerical integration of the general N-body problem. Expressing the action integral at any intermediate points along the curve segment using a discrete Lagrangian that depends only on the end points of the interval, high order integrators can be obtained by defining the discrete Lagrangian in any time segment as a weighted sum on intermediate points, whose expressions for positions and velocities use Galerkin interpolation techniques. When oscillatory behavior is taken into account, the methods derived use trigonometric interpolation functions that depend on a frequency, which needs to be estimated. For that, using phase lag analysis, a new way to derive methods has been developed, that uses frequency estimation for each body at every time step. Results on special cases of the N-body problem show more stable orbits and less energy error when compared with the linear interpolation scheme. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)