Thanks to reviewers in 2009

Acknowledgement to Referees

Thanks to reviewers in 2009     

Comparison of a Rapidely Converging Phase Field Model for Interfaces in Solids with the Allen-Cahn Model

We compare two phase field models for interfaces in elastic solids carrying low surface energy. One model has hybrid properties of a Hamilton-Jacobi and a parabolic equation, the other is the Allen-Cahn model. For vanishing width of the interface we construct asymptotic solutions of second order for the hybrid model and of first order for the Allen-Cahn model. These constructions show that the width of the diffused interface necessary for tracking accurately the sharp interface can be chosen much larger for the hybrid model than for the Allen-Cahn model, and that moreover the hybrid model can describe interfaces with nonlinear kinetic relation. This explains why numerical simulations based on the hybrid model are considerably more effective. These simulations are discussed in the last section.     

A generalised 17-state vibronic-coupling Hamiltonian model for ethylene

In a previous work [B. Lasorne, M. A. Robb, H.-D. Meyer, and F. Gatti, "The electronic excited states of ethylene with large-amplitude deformations: A dynamical symmetry group investigation," Chem. Phys. 377, 30-45 (2010); and ibid. 382, 132 (2011) (Erratum)], we investigated the electronic structure of ethylene (ethene, C(2)H(4)) in terms of 17 dominant configurations selected at the multiconfiguration self-consistent field level of theory. These were shown to be sufficient to recover most of the static electron correlation among the first valence and Rydberg states at all geometries. We also devised a strategy to build a 17-quasidiabatic-state matrix representation of the electronic Hamiltonian for curvilinear coordinates using dynamical symmetry. Here, we present fitted surfaces in the form of a generalised vibronic-coupling Hamiltonian model for two nuclear coordinates, CC bond stretching and torsion. Dynamic electron correlation is included into the electronic structure to improve the energetics of the Rydberg states at the multireference configuration interaction level of theory. The chemical interpretation of the adiabatic states of interest does not change qualitatively, which validates our choice of underlying quasidiabatic states in the model. The absorption spectrum is calculated with quantum dynamics and partially assigned. This first two-dimensional model shows a surprisingly good agreement with the experimental spectrum.     

Numeric kinetic energy operators for molecules in polyspherical coordinates

Generalized curvilinear coordinates, as, e.g., polyspherical coordinates, are in general better adapted to the resolution of the nuclear Schro?dinger equation than rectilinear ones like the normal mode coordinates. However, analytical expressions of the kinetic energy operators (KEOs) for molecular systems in polyspherical coordinates may be prohibitively complicated for large systems. In this paper we propose a method to generate a KEO numerically and bring it to a form practicable for dynamical calculations. To examine the new method we calculated vibrational spectra and eigenenergies for nitrous acid (HONO) and compare it with results obtained with an exact analytical KEO derived previously [F. Richter, P. Rosmus, F. Gatti, and H.-D. Meyer, J. Chem. Phys. 120, 6072 (2004)]. In a second example we calculated π → π* photoabsorption spectrum and eigenenergies of ethene (C(2)H(4)) and compared it with previous work [M. R. Brill, F. Gatti, D. Lauvergnat, and H.-D. Meyer, Chem. Phys. 338, 186 (2007)]. In this ethene study the dimensionality was reduced from 12 to 6 by freezing six internal coordinates. Results for both molecules show that the proposed method for obtaining an approximate KEO is reliable for dynamical calculations. The error in eigenenergies was found to be below 1 cm(-1) for most states calculated.     

Consequences of Strain for the Structure of Aliphatic Molecules

The chemist is accustomed to deriving structures and preferred conformations of organic compounds from rigid molecular models and standard values for bond lengths, bond angles, and torsional profiles. In the case of strained compounds, this rigid structural model has to be abandoned and replaced by a flexible one which takes individual conditions of strain into consideration. It is shown, on the basis of new experimental structure data, that the force field method is suitable and highly reliable for the calculation of structural parameters and preferred conformations of strained compounds. It is, therefore, capable of replacing the rigid molecular model. Furthermore, the systematic analysis of strain induced angle and bond deformation gives a new pivot for the development of a qualitative discussion of deformation in strained molecules and hence for improved conformational analysis. — In the course of this work we were able to isolate two rotamers of D,L -3,4-di(1-adamantyl)-2,2,5,5-tetramethylhexane; this is the first isolation of a rotamer pair of an aliphatic hydrocarbon.