Variational calculations of rovibrational states: a precise high-energy potential surface for HCN [and discussion]

We report the results of variational calculations of the rovibrational energy levels of HCN for J = 0, 1 and 2, where we reproduce all the ca. 100 observed vibrational states for all observed isotopic species, with energies up to 18000 cm$^{-1}$, to about $\pm $1 cm$^{-1}$, and the corresponding rotational constants to about $\pm $0.001 cm$^{-1}$. We use a hamiltonian expressed in internal coordinates r$_{1}$, r$_{2}$ and $\theta $, using the exact expression for the kinetic energy operator T obtained by direct transformation from the cartesian representation. The potential energy V is expressed as a polynomial expansion in the Morse coordinates y$_{i}$ for the bond stretches and the interbond angle $\theta $. The basis functions are built as products of appropriately scaled Morse functions in the bond-stretches and Legendre or associated Legendre polynomials of cos $\theta $ in the angle bend, and we evaluate matrix elements by Gauss quadrature. The hamiltonian matripx is factorized using the full rovibrational symmetry, and the basis is contracted to an optimized form; the dimensions of the final hamiltonian matrix vary from 240 $\times $ 240 to 1000 $\times $ 1000.We believe that our calculation is converged to better than 1 cm$^{-1}$ at 18 000 cm$^{-1}$. Our potential surface is expressed in terms of 31 parameters, about half of which have been refined by least squares to optimize the fit to the experimental data. The advantages and disadvantages and the future potential of calculations of this type are discussed.

Solvent influences on metastable polymorph lifetimes: real-time interconversions using energy dispersive X-ray diffractometry

Solvent influences on the crystallization of polymorph and hydrate forms of the nootropic drug piracetam (2-oxo-pyrrolidineacetamide) were investigated from water, methanol, 2-propanol, isobutanol, and nitromethane. Crystal growth profiles of piracetam polymorphs were constructed using time-resolved diffraction snapshots collected for each solvent system. Measurements were performed by in situ energy dispersive X-ray diffraction recorded in Station 16.4 at the synchrotron radiation source (SRS) at Daresbury Laboratory, CCLRC UK. Crystallizations from methanol, 2-propanol, isobutanol, and nitromethane progressed in a similar fashion with the initial formation of form I which then converted relatively quickly to form II with form III being generated upon further cooling. However, considerable differences were observed for the polymorphs lifetime and both the rate and temperature of conversion using the different solvents. The thermodynamically unstable form I was kinetically favored in isobutanol and nitromethane where traces of this polymorph were observed below 10 degrees C. In contrast, the transformation of form II and subsequent growth of form III were inhibited in 2-propanol and nitromethane solutions. Aqueous solutions produced hydrate forms of piracetam which are different from the reported monohydrate; this crystallization evolved through successive generation of transient structures which transformed upon exchange of intramolecular water between the liquid and crystalline phases. (c) 2007 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 96:1069-1078, 2007.

Probabilistic wind power forecasts with an inverse power curve transformation and censored regression

Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 h are generally made by using statistical methods to post-process forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the non-linear relationship between wind speed and power production and the limited range of power production between zero and nominal power of the turbine. In practice, these problems are often tackled by using non-linear non-parametric regression models. However, such an approach ignores valuable and readily available information: the power curve of the turbine's manufacturer. Much of the non-linearity can be directly accounted for by transforming the observed power production into wind speed via the inverse power curve so that simpler linear regression models can be used. Furthermore, the fact that the transformed power production has a limited range can be taken care of by employing censored regression models. In this study, we evaluate quantile forecasts from a range of methods: (i) using parametric and non-parametric models, (ii) with and without the proposed inverse power curve transformation and (iii) with and without censoring. The results show that with our inverse (power-to-wind) transformation, simpler linear regression models with censoring perform equally or better than non-linear models with or without the frequently used wind-to-power transformation.