On the relationship of normal modes to local modes in molecular vibrations

A simple model for the effective vibrational hamiltonian of the XH stretching vibrations in H2O, NH3 and CH4 is considered, based on a morse potential function for the bond stretches plus potential and kinetic energy coupling between pairs of bond oscillators. It is shown that this model can be set up as a matrix in local mode basis functions, or as a matrix in normal mode basis functions, leading to identical results. The energy levels obtained exhibit normal mode patterns at low vibrational excitation, and local mode patterns at high excitation. When the hamiltonian is set up in the normal mode basis it is shown that Darling-Dennison resonances must be included, and simple relations are found to exist between the xrs, gtt, and Krrss anharmonic constants (where the Darling-Dennison coefficients are denoted K) due to their contributions from morse anharmonicity in the bond stretches. The importance of the Darling-Dennison resonances is stressed. The relationship of the two alternative representations of this local mode/normal mode model are investigated, and the potential uses and limitations of the model are discussed.

Potential for clean yam minisett production by resource-poor farmers in the middle-belt of Nigeria

Yarn minisett technique (YMT) has been promoted throughout West Africa since the 1980s as a sustainable means of producing clean yarn planting material, but adoption of the technique is Often reported as being patchy at best. While there has been much research Oil the factors that influence adoption of the technique, there have been no attempts to assess its economic viability under 'farmer-managed' as distinct from 'on station' conditions. The present paper describes the results of farmer-managed trials employing the YMT (white yarn: Dioscorea rotundata) at two villages in Igalaland, Kogi State, Nigeria. One of the villages (Edeke) is on the banks of the River Niger and represents it specialist yarn environment, whereas the other village (Ekwuloko) is inland, where farmers employ a more general cropping system. Four farmers were selected in each of the two villages and asked to plant a trial comprising two varieties of yam, their popular local variety its well its another variety grown in other parts of Igalaland, and to treat yarn setts (80-100 g) with either woodash or insecticide/nematicide + fungicide mix (chemical treatment). Results suggest that while chemical sett treatment increased yield and hence gross margin compared with woodash, if household labour is costed then YMT is not economically viable. However, the specialist yarn growers of Edeke were far more positive about the use of YMT as they tended to keep the yarn seed tubers for planting rather than sell them. Thus, great care needs to be taken with planning adoption surveys on the assumption that all farmers should adopt a technology.

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.