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

Carter, S., Handy, N. C. and Mills, I. (1990) Variational calculations of rovibrational states: a precise high-energy potential surface for HCN [and discussion]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 332 (1625). pp. 309-327. ISSN 1364-503X

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To link to this item DOI: 10.1098/rsta.1990.0117

## Abstract/Summary

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.

Item Type: Article Yes Faculty of Life Sciences > School of Chemistry, Food and Pharmacy > Department of Chemistry 7606 Royal Society Publishing

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