Theor Chim Acta (1987) 72:265-276 9 Springer-Verlag 1987 The use of supercomputers for the variational calculation of ro-vibrationally excited states of floppy molecules* Brian T. Sutcliffe 1, Jonathan Tennyson 2 and Steven Miller 2 Department of Chemistry, University of York, York Y01 5DD, UK 2 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK The advent of supercomputers has led to great advances in electronic structure calculations and to the ab initio calculation of molecular spectra. Recent theoretical developments have allowed us to develop a two-step variational algorithm for the calculation of rotationally highly excited states of floppy molecules. This algorithm allows highly accurate nuclear motion calculations to be performed on low-lying ro-vibrational states and greatly extends the range of states that can practicably be considered. The algorithm has been adapted to run efficiently on the Cray supercomputers. Analysis of the timings suggest that construction of the secular matrix is highly vectorised and that the special structure of secular matrix can be used to give rapid diagonalisation. The limiting facI:or on these calculations is the available fast storage, but analysis suggests that this bottleneck could be removed by use.of a Solid State Device (SSD). Sample results are given for calculations involving a range of rotational excitation. An adaptation of the algorithm to a loop of parallel processors is also suggested. Key words: Vibration-rotation -- Variational method -- Supercomputers -- Diagonalisation 1. Introduction The impact of supercomputers on molecular structure calculations has been a profound one and is; directly discussed in other contributions here. Since their * This paper was presented at the International Conference on 'The Impact of Supercomputers on Chemistry', held at the University of London, London, UK, 13-16 April 1987