Journal of M olecular Structure, 88 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK (1982) 191-200 THEOCHEM Elsevier Scientific Publishing Company, Amsterdam -Printed in The Netherlands ON THE CONVERGENCE BEHAVIOUR OF THE PADE TYPE VARIATIONAL FUNCTIONS P. JOLLY, R. P. SAXENA and P. K. SRIVASTAVA Department of Physics and Astrophysics, University of Delhi, Delhi-110007 (India) K. V. SANE Department of Chemistry, University of Delhi, Delhi-l 10007 (India) (Received 4 August 1981) ABSTRACT The convergence behaviour of the Pad6 type non-linear functions has been investigated with respect to the helium wavefunction. The expectation values of various operators for both Pade and linear functions have been determined, as have the orbital and correlation cusp values. The faster convergence of Pade type functions is maintained for properties other than energy. INTRODUCTION Studies on a test system [l] , and on the ground states of the helium atom [2,3] and of the anharmonic oscillator [4], have demonstrated that the Pad6 type functions constitute a promising class of trial functions for solving the Schrodinger equation by the variational method. The quality of the wavefunction and the value of the energy show that rational trial functions achieve a given level of precision with fewer number of parameters than the corresponding linear trial functions. The investigations so far have been con- fined to the lower-order forms, not only because they are computationally simpler but also because they are likely to be adequate in situations where extreme accuracy is not desired. The question as to whether the higher-order forms retain the economy in the number of free parameters is interesting since it controls the possibility of obtaining compact but highly precise wave- functions for the helium atom, anharmonic oscillator, Stark effect and similar systems. It is well known that accurate linear variational functions for such problems are unwieldy due to the notoriously slow convergence of the poly- nomial bases. It follows that a comparative evaluation of the convergence behaviour of the sequences of the rational and linear forms serves as a useful prelude to a detailed study of the higher-order forms. 0166,-1280/82/0000-0000/$02.75 0 1982 Elsevier Scientific Publishing Company