On the effectiveness of ultra-soft pseudopotentials in plane-wave based molecular electronic structure calculations Robert J. Meier DSM Research, P.O. Box 18, 6160 MD Geleen, The Netherlands Received 26 January 1998; received in revised form 19 March 1998; accepted 7 September 1998 Abstract The efficiency of the Vanderbilt type pseudopotential is used to study the geometry and total energy for water and ethylene as a function of cut-off energy and box size. Geometrical parameters go through an extreme as a function of the energy cut-off before converging. This seems a more general phenomenon, not typical for Vanderbilt pseudopotentials only. Although the previously claimed value of 25 Ry for the cut-off energy is considered adequate for many purposes, strict convergence requires a substantially higher energy cut-off. However, it is suggested that for relative chemical reaction energies much lower cut-off energies may be employed.  1999 Elsevier Science B.V. All rights reserved. Keywords: Pseudopotentials; Car–Parrinello; Cut-off energy; Molecular structure; Electronic structure; Basis set 1. Introduction In recent years plane-wave based electronic struc- ture calculations have found increasing attention within the computational chemistry community. In particular, it has been shown that Car–Parrinello type [1] dynamics simulations can be applied to reveal the full dynamics of chemical reactions [2–6]. Whereas quite a number of papers can be found addressing applications of the Car–Parrinello and related methods, fewer papers have been devoted to the accuracy of this type of calculations, the compar- ison with quantum mechanical calculations using localised basis sets, and the efficiency of the method. An exception is the excellent paper by Andrews et al. [7] in which results arising from a plane wave basis set were compared to Gaussian basis set calculations. A series of 10 small molecules were studied, with a more extensive account on the water molecule. The quality of the plane-wave description of the molecular electronic wavefunction compared to the Gaussian orbital description was discussed. Plane-wave based calculations are memory intensive, and when the full dynamics is probed they are CPU intensive. There- fore, the efficiency of the scheme is of high relevance. The efficiency of the method is particularly relevant because so far it seems that only this type of methods allows for quantum calculations on, e.g. realistic cata- lyst species comprising up to a few hundred atoms, eventually including the full dynamics. In this contribution we use the claimed efficiency of the ultra-soft Vanderbilt pseudopotentials to study the convergence of geometrical parameters and of the total energy for two, small, molecular systems. The use of the ultra-soft Vanderbilt pseudopotential for the water molecule is not new [8,9]. Its efficiency has been claimed [8], e.g. a cut-off energy of 24Ry has been claimed [10,11] sufficient for oxygen, which is to be compared to 45Ry and more for the pseudopotentials employed by Andrews et al. [7]. However, only a Journal of Molecular Structure (Theochem) 467 (1999) 79–83 0166-1280/99/$ - see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S0166-1280(98)00478-3