Implementation of gradient-corrected exchange-correlation potentials in Car-Parrinello total-energy calculations

Abstract

The application of gradient-corrected exchange-correlation functionals in total-energy calculations using a plane-wave basis set is discussed. The usual form of the exchange-correlation potential includes gradients whose calculation requires the use of a high-quality representation of the density which is computationally expensive in both memory and time. These problems may be overcome by defining an exchange-correlation potential for the discrete set of grid points consistent with the discretized form of the exchange-correlation energy that is used in Car-Parrinello-type total-energy calculations. This potential can be calculated exactly on the minimum fast-Fourier-transform grid and gives improved convergence and stability as well as computational efficiency.First-principles total-energy calculations based on density-functional theory' have become the major theoretical tool in solid-state physics, surface science, and molecular physics. Pseudopotential calculations using a planewave basis set and a Car-Parrinello approach to energy minimization ' have become increasingly important since this allows use to be made of the fast Fourier transform (FFT). Although the local-density approximation (LDA) to exchange and correlation gives a good description of many solid-state properties, for many applications it appears to be essential to go beyond the LDA by including gradient corrections. This is particularly important where accurate molecular bonding energies are required as in, for example, dissociative chemisorption. For bulk properties the need for gradient corrections is less clear although some improvements over LDA have been reported in calculations for semiconductors and transition metals. Unfortunately, the currently popular generalized gradient approximations (GGA) to the exchange-correlation energy functional (such as that of Perdew and Wang or Becke and Perdew ) give rise to potentials which are rapidly varying functions near to ion cores as has been noted previously in the context of pseudopotential generation. ' Because of this, and in order to calculate the required gradients accurately, a large number of plane waves are needed to represent these exchangecorrelation potentials accurately. In this paper it is pointed out that the exchange-correlation energy is, in practice, invariably approximated. It is shown that it is possible to construct an exchange-correlation potential which is consistent with this approximate form of the exchange-correlation energy and which can be calculated exactly much more efficiently than the conventional exchange-correlation potential.First recall the use of FFT's in Car-Parrinello-type totalenergy calculations. ' This makes use of the fact that the kinetic energy and Hartree energy/potential are easily calculated in reciprocal space (the Hartree potential, for example, becomes a simple product in reciprocal space) while the electron-ion potential energy is easily calculated in real space since the required integrals can be performed exactly as sums over the points of the m...

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