Density functional theory with approximate kinetic energy functionals applied to hydrogen bonds

Abstract

Applicability of the approximate kinetic energy functional to study hydrogen-bonded systems by means of the formalism of Kohn-Sham equations with constrained electron density (KSCED) [Cortona, Phys. Rev. B 44, 8454 (1991); Wesołowski and Warshel, J. Phys. Chem. 97, 8050 (1993); Wesołowski and Weber, Chem. Phys. Lett. 248, 71 (1996)] is analyzed. In the KSCED formalism, the ground-state energy of a molecular complex is obtained using a "divide-and-conquer" strategy, which is applied to the Kohn-Sham-like equations to obtain the electron density of a fragment embedded in a larger system. The approximate kinetic energy functional enters into the KSCED formalism in two ways. First, the effective potential in which the electrons of each fragment move contains a component which is expressed by means of a functional derivative of an approximate kinetic energy functional (functional derivative of the non-additive kinetic energy). Second, the KSCED energy functional contains a component (non-additive kinetic energy) which is expressed using the approximate kinetic energy functional. In this work, the KSCED energies and densities of (H2O)2, (HF)2, (HCl)2, and HF⋯NCH are compared to the ones obtained using the standard supermolecule Kohn-Sham approach. The following factors determining the agreement between the KSCED and supermolecule Kohn-Sham results are analyzed: the analytical form of the gradient-dependent terms in the approximate kinetic energy functional and the number of atom-centered orbitals used to expand electron density of fragments. The best agreement between the supermolecule Kohn-Sham and the KSCED results is obtained with the kinetic energy functional derived following the route of Lee, Lee, and Parr [Lee et al., Phys. Rev. A 44, 768 (1991)] from the exchange functional of Perdew and Wang [Perdew and Wang, in Electronic Structure of Solids '91, edited by P. E. Ziesche and H. Eschrig (Academie Verlag, Berlin, 1991), p. 11]. The difference between the KSCED and the supermolecule Kohn-Sham energies of studied complexes amounts to less than 0.35 kcal/mol at the equilibrium geometry. © 1997 American Institute of Physics.