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

Applicability of the approximate kinetic energy functionals 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 HFṡṡṡNCH 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.