Properties of constraint-based single-point approximate kinetic energy functionals

Abstract

We present an analysis and extension of our constraint-based approach to orbital-free ͑OF͒ kinetic-energy ͑KE͒ density functionals intended for the calculation of quantum-mechanical forces in multiscale moleculardynamics simulations. Suitability for realistic system simulations requires that the OF-KE functional yield accurate forces on the nuclei yet be computationally simple. We therefore require that the functionals be based on density-functional theory constraints, be local, be dependent at most upon a small number of parameters fitted to a training set of limited size, and be applicable beyond the scope of the training set. Our previous "modified-conjoint" generalized-gradient-type functionals were constrained to producing a positive-definite Pauli potential. Though distinctly better than several published generalized-gradient-approximation-type functionals in that they gave semiquantitative agreement with Born-Oppenheimer forces from full Kohn-Sham results, those modified-conjoint functionals suffer from unphysical singularities at the nuclei. Here we show how to remove such singularities by introducing higher-order density derivatives and analyze the consequences. We give a simple illustration of such a functional and a few tests of it.

Condition on the Kohn–Sham kinetic energy and modern parametrization of the Thomas–Fermi density

“…Using it would lead automatically to an electronic structure method that scales linearly with the number of electrons N (with the possible exception of the evaluation of the Hartree energy). Thus the KS kinetic energy functional is something of a holy grail of density functional purists, and interest in it has recently revived [3].…”

Orbital-free bond breaking via machine learning

“…6,7 Unfortunately, the relative accuracy requirements of a KE functional are much stricter than those of an XC functional because T S is typically comparable to the total energy of the system. 5,9,10 Worse, one also needs accurate functional derivatives, since ultimately the density must be determined by solving an Euler equation instead of the KS a) Present address: Institute of Physical Chemistry, Department of Chemistry, University of Basel, Klingelbergstr. 80, 4056 Basel, Switzerland.…”

“…8 Some approaches build on Thomas-Fermi theory with gradient expansions or the von Weizsäcker KE. 6,7,13 Others use generalized gradient approximations (GGAs), 9, 10 some with enhancement factors based on "conjointness." 14 An alternative approach is to use non-local KE functionals [15][16][17][18][19] based on linear response theory.…”

Kinetic and Exchange Energy Densities near the Nucleus

“…At the nucleus of the helium isoelectronic series, F s ≈ F W s ≈ 0.2353, i.e., there is an even more pronounced de-enhancement than in the exchange case. On the other hand, most of the GGA KE functionals have F s ≥ 1, while few semilocal KE functionals recover the VW at the nucleus [59,61,62].…”

“…(i.e., F W s = (5/3)s 2 ) is expected to be very accurate at the nucleus [2,[58][59][60]. At the nucleus of the helium isoelectronic series, F s ≈ F W s ≈ 0.2353, i.e., there is an even more pronounced de-enhancement than in the exchange case.…”