Can orbital-free density functional theory simulate molecules?

Abstract

Orbital-free density functional theory (OFDFT), with its attractive linearly scaling computation cost and low prefactor, is one of the most powerful first principles methods for simulating large systems (~10(4)-10(6) atoms). However, approximating the electron kinetic energy with density functionals limits the accuracy and generality of OFDFT compared to Kohn-Sham density functional theory (KSDFT). In this work, we test whether the Huang-Carter (HC) kinetic energy density functional (KEDF), which contains the physics to properly describe covalently bonded semiconductor materials, can also be used to describe covalent bonds in molecules. In particular, we calculate a variety of homonuclear diatomic molecules with the HC functional within OFDFT. The OFDFT bond dissociation energy, equilibrium bond length, and vibrational frequency of these dimers are in remarkably good agreement with benchmark KSDFT results, given the lack of orbitals in the calculation. We vary the two parameters λ (controlling the reduced density gradient contribution to the nonlocal kernel) and β (the exponent of the density in the nonlocal term) present in the HC KEDF and find that the optimal λ correlates with the magnitude of the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap. Although the HC KEDF represents a significant improvement over previous KEDFs in describing covalent systems, deficiencies still exist. Despite the similar overall shape of the KSDFT and OFDFT ground state electron densities, the electron density within the bonding region is still quite different. Furthermore, OFDFT is not yet able to give reasonable description of magnetic states. The energy orderings of the triplet and singlet states of Si(2) and Al family dimers are not consistent with KSDFT or experimental results and the spin polarization distributions also differ widely between the two theories.

Spin in density‐functional theory

“…This is mainly rooted in the difficulty of approximating the kinetic-energy contribution to the HK functional as a functional of the electron density only. [104,105] A possible way out of this dilemma, that forms the basis of almost every present-day application of (approximate) DFT calculations, was suggested by Kohn and Sham. [106] Instead of considering the kinetic energy of the true system of interacting electrons, they proposed to calculate the kinetic energy of a reference system of noninteracting electrons with the same electron density instead.…”

Density-decomposed orbital-free density functional theory for covalently bonded molecules and materials

“…These k-point meshes converge the CD Si elastic constants to within 0.2 GPa, based on the difference between using the 12 12 12 × × mesh in Table II diatomic molecule calculations are the same as given in our previous work. 52 In all OFDFT calculations, a 6000 eV plane wave kinetic energy cutoff is used to achieve convergence of 1 meV/atom. The scale function is considered self-consistent if…”

“…[14][15][16][17][18][19][20][21][22][23] OFDFT provides an efficient and robust approach to study large samples with many well. 52 The HC KEDF undoubtedly broadens OFDFT's range of applications. However, it still has several remaining drawbacks, 49 including insufficiently accurate properties of Si metallic phases, underestimated electron density in the bonding regions of Si and III-V semiconductors, unphysical shear moduli and self-interstitial formation energy.…”

“…However, it describes covalently-bonded systems such as semiconductors or molecules far less accurately. 46,52 In those systems, large density variations due to localized electrons challenge both the theoretical basis (the Lindhard response function of the perturbed free electron gas) and the numerical Taylor expansion. 46 However, an earlier re-parameterized WGC KEDF for various Si phases, though not entirely satisfactory for Si semiconductor phases, 46 features two positive aspects.…”

Kinetic and Exchange Energy Densities near the Nucleus

“…Its practical implementation is based on approximations of the exchange-correlation (XC) energy (E xc ), which is a subject of intense research [4][5][6]. Moreover, subsystem DFT [7][8][9] and orbital-free DFT [10][11][12][13] need the use of kinetic energy (KE) functional approximations.…”