The Liu‐Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell‐inducing traits: Atoms

Abstract

An approximate expression for the Pauli kinetic energy functional Tp is advanced in terms of the Liu‐Parr expansion [S. Liu, R.G. Parr, Phys. Rev. A 1997, 55, 1792] which involves a power series of the one‐electron density. We use this explicit functional for Tp to compute the value of the noninteracting kinetic energy functional Ts of 34 atoms, from Li to Kr (and their positive and negative monoions). In particular, we examine the effect that a shell‐by‐shell mean‐square optimization of the expansion coefficients has on the kinetic energy values and explore the effect that the size of the expansion, given by the parameter n, has on the accuracy of the approximation. The results yield a mean absolute percent error Δabs=(1/N)∑i=1NΔi for 34 neutral atoms of 0.15, 0.08, 0.04, 0.03, and 0.01 for expansions with n = 3, 4, 5, 6, and 7, respectively (where Δi=100|Tnormalsapp(i)−TnormalsHF(i)|/TnormalsHF(i)). We show that these results, which are the most accurate ones obtained to date for the representation of the noninteracting kinetic energy functional, stem from the imposition of shell‐inducing traits. We also compare these Liu‐Parr functionals with the exact but nonexplicit functional generated in the local‐scaling transformation version of DFT.

Deformation Potentials: Towards a Systematic Way beyond the Atomic Fragment Approach in Orbital-Free Density Functional Theory

“…Valuable contributions, via the path of generalized-gradient-expansion techniques and in-depth investigations of parameterization techniques, have been provided by Trickey et al [ 4 , 23 , 24 ]. To date, expansion techniques remain the most common research line in the field of OF-DFT [ 3 , 12 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ]. Surely, one of the highly celebrated benefits of OF-DFT is its enormous gain in computational speed-up, as shown by Carter et al [ 44 , 45 , 46 , 47 ] and related groups [ 48 , 49 ], but also the interest in conceptual insights has recently been renewed [ 50 , 51 ].…”

Detailed analysis of deformation potentials with application in orbital-free density functional theory

“…Although founded in 1964 by the famous Hohenberg-Kohn theorems (Hohenberg & Kohn, 1964), progress in this field was hampered due to the lack of sufficiently accurate kinetic energy functionals (Karasiev & Trickey, 2015). First attempts were made with gradient expansion techniques, which until now remain the most common research line in the field (Thomas, 1927;Fermi, 1928;von Weizsä cker, 1935;Kirzhnits, 1957;Hodges, 1973;Murphy, 1981;Yang, 1986;Yang et al, 1986;Lee & Ghosh, 1986;Kozlowski & Nalewajski, 1986;Lee et al, 1991;Thakkar, 1992;Liu & Parr, 1997;Tran & Wesolowski, 2002;Ayers et al, 2002;Chai & Weeks, 2004;Ghiringhelli & Delle Site, 2008;Lee et al, 2009;Ghiringhelli et al, 2010;Salazar et al, 2016;Ludeñ a et al, 2018). As nicely shown by Trickey and co-workers (Trickey et al, 2011;Karasiev et al, 2014;Karasiev & Trickey, 2015) parameterization of generalized-gradient approximations must be performed with care, otherwise these approximations run the risk of producing negative contributions to the Pauli kinetic energy.…”

Equilibrium Bond Lengths from Orbital-Free Density Functional Theory

“…Later those attempts were extended to generalized-gradient-approximation techniques, where the explicit functional approximation is motivated by conjoint arguments [23,24] or the fulfillment of additional constraints [9,25,26]. Besides GGA-type functionals, kinetic energy expansions based on moment densities were studied [27], as well as functionals based on response theory [28,29], parameterized power series expansions [30][31][32], and information-theory motivated expressions [33][34][35]. Following the ideas of March, it would be sufficient to model the Pauli kinetic energy [36], as it constitutes the only unknown functional part of the kinetic energy, while the remaining part, the so-called von Weizsäcker kinetic energy [12] is known analytically in terms of the electron density.…”