Constraint-based, Non-empirical Parameterization of Generalized Gradient Approximation Kinetic Energy Functionals

Though we have developed constraint-based ``modified conjoint'' generalized gradient approximation forms for the orbital-free Kohn-Sham kinetic energy $T_s[n]$, strategies for parameterizing them without use of small training sets have remained elusive[1]. Here we discuss one possible way to eliminate that empiricism. We take the reparameterized Perdew-Burke-Ernzerhof exchange functional PBEmol [2], which is self-interaction free for the Hydrogen atom density $n_1$. We then constrain the Pauli-term kinetic energy ($T_\theta$ in $T_s=T_W + T_\theta$, with $T_W$ the von Weizs\"acker KE) to cancel the remaining spurious correlation energy $T_\theta[n_1] +E_{c,PBEmol}[n_1] =0$.We bound the functional by $T_W + T_{TF}$, with $T_{TF}$ the Thomas-Fermi KE and retain the original constraint that $T_\theta >0$. We report numerical results and findings for this procedure.\\[4pt] [1] Phys.\ Rev. B \textbf{80}, 245120 (2009);\\[0pt] [2] J.\ Chem.\ Phys.\ \textbf{136}, 104108 (2012)