Rigorous lower bounds to the first-gradient corrections in the gradient expansion of the kinetic and exchange-energy functionals

摘要: Rigorous lower bounds for the first-gradient corrections to kinetic and exchange-energy functionals in atoms are derived using Benson's inequality. They formulated terms of expectation values momentum value a simple manner namely T2[ρ] = (1/72)∫(|∇ρ(r)|2/ρ(r)) dr ≥ (n2/72) rn − 32r2n 4−1 |K2[ρ]| β ∫(|∇ρ(r)|2/ρ4/3(r)) 0.05105 r−12p−1, where n, natural number 1, 2, 3,..., 3 r2n 4 values, p is value, ρ(r) electron density with normalization condition ∫ N, electrons. The this work tested Z 36. A comparison also made previously bound estimates K2[ρ]. presented sharper than previous ones given by Pathak Gadre (atomic units used throughout paper).