Using time-dependent density functional theory (TDDFT) with exchange kernels, we calculate and test imaginary frequency-dependent dipole polarizabilities for all atoms and many ions in rows 1–6 of the periodic table. These are then integrated over frequency to produce C6 coefficients. Results are presented under different models: straight TDDFT calculations using two different kernels; “benchmark” TDDFT calculations corrected by more accurate quantum chemical and experimental data; and “benchmark” TDDFT with frozen orbital anions. Parametrizations are presented for 411+ atoms and ions, allowing results to be easily used by other researchers. A curious relationship, C6,XY ∝ [αX(0)αY(0)]0.73, is found between C6 coefficients and static polarizabilities α(0). The relationship C6,XY = 2C6,XC6,Y/[(αX/αY)C6,Y + (αY/αX)C6,X] is tested and found to work well (<5% errors) in ∼80% of the cases, but can break down badly (>30% errors) in a small fraction of cases.