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 C 6 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, C 6,XY ∝ [α X (0)α Y (0)] 0.73 , is found between C 6 coefficients and static polarizabilities α(0). The relationship C 6,XY = 2C 6,X C 6,Y /[(α X /α Y )C 6,Y + (α Y /α X )C 6,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.